recognition problems for special classes of polynomials in 0 1 variables this paper investigates the complexity of various recognition problems for pseudo boolean functions i e real valued functions defined on the unit hypercubebn 0 1 n when such functions are represented as multilinear polynomials in their variables determining whether a pseudo boolean function a is monotonic or b is supermodular or c is threshold or d has a unique local maximum in each face ofbn or e has a unique local maximum inbn is shown to be np hard a polynomial time recognition algorithm is presented for unimodular functions previously introduced by hansen and simeone as a class of functions whose maximization overbn is reducible to a network minimum cut problem

affirmative action algorithms affirmative action is a new variety of selection rule which employs historical information to favor the choice of elements that have not been selected in the past we categorize three implementations of this principle and discuss their application to the simplex method to bard type schemes for the linear complementarity problem and to augmenting path methods for network flow problems we present analytical and computational results and some open questions

low order polynomial bounds on the expected performance of local improvement algorithms we present a general abstract model of local improvement applicable to such diverse cases as principal pivoting methods for the linear complementarity problem and hill climbing in artificial intelligence the model accurately predicts the behavior of the algorithms and allows for a variety of probabilistic assumptions that permit degeneracy simulation indicates an approximately linear average number of iterations under a variety of probability assumptions we derive theoretical bounds of 2en logn and en2 for different distributions respectively as well as polynomial bounds for a broad class of probability distributions we conclude with a discussion of the applications of the model to lcp and linear programming

the fontaine mazur conjecture for gl _2 introduction 641 1 breuil mezard conjecture and the p adic local langlands 644 1 1 the breuil mezard conjecture 644 1 2 review of colmez s functor 647 1 3 hilbert samuel multiplicities 650 1 4 representations and pseudo representations 653 1 5 gl2 qp representations mod p 657 1 6 local patching and multiplicities 661 1 7 from pseudo representations to representations 669 2 modularity via the breuil mezard conjecture 675 2 1 quaternionic forms 675 2 2 global patching and multiplicities 677 2 3 the breuil mezard conjecture 686 addendum to ki 1 687 references 689

combinatorial structure and randomized subexponential algorithms for infinite games the complexity of solving infinite games including parity mean payoff and simple stochastic is an important open problem in verification automata and complexity theory in this paper we develop an abstract setting for studying and solving such games based on function optimization over certain discrete structures we introduce new classes of recursively local global rlg and partial recursively local global prlg functions and show that strategy evaluation functions for simple stochastic mean payoff and parity games belong to these classes in this setting we suggest randomized subexponential algorithms appropriate for rlg and prlg function optimization we show that the subexponential algorithms for combinatorial linear programming due to kalai and matousek sharir welzl can be adapted for optimizing the rlg and prlg functions

testing for garch effects a one sided approach arch models often lie at the boundary of the parameter space under conditional homoskedasticity which invalidates the usual s2 distribution of lr and wald tests although lm tests are not a ected the one sided nature of the alternative hypothesis should result in more powerful tests we propose a simple one sided version of the lm test which is closely related to the kuhn tucker multiplier test we also present critical values for lr wald and one sided lm tests the results of a monte carlo comparison suggest that one sided tests are indeed more powerful than their two sided counterparts 1998 elsevier science s a all rights reserved jel classification c22

testing for conditional heteroskedasticity with misspecified alternative hypotheses for the multiple linear regression model this paper examines the asymptotic behaviour of some tests for conditional heteroskedasticity when an alternative hypothesis is misspecified in the standard likelihood based framework a lagrange multiplier statistic based on a correctly specified alternative is ranked above one based on an overspecified alternative it is shown that this ranking does not hold for statistics that are robust to the form of conditional heterokurticity it is also shown that the ranking obtained in the standard likelihood based framework does not depend on a joint density being specified in its entirety the same ranking can be obtained when a type of information matrix equality holds

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

some distribution independent results about the asymptotic order of the average number of pivot steps of the simplex method this paper is concerned with the average number of pivot steps of the simplex method which are required to solve linear programming problems of the following kind mbox max v t x quad mbox subject to a t i x leq 1 quad mbox for i 1 ldots m mbox where a i v x in mathbb r n we investigate a certain variant of the simplex method which is particularly suited for theoretical considerations for every pair m nm n we introduce probability spaces whose random samples are the linear programming problems of the above mentioned type the vectors ai v are supposed to be distributed independently identically and symmetrically under rotations on a bounded subset of rn we deduce upper and lower bounds for the expectation values of the number of steps required in phase ii of the simplex method the evaluation of these bounds yields the following result for m and for fixed n 1 the expectation values become om1 n 1 2 there exists a distribution whose expectation values increase like m1 n 1 3 for any distribution which satisfies our conditions the expectation values tend to infinity 4 for every e 0 there are distributions whose expectation values become ome

specification testing and quasi maximum likelihood estimation abstract this paper develops robust regression based conditional moment tests for models estimated by quasi maximum likelihood using a density in the linear exponential family the tests are relatively simple to compute while being robust to distributional assumptions other than those being explicitly tested the conditional mean tests assume only that the conditional mean is correctly specified under the null hypothesis but are asymptotically equivalent to standard forms of the tests if the conditional variance is correctly specified tests for conditional variance misspecification assume only that the first two moments are correctly specified under the null hypothesis an empirical application to individual arrest data is included

multiplicites modulaires et representations de rm gl sb 2 mathbf z sb p et de rm gal overline mathbf q sb p mathbf q sb p en ell p appendice par guy henniart sur l unicite des types pour rm gl sb 2

the simplex algorithm in dimension three we investigate the worst case behavior of the simplex algorithm on linear programs with three variables that is on 3 dimensional simple polytopes among the pivot rules that we consider the random edge rule yields the best asymptotic behavior as well as the most complicated analysis all other rules turn out to be much easier to study but also produce worse results most of them show essentially worst possible behavior this includes both kalai s random facet rule which without dimension restriction is known to be subexponential and zadeh s deterministic history dependent rule for which no nonpolynomial instances in general dimensions have been found so far

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

a heteroscedasticity consistent covariance matrix estimator for time series regressions abstract this paper provides a covariance matrix estimator for the ordinary least squares coefficients of a linear time series model which is consistent even when the disturbances are heteroscedastic this estimator does not require a formal model of the heteroscedasticity one can also obtain a direct test of heteroscedasticity although monte carlo experiments show that it may have low power

modularity of 2 adic barsotti tate representations we prove a modularity lifting theorem for two dimensional 2 adic potentially barsotti tate representations this proves hypothesis h of khare wintenberger and completes the proof of serre s conjecture the main new ingredient is a classification of connected finite flat group schemes over rings of integers of finite extensions of 2

un calcul d anneaux de deformations potentiellement barsotti tate let f be an unramified extension of qp the first aim of this work is to develop a purely local method to compute the potentially barsotti tate deformations rings with tame galois type of irreducible two dimensional representations of the absolute galois group of f we then apply our method in the particular case where f has degree 2 over q p and determine this way almost all these deformations rings in this particular case we observe a close relationship between the structure of these deformations rings and the geometry of the associated kisin variety as a corollary and still assuming that f has degree 2 over q p we prove except in two very particular cases a conjecture of kisin which predicts that intrinsic galois multiplicities are all equal to 0 or 1

automorphic lifts of prescribed types we prove a variety of results on the existence of automorphic galois representations lifting a residual automorphic galois representation we prove a result on the structure of deformation rings of local galois representations and deduce from this and the method of khare and wintenberger a result on the existence of modular lifts of specified type for galois representations corresponding to hilbert modular forms of parallel weight 2 we discuss some conjectures on the weights of n dimensional mod p galois representations finally we use recent work of taylor to prove level raising and lowering results for n dimensional automorphic galois representations

potentially semi stable deformation rings let k qp be a finite extension and gk gal k k the galois group of an alge braic closure k let f be a finite field of characteristic p and vf a finite dimensional f vector space equipped with a continuous action of gkthe study of the defor mation theory of galois representations was initiated by mazur ma who showed that if vf has no non trivial endomorphisms then it admits a universal deformation ring ryw after the work of wiles wi and the conjectures of fontaine mazur fm it became clear that for arithmetic applications it was important to understand cer tain quotients of ry corresponding to deformations satisfying certain conditions for example wiles uses deformations which arise from finite flat group schemes and the corresponding quotient of ryw was constructed by ramakrishna ra suppose that l k is a finite extension and let a b be integers it seems to be a kind of folklore conjecture that there should be a quotient of ry whose points in finite extensions of w f l p correspond to deformations of vf which become semi stable over l and have hodge tate weights in the interval a b this is closely related to the final conjecture of fo 3 special cases of this when vf is 2 dimensional are conjectured in the papers of fontaine mazur fm p 191 breuil conrad diamond taylor bcdt conj 1 1 1 and breuil m zard bm 2 2 2 4 the purpose of this paper is to prove such a result

galois representations with conjectural connections to arithmetic cohomology in this paper we extend a conjecture of a ash and w sinnott relating niveau 1 galois representations to the mod p cohomology of congruence subgroups ofsln z to include galois representations of higher niveau we then present computational evidence for our conjecture in the case n 3 in the form of three dimensional galois representations which appear to correspond to cohomology eigenclasses as predicted by the conjecture our examples include galois representations with nontrivial weight and level as well as irreducible three dimensional representations that are in no obvious way related to lower dimensional representations in addition we prove that certain symmetric square representations are actually attached to cohomology eigenclasses predicted by the conjecture

lattices in the cohomology of shimura curves we prove the main conjectures of breuil j reine angew math 2012 including a generalisation from the principal series to the cuspidal case and dembele j reine angew math 2012 subject to a mild global hypothesis that we make in order to apply certain r mathbb t theorems more precisely we prove a multiplicity one result for the mod p cohomology of a shimura curve at iwahori level and we show that certain apparently globally defined lattices in the cohomology of shimura curves are determined by the corresponding local p adic galois representations we also indicate a new proof of the buzzard diamond jarvis conjecture in generic cases our main tools are the geometric breuil mezard philosophy developed in emerton and gee j inst math jussieu 2012 and a new and more functorial perspective on the taylor wiles kisin patching method along the way we determine the tamely potentially barsotti tate deformation rings of generic two dimensional mod p representations generalising a result of breuil and mezard bull soc math de france 2012 in the principal series case

some results on the glejser and koenker tests for heteroskedasticity abstract the glejser and koenker studentized lagrange multiplier tests for heteroskedasticity are considered asymptotic theory and monte carlo experiments are used to investigate the effects of nonnormality under null and alternative hypotheses and also the consequences of using an incorrect alternative a method for using test outcomes to select models of heteroskedasticity is critically examined glejser s test is not in general asymptotically valid under asymmetric disturbances koenker s test is asymptotically valid under asymmetric and other nonnormal disturbances but has estimated finite sample significance levels that are sometimes sensitive to skewness an adjusted version of koenker s statistic is discussed

a simple heuristic approach to simplex efficiency abstract consider the standard linear program minimize cx subject to ax b x 0 where a is an m n matrix the simplex algorithm solves this linear program by moving from an extreme point of the feasibility region to a better in terms of the objective function cx extreme point via the pivot operation until the optimal is reached in order to obtain a feel for the number of necessary iterations we consider a simple probabilistic markov chain model as to how the algorithm moves along the extreme points at first we suppose that if at any time the algorithm is at the j th best extreme point then after the next pivot the resulting extreme point is equally likely to be any of the j 1 best under this assumption we show that the time to get from the n th best to the best extreme point has approximately for large n a poisson distribution with mean equal to the algorithm base e of n we also consider a more general probabilistic model in which we drop the uniformity assumption and suppose that when at the j th best the next one is chosen probabilistically according to weights w i i 1 j 1

modularity of certain potentially barsotti tate galois representations where is the reduction of p these results were subject to hypotheses on the local behavior of p at x i e the restriction of p to a decomposition group at x and to irreducibility hypotheses on 1p in this paper we build on the methods of 461 451 and 121 and relax the hypotheses on local behavior in particular we treat certain adic representations which are not semistable at x but potentially semistable we do this using results of 61 generalizing a theorem of ramakrishna 321 see fontaine mazur 22 131 for a slightly different point of view the results in 61 show that certain potentially barsotti tate deformation problems are smooth allowing us to define certain universal deformations for with the necessary galoistheoretic properties to apply wiles method to carry out the proof that these deformations are indeed realized in the cohomology of modular curves i e that the universal deformation rings are hecke algebras we need to identify the corresponding cohomology groups and prove they have the modular theoretic properties needed to apply wiles method as in 151 and 121 the identification is made by matching local behavior of automorphic representations and galois representations via the local langlands correspondence together with fontaine s theory at the prime we work directly with cohomology of modular curves instead of

local models of shimura varieties and a conjecture of kottwitz we give a group theoretic definition of local models as sought after in the theory of shimura varieties these are projective schemes over the integers of a p adic local field that are expected to model the singularities of integral models of shimura varieties with parahoric level structure our local models are certain mixed characteristic degenerations of grassmannian varieties they are obtained by extending constructions of beilinson drinfeld gaitsgory and the second named author to mixed characteristics and to the case of general tamely ramified reductive groups we study the singularities of local models and hence also of the corresponding integral models of shimura varieties in particular we study the monodromy inertia action and show a commutativity property for the sheaves of nearby cycles as a result we prove a conjecture of kottwitz which asserts that the semi simple trace of frobenius on the nearby cycles gives a function which is central in the parahoric hecke algebra

potentially crystalline deformation rings and serre weight conjectures shapes and shadows we prove the weight part of serre s conjecture in generic situations for forms of u 3 which are compact at infinity and split at places dividing p as conjectured by herzig duke math j 149 1 37 116 2009 we also prove automorphy lifting theorems in dimension three the key input is an explicit description of tamely potentially crystalline deformation rings with hodge tate weights 2 1 0 for k mathbb q p unramified combined with patching techniques our results show that the geometric breuil mezard conjectures hold for these deformation rings

potential automorphy and change of weight we prove an automorphy lifting theorem for l adic representations where we impose a new condition at l which we call potentential diagonalizability this result allows for change of weight and seems to be substantially more exible than previous theorems along the same lines we derive several applications for instance we show that any irreducible totally odd essentially self dual regular weakly compatible system of l adic representations of the absolute galois group of a totally real eld is potentially automorphic and hence is pure and its l function has meromorphic continuation to the whole complex plane and satises the expected functional equation

moduli of finite flat group schemes and modularity we prove that under some mild conditions a two dimensional p adic galois representation which is residually modular and potentially barsotti tate at p is modular this provides a more conceptual way of establishing the shimura taniyama weil conjecture especially for elliptic curves which acquire good reduction over a wildly ramified extension of 3 the main ingredient is a new technique for analyzing flat deformation rings it involves resolving them by spaces which parametrize finite flat group scheme models of galois representations introduction