exact solution of a 1d asymmetric exclusion model using a matrix formulation several recent works have shown that the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions can be solved exactly in the case of open boundaries here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices with this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules they obtain several explicit forms for these non commuting matrices which are in the general case infinite dimensional their approach allows exact expressions to be derived for the current and density profiles finally they discuss briefly two possible generalizations of their results the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles

empirical bayes confidence intervals for selected parameters in high dimensional data modern statistical problems often involve a large number of populations and hence a large number of parameters that characterize these populations it is common for scientists to use data to select the most significant populations such as those with the largest t statistics the scientific interest often lies in studying and making inferences regarding these parameters called the selected parameters corresponding to the selected populations the current statistical practices either apply a traditional procedure assuming there were no selection a practice that is not valid or they use the bonferroni type procedure that is valid but very conservative and often noninformative in this article we propose valid and sharp confidence intervals that allow scientists to select parameters and to make inferences for the selected parameters based on the same data this type of confidence interval allows the users to zero in on the most interesting selected parameters without collecting more data the validity of

empirical bayes false coverage rate controlling confidence intervals summary benjamini and yekutieli suggested that it is important to account for multiplicity correction for confidence intervals when only some of the selected intervals are reported they introduced the concept of the false coverage rate fcr for confidence intervals which is parallel to the concept of the false discovery rate in the multiple hypothesis testing problem and they developed confidence intervals for selected parameters which control the fcr their approach requires the fcr to be controlled in the frequentist s sense i e controlled for all the possible unknown parameters in modern applications the number of parameters could be large as large as tens of thousands or even more as in microarray experiments we propose a less conservative criterion the bayes fcr and study confidence intervals controlling it for a class of distributions the bayes fcr refers to the average fcr with respect to a distribution of parameters under such a criterion we propose some confidence intervals which by some analytic and numerical calculations are demonstrated to have the bayes fcr controlled at level q for a class of prior distributions including mixtures of normal distributions and zero where the mixing probability is unknown the confidence intervals are shrinkage type procedures which are more efficient for the is that have a sparsity structure which is a common feature of microarray data more importantly the centre of the proposed shrinkage intervals reduces much of the bias due to selection consequently the proposed empirical bayes intervals are always shorter in average length than the intervals of benjamini and yekutieli and can be only 50 or 60 as long in some cases we apply these procedures to the data of choe and colleagues and obtain similar results

phase transitions in an exactly soluble one dimensional exclusion process we consider an exclusion process with particles injected with rate at the origin and removed with rate at the right boundary of a one dimensional chain of sites the particles are allowed to hop onto unoccupied sites to the right only for the special case of 1 the model was solved previously by derridaet al here we extend the solution to general the phase diagram obtained from our exact solution differs from the one predicted by the mean field approximation

tweedie s formula and selection bias we suppose that the statistician observes some large number of estimates zi each with its own unobserved expectation parameter i the largest few of the zi s are likely to substantially overestimate their corresponding i s this being an example of selection bias or regression to the mean tweedie s formula first reported by robbins in 1956 offers a simple empirical bayes approach for correcting selection bias this article investigates its merits and limitations in addition to the methodology tweedie s formula raises more general questions concerning empirical bayes theory discussed here as relevance and empirical bayes information there is a close connection between applications of the formula and james stein estimation

a diagrammatic approach to hecke algebras of the reflection equation hecke algebra deformations of the wreath product cd sn arise in solutions to the yang baxter equations with boundary the reflection equation we use a simple diagrammatic approach to construct bases for these algebras we hence introduce quotient algebras suitable for constructing physical solutions to the reflection equation with a well defined thermodynamic large n limit for all d and n we determine the generic representation theory of these algebras developing a formalism suitable for the analysis of corresponding q spin chain hamiltonian and transfer matrix spectra

on decomposition matrices for graded algebras abstract we study the relations between the decomposition matrix of a module over a graded algebra and the decomposition matrix of its restriction to the grading subalgebra we show that under appropriate hypotheses if one of the decomposition matrices is stable unitriangular then so is the other a particular case is when one of them is square unitriangular then both are using these results we describe the decomposition matrices of the hecke algebras of the complex reflection groups g de e n with respect to the ones of the ariki koike algebras or the decomposition matrices of q schur algebras of type dn with respect to the ones of q schur algebras of type bn

isomorphisms between simple modules of degenerate cyclotomic hecke algebras abstract we give explicit isomorphisms between simple modules of degenerate cyclotomic hecke algebras defined via various cellular bases a special case gives a generalized mullineux involution in the degenerate case

blocks of cyclotomic hecke algebras abstract this paper classifies the blocks of the cyclotomic hecke algebras of type g r 1 n over an arbitrary field rather than working with the hecke algebras directly we work instead with the cyclotomic schur algebras the advantage of these algebras is that the cyclotomic jantzen sum formula gives an easy combinatorial characterization of the blocks of the cyclotomic schur algebras we obtain an explicit description of the blocks by analyzing the combinatorics of jantzen equivalence we remark that a proof of the classification of the blocks of the cyclotomic hecke algebras was announced in 1999 unfortunately cox has discovered that this previous proof is incomplete

simultaneous confidence regions for multivariate bioequivalence demonstrating bioequivalence of several pharmacokinetic pk parameters such as auc and cmax that are calculated from the same biological sample measurements is in fact a multivariate problem even though this is neglected by most practitioners and regulatory bodies who typically settle for separate univariate analyses we believe however that a truly multivariate evaluation of all pk measures simultaneously is clearly more adequate in this paper we review methods to construct joint confidence regions around multivariate normal means and investigate their usefulness in simultaneous bioequivalence problems via simulation some of them work well for idealised scenarios but break down when faced with real data challenges such as unknown variance and correlation among the pk parameters we study the shapes of the confidence regions resulting from different methods discuss how marginal simultaneous confidence intervals for the individual pk measures can be derived and illustrate the application to data from a trial on ticlopidine hydrochloride an r package is available

inference for multivariate normal hierarchical models this paper provides a new method and algorithm for making inferences about the parameters of a two level multivariate normal hierarchical model one has observed j p dimensional vector outcomes distributed at level 1 as multivariate normal with unknown mean vectors and with known covariance matrices at level 2 the unknown mean vectors also have normal distributions with common unknown covariance matrix a and with means depending on known covariates and on unknown regression coefficients the algorithm samples independently from the marginal posterior distribution of a by using rejection procedures functions such as posterior means and covariances of the level 1 mean vectors and of the level 2 regression coefficient are estimated by averaging over posterior values calculated conditionally on each value of a drawn this estimation accounts for the uncertainty in a unlike standard restricted maximum likelihood empirical bayes procedures it is based on independent draws from the exact posterior distributions unlike gibbs sampling the procedure is demonstrated for profiling hospitals based on patients responses concerning p 2 types of problems non surgical and surgical the frequency operating characteristics of the rule corresponding to a particular vague multivariate prior distribution are shown via simulation to achieve their nominal values in that setting

fixed points and boundary layers in asymmetric simple exclusion processes in this paper we show how a fixed point based boundary layer analysis can be used to understand phases and phase transitions in asymmetric simple exclusion processes aseps with open boundaries in order to illustrate this method we choose a two species asep which has interesting phase transitions not seen in the one species case we also apply this method to the single species problem where the analysis is simple but nevertheless quite insightful

adjusted bayesian inference for selected parameters summary we address the problem of providing inference from a bayesian perspective for parameters selected after viewing the data we present a bayesian framework for providing inference for selected parameters based on the observation that providing bayesian inference for selected parameters is a truncated data problem we show that if the prior for the parameter is non informative or if the parameter is a fixed unknown constant then it is necessary to adjust the bayesian inference for selection our second contribution is the introduction of bayesian false discovery rate controlling methodology which generalizes existing bayesian false discovery rate methods that are only defined in the two group mixture model we illustrate our results by applying them to simulated data and data from a microarray experiment

schur weyl reciprocity between quantum groups and hecke algebras of type g p p n abstract let u q gl m p be the quantized universal enveloping algebra of gl m p let be the automorphism of u q gl m p which is defined on generators by e i e i m f i f i m k j k j m for any i z p m z 0 m p 1 m and any j z p m z let h p p n be the hecke algebra of type g p p n with parameters q e where e is a primitive pth root of unity in this paper we establish a schur weyl reciprocity between h p p n and a twisted tensor product of u q gl m p and the group algebra for a cyclic group of order p by using the results in j hu j algebra 274 2004 446 490

hecke algebras of classical type and their representation type the purpose of this article is to determine the representation type for all of the hecke algebras of classical type to do this we combine methods from our previous work which is used to obtain information on their gabriel quivers and recent advances in the theory of finite dimensional algebras the principal computation is for hecke algebras of type b with two parameters then we show that the representation type of hecke algebras is governed by their poincare polynomials

kleshchev multipartitions and extended young diagrams abstract we give a new simple characterization of the set of kleshchev multipartitions and more generally of the set of uglov multipartitions these combinatorial objects play an important role in various areas of representation theory of quantum groups hecke algebras or finite reductive groups as a consequence we obtain a proof of a generalization of a conjecture by dipper james and murphy and a generalization of the llt algorithm for arbitrary level

on the action of ariki koike algebras on tensor space the action of the ariki koike algebra on tensor space is used to show an isomorphism theorem between the ariki koike algebra and a direct sum of matrix rings over tensorproducts of smaller ariki koike algebras as an application we get schur weyl duality for the action of the ariki koike algebra and the levi subalgebra of the q schur algebra when separation conditions holds mit hilfe der operation der ariki koike algebra auf dem tensorraum wird ein isomorphismus zwischen der ariki koike algebra und einer direkten summe von matrizenringen uber tensorprodukten kleinerer ariki koike algebren gezeigt als anwendung ergibt sich das die ariki koike algebra und die leviunteralgebra der q schur algebra schur weyl dualitat erfullen falls die separationsbedingung erfullt ist

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

modular representations of hecke algebras of type g p p n hecke algebras for the complex reflection groups g r p n where p 1 and p r were introduced in the work of ariki j algebra 177 1995 164 185 broue and malle asterisque 212 1993 119 189 in this paper we consider modular representation theory for these algebras in the case where r p we assume that the field k contains a primitive pth root of unity e our method is to study the restrictions of specht modules s for hecke algebras hp n of type g p 1 n with parameters q 1 e ep 1 suppose that f q e 0 in k see 4 7 for definition of f q e for any multipartition 1 p of n we prove that s hp p n s k hp p n for any 1 k p 1 where k k 1 k 2 p 1 2 k and if k is the smallest positive integer such that k hence k p we explicitly decompose s hp p n into a direct sum of p k smaller hp p n submodules with the same dimensions as a result when f q e 0 in k we show that hp p n is split over k and get a complete classification of all the absolutely irreducible hp p n modules this generalizes earlier work of c pallikaros j algebra 169 1994 20 48 and j hu manuscripta math 108 2002 409 430 on hecke algebras of type dn which are included as a special case of our main results

representations of ariki koike algebras and grobner shirshov bases in this paper we investigate the structure of ariki koike algebras and their specht modules using grobner shirshov basis theory and combinatorics of young tableaux for a multipartition lambda we find a presentation of the specht module s lambda given by generators and relations and determine its grobner shirshov pair as a consequence we obtain a linear basis of s lambda consisting of standard monomials with respect to the grobner shirshov pair we show that this monomial basis can be canonically identified with the set of cozy tableaux of shape lambda

the number of simple modules for the hecke algebras of type g r p n with an appendix by xiaoyi cui abstract we derive a parameterization of simple modules for the cyclotomic hecke algebras of type g r p n with p 1 and n 3 over fields of any characteristic coprime to p we give explicit formulas for the number of simple modules over these cyclotomic hecke algebras

on the decomposition numbers of the hecke algebra of type dn when n is even abstract let n 4 be an even integer let k be a field with char k 2 and q an invertible element in k such that i 1 n 1 1 q i 0 in this paper we study the decomposition numbers over k of the iwahori hecke algebra h q d n of type d n we obtain some equalities which relate its decomposition numbers with certain schur elements and the decomposition numbers of various iwahori hecke algebras of type a with the same parameter q when char k 0 this completely determine all of its decomposition numbers the main tools we used are the morita equivalence theorem established in j hu a morita equivalence theorem for hecke algebra h q d n when n is even manuscripta math 108 2002 409 430 and certain twining character formulae of weyl modules over a tensor product of two q schur algebras

multishocks in driven diffusive processes insights from fixed point analysis of the boundary layers boundary induced phase transitions in a driven diffusive process can be studied through a phase plane analysis of the boundary layer equations in this paper we generalize this approach further to show how various shapes including multishocks and downward shocks in the bulk particle density profile can be understood by studying the dependence of the fixed points of the boundary layer equation on an appropriate parameter this is done for a particular driven interacting particle system as a prototypical example the present analysis shows the special role of a specific bifurcation of the fixed points in giving rise to different kinds of shocks

q tensor space and q weyl modules we obtain the irreducible representations of the q schur algebra motivated by the fact that these representations give all the irreducible representations of gln q in the nondescribing characteristic the irreducible polynomial representations of the general linear groups in the describing characteristic are a special case of this construction the theory of polynomial representations of general linear groups is equivalent to the representation theory of schur algebras see green s book 5 and the bibliography therein in 4 we defined q analogues of schur algebras when q 1 these are the usual schur algebras and when q is a prime power representations of q schur algebras give a substantial part of the representation theory of finite general linear groups in the nondescribing characteristic case including all irreducible representations of these groups and important information about decomposition numbers it is natural to ask what features of the classical schur algebras have qanalogues in this paper we define q analogues of tensor space of weyl modules and of weight spaces thereby generalizing the main reslllts which appear in green s book 5 for example we classify the irreducible modules for qschur algebras we determine bases for q weyl modules compatible with weight spaces and we give results on composition multiplicities of the irreducible modules in q weyl modules the proofs are largely self contained so by specializing q to 1 we recover the corresponding results in 5 this paper therefore is relevant to the representation theory of symmetric groups and to the representation theory of general linear groups in the describing and in the nondescribing characteristics 1 the q schur algebra let r be a natural number let r be an integral domain and let q be a unit in r we denote the symmetric group on r letters by er the hecke algebra z is the r free r algebra with basis twlw e er where the multiplication is determined by the following rule if a i i 1 is a basic transposition in received by the editors august 15 1989 1980 mathematics subject classification 198 5 revision primary 1 6a64 1 6a6 5 secondary 20c30 this research was supported in part by nsf grant no dms 8802290 the authors gratefully acknowledge support received from nato grant no 0222 87 r 1991 american mathematical society 0002 9947 91 1 00 25 per page

on the semisimplicity of the cyclotomic brauer algebras ii abstract in this paper we give a necessary and sufficient condition for the semisimplicity of cyclotomic brauer algebras b m n of types g m 1 n with m 2 this generalizes h rui a criterion on the semisimple brauer algebras j combin theory ser a 111 2005 78 88 1 2 1 3 and h rui m si a criterion on the semisimple brauer algebras ii j combin theory ser a 113 2006 1199 1203 2 5 on brauer algebras

the jantzen sum formula for cyclotomic schur algebras the cyclotomic q schur algebra was introduced by dipper james and mathas in order to provide a new tool for studying the ariki koike algebra we here prove an analogue of jantzen s sum formula for the cyclotomic q schur algebra among the applications is a criterion for certain specht modules of the ariki koike algebras to be irreducible

schur weyl duality for infinitesimal q schur algebras sq 2 r 1 abstract using the result of s r doty d k nakano k m peters polynomial representations of frobenius kernels of gl 2 in contemp math vol 194 1996 pp 57 67 s konig c xi when is a cellular algebra quasi hereditary math ann 315 1999 281 293 we prove that a non semisimple infinitesimal schur algebra s 2 r 1 is not cellular furthermore we determine the structure of the endomorphism ring of tensor space as a module for the infinitesimal schur algebra s 2 r 1 up to morita equivalence both results generalize to the quantum case

parametric empirical bayes inference theory and applications abstract this article reviews the state of multiparameter shrinkage estimators with emphasis on the empirical bayes viewpoint particularly in the case of parametric prior distributions some successful applications of major importance are considered recent results concerning estimates of error and confidence intervals are described and illustrated with data

cellular structures on hecke algebras of type b abstract the aim of this paper is to gather and try to unify several approaches for the modular representation theory of hecke algebras of type b we attempt to explain the connections between geck s cellular structures coming from kazhdan lusztig theory with unequal parameters and ariki s theorem on the canonical basis of the fock spaces

an algorithm for the computation of the decomposition matrices for ariki koike algebras abstract we give a purely combinatorial algorithm for the computation of the decomposition matrices for ariki koike algebras when the parameters are powers of the same root of unity

false discovery rate adjusted multiple confidence intervals for selected parameters often in applied research confidence intervals cis are constructed or reported only for parameters selected after viewing the data we show that such selected intervals fail to provide the assumed coverage probability by generalizing the false discovery rate fdr approach from multiple testing to selected multiple cis we suggest the false coverage statement rate fcr as a measure of interval coverage following selection a general procedure is then introduced offering fcr control at level q under any selection rule the procedure constructs a marginal ci for each selected parameter but instead of the confidence level 1 q being used marginally q is divided by the number of parameters considered and multiplied by the number selected if we further use the fdr controlling testing procedure of benjamini and hochberg for selecting the parameters the newly suggested procedure offers cis that are dual to the testing procedure and are shown to be optimal in the independent case under the positive re

tilting modules for cyclotomic schur algebras this paper investigates the tilting modules of the cycloto mic q schur alge bras the young modules of the ariki koike algebras and the interconnections between them the main tools used to understand the tilting modules are contragredient duality and the specht filtrations and dual specht filtrations of cert ain permutation modules sur prisingly weyl filtrations which are in general more power ful than specht filtrations play only a secondary role

on the number of constituents of induced modules of ariki koike algebras abstract we examine the crystal graph of the sl e module arising from an sl e categorification to study the defining endo functors of the categorification this yields lower bounds on the number of irreducible constituents of certain objects we use ariki s categorification result on ariki koike algebras to obtain a new lower bound on the number of constituents of their parabolically induced modules in particular this will imply reducibility of every induced module

combinatorics of representations of u_q widehat mathfrak s mathfrak l n atq 0 theq 0 combinatorics for u q widehat mathfrak s mathfrak l n is studied in connection with solvable lattice models crystal bases of highest weight representations of u q widehat mathfrak s mathfrak l n are labelled by paths which were introduced as labels of corner transfer matrix eigenvectors atq 0 it is shown that the crystal graphs for finite tensor products ofl th symmetric tensor representations of u q widehat mathfrak s mathfrak l n approximate the crystal graphs of levell representations of u q widehat mathfrak s mathfrak l n the identification is made between restricted paths for the rsos models and highest weight vectors in the crystal graphs of tensor modules for u q widehat mathfrak s mathfrak l n

on the classification of finite dimensional irreducible modules for affine bmw algebras in this paper we classify the finite dimensional irreducible modules for affine bmw algebra over an algebraically closed field with arbitrary characteristic

morita equivalences of ariki koike algebras we prove that every ariki koike algebra is morita equivalent to a direct sum of tensor products of smaller ariki koike algebras which have q connected parameter sets a similar result is proved for the cyclotomic q schur algebras combining our results with work of ariki and uglov the decomposition numbers for the ariki koike algebras defined over fields of characteristic zero are now known in principle

cyclotomic double affine hecke algebras and affine parabolic category o using the orbifold kz connection we construct a functor from an affine parabolic category o of type a to the category o of a cyclotomic rational double affine hecke algebra h then we give several results concerning this functor

the degenerate analogue of ariki s categorification theorem we explain how to deduce the degenerate analogue of ariki s categorification theorem over the ground field mathbb c as an application of schur weyl duality for higher levels and the kazhdan lusztig conjecture in finite type a we also discuss some supplementary topics including young modules tensoring with sign tilting modules and ringel duality

canonical basic sets in type bn more than 10 years ago dipper james and murphy developed the theory of specht modules for hecke algebras of type bn more recently using lusztig s a function geck and rouquier showed how to obtain parametrizations of the irreducible representations of hecke algebras of any finite type in terms of so called canonical basic sets for certain values of the parameters in type bn combinatorial descriptions of these basic sets were found by jacon based on work of ariki and foda leclerc okado thibon welsh here we consider the canonical basic sets for all the remaining choices of the parameters

duality and phase diagram of one dimensional transport the idea of duality in one dimensional nonequilibrium transport is introduced by generalizing the observations by mukherji and mishra a general approach is developed for the classification and characterization of the steady state phase diagrams which are shown to be determined by the nature of the zeros of a set of coarse grained functions that encode the microscopic dynamics a new class of nonequilibrium multicritical points has been identified

sharp simultaneous confidence intervals for the means of selected populations with application to microarray data analysis simultaneous inference for a large number n of parameters is a challenge in some situations such as microarray experiments researchers are only interested in making inference for the k parameters corresponding to the k most extreme estimates hence it seems important to construct simultaneous confidence intervals for these k parameters the naive simultaneous confidence intervals for the k means applied directly without taking into account the selection have low coverage probabilities we take an empirical bayes approach or an approach based on the random effect model to construct simultaneous confidence intervals with good coverage probabilities for n 10 000 and k 100 typical for microarray data our confidence intervals could be 77 shorter than the naive k dimensional simultaneous intervals

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

empirical bayes confidence intervals shrinking both means and variances summary we construct empirical bayes intervals for a large number p of means the existing intervals in the literature assume that variances are either equal or unequal but known when the variances are unequal and unknown the suggestion is typically to replace them by unbiased estimators however when p is large there would be advantage in borrowing strength from each other we derive double shrinkage intervals for means on the basis of our empirical bayes estimators that shrink both the means and the variances analytical and simulation studies and application to a real data set show that compared with the t intervals our intervals have higher coverage probabilities while yielding shorter lengths on average the double shrinkage intervals are on average shorter than the intervals from shrinking the means alone and are always no longer than the intervals from shrinking the variances alone also the intervals are explicitly defined and can be computed immediately

constructing confidence intervals for selected parameters in large scale problems it is common practice to select important parameters by a procedure such as the benjamini and hochberg procedure and construct confidence intervals cis for further investigation while the false coverage statement rate fcr for the cis is controlled at a desired level although the well known by cis control the fcr they are uniformly inflated in this paper we propose two methods to construct shorter selective cis the first method produces shorter cis by allowing a reduced number of selective cis the second method produces shorter cis by allowing a prefixed proportion of cis containing the values of uninteresting parameters we theoretically prove that the proposed cis are uniformly shorter than by cis and control the fcr asymptotically for independent data numerical results confirm our theoretical results and show that the proposed cis still work for correlated data we illustrate the advantage of the proposed procedures by analyzing the microarray data from a hiv study

categorifications and cyclotomic rational double affine hecke algebras varagnolo and vasserot conjectured an equivalence between the category mathcal o for crdaha s and a subcategory of an affine parabolic category o of type a we prove this conjecture as applications we prove a conjecture of rouquier on the dimension of simple modules of crdaha s and a conjecture of chuang miyachi on the koszul duality for the category mathcal o of crdaha s