uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory we consider asymptotics for orthogonal polynomials with respect to varying exponential weights wn x dx e nv x dx on the line as n the potentials v are assumed to be real analytic with sufficient growth at infinity the principle results concern plancherel rotach type asymptotics for the orthogonal polynomials down to the axis using these asymptotics we then prove universality for a variety of statistical quantities arising in the theory of random matrix models some of which have been considered recently in 31 and also in 4 an additional application concerns the asymptotics of the recurrence coefficients and leading coefficients for the orthonormal polynomials see also 4 the orthogonal polynomial problem is formulated as a riemann hilbert problem following 19 20 the riemann hilbert problem is analyzed in turn using the steepest descent method introduced in 12 and further developed in 11 13 a critical role in our method is played by the equilibrium measure d v for v as analyzed in 8 1999 john wiley sons inc

correlation functions cluster functions and spacing distributions for random matrices the usual formulas for the correlation functions in orthogonal and symplectic matrix models express them as quaternion determinants from this representation one can deduce formulas for spacing probabilities in terms of fredholm determinants of matrix valued kernels the derivations of the various formulas are somewhat involved in this article we present a direct approach which leads immediately to scalar kernels for the unitary ensembles and matrix kernels for the orthogonal and symplectic ensembles and the representations of the correlation functions cluster functions and spacing distributions in terms of them

a finitization of the bead process the bead process is the particle system defined on parallel lines with underlying measure giving constant weight to all configurations in which particles on neighbouring lines interlace and zero weight otherwise motivated by the statistical mechanical model of the tiling of an abc hexagon by three species of rhombi a finitized version of the bead process is defined the corresponding joint distribution can be realized as an eigenvalue probability density function for a sequence of random matrices the finitized bead process is determinantal and we give the correlation kernel in terms of jacobi polynomials two scaling limits are considered a global limit in which the spacing between lines goes to zero and a certain bulk scaling limit in the global limit the shape of the support of the particles is determined while in the bulk scaling limit the bead process kernel of boutillier is reclaimed after appropriate identification of the anisotropy parameter therein

sorted consecutive local binary pattern for texture classification in this paper we propose a sorted consecutive local binary pattern sclbp for texture classification conventional methods encode only patterns whose spatial transitions are not more than two whereas sclbp encodes patterns regardless of their spatial transition conventional methods do not encode patterns on account of rotation invariant encoding on the other hand patterns with more than two spatial transitions have discriminative power the proposed sclbp encodes all patterns with any number of spatial transitions while maintaining their rotation invariant nature by sorting the consecutive patterns in addition we introduce dictionary learning of sclbp based on kd tree which separates data with a space partitioning strategy since the elements of sorted consecutive patterns lie in different space it can be generated to a discriminative code with kd tree finally we present a framework in which sclbps and the kd tree can be combined and utilized the results of experimental evaluation on five texture data sets outex curet uiuc umd and kth tips2 a indicate that our proposed framework achieves the best classification rate on the curet umd and kth tips2 a data sets compared with conventional methods the results additionally indicate that only a marginal difference exists between the best classification rate of conventional methods and that of the proposed framework on the uiuc and outex data sets

non intersecting paths random tilings and random matrices we investigate certain measures induced by families of non intersecting paths in domino tilings of the aztec diamond rhombus tilings of an abc hexagon a dimer model on a cylindrical brick lattice and a growth model the measures obtained e g the krawtchouk and hahn ensembles have the same structure as the eigenvalue measures in random matrix theory like gue which can in fact can be obtained from non intersecting brownian motions the derivations of the measures are based on the karlin mcgregor or lindstrom gessel viennot method we use the measures to show some asymptotic results for the models

random matrices in 2d laplacian growth and operator theory since it was first applied to the study of nuclear interactions by wigner and dyson almost 60 years ago random matrix theory rmt has developed into a field of its own within applied mathematics and is now essential to many parts of theoretical physics from condensed matter to high energy the fundamental results obtained so far rely mostly on the theory of random matrices in one dimension the dimensionality of the spectrum or equilibrium probability density in the last few years this theory has been extended to the case where the spectrum is two dimensional or even fractal with dimensions between 1 and 2 in this paper we review these recent developments and indicate some physical problems where the theory can be applied

mellin polar coordinate moment and its affine invariance abstract the moment based method is a fundamental approach to the extraction of affine invariants however only integer order traditional moments can be used to construct affine invariants no invariants can be constructed by moments with an order lower than 2 consequently the obtained invariants are sensitive to noise in this paper the moment order is generalized from integer to non integer however the moment order cannot simply be generalized from integer to non integer to achieve affine invariance the difficulty of this generalization lies in the fact that the angular factor owing to shearing in the affine transform can hardly be eliminated for non integer order moments in order to address this problem the mellin polar coordinate moment mpcm is proposed which is directly defined by a repeated integral the angular factor can easily be eliminated by appropriately selecting a repeated integral a method is provided for constructing affine invariants by means of mpcms the traditional affine moment invariants amis can be derived in terms of the proposed mpcm furthermore affine invariants constructed with real order lower than 2 mpcms can be derived using the proposed method these invariants may be more robust to noise than amis several experiments were conducted to evaluate the proposed method performance

strong asymptotics of orthogonal polynomials with respect to exponential weights we consider asymptotics of orthogonal polynomials with respect to weights w x dx e q x dx on the real line where q x 2m k 0 qkx k q2m 0 denotes a polynomial of even order with positive leading coefficient the orthogonal polynomial problem is formulated as a riemann hilbert problem following 22 23 we employ the steepest descent type method introduced in 18 and further developed in 17 19 in order to obtain uniform plancherel rotach type asymptotics in the entire complex plane as well as asymptotic formulae for the zeros the leading coefficients and the recurrence coefficients of the orthogonal polynomials c 1999 john wiley sons inc

a statistical approach to texture classification from single images we investigate texture classification from single images obtained under unknown viewpoint and illumination a statistical approach is developed where textures are modelled by the joint probability distribution of filter responses this distribution is represented by the frequency histogram of filter response cluster centres textons recognition proceeds from single uncalibrated images and the novelty here is that rotationally invariant filters are used and the filter response space is low dimensional classification performance is compared with the filter banks and methods of leung and malik ijcv 2001 schmid cvpr 2001 and cula and dana ijcv 2004 and it is demonstrated that superior performance is achieved here classification results are presented for all 61 materials in the columbia utrecht texture database we also discuss the effects of various parameters on our classification algorithm such as the choice of filter bank and rotational invariance the size of the texton dictionary as well as the number of training images used finally we present a method of reliably measuring relative orientation co occurrence statistics in a rotationally invariant manner and discuss whether incorporating such information can enhance the classifier s performance

invariant image recognition by zernike moments the problem of rotation scale and translation invariant recognition of images is discussed a set of rotation invariant features are introduced they are the magnitudes of a set of orthogonal complex moments of the image known as zernike moments scale and translation invariance are obtained by first normalizing the image with respect to these parameters using its regular geometrical moments a systematic reconstruction based method for deciding the highest order zernike moments required in a classification problem is developed the quality of the reconstructed image is examined through its comparison to the original one the orthogonality property of the zernike moments which simplifies the process of image reconstruction make the suggest feature selection approach practical features of each order can also be weighted according to their contribution to the reconstruction process the superiority of zernike moment features over regular moments and moment invariants was experimentally verified

bayesian texture classification based on contourlet transform and byy harmony learning of poisson mixtures as a newly developed 2 d extension of the wavelet transform using multiscale and directional filter banks the contourlet transform can effectively capture the intrinsic geometric structures and smooth contours of a texture image that are the dominant features for texture classification in this paper we propose a novel bayesian texture classifier based on the adaptive model selection learning of poisson mixtures on the contourlet features of texture images the adaptive model selection learning of poisson mixtures is carried out by the recently established adaptive gradient bayesian ying yang harmony learning algorithm for poisson mixtures it is demonstrated by the experiments that our proposed bayesian classifier significantly improves the texture classification accuracy in comparison with several current state of the art texture classification approaches

topological recursion in enumerative geometry and random matrices we review the method of symplectic invariants recently introduced to solve matrix models loop equations in the so called topological expansion and further extended beyond the context of matrix models for any given spectral curve one defines a sequence of differential forms and a sequence of complex numbers fg called symplectic invariants we recall the definition of fg s and we explain their main properties in particular symplectic invariance integrability modularity as well as their limits and their deformations then we give several examples of applications in particular matrix models enumeration of discrete surfaces maps algebraic geometry and topological strings and non intersecting brownian motions

combining lbp difference and feature correlation for texture description effective characterization of texture images requires exploiting multiple visual cues from the image appearance the local binary pattern lbp and its variants achieve great success in texture description however because the lbp like feature is an index of discrete patterns rather than a numerical feature it is difficult to combine the lbp like feature with other discriminative ones by a compact descriptor to overcome the problem derived from the nonnumerical constraint of the lbp this paper proposes a numerical variant accordingly named the lbp difference lbpd the lbpd characterizes the extent to which one lbp varies from the average local structure of an image region of interest it is simple rotation invariant and computationally efficient to achieve enhanced performance we combine the lbpd with other discriminative cues by a covariance matrix the proposed descriptor termed the covariance and lbpd descriptor cov lbpd is able to capture the intrinsic correlation between the lbpd and other features in a compact manner experimental results show that the cov lbpd achieves promising results on publicly available data sets

unsupervised texture segmentation using gabor filters abstract this paper presents a texture segmentation algorithm inspired by the multi channel filtering theory for visual information processing in the early stages of human visual system the channels are characterized by a bank of gabor filters that nearly uniformly covers the spatial frequency domain and a systematic filter selection scheme is proposed which is based on reconstruction of the input image from the filtered images texture features are obtained by subjecting each selected filtered image to a nonlinear transformation and computing a measure of energy in a window around each pixel a square error clustering algorithm is then used to integrate the feature images and produce a segmentation a simple procedure to incorporate spatial information in the clustering process is proposed a relative index is used to estimate the true number of texture categories

headway statistics of public transport in mexican cities we present a cellular automaton simulating the behaviour of public bus transport in several mexican cities the headway statistics obtained from the model is compared to the measured time intervals between subsequent bus arrivals to a given bus stop and to a spacing distribution resulting from a random matrix theory

eynard mehta theorem schur process and their pfaffian analogs we give simple linear algebraic proofs of the eynard mehta theorem the okounkov reshetikhin formula for the correlation kernel of the schur process and pfaffian analogs of these results we also discuss certain general properties of the spaces of all determinantal and pfaffian processes on a given finite set

a model for the bus system in cuernavaca mexico the bus system in cuernavaca mexico and its connections to random matrix distributions have been the subject of an interesting recent study by m krbalek and p seba in 15 16 in this paper we introduce and analyse a microscopic model for the bus system we show that introducing a natural repulsion does produce random matrix distributions in natural double scaling regimes the techniques employed include non intersecting paths logarithmic potential theory determinantal point processes and asymptotic analysis of several orthogonal polynomial ensembles in addition we introduce a circular bus model and include various calculations of non crossing probabilities

weakly supervised learning of visual models and its application to content based retrieval this paper presents a method for weakly supervised learning of visual models the visual model is based on a two layer image description a set of generic descriptors and their distribution over neighbourhoods generic descriptors represent sets of similar rotational invariant feature vectors statistical spatial constraints describe the neighborhood structure and make our description more discriminant the joint probability of the frequencies of generic descriptors over a neighbourhood is multi modal and is represented by a set of neighbourhood frequency clusters our image description is rotationally invariant robust to model deformations and characterizes efficiently appearance based visual structure the selection of distinctive clusters determines model features common to the positive and rare in the negative examples visual models are retrieved and localized using a probabilistic score experimental results for textured animals and faces show a very good performance for retrieval as well as localization

markov random field texture models we consider a texture to be a stochastic possibly periodic two dimensional image field a texture model is a mathematical procedure capable of producing and describing a textured image we explore the use of markov random fields as texture models the binomial model where each point in the texture has a binomial distribution with parameter controlled by its neighbors and number of tries equal to the number of gray levels was taken to be the basic model for the analysis a method of generating samples from the binomial model is given followed by a theoretical and practical analysis of the method s convergence examples show how the parameters of the markov random field control the strength and direction of the clustering in the image the power of the binomial model to produce blurry sharp line like and blob like textures is demonstrated natural texture samples were digitized and their parameters were estimated under the markov random field model a hypothesis test was used for an objective assessment of goodness of fit under the markov random field model overall microtextures fit the model well the estimated parameters of the natural textures were used as input to the generation procedure the synthetic microtextures closely resembled their real counterparts while the regular and inhomogeneous textures did not

affine invariant classification and retrieval of texture images in this paper we propose a new method of extracting affine invariant texture signatures for content based affine invariant image retrieval cbair the algorithm discussed in this paper exploits the spectral signatures of texture images based on spectral representation of affine transform anisotropic scale invariant signatures of orientation spectrum distributions are extracted peaks distribution vector pdv obtained from signature distributions captures texture properties invariant to affine transform the pdv is used to measure the similarity between textures extensive experimental results are included to demonstrate the performance of the method in texture classification and cbair c 2002 pattern recognition society published by elsevier science ltd all rights reserved

the statistical properties of the city transport in cuernavaca mexico and random matrix ensembles we analyse the statistical properties of the city bus transport in cuernavaca mexico and show that the subsequent bus arrivals display probability distributions conforming to those given by the unitary ensemble of random matrices

matrices coupled in a chain i eigenvalue correlations the general correlation function for the eigenvalues of p complex hermitian matrices coupled in a chain is given as a single determinant for this we use a slight generalization of a theorem of dyson

radon representation based feature descriptor for texture classification in this paper we aim to handle the intraclass variation resulting from the geometric transformation and the illumination change for more robust texture classification to this end we propose a novel feature descriptor called radon representation based feature descriptor rrfd rrfd converts the original pixel represented images into radon pixel images by using the radon transform the new radon pixel representation is more informative in geometry and has a much lower dimension subsequently rrfd efficiently achieves affine invariance by projecting an image or an image patch from the space of radon pixel pairs onto an invariant feature space by using a ratiogram i e the histogram of ratios between the areas of triangle pairs the illumination invariance is also achieved by defining an illumination invariant distance metric on the invariant feature space comparing to the existing radon transform based texture features which only achieve rotation and or scaling invariance rrfd achieves affine invariance the experimental results on curet show that rrfd is a powerful feature descriptor that is suitable for texture classification

recognition of arabic characters a statistical approach for the recognition of arabic characters is introduced as a first step the character is segmented into primary and secondary parts dots and zigzags the secondary parts of the character are then isolated and identified separately thereby reducing the number of classes from 28 to 18 the moments of the horizontal and vertical projections of the remaining primary characters are then calculated and normalized with respect to the zero order moment simple measures of the shape are obtained from the normalized moments a 9 d feature vector is obtained for each character classification is accomplished using quadratic discriminant functions the approach was evaluated using isolated handwritten and printed characters from a database established for this purpose the results indicate that the technique offers better classification rates in comparison with existing methods

multivariate analysis and jacobi ensembles largest eigenvalue tracy widom limits and rates of convergence abstract let a and b be independent central wishart matrices in p variables with common covariance and having m and n degrees of freedom respectively the distribution of the largest eigenvalue of a b 1 b has numerous applications in multivariate statistics but is difficult to calculate exactly suppose that m and n grow in proportion to p we show that after centering and scaling the distribution is approximated to second order o p 2 3 by the tracy widom law the results are obtained for both complex and then real valued data by using methods of random matrix theory to study the largest eigenvalue of the jacobi unitary and orthogonal ensembles asymptotic approximations of jacobi polynomials near the largest zero play a central role

two step asymptotics of scaled dunkl processes dunkl processes are generalizations of brownian motion obtained by using the differential difference operators known as dunkl operators as a replacement of spatial partial derivatives in the heat equation special cases of these processes include dyson s brownian motion model and the wishart laguerre eigenvalue processes which are well known in random matrix theory it is known that the dynamics of dunkl processes is obtained by transforming the heat kernel using dunkl s intertwining operator it is also known that under an appropriate scaling their distribution function converges to a steady state distribution which depends only on the coupling parameter as the process time t tends to infinity we study scaled dunkl processes starting from an arbitrary initial distribution and we derive expressions for the intertwining operator in order to calculate the asymptotics of the distribution function in two limiting situations in the first one is fixed and t tends to infinity approach to the steady s

filtering for texture classification a comparative study in this paper we review most major filtering approaches to texture feature extraction and perform a comparative study filtering approaches included are laws masks 1980 ring wedge filters dyadic gabor filter banks wavelet transforms wavelet packets and wavelet frames quadrature mirror filters discrete cosine transform eigenfilters optimized gabor filters linear predictors and optimized finite impulse response filters the features are computed as the local energy of the filter responses the effect of the filtering is highlighted keeping the local energy function and the classification algorithm identical for most approaches for reference comparisons with two classical nonfiltering approaches co occurrence statistical and autoregressive model based features are given we present a ranking of the tested approaches based on extensive experiments

wavelet based rotational invariant roughness features for texture classification and segmentation we introduce a rotational invariant feature set for texture segmentation and classification based on an extension of fractal dimension fd features the fd extracts roughness information from images considering all available scales at once in this work a single scale is considered at a time so that textures with scale dependent properties are satisfactorily characterized single scale features are combined with multiple scale features for a more complete textural representation wavelets are employed for the computation of single and multiple scale roughness features because of their ability to extract information at different resolutions features are extracted in multiple directions using directional wavelets and the feature vector is finally transformed to a rotational invariant feature vector that retains the texture directional information an iterative k means scheme is used for segmentation and a simplified form of a bayesian classifier is used for classification the use of the roughness feature set results in high quality segmentation performance furthermore it is shown that the roughness feature set exhibits a higher classification rate than other feature vectors presented in this work the feature set retains the important properties of fd based features namely insensitivity to absolute illumination and contrast

quaternionic local ranking binary pattern a local descriptor of color images this paper proposes a local descriptor called quaternionic local ranking binary pattern qlrbp for color images different from traditional descriptors that are extracted from each color channel separately or from vector representations qlrbp works on the quaternionic representation qr of the color image that encodes a color pixel using a quaternion qlrbp is able to handle all color channels directly in the quaternionic domain and include their relations simultaneously applying a clifford translation to qr of the color image qlrbp uses a reference quaternion to rank qrs of two color pixels and performs a local binary coding on the phase of the transformed result to generate local descriptors of the color image experiments demonstrate that the qlrbp outperforms several state of the art methods

the explicit formulas and evaluations of ramanujan s theta function ψ abstract we define two quotients of theta function depending on two positive real parameters we then show how they are connected with two parameters of dedekind eta function theta function and the ramanujan weber class invariants explicit formulas for determining values of the theta function are derived and several examples will be given in addition we give some applications of these parameters for the famous rogers ramanujan continued fraction r q ramanujan s cubic continued fraction g q and the modular j invariant

geometric invariant features in the radon transform domain for near duplicate image detection radon transform has been widely used in content based image representation due to its excellent geometric properties in this paper we propose a family of geometric invariant features based on radon transform for near duplicate image detection according to the theoretical analysis between geometric operations translation scaling and rotation and radon transform we present a geometric invariant feature model based on the feature model we developed four kinds of geometric invariant features in addition a uniform sampling technique is introduced to combine different features the comprehensive performance of the combined feature is better than that of a single one extensive experiments show that the proposed features are robust not only to rotation and scaling but also to other operations such as compression noise contamination blurring illumination modification cropping etc and achieve strong competitive performance compared with the state of the art image features