an efficient numerical method for the solution of sliding contact problems in this paper an efficient numerical method to solve sliding contact problems is proposed explicit formulae for the gauss jacobi numerical integration scheme appropriate for the singular integral equations of the second kind with cauchy kernels are derived the resulting quadrature formulae for the integrals are valid at nodal points determined from the zeroes of a jacobi polynomial gaussian quadratures obtained in this manner involve fixed nodal points and are exact for polynomials of degree 2n 1 where n is the number of nodes from this gauss jacobi quadrature the existing gauss chebyshev quadrature formulas can be easily derived another apparent advantage of this method is its ability to capture correctly the singular or regular behaviour of the tractions at the edge of the region of contact also this analysis shows that once if the total normal load and the friction coefficient are given the external moment m and contact eccentricity e for incomplete contact in fully sliding contact are uniquely determined finally numerical solutions are computed for two typical contact cases including sliding hertzian contact and a sliding contact between a flat punch with rounded corners pressed against the flat surface of a semi infinite elastic solid these results provide a demonstration of the validity of the proposed method copyright 2005 john wiley sons ltd

fundamental formulation for frictional contact problems of coated systems abstract the plane problem about surface loading of an elastic layer perfectly bonded to an elastically dissimilar half plane is considered the fundamental solutions for concentrated forces acting perpendicular and parallel to the layer surface are obtained the stress and displacement fields in the coating layer and the substrate due to these concentrated forces are found on the basis of these expressions the fundamental integral equations are obtained which describe the frictional contact between an elastic body and a coated substrate from the fundamental integral equations a series of integral equations for special cases are deduced corresponding to practical contact situations finally the numerical results for a typical example are given to demonstrate the validity of the fundamental equations and numerical procedures given in this paper

a global structure based algorithm for detecting the principal graph from complex data principal curves arising as an essential construct in dimensionality reduction and pattern recognition have recently attracted much attention from theoretical as well as practical perspective existing methods usually employ the first principal component of the data as an initial estimate of principal curves however they may be ineffective when dealing with complex data with self intersecting characteristics high curvature and significant dispersion in this paper a new method based on global structure is proposed to detect the principal graph a set of principal curves from complex data first the global structure of the data called an initial principal graph is extracted based on a thinning technique which captures the approximate topological features of the complex data in terms of the characteristics of the data vertex merge step and the improved fitting and smoothing phase are then proposed to control the deviation of the principal graph and improve the process of optimizing the principal graph finally the restructuring step introduced by kegl is used to rectify imperfections of the principal graph by using synthetic and real world data sets the proposed method is compared with other existing algorithms experimental results show the effectiveness of the global structure based method

piecewise linear skeletonization using principal curves proposes an algorithm to find piecewise linear skeletons of handwritten characters by using principal curves the development of the method was inspired by the apparent similarity between the definition of principal curves smooth curves which pass through the middle of a cloud of points and medial axes smooth curves that run equidistantly from the contours of a character image the central fitting and smoothing step of the algorithm is an extension of the polygonal line algorithm which approximates principal curves of data sets by piecewise linear curves the polygonal line algorithm is extended to find principal graphs and complemented with two steps specific to the task of skeletonization an initialization method to capture the approximate topology of the character and a collection of restructuring operations to improve the structural quality of the skeleton produced by the initialization method an advantage of our approach over existing methods is that we optimize the skeleton graph by minimizing an intuitive and explicit objective function that captures the two competing criteria of smoothing the skeleton and fitting it closely to the pixels of the character image we tested the algorithm on isolated handwritten digits and images of continuous handwriting the results indicated that the proposed algorithm can find a smooth medial axis in the great majority of a wide variety of character templates and that it substantially improves the pixel wise skeleton obtained by traditional thinning methods

asymptotic behavior of thermal nonequilibrium steady states for a driven chain of anharmonic oscillators we consider a model of heat conduction introduced in 6 which consists of a finite nonlinear chain coupled to two heat reservoirs at different temperatures we study the low temperature asymptotic behavior of the invariant measure we show that in this limit the invariant measure is characterized by a variational principle the main technical ingredients are some control theoretic arguments to extend the freidlin wentzell theory of large deviations to a class of degenerate diffusions

ergodic systems of n balls in a billiard table we consider the motion ofn balls in billiard tables of a special form and we prove that the resulting dynamical systems are ergodic on a constant energy surface in fact they enjoy thek property these are the first systems of interacting particles proven to be ergodic for an arbitrary number of particles

sufficient burn in for gibbs samplers for a hierarchical random effects model we consider gibbs and block gibbs samplers for a bayesian hierarchical version of the one way random effects model drift and minorization conditions are established for the underlying markov chains the drift and minorization are used in conjunction with results from j s rosenthal j amer statist assoc 90 1995 558 566 and g o roberts and r l tweedie stochastic process appl 80 1999 211 229 to construct analytical upper bounds on the distance to stationarity these lead to upper bounds on the amount of burn in that is required to get the chain within a prespecified total variation distance of the stationary distribution the results are illustrated with a numerical example 1 introduction we consider a bayesian hierarchical version of the standard normal theory one way random effects model the posterior density for this model is intractable in the sense that the integrals required for making inferences cannot be computed in closed form hobert and geyer 1998 analyzed a gibbs sampler and a block gibbs sampler for this problem and showed that the markov chains underlying these algorithms converge to the stationary i e posterior distribution at a geometric rate however hobert and geyer stopped short of constructing analytical upper bounds on the total variation distance to stationarity in this article we construct such upper bounds and this leads to a method for determining a sufficient burn in our results are useful from a practical standpoint because they obviate troublesome ad hoc convergence diagnostics cowles and carlin 1996 and

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

on the use of interpolative quadratures for hypersingular integrals in fracture mechanics the implementation of finitepart integration of hypersingular boundary integrals is discussed in the context of the applications in engineering fracture mechanics the approach uses a formulation o

a fast algorithm for the computation of axial moments and its application to the orthogonal fitting of curves this paper describes a fast algorithm to compute local axial moments used in the detection of objects of interest in images the basic idea is the elimination of redundant operations while computing axial moments for two neighboring angles of orientation the main result is that the complexity of the recursive computation of axial moments becomes independent of the total number of computed moments at a given point i e it is of the order o n where n is the size of the data set this result is of great importance in computer vision since many feature extraction methods rely on the computation of axial moments the use of this algorithm for fast object skeletonization in images by orthogonal regression fitting is described in detail with the experimental results confirming the theoretical computational complexity

frictional contact problem for a rigid cylindrical stamp and an elastic layer resting on a half plane abstract the frictional contact problem for a layer resting on a homogeneous half plane is handled using linear elasticity theory in this study the layer is in contact with a rigid cylindrical stamp that is on the layer and applies a concentrated force in the normal and tangential directions friction between the component couples of layer stamp and layer half plane is taken into account the problem is reduced to a system of singular integral equations in which the contact pressures and the contact areas are the unknowns and it is treated using fourier transforms and the boundary conditions for the problem the system of singular integral equations is solved numerically using the gauss jacobi integration formula with equilibrium and consistency conditions numerical results for the contact pressures and the contact areas are given as a solution for both the frictional and the frictionless cases this work is the first study that investigates the effect of friction on the receding contact problem of a layer and a half plane with two contact areas

learning and design of principal curves principal curves have been defined as self consistent smooth curves which pass through the middle of a d dimensional probability distribution or data cloud they give a summary of the data and also serve as an efficient feature extraction tool we take a new approach by defining principal curves as continuous curves of a given length which minimize the expected squared distance between the curve and points of the space randomly chosen according to a given distribution the new definition makes it possible to theoretically analyze principal curve learning from training data and it also leads to a new practical construction our theoretical learning scheme chooses a curve from a class of polygonal lines with k segments and with a given total length to minimize the average squared distance over n training points drawn independently convergence properties of this learning scheme are analyzed and a practical version of this theoretical algorithm is implemented in each iteration of the algorithm a new vertex is added to the polygonal line and the positions of the vertices are updated so that they minimize a penalized squared distance criterion simulation results demonstrate that the new algorithm compares favorably with previous methods both in terms of performance and computational complexity and is more robust to varying data models

towards a derivation of fourier s law for coupled anharmonic oscillators we consider a hamiltonian system made of weakly coupled anharmonic oscillators arranged on a three dimensional lattice mathbb z 2n times mathbb z 2 and subjected to stochastic forcing mimicking heat baths of temperatures t1 and t2 on the hyperplanes at 0 and n we introduce a truncation of the hopf equations describing the stationary state of the system which leads to a nonlinear equation for the two point stationary correlation functions we prove that these equations have a unique solution which for n large is approximately a local equilibrium state satisfying fourier law that relates the heat current to a local temperature gradient the temperature exhibits a nonlinear profile

nonparametric maximum likelihood estimation of features in spatial point processes using voronoi tessellation abstract this article addresses the problem of estimating the support domain of a bounded point process in presence of background noise this situation occurs for example in the detection of a minefield from aerial observations a maximum likelihood estimator for a mixture of uniform point processes is derived using a natural partition of the space defined by the data themselves the voronoi tessellation the methodology is tested on simulations and compared to a model based clustering technique

self organization as an iterative kernel smoothing process kohonen s self organizing map when described in a batch processing mode can be interpreted as a statistical kernel smoothing problem the batch som algorithm consists of two steps first the training data are partitioned according to the voronoi regions of the map unit locations second the units are updated by taking weighted centroids of the data falling into the voronoi regions with the weighing function given by the neighborhood then the neighborhood width is decreased and steps 1 2 are repeated the second step can be interpreted as a statistical kernel smoothing problem where the neighborhood function corresponds to the kernel and neighborhood width corresponds to kernel span to determine the new unit locations kernel smoothing is applied to the centroids of the voronoi regions in the topological space this interpretation leads to some new insights concerning the role of the neighborhood and dimensionality reduction it also strengthens the algorithm s connection with the principal curve algorithm a generalized self organizing algorithm is proposed where the kernel smoothing step is replaced with an arbitrary nonparametric regression method

model based clustering for integrated circuit yield enhancement this paper studies the defect data analysis method for semiconductor yield enhancement given the defect locations on a wafer the local defects generated from the assignable causes are classified from the global defects generated from the random causes by model based clustering and the clustering methods can identify the characteristics of local defect clusters the information obtained from this method can facilitate process control particularly root cause analysis the global defects are modeled by the spatial non homogeneous poisson process and the local defects are modeled by the bivariate normal distribution or by the principal curve

on use of the em algorithm for penalized likelihood estimation summary the em algorithm is a popular approach to maximum likelihood estimation but has not been much used for penalized likelihood or maximum a posteriori estimation this paper discusses properties of the em algorithm in such contexts concentrating on rates of conver gence and presents an alternative that is usually more practical and converges at least as quickly the em algorithm is a general approach to maximum likelihood estimation rather than a specific algorithm dempster et al 1977 discussed the method and derived basic properties demonstrating that a variety of procedures previously developed rather informally could be unified the common strand to problems where the approach is applicable is a notion of incomplete data this includes the conventional sense of missing data but is much broader than that the em algorithm demon strates its strength in situations where some hypothetical experiment yields data from which estimation is particularly convenient and economical the incomplete data actually at hand are regarded as observable functions of these complete data the resulting algorithms while usually slow to converge are often extremely simple and remain practical in large problems where no other approaches may be feasible dempster et al 1977 briefly refer to the use of the same approach to the problem of finding the posterior mode maximum a posteriori estimate in a bayesian estima

a direct search algorithm for optimization with noisy function evaluations we consider the unconstrained optimization of a function when each function evaluation is subject to a random noise we assume that there is some control over the variance of the noise term in the sense that additional computational effort will reduce the amount of noise this situation may occur when function evaluations involve simulation or the approximate solution of a numerical problem it also occurs in an experimental setting when averaging repeated observations at the same point can lead to a better estimate of the underlying function value we describe a new direct search algorithm for this type of problem we prove convergence of the new algorithm when the noise is controlled so that the standard deviation of the noise approaches zero faster than the step size we also report some numerical results on the performance of the new algorithm

spectral gaps in wasserstein distances and the 2d stochastic navier stokes equations we develop a general method to prove the existence of spectral gaps for markov semigroups on banach spaces unlike most previous work the type of norm we consider for this analysis is neither a weighted supremum norm nor an lp type norm but involves the derivative of the observable as well and hence can be seen as a type of 1 wasserstein distance this turns out to be a suitable approach for infinite dimensional spaces where the usual harris or doeblin conditions which are geared toward total variation convergence often fail to hold in the first part of this paper we consider semigroups that have uniform behavior which one can view its the analog of doeblin s condition we then proceed to study situations where the behavior is not so uniform but the system has a suitable lyapunov structure leading to a type of harris condition we finally show that the latter condition is satisfied by the two dimensional stochastic navier stokes equations even in situations where the forcing is extremely de generate using the convergence result we show that the stochastic navier stokes equations invariant measures depend continuously on the viscosity and the structure of the forcing

finding curvilinear features in spatial point patterns principal curve clustering with noise clustering about principal curves combines parametric modeling of noise with nonparametric modeling of feature shape this is useful for detecting curvilinear features in spatial point patterns with or without background noise applications include the detection of curvilinear minefields from reconnaissance images some of the points in which represent false detections and the detection of seismic faults from earthquake catalogs our algorithm for principal curve clustering is in two steps the first is hierarchical and agglomerative hpcc and the second consists of iterative relocation based on the classification em algorithm cem pcc hpcc is used to combine potential feature clusters while cem pcc refines the results and deals with background noise it is important to have a good starting point for the algorithm this can be found manually or automatically using for example nearest neighbor clutter removal or model based clustering we choose the number of features and the amount of smoothing simultaneously using approximate bayes factors

stationary random metrics on hierarchical graphs via min type recursive distributional equations this paper is inspired by the problem of understanding in a mathematical sense the liouville quantum gravity on surfaces here we show how to define a stationary random metric on self similar spaces which are the limit of nice finite graphs these are the so called hierarchical graphs they possess a well defined level structure and any level is built using a simple recursion stopping the construction at any finite level we have a discrete random metric space when we set the edges to have random length using a multiplicative cascade with fixed law m we introduce a tool the cut off process by means of which one finds that renormalizing the sequence of metrics by an exponential factor they converge in law to a non trivial metric on the limit space such limit law is stationary in the sense that glueing together a certain number of copies of the random limit space according to the combinatorics of the brick graph the obtained random metric has the same law when rescaled by a random factor of law m in other words the stationary random metric is the solution of a distributional equation when the measure m has continuous positive density on mathbf r the stationary law is unique up to rescaling and any other distribution tends to a rescaled stationary law under the iterations of the hierarchical transformation we also investigate topological and geometric properties of the random space when m is log normal detecting a phase transition influenced by the branching random walk associated to the multiplicative cascade

hierarchic voronoi skeletons abstract robust and time efficient skeletonization of a planar shape which is connectivity preserving and based on euclidean metrics can be achieved by first regularizing the voronoi diagram vd of a shape s boundary points i e by removal of noise sensitive parts of the tessellation and then by establishing a hierarchic organization of skeleton constituents each component of the vd is attributed with a measure of prominence which exhibits the expected invariance under geometric transformations and noise the second processing step a hierarchic clustering of skeleton branches leads to a multiresolution representation of the skeleton termed skeleton pyramid

a reference bayesian test for nested hypotheses and its relationship to the schwarz criterion abstract to compute a bayes factor for testing h 0 0 in the presence of a nuisance parameter priors under the null and alternative hypotheses must be chosen as in bayesian estimation an important problem has been to define automatic or reference methods for determining priors based only on the structure of the model in this article we apply the heuristic device of taking the amount of information in the prior on equal to the amount of information in a single observation then after transforming to be null orthogonal to we take the marginal priors on to be equal under the null and alternative hypotheses doing so and taking the prior on to be normal we find that the log of the bayes factor may be approximated by the schwarz criterion with an error of order o p n rather than the usual error of order o p 1 this result suggests the schwarz criterion should provide sensible approximate solutions to bayesian testing problems at least when the hypotheses are nested when

local likelihood estimation abstract a scatterplot smoother is applied to data of the form x 1 y 1 x 2 y 2 xn yn and uses local fitting to estimate the dependence of y on x a simple example is the running lines smoother which fits a least squares line to the y values falling in a window around each x value the value of the estimated function at x is given by the value of the least squares line at x a smoother generalizes the least squares line which assumes that the dependence of y on x is linear in this article we extend the idea of local fitting to likelihood based regression models one such application is to the class of generalized linear models nelder and wedderburn 1972 we enlarge this class by replacing the covariate form 0 x 1 with an unspecified smooth function s x this function is estimated from the data by a technique we call local likelihood estimation the method consists of maximum likelihood estimation for 0 and 1 applied in a window around each x value multiple covariates are incor

self organizing maps for the skeletonization of sparse shapes this paper presents a method for computing the skeleton of planar shapes and objects which exhibit sparseness lack of connectivity within their image regions such sparseness in images may occur due to poor lighting conditions incorrect thresholding or image sub sampling furthermore in document image analysis sparse shapes are characteristic of texts faded due to aging and or poor ink quality given the pixel distribution for a shape the proposed method involves an iterative evolution of a piecewise linear approximation of the shape skeleton by using a minimum spanning tree based self organizing map som by constraining the som to lie on the edges of the delaunay triangulation of the shape distribution the adjacency relationships between regions in the shape are detected and used in the evolution of the skeleton the som on convergence gives the final skeletal shape the skeletonization is invariant to euclidean transformations the potential of the method is demonstrated on a variety of sparse shapes from different application domains

fast curve estimation using preconditioned generalized radon transform a new algorithm for fast curve parameter estimation based on the generalized radon transform is proposed the algorithm works on binary images obtained e g by edge filtering or deconvolution the fundamental idea of the suggested algorithm is the use of a precondition map to reduce the computational cost of the generalized radon transform the precondition map is composed of irregular regions in the parameter domain which contain peaks that represent curves in the image to generate the precondition map a fast mapping procedure named image point mapping is developed as the image point mapping scheme maps image points into the corresponding parameter values in the parameter domain it is possible to improve computational efficiency by recognizing image points with value zero initially the suggested algorithm estimates the precondition map and subsequently applies the generalized radon transform within the regions specified by the precondition map the required parameter domain sampling and the resulting blurring are also investigated the suggested algorithm is successfully applied to the identification of hyperbolas in seismic images and two numerical examples are given

a smoothed em approach to indirect estimation problems with particular reference to stereology and emission tomography there are many practical problems where the observed data are not drawn directly from the density g of real interest but rather from another distribution derived from g by the application of an integral operator the estimation of g then entails both statistical and numerical difficulties a natural statistical approach is by maximum likelihood conveniently implemented using the em algorithm but this provides unsatisfactory reconstructions of g in this paper we modify the maximum likelihood em approach by introducing a simple smoothing step at each em iteration in our experience this algorithm converges in relatively few iterations to good estimates of g that do not depend on the choice of starting configuration some theoretical background is given that relates this smoothed em algorithm to a maximum penalized likelihood approach two applications are considered in detail the first is the classical stereology problem of determining particle size distributions from data collected on a plane section through a composite medium the second concerns the recovery of the structure of a section of the human body from external observations obtained by positron emission tomography for this problem we also suggest several technical improvements on existing methodology

rates of convergence of the hastings and metropolis algorithms we apply recent results in markov chain theory to hastings and metropolis algorithms with either independent or symmetric candidate distributions and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution pi in the independence case in mathbb r k these indicate that geometric convergence essentially occurs if and only if the candidate density is bounded below by a multiple of pi in the symmetric case in mathbb r only we show geometric convergence essentially occurs if and only if pi has geometric tails we also evaluate recently developed computable bounds on the rates of convergence in this context examples show that these theoretical bounds can be inherently extremely conservative although when the chain is stochastically monotone the bounds may well be effective

numerical simulation of polynomial speed convergence phenomenon we provide a hybrid method that captures the polynomial speed of convergence and polynomial speed of mixing for markov processes the hybrid method that we introduce is based on the coupling technique and renewal theory we propose to replace some estimates in classical results about the ergodicity of markov processes by numerical simulations when the corresponding analytical proof is difficult after that all remaining conclusions can be derived from rigorous analysis then we apply our results to seek numerical justification for the ergodicity of two 1d microscopic heat conduction models the mixing rate of these two models are expected to be polynomial but very difficult to prove in both examples our numerical results match the expected polynomial mixing rate well

thinning approach for noisy digital patterns abstract many problems difficult to solve by traditional computer algorithms can be explored by the principles of human visual perception from the hint of human visual symmetry a thinning approach for noisy digital patterns is presented in this paper it includes three main algorithms algorithm 1 is designed to find the effective circular range for each pixel containing the maximum effective information algorithm 2 is designed to compute the symmetry score of the pixel distribution in the circular range and convert the symmetry information into a gray scale image algorithm 3 provides a modified gray scale thinning algorithm for thinning the gray scale image to obtain a connected thin line experiments show that the thinning results obtained by the proposed method are properly acceptable whensnr 2 2 db and the connectedness of the thin line can be preserved

nearest neighbor clutter removal for estimating features in spatial point processes abstract we consider the problem of detecting features in spatial point processes in the presence of substantial clutter one example is the detection of minefields using reconnaissance aircraft images that identify many objects that are not mines our solution uses kth nearest neighbor distances of points in the process to classify them as clutter or otherwise the observed kth nearest neighbor distances are modeled as a mixture distribution the parameters of which are estimated by a simple em algorithm this method allows for detection of generally shaped features that need not be path connected in the minefield example this method yields high detection and low false positive rates another application to outlining seismic faults is considered with some success the method works well in high dimensions the method can also be used to produce very high breakdown point robust estimators of a covariance matrix

on the convergence of the markov chain simulation method the markov chain simulation method has been successfully used in many problems including some that arise in bayesian statistics we give a self contained proof of the convergence of this method in general state spaces under conditions that are easy to verify

practical bayesian density estimation using mixtures of normals abstract mixtures of normals provide a flexible model for estimating densities in a bayesian framework there are some difficulties with this model however first standard reference priors yield improper posteriors second the posterior for the number of components in the mixture is not well defined if the reference prior is used third posterior simulation does not provide a direct estimate of the posterior for the number of components we present some practical methods for coping with these problems finally we give some results on the consistency of the method when the maximum number of components is allowed to grow with the sample size

assessing quantification for the ems algorithm abstract a framework is developed for assessing the potential of the ems estimate maximize and smooth algorithm to correctly quantify the emission it aims to reconstruct maximal eigenvector localization bounds of perron frobenius theory are used to show that the ability of the ems algorithm to quantify differences in emission is fundamentally limited by the smoothing imposed and the properties of the underlying model matrix in the algorithm in particular it is established that for nonnegative irreducible smoothing the ems algorithm will always fail to correctly reconstruct zero emission intensity

noise can speed convergence in markov chains a new theorem shows that noise can speed convergence to equilibrium in discrete finite state markov chains the noise applies to the state density and helps the markov chain explore improbable regions of the state space the theorem ensures that a stochastic resonance noise benefit exists for states that obey a vector norm inequality such noise leads to faster convergence because the noise reduces the norm components a corollary shows that a noise benefit still occurs if the system states obey an alternate norm inequality this leads to a noise benefit algorithm that requires knowledge of the steady state an alternative blind algorithm uses only past state information to achieve a weaker noise benefit simulations illustrate the predicted noise benefits in three well known markov models the first model is a two parameter ehrenfest diffusion model that shows how noise benefits can occur in the class of birth death processes the second model is a wright fisher model of genotype drift in population genetics the third model is a chemical reaction network of zeolite crystallization a fourth simulation shows a convergence rate increase of 64 for states that satisfy the theorem and an increase of 53 for states that satisfy the corollary a final simulation shows that even suboptimal noise can speed convergence if the noise applies over successive time cycles noise benefits tend to be sharpest in markov models that do not converge quickly and that do not have strong absorbing states

heat flow in an exactly solvable model a chain of one dimensional oscillators is considered they are mechanically uncoupled and interact via a stochastic process which redistributes the energy between nearest neighbors the total energy is kept constant except for the interactions of the extremal oscillators with reservoirs at different temperatures the stationary measures are obtained when the chain is finite the thermodynamic limit is then considered approach to the gibbs distribution is proven and a linear temperature profile is obtained

a bottom up algorithm for finding principal curves with applications to image skeletonization this paper proposes a new method for finding principal curves from data sets motivated by solving the problem of highly curved and self intersecting curves we present a bottom up strategy to construct a graph called a principal graph for representing a principal curve the method initializes a set of vertices based on principal oriented points introduced by delicado and then constructs the principal graph from these vertices through a two layer iteration process in inner iteration the kernel smoother is used to smooth the positions of the vertices in outer iteration the principal graph is spanned by minimum spanning tree and is modified by detecting closed regions and intersectional regions and then new vertices are inserted into some edges in the principal graph we tested the algorithm on simulated data sets and applied it to image skeletonization experimental results show the effectiveness of the proposed algorithm

derivation of a class of training algorithms a novel derivation is presented of t kohonen s topographic mapping training algorithm self organization and associative memory 1984 based upon an extension of the linde buzo gray lbg algorithm for vector quantizer design thus a vector quantizer is designed by minimizing an l sub 2 reconstruction distortion measure including an additional contribution from the effect of code noise which corrupts the output of the vector quantizer the neighborhood updating scheme of kohonen s topographic mapping training algorithm emerges as a special case of this code noise model this formulation of kohonen s algorithm is a specific instance of the robust hidden layer principle which stabilizes the internal representations chosen by a network against anticipated noise or distortion processes

asymptotic coupling and a general form of harris theorem with applications to stochastic delay equations there are many markov chains on infinite dimensional spaces whose one step transition kernels are mutually singular when starting from different initial conditions we give results which prove unique ergodicity under minimal assumptions on one hand and the existence of a spectral gap under conditions reminiscent of harris theorem the first uses the existence of couplings which draw the solutions together as time goes to infinity such asymptotic couplings were central to mattingly and sinai in comm math phys 219 3 523 565 2001 mattingly in comm math phys 230 3 461 462 2002 hairer in prob theory relat field 124 345 380 2002 bakhtin and mattingly in commun contemp math 7 553 582 2005 on which this work builds as in bakhtin and mattingly 2005 the emphasis here is on stochastic differential delay equations harris celebrated theorem states that if a markov chain admits a lyapunov function whose level sets are small in the sense that transition probabilities are uniformly bounded from below then it admits a unique invariant measure and transition probabilities converge towards it at exponential speed this convergence takes place in a total variation norm weighted by the lyapunov function a second aim of this article is to replace the notion of a small set by the much weaker notion of a d small set which takes the topology of the underlying space into account via a distance like function d with this notion at hand we prove an analogue to harris theorem where the convergence takes place in a wasserstein like distance weighted again by the lyapunov function this abstract result is then applied to the framework of stochastic delay equations in this framework the usual theory of harris chains does not apply since there are natural examples for which there exist no small sets except for sets consisting of only one point this gives a solution to the long standing open problem of finding natural conditions under which a stochastic delay equation admits at most one invariant measure and transition probabilities converge to it

non equilibrium statistical mechanics of anharmonic chains coupled to two heat baths at different temperatures we study the statistical mechanics of a finite dimensional non linear hamiltonian system a chain of anharmonic oscillators coupled to two heat baths described by wave equations assuming that the initial conditions of the heat baths are distributed according to the gibbs measures at two different temperatures we study the dynamics of the oscillators under suitable assumptions on the potential and on the coupling between the chain and the heat baths we prove the existence of an invariant measure for any temperature difference i e we prove the existence of steady states furthermore if the temperature difference is sufficiently small we prove that the invariant measure is unique and mixing in particular we develop new techniques for proving the existence of invariant measures for random processes on a non compact phase space these techniques are based on an extension of the commutator method of hormander used in the study of hypoelliptic differential operators

large deviation of the density profile in the steady state of the open symmetric simple exclusion process we consider an open one dimensional lattice gas on sites i 1 n with particles jumping independently with rate 1 to neighboring interior empty sites the simple symmetric exclusion process the particle fluxes at the left and right boundaries corresponding to exchanges with reservoirs at different chemical potentials create a stationary nonequilibrium state sns with a steady flux of particles through the system the mean density profile in this state which is linear describes the typical behavior of a macroscopic system i e this profile occurs with probability 1 when n the probability of microscopic configurations corresponding to some other profile x x i n has the asymptotic form exp n f f is the large deviation functional in contrast to equilibrium systems for which f eq is just the integral of the appropriately normalized local free energy density the f we find here for the nonequilibrium system is a nonlocal function of this gives rise to the long range correlations in the sns predicted by fluctuating hydrodynamics and suggests similar non local behavior of f in general sns where the long range correlations have been observed experimentally

adaptive principal surfaces abstract we develop a nonlinear generalization of principal components analysis a principal surface of the data is constructed adaptively using some ideas from the mars procedure of friedman we explore applications to curve and surface reconstruction and to data summarization

variants of self organizing maps self organizing maps have a bearing on traditional vector quantization a characteristic that makes them more closely resemble certain biological brain maps however is the spatial order of their responses which is formed in the learning process a discussion is presented of the basic algorithms and two innovations dynamic weighting of the input signals at each input of each cell which improves the ordering when very different input signals are used and definition of neighborhoods in the learning algorithm by the minimal spanning tree which provides a far better and faster approximation of prominently structured density functions it is cautioned that if the maps are used for pattern recognition and decision process it is necessary to fine tune the reference vectors so that they directly define the decision borders