series estimation under cross sectional dependence an asymptotic theory is developed for series estimation of nonparametric and semiparametric regression models for cross sectional data under conditions on disturbances that allow for forms of cross sectional dependence and hetero geneity including conditional and unconditional heteroskedascity along with conditions on regressors that allow dependence and do not require existence of a density the conditions aim to accommodate various settings plausible in economic applications and can apply also to panel spatial and time series data a mean square rate of convergence of nonparametric regression estimates is established followed by asymptotic normality of a quite general statistic data driven studentizations that rely on single or double indices to order the data are justified in a partially linear model setting monte carlo investigation of finite sample properties and two empirical applications are carried out

tauberian theorems and the central limit theorem 1 results let xn be independent and identically distributed random variables with law p mean 0 and variance a2 00 s 1 xk write p qn 1 for the laws of sn sn nyi a n and the standard normal n o 1 thus qn 1d weak convergence by the global central limit theorem we shall need the local central limit theorem see e g ibragimov and linnik 1971 theorems 4 4 1 4 2 1 4 2 2 we shall assume either llt i some pk has an absolutely continuous component in which case qn 11 3 0 as n x oo variation norm or llt ii p is lattice supported by some arithmetic progression a hk with k integer and h maximal we shall suppose for simplicity that a 0 and h 1 when writing pnk for pn k

nonparametric bayes dynamic modelling of relational data symmetric binary matrices representing relations are collected in many areas our focus is on dynamically evolving binary relational matrices with interest being on inference on the relationship structure and prediction we propose a nonparametric bayesian dynamic model which reduces dimensionality in characterizing the binary matrix through a lower dimensional latent space representation with the latent coordinates evolving in continuous time via gaussian processes by using a logistic mapping function from the link probability matrix space to the latent relational space we obtain a flexible and computationally tractable formulation employing polya gamma data augmentation an efficient gibbs sampler is developed for posterior computation with the dimension of the latent space automatically inferred we provide theoretical results on flexibility of the model and illustrate its performance via simulation experiments we also consider an application to co movements in world financial markets

probability laws related to the jacobi theta and riemann zeta functions and brownian excursions this paper reviews known results which connect riemann s integral representations of his zeta function involving jacobi s theta function and its derivatives to some particular probability laws governing sums of independent exponential variables these laws are related to one dimensional brownian motion and to higher dimensional bessel processes we present some characterizations of these probability laws and some approximations of riemann s zeta function which are related to these laws

sequentially additive nonignorable missing data modelling using auxiliary marginal information summarywe study a class of missingness mechanisms referred to as sequentially additive nonignorable for modelling multivariate data with item nonresponse these mechanisms explicitly allow the probability of nonresponse for each variable to depend on the value of that variable thereby representing nonignorable missingness mechanisms these missing data models are identified by making use of auxiliary information on marginal distributions such as marginal probabilities for multivariate categorical variables or moments for numeric variables we prove identification results and illustrate the use of these mechanisms in an application

decomposition numbers of so7 q and sp6 q abstract we complete the l modular decomposition numbers of the unipotent characters in the principal block of the special orthogonal groups so 7 q and the symplectic groups sp 6 q for all prime powers q and all odd primes l different from the defining characteristic

vers une decomposition de jordan des blocs des groupes reductifs finis abstract let g be a reductive algebraic group over an algebraic closure of a prime field f p defined over f q with frobenius endomorphism f let g f be the subgroup of rational points let l be a prime number assume that l is different from p if g f is in duality with g f then by a theorem of m broue and j michel m broue j michel blocs et series de lusztig dans un groupe reductif fini j reine angew math 395 1989 56 67 for any l bloc b of g f there exists a unique g f conjugacy class s of l semi simple elements such that some irreducible representation of b is in the rational lusztig s series associated to s if s 1 b is said to be unipotent if g is not connected with identity component g define the unipotent l blocs of g f as the l blocks that cover some unipotent l bloc of g f assuming l is good for g we construct from g f and s some reductive algebraic group g s f defined over f q and a one to one map from the set of l blocks of g f with associated class s onto the set of unipotent l blocks of g s f such that if b corresponds to b then there is a significant height preserving one to one map from the set of irreducible representations irr b onto the set irr b the respective defect groups of b and b are isomorphic the associated brauer categories are equivalent one do not assume that the center of g is connected the class of s may be isolated in g

reduced fusion systems over p groups with abelian subgroup of index p ii abstract for an odd prime p we look at simple fusion systems over a finite nonabelian p group s which has an abelian subgroup a of index p when s has more than one such subgroup we reduce this to a case already studied by ruiz and viruel when a is the unique abelian subgroup of index p in s and is not essential equivalently is not radical in the fusion system we give a complete list of all possibilities which can occur this includes several families of exotic fusion systems including some which have proper strongly closed subgroups

bayesian multivariate logistic regression bayesian analyses of multivariate binary or categorical outcomes typically rely on probit or mixed effects logistic regression models that do not have a marginal logistic structure for the individual outcomes in addition difficulties arise when simple noninformative priors are chosen for the covariance parameters motivated by these problems we propose a new type of multivariate logistic distribution that can be used to construct a likelihood for multivariate logistic regression analysis of binary and categorical data the model for individual outcomes has a marginal logistic structure simplifying interpretation we follow a bayesian approach to estimation and inference developing an efficient data augmentation algorithm for posterior computation the method is illustrated with application to a neurotoxicology study

local shrinkage rules levy processes and regularized regression we use l evy processes to generate joint prior distributions and therefore penalty functions for a location parameter b b1 bp as p grows large this generalizes the class of local global shrinkage rules based on scale mixtures of normals illuminates new connections among disparate methods and leads to new results for computing posterior means and modes under a wide class of priors we extend this framework to large scale regularized regression problems where p n and provide comparisons with other methodologies

radical subgroups of the finite exceptional groups of lie type e6 abstract we consider the finite exceptional groups of lie type e 6 1 q e 6 q and e 6 1 q e 6 2 q both the universal versions we classify up to conjugacy the maximal p local subgroups and radical p subgroups of g e 6 e q for p 5 with p q and q e mod p and for p 3 with 3 q and q e mod 3 as an application the essential p rank of the frobenius category f d g is determined where d is a sylow p subgroup of g moreover if p 3 then we show that there is a subgroup h f 4 q of g containing d such that f d g f d h that is h controls 3 fusion in g

efficient posterior sampling for high dimensional imbalanced logistic regression classification with high dimensional data is of widespread interest and often involves dealing with imbalanced data bayesian classification approaches are hampered by the fact that current markov chain monte carlo algorithms for posterior computation become inefficient as the number formula see text of predictors or the number formula see text of subjects to classify gets large because of the increasing computational time per step and worsening mixing rates one strategy is to employ a gradient based sampler to improve mixing while using data subsamples to reduce the per step computational complexity however the usual subsampling breaks down when applied to imbalanced data instead we generalize piecewise deterministic markov chain monte carlo algorithms to include importance weighted and mini batch subsampling these maintain the correct stationary distribution with arbitrarily small subsamples and substantially outperform current competitors we provide theoretical support for the proposed approach and demonstrate its performance gains in simulated data examples and an application to cancer data

nonparametric bayes modeling of populations of networks abstractreplicated network data are increasingly available in many research fields for example in connectomic applications interconnections among brain regions are collected for each patient under study motivating statistical models which can flexibly characterize the probabilistic generative mechanism underlying these network valued data available models for a single network are not designed specifically for inference on the entire probability mass function of a network valued random variable and therefore lack flexibility in characterizing the distribution of relevant topological structures we propose a flexible bayesian nonparametric approach for modeling the population distribution of network valued data the joint distribution of the edges is defined via a mixture model that reduces dimensionality and efficiently incorporates network information within each mixture component by leveraging latent space representations the formulation leads to an efficient gibbs sampler and provides simple and c

weighted sums of i i d random variables attracted to integrals of stable processes under the assumption of the convergence of partial sum processesz n t of i i d random variables to an stable levy processz t 0 2 the convergence of weighted sums f n u dz n u to f u dz u is studied the general convergence result is then applied to examine the domain of attraction of the fractional stable process

controlled 2 blocks of quasisimple groups abstract controlled p blocks introduced by alperin and broue in 1979 were classified for quasisimple groups g for odd primes in 10 we classify the controlled 2 blocks of quasisimple groups g the results imply that every nilpotent 2 block of g has abelian defect groups this agrees with one of the main results proved in 15 we also give an explicit characterization of non controlled 2 blocks of all quasisimple groups this implies that the p 2 version of the block theoretic analogue of glauberman s zj theorem proved by kessar linckelmann and robinson in 27 holds for quasisimple groups g

functional limit theorems for weighted sums of i i d random variables on etudie des theoremes limites fonctionnels pour des sommes ponderees specialement pour des poids concernant les methodes de sommabilite classiques telles que celles de cesaro abel borel et euler

decoupling shrinkage and selection in bayesian linear models a posterior summary perspective selecting a subset of variables for linear models remains an active area of research this article reviews many of the recent contributions to the bayesian model selection and shrinkage prior literature a posterior variable selection summary is proposed which distills a full posterior distribution over regression coefficients into a sequence of sparse linear predictors

inferring network structure in non normal and mixed discrete continuous genomic data summary inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high dimensional genomic markers that are potentially associated with cancer traditionally conditional independence has been studied using sparse gaussian graphical models for continuous data and sparse ising models for discrete data however there are two clear situations when these approaches are inadequate the first occurs when the data are continuous but display non normal marginal behavior such as heavy tails or skewness rendering an assumption of normality inappropriate the second occurs when a part of the data is ordinal or discrete e g presence or absence of a mutation and the other part is continuous e g expression levels of genes or proteins in this case the existing bayesian approaches typically employ a latent variable framework for the discrete part that precludes inferring conditional independence among the data that are actually observed the current article overcomes these two challenges in a unified framework using gaussian scale mixtures our framework is able to handle continuous data that are not normal and data that are of mixed continuous and discrete nature while still being able to infer a sparse conditional sign independence structure among the observed data extensive performance comparison in simulations with alternative techniques and an analysis of a real cancer genomics data set demonstrate the effectiveness of the proposed approach

conjugate bayes for probit regression via unified skew normal distributions regression models for dichotomous data are ubiquitous in statistics besides being useful for inference on binary responses these methods serve also as building blocks in more complex formulations such as density regression nonparametric classification and graphical models within the bayesian framework inference proceeds by updating the priors for the coefficients typically set to be gaussians with the likelihood induced by probit or logit regressions for the responses in this updating the apparent absence of a tractable posterior has motivated a variety of computational methods including markov chain monte carlo routines and algorithms which approximate the posterior despite being routinely implemented markov chain monte carlo strategies face mixing or time inefficiency issues in large p and small n studies whereas approximate routines fail to capture the skewness typically observed in the posterior this article proves that the posterior distribution for the probit coefficients has a unified skew normal kernel under gaussian priors such a novel result allows efficient bayesian inference for a wide class of applications especially in large p and small to moderate n studies where state of the art computational methods face notable issues these advances are outlined in a genetic study and further motivate the development of a wider class of conjugate priors for probit models along with methods to obtain independent and identically distributed samples from the unified skew normal posterior

stochastic random walk summability on etudie les proprietes limites des sommes partielles ponderees lorsque les poids sont donnes par une procedure de sommation en marche aleatoire

the 2 blocks of the covering groups of the symmetric groups abstract let n be a double cover of the finite symmetric group s n of degree n i e n has a central involution z such that n z s n an irreducible character of n is called ordinary or spin according to whether it has z in its kernel or not the purpose of this paper is to determine the distribution of the spin characters of n into 2 blocks the methods applied here are essentially different from those applied to previous questions of this type we also discuss some consequences of our main result for the decomposition numbers an analogue of james well known result for the decomposition numbers of the symmetric groups is proved providing also a generalization of a theorem of benson ben theorem 1 2 in section 1 we present the background for our results and give some preliminaries in section 2 we give an explicit formula for the number of spin characters in a 2 block we also prove a result about the weight of a block containing a given non self associate spin character which will be important for the proof of our theorem on the 2 block distribution of spin characters section 3 presents some fundamental combinatorial concepts used in sections 4 and 5 the theorem concerning the spin characters in a given 2 block is proved in section 4 and in section 5 we present our results on the decomposition numbers

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 spectral modeling for multiple time series we develop a novel bayesian modeling approach to spectral density estimation for multiple time series the log periodogram distribution for each series is modeled as a mixture of gaussian distribut

abelian subgroups nilpotent subgroups and the largest character degree of a finite group abstract let h be an abelian subgroup of a finite group g and the set of prime divisors of h we prove that h o g o g is bounded above by the largest character degree of g a similar result is obtained when h is nilpotent

the structure of blocks with a klein four defect group we prove erdmann s conjecture stating that every block with a klein four defect group has a simple module with trivial source and deduce from this that puig s finiteness conjecture holds for source algebras of blocks with a klein four defect group the proof uses the classification of finite simple groups

a model of text for experimentation in the social sciences abstractstatistical models of text have become increasingly popular in statistics and computer science as a method of exploring large document collections social scientists often want to move beyond exploration to measurement and experimentation and make inference about social and political processes that drive discourse and content in this article we develop a model of text data that supports this type of substantive research our approach is to posit a hierarchical mixed membership model for analyzing topical content of documents in which mixing weights are parameterized by observed covariates in this model topical prevalence and topical content are specified as a simple generalized linear model on an arbitrary number of document level covariates such as news source and time of release enabling researchers to introduce elements of the experimental design that informed document collection into the model within a generally applicable framework we demonstrate the proposed methodology by analyzi

meta analysis for 2 2 tables a bayesian approach this paper develops and implements a fully bayesian approach to meta analysis in which uncertainty about effects in distinct but comparable studies is represented by an exchangeable prior distribution specifically hierarchical normal models are used along with a parametrization that allows a unified approach to deal easily with both clinical trial and case control study data monte carlo methods are used to obtain posterior distributions for parameters of interest integrating out the unknown parameters of the exchangeable prior or random effects distribution the approach is illustrated with two examples the first involving a data set on the effect of beta blockers after myocardial infarction and the second based on a classic data set comprising 14 case control studies on the effects of smoking on lung cancer in both examples rather different conclusions from those previously published are obtained in particular it is claimed that widely used methods for meta analysis which involve complete pooling of o e values lead to understatement of uncertainty in the estimation of overall or typical effect size

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

splendid morita equivalences for principal 2 blocks with dihedral defect groups given a dihedral 2 group p of order at least 8 we classify the splendid morita equivalence classes of principal 2 blocks with defect groups isomorphic to p to this end we construct explicit stable equivalences of morita type induced by specific scott modules using brauer indecomposability and gluing methods we then determine when these stable equivalences are actually morita equivalences and hence automatically splendid morita equivalences finally we compute the generalised decomposition numbers in each case

2 blocks with abelian defect groups we give a classification up to morita equivalence of 2 blocks of quasi simple groups with abelian defect groups as a consequence we show that donovan s conjecture holds for elementary abelian 2 groups and that the entries of the cartan matrices are bounded in terms of the defect for arbitrary abelian 2 groups we also show that a block with defect groups of the form c2m c2m for m 2 has one of two morita equivalence types and hence is morita equivalent to the brauer correspondent block of the normaliser of a defect group this completes the analysis of the morita equivalence types of 2 blocks with abelian defect groups of rank 2 from which we conclude that donovan s conjecture holds for such 2 groups a further application is the completion of the determination of the number of irreducible characters in a block with abelian defect groups of order 16 the proof uses the classification of finite simple groups

an equivariant bijection between irreducible brauer characters and weights for sp 2n q abstract the longstanding alperin weight conjecture and its blockwise version have been reduced to simple groups recently by navarro tiep spath and koshitani thus to prove this conjecture it suffices to verify the corresponding inductive condition for all finite simple groups the first is to establish an equivariant bijection between irreducible brauer characters and weights for the universal covering groups of simple groups assume q is a power of some odd prime p we first prove the blockwise alperin weight conjecture for sp 2 n q and odd non defining characteristics if the decomposition matrix of sp 2 n q is unitriangular with respect to an aut sp 2 n q stable basic set this assumption holds for linear primes we can establish an equivariant bijection between the irreducible brauer characters and weights

false discovery rate regression an application to neural synchrony detection in primary visual cortex this article introduces false discovery rate regression a method for incorporating covariate information into large scale multiple testing problems fdr regression estimates a relationship between test level covariates and the prior probability that a given observation is a signal it then uses this estimated relationship to inform the outcome of each test in a way that controls the overall false discovery rate at a prespecified level this poses many subtle issues at the interface between inference and computation and we investigate several variations of the overall approach simulation evidence suggests that 1 when covariate effects are present fdr regression improves power for a fixed false discovery rate and 2 when covariate effects are absent the method is robust in the sense that it does not lead to inflated error rates we apply the method to neural recordings from primary visual cortex the goal is to detect pairs of neurons that exhibit fine time scale interactions in the sense that t

uno s invariant conjecture for chevalley groups g2 q in nondefining characteristics abstract uno s invariant conjecture for the chevalley groups g 2 q has been verified when the characteristic of the modular representation is distinct from the defining characteristic of the groups thus dade s reductive conjecture and the isaacs navarro conjecture both hold for g 2 q in non defining characteristics

on perturbed proximal gradient algorithms we study a version of the proximal gradient algorithm for which the gradient is intractable and is approximated by monte carlo methods and in particular markov chain monte carlo we derive conditions on the step size and the monte carlo batch size under which convergence is guaranteed both increasing batch size and constant batch size are considered we also derive non asymptotic bounds for an averaged version our results cover both the cases of biased and unbiased monte carlo approximation to support our findings we discuss the inference of a sparse generalized linear model with random effect and the problem of learning the edge structure and parameters of sparse undirected graphical models

controlled blocks of the finite quasisimple groups for odd primes abstract we classify controlled blocks introduced by alperin and broue in 1979 for all quasisimple groups g for odd primes the results imply that every nilpotent block of g has abelian defect groups which in turn is one of the main results proved in an and eaton 2011 6 we also give an explicit characterization of non controlled blocks of all quasisimple groups g for odd primes this implies the block theoretic analogue of glauberman s zj theorem for g proved by kessar linckelmann and robinson 2002 18

some matrix variate distribution theory notational considerations and a bayesian application summary we introduce and justify a convenient notation for certain matrix variate distributions which by its emphasis on the important underlying parameters and the theory on which it is based eases greatly the task of manipulating such distributions important examples include the matrix variate normal t f and beta and the wishart and inverse wishart distributions the theory is applied to compound matrix distributions and to bayesian prediction in the multivariate linear model

on rouquier blocks for finite classical groups at linear primes abstract w turner has proved that broue s abelian defect group conjecture holds for certain unipotent blocks of the finite general linear group the so called rouquier blocks this together with theorems of a marcus and of j chuang and r rouquier proves that the conjecture holds for all blocks of such groups we prove that other finite classical groups also possess analogues of rouquier blocks at linear primes

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

cartan matrices and morita equivalence for blocks of the symmetric groups theorem 1 the blocks of the symmetric groups with a given weight w 0 over a field of characteristic p can be collected into families according to the shapes of their cores each family consists of morita equivalent blocks the number of such families is at most flf 1 i l w 1 11 and each family contains a block of some g where n is less than or equal to p2 p 1 2 w 1 2 4 wp

on the endomorphism algebra of modular gelfand graev representations abstract we study the endomorphism algebras of a modular gelfand graev representation of a finite reductive group by investigating modular properties of homomorphisms constructed by curtis and curtis shoji

weighted sums of random variables attracted to stable laws on etudie des sommes ponderees de variables aleatoires en relation avec la loi des grands nombres et la loi du logarithme itere

radical 3 subgroups of f4 q with q even abstract in a recent paper an and huang classified the radical 3 subgroups of f 4 q for q odd here we use a similar approach to classify the radical 3 subgroups of f 4 q with q even as an application we determine the essential rank of the frobenius category f d f 4 q for q even where d is a sylow 3 subgroup of f 4 q

splendid morita equivalences for principal blocks with generalised quaternion defect groups abstract we prove that splendid morita equivalences between principal blocks of finite groups with dihedral sylow 2 subgroups realised by scott modules can be lifted to splendid morita equivalences between principal blocks of finite groups with generalised quaternion sylow 2 subgroups realised by scott modules

on the inductive blockwise alperin weight condition for classical groups abstract recently there has been substantial progress on the alperin weight conjecture as a step to establish the alperin weight conjecture for all finite groups we prove the inductive blockwise alperin weight condition for simple groups of classical type under some additional assumption

discriminative relational topic models relational topic models rtms provide a probabilistic generative process to describe both the link structure and document contents for document networks and they have shown promise on predicting network structures and discovering latent topic representations however existing rtms have limitations in both the restricted model expressiveness and incapability of dealing with imbalanced network data to expand the scope and improve the inference accuracy of rtms this paper presents three extensions 1 unlike the common link likelihood with a diagonal weight matrix that allows the same topic interactions only we generalize it to use a full weight matrix that captures all pairwise topic interactions and is applicable to asymmetric networks 2 instead of doing standard bayesian inference we perform regularized bayesian inference regbayes with a regularization parameter to deal with the imbalanced link structure issue in real networks and improve the discriminative ability of learned latent representations and 3 instead of doing variational approximation with strict mean field assumptions we present collapsed gibbs sampling algorithms for the generalized relational topic models by exploring data augmentation without making restricting assumptions under the generic regbayes framework we carefully investigate two popular discriminative loss functions namely the logistic log loss and the max margin hinge loss experimental results on several real network datasets demonstrate the significance of these extensions on improving prediction performance

mixtures envelopes and hierarchical duality summary we develop a connection between mixture and envelope representations of objective functions that arise frequently in statistics we refer to this connection by using the term hierarchical duality our results suggest an interesting and previously underexploited relationship between marginalization and profiling or equivalently between the fenchel moreau theorem for convex functions and the bernstein widder theorem for laplace transforms we give several different sets of conditions under which such a duality result obtains we then extend existing work on envelope representations in several ways including novel generalizations to variance mean models and to multivariate gaussian location models this turns out to provide an elegant missing data interpretation of the proximal gradient method which is a widely used algorithm in machine learning we show several statistical applications in which the framework proposed leads to easily implemented algorithms including a robust version of the fused lasso non linear quantile regression via trend filtering and the binomial fused double pareto model code for the examples is available on github at https github com jgscott hierduals

the bayesian bridge summary we propose the bayesian bridge estimator for regularized regression and classification two key mixture representations for the bayesian bridge model are developed a scale mixture of normal distributions with respect to an stable random variable a mixture of bartlett fejer kernels or triangle densities with respect to a two component mixture of gamma random variables both lead to markov chain monte carlo methods for posterior simulation and these methods turn out to have complementary domains of maximum efficiency the first representation is a well known result due to west and is the better choice for collinear design matrices the second representation is new and is more efficient for orthogonal problems largely because it avoids the need to deal with exponentially tilted stable random variables it also provides insight into the multimodality of the joint posterior distribution which is a feature of the bridge model that is notably absent under ridge or lasso type priors we prove a theorem that extends this representation to a wider class of densities representable as scale mixtures of beta distributions and we provide an explicit inversion formula for the mixing distribution the connections with slice sampling and scale mixtures of normal distributions are explored on the practical side we find that the bayesian bridge model outperforms its classical cousin in estimation and prediction across a variety of data sets both simulated and real we also show that the markov chain monte carlo algorithm for fitting the bridge model exhibits excellent mixing properties particularly for the global scale parameter this makes for a favourable contrast with analogous markov chain monte carlo algorithms for other sparse bayesian models all methods described in this paper are implemented in the r package bayesbridge an extensive set of simulation results is provided in two on line supplemental files

radical 3 subgroups and essential 3 rank of f4 q abstract we classify maximal 3 local subgroups and radical 3 subgroups of g f 4 q when q odd and then determine the essential 3 rank of the frobenius category f d g where d is a sylow 3 subgroup of g

fast bayesian factor analysis via automatic rotations to sparsity abstractrotational post hoc transformations have traditionally played a key role in enhancing the interpretability of factor analysis regularization methods also serve to achieve this goal by prioritizing sparse loading matrices in this work we bridge these two paradigms with a unifying bayesian framework our approach deploys intermediate factor rotations throughout the learning process greatly enhancing the effectiveness of sparsity inducing priors these automatic rotations to sparsity are embedded within a pxl em algorithm a bayesian variant of parameter expanded em for posterior mode detection by iterating between soft thresholding of small factor loadings and transformations of the factor basis we obtain a dramatic accelerations b robustness against poor initializations and c better oriented sparse solutions to avoid the prespecification of the factor cardinality we extend the loading matrix to have infinitely many columns with the indian buffet process ibp prior the factor dimen

on unipotent blocks and their ordinary characters there is a great deal of evidence suggesting that block theory for finite reductive groups should lead to an enrichment of the harish chandra theory for those groups see s 5 1 fs2 p2 3 4 h 6 1 10 an e generalized harish chandra theory for e a positive integer is introduced in bmm i a the context is as follows let g be a connected reductive group defined over lfq with associated frobenius endomorphism f let e 1 an integer when l is an f stable levi subgroup of g one denotes by r and re the lusztig functor and its adjoint a unipotent e pair l l is defined by an e split levi subgroup l of g and a unipotent character z d l 1 one writes li z1 l2 j 2 if and only if l1 c l 2 and zl l2 l 1 2 l 4 0 see 3 l the notion of unipotent e cuspidal pairs and the resulting partition of g g v 1 are defined as in the classical case corresponding to e 1 if f is a prime not dividing q and e is the order of q mod f it seems natural in connection with blocks to ask if the partition of the unipotent characters 8 g v l resulting from e theory coincides with f blocks the blocks of g v which are defined by unipotent characters are called unipoteut f blocks we prove

unipotent elements of finite groups of lie type and realization fields of their complex representations abstract let p be a prime this paper classifies finite connected reductive groups g in characteristic p with the property that all complex character values of g belong to an unramified above p extension of the field of rational numbers the main application of these results is to the problem of describing the irreducible complex or p adic representations of g that remain absolutely irreducible under the brauer reduction modulo p an efficient approach to solve this problem for p 3 has been developed in our paper proc london math soc 3 84 2002 439 together with proc london math soc 3 84 2002 439 theorem 1 9 of the paper solves this problem for many finite connected reductive groups in characteristic p 3 additionally we show that all complex representations of any finite connected reductive group with no composition factor of type e7 2f e8 2f and e8 5f can be realized over a quadratic extension of an unramified above p extension of q

scopes reduction and morita equivalence classes of blocks in finite classical groups ii abstract we extend our work of j algebra 230 2000 378 423 on unipotent blocks of classical groups to blocks of orthogonal groups containing characters labelled by degenerate symbols we also show that for classical groups in the linear prime case there are only finitely many morita types of unipotent blocks with a given defect group