are grades of membership probabilities abstract a small sample is given of the difficulties with present day fuzzy set theory with respect to the requirements of a scientific theory and a summary of some probabilistic interpretations of grades of membership to be found in the literature the tee model for grades of membership is then suggested instead of starting out from mathematical postulates such as the assumed max and min operations for or and and the tee model uses a semantic physio logical psycho logical starting point by investigating the possibilities which a person has for assigning linguistic labels and partial grades of membership in a meaningful way the assignment of partial grades of membership is explained by the assumption that humans have the ability to take errors of observation and intersubject differences into consideration a membership value uex is identified with the subject s estimate of the probability that the label e g tall would be assigned to an object of exact attribute value uex in a natural language situation this situation being a labeling or a yes no one in which at least one of three possible sources of uncertainty is present almost all the accepted formulas of fuzzy set theory as well as the shapes of the grade of membership curves are then derived instead of having to be postulated however the derived formulas for or and and reduce to the max and min operations only in a number of special cases in another special case they reduce to the summation and the zero operation respectively the generally valid formulas are presented

higher order method for singular boundary value problems by using spline function abstract in problems of physics and engineering we often come across singular boundary value problems which cannot be solved by the usual numerical methods special methods for solving such problems have been developed these methods lead to banded systems linear and non linear depending upon the nature of boundary value problem in this paper we discuss the construction of a spline function for a class of singular two point boundary value problems x x u f x u 0 x 1 u 0 a u 1 b five point finite difference method using the above splines is obtained it is shown to be order h4 convergent for all 0 1 the method is illustrated computationally

a geometrical fuzzy clustering based solution to glottal wave estimation accurate estimation of the glottal waveform gw is required for purposes such as natural speech synthesis speaker recognition physiological speech processing etc most methods available for gw estimation are based on inverse filtering of the speech signal through the vocal tract and they all suffer from inaccuracies due to incorrect assumptions the method for gw estimation developed in the present study is based on fuzzy clustering of quasi linear geometrical substructures represented within the signal shifts hyperspace algorithms for estimation of the driving function to the vocal tract are presented and evaluated on simulated and real data comparison of the fuzzy clustering based method with the psiaif and wong s closed phase algorithms shows that the present method is superior with respect to both the gw estimation and determination of gw event time instants

patterns in eigenvalues the 70th josiah willard gibbs lecture typical large unitary matrices show remarkable patterns in their eigenvalue distribution these same patterns appear in telephone encryption the zeros of riemann s zeta function a variety of physics problems and in the study of toeplitz operators this paper surveys these applications and what is currently known about the patterns

a harmonic retrieval framework for discontinuous motion estimation motion discontinuities arise when there are occlusions or multiple moving objects in the scene that is imaged conventional regularization techniques use smoothness constraints but are not applicable to motion discontinuities in this paper we show that discontinuous or multiple motion estimation can be viewed as a multicomponent harmonic retrieval problem from this viewpoint a number of established techniques for harmonic retrieval ran be applied to solve the challenging problem of discontinuous or multiple motion compared with existing techniques the resulting algorithm is not iterative which not only implies computational efficiency but also obviates concerns regarding convergence or local minima it also adds flexibility to spatio temporal techniques which have suffered from lack of explicit modeling of discontinuous motion experimental verification of our framework on both synthetic data as well as real image data is provided

parameter estimation of chirp signals the problem of the parameter estimation of chirp signals is addressed several closely related estimators are proposed whose main characteristics are simplicity accuracy and ease of online or offline implementation for moderately high signal to noise ratios they are unbiased and attain the cramer rao bound monte carlo simulations verify the expected performance of the estimators it should be easy to extend this approach to signals having polynomials of any degree in the exponent all the derivations will be done under the assumption that the signal to noise ratio is sufficiently high

motion estimation in the frequency domain using fuzzy c planes clustering a previous work explicitly models the discontinuous motion estimation problem in the frequency domain where the motion parameters are estimated using a harmonic retrieval approach the vertical and horizontal components of the motion are independently estimated from the locations of the peaks of respective periodogram analyses and they are paired to obtain the motion vectors using a procedure proposed by chen giannakis nandhakumar see ieee trans image processing vol 7 p 1242 56 1998 in this paper we present a more efficient method that replaces the motion component pairing task and hence eliminates the problems of the pairing method described by chen et al the method described in this paper uses the fuzzy c planes fcp clustering approach to fit planes to three dimensional 3 d frequency domain data obtained from the peaks of the periodograms experimental results are provided to demonstrate the effectiveness of the proposed method

a study of parameter values for a mahalanobis distance fuzzy classifier a supervised mahalanobis distance fuzzy classifier and the related fuzzy c means clustering algorithm requires the a priori selection of a weighting parameter called the fuzzy exponent guidance in the existing literature on an appropriate value is not definitive this paper attempts to rigorously justify previous experimental findings on suitable values for this fuzzy exponent using the criterion that fuzzy set memberships reflect class proportions in the mixed pixels of a remotely sensed image

technical communique identification of dynamical systems with a robust interval fuzzy model in this paper we present a new method of interval fuzzy model identification the method combines a fuzzy identification methodology with some ideas from linear programming theory on a finite set of measured data an optimality criterion that minimizes the maximal estimation error between the data and the proposed fuzzy model output is used the idea is then extended to modelling the optimal lower and upper bound functions that define the band that contains all the measurement values this results in a lower and an upper fuzzy model or a fuzzy model with a set of lower and upper parameters the model is called the interval fuzzy model infumo the method can be used when describing a family of uncertain nonlinear functions or when the systems with uncertain physical parameters are observed we believe that the fuzzy interval model can be very efficiently used especially in fault detection and in robust control design

fuzzy shell clustering algorithms in image processing fuzzy c rectangular and 2 rectangular shells objective function based clustering has been generalized recently to detect contours of circles and ellipses or even hyperbolas in a set of binary data vectors although there are special algorithms to discover lines the detection of rectangles needs further treatment a simple line detection algorithm is not sufficient for rectangles since for identifying four lines as one rectangle additional information such as the length of the lines and whether they are parallel or meet at a right angle is necessary in this paper a special fuzzy shell clustering algorithm for rectangular contours is developed the principal idea behind it can be generalized for other polygons so we also derive an algorithm that is capable of detecting rectangles and other polygons as well as approximating circles ellipses and lines

comments on discrete chirp fourier transform and its application to chirp rate estimation with reply this comment points out that the sample rate of the discrete chirp fourier transform dcft proposed by xia see ibid vol 48 p 3122 33 2000 is not sufficient to avoid severe picket fence effect and causes some restrictions for its practical applications by increasing the sample rate and modifying the dcft definition a new robust dcft is proposed xia see ibid vol 50 no 12 p 3116 2002 replies by first correcting an error on the analog to discrete parameter conversions of a chirp signal xia also add that when the chirp rate detection resolution is increased it is more robust to the chirp rate error on the other hand what is sacrificed by doing so is that the magnitudes of the sidelobes of the transform are increased which may limit its capability of detecting chirps in a multicomponent or low snr signal therefore which dcft needs to be used has to depend on the practical application

a uniform mesh finite difference method for a class of singular two point boundary value problems a new finite difference method based on uniform mesh is given for the weakly singular two point boundary value problem x alpha y f x y y 0 a y 1 b 0 alpha 1 under quite general conditions on f and f we show that our present method based on uniform mesh provides o h 2 convergent approximations for all alpha in 0 1 our method is based on one evaluation of f and for alpha 0 it reduces to the classical second order method for y f x y

a parametric model for fusing heterogeneous fuzzy data presented is a model that integrates three data types numbers intervals and linguistic assessments data of these three types come from a variety of sensors one objective of sensor fusion models is to provide a common framework for data integration processing and interpretation that is what our model does we use a small set of artificial data to illustrate how problems as diverse as feature analysis clustering cluster validity and prototype classifier design can all be formulated and attacked with standard methods once the data are converted to the generalized coordinates of our model the effects of reparameterization on computational outputs are discussed numerical examples illustrate that the proposed model affords a natural way to approach problems which involve mixed data types

powers of large random unitary matrices and toeplitz determinants we study the limiting behavior of tr u k n where u is an n x n random unitary matrix and k n is a natural number that may vary with n in an arbitrary way our analysis is based on the connection with toeplitz determinants the central observation of this paper is a strong szego limit theorem for toeplitz determinants associated to symbols depending on n in a particular way as a consequence of this result we find that for each fixed m n the random variables tru k j n min k j n n j 1 m converge to independent standard complex normals

estimation of multiple 2 d uniform motions by slide subspace based line detection a technique is proposed for estimating the parameters of two dimensional 2 d uniform motion of multiple moving objects in a scene based on long sequence image processing and the application of a multiline fitting algorithm plots of the vertical and horizontal projections versus frame number give new images in which uniformly moving objects are represented by skewed band regions with the angles of the skew from the vertical being a measure of the velocities of the moving objects for example vertical bands will correspond to objects with zero velocity an algorithm called subspace based line detection slide can be used to efficiently determine the skew angles slide exploits the temporal coherence between the contributions of each of the moving patterns in the frame projections to enhance and distinguish a signal subspace that is defined by the desired motion parameters a similar procedure can be used to determine the vertical velocities some further steps must then be taken to properly associate the horizontal and vertical velocities

unsupervised optimal fuzzy clustering this study reports on a method for carrying out fuzzy classification without a priori assumptions on the number of clusters in the data set assessment of cluster validity is based on performance measures using hypervolume and density criteria an algorithm is derived from a combination of the fuzzy k means algorithm and fuzzy maximum likelihood estimation the unsupervised fuzzy partition optimal number of classes algorithm performs well in situations of large variability of cluster shapes densities and number of data points in each cluster the algorithm was tested on different classes of simulated data and on a real data set derived from sleep eeg signal

estimation of motions in color image sequences using hypercomplex fourier transforms although the motion estimation problem has been extensively studied most of the proposed estimation approaches deal mainly with monochrome videos the most usual way to apply them also in color image sequences is to process each color channel separately a different more sophisticated approach is to process the color channels in a ldquoholisticrdquo manner using quaternions as proposed by ell and sangwine in this paper we extend standard spatiotemporal fourier based approaches to handle color image sequences using the hypercomplex fourier transform we show that translational motions are manifested as energy concentration along planes in the hypercomplex 3d fourier domain and we describe a methodology to estimate the motions based on this property furthermore we compare the three channels separately approach with our approach and we show that the computational effort can be reduced by a factor of 1 3 using the hypercomplex fourier transform also we propose a simple accompanying method to extract the moving objects in the hypercomplex fourier domain our experimental results on synthetic and natural images verify our arguments throughout the paper

a fourth order spline method for singular two point boundary value problems this paper describes a new fourth order spline approximation method for the class of singular two point boundary value problems y frac alpha x y f x y 0 0 x 1 y 0 0 y 1 a for all alpha geqslant 1

a frequency domain algorithm for multiframe detection and estimation of dim targets an algorithm for detecting moving targets by imaging sensors and estimating their trajectories is proposed the algorithm is based on directional filtering in the frequency domain using a bank of filters for all possible target directions the directional filtering effectively integrates the target signal resulting in an improved signal to noise ratio working in the frequency domain facilitates a considerable reduction in computational requirements compared to time domain algorithms the algorithm is described in detail and its false alarm and detection probabilities are analyzed

a new variational approach for restoring images with multiplicative noise this paper proposes a novel variational model for restoration of images corrupted with multiplicative noise it combines a fractional order total variational filter with a high order pde laplacian norm the combined approach is able to preserve edges while avoiding the blocky effect in smooth regions this strategy minimizes a certain energy subject to a fitting term derived from a maximum a posteriori map semi implicit gradient descent scheme is applied to efficiently finding the minimizer of the proposed functional to improve the numerical results we opt for an adaptive regularization parameter selection procedure for the proposed model by using the trial and error method the existence and uniqueness of a solution to the proposed variational model is established in this study parameter dependence is also discussed experimental results demonstrate the effectiveness of the proposed model in visual improvement as well as an increase in the peak signal to noise ratio comparing to corresponding pde methods

on the convergence of finite difference methods for weakly regular singular boundary value problems the second order finite difference methods m 1 based on a non uniform mesh and m 2 based on an uniform mesh developed by chawla and katti finite difference methods and their convergence for a class of singular two point boundary value problems numer math 39 1982 341 350 for weakly regular singular boundary value problems p x y f x y 0

on the galerkin and collocation methods for two point boundary value problems using sinc bases this paper presents a study of the performance of the collocation and galerkin methods using sinc basis functions for solving linear and nonlinear second order two point boundary value problems the two methods have the linear systems solved by the q r method and have the nonlinear systems solved by newton s method this study shows that the collocation method performs better than the galerkin method for the cases considered

detection and separation of ring shaped clusters using fuzzy clustering a new fuzzy clustering algorithm designed to detect and characterize ring shaped clusters and combinations of ring shaped and compact spherical clusters has been developed this fkr algorithm includes automatic search for proper initial conditions in the two cases of concentric and excentric intersected combinations of clusters validity criteria based on total fuzzy area and fuzzy density are used to estimate the optimal number of substructures in the data set the fkr algorithm has been tested on a variety of simulated combinations of ring shaped and compact spherical clusters and its performance proved to be very good both in identifying the input shapes and in recovering the input parameters application of the fkr algorithm to an mri image of the heart s left ventricle was used to investigate the possibility of using this algorithm as an aid in image processing

geometrical fuzzy clustering algorithms fuzzy clustering algorithms are a basic tool for cluster analysis among these the geometrical fuzzy clustering algorithms are used when the clustering problem can be viewed as trying to find linear or ellipsoidal concentrations in data this paper provides a theoretical framework in which currently used geometrical fuzzy clustering algorithms become special cases also a family of functions called feasible are defined which can be used to construct such algorithms and convergence results are obtained

discrete chirp fourier transform and its application to chirp rate estimation the discrete fourier transform dft has found tremendous applications in almost all fields mainly because it can be used to match the multiple frequencies of a stationary signal with multiple harmonics in many applications wideband and nonstationary signals however often occur one of the typical examples of such signals is chirp type signals that are usually encountered in radar signal processing such as synthetic aperture radar sar and inverse sar imaging due to the motion of a target the radar return signals are usually chirps and their chirp rates include the information about the target such as the location and the velocity in this paper we study discrete chirp fourier transform dcft which is analogous to the dft besides the multiple frequency matching similar to the dft the dcft can be used to match the multiple chirp rates in a chirp type signal with multiple chirp components we show that when the signal length n is prime the magnitudes of all the sidelobes of the dcft of a quadratic chirp signal are 1 whereas the magnitude of the mainlobe of the dcft is spl radic n with this result an upper bound for the number of the detectable chirp components using the dcft is provided in terms of signal length and signal and noise powers we also show that the n point dcft performs optimally when n is a prime

a clustering algorithm for fuzzy model identification the fuzzy model proposed by takagi and sugeno can represent highly nonlinear systems and is widely used for the representation of fuzzy rules in this paper the model is firstly modified to make its identification easier based on the fuzzy c partition space four criteria are proposed for optimization of the model parameters following that a clustering algorithm composed of fuzzy c linear functions clustering and like fuzzy c means clustering is developed for minimizing the four criteria an identification scheme for rule s premise and consequence parameters is deduced from the clustering algorithm in succession finally four examples are demonstrated to verify the effectiveness of the proposed algorithm

relational generalizations of cluster validity indices numerous computational schemes have arisen over the years that attempt to learn information about objects based upon the similarity or dissimilarity of one object to another one such scheme clustering looks for self similar groups of objects to use clustering algorithms an investigator must often have a priori knowledge of the number of clusters i e c to search for in the data moreover it is often convenient to have ways to rank the returned results either for a single value of c a range of c s different clustering methods or any combination thereof however the task of assessing the quality of the results so that c may be determined objectively is currently ill defined for object object relationships to bridge this gap we generalize three well known validity indices the modified hubert s gamma xie beni and the generalized dunn s indices to relational data in doing so we develop a framework to convert many other validity indices to a relational form numerical examples on 12 datasets samples from four normal mixtures four real world object datasets and four real world pure relational datasets using the relational duals of the hard fuzzy and possibilistic c means cluster algorithms are offered to illustrate and evaluate the new indices

linear fuzzy clustering techniques with missing values and their application to local principal component analysis in this paper we propose two methods for partitioning an incomplete data set with missing values into several linear fuzzy clusters by extracting local principal components one is an extension of fuzzy c varieties clustering that can be regarded as the algorithm for the local principal component analysis of fuzzy covariance matrices the other is a simultaneous application of fuzzy clustering and principal component analysis of fuzzy correlation matrices both methods estimate prototypes ignoring only missing values and they need no preprocessing of data such as the elimination of samples with missing values or the imputation of missing elements numerical examples show that the methods provide useful tools for interpretation of the local structures of a database

eigenvalue distributions of random unitary matrices let u be an n n random matrix chosen from haar measure on the unitary group for a fixed arc of the unit circle let x be the number of eigenvalues of m which lie in the specified arc we study this random variable as the dimension n grows using the connection between toeplitz matrices and random unitary matrices and show that x e x var x 1 2 is asymptotically normally distributed in addition we show that for several fixed arcs i1 im the corresponding random variables are jointly normal in the large n limit

estimation of multiple time varying motions using time frequency representations and moving objects segmentation we extend existing spatiotemporal approaches to handle time varying motions estimation of multiple objects it is shown that multiple time varying motions estimation is equivalent to the instantaneous frequency estimation of superpoliteness fm sinusoids therefore we apply established signal processing tools such as time frequency representations to show that for each time instant the energy is concentrated along planes in the 3 d space spatial frequencies instantaneous frequency using fuzzy c planes we estimate indirectly the instantaneous velocities furthermore adapting existing approaches to our problem we attain the identification of the moving objects the experimental results verify the effectiveness of our methodology

high powers of random elements of compact lie groups if a random unitary matrix u is raised to a sufficiently high power its eigenvalues are exactly distributed as independent uniform phases we prove this result and apply it to give exact asymptotics of the variance of the number of eigenvalues of u falling in a given arc as the dimension of u tends to infinity the independence result it turns out extends to arbitrary representations of arbitrary compact lie groups we state and prove this more general theorem paying special attention to the compact classical groups and to wreath products this paper is excerpted from the author s doctoral thesis 9

relational duals of cluster validity functions for the c means family clustering aims to identify groups of similar objects to evaluate the results of cluster algorithms an investigator uses cluster validity indices while the theory of cluster validity is well established for vector object data little effort has been made to extend it to relationship based data as such this paper proposes a theory of reformulation for object data validity indices so that they can be used to rank the results produced by the relational means clustering algorithms more specifically we create a class of relational validity indices which is called dual relational indices that are guaranteed under certain but easily met constraints to produce the same results and hence the same cluster counts as their object data counterparts

an investigation of smoothness constraints for the estimation of displacement vector fields from image sequences a mapping between one frame from an image sequence and the preceding or following frame can be represented as a displacement vector field in most situations the mere gray value variations do not provide sufficient information in order to estimate such a displacement vector field supplementary constraints are necessary for example the postulate that a displacement vector field varies smoothly as a function of the image position taken as a general requirement this creates difficulties at gray value transitions which correspond to occluding contours nagel therefore introduced the oriented smoothness requirement which restricts variations of the displacement vector field only in directions with small or no variation of gray values this contribution reports results of an investigation about how such an oriented smoothness constraint may be formulated and evaluated

the discrete polynomial phase transform the discrete polynomial phase transform dpt is a new tool for analyzing constant amplitude polynomial phase signals the main properties of the dpt are its ability to identify the degree of the phase polynomial and to estimate its coefficients the transform is robust to deviations from the ideal signal model such as slowly varying amplitude additive noise and nonpolynomial phase the authors define the dpt derive its basic properties and use it to develop computationally efficient estimation and detection algorithms a statistical accuracy analysis of the estimated parameters is also presented

a fourth order finite difference method based on uniform mesh for singular two point boundary value problems we present a new fourth order finite difference method based on uniform mesh for the weakly singular two point boundary value problem x y f x y 0 x 1 y 0 a y 1 b 0 1 our method provides o h4 convergent approximations for all 0 1 for 0 it reduces to the well known fourth order method of numerov for y x y

frequency domain analysis of translations with piecewise cubic trajectories translations with piecewise cubic trajectories are studied in the frequency domain this class of motion has as an important subcase cubic spline trajectories translations with trajectories depending on time with general polynomial law are preliminarily considered and a general theorem concerning this type of motion is introduced the application of this theorem to the case of cubic time dependence and the consideration of finite duration effects lead to the solution of the piecewise cubic trajectory case the results which are remarkably different from those concerning constant velocity translations clearly indicate the importance of the role of velocity and time duration in this respect they confirm the validity of constant velocity motion as a first order model for frequency domain analysis of motion

integral methods for computing solutions of a class of singular two point boundary value problems in this paper we establish three iteration methods to compute solutions for a class of weakly singular two point boundary value problems x y f x y where x 0 1 and 2 we obtain the sufficient conditions for existence of a unique solution on r finally we given some numerical examples

local convergence of the fuzzy c means algorithms abstract much understanding has recently been gained concerning global convergence properties of the fuzzy c means fcm family of clustering algorithms these global convergence properties which hold for all iteration sequences guarantee that every fcm iteration sequence converges at least along a subsequence to a stationary point of an fcm objective function in this paper we prove a local convergence property that is a property pertaining to iteration sequences started near a solution specifically a simple result is proved which shows that whenever an fcm algorithm is started sufficiently near a minimizer of the corresponding objective function then the iteration sequence must converge to that particular minimizer the result guarantees that once captured by the local neighborhood of a minimizer the succeeding iterate sequence will not escape thus infinite oscillation of such a sequence cannot occur the rate of convergence of the sequence to such a point is also discussed

the central limit theorem for local linear statistics in classical compact groups and related combinatorial identities author s soshnikov alexander abstract we discuss clt for the global and local linear statistics of random matrices from classical compact groups the main part of our proofs are certain combinatorial identities much in the spirit of works by kac and spohn

estimation of multiple accelerated motions using chirp fourier transform and clustering motion estimation in the spatiotemporal domain has been extensively studied and many methodologies have been proposed which however cannot handle both time varying and multiple motions extending previously published ideas we present an efficient method for estimating multiple linearly time varying motions it is shown that the estimation of accelerated motions is equivalent to the parameter estimation of superpositioned chirp signals from this viewpoint one can exploit established signal processing tools such as the chirp fourier transform it is shown that accelerated motion results in energy concentration along planes in the 4 d space spatial frequencies temporal frequency chirp rate using fuzzy c planes clustering we estimate the plane motion parameters the effectiveness of our method is verified on both synthetic as well as real sequences and its advantages are highlighted

a fuzzy based customer classification method for demand responsive logistical distribution operations in some cases customer classification is important for the development of advanced logistical distribution strategies in response to the growing complexity in business logistical markets this paper presents a new approach that can be employed to cluster customers before executing fleet routing in logistical operations the proposed approach is developed on the basis of fuzzy clustering techniques and involves three sequential mechanisms including 1 binary transformation 2 generation of a fuzzy correlation matrix and 3 customer clustering such a customer clustering method should be performed prior to vehicle dispatching and routing in the process of goods distribution the proposed methodology clusters customers on the basis of their demand attributes rather than the static geographic property which is considered extensively in most published vehicle routing algorithms in addition to methodology development a case study was conducted to demonstrate the potential advantages of the proposed fuzzy clustering based method it is expected that this study can stimulate more research on time based logistics control and management

two dimensional matched filtering for motion estimation in this work we describe a frequency domain technique for the estimation of multiple superimposed motions in an image sequence the least squares optimum approach involves the computation of the three dimensional 3 d fourier transform of the sequence followed by the detection of one or more planes in this domain with high energy concentration we present a more efficient algorithm based on the properties of the radon transform and the two dimensional 2 d fast fourier transform which can sacrifice little performance for significant computational savings we accomplish the motion detection and estimation by designing appropriate matched filters the performance is demonstrated on two image sequences

spatiotemporal approach for time varying global image motion estimation image motion estimation using the spatiotemporal approach has largely relied on the constant velocity assumption and thus becomes inappropriate when the velocity of the imaged scene or the camera changes during the data acquisition time using a polynomial or a trigonometric polynomial model for the time variation of the image motion spatiotemporal algorithms are developed in this paper to handle time varying but space invariant motion under these models it is shown that time varying image motion estimation is equivalent to parameter estimation of one dimensional 1 d polynomial phase or phase modulated signals which allows one to exploit well established results in radar signal processing when compared with alternative approaches the resulting motion estimation algorithms produce more accurate estimates simulation results are provided to demonstrate the proposed schemes

finite difference methods for certain singular two point boundary value problems the aim of this paper is to study the outcome of finite difference methods of mainly second order for the numerical solution of certain singular two point boundary value problems the method is mainly an extension of the method of gustafsson 1973 from the linear to nonlinear differential equation and is particularly suitable when the differential equation in question cannot be reduced easily to an elegant system of first order equations

recognition and velocity computation of large moving objects in images two one dimensional time sequences are generated from the projections of the two dimensional sequence on the x and y axes then the two dimensional fast fourier transform for the generated time sequences is computed a peak in the spectrum for the selected spatial frequency is detected the temporal frequency at which the peak is detected gives an estimate of the velocity of the moving object analytical formulations for large moving objects in a time sequence with zero background are presented an algorithm is given for velocity formulation

mock gaussian behaviour for linear statistics of classical compact groups we consider the scaling limit of linear statistics for eigenphases of a matrix taken from one of the classical compact groups we compute their moments and find that the first few moments are gaussian whereas the limiting distribution is not the precise number of gaussian moments depends upon the particular statistic considered

correction method and extrapolation method for singular two point boundary value problems abstract in this paper we first discuss the constructions of three point finite difference approximation and a spline approximation for a class of singular two point boundary value problems x x u f x u u 0 0 u 1 a 1 the asymptotic error expansions of the numerical solutions of these problems are obtained from these asymptotic error expansions we find that the finite difference solution and the spline approximation solution approximate the exact solution from two sides so we can obtain correct solution of high order accuracy richardson s extrapolation can also be done and the accuracy of numerical solution can be improved greatly we also present numerical examples which show the performance and efficiency of our methods

numerical solution of nonlinear singular boundary value problems in this paper an efficient method based on the simplified reproducing kernel method srkm and least squares method lsm is proposed for solving nonlinear singular boundary value problems the algorithm consists of two steps first we apply srkm to solve a linear equation which contains a set of parameters second the lsm is used to find the optimal parameters error estimation and convergence order for the presented method are also discussed our numerical experiments validate our theoretical findings and demonstrate the performance of the algorithm in terms of simplicity accuracy and efficiency

detection and characterization of cluster substructure ii fuzzy c varieties and convex combinations thereof in part i siam j appl math 40 1981 pp 339 357 fuzzy c lines was introduced as an algorithm for detection and characterization of linearly clustered data in part ii we address two extensions of the theory in part i specifically we will first generalize the straight line prototype of a cluster developed in part i to any r dimensional linear variety of r s 0 leqq r s secondly we will consider a distance functional which utilizes convex combinations of the distance functionals developed here and in part i all of the notation and symbols used here are unchanged from part i

estimation of time varying velocities of moving objects by time frequency representations an approach to the estimation of motion parameters of moving objects in a video sequence by using the slide subspace based line detection algorithm algorithm is considered the proposed procedure projects video frames to the coordinate axes in order to obtain synthetic images containing information about the motion parameters these synthetic images are mapped to the fm signals by using constant spl mu propagation the problem of velocity estimation is reduced to the instantaneous frequency if estimation if estimators based on time frequency tf representations are used three tf representations spectrogram spec wigner distribution wd and s method sm are used and compared to this aim a tradeoff between concentration of the tf representation velocity estimation accuracy and reduction of the cross terms possibility for estimation of the multiple objects parameters is achieved by the sm a performance analysis of the algorithm is done theoretical results are illustrated on several numerical examples

detection and characterization of cluster substructure i linear structure fuzzy c lines in part i a generalization of the fuzzy c means or fuzzy isodata clustering algorithms is developed necessary conditions for minimization of a generalized total weighted squared orthogonal error objective function lead to a picard iteration scheme which generates simultaneously i c fuzzy clusters in the data ii a set of c prototypical straight lines in feature space which best fit the data in a well defined sense iii a set of c prototpyical centers of mass on the c lines which characterize the core of each linear fuzzy cluster theoretical optimization is achieved using principal components of generalized within cluster fuzzy scatter matrices a convergence theorem for each algorithm in the infinite family is given the algorithms are exemplified by five numerical examples using both real and artificial data sets having essentially linear substructure in part ii the fuzzy c means and fuzzy c lines algorithms are shown to be special cases of a more general class of fuzzy algorithms the

toeplitz and wiener hopf determinants with piecewise continuous symbols abstract the asymptotics for determinants of toeplitz and wiener hopf operators with piecewise continuous symbols are obtained in this paper if w is the wiener hopf operator defined on l2 0 with piecewise continuous symbol having a finite number of discontinuities at r then under appropriate conditions it is shown that det w g r2k where g exp log 0 r 1 2 log r r and k is a completely determined constant an analogous result is obtained for toeplitz operators the main point of the paper is to obtain a result in the wiener hopf case since the toeplitz case had been treated earlier in the toeplitz case it was discovered that one could obtain asymptotics fairly easily for symbols with several singularities if for each singularity one could find a single example of a symbol with a singularity of that kind whose associated asymptotics were known fortunately in the toeplitz case such asymptotics were known the difficulty in the wiener hopf case is that there was not a single singular case where the determinant was explicitly known this problem was overcome by using the fact that wiener hopf determinants when discretized become toeplitz determinants whose entries depend on the size of the matrix no theorem on toeplitz matrices can be applied directly but these theorems are modified to obtain the desired results

a second order spline finite difference method for singular two point boundary value problems a second order spline finite difference method based on a non uniform mesh for singular two point boundary value problems of the form x a x au f x u 0