homogenization for semilinear hyperbolic systems with oscillatory data abstract the behavior of multi dimensional discrete boltzmann systems with highly oscillatory data is studied homogenized equations for the mean solutions are obtained uniform convergence of the oscillatory solutions of the discrete boltzmann equations to the solutions of the corresponding homogenized equations is established moreover we find that the weak limits of the oscillatory solutions for a model of broadwell type are not continuous functions of the discrete velocities generalization of the above results to problems with multiple scale initial data is also established reprints

quasipolynomial generalization of lotka volterra mappings in recent years it has been shown that lotka volterra mappings constitute a valuable tool from both the theoretical and the applied points of view with developments in very diverse fields such as physics population dynamics chemistry and economy the purpose of this work is to demonstrate that many of the most important ideas and algebraic methods that constitute the basis of the quasipolynomial formalism originally conceived for the analysis of ordinary differential equations can be extended into the mapping domain the extension of the formalism into the discrete time context is remarkable as far as the quasipolynomial methodology had never been shown to be applicable beyond the differential case it will be demonstrated that lotka volterra mappings play a central role in the quasipolynomial formalism for the discrete time case moreover the extension of the formalism into the discrete time domain allows a significant generalization of lotka volterra mappings as well as a whole transfer of algebraic methods into the discrete time context the result is a novel and more general conceptual framework for the understanding of lotka volterra mappings as well as a new range of possibilities that become open not only for the theoretical analysis of lotka volterra mappings and their generalizations but also for the development of new applications

consistent estimation of non bandlimited spectral density from uniformly spaced samples in the matter of selection of sample time points for the estimation of the power spectral density of a continuous time stationary stochastic process irregular sampling schemes such as poisson sampling are often preferred over regular uniform sampling a major reason for this preference is the well known problem of inconsistency of estimators based on regular sampling when the underlying power spectral density is not bandlimited it is argued in this paper that in consideration of a large sample property like consistency it is natural to allow the sampling rate to go to infinity as the sample size goes to infinity through appropriate asymptotic calculations under this scenario it is shown that the smoothed periodogram based on regularly spaced data is a consistent estimator of the spectral density even when the latter is not band limited it transpires that under similar assumptions the estimators based on uniformly sampled and poisson sampled data have about the same rate of convergence apart from providing this reassuring message the paper also gives a guideline for practitioners regarding appropriate choice of the sampling rate theoretical calculations for large samples and monte carlo simulations for small samples indicate that the smoothed periodogram based on uniformly sampled data have less variance and more bias than its counterpart based on poisson sampled data

nonuniform sampling and antialiasing in image representation a unified approach to the representation and processing of a class of images which are not bandlimited but belong to the space of locally bandlimited signals is presented a nonuniform sampling theorem clark et al 1985 for functions belonging to this space is extended and a class of nonstationary stochastic processes is considered the space of locally bandlimited signals is shown to be a reproducing kernel space a generalized projection theorem can therefore be applied yielding either a continuous or a discrete projection filter the former can be used for image conditioning prior to nonuniform sampling while the latter provides a general tool for image representation by nonuniform sampling schemes the problem of finding the local bandwidth of a given signal in order to generate an optimal sampling scheme is addressed in the context of signal representation in the combined position frequency space the stochastic estimation of parameters which characterize the local bandwidth is discussed bounds on the error resulting from the utilization of nonexact position varying signal parameters are derived

derivation of determinantal structures for random matrix ensembles in a new way there are several methods to treat ensembles of random matrices in symmetric spaces circular matrices chiral matrices and others orthogonal polynomials and the supersymmetry method are particular powerful techniques here we present a new approach to calculate averages over ratios of characteristic polynomials at first sight paradoxically one can call our approach supersymmetry without supersymmetry because we use structures from supersymmetry without actually mapping onto superspaces we address two kinds of integrals which cover a wide range of applications for random matrix ensembles for probability densities factorizing in the eigenvalues we find determinantal structures in a unifying way as a new application we derive an expression for the k point correlation function of an arbitrary rotation invariant probability density over the hermitian matrices in the presence of an external field

a comparison of the superbosonization formula and the generalized hubbard stratonovich transformation recently two different approaches were put forward to extend the supersymmetry method in random matrix theory from gaussian ensembles to general rotation invariant ensembles these approaches are the generalized hubbard stratonovich transformation and the superbosonization formula here we prove the equivalence of both approaches to this end we reduce integrals over functions of supersymmetric wishart matrices to integrals over quadratic supermatrices of certain symmetries

parameter shifts d4 symmetry and joint eigenfunctions for commuting askey wilson type difference operators in previous papers we studied a generalized hypergeometric function that is a joint eigenfunction of four hyperbolic askey wilson difference operators using parameter shifts related to the d4 weight lattice we show that this function is the even linear combination of two elementary joint eigenfunctions for a dense subset of the parameter space more specifically the latter eigenfunctions are equal to a plane wave multiplied by hyperbolic functions

learning spectral descriptors for deformable shape correspondence informative and discriminative feature descriptors play a fundamental role in deformable shape analysis for example they have been successfully employed in correspondence registration and retrieval tasks in recent years significant attention has been devoted to descriptors obtained from the spectral decomposition of the laplace beltrami operator associated with the shape notable examples in this family are the heat kernel signature hks and the recently introduced wave kernel signature wks the laplacian based descriptors achieve state of the art performance in numerous shape analysis tasks they are computationally efficient isometry invariant by construction and can gracefully cope with a variety of transformations in this paper we formulate a generic family of parametric spectral descriptors we argue that to be optimized for a specific task the descriptor should take into account the statistics of the corpus of shapes to which it is applied the signal and those of the class of transformations to which it is made insensitive the noise while such statistics are hard to model axiomatically they can be learned from examples following the spirit of the wiener filter in signal processing we show a learning scheme for the construction of optimized spectral descriptors and relate it to mahalanobis metric learning the superiority of the proposed approach in generating correspondences is demonstrated on synthetic and scanned human figures we also show that the learned descriptors are robust enough to be learned on synthetic data and transferred successfully to scanned shapes

ensemble inequivalence a formal approach abstract ensemble inequivalence has been observed in several systems in particular it has been recently shown that negative specific heat can arise in the microcanonical ensemble in the thermodynamic limit for systems with long range interactions we display a connection between such behaviour and a mean field like structure of the partition function since short range models cannot display this kind of behaviour this strongly suggests that such systems are necessarily non mean field in the sense indicated here we further show that a broad class of systems with non integrable interactions are indeed of mean field type in the sense specified so that they are expected to display ensemble inequivalence as well as the peculiar behaviour described above in the microcanonical ensemble

the factorization method for the general second order q difference equation and the laguerre hahn polynomials on the general q lattice for the general linear second order q difference equation we show the interconnection between the factorization method and the laguerre hahn polynomials on the general q lattice applications are then given in the cases of the hypergeometric and askey wilson second order q difference equations

blind adaptive sampling of images adaptive sampling schemes choose different sampling masks for different images blind adaptive sampling schemes use the measurements that they obtain without any additional or direct knowledge about the image to wisely choose the next sample mask in this paper we present and discuss two blind adaptive sampling schemes the first is a general scheme not restricted to a specific class of sampling functions it is based on an underlying statistical model for the image which is updated according to the available measurements a second less general but more practical method uses the wavelet decomposition of an image it estimates the magnitude of the unsampled wavelet coefficients and samples those with larger estimated magnitude first experimental results show the benefits of the proposed blind sampling schemes

particle method approximation of oscillatory solutions to hyperbolic differential equations particle methods approximating hyperbolic partial diferential equations with oscillatory solutions are studied convergence is proved for approximations for which the continuous solution is not well resolved on the computational grid highly oscillatory solutions to the broadwell and variable coefficient carleman models are considered homogenization results are given and the approximations of more general systems are discussed numerical examples are presented

noncommutative torus from fibonacci chains via foliation we classify the fibonacci chains f chains by their index sequences and construct an approximately finite dimensional af c algebra on the space of f chains as connes did on the space of penrose tiling the k theory on this af algebra suggests a connection between the noncommutative torus and the space of f chains a noncommutative torus which can be regarded as the c algebra of a foliation on the torus is explicitly embedded into the af algebra on the space of f chains as a counterpart of that we obtain a relation between the space of f chains and the leaf space of kronecker foliation on the torus using the cut procedure of constructing f chains our embedding of the c algebra of the foliation is consistent with the recent result of landi lizzi and szabo that the c algebra of noncommutative torus can be embedded into an af algebra

holographic representations of images we discuss a new type of holographic image representations that have advantages in a distributed world we call these representations holographic arbitrary portions of a holographic representation enable reconstruction of the whole image with distortions that decrease gradually with the increase in the size of the portions available holographic representations enable progressive refinement in image communication or retrieval tasks with no restrictions on the order in which the data fragments sections of the representation are accessed or become available

spectral symmetry analysis we present a spectral approach for detecting and analyzing rotational and reflectional symmetries in n dimensions our main contribution is the derivation of a symmetry detection and analysis scheme for sets of points irn and its extension to image analysis by way of local features each object is represented by a set of points s irn where the symmetry is manifested by the multiple self alignments of s the alignment problem is formulated as a quadratic binary optimization problem with an efficient solution via spectral relaxation for symmetric objects this results in a multiplicity of eigenvalues whose corresponding eigenvectors allow the detection and analysis of both types of symmetry we improve the scheme s robustness by incorporating geometrical constraints into the spectral analysis our approach is experimentally verified by applying it to 2d and 3d synthetic objects as well as real images

surprising pfaffian factorizations in random matrix theory with dyson index β 2 in recent decades determinants and pfaffians were found for eigenvalue correlations of various random matrix ensembles these structures simplify the average over a large number of ratios of characteristic polynomials to integrations over one and two characteristic polynomials only up to now it was thought that determinants occur for ensembles with dyson index 2 whereas pfaffians only for ensembles with 1 4 we derive a non trivial pfaffian determinant for 2 random matrix ensembles which is similar to the one for 1 4 thus it unveils a hidden universality of this structure we also give a general relation between the orthogonal polynomials related to the determinantal structure and the skew orthogonal polynomials corresponding to the pfaffian as a particular example we consider the chiral unitary ensembles in great detail

multivariate block polar quantization we introduce multivariate block polar quantization mbpq mbpq minimizes the weighted squared error distortion for a set of complex variables representing one block of a signal under a resolution constraint for the entire block mbpq performs below the lower bound for classical bivariate quantization both for gaussian complex variables and for complex variables found from sinusoidal analysis of audio data still it is of similar complexity as traditional polar quantizers in the case of audio data we found a performance gain of about 2 5 db over the best performing conventional resolution constrained polar quantization an extension of unrestricted polar quantization

multiple description wavelet based image coding we consider the problem of coding images for transmission over error prone channels the impairments we target are transient channel shutdowns as would occur in a packet network when a packet is lost or in a wireless system during a deep fade when data is delivered it is assumed to be error free but some of the data may never reach the receiver the proposed algorithms are based on a combination of multiple description scalar quantizers with techniques successfully applied to the construction of some of the most efficient subband coders a given image is encoded into multiple independent packets of roughly equal length when packets are lost the quality of the approximation computed at the receiver depends only on the number of packets received but does not depend on exactly which packets are actually received when compared with previously reported results on the performance of robust image coders based on multiple descriptions on standard test images our coders attain similar psnr values using typically about 50 60 of the bit rate required by these other state of the art coders while at the same time providing significantly more freedom in the mechanism for allocation of redundancy among descriptions

nonlinear dimensionality reduction by topologically constrained isometric embedding many manifold learning procedures try to embed a given feature data into a flat space of low dimensionality while preserving as much as possible the metric in the natural feature space the embedding process usually relies on distances between neighboring features mainly since distances between features that are far apart from each other often provide an unreliable estimation of the true distance on the feature manifold due to its non convexity distortions resulting from using long geodesics indiscriminately lead to a known limitation of the isomap algorithm when used to map non convex manifolds presented is a framework for nonlinear dimensionality reduction that uses both local and global distances in order to learn the intrinsic geometry of flat manifolds with boundaries the resulting algorithm filters out potentially problematic distances between distant feature points based on the properties of the geodesics connecting those points and their relative distance to the boundary of the feature manifold thus avoiding an inherent limitation of the isomap algorithm since the proposed algorithm matches non local structures it is robust to strong noise we show experimental results demonstrating the advantages of the proposed approach over conventional dimensionality reduction techniques both global and local in nature

poschl teller paradoxes in the well known poschl teller trigonometric potential well a symmetric regularization x x ie of the impenetrable end point barriers is performed this leads to the four different solvable generalizations of the model as a byproduct the scheme clarifies certain apparent paradoxes encountered in the classically forbidden coupling regime

partial similarity of objects or how to compare a centaur to a horse similarity is one of the most important abstract concepts in human perception of the world in computer vision numerous applications deal with comparing objects observed in a scene with some a priori known patterns often it happens that while two objects are not similar they have large similar parts that is they are partially similar here we present a novel approach to quantify partial similarity using the notion of pareto optimality we exemplify our approach on the problems of recognizing non rigid geometric objects images and analyzing text sequences

analysis of two dimensional non rigid shapes analysis of deformable two dimensional shapes is an important problem encountered in numerous pattern recognition computer vision and computer graphics applications in this paper we address three major problems in the analysis of non rigid shapes similarity partial similarity and correspondence we present an axiomatic construction of similarity criteria for deformation invariant shape comparison based on intrinsic geometric properties of the shapes and show that such criteria are related to the gromov hausdorff distance next we extend the problem of similarity computation to shapes which have similar parts but are dissimilar when considered as a whole and present a construction of set valued distances based on the notion of pareto optimality finally we show that the correspondence between non rigid shapes can be obtained as a byproduct of the non rigid similarity problem as a numerical framework we use the generalized multidimensional scaling gmds method which is the numerical core of the three problems addressed in this paper

dynamic voronoi diagrams a new dynamizing technique is introduced whereby n point voronoi diagrams both closest and farthest point can be updated in o n time per insertion or deletion in the worst case general properties of these dynamic voronoi diagrams are explored including a storage deletion time trade off in addition their application to such problems as nearest neighbor search and the 2 minimum spanning circle problem is discussed

renormalization theoretic analysis of non equilibrium phase transitions i the becker doring equations with power law rate coefficients we study in detail the application of renormalization theory to models of cluster aggregation and fragmentation of relevance to nucleation and growth processes we investigate the becker d oring equations originally formulated to describe and analyse non equilibrium phase transitions and more recently generalized to describe a wide range of physicochemical problems in this paper we analyse how the systematic coarse graining renormalization of the becker d oring system of equations affects the aggregation and fragmentation rate coefficients we consider the case of power law size dependent cluster rate coefficients which we show lead to only three classes of system that require analysis coagulation dominated systems fragmentation dominated systems and those where coagulation and fragmentation are exactly balanced we analyse the late time asymptotics associated with each class

a symmetric green function for the non collinear magnetic multilayer symmetry properties of the green function in magnetic multilayers with non collinear magnetization of the layers are investigated on the basis of the transfer matrix method the green function symmetric with respect to permutation of its arguments is constructed it is shown how the boundary conditions can be imposed on this green function

the torus parametrization of quasiperiodic li classes the torus parametrization of quasiperiodic local isomorphism classes is introduced and used to determine the number of elements in such a class with special symmetries or inflation properties the method is explained in an illustrative fashion for some widely used tiling classes with golden mean rescaling namely for the fibonacci chain one dimensional the triangle and penrose patterns two dimensional and for kramer s and danzer s icosahedral tilings three dimensional we obtain a rather complete picture of the orbit structure within these classes and also discuss various general results

the generalized gabor scheme of image representation in biological and machine vision a scheme suitable for visual information representation in a combined frequency position space is investigated through image decomposition into a finite set of two dimensional gabor elementary functions gef the scheme is generalized to account for the position dependent gabor sampling rate oversampling logarithmic frequency scaling and phase quantization characteristic of the visual system comparison of reconstructed signal highlights the advantages of the generalized gabor scheme in coding typical bandlimited images it is shown that there exists a tradeoff between the number of frequency components used per position and the number of such clusters sampling rate utilized along the spatial coordinate

the farthest point strategy for progressive image sampling a new method of farthest point strategy fps for progressive image acquisition an acquisition process that enables an approximation of the whole image at each sampling stage is presented its main advantage is in retaining its uniformity with the increased density providing efficient means for sparse image sampling and display in contrast to previously presented stochastic approaches the fps guarantees the uniformity in a deterministic min max sense within this uniformity criterion the sampling points are irregularly spaced exhibiting anti aliasing properties comparable to those characteristic of the best available method poisson disk a straightforward modification of the fps yields an image dependent adaptive sampling scheme an efficient o n log n algorithm for both versions is introduced and several applications of the fps are discussed

design of optimal entropy constrained unrestricted polar quantizer for bivariate circularly symmetric sources this paper proposes an algorithm for the design of entropy constrained unrestricted polar quantizer ecupq for bivariate circularly symmetric sources the algorithm is globally optimal for the class of ecupqs with magnitude quantizer thresholds confined to a finite set the optimization problem is formulated as the minimization of a weighted sum of distortion and entropy and the proposed solution is based on modeling the problem as a minimum weight path problem in a certain weighted directed acyclic graph each graph edge corresponds to a possible magnitude quantizer bin and computing its weight involves solving another optimization problem we develop a fast strategy for evaluating all edge weights leading to a o k 2 textit kp mathrm max time solution algorithm where k is the size of the set of possible magnitude thresholds and p mathrm max is the maximum number of phase levels the practical performance of the proposed algorithm is assessed for a bivariate circularly symmetric gaussian source at rates ranging from 0 5 to 6 bits sample our results demonstrate that the proposed approach achieves performance very close to the asymptotically optimal ecupq at all rates while at low rates it significantly outperforms all previous upq schemes notably peak improvement of 0 755 db can be achieved for rates below 2 5

large time behavior of discrete velocity boltzmann equations we study the asymptotic behavior of equations representing one dimensional motions in a fictitious gas with a discrete set of velocities the solutions considered have finite mass but arbitrary amplitude with certain assumptions every solution approaches a state in which each component is a traveling wave without interaction the techniques are similar to those in an earlier treatment of the broadwell model 1

three attractive osculating walkers and a polymer collapse transition consider n interacting lock step walkers in one dimension which start at the points 0 2 4 2 n 1 and at each tick of a clock move unit distance to the left or right with the constraint that if two walkers land on the same site their next steps must be in the opposite direction so that crossing is avoided when two walkers visit and then leave the same site an osculation is said to take place the space time paths of these walkers may be taken to represent the configurations of n fully directed polymer chains of length t embedded on a directed square lattice if a weight is associated with each of the i osculations the partition function is z t n lambda sum nolimits i 0 left lfloor tfrac n 1 t 2 right rfloor z t i n lambda i where z n t i is the number of t step configurations having i osculations when 0 the partition function is asymptotically equal to the number of vicious walker star configurations for which an explicit formula is known the asymptotics of such configurations was discussed by fisher in his boltzmann medal lecture also for n 2 the partition function for arbitrary is easily obtained by fisher s necklace method for n 2 and 0 the only exact result so far is that of guttmann and voge who obtained the generating function g n lambda u equiv sum nolimits t 0 infty z t n lambda u t for 1 and n 3 the main result of this paper is to extend their result to arbitrary by fitting computer generated data it is conjectured that z 3 t satisfies a third order inhomogeneous difference equation with constant coefficients which is used to obtain g n lambda u frac lambda 3 lambda 2 lambda 12 5 lambda lambda 2 u 2 lambda 3 u 2 2 lambda 4 lambda 2 u 2 1 text c 2u lambda 2 lambda 2 u lambda 1 4 lambda u 4 lambda 2 u 2 where c u tfrac 1 sqrt 1 4u 2u the generating function for catalan numbers the nature of the collapse transition which occurs at 4 is discussed and extensions to higher values of n are considered it is argued that the position of the collapse transition is independent of n

design of general entropy constrained successively refinable unrestricted polar quantizer this paper presents an algorithm for the optimal design of general entropy constrained successively refinable unrestricted polar quantizer i e with arbitrary number l of refinement levels for bivariate circularly symmetric sources the optimization problem is formulated as the minimization of a weighted sum of distortions and entropies for the scenario where the magnitude quantizers thresholds are confined to a predefined finite set the proposed solution algorithm is globally optimal it involves l stages where each stage corresponds to an unrestricted polar quantizer upq level and includes solving the minimum weight path problem for multiple node pairs in a series of weighted directed acyclic graphs additionally we derive an upper bound p l max l in 1 l on the possible number of phase levels in any phase quantizer of the l th level upq which grows linearly with l the time complexity of the proposed approach is o l 2 k 3 p 1 max where k is the cardinality of the predefined set of possible magnitude thresholds finally the experimental results for l 3 demonstrate the effectiveness in practice of the proposed scheme

construction of iso contours bisectors and voronoi diagrams on triangulated surfaces in the research of computer vision and machine perception 3d objects are usually represented by 2 manifold triangular meshes m in this paper we present practical and efficient algorithms to construct iso contours bisectors and voronoi diagrams of point sites on m based on an exact geodesic metric compared to euclidean metric spaces the voronoi diagrams on m exhibit many special properties that fail all of the existing euclidean voronoi algorithms to provide practical algorithms for constructing geodesic metric based voronoi diagrams on m this paper studies the analytic structure of iso contours bisectors and voronoi diagrams on m after a necessary preprocessing of model m practical algorithms are proposed for quickly obtaining full information about iso contours bisectors and voronoi diagrams on m the complexity of the construction algorithms is also analyzed finally three interesting applications surface sampling and reconstruction 3d skeleton extraction and point pattern analysis are presented that show the potential power of the proposed algorithms in pattern analysis