quasi hereditary twisted category algebras we give a sufficient criterion for when a twisted finite category algebra over a field is quasi hereditary in terms of the partially ordered set of l classes in the morphism set of the category we show that this is a common generalisation of a long list of results in the context of ei categories regular monoids brauer algebras temperley lieb algebras partition algebras

an extended mallows model for ranked data aggregation in this article we study the rank aggregation problem which aims to find a consensus ranking by aggregating multiple ranking lists to address the problem probabilistically we formulate an elabo

cellular algebras and inverse semigroups abstract we show that under certain compatability assumptions the semigroup algebra of an inverse semigroup is cellular if the group algebras of its maximal subgroups are cellular motivating examples include the symmetric inverse semigroup also known as the rook monoid and the dual symmetric inverse semigroup

congruence lattices of finite diagram monoids abstract we give a complete description of the congruence lattices of the following finite diagram monoids the partition monoid the planar partition monoid the brauer monoid the jones monoid also known as the temperley lieb monoid the motzkin monoid and the partial brauer monoid all the congruences under discussion arise as special instances of a new construction involving an ideal i a retraction i m onto the minimal ideal a congruence on m and a normal subgroup of a maximal subgroup outside i

enumeration of idempotents in planar diagram monoids we classify and enumerate the idempotents in several planar diagram monoids namely the motzkin jones a k a temperley lieb and kauffman monoids the classification is in terms of certain vertex and edge coloured graphs associated to motzkin diagrams the enumeration is necessarily algorithmic in nature and is based on parameters associated to cycle components of these graphs we compare our algorithms to existing algorithms for enumerating idempotents in arbitrary regular semigroups and give several tables of calculated values

equational theories of semigroups with involution abstract we employ the techniques developed in an earlier paper to show that involutory semigroups arising in various contexts do not have a finite basis for their identities among these are partition semigroups endowed with their natural inverse involution including the full partition semigroup c n for n 2 the brauer semigroup b n for n 4 and the annular semigroup a n for n 4 n even or a prime power also all of these semigroups as well as the jones semigroup j n for n 4 turn out to be inherently nonfinitely based when equipped with another involution the skew one finally we show that similar techniques apply to the finite basis problem for existence varieties of locally inverse semigroups

the partition algebra and the potts model transfer matrix spectrum in high dimensions we construct generalizations pmn q of the partition algebra pn q martin p p 1996 j algebra 183 319 facilitating a representation theoretic approach to the n site transfer matrix spectrum of a high dimensional q state potts model with magnetic field and source terms and to corresponding dichromatic polynomials for each q we describe the irreducible representation theory of the sequence of algebras p q pn q pn1 q pn 1 q n 0 1 2 approaching the large n limit for each positive integer q we extend the potts model representation n of pn q to a representation of p1n q we show how these potts representations embed in the representation theory of the partition algebras these results together provide a tool with which to examine the nature of physical correlation functions for large n the irreducible content of the potts representations can be summarized by sq endpn q vq n and sq 1 endpn1 q vq n where sq is the symmetric group and vq is the space of states of a potts spin we show how the partition algebra formalism matches up the correlation functions of the potts model and the corresponding absolute spectrum degeneracies of its transfer matrix

cellularity of diagram algebras as twisted semigroup algebras abstract the temperley lieb and brauer algebras and their cyclotomic analogues as well as the partition algebra are all examples of twisted semigroup algebras we prove a general theorem about the cellularity of twisted semigroup algebras of regular semigroups which allows us to easily reproduce the cellularity of these algebras this theorem generalizes a result of east about the cellularity of semigroup algebras of inverse semigroups

ramified partition algebras for each natural number n poset t and t tuple of scalars q we introduce the ramified partition algebra q which is a physically motivated and natural generalization of the partition algebra 24 25 the partition algebra coincides with case t 1 for fixed n and t these algebras like the partition algebra have a basis independent of q we investigate their representation theory in case t 1 2 leq we show that q is quasi hereditary over field k when q 1 q 2 is invertible in k and k is such that certain finite group algebras over k are semisimple e g when k is algebraically closed characteristic zero under these conditions we determine an index set for simple modules of q and construct standard modules with this index set we show that there are unboundedly many choices of q such that q is not semisimple for sufficiently large n but that it is generically semisimple for all n we construct tensor space representations of certain non semisimple specializations of q and show how to use these to build clock model transfer matrices 24 in arbitrary physical dimensions

on groups generated by involutions of a semigroup abstract an involution on a semigroup s or any algebra with an underlying associative binary operation is a function s s that satisfies x y y x and x x for all x y s the set i s of all such involutions on s generates a subgroup c s i s of the symmetric group sym s on the set s we investigate the groups c s for certain classes of semigroups s and also consider the question of which groups are isomorphic to c s for a suitable semigroup s

the semigroup generated by the idempotents of a partition monoid we study the idempotent generated subsemigroup of the partition monoid in the finite case this subsemigroup consists of the identity and all the singular partitions in the infinite case the subsemigroup is described in terms of certain parameters that measure how far a partition is from being a permutation as one of several corollaries we deduce howie s description from 1966 of the semigroup generated by the idempotents of a full transformation semigroup

maximal subsemigroups of finite transformation and diagram monoids abstract we describe and count the maximal subsemigroups of many well known transformation monoids and diagram monoids using a new unified framework that allows the treatment of several classes of monoids simultaneously the problem of determining the maximal subsemigroups of a finite monoid of transformations has been extensively studied in the literature to our knowledge every existing result in the literature is a special case of the approach we present in particular our technique can be used to determine the maximal subsemigroups of the full spectrum of monoids of order or orientation preserving transformations and partial permutations considered by i dimitrova v h fernandes and co authors we only present details for the transformation monoids whose maximal subsemigroups were not previously known and for certain diagram monoids such as the partition brauer jones and motzkin monoids the technique we present is based on a specialised version of an algorithm for determining the maximal subsemigroups of any finite semigroup developed by the third and fourth authors and available in the semigroups package for gap an open source computer algebra system this allows us to concisely present the descriptions of the maximal subsemigroups and to clearly see their common features

significance testing for small microarray experiments summary which signicance test is carried out when the number of repeats is small in microarray experiments can dramatically inuence the results when in two sample comparisons both conditions have fewer than say ve repeats traditional test statistics require extreme results before a gene is considered statis tically signicant dierentially expressed after a multiple comparisons correction in the literature many approaches to circumvent this problem have been proposed some of these proposals use empirical bayes arguments to moderate the variance estimates for individual genes other proposals try to stabilize these variance estimate by combining groups of genes or similar experiments in this paper we compare several of these approaches both on data sets where both experimental conditions are the same and thus few statistically signicant dierentially expressed genes should be identied and on experiments where both conditions do dier this allows us to identify which approaches are most powerful without identifying many false positives we conclude that after balancing the numbers of false positives and true positives an empirical bayes approach and an approach which combines experiments perform best standard t tests are inferior and oer almost no power when the sample size is small copyright 2005 john wiley sons ltd

extracting string motif bases for quorum higher than two bases of generators of motifs consisting of strings in which some positions can be occupied by a don t care provide a useful conceptual tool for their description and a way to reduce the time and space involved in the discovery process in the last few years a few algorithms have been proposed for the extraction of a basis building in large part on combinatorial properties of strings and their autocorrelations currently the most efficient techniques for binary alphabets and quorum q 2 require time quadratic in the length of the host string the present paper explores properties of motif bases for quorum q 2 both with binary and general alphabets by also showing that important results holding for quorum q 2 cannot be extended to this more general case furthermore the extraction of motifs in which a bound is set on the maximum allowed number of don t cares is addressed and suitable algorithms are proposed whose computational complexity depends on the fixed bound

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

an investigation of two multivariate permutation methods for controlling the false discovery proportion identifying genes that are differentially expressed between classes of samples is an important objective of many microarray experiments because of the thousands of genes typically considered there is a tension between identifying as many of the truly differentially expressed genes as possible but not too many genes that are not really differentially expressed false discoveries controlling the proportion of identified genes that are false discoveries the false discovery proportion fdp is a goal of interest in this paper two multivariate permutation methods are investigated for controlling the fdp one is based on a multivariate permutation testing mpt method that probabilistically controls the number of false discoveries and the other is based on the significance analysis of microarrays sam procedure that provides an estimate of the fdp both methods account for the correlations among the genes we find the ability of the methods to control the proportion of false discoveries varies substantially depending on the implementation characteristics for example for both methods one can proceed from the most significant gene to the least significant gene until the estimated fdp is just above the targeted level top down approach or from the least significant gene to the most significant gene until the estimated fdp is just below the targeted level bottom up approach we find that the top down mpt based method probabilistically controls the fdp whereas our implementation of the top down sam based method does not bottom up mpt based or sam based methods can result in poor control of the fdp

quiver mutations and boolean reflection monoids abstract in 2010 everitt and fountain introduced the concept of reflection monoids the boolean reflection monoids form a family of reflection monoids symmetric inverse semigroups are boolean reflection monoids of type a in this paper we give a family of presentations of boolean reflection monoids and show how these presentations are compatible with quiver mutations of orientations of dynkin diagrams with frozen vertices our results recover the presentations of boolean reflection monoids given by everitt and fountain and the presentations of symmetric inverse semigroups given by popova respectively surprisingly inner by diagram automorphisms of irreducible weyl groups and boolean reflection monoids can be constructed by sequences of mutations preserving the same underlying diagrams besides we show that semigroup algebras of boolean reflection monoids are cellular algebras

irredundant tandem motifs eliminating the possible redundancy from a set of candidate motifs occurring in an input string is fundamental in many applications the existing techniques proposed to extract irredundant motifs are not suitable when the motifs to search for are structured i e they are made of two or several subwords that co occur in a text string s of length n the main effort of this work is studying and characterizing a compact class of tandem motifs that is pairs of substrings occurring in tandem within a maximum distance of d symbols in s where d is an integer constant given in input to this aim we first introduce the concept of maximality related to four specific conditions that hold only for this class of motifs then we eliminate the remaining redundancy by defining the notion of irredundancy for tandem motifs we prove that the number of non overlapping irredundant tandem motifs is o d 2n which considering d as a constant leads to a linear number of tandems in the length of the input string this is an order of magnitude less than previously developed compact indexes for tandem extraction the notions and bounds provided for tandem motifs are generalized for the case r 2 if r is the number of subwords composing the motifs finally we also provide an algorithm to extract irredundant tandem motifs

generators and relations for partition monoids and algebras abstract we investigate the manner in which the partition monoid p n and algebra p n may be presented by generators and relations making use of structural properties of p n as well as presentations for several key submonoids we obtain a number of presentations for p n including that given without a complete proof by halverson and ram in 2005 we then conclude by showing how each of these presentations gives rise to an algebra presentation for p n

quasi hereditary structure of twisted split category algebras revisited abstract let k be a field of characteristic 0 let c be a finite split category let be a 2 cocycle of c with values in the multiplicative group of k and consider the resulting twisted category algebra a k c several interesting algebras arise that way for instance the brauer algebra moreover the category of biset functors over k is equivalent to a module category over a condensed algebra eae for an idempotent e of a in 2 the authors proved that a is quasi hereditary with respect to an explicit partial order on the set of irreducible modules and standard modules were given explicitly here we improve the partial order by introducing a coarser order leading to the same results on a but which allows to pass the quasi heredity result to the condensed algebra eae describing biset functors thereby giving a different proof of a quasi heredity result of webb see 21 the new partial order has not been considered before even in the special cases and we evaluate it explicitly for the case of biset functors and the brauer algebra it also puts further restrictions on the possible composition factors of standard modules

motif patterns in 2d motif patterns consisting of sequences of intermixed solid and don t care characters have been introduced and studied in connection with pattern discovery problems of computational biology and other domains in order to alleviate the exponential growth of such motifs notions of maximal saturation and irredundancy have been formulated whereby more or less compact subsets of the set of all motifs can be extracted that are capable of expressing all others by suitable combinations in this paper we introduce the notion of maximal irredundant motifs in a two dimensional array and develop initial properties and a combinatorial argument that poses a linear bound on the total number of such motifs the remainder of the paper presents approaches to the discovery of irredundant motifs both by offline and incremental algorithms

a tower construction for the radical in brauer s centralizer algebras abstract in this paper we study the structure of the brauer centralizer algebras in the case that the multiplication constant x is a rational integer several authors have studied the structure of these algebras for generic values of x in particular hans wenzl showed that the brauer algebras can be obtained from jones basic construction and he used that fact to prove that the brauer algebras are semisimple when x is not a rational integer the tower construction is a method to study towers of semisimple algebras hence it does not apply in our case where the algebras in the tower eventually have radicals our first step in this paper is to modify the tower construction so that it does a simultaneous tower construction of the radicals and the semisimple quotients of a tower of algebras the rest of the paper is devoted to describing these constructions explicitly in the brauer algebra case one surprising corollary of this method is a connection between two seemingly distinct criteria for the simplicity of certain subrings of the brauer algebras it is possible to identify explicitly certain subrings of the brauer algebras which are the matrix rings corresponding to irreducible representations in the semisimple case in previous work these authors gave a combinatorial condition for simplicity of these individual matrix rings when x is a rational integer the tower construction gives a second algebraic condition for simplicity it is difficult to see why these two conditions are equivalent however the methods used in this paper make that clear

a version of alperinʼs weight conjecture for finite category algebras let p be a prime and k an algebraically closed field of characteristic p we construct a functor c oc on the category of finite categories with the property that if g c is a finite group then oc is the orbit category of p subgroups of g this leads to an extension of alperin s weight conjecture to any finite category c stating that the number of isomorphism classes of simple kc modules should be equal to that of the weight algebra w koc of oc we show that the versions of alperin s weight conjecture for finite groups and for finite categories are in fact equivalent 2013 elsevier inc

on the radical of brauer algebras the radical of the brauer algebra mathcal b f x is known to be non trivial when the parameter x is an integer subject to certain conditions with respect to f in these cases we display a wide family of elements in the radical which are explicitly described by means of the diagrams of the usual basis of mathcal b f x the proof is by direct approach for x 0 and via classical invariant theory in the other cases exploiting then the well known representation of brauer algebras as centralizer algebras of orthogonal or symplectic groups acting on tensor powers of their standard representation this also gives a great part of the radical of the generic indecomposable mathcal b f x modules we conjecture that this part is indeed the whole radical in the case of modules and it is the whole part in a suitable step of the standard filtration in the case of the algebra as an application we find some more precise results for the module of pointed chord diagrams and for the temperley lieb algebra realised inside mathcal b f 1 acting on it ahi quanto a dir che sia e cosa dura lo radical dell algebra di brauer pur se l pensier gia muove a congettura n barbecue scholia

a characteristic free approach to brauer algebras brauer algebras arise in representation theory of orthogonal or symplectic groups these algebras are shown to be iterated inflations of group algebras of symmetric groups in particular they are cellular as had been shown before by graham and lehrer this gives some information about block decomposition of brauer algebras

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

brauer algebras and centralizer algebras for so 2n c abstract in 1937 richard brauer identified the centralizer algebra of transformations commuting with the action of the complex special orthogonal groups so 2 n corresponding to the centralizer algebra e k 2 n end so 2 n v k for v c 2 n is a set of diagrams to each diagram d brauer associated a linear transformation d in e k 2 n and showed that e k 2 n is spanned by the transformations d in this paper we first define a product on d k 2 n the c linear span of the diagrams under this product d k 2 n becomes an algebra and extends to an algebra epimorphism since d k 2 n is not associative we denote by d k 2n its largest associative quotient we then show that when k 2 n the semisimple quotient of d k 2n is equal to e k 2 n next we prove some facts about the representation theory of e k 2 n we compute the dimensions of the irreducible e k 2 n modules and give some branching rules

motzkin monoids and partial brauer monoids we study the partial brauer monoid and its planar submonoid the motzkin monoid we conduct a thorough investigation of the structure of both monoids providing information on normal forms green s relations regularity ideals idempotent generation minimal idempotent generating sets and so on we obtain necessary and sufficient conditions under which the ideals of these monoids are idempotent generated we find formulae for the rank smallest size of a generating set of each ideal and for the idempotent rank smallest size of an idempotent generating set of the idempotent generated subsemigroup of each ideal in particular when an ideal is idempotent generated the rank and idempotent rank are equal along the way we obtain a number of results of independent interest and we demonstrate the utility of the semigroup theoretic approach by applying our results to obtain new proofs of some important representation theoretic results concerning the corresponding diagram algebras the partial or rook brauer algebra and motzkin algebra