formal geometry for noncommutative manifolds abstract this paper develops the tools of formal algebraic geometry in the setting of noncommutative manifolds roughly ringed spaces locally modeled on the free associative algebra we define a notion of noncommutative coordinate system which is a principal bundle for an appropriate group of local coordinate changes these bundles are shown to carry a natural flat connection with properties analogous to the classical gelfand kazhdan structure every noncommutative manifold has an underlying smooth variety given by abelianization a basic question is existence and uniqueness of noncommutative thickenings of a smooth variety i e finding noncommutative manifolds abelianizing to a given smooth variety we obtain new results in this direction by showing that noncommutative coordinate systems always arise as reductions of structure group of the commutative bundle of coordinate systems on the underlying smooth variety this also explains a relationship between d modules on the commutative variety and sheaves of modules for the noncommutative structure sheaf

inference for mixtures of finite polya tree models mixtures of polya tree models provide a flexible alternative when a parametric model may only hold approximately i provide computational strategies for obtaining full semiparametric inference for mixtures of finite polya tree models given a standard parameterization including models that would be troublesome to fit using dirichlet process mixtures recommendations are put forth on choosing the level of a finite polya tree and model comparison is discussed several examples demonstrate the utility of finite polya tree modeling including data fit to generalized linear mixed models and several survival models

qurves and quivers abstract in this paper we associate to a k qurve a formerly known as a quasi free algebra j cuntz d quillen algebra extensions and nonsingularity j amer math soc 8 1995 251 289 or formally smooth algebra m kontsevich a rosenberg noncommutative smooth spaces math ag 9812158 1998 the one quiver q 1 a and dimension vector 1 a this pair contains enough information to reconstruct for all n n the gl n etale local structure of the representation scheme rep n a in an appendix we indicate how one might extend this to qurves over non algebraically closed fields further we classify all finitely generated groups g such that the group algebra kg is a k qurve if char k 0 these are exactly the virtually free groups we determine the one quiver setting in this case and indicate how it can be used to study the finite dimensional representations of virtually free groups as this approach also applies to fundamental algebras of graphs of separable k algebras we state the results in this more general setting

marginal likelihood from the metropolis hastings output this article provides a framework for estimating the marginal likelihood for the purpose of bayesian model comparisons the approach extends and completes the method presented in chib 1995 by overcoming the problems associated with the presence of intractable full conditional densities the proposed method is developed in the context of mcmc chains produced by the metropolis hastings algorithm whose building blocks are used both for sampling and marginal likelihood estimation thus economizing on prerun tuning effort and programming experiments involving the logit model for binary data hierarchical random effects model for clustered gaussian data poisson regression model for clustered count data and the multivariate probit model for correlated binary data are used to illustrate the performance and implementation of the method these examples demonstrate that the method is practical and widely applicable

objective bayesian survival analysis using shape mixtures of log normal distributions survival models such as the weibull or log normal lead to inference that is not robust to the presence of outliers they also assume that all heterogeneity between individuals can be modeled through covariates this article considers the use of infinite mixtures of lifetime distributions as a solution for these two issues this can be interpreted as the introduction of a random effect in the survival distribution we introduce the family of shape mixtures of log normal distributions which covers a wide range of density and hazard functions bayesian inference under nonsubjective priors based on the jeffreys rule is examined and conditions for posterior propriety are established the existence of the posterior distribution on the basis of a sample of point observations is not always guaranteed and a solution through set observations is implemented in addition we propose a method for outlier detection based on the mixture structure a simulation study illustrates the performance of our methods under dif

computing bayes factors using a generalization of the savage dickey density ratio abstract we present a simple method for computing bayes factors the method derives from observing that in general a bayes factor can be written as the product of a quantity called the savage dickey density ratio and a correction factor both terms are easily estimated from posterior simulation in some cases it is possible to do these computations without ever evaluating the likelihood

multivariate student t regression models pitfalls and inference we consider likelihood based inference from multivariate regression models with independent student t errors some very intruiging pitfalls of both bayesian and classical methods on the basis of point observations are uncovered bayesian inference may be precluded as a consequence of the coarse nature of the data global maximization of the likelihood function is a vacuous exercise since the likelihood function is unbounded as we tend to the boundary of the parameter space a bayesian analysis on the basis of set observations is proposed and illustrated by several examples

bayesian case influence diagnostics for survival models we propose bayesian case influence diagnostics for complex survival models we develop case deletion influence diagnostics for both the joint and marginal posterior distributions based on the kullback leibler divergence k l divergence we present a simplified expression for computing the k l divergence between the posterior with the full data and the posterior based on single case deletion as well as investigate its relationships to the conditional predictive ordinate all the computations for the proposed diagnostic measures can be easily done using markov chain monte carlo samples from the full data posterior distribution we consider the cox model with a gamma process prior on the cumulative baseline hazard we also present a theoretical relationship between our case deletion diagnostics and diagnostics based on cox s partial likelihood a simulated data example and two real data examples are given to demonstrate the methodology

a new narrowband interference suppression scheme for spread spectrum cdma communications this paper presents a new nonlinear approach for narrowband interference nbi suppression in code division multiple access cdma systems the proposed scheme is an adaptive nonlinear predictor that consists of an n 1 level quantizer four adders and two adaptive linear filters where n is the number of users in the cdma system both adaptive filters have the same coefficients at each iteration one for feedforward estimation of nbi and the other for feedback compensation for the estimated result it could be regarded as an improved version of the nonlinear predictor with offset outputs presented recently by wang et al 1996 computer simulation results support that the improved offset predictor performs much better than the original one under the same complexity as compared with the nearly optimal approximate conditional mean filter it achieves almost the same performance even at very low signal to noise ratio but involves much less complexity

local model influence abstract this article develops a general method for assessing the influence of model assumptions in a bayesian analysis we assume that model choices are indexed by a hyperparameter with some given initial choice we use the term model to encompass both the sampling model and the prior distribution we wish to assess the effect of changing the hyperparameter away from the initial choice we are performing a sensitivity analysis with the hyperparameter defining our perturbations we use the kullback leibler divergence to measure the difference between posteriors corresponding to different choices of the hyperparameter we also measure the change in priors if small changes in the priors lead to large changes in posteriors the choice of hyperparameter is influential the second order difference in the kullback leibler divergence is expressed by fisher information matrices the relative change in posteriors compared with priors may be summarized by the relative eigenvalue of the posterior and prior fishe

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

double poisson algebras in this paper we develop poisson geometry for non commutative algebras this generalizes the bi symplectic geometry which was recently and independently introduced by crawley boevey etingof and ginzburg our quasi poisson brackets induce classical quasi poisson brackets on representation spaces as an application we show that the moduli spaces of representations associated to the deformed multiplicative preprojective algebras recently introduced by crawley boevey and shaw carry a natural poisson structure

nonlinear techniques for interference suppression in spread spectrum systems the binary nature of direct sequence signals is exploited to obtain nonlinear filters that outperform the linear filters hitherto used for this purpose the case of a gaussian interferer with known autoregressive parameters is considered using simulations it is shown that an approximate conditional mean acm filter of the masreliez type performs significantly better than the optimum linear kalman bucy filter for the case of interferers with unknown parameters the nature of the nonlinearity in the acm filter is used to obtain an adaptive filtering algorithm that is identical to the linear transversal filter except that the previous prediction errors are transformed nonlinearly before being incorporated into the linear prediction two versions of this filter are considered one in which the filter coefficients are updated using the widrow lms algorithm and another in which the coefficients are updated using an approximate gradient algorithm simulations indicate that the nonlinear filter with lms updates performs substantially better than the linear filter for both narrowband gaussian and single tone interferers whereas the gradient algorithm gives slightly better performance for gaussian interferers but is rather ineffective in suppressing a sinusoidal interferer

quantum harmonic analysis and geometric invariants we develop two topics in parallel and show their inter relation the first centers on the notion of a fractional differentiable structure on a commutative or a non commutative space we call this studyquantum harmonic analysis the second concerns homotopy invariants for these spaces and is an aspect of non commutative geometry we study an algebra a which will be a banach algebra with unit represented as an algebra of operators on a hilbert space h in order to obtain a geometric interpretation of a we define a derivative on elements of a we do this in a hilbert space context takingdaas a commutatorda q a hereqis a basic self adjoint operator with discrete spectrum increasing sufficiently rapidly that exp q 2has a trace whenever 0 we can define fractional differentiability of order with 0 0 we concentrate on subalgebras a of j which have certain additional covariance properties under a group z2 g acting on h by a unitary representation u g in addition the derivativeqis assumed to be g invariant the geometric interpretation flows from the assumption that elements of a possess an arbitrarily small fractional derivative we study homotopy invariants of a in terms of equivariant entire cyclic cohomology in fact the existence of a fractional derivative on a allows the construction of the cochain jlo which plays the role of the integral of differential forms we give a simple expression for a homotopy invariant zq a g determined by pairing jlo with a g invariant elementa a such thatais a square root of the identity this invariant is zq a g 1 e t2tr u g ae q2 it da dt this representation of the pairing is reminiscent of the heat kernel representation for an index in fact this quantity is an invariant in the following sense we isolate a simple condition on a familyq of differentiations that yields a continuously differentiable family jlo of cochains since zq a g need not be an integer continuity of jlo in is insufficient to prove the constancy of the pairing however the existence of the derivative leads to the existence of the homotopy as a vanishes for a coboundary and asd jlo d is a coboundary our condition onq ensures that zq a g is independent of hence it is a homotopy invariant the theory of zq a g reduces to the study of the radon transform of sequences of certain functions the fractional differentiability properties of elements of a translate into properties of the asymptotics of the sequences of radon transforms the condition that jlofit into the framework of entire cyclic cohomology translates to the existence of some fractional derivative for functions in the algebra under study and in particular the assumption 1 thus the study of fractionally differentiable structures dove tails naturally with the theory of homotopy invariants in our study of quantum harmonic analysis we introduce spaces t of operator valued distributions these spaces are bounded linear operators between sobolev spaces the elements of the interpolation spaces the banach algebras j have derivativesdawhich belong to the spaces t for a certain range of and we extend the theory of the radon transform from products of regularized bounded operators to products of regularized operator valued distributions we sometimes wish to evaluate such an invariant at the endpoint of an interval such as 0 1 where zq a g becomes singular as 0 we discuss in brief a procedure to regularize the endpoint and a method to recover zq a g fully from certain partial information at the endpoint finally we generalize this approach to cover the case whenqcan be split into the sum of independent partsq1 q2 such that q1 q2 2 q1 2 q2 2 here we assume thatq1and q2 2are g invariant but not necessarilyq2 with further assumptions ona the most important being that q1 2 q2 2commutes witha we obtain a modified formula for an invariant namely z qj a g 1 e t2tr u g ae q21 q22 2 itd1a dt

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

objective bayesian analysis for the student t regression model we develop a bayesian analysis based on two different jeffreys priors for the student t regression model with unknown degrees of freedom it is typically difficult to estimate the number of degrees of freedom improper prior distributions may lead to improper posterior distributions whereas proper prior distributions may dominate the analysis we show that bayesian analysis with either of the two considered jeffreys priors provides a proper posterior distribution finally we show that bayesian estimators based on jeffreys analysis compare favourably to other bayesian estimators based on priors previously proposed in the literature

a recursive maximum likelihood algorithm for arma line enhancement optimal filtering of narrow band signals corrupted by noise requires an infinite impulse response iir filter a recursive maximum likelihood algorithm is proposed for adaptively adjusting the coefficients of an iir line enhancer the performance of this adaptive iir filter is analyzed and compared to that of a finite impulse response filter preliminary simulation results are presented to illustrate the behavior of the proposed algorithm under various signal to noise conditions

exact sequences hochschild cohomology and the lie module structure over the m relative center abstract in this article we present actions by central elements on hochschild cohomology groups with arbitrary bimodule coefficients as well as an interpretation of these actions in terms of exact sequences since our construction utilizes the monoidal structure that the category of bimodules possesses we will further recognize that these actions are compatible with monoidal functors and thus as a consequence are invariant under morita equivalences by specializing the bimodule coefficients to the underlying algebra itself our efforts in particular yield a description of the degree n 0 part of the lie bracket in hochschild cohomology and thereby close a gap in earlier work by s schwede

derived representation schemes and cyclic homology we describe the derived functor drepv a of the affine representation scheme repv a parametrizing the representations of an associative k algebra a on a finite dimensional vector space v we construct the characteristic maps trv a n hcn a hn drepv a extending the canonical trace trv a hc0 a k repv a to the higher cyclic homology of the algebra a and describe a related derived version of the representation functor introduced recently by m van den bergh we study various operations on the homology of drepv a induced by known operations on cyclic and hochschild homology of a

mixtures of exponential distributions arbitrary nonparametric mixtures of exponential and weibull fixed shape distributions are considered as possible models for a lifetime distribution a characterization of such distributions is given by the well known characterization of laplace transforms the maximum likelihood estimate of the mixing distribution is investigated and found to be supported on a finite number of points it is shown to be unique and weakly convergent to the true mixing measure with probability one a practical algorithm for computing the maximum likelihood estimate is described its performance is briefly discussed and some illustrative examples given

an additive formula for samuel multiplicities on hilbert spaces of analytic functions abstract we establish a short exact sequence to relate the germ model of invariant subspaces of a hilbert space of vector valued analytic functions and the sheaf model of the corresponding coinvariant subspaces as a consequence we obtain an additive formula for samuel multiplicities as an application we give a different proof for a formula relating the fibre dimension and the samuel multiplicity which is first proved in fang 2005 11 the feature of the new proof is that the analytic arguments in fang 2005 11 are now subsumed by algebraic machinery

open embeddings and pseudoflat epimorphisms abstract we characterize open embeddings of stein spaces and of c manifolds in terms of certain flatness type conditions on the respective homomorphisms of function algebras

on the lower central series of an associative algebra abstract for an associative algebra a define its lower central series l 0 a a l i a a l i 1 a and the corresponding quotients b i a l i a l i 1 a in this paper we study the structure of b i a n for a free algebra a n we construct a basis for b 2 a n and determine the structure of b 3 a 2 and b 4 a 2 in appendix a we study the structure of b 2 a for any associative algebra a over c

outlier models and prior distributions in bayesian linear regression summary bayesian inference in regression models is considered using heavy tailed error distri butions to accommodate outliers the particular class of distributions that can be con structed as scale mixtures of normal distributions are examined and use is made of them as both error models and prior distributions in bayesian linear modelling includ ing simple regression and more complex hierarchical models with structured priors depending on unknown hyperprior parameters the modelling of outliers in nominally normal linear regression models using alternative error distributions which are heavy tailed relative to the normal provides an automatic means of both detecting and accommodating possibly aberrant observations such realistic models do however often lead to analytically intractable analyses with complex posterior distributions in several dimensions that are difficult to summarize and understand in this paper we consider a special yet rather wide class of heavy tailed unimodal and symmetric error distributions for which the analyses though apparently intractable can be examined in some depth by exploiting certain properties of the assumed error form the distributions concerned are those that can be con structed as scale mixtures of normal distributions in his paper concerning location parameters de finetti 1961 discusses such distributions and suggests the hypothetical interpretation that each observation is taken using an instrument with normal error but each time chosen at random from a collection of instruments of different precisions the distribution of the

stein domains in banach algebraic geometry abstract in this article we give a homological characterization of the topology of stein spaces over any valued base field in particular when working over the field of complex numbers we obtain a characterization of the usual euclidean transcendental topology of complex analytic spaces for non archimedean base fields the topology we characterize coincides with the topology of the berkovich analytic space associated to a non archimedean stein algebra because the characterization we used is borrowed from a definition in derived geometry this work should be read as a derived perspective on analytic geometry

necklace lie algebras and noncommutative symplectic geometry recently v ginzburg proved that calogero phase space is a coadjoint orbit for some infinite dimensional lie algebra coming from noncommutative symplectic geometry 12 in this note we generalize his argument to specific quotient varieties of representations of deformed preprojective algebras this result was also obtained independently by v ginzburg 13 using results of w crawley boevey and m holland 10 8 and 9 we give a combinatorial description of all the relevant couples alpha lambda which are coadjoint orbits we give a conjectural explanation for this coadjoint orbit result and relate it to different noncommutative notions of smoothness

robust statistical modeling using the t distribution abstract the t distribution provides a useful extension of the normal for statistical modeling of data sets involving errors with longer than normal tails an analytical strategy based on maximum likelihood for a general model with multivariate t errors is suggested and applied to a variety of problems including linear and nonlinear regression robust estimation of the mean and covariance matrix with missing data unbalanced multivariate repeated measures data multivariate modeling of pedigree data and multivariate nonlinear regression the degrees of freedom parameter of the t distribution provides a convenient dimension for achieving robust statistical inference with moderate increases in computational complexity for many models estimation of precision from asymptotic theory and the bootstrap is discussed and graphical methods for checking the appropriateness of the t distribution are presented

new nonlinear algorithms for estimating and suppressing narrowband interference in ds spread spectrum systems it has been shown that the narrowband nb interference suppression capability of a direct sequence ds spread spectrum system can be enhanced considerably by processing the received signal via a prediction error filter the conventional approach to this problem makes use of a linear filter however the binary ds signal that acts as noise in the prediction process is highly non gaussian thus linear filtering is not optimal vijayan and poor 1990 first proposed using a nonlinear approximate conditional mean acm filter of the masreliez 1975 type and obtained significant results this paper proposes a number of new nonlinear algorithms our work consists of three parts 1 we develop a decision directed kalman ddk filter that has the same performance as the acm filter but a simpler structure 2 using the nonlinear function in the acm and the ddk filters we develop other nonlinear least mean square lms filters with improved performance 3 we further use the nonlinear functions to develop nonlinear recursive least squares rls filters that can be used independently as predictors or as interference identifiers so that the acm or the ddk filter can be applied simulations show that our nonlinear algorithms outperform conventional ones

bayesian linear regression with skew symmetric error distributions with applications to survival analysis we study bayesian linear regression models with skew symmetric scale mixtures of normal error distributions these kinds of models can be used to capture departures from the usual assumption of normality of the errors in terms of heavy tails and asymmetry we propose a general noninformative prior structure for these regression models and show that the corresponding posterior distribution is proper under mild conditions we extend these propriety results to cases where the response variables are censored the latter scenario is of interest in the context of accelerated failure time models which are relevant in survival analysis we present a simulation study that demonstrates good frequentist properties of the posterior credible intervals associated with the proposed priors this study also sheds some light on the trade off between increased model flexibility and the risk of over fitting we illustrate the performance of the proposed models with real data although we focus on models with univariate response variables we also present some extensions to the multivariate case in the supporting information copyright 2016 john wiley sons ltd

quasi homomorphismes cohomologie cyclique et positivite we show that cyclic cohomology of an algebraa is obtained from traces with suitable domains on the algebraqa of the second author whena is ac algebra so isqa and the notion of positive trace makes sense we hence get a notion of positivity for cyclic cocycles we prove that a positive trace onqa defines a type i or ii fredholm module ona

the dirac operator of a commuting d tuple abstract given a commuting d tuple t t1 td of otherwise arbitrary operators on a hilbert space there is an associated dirac operator dt significant attributes of the d tuple are best expressed in terms of dt including the taylor spectrum and the notion of fredholmness in fact all properties of t derive from its dirac operator we introduce a general notion of dirac operator in dimension d 1 2 that is appropriate for multivariable operator theory we show that every abstract dirac operator is associated with a commuting d tuple and that two dirac operators are isomorphic iff their associated operator d tuples are unitarily equivalent by relating the curvature invariant introduced in a previous paper to the index of a dirac operator we establish a stability result for the curvature invariant for pure d contractions of finite rank it is shown that for the subcategory of all such t that are a fredholm and and b graded the curvature invariant k t is stable under compact perturbations we do not know if this stability persists when t is fredholm but ungraded although there is concrete evidence that it does

adaptive time varying cancellation of wideband interferences in spread spectrum communications based on time frequency distributions the paper proposes an adaptive method for suppressing wideband interferences in spread spectrum ss communications the proposed method is based on the time frequency representation of the received signal from which the parameters of an adaptive time varying interference excision filter are estimated the approach is based on the generalized wigner hough transform as an effective way to estimate the instantaneous frequency of parametric signals embedded in noise the performance of the proposed approach is evaluated in the presence of linear and sinusoidal fm interferences plus white gaussian noise in terms of the snr improvement factor and bit error rate ber

algebra extensions and nonsingularity this paper is concerned with a notion of nonsingularity for noncommutative algebras which arises naturally in connection with cyclic homology let us consider associative unital algebras over the complex numbers we call an algebra a quasi free when it behaves like a free algebra with respect to nilpotent extensions in the sense that any homomorphism a r i where i is a nilpotent ideal in r can be lifted to a homomorphism a r if we restrict to the category of finitely generated commutative algebras then this lifting property characterizes smooth algebras the ones corresponding to nonsingular affine varieties in this way quasi free algebras appear as noncommutative analogues of smooth algebras stretching the analogy we can even regard quasi free algebras as analogues of manifolds one of the aims of this paper is to develop the analogy further by showing that quasi free algebras provide a natural setting for noncommutative versions of certain aspects of manifolds to give an example let us consider the analogue of an embedding an extension a r i where a and r are quasi free algebras playing the role of the submanifold and ambient manifold respectively in the manifold situation i i2 is the module of linear functions on the nor2 mal bundle and the symmetric algebra sa iii is the algebra of polynomial functions now in passing from commutative to noncommutative algebras the symmetric algebra of a module is replaced by the tensor algebra of a bimodule

performance analysis of narrow band interference rejection techniques in ds spread spectrum systems linear least squares estimation llse techniques can provide an effective means of suppressing narrow band interference in direct sequence ds spread spectrum systems in the results presented here analytical expressions for bit error rate are derived for two ds spread spectrum systems under the conditions of either tone or narrowband gaussian interference it is shown that the most common llse filter design can lead to performance inferior to that of various other filter designs however results are also presented demonstrating that an llse filter design motivated by the structure of the maximum likelihood receiver leads to consistently superior performance the performance of a system using this new design criterion is compared with that of an approximation to the maximum likelihood ml receiver for the tone interference model and with that of the exact ml receiver for the gaussian interference finally it is shown that the bit error rate estimate obtained from application of a gaussian approximation for the test statistic is overly pessimistic for the systems studied here

fiber dimension for invariant subspaces abstract in this paper we study the fiber dimension of invariant subspaces for a large class of operators we define a class of invariant subspaces called cf subspaces which are related to the codimension one property we obtain several characterizations of cf subspaces including one in terms of samuel multiplicity other new findings include 1 a lattice additive formula and its applications section 4 2 a new concept of absorbance which describes a rough containment relation for invariant subspaces section 5 3 the existence of a unique smallest cf subspace containing an arbitrary invariant subspace and preserving the fiber dimension section 6

unitary invariants for hilbert modules of finite rank we associate a sheaf model to a class of hilbert modules satisfying a natural finiteness condition it is obtained as the dual to a linear system of hermitian vector spaces in the sense of grothendieck a refined notion of curvature is derived from this construction leading to a new unitary invariant for the hilbert module a division problem with bounds originating in douady s privilege is related to this framework a series of concrete computations illustrate the abstract concepts of the paper

perpendicular categories with applications to representations and sheaves this paper is concerned with the omnipresence of the formation of the subcategories right left perpendicular to a subcategory of objects in an abelian category we encounter these subcategories in various contexts the formation of quotient categories with respect to localizing subcategories cf section 2 the deletion of vertices and shrinking of arrows see 37 in the representation theory of finite dimensional algebras cf section 5 the comparison of the representation theories of different extended dynkin quivers cf section 10 the theory of tilting cf sections 4 and 6 the study of homological epimorphisms of rings cf section 4 the passage from graded modules to coherent sheaves on a possibly weighted projective variety or scheme cf section 7 and 21 the study of maximal cohen macaulay modules over surface singularities cf sections the comparison of weighted projective lines for different weight sequences cf section 9 the formation of affine and local algebras attached to path algebras of extended dynkin quivers canonical algebras and weighted projective lines cf section 11 and 21 and the concept of universal localization in 40 formation of the perpendicular category has many aspects in common with localization and allows one to dispose of localization techniques in situations not accessible to any of the classical concepts of localization this applies in particular to applications in the domain of finite dimensional algebras and their representations several applications of the methods presented in this paper are already in existence partly published or appearing in print in the near future see for instance 40 39 4 45 26 49 46 and have show the versatility of the notion of a perpendicular category it seems that right perpendicular categories first appeared as the subcategories of so called closed objects in the process of the formation of the quotient cateogory of an abelian category with respect to a localizing serre subcategory see 18 47 34 another natural occurrence is encountered in commutative algebra forming the possibly infinitely generated modules of depth 2 cf section 7 the concept and some of the central applications were first presented in a talk given by the first author at the honnef meeting in january 1985 we also note that the perfectly matching nomination perpendicular category was coined by a schofield who discovered independently the usefulness of this concept in dealing with hereditary algebras see 39 cf also section 7 the authors further acknowledge the support of the deutsche forschungsgemeinschaft spp darstellungstheorie von endlichen gruppen und endlichdimensionalen algebren throughout this paper rings are associative with unit and modules are unitary right modules mod r respectively mod r denotes the category of all respectively all finitely presented right r modules

closed form analytical results for the rejection of narrow band interference in pn spread spectrum systems part ii linear interpolation filters the performance of pn spread spectrum communication systems in the presence of narrow band interference is studied when linear interpolation filters are employed for the estimation and subsequent suppression of the interference closed form analytical expressions for the system s performance are established for a broad class of interference processes the advantages of linear interpolation filters over predictive filters with identical number of taps are examined analytically and some unexpected results are obtained the analytical results are illustrated by examples

recollements and hochschild theory it is shown that a recollement of derived categories of algebras induces those of tensor product algebras and opposite algebras respectively which is applied to clarify the relations between recollements of derived categories of algebras and smoothness and hochschild cohomology of algebras

the kadison kaplansky conjecture for word hyperbolic groups in this paper we prove the kadison kaplansky idempotent conjecture for torsion free word hyperbolic groups the conjecture asserts that the following equivalent statements hold for a torsion free discrete group the reduced group c algebra c r contains no idempotents except 0 and 1 the spectrum of every element of the reduced group c algebra is connected the canonical trace on c r takes integer values on idempotents the last assertion can be viewed as a statement about the pairing between the k theory and the local cyclic cohomology of the group c algebra it is in this setting that we will prove the conjecture our proof is based on a partial analysis of the assembly maps in k theory and local cyclic homology we compare these assembly maps by means of an equivariant bivariant chern connes character before going into details we recall some previous work on the conjecture the first progress was achieved by pimsner and voiculescu pv who proved the kadison kaplansky conjecture for free groups as a consequence of their computation of the k theory of the group c algebra subsequently it was realized that more generally the kadison kaplansky conjecture was a consequence of the baum connes conjecture which gives a geometric description of k c r for any torsion free discrete group in fact the baum connes conjecture states that the k theoretic assembly map

estimates for hilbertian koszul homology abstract the objective of this paper is to give new kind of estimates for hilbertian koszul homology inspired by commutative algebra in multivariable fredholm theory

excision in cyclic homology theories in this paper we establish excision for z 2z graded cyclic homology theories including periodic entire asymptotic and local bivariant cyclic cohomology our work is a modification of the approach of cuntz quillen cq to excision in bivariant periodic cyclic homology and makes also use of the work of wodzicki wo we study the dimension shift of periodic cyclic cohomology under the boundary map associated to an extension of algebras and obtain the possible values of this dimension shift excision in entire cyclic cohomology is used to calculate these groups in a number of hitherto unknown cases finally a bivariant and multiplicative chern connes character on kasparov s bivariant k theory ka with values in bivariant local cyclic cohomology is constructed to put our approach into perspective we recall the previous work on excision in cyclic homology ever since the invention of cyclic homology by connes and independently by tsygan the problem of excision played a central role in the theory it is concerned with the question of to what extent an extension

on curvature in noncommutative geometry a general definition of a bimodule connection in noncommutative geometry has been recently proposed for a given algebra this definition is compared with the ordinary definition of a connection on a left module over the associated enveloping algebra the corresponding curvatures are also compared

marginal likelihood from the gibbs output abstract in the context of bayes estimation via gibbs sampling with or without data augmentation a simple approach is developed for computing the marginal density of the sample data marginal likelihood given parameter draws from the posterior distribution consequently bayes factors for model comparisons can be routinely computed as a by product of the simulation hitherto this calculation has proved extremely challenging our approach exploits the fact that the marginal density can be expressed as the prior times the likelihood function over the posterior density this simple identity holds for any parameter value an estimate of the posterior density is shown to be available if all complete conditional densities used in the gibbs sampler have closed form expressions to improve accuracy the posterior density is estimated at a high density point and the numerical standard error of resulting estimate is derived the ideas are applied to probit regression and finite mixture models

an approximate statistical analysis of the widrow lms algorithm with application to narrow band interference rejection the widrow lms algorithm is considered for the implementation of an adaptive prewhitening filter in a direct sequence ds spread spectrum receiver exact expressions for the steady state tapweight covariance matrix and resulting average excess mean square error are developed for the real lms algorithm when the input contains a random binary sequence used to model a pseudonoise spreading sequence it is shown here that the output samples of the adaptive filter possess approximately gaussian statistics under the conditions of slow convergence and a large number of filter taps using this approximation expressions for the resulting bit error rate ber when the adaptive algorithm is used to suppress a fading gone jammer are developed and numerical results obtained from these expressions are compared to simulation results for the ds receiver

the fredholm index of a pair of commuting operators ii this paper concerns fredholm theory in several variables and its applications to hilbert spaces of analytic functions one feature is the introduction of ideas from commutative algebra to operator theory specifically we introduce a method to calculate the fredholm index of a pair of commuting operators to achieve this we define and study the hilbert space analogs of samuel multiplicities in commutative algebra then the theory is applied to the symmetric fock space in particular our results imply a satisfactory answer to arveson s program on developing a fredholm theory for pure d contractions when d 2 including both the fredholmness problem and the calculation of indices we also show that arveson s curvature invariant is in fact always equal to the samuel multiplicity for an arbitrary pure d contraction with finite defect rank it follows that the curvature is a similarity invariant

resolvent estimates and decomposable extensions of generalized cesaro operators we determine the spectrum of generalized cesaro operators with essentially rational symbols acting on various spaces of analytic functions including hardy spaces weighted bergman and dirichlet spaces then we show that in all cases these operators are subdecomposable c 2009 elsevier inc all rights reserved

discussion to bayesian measures of model complexity and fit by spiegelhalter d j best n g carlin b p and van der linde a

unbounded bivariant k theory and correspondences in noncommutative geometry by adapting the algebraic notion of universal connection to the setting of unbounded kk cycles we show that the kasparov product of such cycles can be defined directly by an algebraic formula in order to achieve this it is necessary to develop a framework of smooth algebras and a notion of differentiable c module the theory of operator spaces provides the required tools finally the above mentioned kk cycles with connection can be viewed as the morphisms in a category whose objects are spectral triples

on the spectrum of the cesaro operator on spaces of analytic functions this paper concerns the cesaro operator acting on various spaces of analytic functions on the unit disc the remarkable fact that this operator is subnormal when acting on the hardy space h2 has lead to extensive studies of its spectral picture on other spaces of this type we present some of the methods that have been used to obtain information about the spectrum of the cesaro operator acting on hardy and bergman spaces and give a unified approach to these problems which also yields new results in this direction in particular we prove that the cesaro operator is subdecomposable on h1 and on the standard weighted bergman spaces 0

on the estimation of long tailed skewed distributions with actuarial applications abstract very long tailed skewed distributions often arise in practice in particular we find that size of loss distributions in casualty insurance are mainly of this type compounding explains why many of these losses have approximate pareto generalized pareto burr and log t distributions an adaptation of the empirical mean residual life function helps the statistician select the correct model to fit in these cases it is then discovered that minimum distance estimates in particular that of cramer von mises and minimum chi square estimates are extremely valuable and easy to use in the case of grouped data two substantial examples are given one involving hurricane losses and the other dealing with malpractice claims

free products cyclic homology and the gauss manin connection abstract we use the techniques of cuntz and quillen to present a new approach to periodic cyclic homology our construction is based on a t d t i a noncommutative equivariant de rham complex of an associative algebra a here d is the karoubi de rham differential and i is an operation analogous to contraction with a vector field as a byproduct we give a simple explicit construction of the gauss manin connection introduced earlier by e getzler on the relative periodic cyclic homology of a flat family of associative algebras over a central base ring we introduce and study free product deformations of an associative algebra a new type of deformation over a not necessarily commutative base ring natural examples of free product deformations arise from preprojective algebras and group algebras for compact surface groups

noncommutative smoothness and coadjoint orbits abstract in math ag 0010030 math z to appear r bocklandt and the author proved that certain quotient varieties of representations of deformed preprojective algebras are coadjoint orbits for the necklace lie algebra n q of the corresponding quiver q a conjectural ring theoretical explanation of these results was given in terms of noncommutative smoothness in the sense of c procesi j algebra 107 1987 63 74 in this paper we prove these conjectures the main tool in the proof is the etale local description due to w crawley boevey math ag 0105247 along the way we determine the smooth locus of the marsden weinstein reductions for quiver representations

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea