detecting features in spatial point processes with clutter via model based clustering abstract we consider the problem of detecting features such as minefields or seismic faults in spatial point processes when there is substantial clutter we use model based clustering based on a mixture model for the process in which features are assumed to generate points according to highly linear multivariate normal densities and the clutter arises according to a spatial poisson process nonlinear features are represented by several densities giving a piecewise linear representation hierarchical model based clustering provides a first estimate of the features and this is then refined using the em algorithm the number of features is estimated from an approximation to its posterior distribution the method gives good results for the minefield and seismic fault problems software to implement it is available on the world wide web

model based gaussian and non gaussian clustering abstract the classification maximum likelihood approach is sufficiently general to encompass many current clustering algorithms including those based on the sum of squares criterion and on the criterion of friedman and rubin 1967 however as currently implemented it does not allow the specification of which features orientation size and shape are to be common to all clusters and which may differ between clusters also it is restricted to gaussian distributions and it does not allow for noise we propose ways of overcoming these limitations a reparameterization of the covariance matrix allows us to specify that some features but not all be the same for all clusters a practical framework for non gaussian clustering is outlined and a means of incorporating noise in the form of a poisson process is described an approximate bayesian method for choosing the number of clusters is given the performance of the proposed methods is studied by simulation with encouraging results the methods are applied to the analysis of a data set arising in the study of diabetes and the results seem better than those of previous analyses rh

numerical solution of the neural field equation in the two dimensional case we are concerned with the numerical solution of a class of integro differential equations known as neural field equations which describe the large scale dynamics of spatially structured networks of neurons these equations have many applications in neuroscience and robotics we describe a numerical method for the approximation of solutions in the two dimensional case including a space dependent delay in the integrand function compared with known algorithms for this type of equation we propose a scheme with higher accuracy in the time discretization since computational efficiency is a key issue in this type of calculation we use a new method for reducing the complexity of the algorithm the convergence issues are discussed in detail and a number of numerical examples are presented which illustrate the performance of the method

an efficient method for the numerical solution of hammerstein mixed vf integral equations on 2d irregular domains abstract in this work we adapt the implicity linear collocation method for solving nonlinear two dimensional mixed volterra fredholm integral equations of hammerstein type by using imq rbfs on a non rectangular domain the proposed method is mesh free and it is independent of the geometry of domain convergence analysis of the proposed method together with some benchmark examples is provided which support its reliability and numerical stability

iterative method and convergence analysis for a kind of mixed nonlinear volterra fredholm integral equation in this paper the iterative method is presented for numerically solving the nonlinear volterra fredholm integral equation first considering some conditions on k i and l i i 1 2 of the integral equation then we define the equidistance collocation points and the integral part of equation is discretized by newton cotes integration formula finally the approximate solutions of integral equation are obtain by iterative method the convergence analysis of the integral equation is given some numerical examples are given to illustrate the accuracy and dependability of the method

texture analysis through a markovian modelling and fuzzyclassification application to urban area extraction fromsatellite images herein we propose a complete procedure to analyze and classify the texture of an image we apply this scheme to solve a specific image processing problem urban areas detection in satellite images first we propose to analyze the texture through the modelling of the luminance field with eight different chain based models we then derived a texture parameter from these models the effect of the lattice anisotropy is corrected by a renormalization group technique coming from statistical physics this parameter which takes into account local conditional variances of the image is compared to classical methods of texture analysis afterwards we develop a modified fuzzy cmeans algorithm that includes an entropy term the advantage of such an algorithm is that the number of classes does not need to be known a priori besides this algorithm provides us with further information i e the probability that a given pixel belongs to a given cluster finally we introduce this information in a markovian model of segmentation some results on spot5 simulated images spot3 images and ers1 radar images are presented these images are provided by the french national space agency cnes and the european space agency esa

computing bayes factors by combining simulation and asymptotic approximations abstract the bayes factor is a ratio of two posterior normalizing constants which may be difficult to compute we compare several methods of estimating bayes factors when it is possible to simulate observations from the posterior distributions via markov chain monte carlo or other techniques the methods that we study are all easily applied without consideration of special features of the problem provided that each posterior distribution is well behaved in the sense of having a single dominant mode we consider a simulated version of laplace s method a simulated version of bartlett correction importance sampling and a reciprocal importance sampling technique we also introduce local volume corrections for each of these in addition we apply the bridge sampling method of meng and wong we find that a simulated version of laplace s method with local volume correction furnishes an accurate approximation that is especially useful when likelihood function evaluations are costly a simple bridge sampli

regularized gaussian discriminant analysis through eigenvalue decomposition abstract friedman proposed a regularization technique rda of discriminant analysis in the gaussian framework rda uses two regularization parameters to design an intermediate classifier between the linear the quadratic the nearest means classifiers in this article we propose an alternative approach called edda that is based on the reparameterization of the covariance matrix k of a group gk in terms of its eigenvalue decomposition k k d k a k d k where k specifies the volume of density contours of gk the diagonal matrix of eigenvalues specifies its shape the eigenvectors specify its orientation variations on constraints concerning volumes shapes orientations k a k and d k lead to 14 discrimination models of interest for each model we derived the normal theory maximum likelihood parameter estimates our approach consists of selecting a model by minimizing the sample based estimate of future misclassification risk by cross validation numerical experiments on simulated and rea

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

a modified homotopy perturbation method for solving the nonlinear mixed volterra fredholm integral equation the purpose of this paper is to obtain the approximation solution of the strongly nonlinear mixed volterra fredholm integral equation vfie for some strongly nonlinear problems the traditional homotopy perturbation method is divergent so we propose a modified homotopy perturbation method which is still convergent when solving the strongly nonlinear mixed vfie by means of this method an algorithm is successfully established for solving the strongly nonlinear mixed vfie and the convergence of the algorithm is proved strictly finally several examples are presented to illustrate the application of the algorithm

numerical solution of volterra fredholm integral equations using parameterized pseudospectral integration matrices the main purpose of this work is to provide parameterized pseudospectral integration matrices ppims for solving volterra fredholm integral equations we present an exact efficient and stable approach for computing ppims furthermore we provide a rigorous convergence analysis for the pseudospectral scheme with collocation at the jacobi type points in both l and l 2 spaces numerical results confirm the spectral rate of convergence for the proposed pseudospectral schemes

a new computational method for volterra fredholm integral equations abstract the main purpose of this article is to demonstrate the use of the adomian decomposition method for mixed nonlinear volterra fredholm integral equations a bound is also given for the adomian decomposition series finally numerical examples are presented to illustrate the implementation and accuracy of the decomposition method

the exact solution for solving a class nonlinear operator equations in the reproducing kernel space in this paper the author will introduce the sobolev space w 1 2 w n firstly and then give the reproducing properties of the space w 1 2 w n as these results of those a class of the nonlinear operator equation n i 1 m i j 1 a i ju f is transformed to the n dimensional linear operator equation au f finally we also give the exact solution of this nonlinear operator equation

numerical solution of a class of mixed two dimensional nonlinear volterra fredholm integral equations using multiquadric radial basis functions an efficient numerical method is proposed for solving the mixed nonlinear volterra fredholm two dimensional integral equations ies using two dimensional radial basis functions rbfs this method is based on interpolation by radial basis functions including multiquadrics mqs using legendre gauss lobatto nodes and weights also a theorem is proved for convergence analysis some numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the proposed method

continuous time collocation methods for volterra fredholm integral equations integral equations of mixed volterra fredholm type arise in various physical and biological problems in the present paper we study continuous time collocation time discretization and their global and discrete convergence properties

numerical solution of volterra fredholm integral equations via modification of hat functions abstract in this paper a new numerical approach is developed for solving linear and nonlinear volterra fredholm integral equations the fundamental structure of the presented method is based on the modification of hat functions the properties of modification of hat functions mhfs are first presented after implementation of our scheme the solution of the main problem would be transformed into the solution of a system of linear or nonlinear algebraic equations also an error analysis is provided under several mild conditions in addition examples are presented to illustrate the pertinent features of the method and the results are discussed

a hybrid legendre block pulse method for mixed volterra fredholm integral equations abstract mixed volterra fredholm integral equations can arise from mathematical modelling of the spatio temporal development of an epidemic in this paper a hybrid legendre block pulse method is used to provide solutions to a general integral equation of this type the main idea of this approach is to reduce a volterra fredholm integral equation to a system of algebraic equations an order convergence analysis is provided the accuracy of the proposed method is then confirmed by solving some problems the first being a nonlinear epidemic problem

on a method for solving an integral equation in the displacement contact problem in this paper the solution in a series form of the integral equation of the mixed type in the space l w xc 0 t is obtained where w x y z

on the foundations of relaxation labeling processes a large class of problems can be formulated in terms of the assignment of labels to objects frequently processes are needed which reduce ambiguity and noise and select the best label among several possible choices relaxation labeling processes are just such a class of algorithms they are based on the parallel use of local constraints between labels this paper develops a theory to characterize the goal of relaxation labeling the theory is founded on a definition of con sistency in labelings extending the notion of constraint satisfaction in certain restricted circumstances an explicit functional exists that can be maximized to guide the search for consistent labelings this functional is used to derive a new relaxation labeling operator when the restrictions are not satisfied the theory relies on variational cal culus it is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality a procedure nearly identical to the relaxation operator derived under restricted circum stances serves in the more general setting further a local convergence result is established for this operator the standard relaxation labeling formulas are shown to approximate our new operator which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here observations about con vergence and generalizations to higher order compatibility relations are described

bayesian morphology fast unsupervised bayesian image analysis abstract we consider the problems of image segmentation and classification and image restoration when the true image is made up of a small number of unordered colors our emphasis is on both performance and speed speed has become increasingly important for analyzing large images and multispectral images with many bands processing large image databases real time or near realtime image analysis and the online analysis of video bayesian image analysis provides an elegant solution to these problems but it is computationally expensive and the solutions it provides may be sensitive to unrealistic global properties of the models on which it is based the icm algorithm is faster and based on the local properties of the models underlying bayesian image analysis parameter estimation is performed iteratively via pseudolikelihood mathematical morphology is faster again and is widely considered to perform well but lacks a statistical basis method selection analogous to parameter estimation is done in a

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

numerical solution for three dimensional nonlinear mixed volterra fredholm integral equations via three dimensional block pulse functions we are concerned here with a three dimensional nonlinear mixed volterra fredholm integral equations of the second kind which include many key integral that appear in the theory of nonlinear parabolic boundary value problems the existence of a unique solution will be proved a new numerical method for solving these type of equations will be presented the method is based upon three dimensional block pulse functions approximation in addition convergence analysis of the method is discussed illustrative examples are included to demonstrate the validity and applicability of the technique

asymptotic error expansion for the nystro m method for a nonlinear volterra fredholm integral equation in this paper we study the numerical solution of general nonlinear mixed volterra fredholm integral equations by the trapezoidal nystrom method it focuses on the derivation and analysis of asymptotic error expansion of the nystrom solution providing the basis for richardson s extrapolation this will greatly increase the accuracy of the numerical solution some numerical results are given to illustrate this theory

two scale boolean galerkin discretizations for fredholm integral equations of the second kind in this paper some two scale boolean galerkin discretizations are proposed and analyzed for a class of fredholm integral equations of the second kind in multidimensions it is shown by both theory and numerics that this type of multiscale discretization algorithm not only significantly reduces the number of degrees of freedom but also produces very accurate approximations

representation of exact solution for the nonlinear volterra fredholm integral equations abstract in this paper the representation of the exact solution for the nonlinear volterra fredholm integral equations will be obtained in the reproducing kernel space the exact solution is given by the form of series its approximate solution is obtained by truncating the series and a new numerical approximate method is obtained the error of the approximate solution is monotone deceasing in the sense of w 2 1 a b the intrinsic merit of the method given in the paper lies in its speedy convergence in addition it must be pointed out that additional conditions as linearization or unjustified assumptions are not required for nonlinear cases

iterated collocation methods and their discretizations for volterra integral equations it is known that the numerical solution of volterra integral equations of the second kind by polynomial spline collocation at the gauss legendre points does not lead to local superconvergence at the knots of the approximating function in the present paper we show that iterated collocation approximation restores optimal local superconvergence at the knots but does not yield global superconvergence on the entire interval of integration in contrast to fredholm integral equations with smooth kernels we also analyze the discretized versions obtained by suitable numerical quadrature of the collocation and iterated collocation methods

new algorithm for second order boundary value problems of integro differential equation this paper is concerned with a new algorithm for giving the analytical and approximate solutions of a class of boundary value problems in the reproducing kernel space the analytical solution u x and approximate solution u n x are represented in terms of series for any initial function u 1 x w 2 3 0 1 we prove u n x u x u n x u x u n x u x n two numerical examples are studied to demonstrate the accuracy of the present method results obtained by the method indicate the method is simple and effective

estimation of markov random field prior parameters using markov chain monte carlo maximum likelihood developments in statistics now allow maximum likelihood estimators for the parameters of markov random fields mrfs to be constructed we detail the theory required and present an algorithm that is easily implemented and practical in terms of computation time we demonstrate this algorithm on three mrf models the standard potts model an inhomogeneous variation of the potts model and a long range interaction model better adapted to modeling real world images we estimate the parameters from a synthetic and a real image and then resynthesize the models to demonstrate which features of the image have been captured by the model segmentations are computed based on the estimated parameters and conclusions drawn

about some numerical approaches for mixed integral equations abstract in this paper we tackle on mixed volterra fredholm integral equations as in linear as in non linear cases to the aim to obtain numerical solutions of these models the authors propose in the linear case the direct collocation method using a p order quasi interpolating spline class and in the nonlinear case the fixed point method based on polynomial approximation built by schauder tensor bases the advantages of both methods are outlined and their convergence is studied numerical results confirm the theoretical statements

a reliable treatment for mixed volterra fredholm integral equations the main goal of this paper is to demonstrate the use of the modified decomposition method for mixed nonlinear volterra fredholm integral equations the modified method combined with the noise terms phenomena may provide the exact solution by using two iterations only two numerical illustrations are given to show the pertinent features of the technique

on the numerical solution of linear and nonlinear volterra integral and integro differential equations abstract sinc bases are developed to approximate the solutions of linear and nonlinear volterra integral and integro differential equations properties of these sinc bases and some operational matrices are first presented these properties are then used to reduce the integral and integro differential equations to systems of linear or nonlinear algebraic equations numerical examples illustrate the pertinent features of the method and its applicability to a large variety of problems the examples include convolution type singular as well as singularly perturbed problems

the combined reproducing kernel method and taylor series for handling nonlinear volterra integro differential equations with derivative type kernel abstract the reproducing kernel method is applied to volterra nonlinear integro differential equations in this technique the nonlinear term is replaced by its taylor series the exact solution is represented in the form of series in the reproducing hilbert kernel space the approximation solution is expressed by n term summation of reproducing kernel functions some numerical examples are solved in two different spaces and parameters of n measurements of the experimental data is an indications of stability and convergence on the reproducing kernel

taylor polynomial solutions of nonlinear volterra fredholm integral equations the kanwal and liu method for the solution of fredholm integral equations is applied to certain nonlinear volterra fredholm integral equations in addition examples that illustrate the pertinent features of the method are presented and the results of study are discussed

he s variational iteration method for solving nonlinear mixed volterra fredholm integral equations in this paper he s variational iteration method is used to give the approximate solution of nonlinear mixed volterra fredholm integral equations the method constructs a convergent sequence of functions which approximates the exact solution with few iterations numerical results and a comparison with the exact solution are given which reveal its efficiency

a computational method for solving periodic boundary value problems for integro differential equations of fredholm volterra type abstract in this paper the numerical solution of periodic fredholm volterra integro differential equations of first order is discussed in a reproducing kernel hilbert space a reproducing kernel hilbert space is constructed in which the periodic condition of the problem is satisfied the exact solution u x is represented in the form of series in the space w 2 2 in the mean time the n term approximate solution u n x is obtained and is proved to converge to the exact solution u x furthermore we present an iterative method for obtaining the solution in the space w 2 2 some examples are displayed to demonstrate the validity and applicability of the proposed method the numerical result indicates that the proposed method is straightforward to implement efficient and accurate for solving linear and nonlinear equations

on the numerical solution of nonlinear volterra fredholm integral equations by collocation methods particular cases of nonlinear mixed volterra fredholm integral equations of the second kind arise in the mathematical modeling of the spatio temporal development of an epidemic this paper is concerned with the numerical solution of general integral equations of this type by continuous time and discrete time spline collocation methods its focus is on the derivation and analysis of methods of high order of convergence

constrained monte carlo maximum likelihood for dependent data maximum likelihood estimates mles in autologistic models and other exponential family models for dependent data can be calculated with markov chain monte carlo methods the metropolis algorithm or the gibbs sampler which simulate ergodic markov chains having equilibrium distributions in the model from one realization of such a markov chain a monte carlo approximant to the whole likelihood function can be constructed the parameter value if any maximizing this function approximates the mle

numerical solution of volterra fredholm integral equations using legendre collocation method a numerical method for solving the volterra fredholm integral equations is presented the method is based upon shifted legendre polynomials approximation the properties of shifted legendre polynomials are first presented these properties together with the shifted gauss legendre nodes are then utilized to reduce the volterra fredholm integral equations to the solution of a matrix equation an estimation of the error is given illustrative examples are included to demonstrate the validity and applicability of the technique

gaussian parsimonious clustering models gaussian clustering models are useful both for understanding and suggesting powerful criteria banfield and raftery 1993 have considered a parametrization of the variance matrix ek of a cluster pk in terms of its eigenvalue decomposition ek lkdkakd k lk where lk defines the volume of pk dk is an orthogonal matrix which defines its orientation and ak is a diagonal matrix with determinant 1 which defines its shape this parametrization allows us to propose many general clustering criteria from the simplest one spherical cluster with equal volumes which leads to the classical k means criterion to the most complex one unknown and different volumes orientations and shapes for all clusters methods of optimization to derive the maximum likelihood estimates as well as the practical usefulness of these models are discussed we especially analyze the influence of the volumes of clusters we report monte carlo simulations and an application on stellar data which dramatically illustrated the relevance of allowing clusters to have different volumes

a computational method for system of volterra fredholm integral equations adomian decomposition method has been applied for solving volterra fredholm equation by maleknejad k maleknejad m hadizadeh a new computational method for volterra fredholm integral equations comput math appl 37 1999 1 8 in 1999 in this paper we solve the system of nonlinear volterra fredholm integral equations by adomian decomposition method some examples are solved to illustrate the accuracy of this method

orbit equivalence of cantor minimal systems and their continuous spectra to any continuous eigenvalue of a cantor minimal system x t we associate an element of the dimension group k 0 x t associated to x t we introduce and study the concept of irrational miscibility of a dimension group the main property of these dimension groups is the absence of irrational values in the additive group of continuous spectrum of their realizations by cantor minimal systems the strong orbit equivalence respectively orbit equivalence class of a cantor minimal system associated to an irrationally miscible dimension group g u resp with trivial infinitesimal subgroup with trivial rational subgroup have no non trivial continuous eigenvalues

an efficient algorithm for solving nonlinear volterra fredholm integral equations in this work we develop a new effective method for solving nonlinear volterra fredholm integral equation the existence of any e approximate solution is proved at the same time an effective method for obtaining the e approximate solution is established the final numerical examples illustrate that our approach is valid not only for weakly nonlinear problems but also for strongly nonlinear problems

posteriori error estimates for the nonlinear volterra fredholm integral equations abstract we study the numerical approximation of the nonlinear volterra fredholm integral equations by combining the discrete time collocation method 1 and the new formulation of kumar and sloan 2 which converts an integral equation of the conventional hammerstein form into a conductive form for approximation by a collocation method the intrinsic merit of this alternative formulation lies in its computational savings posteriori error estimates of the method for two typical nonlinearities i e algebraic and exponential nonlinearity are obtained some remarks on the generalization of the method to higher dimensional cases are offered and finally some numerical examples are given

solving fredholm integro differential equations using reproducing kernel hilbert space method in this study the numerical solution of fredholm integro differential equation is discussed in a reproducing kernel hilbert space a reproducing kernel hilbert space is constructed in which the initial condition of the problem is satisfied the exact solution ux is represented in the form of series in the space w 2 2 a b in the mean time the n term approximate solution u n x is obtained and is proved to converge to the exact solution u x furthermore we present an iterative method for obtaining the solution in the space w 2 2 a b some examples are displayed to demonstrate the validity and applicability of the proposed method the numerical result indicates that the proposed method is straightforward to implement efficient and accurate for solving linear and nonlinear fredholm integro differential equations