the image foresting transform theory algorithms and applications the image foresting transform ift is a graph based approach to the design of image processing operators based on connectivity it naturally leads to correct and efficient implementations and to a better understanding of how different operators relate to each other we give here a precise definition of the ift and a procedure to compute it a generalization of dijkstra s algorithm with a proof of correctness we also discuss implementation issues and illustrate the use of the ift in a few applications

integration of quantum many body problems by affine knizhnik zamolodchikov equations abstract an equivalence of the affine analogues of knizhnik zamolodchikov and dunkl equations is established for arbitrary root systems as a corollary an isomorphism is obtained from the solutions of the above kz equations in the induced representations of hecke algebras to the eigenfunctions for the corresponding matrix quantum calogero sutherland operators which generalizes the matsuo map

on gradient type optimization method utilizing mixed finite element approximation for optimal boundary control problem governed by bi harmonic equation in this paper a numerical method based on mixed finite element method for optimal boundary control problem governed by bi harmonic equation is presented the system of optimality equations consisting of state and costate function is derived based on the system a gradient type optimization method using a mixed finite approximation for solving the optimal boundary control is developed in our algorithm the trace of vortex function of costate equation on boundary plays a key role finally a local error analysis at every iteration for this gradient type optimization method is given

generic simplicity of the spectrum and stabilization for a plate equation in this work we prove the generic simplicity of the spectrum of the clamped plate equation in a bounded regular domain of mathbb r d that is given omega subset mathbb r d we show that there exists an arbitrarily small deformation of the domain u such that all the eigenvalues of the plate system in the deformed domain omega u are simple to prove this result we first prove a nonstandard unique continuation property for this system that also holds generically with respect to the perturbations of the domain both the proof of this generic uniqueness result and the generic simplicity of the spectrum use baire s lemma and shape differentiation finally we show an application of this unique continuation property to a result of generic stabilization for a plate system with one dissipative boundary condition

color texture segmentation based on the modal energy of deformable surfaces this paper presents a new approach for the segmentation of color textured images which is based on a novel energy function the proposed energy function which expresses the local smoothness of an image area is derived by exploiting an intermediate step of modal analysis that is utilized in order to describe and analyze the deformations of a 3 d deformable surface model the external forces that attract the 3 d deformable surface model combine the intensity of the image pixels with the spatial information of local image regions the proposed image segmentation algorithm has two steps first a color quantization scheme which is based on the node displacements of the deformable surface model is utilized in order to decrease the number of colors in the image then the proposed energy function is used as a criterion for a region growing algorithm the final segmentation of the image is derived by a region merge approach the proposed method was applied to the berkeley segmentation database the obtained results show good segmentation robustness when compared to other state of the art image segmentation algorithms

the differentiability of the drag with respect to the variations of a lipschitz domain in a navier stokes flow this paper is concerned with the computation of the drag t associated with a body traveling at uniform velocity in a fluid governed by the stationary navier stokes equations it is assumed that the fluid fills a domain of the form omega u where omega subset reels 3 is a reference domain and u is a displacement field we assume only that omega is a lipschitz domain and that u is lipschitz continuous we prove that at least when the velocity of the body is sufficiently small u mapsto t omega u is a c infty mapping in a ball centered at 0 we also compute the derivative at 0

a unification of knizhnik zamolodchikov and dunkl operators via affine hecke algebras some generalizations of the lusztig lascoux schutzenberger operators for affine hecke algebras are considered as corollaries we obtain lusztig s isomorphisms from affine hecke algebras to their degenerate versions a natural interpretation of the dunkl operators and a new class of differential difference operators generalizing dunkl s ones and the knizhnik zamolodchikov operators from the two dimensional conformal field theory

generic simplicity of the eigenvalues for a supported plate equation abstract in this work we show that the eigenvalues of the problem 2 v x u x 0 x u x u x 0 x are generically simple in the set of c 4 regular regions of r n n 2 in fact we prove that there exists a residual set of regions c 4 diffeomorphic to a given such that all the eigenvalues for a supported plate equation are simple

interactive image segmentation based on synthetic graph coordinates in this paper we propose a framework for interactive image segmentation the goal of interactive image segmentation is to classify the image pixels into foreground and background classes when some foreground and background markers are given the proposed method minimizes a min max bayesian criterion that has been successfully used on image segmentation problem and it consists of several steps in order to take into account visual information as well as the given markers without any requirement of training first we partition the image into contiguous and perceptually similar regions superpixels then we construct a weighted graph that represents the superpixels and the connections between them an efficient algorithm for graph clustering based on synthetic coordinates is used yielding an initial map of classified pixels this method reduces the problem of graph clustering to the simpler problem of point clustering instead of solving the problem on the graph data structure as most of the known algorithms from literature do finally having available the data modeling and the initial map of classified pixels we use a markov random field mrf model or a flooding algorithm to get the image segmentation by minimizing a min max bayesian criterion experimental results and comparisons with other methods from the literature are presented on lhi gulshan and zhao datasets demonstrating the high performance and accuracy of the proposed scheme

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

existence stability and smoothness of a bounded solution for nonlinear time varying thermoelastic plate equations in this paper we study the existence stability and the smoothness of a bounded solution of the following nonlinear time varying thermoelastic plate equation with homogeneous dirichlet boundary conditions utt 2u f1 t u t 0 x t ut f2 t u t 0 x u u 0 t 0 x where 0 0 is a sufficiently regular bounded domain in rn n 1 and fe1 fe2 r l2 2 l2 define by fe t u x f t u x x x are continuous and locally lipschitz functions first we prove that the linear system f1 f2 0 generates an analytic strongly continuous semigroup which decays exponentially to zero second under some additional condition we prove that the nonlinear system has a bounded solution which is exponentially stable and for a large class of functions f1 f2 this bounded solution is almost periodic finally we use the analyticity of the semigroup generated by the linear system to prove the smoothness of the bounded solution

kernel density estimation via diffusion we present a new adaptive kernel density estimator based on linear diffusion processes the proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate in addition we propose a new plug in bandwidth selection method that is free from the arbitrary normal reference rules used by existing methods we present simulation examples in which the proposed approach outperforms existing methods in terms of accuracy and reliability

some combinatorial properties of jack symmetric functions if 1 l n then write 2 n or 1 n if p is another partition then write p c j if pi 6 for all i i e if the diagram of 1 contains the diagram of p if ipl ii 1 then write p 2 1 reverse lexicographic order if either j i or the first nonvanishing difference e pi is positive for instance writing 2 1 i for ai i it 5 5 41 32 5 311 221 2111 11111 finally write p i if ipl lal and p1 pl2 pli a1 a2 li for all i macdonald m p 63 call the partial ordering the natural ordering but we will call it the dominance ordering let x x x2 be an infinite set of indeterminates as in mi we

hierarchical image segmentation based on iterative contraction and merging in this paper we propose a new framework for hierarchical image segmentation based on iterative contraction and merging in the proposed framework we treat the hierarchical image segmentation problem as a sequel of optimization problems with each optimization process being realized by a contraction and merging process to identify and merge the most similar data pairs at the current resolution at the beginning we perform pixel based contraction and merging to quickly combine image pixels into initial region elements with visually indistinguishable intra region color difference after that we iteratively perform region based contraction and merging to group adjacent regions into larger ones to progressively form a segmentation dendrogram for hierarchical segmentation comparing with the state of the art techniques the proposed algorithm can not only produce high quality segmentation results in a more efficient way but also keep a lot of boundary details in the segmentation results

crystallization of deformed virasoro algebra ding iohara miki algebra and 5d agt correspondence in this paper we consider the q 0 limit of the deformed virasoro algebra and that of the level 1 2 representation of the ding iohara miki algebra moreover 5d agt correspondence in this limit is discussed this specialization corresponds to the limit from macdonalds functions to hall littlewood functions using the theory of hall littlewood functions some problems are solved for example the simplest case of 5d agt conjectures is proven in this limit and we obtain a formula for the 4 point correlation function of a certain operator

efficient graph based image segmentation this paper addresses the problem of segmenting an image into regions we define a predicate for measuring the evidence for a boundary between two regions using a graph based representation of the image we then develop an efficient segmentation algorithm based on this predicate and show that although this algorithm makes greedy decisions it produces segmentations that satisfy global properties we apply the algorithm to image segmentation using two different kinds of local neighborhoods in constructing the graph and illustrate the results with both real and synthetic images the algorithm runs in time nearly linear in the number of graph edges and is also fast in practice an important characteristic of the method is its ability to preserve detail in low variability image regions while ignoring detail in high variability regions

generalized quotients in coxeter groups for w s a coxeter group we study sets of the form w v w e w i l wv 1 w i v for all v e v where v c w such sets w v here called generalized quotients are shown to have much of the rich combinatorial structure under bruhat order that has previously been known only for the case when v c s i e for minimal coset representatives modulo a parabolic subgroup we show that bruhat intervals in w v for general v c w are lexicographically shellable the mobius function on w v under bruhat order takes values in 1 0 1 for finite groups w generalized quotients are the same thing as lower intervals in the weak order this is however in general not true connections with the weak order are explored and it is shown that w v is always a complete meet semilattice and a convex order ideal as a subset of w under weak order descent classes di w e w il1 ws 1 w xt s e i for all s e s i c s are also analyzed using generalized quotients it is shown that each descent class as a poset under bruhat order or weak order is isomorphic to a generalized quotient under the corresponding ordering the latter half of the paper is devoted to the symmetric group and to the study of some specific examples of generalized quotients which arise in combinatorics for instance the set of standard young tableaux of a fixed shape or the set of linear extensions of a rooted forest suitably interpreted form generalized quotients we prove a factorization result for the quotients that come from rooted forests which shows that algebraically these quotients behave as a system of minimal coset representatives of a subset which is in general not a subgroup we also study the rank generating function for certain quotients in the symmetric group

ramond singular vectors and jack superpolynomials the explicit formula for the superconformal singular vectors in the neveu schwarz sector has been obtained recently via its symmetric polynomial representation as a sum of jack superpolynomials here we present the analogous but slightly more complicated closed form expression for the ramond singular vectors

affine hecke algebras and generalized standard young tableaux abstract this paper introduces calibrated representations for affine hecke algebras and classifies and constructs all finite dimensional irreducible calibrated representations the primary technique is to provide indexing sets for controlling the weight space structure of finite dimensional modules for the affine hecke algebra using these indexing sets we show that 1 irreducible calibrated representations are indexed by skew local regions 2 the dimension of an irreducible calibrated representation is the number of chambers in the local region 3 each irreducible calibrated representation is constructed explicitly by formulas which describe the action of the generators of the affine hecke algebra on a specific basis in the representation space the indexing sets for weight spaces are generalizations of standard young tableaux and the construction of the irreducible calibrated affine hecke algebra modules is a generalization of a young s seminormal construction of the irreducible representations of the symmetric group in this sense young s construction has been generalized to arbitrary lie type

jack polynomials with prescribed symmetry and hole propagator of spin calogero sutherland model we study the hole propagator of the calogero sutherland model with su 2 internal symmetry we obtain the exact expression for arbitrary non negative integer coupling parameter and prove the conjecture proposed by one of the authors our method is based on the theory of the jack polynomials with a prescribed symmetry

hyperplane arrangements interval orders and trees abstract a hyperplane arrangement is a finite set of hyperplanes in a real affine space an especially important arrangement is the braid arrangement which is the set of all hyperplanes xi xj 1 1 i j n in rn some combinatorial properties of certain deformations of the braid arrangement are surveyed in particular there are unexpected connections with the theory of interval orders and with the enumeration of trees for instance the number of labeled interval orders that can be obtained from n intervals i1 in of generic lengths is counted there is also discussed an arrangement due to n linial whose number of regions is the number of alternating or intransitive trees as defined by gelfand graev and postnikov gelfand i m graev m i and postnikov a 1995 preprint finally a refinement is given related to counting labeled trees by number of inversions of a result of shi shi j y 1986 lecture notes in mathematics no 1179 springer verlag that a certain deformation of the braid arrangement has n 1 n 1 regions

weight bases of gelfand tsetlin type for representations of classical lie algebras this paper completes a series devoted to explicit constructions of finite dimensional irreducible representations of the classical lie algebras here the case of odd orthogonal lie algebras of type b is considered two previous papers dealt with c and d types a weight basis for each representation of the lie algebra 2n 1 is constructed the basis vectors are parametrized by gelfand tsetlin type patterns explicit formulae for the matrix elements of generators of 2n 1 in this basis are given the construction is based on the representation theory of the yangians

yangian gelfand zetlin bases gl n jack polynomials and computation of dynamical correlation functions in the spin calogero sutherland model we consider the invariant calogero sutherland models with n 1 2 3 in the framework of symmetric polynomials

finite dimensional irreducible representations of twisted yangians we study quantized enveloping algebras called twisted yangians they are analogs of the yangian y gl n for the classical lie algebras of b c and d series the twisted yangians are subalgebras in y gl n and coideals with respect to the coproduct in y gl n we give a complete description of their finite dimensional irreducible representations every such representation is highest weight and we give necessary and sufficient conditions for an irreducible highest weight representation to be finite dimensional the result is analogous to drinfeld s theorem for the ordinary yangians its detailed proof for the a series is also reproduced for the simplest twisted yangians we construct an explicit realization for each finite dimensional irreducible representation in tensor products of representations of the corresponding lie algebras

generic hyperbolicity of stationary solutions for a reaction diffusion system abstract in this paper we study the generic hyperbolicity of equilibria of a reaction diffusion system with respect to nonlinear terms in the set of c 2 functions equipped with the whitney topology to accomplish this we combine baire s lemma and the usual transversality theorem

derivation of green s function of a spin calogero sutherland model by uglov s method the hole propagator of a spin 1 2 calogero sutherland model is derived using uglov s method which maps the exact eigenfunctions of the model called the yangian gelfand zetlin basis to a limit of macdonald polynomials gl2 jack polynomials to apply this mapping method to the calculation of 1 particle green s function we confirm that the sum of the field annihilation operator on a yangian gelfand zetlin basis is transformed to the field annihilation operator on gl2 jack polynomials by the mapping the resultant expression for the hole propagator for a finite size system is written in terms of renormalized momenta and spin of quasi holes and the expression in the thermodynamic limit coincides with the earlier result derived by another method we also discuss the singularity of the spectral function for a specific coupling parameter where the hole propagator of the spin calogero sutherland model becomes equivalent to the dynamical colour correlation function of an su 3 haldane shastry model

exact controllability stabilization and perturbations for distributed systems exact controllability is studied for distributed systems of hyperbolic type or for petrowsky systems like plate equations the control is a boundary control or a local distributed control exact controllability consists in trying to drive the system to rest in a given finite time the solution of the problems depends on the function spaces where the initial data are taken and also depends on the function space where the control can be chosen a systematic method named hum for hilbert uniqueness method is introduced as the terminology indicates it is based on uniqueness results classical or new and on hilbert spaces constructed in infinitely many ways by using uniqueness a number of applications are indicated having a general method for exact controllability implies having a general method for stabilization this leads to new and complicated nonlinear riccati s type pdes to be compared with direct methods when available in the last part of the paper we consider how all this behaves fo

parabolic presentations of the yangian we introduce some new presentations for the yangian associated to the lie algebra open image in new window these presentations are parametrized by tuples of positive integers summing to n at one extreme for the tuple n the presentation is the usual rtt presentation of y n at the other extreme for the tuple 1 n the presentation is closely related to drinfeld s presentation in general the presentations are useful for understanding the structure of the standard parabolic subalgebras of y n

complete integrability of relativistic calogero moser systems and elliptic function identities poincare invariant generalizations of the galilei invariant calogero moser a particle systems are studied a quantization of the classical integrals s1 sn is presented such that the operators si9 sn mutually commute as a corollary it follows that si9 9sn poisson commute these results hinge on functional equations satisfied by the weierstrass and 0 functions a generalized cauchy identity involving the function leads to an n x n matrix l whose symmetric functions are proportional to sl5 9sn

a decomposition of solomon s descent algebra abstract a descent class in the symmetric group sn is the collection of permutations with a given descent set it was shown by l solomon j algebra41 1976 255 264 that the product in the group algebra q sn of two descent classes is a linear combination of descent classes thus descent classes generate a subalgebra of q sn we refer to it here as solomon s descent algebra and denote it by n this algebra is not semisimple but it has a faithul representation in terms of upper triangular matrices the main goal of this paper is a decomposition of its multiplicative structure it develops that n acts in a natural way on the so called lie monomials this action has a purely combinatorial description and is a crucial tool in the construction of a complete set of indecomposable representations of n in particular we obtain a natural basis of irreducible orthogonal idempotents indexed by partitions of n for the quotient n n natural bases of nilpotents and idempotents for the subspaces e ne for two arbitrary partitions and are also constructed and the dimensions of these spaces are given a combinatorial interpretation in terms of the so called decreasing factorization of an arbitary word into a product of lyndon words

shifted yangians and finite w algebras we give a presentation for the finite w algebra associated to a nilpotent matrix in the general linear lie algebra over c in the special case that the nilpotent matrix consists of n jordan blocks each of the same size l the presentation is that of the yangian of level l associated to gln as was first observed by ragoucy and sorba in the general case we are lead to introduce some generalizations of the yangian which we call the shifted yangians

the yangian symmetry in the spin calogero model and its applications by using the non symmetric hermite polynomials and a technique based on the yangian gelfand zetlin bases we decompose the space of states of the calogero model with spin into irreducible yangian modules construct an orthogonal basis of eigenvectors and derive product type formulae for norms of these eigenvectors

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

agt correspondence ding iohara algebra at roots of unity and lepowsky wilson construction it was recently conjectured that the agt correspondence between the instanton counting on and the two dimensional field theories with the conformal symmetry algebra can be considered as a root of unity limit of its k theoretic analogue from this point of view the algebra and a special basis in its representation are limits of the ding iohara algebra and the macdonald polynomials respectively in this paper we confirm this conjecture for the special case r 1 we uncover the implicit symmetry in this limit we also found that the vertex operators in the special basis have factorized aflt form

factorization based texture segmentation this paper introduces a factorization based approach that efficiently segments textured images we use local spectral histograms as features and construct an m times n feature matrix using m dimensional feature vectors in an n pixel image based on the observation that each feature can be approximated by a linear combination of several representative features we factor the feature matrix into two matrices one consisting of the representative features and the other containing the weights of representative features at each pixel used for linear combination the factorization method is based on singular value decomposition and nonnegative matrix factorization the method uses local spectral histograms to discriminate region appearances in a computationally efficient way and at the same time accurately localizes region boundaries the experiments conducted on public segmentation data sets show the promise of this simple yet powerful approach

degenerate affine hecke algebras and centralizer construction for the symmetric groups in our recent papers the centralizer construction was applied to the series of classical lie algebras to produce the quantum algebras called twisted yangians here we extend this construction to the series of the symmetric groups s n we study the stable properties of the centralizers of s n m in the group algebra c s n as n with m fixed we construct a limit centralizer algebra a and describe its algebraic structure the algebra a turns out to be closely related with the degenerate affine hecke algebras we also show that the so called tame representations of s yield a class of natural a modules

yang baxter equation in long range interacting systems we consider the su p spin chains with long range interactions and the spin generalization of the calogero sutherland models we show that their properties derive from a transfer matrix obeying the yang baxter equation we obtain the expression of the conserved quantities of the dynamical models and we diagonalise them in the spin chain case we establish the connection between the degeneracies of the spectrum and the representation theory of the yangians we use a correspondence with the dynamical models to diagonalise the hamiltonian finally we extend the previous results to the case of a trigonometric r matrix

natural image segmentation based on tree equipartition bayesian flooding and region merging we propose a general purpose image segmentation framework which involves feature extraction and classification in feature space followed by flooding and merging in spatial domain region growing is based on the computed local measurements and distances from the distribution of features describing the different classes using the properties of the label dependent distances spatial coherence is ensured since the image features are described globally the distribution of the features for the different classes are obtained by block wise unsupervised clustering based on the construction of the minimum spanning tree of the blocks grid using the mallows distance and the equipartition of the resulting tree the final clustering is obtained by using the k centroids algorithm with high probability and under topological constraints connected components of the maximum likelihood classification map are used to compute a map of initially labelled pixels an efficient flooding algorithm is introduced namely priority multi class flooding algorithm pmcfa that assign pixels to labels using bayesian dissimilarity criteria a new region merging method which incorporates boundary information is introduced for obtaining the final segmentation map therefore the merging stage is based on region features and edge localization segmentation results on the berkeley benchmark data set demonstrate the effectiveness of the proposed methods

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

orthogonal polynomials of types a and b and related calogero models there are examples of calogero sutherland models associated to the weyl groups of type a and b when exchange terms are added to the hamiltonians the systems have non symmetric eigenfunctions which can be expressed as products of the ground state with members of a family of orthogonal polynomials these polynomials can be defined and studied by using the differential difference operators introduced by the author in trans am math soc 311 167 183 1989 after a description of known results particularly from the works of baker and forrester and sahi there is a study of polynomials which are invariant or alternating for parabolic subgroups of the symmetric group the detailed analysis depends on using two bases of polynomials one of which transforms monomially under group actions and the other one is orthogonal there are formulas for norms and point evaluations which are simplifications of those of sahi for any parabolic subgroup of the symmetric group there is a skew operator on polynomials which leads to evaluation at 1 1 1 of the quotient of the unique skew polynomial in a given irreducible subspace by the minimum alternating polynomial analogously to a weyl character formula the last section concerns orthogonal polynomials for the type b weyl group with an emphasis on the hermite type polynomials these can be expressed by using the generalized binomial coefficients a complete basis of eigenfunctions of yamamoto s b n spin calogero model is obtained by multiplying these polynomials by the ground state

exact calculation of the ground state single particle green s function for the 1 r2 quantum many body system at integer coupling the ground state single particle green s function describing hole propagation is calculated exactly for the 1 r2 quantum many body system at integer coupling the result is in agreement with a recent conjecture of haldane

on irreducibility of tensor products of evaluation modules for the quantum affine algebra every irreducible finite dimensional representation of the quantized enveloping algebra can be extended to the quantum affine algebra via the evaluation homomorphism we give in explicit form the necessary and sufficient conditions for irreducibility of tensor products of such evaluation modules

parameter independent clustering based on dominant sets and cluster merging abstract clustering is an important unsupervised learning approach with wide application in data mining pattern recognition and intelligent information processing however existing clustering algorithms usually involve one or more user specified parameters as input and their clustering results depend heavily on these parameters in order to solve this problem we present a parameter independent clustering algorithm based on the dominant sets algorithm and cluster merging in the first step histogram equalization transformation is applied to solve the parameter dependence problem of the dominant sets algorithm we provide the theoretic foundation of this method and discuss the implementation details the clustering result is then refined with a cluster merging method which is based on a new clustering quality evaluation criterion we use extensive experiments on several datasets to validate each step and the whole procedures of our algorithm it is shown that our parameter independent algorithm performs comparably to some existing clustering algorithms which benefit from user specified parameters

contour and texture analysis for image segmentation this paper provides an algorithm for partitioning grayscale images into disjoint regions of coherent brightness and texture natural images contain both textured and untextured regions so the cues of contour and texture differences are exploited simultaneously contours are treated in the intervening contour framework while texture is analyzed using textons each of these cues has a domain of applicability so to facilitate cue combination we introduce a gating operator based on the texturedness of the neighborhood at a pixel having obtained a local measure of how likely two nearby pixels are to belong to the same region we use the spectral graph theoretic framework of normalized cuts to find partitions of the image into regions of coherent texture and brightness experimental results on a wide range of images are shown

rtt presentation of finite algebras we construct a wide class of finite algebras as truncations of yangians these truncations correspond to algebra homomorphisms and allow us to construct the algebras as exchange algebras the r matrix being the yangian one as an application we classify all irreducible finite dimensional representations of these algebras and determine their centre

drinfeld functor and finite dimensional representations of yangian we extend the results of drinfeld on the drinfeld functor to the case l n we present the character of finite dimensional representations of the yangian y mathfrak s mathfrak l n in terms of the kazhdan lusztig polynomials as a consequence

double affine hecke algebras and macdonald s conjectures in this paper we prove the main results about the structure of double affine hecke algebras announced in c1 c2 the technique is based on the realization of these algebras in terms of demazure lusztig operators bgg d l2 ls c3 and rather standard facts from the theory of affine weyl groups in particular it completes the proof partially published in c2 of the macdonald scalar product conjecture see ml 12 6 including the famous macdonald constant term conjecture the q t case we mainly follow the opdam paper 0 where the macdonald mehta conjectures in the degenerate differential case were deduced from certain properties of the heckman opdam operators ho and the existence of the shift operators heckman s interpretation of these operators via the so called dunkl operators see he and also c5 was important to our approach we note that the ho operators are closely related to the so called quantum many body problem calogero sutherland moser olshanetsky perelomov the conformal field theory knizhnik zamolodchikov equations the harmonic analysis on symmetric spaces harish chandra helgason etc and last but not the least the classic theory of the hypergeometric functions establishing the connection between the difference counterparts of heckman opdam operators introduced in c4 and the macdonald theory ml m2 including the construction of the difference shift operators is the main thrust of this paper once the connection is established it is not very difficult to calculate the scalar squares of the macdonald polynomials and to prove the constant term conjecture from his fundamental paper m3 to simplify the exposition we discuss the reduced root systems only and impose the relation q tk for k e z to avoid infinite products in the definition of macdonald s pairing the purpose of this work is to present a concrete application of the new technique arbitrary q t can be handled in a

level 0 action of on the q deformed fock spaces on the level 1 fock space modules of the algebra we define a level 0 action u0 of the and an action of an abelian algebra of conserved hamiltonians commuting with the u0 an irreducible decomposition of the fock space with respect to the level 0 action is derived by constructing a base of the fock space in terms of the non symmetric macdonald polynomials

dynamical correlation functions of the spin calogero sutherland model the thermodynamic limit of the dynamical density and spin density two point correlation functions for the spin calogero sutherland model are derived from uglov s finite size results the resultant formula for the density two point correlation function is consistent with the previous conjecture on the basis of the minimal number of elementary excitations

bosonic and fermionic eigenstates for generalized sutherland models we construct bosonic and fermionic eigenstates for the generalized sutherland models associated with arbitrary reduced root systems respectively through w symmetrization and w anti symmetrization of heckman opdam s nonsymmetric jacobi polynomials square norms of the nonsymmetric heckman opdam polynomials are evaluated from their rodrigues formulae the w symmetrization and w anti symmetrization of the nonsymmetric polynomials enable us to evaluate square norms of bosonic and fermionic eigenstates for the generalized sutherland models

the orthogonal eigenbasis and norms of eigenvectors in the spin calogero sutherland model using a technique based on the yangian gelfand zetlin algebra and the associated yangian gelfand zetlin bases we construct an orthogonal basis of eigenvectors in the calogero sutherland model with spin and derive product type formulae for norms of these eigenvectors

composite particles and the eigenstates of calogero sutherland and ruijsenaars schneider we establish a one to one correspondence between the composite particles with n particles and the young tableaux with at most n rows we apply this correspondence to the models of calogero sutherland and ruijsenaars schneider and we obtain a momentum space representation of the composite particles in terms of creation operators attached to the young tableaux using the technique of bosonization we obtain a position space representation of the composite particles in terms of products of vertex operators in the special case where the composite particles are bosons and if we add one extra quasiparticle or quasihole we construct the ground state wave functions corresponding to the jain series p 2np 1 of the fractional quantum hall effect