a note on the one particle and hilbert schmidt cohomologies of the poincare group in three spacetime dimensions cocycles for p up arrow 2 1 with values in a hilbert space are studied it is found that cocycles for irreducible representations apart from the case of vanishing momentum are trivial further cocycles for the action v v 1 with values in the representation space of v are investigated and found to be trivial some consequences for physics are obtained

base change and a problem of serre we establish a version of level lowering for mod p galois representations arising from the reductions of representations associated to hilbert modular forms in particular we show that level lowering can be easily achieved if one replaces the base field with a suitable solvable extension this is often enough for applications to proving the modularity of p adic representations

marginal likelihood estimation via power posteriors model choice plays an increasingly important role in statistics from a bayesian perspective a crucial goal is to compute the marginal likelihood of the data for a given model however this is typically a difficult task since it amounts to integrating over all model parameters the aim of the paper is to illustrate how this may be achieved by using ideas from thermodynamic integration or path sampling we show how the marginal likelihood can be computed via markov chain monte carlo methods on modified posterior distributions for each model this then allows bayes factors or posterior model probabilities to be calculated we show that this approach requires very little tuning and is straightforward to implement the new method is illustrated in a variety of challenging statistical settings

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

serre weights for rank two unitary groups we study the weight part of a generalisation of serre s conjecture for mod l galois representations associated to automorphic representations on rank two unitary groups for odd primes l we propose a conjectural set of serre weights agreeing with all conjectures in the literature and under a mild assumption on the image of the mod l galois representation we are able to show that any modular representation is modular of each conjectured weight we make no assumptions on the ramification or inertial degrees of l our main innovations are the use of outer forms of text gl 2 to avoid the parity difficulties with inner forms and the use of the lifting techniques and change of weight results introduced in barnet lamb et al j am math soc 24 2 411 469 2011 duke math j 161 8 1521 1580 2012 potential automorphy and change of weight preprint 2010

efficient bayes factor estimation from the reversible jump output summary we propose a class of estimators of the bayes factor which is based on an extension of the bridge sampling identity of meng wong 1996 and makes use of the output of the reversible jump algorithm of green 1995 within this class we give the optimal estimator and also a suboptimal one which may be simply computed on the basis of the acceptance probabilities used within the reversible jump algorithm for jumping between models the proposed estimators are very easily computed and lead to a substantial gain of efficiency in estimating the bayes factor over the standard estimator based on the reversible jump output this is illustrated through a series of monte carlo simulations involving a linear and a logistic regression model

twisted condensates of quantised fields the authors construct some quasi free pure states of three quantised fields in 1 1 dimensions that are localised in the sense of knight 1961 they consider massless or massive dirac fields forming a u n n or 1 multiplet and subject it to a local gauge transformation they also subject a doublet of massive klein gordon fields to local so 2 transformations they find the conditions that the resulting automorphisms are spatial in fock space in some cases the conditions turn out to require that certain parameters identified as the winding numbers of the gauge are integers it is argued that this integer labels states of various charge

on serre s conjecture for mod l galois representations over totally real fields in 1987 serre conjectured that any mod two dimensional irre ducible odd representation of the absolute galois group of the rationals came from a modular form in a precise way we present a generalisation of this conjecture to 2 dimensional representations of the absolute galois group of a totally real eld where is unramied the hard work is in formulating an analogue of the weight part of serre s conjecture serre furthermore asked whether his conjecture could be rephrased in terms of a mod langlands philosophy using ideas of emerton and vign eras we formulate a mod local global principle for the group d where d is a quaternion algebra over a totally real eld split above and at 0 or 1 innite places and show how it implies the conjecture

serre s modularity conjecture ii we provide proofs of theorems 4 1 and 5 1 of khare and wintenberger invent math doi 10 1007 s00222 009 0205 7 2009

weights of galois representations associated to hilbert modular forms let f be a totally real field p 3 a rational prime unramified in f and p a place of f over p let gal f f gl2 fp be a two dimensional mod p galois representation which is assumed to be modular of some weight and whose restriction to a decomposition subgroup at p is irreducible we specify a set of weights determined by the restriction of to inertia at p which contains all the modular weights for this proves part of a conjecture of diamond buzzard and jarvis which provides an analogue of serre s epsilon conjecture for hilbert modular forms mod p

on monte carlo methods for estimating ratios of normalizing constants recently estimating ratios of normalizing constants has played an important role in bayesian computations applications of estimating ratios of normalizing constants arise in many aspects of bayesian statistical inference in this article we present an overview and discuss the current monte carlo methods for estimating ratios of normalizing constants then we propose a new ratio importance sampling method and establish its theoretical framework we find that the ratio importance sampling method can be better than the current methods for example the bridge sampling method meng and wong and the path sampling method gelman and meng in the sense of minimizing asymptotic relative mean square errors of estimators an example is given for illustrative purposes finally we present two special applications and the general implementation issues for estimating ratios of normalizing constants

some local covariant representations of the canonical anticommutation relations the authors find some non fock representations of the canonical anticommutation relations in 1 1 dimensions these representations obtained by a bogoliubov transformation of the fock annihilation and creation operators are poincare covariant have positive energy and are labelled by two conserved charges which take on continuous values in the interval 0 2 pi

on serre s conjecture for 2 dimensional mod p representations of gal q q we prove the existence in many cases of minimally ramified p adic lifts of 2 dimensional continuous odd absolutely irreducible mod p representations of the absolute galois group of q it is predicted by serre s conjecture that such representations arise from newforms of optimal level and weight

galilei covariance and quasi free representations of fermi fields some quasi free irreducible representations of the car algebra of a non relativistic free fermi field are constructed which are covariant under certain subgroups of the extended galilei group the construction of fully covariant but reducible representations as direct integrals of partially covariant ones is described this method is also applicable to arbitrary c algebras and other covariance groups

markov chain monte carlo methods for computing bayes factors a comparative review the problem of calculating posterior probabilities for a collection of competing models and associated bayes factors continues to be a formidable challenge for applied bayesian statisticians current approaches that take advantage of modern markov chain monte carlo computing methods include those that attempt to sample over some form of the joint space created by the model indicators and the parameters for each model others that sample over the model space alone and still others that attempt to estimate the marginal likelihood of each model directly because the collection of these is equivalent to the collection of model probabilities themselves we review several methods and compare them in the context of three examples a simple regression example a more challenging hierarchical longitudinal model and a binary data latent variable model we find that the joint model parameter space search methods perform adequately but can be difficult to program and tune whereas the marginal likelihood methods o

an analogue of serre s conjecture for galois representations and hecke eigenclasses in the mod p cohomology of gl n ℤ

constructing hilbert modular forms without exceptional primes in this paper we construct families of hilbert modular newforms without exceptional primes this is achieved by generalizing the notion of good dihedral primes introduced by khare and wintenberger in their proof of serre s modularity conjecture to totally real fields

some covariant representations of massless fermi fields studies the class of pure quasi free gauge invariant states of the fermion algebra the authors show that the question of g covariance of the corresponding representations i e implementability of some group g of one particle symmetry transformations is related to a cohomology group with values in the hilbert schmidt class in four dimensional space time this cohomology is nontrivial thus leading to g covariant non fock representations when g is taken to be the space time translation group together with rotations or space time translations together with boosts in one direction and rotations about it and the fermion mass is zero in two space time dimensions some new fully poincare covariant representations for free massless fermions are constructed

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

quasi free photon states and the poincare group it is proven that every projectively poincare covariant representation of the free photon field defined by a pure quasi free state is unixarily equivalent to the fock representation of that field

on deformation rings of residually reducible galois representations and r t theorems we introduce a new method of proof for r t theorems in the residually reducible case we study the crystalline universal deformation ring r and its ideal of reducibility i of a mod p galois representation 0 of dimension n whose semisimplification is the direct sum of two absolutely irreducible mutually non isomorphic constituents 1 and 2 under some assumptions on selmer groups associated with 1 and 2 we show that r i is cyclic and often finite using ideas and results of but somewhat different assumptions from bellaiche and chenevier we prove that i is principal for essentially self dual representations and deduce statements about the structure of r using a new commutative algebra criterion we show that given enough information on the hecke side one gets an r t theorem we then apply the technique to modularity problems for 2 dimensional representations over an imaginary quadratic field and a 4 dimensional representation over q

on modular representations of bar q q arising from modular forms where g is the galois group gai i q and f is a finite field of characteristic i 3 suppose that p is modular of level n i e that it arises from a weight 2 newform of level dividing n and trivial nebentypus character then p is an odd representation the matrix p c where c is a complex conjugation in g has eigenvalues 1 1 since 1 and 1 are distinct in f p is absolutely irreducible and has a model over every subfield of f containing the set trace p we assume that f has been chosen so that it is generated by this set assume that p is a prime which exactly divides n we write p i n and restrict p to a decomposition group of g for the prime p view the restriction as a representation p p of gal t p qp we say that p is finite at p 34 or 35 w if there is a finite flat f vector space scheme h over zp for which the action of gal t p qp on the f vector space h 1 p gives pp i f p 9 is finite at p if and only if pp is unramified it is clear that p is finite at p whenever p is already modular of level n p in w of 34 cf 35 serre conjectured the converse i e that if p is finite then p is modular of level n p soon thereafter mazur 1 20 proved this conjecture in the case

implementability of gauge transformations and quantization of fermions in external fields quantization of fermions in an external soliton field leading to a representation of the canonical anticommutation relation car which is inequivalent to the representation connected to the massive dirac operator is studied classes of gauge and axial gauge transformations that can be unitarily implemented are determined in the latter case quantization conditions for gauge functions are obtained integers entering can be interpreted as winding numbers

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

some covariant representations of massless boson fields considers the c algebra of the canonical commutation relations ccr acted on by a group g of one particle symmetry transformations v a symplectic operator t defines a representation pi t pi f omicron t where pi f is the fock representation the automorphisms of the ccr algebra that are induced by g are shown to be continuously implemented in pi t if and only if a v g av g is a continuous hilbert schmidt 1 cocycle of g here a is related to t by t exp a a being a suitable bounded antilinear self adjoint operator some new examples of fully poincare covariant representations of massless fields in 1 1 dimensions are constructed

smith theory and hecke operators abstract of the connections between the cohomology of arithmetic groups and representations of galois groups some are known and more are conjectured this paper proves one of these conjectures for certain monomial galois representations let p be a prime we show that the representation of the absolute galois group of q induced from an f p valued ray class character of the cyclotomic field q p is attached to a hecke eigenclass in the mod p cohomology of a torsion free congruence subgroup m of gl p 1 z the method involves constructing an action of the hecke algebra on the fundamental exact sequence of smith theory arising from the action by conjugation of an element of order p in gl p 1 z on m

rao blackwellisation of sampling schemes summary this paper proposes a post simulation improvement for two common monte carlo methods the accept reject and metropolis algorithms the improvement is based on a rao blackwellisation method that integrates over the uniform random variables involved in the algorithms and thus post processes the standard estimators we show how the rao blackwellised versions of these algorithms can be implemented and through examples illustrate the improvement in variance brought by these new procedures we also compare the improved version of the metropolis algorithm with ordinary and rao blackwellised importance sampling procedures for independent and general metropolis set ups

the hilbert schmidt cohomology for the poincare group we consider cocycles for the poincart group pi satisfying gk v k v g where v is an irreducible strongly continuous representation of pi and g e b y the hilbert schmidt operators on the representation space 3 of v it is shown that i ii must be of the form g v av a with a e b x the method can be extended to analyse the cocycles of products of arbitrary irreducible representations of pi providing neither representation belongs to the little group of vanishing four momentum

bayesian model choice via markov chain monte carlo methods summary markov chain monte carlo mcmc integration methods enable the fitting of models of virtually unlimited complexity and as such have revolutionized the practice of bayesian data analysis however comparison across models may not proceed in a completely analogous fashion owing to violations of the conditions sufficient to ensure convergence of the markov chain in this paper we present a framework for bayesian model choice along with an mcmc algorithm that does not suffer from convergence difficulties our algorithm applies equally well to problems where only one model is contemplated but its proper size is not known at the outset such as problems involving integer valued parameters multiple changepoints or finite mixture distributions we illustrate our approach with two published examples

hyperspectral image unmixing using a multiresolution sticky hdp this paper is concerned with joint bayesian endmember extraction and linear unmixing of hyperspectral images using a spatial prior on the abundance vectors we propose a generative model for hyperspectral images in which the abundances are sampled from a dirichlet distribution dd mixture model whose parameters depend on a latent label process the label process is then used to enforces a spatial prior which encourages adjacent pixels to have the same label a gibbs sampling framework is used to generate samples from the posterior distributions of the abundances and the parameters of the dd mixture model the spatial prior that is used is a tree structured sticky hierarchical dirichlet process shdp and when used to determine the posterior endmember and abundance distributions results in a new unmixing algorithm called spatially constrained unmixing scu the directed markov model facilitates the use of scale recursive estimation algorithms and is therefore more computationally efficient as compared to standard markov random field mrf models furthermore the proposed scu algorithm estimates the number of regions in the image in an unsupervised fashion the effectiveness of the proposed scu algorithm is illustrated using synthetic and real data