generalized practical stability analysis of filippov type systems in this paper we study the generalized practical stability and the totally generalized practical stability of filippov type piecewise smooth systems we also apply these properties to a brake model of bike to study its practical stability some numerical computations are presented to illustrate our theories

a monte carlo method for series expansions the authors describe a simple and general algorithm to calculate series expansions in enumeration problems to large orders approximately by a monte carlo method it can be used to generate unbiased samples in cluster studies e g linear or branched polymers random surfaces etc in any dimension they calculate the number of site animals of size n on the square lattice for n or 50 and their average size to better than 1 accuracy

melnikov method for discontinuous planar systems abstract this paper treats the occurrence of homoclinic solutions in planar systems with discontinuous right hand side more precisely we deal with a t periodic perturbed system such that the unperturbed system is an autonomous possessing homoclinic orbit by means of the so called non smooth melnikov function there is shown the existence of a homoclinic solution for a perturbed system the non smooth melnikov function is derived and the method of how to find it in concrete problems is also introduced

eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

two dimensional percolation logarithmic corrections to the critical behaviour from series expansions analyses several extant series for the mean cluster size the zeroth moment of the pair connectedness and the percolation probability for bond and site percolation on two dimensional lattices with a view to detecting possible logarithmic corrections the logarithmic correction exponent z is found to be in the range 0 or z or 0 15 and our analysis also provides some new information about the critical exponents gamma and beta

algebraic feature extraction for image recognition based on an optimal discriminant criterion abstract a novel algebraic feature extraction method for image recognition is presented the main difference between the present method and any other existing algebraic feature extraction method is that the present method uses an optimal discriminant criterion to extract algebraic features for the given training image samples a set of optimal discriminant projection vectors is calculated according to a generalized fisher criterion function on the basis of the optimal discriminant projection vector the projective feature vectors of an image i e algebraic features are extracted by projecting the image onto all optimal discriminant projection vectors the method of calculating the set of optimal discriminant projection vectors is discussed a minimum distance classifier is also proposed for classifying projective feature vectors experimental results showed that the present method has good recognition performance an important conclusion about the present method is that the foley sammon optimal set of discriminant vectors is a special case of the set of optimal discriminant projection vectors

branched polymers exact enumeration study of three dimensional lattice animals classified by valence distribution the partial generating function method is applied to the enumeration of lattice animals classified according to their valence distribution this detailed information allows one to study the effects of the number and nature of branch points on the properties of branched polymers several series analysis techniques are applied to the data particular attention is given to the effects of correction to scaling terms

jumps of the fundamental solution matrix in discontinuous systems and applications abstract this paper deals with differential equations with discontinuous right hand side the concept of a solution for a discontinuous system is defined on the basis of differential inclusions using filippov s method we study in particular the behaviour of solutions crossing a discontinuity surface transversally a formula characterizing jumps of the fundamental solution matrix is derived as an application of it the concept of poincare mapping is defined for such systems

stochastic models for closed boundary analysis representation and reconstruction the analysis of closed boundaries of arbitrary shapes on a plane is discussed specifically the problems of representation and reconstruction are considered a one to one correspondence between the given closed boundary and a univariate or multivariate sequence of real numbers is set up univariate or multivariate circular autoregressive models are suggested for the representation of the sequence of numbers derived from the closed boundary the stochastic model representing the closed boundary is invariant to transformations like sealing translation choice of starting point and rotation over angles that are multiples of 2 pi n where n is the number of observations methods for estimating the unknown parameters of the model are given and a decision rule for choosing the appropriate number of coefficients is included constraints on the estimates are derived so that the estimates are invariant to the transformations of the boundaries the stochastic model enables the reconstruction of a dosed boundary using fft algorithms results of simulations are included and the application to contour coding is discussed

caliper diameter of branched polymers the authors report analyses of exact numerical data for the spanning diameter of two dimensional lattice animals up to size n 17 estimates of the exponent nu are consistent with previous studies the leading correction to scaling has an exponent sigma approximately nu which does not result from irrelevant variable effects interpretation of this correction as a surface term is proposed

punctured polygons and polyominoes on the square lattice we use the finite lattice method to count the number of punctured staircase and self avoiding polygons with up to three holes on the square lattice new or radically extended series have been derived for both the perimeter and area generating functions we show that the critical point is unchanged by a finite number of punctures and that the critical exponent increases by a fixed amount for each puncture the increase is 1 5 per puncture when enumerating by perimeter and 1 0 when enumerating by area a refined estimate of the connective constant for polygons by area is given a similar set of results is obtained for finitely punctured polyominoes the exponent increase is proved to be 1 0 per puncture for polyominoes

superuniversal spectral dimension for dilute branched polymers the authors introduce the problem of random walks on lattice animals dilute branched polymers and calculate the spectral dimension ds of animals in two and three dimensions by using a two parameter position space renormalisation group method this problem which is a generalisation of the problem of the ant in the labyrinth has been independently proposed and investigated by wilke et al 1984 the spectral dimension is given by ds 2da dw where da is the fractal dimension of the lattice animal and dw the fractal dimension of the random walk on the lattice animal the results indicate that ds may be a superuniversal quantity i e its value is independent of dimension moreover the authors find ds to be close to 4 3 which is the spectral dimension of the largest percolation cluster at the percolation threshold pc as conjectured by alexander and orbach 1982 since both lattice animals and the largest percolation cluster at pc have a homogeneous interior structure the results suggest that the spectral dimension of all such fractals may equal 4 3

on the use of singular value decomposition and decimation in discrete time band limited signal extrapolation the problem of extrapolating a band limited signal in discrete time is viewed as one of solving an underdetermined system of linear equations choosing the minimum norm least squares mnls solution is one criterion for singling out an extrapolation from all the possible solutions to the linear system use of the moore penrose inverse yields the mnls solution and singular value decomposition svd provides a means for implementing the moore penrose inverse an expression for the mean square error incurred in solving a linear system via svd is derived this can be used to estimate the number of singular values needed to form the inverse the error expression also indicates that decimation can be applied in the extrapolation problem to reduce the high computational cost of svd without degrading the extrapolation the results developed for the one dimensional case are extended to higher dimensions examples of the svd approach to extrapolation are given along with examples using other extrapolation techniques for comparison the svd approach compares favorably with known mnls extrapolation methods

learning discriminative singular value decomposition representation for face recognition abstract face representation is a critical step in face recognition recently singular value decomposition svd based representation methods have attracted researchers attentions for their power of alleviating the facial variations the svd representation reveals that the svd basis set is important for the recognition purpose and the corresponding singular values svs are regulated to form a more effective representation image however there exists a common problem in the existing svd based representation methods they all empirically make a rule to regulate the svs which is obviously not optimal in theory to address this problem in this paper we propose a novel method named learning discriminative singular value decomposition representation ldsvdr for face recognition we build an individual svd basis set for each image and then learn a common set of svs by taking account of the information in the basis sets according to a discriminant criterion across the training images the proposed model is solved by sequential quadratic programming sqp method extensive experiments are conducted on three popular face databases and the results demonstrate the effectiveness of our method when dealing with variations of illumination occlusion disguise and face sketch recognition task

a new simulation of branched polymers the scanning method for the simulation of linear chain is extended to general models of branched polymers without loops a branched chain grows in time namely a number of steps from the origin therefore i in contrast to other simulation techniques which are of a relaxation type the chains are statistically independent and the statistical error can reliably be estimated ii the probability of a chain is known and hence the entropy and iii the scanning construction enables one to study geometrical properties which depend on time for self avoiding trees on a square lattice the author obtains the relatively accurate estimates for the static critical exponents nu 0 640 or 0 004 and theta 1 003 or 0 02 and for the connective constant mu 5 1419 or 0 003 the author also obtains critical exponents gamma t approximately 1 26 and nu t approximately 0 83 which characterise the growth in time of the number of bonds and the gyration radius respectively application of the scanning method to more complex branched polymers is discussed

cluster size distribution above the percolation threshold discusses how the cluster size distribution above the percolation threshold is related to the existence of metastable states of the potts model the authors thus find that the average number of clusters per site containing n sites is given by c n approximately n theta exp constant n1 1 d where d is the dimensionality of the lattice the exponent theta is given for a range of values of d

optimal discriminant plane for a small number of samples and design method of classifier on the plane abstract in a previous work zi quan hong and jing yu yang minimum distance classifier on the optimal discriminant plane we suggested and derived a method for constructing classifier on the optimal discriminant plane using minimum distance criteria in this paper the problem of solving optimal discriminant plane for a small number of samples is discussed which is based on the above paper by the same authors in the case of a small number of samples generalized eigenequation ax bx established for a large number of samples usually has no solution because within class scatter matrix is singular to obtain the solution of the generalized eigenequation a new method is suggested in which the singular value perturbation is added to the within class scatter matrix such that the matrix becomes a nonsingular matrix therefore the generalized eigenequation can be solved using existing algorithms we proved that the generalized eigenequations on the optimal discriminant plane are stable in respect of eigenvalues and the generalized eigenvectors are indeed the optimal discriminant directions if the perturbation is subject to some certain conditions the experimental results have shown that our method works well and the minimum distance classifier on the optimal discriminant plane can be constructed with high performance even in the case of a small number of samples

cubic bezier approximation of a digitized curve in this paper we present an efficient technique for piecewise cubic bezier approximation of digitized curve an adaptive breakpoint detection method divides a digital curve into a number of segments and each segment is approximated by a cubic bezier curve so that the approximation error is minimized initial approximated bezier control points for each of the segments are obtained by interpolation technique i e by the reverse recursion of de castaljau s algorithm two methods two dimensional logarithmic search algorithm tdlsa and an evolutionary search algorithm esa are introduced to find the best fit bezier control points from the approximate interpolated control points esa based refinement is proved to be better experimentally experimental results show that bezier approximation of a digitized curve is much more accurate and uses less number of points compared to other approximation techniques

fast and efficient second order method for training radial basis function networks this paper proposes an improved second order iso algorithm for training radial basis function rbf networks besides the traditional parameters including centers widths and output weights the input weights on the connections between input layer and hidden layer are also adjusted during the training process more accurate results can be obtained by increasing variable dimensions initial centers are chosen from training patterns and other parameters are generated randomly in limited range taking the advantages of fast convergence and powerful search ability of second order algorithms the proposed iso algorithm can normally reach smaller training testing error with much less number of rbf units during the computation process quasi hessian matrix and gradient vector are accumulated as the sum of related sub matrices and vectors respectively only one jacobian row is stored and used for multiplication instead of the entire jacobian matrix storage and multiplication memory reduction benefits the computation speed and allows the training of problems with basically unlimited number of patterns several practical discrete and continuous classification problems are applied to test the properties of the proposed iso training algorithm

on the number of lattice animals embeddable in the square lattice enumeration of lattice animals embeddable in a square lattice has been extended to 24 cell animals by redelmeier 1981 it is shown that the number of animals per site an approximately 0 317 4 0626 nn 1 exp 0 465 n 0 87 to a high degree of accuracy

low concentration series in general dimension we discuss recent work on the development and analysis of low concentration series for many models the recent breakthrough in the extremely efficient no free end method of series generation facilitates the derivation of 15th order series for multiple moments in general dimension the 15th order series have been obtained for lattice animals percolation and the edwards anderson ising spin glass in the latter cases multiple moments have been found from complete graph tables through to 13th order general dimension 13th order series have been derived for the resistive susceptibility the moments of the logarithms of the distribution of currents in resistor networks and the average transmission coefficient in the quantum percolation problem 11th order series have been found for several other systems including the crossover from animals to percolation the full resistance distribution nonlinear resistive susceptibility and current distribution in dilute resistor networks diffusion on percolation clusters the dilute ising model dilute antiferromagnet in a field and random field ising model and self avoiding walks on percolation clusters series for the dilute spin 1 2 quantum heisenberg ferromagnet are in the process of development analysis of these series gives estimates for critical thresholds amplitude ratios and critical exponents for all dimensions where comparisons are possible our series results are in good agreement with bothe expansion results near the upper critical dimension and with exact results when available in low dimensions and are competitive with other numerical approaches in intermediate realistic dimensions

generating random percolation clusters a fortran 77 program generator f is presented to generate random percolation clusters cluster sizes up to n 500 pixels can be generated random numbers are generated using the manly random number generator and clock time a second fortran 77 program cluster f enables the identification of the different clusters out of a set of randomly generated clusters using cluster f the 63 possible different clusters for n 5 are selected the percolation clusters are generated and presented using a matrix approach

algebraic feature extraction of image for recognition abstract the extraction of image features is one of the fundamental tasks in image recognition up until now there have been several kinds of features to be used for the purpose of image recognition as follows 1 visual features 2 statistical features of pixel 3 transform coefficient features in addition there is another kind of feature which the author believes is very useful i e 4 algebraic features which represent intrinsic attributions of an image singular values sv of image are this kind of feature in this paper we prove that sv feature vector has some important properties of algebraic and geometric invariance and insensitiveness to noise these properties are very useful for the description and recognition of images as an example sv feature vector is used for the problem of recognizing human facial images in this paper using sv feature vector samples of facial images a normal pattern bayes classification model based on sammon s optimal descriminant plane is constructed the experimental result shows that sv feature vector has good performance of class separation

cluster diversity and entropy on the percolation model the lattice animal identification algorithm we present an algorithm to identify and count different lattice animals la s in the site percolation model this algorithm allows a definition of clusters based on the distinction of cluster shapes in contrast with the well known hoshen kopelman algorithm in which the clusters are differentiated by their sizes it consists in coding each unit cell of a cluster according to the nearest neighbors nn and ordering the codes in a proper sequence in this manner a la is represented by a specific code sequence in addition with some modification the algorithm is capable of differentiating between fixed and free la s the enhanced hoshen kopelman algorithm j hoshen m w berry and k s minser phys rev e 56 1455 1997 is used to compose the set of nn code sequences of each cluster using monte carlo simulations on planar square lattices up to 2000x2000 we apply this algorithm to the percolation model we calculate the cluster diversity and cluster entropy of the system which leads to the determination of probabilities associated with the maximum of these functions we show that these critical probabilities are associated with the percolation transition and with the complexity of the system

scaling and critical probabilities for cluster size and la diversity on randomly occupied square lattices using monte carlo simulations we report the behaviour of the total number of clusters the cluster size diversity and the lattice animals la diversity on randomly occupied square lattices the critical probability associated with the maximum of these variables is determined in comparison with the percolation probability pc our simulations indicate that pc and the critical probability of the maximum cluster size diversity pc d s max occur at the same point as indicated in a previous paper tsang i r and tsang i j 1997 j phys a math gen 30 l239 the probability for the maximum number of clusters is obtained at a lower value pc n max 0 27 0 01 we describe the cluster identification algorithm used to count the different la and determined the critical probability for the maximum la diversity pc d f max 0 45 0 02 we derive the exponents characterizing the relation between d s max d f max and n max and several scaling relations between the variables measured the lattice size and the probability of occupation p in addition we show the scaling behaviour of la diversity versus cluster size diversity for each value of p

enumerating 2d percolation series by the finite lattice method theory this paper describes a transfer matrix algorithm for enumeration of series of interest in percolation on the square lattice it allows efficient generation of both low temperature and high temperature expansions as well as the combinatorially interesting enumeration of undirected animals by area or perimeter with moments of the other property

classification of partial 2 d shapes using fourier descriptors we present a method for the classification of 2 d partial shapes using fourier descriptors we formulate the problem as one of estimating the fourier descriptors of the unknown complete shape from the observations derived from an arbitrarily rotated and scaled shape with missing segments the method used for obtaining the estimates of the fourier descriptors minimizes a sum of two terms the first term of which is a least square fit to the given data subject to the condition that the number of missing boundary points is not known and the second term is the perimeter2 area of the unknown shape experiments with synthetic and real boundaries show that estimates closer to the true values of fourier descriptors of complete boundaries are obtained also classification experiments performed using real boundaries indicate that reasonable classification accuracies are obtained even when 20 30 percent of the data is missing

alternative area perimeter ratios for measurement of 2d shape compactness of habitats area perimeter ratios are often used to quantify 2d shape compactness shape compactness is of main importance to evaluate the effect of external disturbance on natural habitats reference values a m i n p a m a x p p m i n a p m a x a for area a and perimeter p are defined and proven the calculation of these reference values is based on the characteristics of the object studied and on pixel geometry the cases for 4 and 8 connectivity are discussed using these references alternative area perimeter ratios are composed examples are elaborated to illustrate the use of the indices and their performance

on two dimensional percolation we present new series data for both high and low density bond and site percolation on the square lattice the series have been obtained by the finite lattice method and in all cases extend pre existing series an analysis of these series gives refined estimates of critical points critical exponents and amplitudes for bond and site animals and for the percolation probability and mean size exponents

convergence and extrapolation in finite size scaling renormalization abstract finite size renormalization technique is studied by examining a test model which is exactly solvable and the problem of lattice animals and self avoiding walks bulk estimates of the leading irrelevant rg eigenvalue are found and compared with independent estimates from finite size data we introduce an extrapolation technique which is applicable to non monotonic sequences of exponent approximants

on image analysis by the methods of moments various types of moments have been used to recognize image patterns in a number of applications a number of moments are evaluated and some fundamental questions are addressed such as image representation ability noise sensitivity and information redundancy moments considered include regular moments legendre moments zernike moments pseudo zernike moments rotational moments and complex moments properties of these moments are examined in detail and the interrelationships among them are discussed both theoretical and experimental results are presented

a new monte carlo simulation for two models of self avoiding lattice trees in two dimensions by means of a new monte carlo sampling of a grand canonical ensemble we verify universality for the critical exponents and of two models of lattice trees constrained to be self avoiding on sites or on bonds the attrition constants are also obtained this algorithm a generalization of that recently proposed by berretti and sokal for random walks appears to optimize the critical slowing down in the scaling region systematic and statistical errors are carefully estimated

critical exponents and corrections to scaling for bond trees in two dimensions the author has analysed the newly obtained series of the radius of gyration rn and the number of clusters nn for n bond trees i e branch polymers without loops on the square n or 14 and triangular n or 11 lattices to estimate the critical parameters respective estimates of the exponents nu and theta for rn and nn are consistent with the corresponding values for lattice animals while the correction to scaling exponent delta 1 is inconsistent with the animal value in addition delta 1 has different values for rn delta 1 0 635 and nn delta 1 1 3 for bond trees he has also estimated an exponent delta characterising the density distribution delta 2 69 for the triangular lattice

spatial aggregation of two dimensional objects in raster data structures raster data structures are characterized by pixel geometry and resolution a method is proposed to reduce resolution to a minimum using spatial aggregation without information loss the method is based on a matrix approach and developed for a two dimensional spatial object perimeter measures and fractal dimension are shown not to be invariant to spatial aggregation

identification of actors drawn in ukiyoe pictures abstract this paper presents the development of line image keywords for the identification of actors drawn in japanese traditional painting pictures known as ukiyoe pictures the system is based on visual features of the face from the image database files and is organized as a set of classifiers whose outputs are integrated after a normalization step line profile from the picture has been extracted in this investigation and has been approximated by bezier curves a learning algorithm has been developed to obtain the control points at high accuracy a new curve matching method has been developed based on the feature points rather than the corresponding points this method can automatically fit a set of data points with piecewise geometrically continuous third order bezier curves last of all a new approach for distance calculation namely apple node distance has been introduced here for similarity calculation in image retrieval systems the computation of similarity between curves has been established on the basis of this apple node distance the effectiveness of our method has been confirmed through computer simulation the method developed here can be expanded to one of three dimensional shape analyzing tools