invariant algebra and cuspidal representations of finite monoids abstract motivated by the theories of hecke algebras and schur algebras we consider in this paper the algebra c mgofg invariants of a finite monoidmwith unit groupg ifmis a regular balanced monoid we show that c mgis a quasi hereditary algebra in such a case we find the blocks of c mgto be the sections of the blocks of c m we go on to develop a theory of cuspidal representations for balanced monoids we then apply our results to the full transformation semigroup and the multiplicative monoid of triangular matrices over a finite field

on liouville systems at critical parameters part 1 one bubble abstract in this paper we consider bubbling solutions to the general liouville system 0 1 g u i k j 1 n a i j j k h j e u j k h j e u j k 1 0 in m i 1 n n 2 where m g is a riemann surface and a a i j n n is a constant non negative matrix and j k j as k among other things we prove the following sharp estimates 1 the location of the blowup point 2 the convergence rate of j k j j 1 n these results are of fundamental importance for constructing bubbling solutions it is interesting to compare the difference between the general liouville system and the su 3 toda system on estimates 1 and 2

complex representations of finite monoids ii highest weight categories and quivers abstract in this paper we continue our study of complex representations of finite monoids we begin by showing that the complex algebra of a finite regular monoid is a quasi hereditary algebra and we identify the standard and costandard modules we define the concept of a monoid quiver and compute it in terms of the group characters of the standard and costandard modules we use our results to determine the blocks of the complex algebra of the full transformation semigroup we show that there are only two blocks when the degree 3 we also show that when the degree 5 the complex algebra of the full transformation semigroup is not of finite representation type answering negatively a conjecture of ponizovskii

monoids on groups with bn pairs the theory of linear algebraic monoids has been developed in the last few years by l renner and the author 21 361 as a generalization of the theory of linear algebraic groups 16 40 in applications of the theory of linear algebraic groups one is naturally led to consider groups with bnpairs or tits systems 12 4 9 42 431 this class of groups includes in particular the groups of lie type so that the abstract properties of tits systems are useful in studying the conjugacy classes and representations of groups of lie type see 4 9 our interest is in monoids so let m be a monoid such that the group of units g has a bn pair in general g has very little to do with the rest of m in fact for a given g m g could be an arbitrary semigroup so we introduce three axioms which intimately connect the idempotent structure of m with the structure of g we then say that m is a monoid on g the prime example is a connected regular linear algebraic monoid with zero but there are other natural examples for instance renner 37 is developing a theory of monoids of lie type along the lines of steinberg 41 for groups another example arises from the work of smith 39 and cabanes 3 from their work one can associate with certain irreducible modular representations 4 g gl v a set of idempotents es end v then the monoid m generated by 4 g and e is a monoid on 4 g in the examples we have worked out and very likely in general in the situation of linear algebraic monoids there is a natural type map from the finite lattice of conjugacy classes of idempotents g the lattice of f classes into the power set of the dynkin diagram of g the idea of the type map is due to lex renner and is exploited by renner and the author 31 to show in particular that the system of idempotents can be constructed from the type map in the present situation of monoids on g there is again a type map i which characterizes the system of idempotents 139 0021 8693 89 3 00

hecke algebras and semisimplicity of monoid algebras abstract we begin by constructing hecke algebras for arbitrary finite regular monoids m we then show that the semisimplicity of the complex monoid algebra c m is equivalent to the semisimplicity of the associated hecke algebras and a condition on induced group characters we apply these results to finite lie type monoids m we show that the monoid algebra fm over a field f is semisimple if and only if the characteristic of f does not divide the order of the unit group g this is accomplished by developing formulas for the unities of c j j a j class of m the unity is explicitly given when g is a simply connected chevalley group and j is associated with a borel subgroup of g

representation theory of finite semigroups semigroup radicals and formal language theory in this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field generalizing results of rhodes for the field of complex numbers applications are given to obtain many new results as well as easier proofs of several results in the literature involving triangularizability of finite semigroups which semigroups have split basic semigroup algebras two sided semidirect product decompositions of finite monoids unambiguous products of rational languages products of rational languages with counter and cerny s conjecture for an important class of automata

a topological degree counting for some liouville systems of mean field type let a a ij n n be an invertible matrix and a 1 a ij n n be the inverse of a in this paper we consider the generalized liouville system n 0 1 g u i n a ij j h j e u j h j e u j 1 0 in m j 1 where 0 h j c 1 m and j and prove that under the assumptions of h 1 and h 2 see introduction the leray schauder degree of 0 1 is equal to m 1 m n n if 1 n satisfies 8 n n n i 1 i 1 i j n a ij i j 8 n 1 n n i 1 i equation 0 1 is a natural generalization of the classic liouville equation and is the euler lagrangian equation of the nonlinear function u 1 2 m 1 i j n a ij g u i g u j n n i 1 m i u i n n i 1 i log m h i e u i the liouville system 0 1 has arisen in many different research areas in mathematics and physics our counting formulas are the first result in degree theory for liouville systems

the earth mover s distance as a metric for image retrieval we investigate the properties of a metric between two distributions the earth mover s distance emd for content based image retrieval the emd is based on the minimal cost that must be paid to transform one distribution into the other in a precise sense and was first proposed for certain vision problems by peleg werman and rom for image retrieval we combine this idea with a representation scheme for distributions that is based on vector quantization this combination leads to an image comparison framework that often accounts for perceptual similarity better than other previously proposed methods the emd is based on a solution to the transportation problem from linear optimization for which efficient algorithms are available and also allows naturally for partial matching it is more robust than histogram matching techniques in that it can operate on variable length representations of the distributions that avoid quantization and other binning problems typical of histograms when used to compare distributions with the same overall mass the emd is a true metric in this paper we focus on applications to color and texture and we compare the retrieval performance of the emd with that of other distances

the representation theory of the monoid of all partial functions on a set and related monoids as ei category algebras the ordinary quiver of an algebra a is a graph that contains information about the algebra s representations we give a description of the quiver of cptn the algebra of the monoid of all partial functions on n elements our description uses an isomorphism between cptn and the algebra of the epimorphism category en whose objects are the subsets of 1 n and morphism are all total epimorphisms this is an extension of a well known isomorphism of the algebra of isn the monoid of all partial injective maps on n elements and the algebra of the groupoid of all bijections between subsets of an n element set the quiver of the category algebra is described using results of margolis steinberg and li on the quiver of ei categories we use the same technique to compute the quiver of other natural transformation monoids we also show that the algebra cptn has three blocks for n 1 and we give a natural description of the descending loewy series of cptn in the category form

adapting a classification rule to local and global shift when only unlabelled data are available abstract for evolving populations the training data and the test data need not follow the same distribution thus the performance of a prediction model will deteriorate over the course of time this requires the re estimation of the prediction model after some time however in many applications e g credit scoring new labelled data are not available for re estimation due to verification latency i e label delay thus methods which enable a prediction model to adapt to distributional changes by using only unlabelled data are highly desirable a shift adaptation method for binary classification is presented here the model is based on mixture distributions the conditional feature distributions are determined at the time where labelled data are available and the unconditional feature distribution is determined at the time where new unlabelled data are accessible these mixture distributions provide information on the old and the new positions of subpopulations a transition model then describes how the subpopulations of each class have drifted to form the new unconditional feature distribution assuming that the conditional distributions are reorganised using a minimum of energy a two step estimation procedure results first for a given class prior distribution the transfer of probability mass is estimated such that the energy required to obtain the new unconditional distribution by a local transfer of the old conditional distributions is a minimum since the optimal solution of the resulting transportation problem measures the distance between the old and the new distributions the change of the class prior distribution is found in a second step by solving the transportation problem for varying class prior distributions and selecting the value for which the objective function is a minimum using the solution of the transportation problem and the component parameters of the unconditional feature distribution the new conditional feature distribution can be determined this thus allows for a shift adaptation of the classification rule the performance of the proposed model is investigated using a large real world dataset on default rates in danish companies the results show that the shift adaptation improves classification results

scalar curvatures on sn soit m n g une variete de riemann compacte de dimension n 3 et r x une fonction lisse sur m n on etudie si r x peut etre la courbure scalaire d une metrique g qui est conforme point par point a la metrique originale g

qualitative properties of solutions to some nonlinear elliptic equations in r 2 o introduction elliptic equations in this paper we investigate properties of the solutions to the au r x e u x x r 2 for functions r x which are positive near infinity equations of this kind arise from a variety of situations such as from prescribing gaussian curvature in geometry i 2 and from combustion theory in physics 3 recently a series ofworks have been sought to understand the existence and the qualitative properties of the solutions of ni i 5 and ni cheng 4 1 considered the case where r x is nonpositive mcowen 6 1 and aviles 7 investigated the situation where r x 0 in some order as ixl in our previous paper 1 we consider a special case where r is a constant we proved that the solutions are radially symmetric and hence classified all the solutions in this paper we consider more general functions r x first we obtain the asymptotic behavior of the solution near infinity consequently we prove that all the solutions satisfy an identity which is somewhat of a generalization of the well known kazdan warner condition finally using the asymptotic behavior together with the further development of the method employed in our previous paper i 1 we show that all the solutions are radially symmetric provided r is radially symmetric and nonincreasing this part can be viewed as the completion of 1 throughout this paper we assume that the function r x is positive near infinity in 1 we study the asymptotic behavior of the solution u x of let fl 1 2n r2 r x e dx under some appropriate conditions we show that the solutions approach

character theory of monoids over an arbitrary field abstract the basic character theory of finite monoids over the complex numbers was developed in the sixties and seventies based on work of munn ponizovski mcalister rhodes and zalcstein in particular mcalister determined the space of functions spanned by the irreducible characters of a finite monoid over c and the ring of virtual characters in this paper we present the corresponding results over an arbitrary field as a consequence we obtain a quick proof of the theorem of berstel and reutenauer that the characteristic function of a regular cyclic language is a virtual character of the free monoid this is a crucial ingredient in their proof of the rationality of the zeta function of a sofic shift in symbolic dynamics

energy quantization for a singular super liouville boundary value problem in this paper we develop the blow up analysis and establish the energy quantization for solutions to super liouville type equations on riemann surfaces with conical singularities at the boundary in other problems in geometric analysis the blow up analysis usually strongly utilizes conformal invariance which yields a noether current from which strong estimates can be derived here however the conical singularities destroy conformal invariance therefore we develop another more general method that uses the vanishing of the pohozaev constant for such solutions to deduce the removability of boundary singularities

a compactness result for periodic multivortices in the electroweak theory we derive a priori uniform bounds for solutions of an elliptic system of liouville type equations first analyzed by j spruck and y yang comm math phys 144 1992 1 yielding periodic multivortices in the classical electroweak theory of glashow salam weinberg our proof is based on a concentration quantization result in the same spirit of brezis merle comm partial differential equations 16 8 9 1991 1223 and li shafrir indiana univ math j 43 4 1994 1255 for mean field equations on riemannian compact 2 manifolds

off the beaten track a new linear model for interval data abstract we propose a new linear regression model for interval valued variables the model uses quantile functions to represent the intervals thereby considering the distributions within them in this paper we study the special case where the uniform distribution is assumed in each observed interval and we analyze the extension to the symmetric triangular distribution the parameters of the model are obtained solving a constrained quadratic optimization problem that uses the mallows distance between quantile functions as in the classical case a goodness of fit measure is deduced two applications on up to date fields are presented one predicting duration of unemployment and the other allowing forecasting burned area by forest fires

the canonical compactification of a finite group of lie type let g be a finite group of lie type we construct a finite monoid m having g as the group of units m has properties analogous to the canonical compactification of a reductive group the complex representation theory of m yields harish chandra s philosophy of cuspidal representations of g the main purpose of this paper is to determine the irreducible modular representations of m we then show that all the irreducible modular representations of g come via the 1942 work of clifford from the one dimensional representations of the maximal subgroups of m this yields a semigroup approach to the modular representation theory of g via the full rank factorizations of the sandwich matrices of m we then determine the irreducible modular representations of any finite monoid of lie type

an efficient earth mover s distance algorithm for robust histogram comparison we propose emd l1 a fast and exact algorithm for computing the earth mover s distance emd between a pair of histograms the efficiency of the new algorithm enables its application to problems that were previously prohibitive due to high time complexities the proposed emd l1 significantly simplifies the original linear programming formulation of emd exploiting the l1 metric structure the number of unknown variables in emd l1 is reduced to o n from o n2 of the original emd for a histogram with n bins in addition the number of constraints is reduced by half and the objective function of the linear program is simplified formally without any approximation we prove that the emd l1 formulation is equivalent to the original emd with a l1 ground distance to perform the emd l1 computation we propose an efficient tree based algorithm tree emd tree emd exploits the fact that a basic feasible solution of the simplex algorithm based solver forms a spanning tree when we interpret emd l1 as a network flow optimization problem we empirically show that this new algorithm has an average time complexity of o n2 which significantly improves the best reported supercubic complexity of the original emd the accuracy of the proposed methods is evaluated by experiments for two computation intensive problems shape recognition and interest point matching using multidimensional histogram based local features for shape recognition emd l1 is applied to compare shape contexts on the widely tested mpeg7 shape data set as well as an articulated shape data set for interest point matching sift shape context and spin image are tested on both synthetic and real image pairs with large geometrical deformation illumination change and heavy intensity noise the results demonstrate that our emd l1 based solutions outperform previously reported state of the art features and distance measures in solving the two tasks

conjugacy classes in algebraic monoids let m be a connected linear algebraic monoid with zero and a reductive group of units g the following theorem is established theorem there exist affne subsets ml mk of m reductive groups g1 gk with antiautomorphisms surjective morphisms 0t mi gi such that 1 every element of m is conjugate to an element of some ms and 2 two elements a b in mi are conjugate in m if and only if there exists x e gi such that x0 a x si b as a consequence it is shown that m is a union of its inverse submonoids introduction the objects of study in this paper are connected linear algebraic monoids m with zero this means by definition that the underlying set of m is an irreducible affine variety and that the product map is a morphism i e a polynomial map we will further assume that the group of units g of m is reductive this means 1 3 that the unipotent radical of g is trivial then by 6 10 m is unit regular i e m e m g where e e m e e mle2 e in this paper we study the conjugacy classes of m an initial study was made by the author 8 where the general problem was reduced to nilpotent elements the approach here is quite different yielding a more complete answer to be precise we show that there exist affine subsets m1 mk of m reductive groups g1 gk with antiautomorphisms surjective morphisms si mi gi i 1 k such that 1 every element of m is conjugate to an element of some mi and 2 if a b e mi then a is conjugate to b in m if and only if there exists x e gi such that xsi a x si b as an application of this result we show that m is a union of its inverse submonoids an inverse semigroup is a semigroup s with the property that for each a e s there exists a unique a e s such that aaa a and aaa a see 2 finally in 3 we use our main results to briefly analyze the conjugacy classes of nilpotent elements 1 preliminaries throughout this paper z will denote the set of all positive integers and k an algebraically closed field let g be a connected linear algebraic group defined over k the radical r g is the maximal closed connected normal solvable subgroup of g and the unipotent radical ru g is the group of unipotent elements of r g we will assume throughout that g is a reductive group i e ru g 1 then r g c c g the center of g moreover g r g go where go g g is a semisimple group i e r go 1 also 3 theorem 27 5 go is a product of the simple closed normal subgroups of g in particular we have the following received by the editors november 3 1986 1980 mathematics subject classification 1985 revision primary 20g99 20m10 c 1987 american mathematical society 0002 9947 87 1 00 25 per page

classification of semisimple algebraic monoids let x be a semisimple algebraic monoid with unit group g associated with e is its polyhedral root system x c where x x t is the character group of the maximal torus t c g c x t is the set of roots and c x t is the character monoid of t c e zariski closure the correspondence e x c is a complete and discriminating invariant of the semisimple monoid e extending the well known classification of semisimple groups in establishing this result monoids with preassigned root data are first constructed from linear representations of g that done we then show that any other semisimple monoid must be isomorphic to one of those constructed to do this we devise an extension principle based on a monoid analogue of the big cell construction of algebraic group theory thls ultimately yields the desired conclusions consider the classification problem for semisimple algebraic monoids over the algebraically closed field k what sort of problem is this first the definition a semisimple algebraic monoid is an irreducible affine algebraic variety e defined over k together with an associative morphlsm m e x e e and a two sided unit 1 e e for m we assume further that e has a 0 the unit group g which is always linear algebraic and dense in e is reductive e g gl k dim zg 1and e is a normal variety the problem then presents us with two familiar objects let t c g be a maximal torus then z t c e zariski closure is an affine torus embedding and g c e is a reductive algebraic group torus embeddings have been introduced by demazure in 6 in his study of cremona groups and are classified numerically using rational polyhedral cones 14 on the other hand reductive groups have been studied at least in principle since the nineteenth century their classification in the modern sense being achieved largely by chevalley 4 that numerical classification uses the now familiar root systems l l chapter 31 of killing that were introduced by him 15 in his penetrating formulation of the classification e cartan s of semisimple lie algebras thus in the classification of semisimple monoids we are compelled to consider the root system x x t t of g and the polyhedral cone c x z c x t of t c z the two objects are canonically related by the weyl group action on x which leaves c stable received by the editors november 16 1984 1980 mathematics subject classification primary 14m99 secondary 20m99

mobius functions and semigroup representation theory ii character formulas and multiplicities abstract we generalize the character formulas for multiplicities of irreducible constituents from group theory to semigroup theory using rota s theory of mobius inversion the technique works for a large class of semigroups including inverse semigroups semigroups with commuting idempotents idempotent semigroups and semigroups with basic algebras using these tools we are able to give a complete description of the spectra of random walks on finite semigroups admitting a faithful representation by upper triangular matrices over the complex numbers these include the random walks on chambers of hyperplane arrangements studied by bidigare hanlon rockmore brown and diaconis applications are also given to decomposing tensor powers and exterior products of rook matrix representations of inverse semigroups generalizing and simplifying earlier results of solomon for the rook monoid

fidos a generalized fisher based feature extraction method for domain shift traditional pattern recognition techniques often assume that the data sets used for training and testing follow the same distribution however this assumption is usually not true for many real world problems as data from the same classes but different domains e g data are collected under different conditions may show different characteristics we introduce fidos a generalized fisher based method for domain shift problem that aims at learning invariant features across domains in a supervised manner different from classical fisher feature extraction fidos aims to minimize not only the within class scatter but also the difference in distributions between domains therefore the subspace constructed by fidos reduces the drift in distributions among different domains and at the same time preserves the discriminants across classes another advantage of fidos over classical fisher is that fidos extracts more features when multiple source domains are available in the training set this is essential for a good classification especially when the number of classes is small experimental results on both artificial and real data and comparisons with other methods demonstrate the efficiency of our method in classifying objects under domain shift situations

a generalized discriminant rule when training population and test population differ on their descriptive parameters summary standard discriminant analysis methods make the assumption that both the labeled sample used to estimate the discriminant rule and the non labeled sample on which this rule is applied arise from the same population in this work we consider the case where the two populations are slightly dierent in the multinormal context we establish that both populations are linked through linear mapping estimation of the non labeled sample discriminant rule is then obtained by estimating parameters of this linear relationship several models describing this relation are proposed and associated estimated parameters are given an experimental illustration is also provided in which sex of birds which dier morphometrically over their geographical range is to be determined and a comparison with the standard allocation rule is performed extension to a partially labeled sample is also discussed

on multivortices in the electroweak theory ii existence of bogomol nyi solutions in ℝ2 in this paper we study the bogomol nyi equations of the electroweak theory in the full plane we will show that for any distribution of the vortices there exists a two parameter family of gauge distinct solutions moreover we also establish some sharp decay rate estimates for these solutions

on a sharp sobolev type inequality on two dimensional compact manifolds motivated by the asymptotic analysis of double vortex condensates in the chern simons higgs theory we construct a suitable minimizing sequence for a sharp sobolev inequality a la moser for two dimensional compact manifolds as a consequence we first obtain a direct proof of the sharp character of such an inequality secondly and more interestingly we use such minimizing sequence to show that for the flat torus the corresponding extremal problem attains its infimum

the existence of non topological multivortex solutions in the relativistic self dual chern simons theory we construct a general type of multivortex solutions of the self duality equations the bogomol nyi equations of 2 1 dimensional relativistic chern simons model with the non topological boundary condition near infinity for such construction we use a perturbation argument around the explicit solutions of the liouville equation

discriminative learning under covariate shift we address classification problems for which the training instances are governed by an input distribution that is allowed to differ arbitrarily from the test distribution problems also referred to as classification under covariate shift we derive a solution that is purely discriminative neither training nor test distribution are modeled explicitly the problem of learning under covariate shift can be written as an integrated optimization problem instantiating the general optimization problem leads to a kernel logistic regression and an exponential model classifier for covariate shift the optimization problem is convex under certain conditions our findings also clarify the relationship to the known kernel mean matching procedure we report on experiments on problems of spam filtering text classification and landmine detection

generic hecke algebra for renner monoids abstract to each renner monoid r we associate a generic hecke algebra h r over z q which is a deformation of the monoid z algebra of r if m is a finite reductive monoid with borel subgroup b and associated renner monoid r then we obtain the associated iwahori hecke algebra h m b by specialising q in h r and tensoring by c over z as in the classical case of finite reductive groups

the i class structure of connected algebraic monoids abstract let s be a connected algebraic monoid and let u s denote the finite lattice of all regular i classes of s the main theorem of this paper is that u s is relatively complemented if and only if s is a semilattice of archimedean semigroups if further s has a zero then u s is relatively complemented if and only if the group of units g of s is solvable another characterization for the solvability of g is that the product of any two nilpotent elements of s is again nilpotent the width and depth of any j u s are defined also the width depth and height of s are defined these structure numbers are studied in some detail and the solvability of g is characterized in terms of them

shellability in reductive monoids the purpose of this paper is to extend to monoids the work of bjorner wachs and proctor on the shellability of the bruhat chevalley order on weyl groups let m be a reductive monoid with unit group g borel subgroup b and weyl group w we study the partially ordered set of b x b orbits with respect to zariski closure inclusion within a g x g orbit of m this is the same as studying a w x w orbit in the renner monoid r such an orbit is the retract of a universal orbit which is shown to be lexicograhically shellable in the sense of bjorner and wachs

the monoid generated by projections in an algebraic group let g be a simple algebraic group g g the set of all bore1 subgroups of g and a the set of all parabolic subgroups of g for pea let proj g g g be given by proj b pnb r p cp where r p is the unipotent radical of p tits 9 has given a purely combinatorial i e in terms of the tits building a definition of proj in this paper we are interested in the monoid m m g generated with respect to composition by proj pea let pea p g l a levi factor of p let h denote the group of automorphisms of i l induced by n l thus h is a finite extension of l l c l where c l denotes the center of l the following results are established 1 the maximal subgroup of a4 with identity element proj is isomorphic to h and moreover every maximal subgroup of a4 with identity element e 1 is isomorphic to some h 2 m is a fundamental regular monoid 3 the idempotent set e m proj p 0 proj o 1 p q e a 4 the set of principal right ideals of m is in one to one correspondence with a 5 the set a with all the bore1 subgroups identified is in one to one correspondence with the set of all principal left ideals of m 6 the principal ideals of m are in one to one correspondence with the conjugacy classes in w of w is s where w is the weyl group of g with fundamental generating set s 7 if r is then for all a em ar lies in a subgroup of m

vanishing pohozaev constant and removability of singularities conformal invariance of two dimensional variational problems is a condition known to enable a blow up analysis of solutions and to deduce the removability of singularities in this paper we identify another condition that is not only sufficient but also necessary for such a removability of singularities this is the validity of the pohozaev identity in situations where such an identity fails to hold we introduce a new quantity called the pohozaev constant which on one hand measures the extent to which the pohozaev identity fails and on the other hand provides a characterization of the singular behavior of a solution at an isolated singularity we apply this to the blow up analysis for super liouville type equations on riemann surfaces with conical singularities because in the presence of such singularities conformal invariance no longer holds and a local singularity is in general non removable unless the pohozaev constant is vanishing