minimum cross entropy thresholding abstract the threshold selection problem is solved by minimizing the cross entropy between the image and its segmented version the cross entropy is formulated in a pixel to pixel basis between the two images and a computationally attractive algorithm employing the histogram is developed without making a priori assumptions about the population distribution this method provides an unbiased estimate of a binarized version of the image in an information theoretic sense

the asymptotics of a bessel kernel determinant which arises in random matrix theory in random matrix theory the local correlations of the laguerre and jacobi unitary ensemble in the hard edge scaling limit can be described in terms of the bessel kernel b x y xyj x yj y j y xj x x2 y2 x y 0 1 in particular the so called hard edge gap probabilities p r can be expressed as the fredholm determinants of the corresponding integral operator b restricted to the finite interval 0 r using operator theoretic methods we are going to compute their asymptotics as r i e we show that p r det i b l2 0 r exp r24 r 22logr g 1 2 2 where g stands for the barnes g function in fact this asymptotic formula will be proved for all complex parameters satisfying re 1

exit problems associated with affine reflection groups we obtain a formula for the distribution of the first exit time of brownian motion from the alcove of an affine weyl group in most cases the formula is expressed compactly in terms of pfaffians expected exit times are derived in the type widetilde a case the results extend to other markov processes we also give formulas for the real eigenfunctions of the dirichlet and neumann laplacians on alcoves observing that the hot spots conjecture of j rauch is true for alcoves

gaudi surfaces and curvature based functional variations in view of the meaning of ruled surfaces in aesthetics statics scale and manufacturing technologies we point out the possibility of a mathematical analysis in the case of infinitesimal deformations by considering the rigidity of surfaces in this work we consider variations of the shape operator the normal curvature and the principal curvatures of gaudi surfaces under infinitesimal bending

on the willmore energy of shells under infinitesimal deformations in this paper we apply tensor calculus and differential geometry to consider shell structure using tensor calculus we examine the stationarity of the willmore energy under infinitesimal deformations of the surfaces in 3 we obtain the class of the surfaces which does not change its willmore energy under infinitesimal deformations in particular a special kind of deformation is considered infinitesimal bending which preserves the arc length the change of the willmore energy under such deformations is determined also we give a new proof of a well known theorem that reads that the total mean curvature of a surface is stationary under an infinitesimal bending applying tensor calculus

toeplitz matrices with an exponential growth of entries and the first szego limit theorem the toeplitz or block toeplitz matrices s r sj k rk j 1 generated by the taylor coefficients at zero of analytic functions s02 p 1 s p p and s02 p 1 sp p are considered a method is proposed for removing the poles of and or in other words for replacing s whose entries grow exponentially by a matrix j k k j 1 with better behaviour and the same asymptotics of r det r r as the sequence r det s r a szego type limit formula for the case when s r s r r n0 have a fixed number of negative eigenvalues is obtained

sobolev orthogonal polynomials in computing of hankel determinants abstract in this paper we study closed form evaluation for some special hankel determinants arising in combinatorial analysis especially for the bidirectional number sequences we show that such problems are directly connected with the theory of quasi definite discrete sobolev orthogonal polynomials it opens a lot of procedural dilemmas which we will try to exceed a few examples deal with fibonacci numbers and power sequences will illustrate our considerations we believe that our usage of sobolev orthogonal polynomials in hankel determinant computation is quite new

threshold selection using renyi s entropy image segmentation is an important and fundamental task in many digital image processing systems image segmentation by thresholding is the simplest technique and involves the basic assumption that objects and background in the digital image have distinct gray level distributions in this paper we present a general technique for thresholding of digital images based on renyi s entropy our method includes two of the previously proposed well known global thresholding methods the effectiveness of the proposed method is demonstrated by using examples from the real world and synthetic images

binomial determinants paths and hook length formulae abstract we give a combinatorial interpretation for any minor or binomial determinant of the matrix of binomial coefficients this interpretation involves configurations of nonintersecting paths and is related to young tableaux and hook length formulae

some identities for determinants of structured matrices abstract in this paper we establish several relations between the determinants of the following structured matrices hankel matrices symmetric toeplitz hankel matrices and toeplitz matrices using known results for the asymptotic behavior of toeplitz determinants these identities are used in order to obtain fisher hartwig type results on the asymptotics of certain skew symmetric toeplitz determinants and certain hankel determinants

young diagrammatic methods for the representation theory of the classical groups of type bn cn dn since the appearance of the celebrated article the classical groups of weyl 7 numerous influences have occurred in the representation theory of the classical groups especially it has become folklore that the facts in this field should be expressed only in terms of young diagrams the aim of this paper is one of the realizations of this principle a classical model of our approach is the results for gl n which are known as littlewood richardson coefficients and the kostka coefficients these two coefficients can be stated in the combinatorial manner using only young diagrams independently of the rank n of gl n we generalize these results to the other classical groups over c namely we give explicit formulas to decompose the tensor product of two irreducible representations into irreducible constituents also we have obtained an interesting relationship linking the irreducible characters of sp and so which we call duality relation between the representations of sp and so as for explicit formulas for the multiplicities of weights in the form of polynomials in the rank n we refer to 3

minimum cross entropy threshold selection thresholding is a common and easily implemented form of image segmentation many methods of automatic threshold selection based on the optimization of some discriminant function have been proposed such functions often take the form of a metric distance or similarity measure between the original image and the segmented result a non metric measure the cross entropy is used here to determine the optimum threshold it is shown that this measure is related to other commonly used measures of distance or similarity under special conditions although it is in some senses more general some typical results using this method are presented together with results using a metric form of the cross entropy

asymptotics of toeplitz hankel and toeplitz hankel determinants with fisher hartwig singularities we study the asymptotics in n for n dimensional toeplitz determinants whose symbols possess fisher hartwig singularities on a smooth background we prove the general nondegenerate asymptotic behavior as conjectured by basor and tracy we also obtain asymptotics of hankel determinants on a nite interval as well as determinants of toeplitz hankel type our analysis is based on a study of the related system of orthogonal polynomials on the unit circle using the riemann hilbert approach

optimal multilevel thresholding using molecular kinetic theory optimization algorithm abstract multilevel thresholding is one of the most widely used techniques for image segmentation however the conventional multilevel thresholding methods are time consuming algorithms since they exhaustively search for the optimal thresholds to optimize the objective functions in this paper a molecular kinetic theory optimization algorithm mktoa is applied to overcome this drawback mktoa is used to find the optimal threshold values for maximizing the kapur s and otsu s objective functions three different methods are compared to this proposed method the molecular force based particle swarm optimization mpso algorithm the differential evolution de algorithm and the bacterial foraging bf algorithm experimental results show that mktoa is much better in terms of robustness computational efficiency peak signal to noise ratio psnr and ability to conquer the curse of dimensionality than mpso de and bf

multilevel image thresholding based on 2d histogram and maximum tsallis entropy a differential evolution approach multilevel thresholding amounts to segmenting a gray level image into several distinct regions this paper presents a 2d histogram based multilevel thresholding approach to improve the separation between objects recent studies indicate that the results obtained with 2d histogram oriented approaches are superior to those obtained with 1d histogram based techniques in the context of bi level thresholding here a method to incorporate 2d histogram related information for generalized multilevel thresholding is proposed using the maximum tsallis entropy differential evolution de a simple yet efficient evolutionary algorithm of current interest is employed to improve the computational efficiency of the proposed method the performance of de is investigated extensively through comparison with other well known nature inspired global optimization techniques such as genetic algorithm particle swarm optimization artificial bee colony and simulated annealing in addition the outcome of the proposed method is evaluated using a well known benchmark the berkley segmentation data set bsds300 with 300 distinct images

simulating the deformation of vesicle membranes under elastic bending energy in three dimensions in this paper we study the three dimensional deformation of a vesicle membrane under the elastic bending energy with prescribed bulk volume and surface area both static and dynamic deformations are considered a newly developed energetic variational formulation is employed to give an effective eulerian description efficient time and spatial discretizations are considered and implemented numerical experiments illustrate some fascinating phenomena that are of interests in real applications

on minimum cross entropy thresholding over last few years several papers have been written on entropy based thresholding some of these methods use the gray level histogram while others use entropy associated with the two dimensional histogram or the co occurrence matrix recently li and lee proposed a thresholding scheme that is aimed to minimize the cross entropy this note first points out a certain conceptual problem and then proposes two algorithms which are free from that problem the proposed schemes are tested on several data sets the results are encouraging

a combinatorial proof of the giambelli identity for schur functions the giambelli identity provides a formula for expressing an arbitrary schur function of shape as a determinant of schur functions of hook shapes l 1k we give the first complete combinatorial proof of the giambelli identity we show how to derive various hook formulas from the giambelli identity and show how to extend our methods to derive extensions of the giambelli identity and the hook formula for the number of standard tableaux to certain skew shapes

dyson s constant in the asymptotics of the fredholm determinant of the sine kernel we prove that the asymptotics of the fredholm determinant of i k where k is the integral operator with the sine kernel open image in new window on the interval 0 are given by

multilevel minimum cross entropy threshold selection based on particle swarm optimization thresholding is one of the popular and fundamental techniques for conducting image segmentation many thresholding techniques have been proposed in the literature among them the minimum cross entropy thresholding mcet have been widely adopted although the mcet method is effective in the bilevel thresholding case it could be very time consuming in the multilevel thresholding scenario for more complex image analysis this paper first presents a recursive programming technique which reduces an order of magnitude for computing the mcet objective function then a particle swarm optimization pso algorithm is proposed for searching the near optimal mcet thresholds the experimental results manifest that the proposed pso based algorithm can derive multiple mcet thresholds which are very close to the optimal ones examined by the exhaustive search method the convergence of the proposed method is analyzed mathematically and the results validate that the proposed method is efficient and is suited for real time applications

painleve transcendent evaluations of finite system density matrices for 1d impenetrable bosons the recent experimental realisation of a one dimensional bose gas of ultra cold alkali atoms has renewed attention on the theoretical properties of the impenetrable bose gas of primary concern is the ground state occupation of effective single particle states in the finite system and thus the tendency for bose einstein condensation this requires the computation of the density matrix for the impenetrable bose gas on a circle we evaluate the density matrix in terms of a particular painleve vi transcendent in form and furthermore show that the density matrix satisfies a recurrence relation in the number of particles for the impenetrable bose gas in a harmonic trap and with dirichlet or neumann boundary conditions we give a determinant form for the density matrix a form as an average over the eigenvalues of an ensemble of random matrices and in special cases an evaluation in terms of a transcendent related to painleve v and vi we discuss how our results can be used to compute the ground state occupations

a geometric theory on the elasticity of bio membranes the purpose of this paper is to study the shapes and stabilities of bio membranes within the framework of exterior differential forms after a brief review of the current status of theoretical and experimental studies on the shapes of bio membranes a geometric scheme is proposed to discuss the shape equation of closed lipid bilayers the shape equation and boundary conditions of open lipid bilayers and two component membranes the shape equation and in plane strain equations of cell membranes with cross linking structures and the stabilities of closed lipid bilayers and cell membranes the key point of this scheme is to deal with the variational problems on surfaces embedded in three dimensional euclidean space by using exterior differential forms

threshold selection based on fuzzy c partition entropy approach abstract thresholding is an important topic for image processing pattern recognition and computer vision selecting thresholds is a critical issue for many applications the fuzzy set theory has been successfully applied to many areas such as control image processing pattern recognition computer vision medicine social science etc it is generally believed that image processing bears some fuzziness in nature in this paper we use the concept of fuzzy c partition and the maximum fuzzy entropy principle to select threshold values for gray level images we have conducted experiments on many images the experimental results demonstrate that the proposed approach can select the thresholds automatically and effectively and the resulting images can preserve the main features of the components of the original images very well

nonintersecting paths pfaffians and plane partitions gessel and viennot have developed a powerful technique for enumerating various classes of plane partitions the purpose of this article is to show by similar means that one may use pfaffiants to enumerate configurations of nonintersecting paths in which the initial and or terminal vertices of the paths are allowed to vary over specified regions of the digraph this leads to the possibility of enumerating classes of plane partitions in which the shape is allowed to vary whereas the previous applications of gessel and viennot were largely confined to plane partitions of a given shape

variation of shape operator under infinitesimal bending of surface in case of bendable surfaces it is useful to discuss the variation of magnitudes such as the shape operator the shape operator is a good way to measure how a regular surface s bends in r 3 by valuation how the surface normal n changes from point to point we considered the variation of shape operator under infinitesimal bending of surface given in an explicit form we also gave two examples of the variation of shape operator of gaudi surface and hyperbolic paraboloid

a dual of macmahon s theorem on plane partitions a classical theorem of macmahon states that the number of lozenge tilings of any centrally symmetric hexagon drawn on the triangular lattice is given by a beautifully simple product formula in this paper we present a counterpart of this formula corresponding to the exterior of a concave hexagon obtained by turning 120 after drawing each side macmahon s hexagon is obtained by turning 60 after each step

toeplitz determinants with one fisher hartwig singularity letcbe a function defined on the unit circle with fourier coefficients cn n the fisher hartwig conjecture describes the asymptotic behaviour of the determinants of then ntoeplitz matricesdn c det ci j n 1i j 0for a certain class of functionsc in this paper we prove this conjecture in the case of functions with one singularity more precisely we consider functions of the formc ei b ei t ei 1 u ei 1 heret ei exp i 0 2 is a function with a jump discontinuity u ei 2 2 cos is a function which may have a zero a pole or a discontinuity of oscillating type andbis a sufficiently smooth nonvanishing function with winding number equal to zero the only restriction we impose on the parameters is that 2 is required not to be a negative integer in the case where re 1 2 i e where the corresponding functioncis not integrable we identifycin an appropriate way with a distribution

a new criterion for automatic multilevel thresholding a new criterion for multilevel thresholding is proposed the criterion is based on the consideration of two factors the first one is the discrepancy between the thresholded and original images and the second one is the number of bits required to represent the thresholded image based on a new maximum correlation criterion for bilevel thresholding the discrepancy is defined and then a cost function that takes both factors into account is proposed for multilevel thresholding by minimizing the cost function the classification number that the gray levels should be classified and the threshold values can be determined automatically in addition the cost function is proven to possess a unique minimum under very mild conditions computational analyses indicate that the number of required mathematical operations in the implementation of our algorithm is much less than that of maximum entropy criterion finally simulation results are included to demonstrate their effectiveness

dyson s constants in the asymptotics of the determinants of wiener hopf hankel operators with the sine kernel let k alpha pm stand for the integral operators with the sine kernels frac sin x y pi x y pm frac sin x y pi x y acting on l2 0 dyson conjectured that the asymptotics of the fredholm determinants of i k alpha pm are given by log det i k alpha pm frac alpha 2 4 mp frac alpha 2 frac log alpha 8 frac log 2 24 pm frac log 2 4 frac 3 2 zeta 1 o 1 as in this paper we are going to give a proof of these two asymptotic formulas

riordan arrays and the ldu decomposition of symmetric toeplitz plus hankel matrices abstract we examine a result of basor and ehrhardt concerning hankel and toeplitz plus hankel matrices within the context of the riordan group of lower triangular matrices this allows us to determine the ldu decomposition of certain symmetric toeplitz plus hankel matrices we also determine the generating functions and hankel transforms of associated sequences

a multilevel image thresholding using the honey bee mating optimization image thresholding is an important technique for image processing and pattern recognition many thresholding techniques have been proposed in the literature among them the maximum entropy thresholding met has been widely applied in this paper a new multilevel met algorithm based on the technology of the honey bee mating optimization hbmo is proposed this proposed method is called the maximum entropy based honey bee mating optimization thresholding mehbmot method three different methods such as the particle swarm optimization pso the hybrid cooperative comprehensive learning based pso algorithm hcoclpso and the fast otsu s method are also implemented for comparison with the results of the proposed method the experimental results manifest that the proposed mehbmot algorithm can search for multiple thresholds which are very close to the optimal ones examined by the exhaustive search method in comparison with the other three thresholding methods the segmentation results using the mehbmot algorithm is the best and its computation time is relatively low furthermore the convergence of the mehbmot algorithm can rapidly achieve and the results validate that the proposed mehbmot algorithm is efficient

on the color image segmentation algorithm based on the thresholding and the fuzzy c means techniques abstract in this paper a segmentation algorithm for color images based on the thresholding and the fuzzy c means fcm techniques is presented the scale space filter is used as a tool for analyzing the histograms of three color components the methodology uses a coarse fine concept to reduce the computational burden required for the fcm the coarse segmentation attempts to segment coarsely using the thresholding technique while the fine segmentation assigns the pixels which remain unclassified after the coarse segmentation to the closest class using the fcm attempts also have been made to compare the performance of the proposed algorithm with other existing algorithms ohlander s rosenfeld s and bezdek s intensive computer simulation has been performed and the results are discussed in this paper the simulation results indicate that the proposed algorithm yields the most accurate segmented image on the color coordinate proposed by ohta et al while requiring a reasonable amount of computational effort

particle swarm optimization based on intermediate disturbance strategy algorithm and its application in multi threshold image segmentation abstract particle swarm optimization pso algorithm simulates social behavior among individuals or particles flying through multidimensional search space for enhancing the local search ability of pso and guiding the search a region that had most number of the particles was defined and analyzed in detail inspired by the ecological behavior we presented a pso algorithm with intermediate disturbance searching strategy idpso which enhances the global search ability of particles and increases their convergence rates the experimental results on comparing the idpso to ten known pso variants on 16 benchmark problems demonstrated the effectiveness of the proposed algorithm furthermore we applied the idpso algorithm to multilevel image segmentation problem for shortening the computational time experimental results of the new algorithm on a variety of images showed that it can effectively segment an image faster

vicious walkers friendly walkers and young tableaux iii between two walls we derive exact and asymptotic results for the number of star and watermelon configurations of vicious walkers confined to lie between two impenetrable walls as well as corresponding results for the analogous problem of friendly walkers our proofs make use of results from symmetric function theory and the theory of basic hypergeometric series

new schur function series this paper presents some new product identities for certain summations of schur functions these identities are generalizations of some famous identities known to littlewood and appearing in macdonald s book we refer to these identities as the littlewood type formulas in addition analogues for summations of characters of the other classical groups are also given the littlewood type formulas in this paper are separated into two classes the rational schur function series and the generalized schur function series an application of a rational schur function series to the infinite product representation of the elliptic theta functions is also given we prove these littlewood type formulas using the cauchy binet formula the cauchy binet formula is a basic but powerful tool applicable in the present context which can be derived from our pfaffian formula as we explain q 1998 academic press

shifted tableaux and the projective representations of symmetric groups les groupes de representation de s n classes de conjugaison algebres de clifford et la representation spin de base produits induits pour des representations spin une application caracteristique pour des caracteres de spin tableaux decales et q fonctions de schur les caracteres de spin irreductibles de s n et a n une analogue decalee de la regle lr produits tensoriels interieurs

the fisher hartwig conjecture and generalizations abstract we discuss the status of the fisher hartwig conjecture concerning the asymptotic expansion of a class of toeplitz determinants with singular generating functions a counterexample is given for a nonrational generating function and we formulate a generalized fisher hartwig conjecture

change of the willmore energy under infinitesimal bending of membranes change of the willmore energy as the special case of elastic bending energy under infinitesimal bending of the vesicle membrane is discussed a membrane is thought of as a smooth surface in r 3 because its thickness is much smaller than its lateral dimension variation of the willmore energy at the surface point under infinitesimal bending of that surface as well as the condition for the stationarity of the willmore energy are given some examples are visualized variation of the willmore energy of a compact path connected smooth surface in the euclidean 3 space is reduced to a line integral of a special vector field and it is found that the willmore energy of a boundary free surface is stationary under an infinitesimal bending also the willmore energy of a minimal surface is stationary under its infinitesimal bending