multiple window parallel adaptive boundary finding in computer vision the problem considered in this paper is the estimation of highly variable object boundaries in noisy images boundaries may be those of a tank in an ir image a spinal canal in a cat scan a cloud in a visible light image etc or they may be internal to an object such as the boundary between a spherical surface and a cylindrical surface in a manufactured object the focus of the paper is on parallel multiple window boundary estimation algorithms here the image field is parti tioned into an array of rectangular windows and boundary finders are run simultaneously within the windows the boundary segments found within the windows are then seamed together to obtain meaningful global boundaries the entire procedure is treated within a maximum likelihood estimation framework that we have developed for boundary finding although our multiple window estimation approach can be used with a number of local boundary finding algorithms we concen trate on one which is based on dynamic programming and will produce the true maximum likelihood boundary some theoretical considera tions for boundary model design and boundary finding runtime are covered included is the use of a low computational cost f test for test ing whether a window contains a boundary and an analytical treatment which shows that use of coarse pixels with a chi square test or an f test improves the probability of correctly recognizing whether a boundary is present in a window

generalized simulated annealing we discuss and illustrate a new stochastic algorithm generalized simulated annealing for computationally finding the global minimum of a given not necessarily convex energy cost function defined in a continuous d dimensional space this algorithm recovers as particular cases the so called classical boltzmann machine and fast cauchy machine simulated annealings and turns out to be quicker than both

3 d image denoising by local smoothing and nonparametric regression three dimensional 3 d images are becoming increasingly popular in image applications such as magnetic resonance imaging mri functional mri fmri and other image applications observed 3 d images often contain noise that should be removed beforehand for improving the reliability of subsequent image analyses in the literature most existing image denoising methods are for 2 d images their direct extensions to 3 d cases generally cannot handle 3 d images efficiently because the structure of 3 d images is often substantially more complicated than that of 2 d images for instance edge locations are surfaces in 3 d cases which are much more challenging to handle compared to edge curves in 2 d cases in this article we propose a novel 3 d image denoising procedure based on nonparametric estimation of a 3 d jump surface from noisy data one important feature of this method is its ability to preserve edges and major edge structures such as intersections of two edge surfaces pyramids pointed corn

transonic separated flow predictions with an eddy viscosity reynolds stress closure model on evalue un modele de fermeture developpe precedemment pour une serie d interactions fortes transsoniques visqueuses non visqueuses avec des degres de decollement variables

persistence of mass in a chemotaxis system with logistic source this paper studies the dynamical properties of the chemotaxis system ut u u v ru u2 x t 0 vt v v u x t 0 under homogeneous neumann boundary conditions in bounded convex domains rn n 1 with positive constants r and numerical simulations but also some rigorous evidence have shown that depending on the relative size of r and in comparison to the well understood case when 0 this problem may exhibit quite a complex solution behavior including unexpected effects such as asymptotic decay of the quantity u within large subdomains of the present work indicates that any such extinction phenomenon if occurring at all necessarily must be of spatially local nature whereas the population as a whole always persists more precisely it is shown that for any nonnegative global classical solution u v of with u 0 one can find m 0 such that u x t dx m for all t 0 the proof is based on an in this context apparently novel analysis of the functional ln u deriving a lower bound for this quantity along a suitable sequence of times by appropriately exploiting a differential inequality for a suitable linear combination of ln u u and v2

a wavelet or lifting scheme based imputation method summary the paper proposes a new approach to imputation using the expected sparse representation of a surface in a wavelet or lifting scheme basis our method incorporates a bayesian mixture prior for these wavelet coefficients into a gibbs sampler to generate a complete posterior distribution for the variable of interest intuitively the estimator operates by borrowing strength from those observed neighbouring values to impute at the unobserved sites we demonstrate the strong performance of our estimator in both one and two dimensional imputation problems where we also compare its application with the standard imputation techniques of kriging and thin plate splines

approximate random variate generation from infinitely divisible distributions with applications to bayesian inference summary stochastic processes with independent increments play a central role in bayesian nonparametric inference the distributions of the increments of these processes aside from fixed points of discontinuity are infinitely divisible and their laplace and or fourier transforms in the levy representation are usually known conventional bayesian inference in this context has been limited largely to providing point estimates of the random quantities of interest although markov chain monte carlo methods have been used to obtain a fuller analysis in the context of dirichlet process priors in this paper we propose and implement a general method for simulating infinitely divisible random variates when their fourier or laplace transforms are available in the levy representation theoretical justification is established by proving a convergence theorem that is a sampling form of a classical theorem in probability the results provide a method for implementing bayesian nonparametric inference by using a wide range of stochastic processes as priors

aggregation vs global diffusive behavior in the higher dimensional keller segel model abstract we consider the classical parabolic parabolic keller segel system u t u u v x t 0 v t v v u x t 0 under homogeneous neumann boundary conditions in a smooth bounded domain r n it is proved that in space dimension n 3 for each q n 2 and p n one can find e 0 0 such that if the initial data u 0 v 0 satisfy u 0 l q e and v 0 l p e then the solution is global in time and bounded and asymptotically behaves like the solution of a discoupled system of linear parabolic equations in particular u v approaches the steady state m m as t where m is the total mass m u 0 of the population moreover we shall show that if is a ball then for arbitrary prescribed m 0 there exist unbounded solutions emanating from initial data u 0 v 0 having total mass u 0 m

multiscale model for turbulent flows a model is devised for computing general turbulent flows the model is an improvement over two equation turbulence models in a critically important manner that is the new model accounts for disalignment of the reynolds stress tensor and the mean strain rate tensor principal axes the improved representation of the reynolds stress tensor has been accomplished through the introduction of a multiscale description of the turbulence i e two energy scales are used corresponding to upper and lower partitions of the turbulence energy spectrum a novel feature of the formulation is that the differential equation for the reynolds stress tensor is of first order which in effect corresponds to what can be termed an algebraic stress model with convective terms as a consequence of its mathematical simplicity the model is very efficient and easy to implement computationally the model is applied to a wide range of turbulent flows including homogeneous turbulence compressible and incompressible two dimensional boundary layers and unsteady boundary layers including periodic separation and reattachment comparisons with corresponding experimental data show that the model reproducesall salient features of the flows considered perturbation analysis of the viscous sublayer shows that integration through the sublayer can be accomplished with no special viscous modifications to the closure coefficients appearing in the model

wall normal free reynolds stress closure for three dimensional compressible separated flows a near wall reynolds stress closure that is independent of the distance from the wall and of the normal to the walldirection isdevelopedandvalidated particularattention wasgiven intheapplicabilityofthemodeltocomplex three dimensional e ows with shock waves and boundary layer separation in the separated e ow region measurements andmodelcomputations indicatethatthe e atnessparameter aoftheanisotropy tensor aij approaches unity therefore controlofseparation isachieved in themodel through theparticularfunctional dependenceoftherapid pressure strain isotropization of production model coefe cienton a echo termsaretreated by replacing geometric normalsanddistancesbyfunctionsofthegradientsofturbulencelengthscaleandanisotropytensorinvariants the modelisinitiallycomparedwithmeasurementsforcompressiblee at plateboundary layere ows itisthenvalidated by comparison with experimental data in a two dimensional compression corner oblique shock wave boundarylayer interaction at mach 3 finally the model is applied to the computation of the three dimensional interaction of a mach 1 5 1 8 strong shock wave with the boundary layers of a rectangular channel e tted with a swept bump on the lower wall and results are compared with measurements one important advantage of the proposed model is its robustness in complex three dimensional e ows a detailed discussion of therange of validity of the model and possible improvements is presented

a coupling regeneration scheme for diagnosing convergence in markov chain monte carlo algorithms abstract here i propose a convergence diagnostic for markov chain monte carlo mcmc algorithms based on couplings of a markov chain with an auxiliary chain that is periodically restarted from a fixed parameter value the diagnostic provides a mechanism for estimating the specific constants governing the rate of convergence of geometrically and uniformly ergodic chains and provides a lower bound on the effective sample size of a mcmc run it also provides a simple procedure for obtaining what is with high probability an independent sample from the stationary distribution

computation of compression ramp flow with a cross diffusion modified k epsilon model we propose a new k e model with a cross diffusion term that can be used to analyze turbulent nonequilibrium flows

triplet markov fields for the classification of complex structure data we address the issue of classifying complex data we focus on three main sources of complexity namely the high dimensionality of the observed data the dependencies between these observations and the general nature of the noise model underlying their distribution we investigate the recent triplet markov fields and propose new models in this class designed for such data and in particular allowing very general noise models in addition our models can handle the inclusion of a learning step in a consistent way so that they can be used in a supervised framework one advantage of our models is that whatever the initial complexity of the noise model parameter estimation can be carried out using state of the art bayesian clustering techniques under the usual simplifying assumptions as generative models they can be seen as an alternative in the supervised case to discriminative conditional random fields identifiability issues underlying the models in the nonsupervised case are discussed while the models performance is illustrated on simulated and real data exhibiting the mentioned various sources of complexity

blow up in a higher dimensional chemotaxis system despite logistic growth restriction abstract we study radially symmetric solutions of a class of chemotaxis systems generalizing the prototype u t u u v u u x t 0 0 v m t u x t 0 in a ball r n with parameters 0 0 0 and 1 and m t 1 u x t d x it is shown that when n 5 and 3 2 1 2 n 2 then there exist initial data such that the smooth local in time solution of blows up in finite time this indicates that even superlinear growth restrictions may be insufficient to rule out a chemotactic collapse as is known to occur in the corresponding system without any proliferation

outperforming the gibbs sampler empirical estimator for nearest neighbor random fields given a markov chain sampling scheme does the standard empirical estimator make best use of the data we show that this is not so and construct better estimators we restrict attention to nearest neighbor random fields and to gibbs samplers with deterministic sweep but our approach applies to any sampler that uses reversible variable at a time updating with deterministic sweep the structure of the transition distribution of the sampler is exploited to construct further empirical estimators that are combined with the standard empirical estimator to reduce asymptotic variance the extra computational cost is negligible when the random field is spatially homogeneous symmetrizations of our estimator lead to further variance reduction the performance of the estimators is evaluated in a simulation study of the ising model

application of piece wise regression to detecting internal structure of signal abstract the problem of restoring the underlying structure of a signal with the help of piece wise regression is considered the case of interest is that the domain of definition of a response function consists of a number of regions of smoothness the number of regions and the location of change points are not fixed in advance and they should be found by analyzing the signal corrupted with noise for a given number of smooth regions the best piece wise regression may be found with the help of an approach based on dynamic programming the selection of the best model the best number of regions of smoothness is performed with the help of a probabilistic estimate some properties of the estimate and the whole procedure are studied and the results of experiments are presented

comparison between experiment and prediction for a transonic turbulent separated flow solutions of the time dependent mass averaged navier stokes equations are compared in detail with experimental results obtained on an axisymmetric bump model at a transonic mach number that produced an extensive separated now region in addition an inverse boundary method is evaluated for this type of flow the cebeci smith algebraic and the wilcox rubesin two equation turbulence models used in the navier stokes calculations both predict the maximum boundary layer displacement thickness generated by the interaction reasonably well with the details of the now best described with the two equation formulation however both models predict a shock location substantially farther aft on the bump than observed experimentally this error in shock location was slightly less with the two equation model 0 12 chord compared with 0 16 chord in the vicinity of the shock the calculations predict a more rapid increase in turbulent shear stress than observed in the experimental results this more rapid increase is believed to be the cause or the poor predictions in shock position

em and beyond the basic theme of the em algorithm to repeatedly use complete data methods to solve incomplete data problems is also a theme of several more recent statistical techniques these techniques multiple imputation data augmentation stochastic relaxation and sampling importance resampling combine simulation techniques with complete data methods to attack problems that are difficult or impossible for em

blowup and global solutions in a chemotaxis growth system abstract we study a keller segel type of system which includes growth and death of the chemotactic species and an elliptic equation for the chemo attractant the problem is considered in bounded domains with smooth boundary as well as in the whole space in case the random motion of the chemotactic species is neglected a hyperbolic elliptic problem results for which we characterize blow up of solutions in finite time and existence of regular solutions globally in time in dependence on the systems parameters in this case convexity of the domain is needed for the parabolic elliptic problem in dimensions three and higher we establish global existence of regular solutions in a limiting case which is an extension of the results given by tello and winkler 2007

on the equivalence of soft wavelet shrinkage total variation diffusion total variation regularization and sides soft wavelet shrinkage total variation tv diffusion tv regularization and a dynamical system called sides are four useful techniques for discontinuity preserving denoising of signals and images in this paper we investigate under which circumstances these methods are equivalent in the one dimensional case first we prove that haar wavelet shrinkage on a single scale is equivalent to a single step of space discrete tv diffusion or regularization of two pixel pairs in the translationally invariant case we show that applying cycle spinning to haar wavelet shrinkage on a single scale can be regarded as an absolutely stable explicit discretization of tv diffusion we prove that space discrete tv diffusion and tv regularization are identical and that they are also equivalent to the sides system when a specific force function is chosen afterwards we show that wavelet shrinkage on multiple scales can be regarded as a single step diffusion filtering or regularization of the laplacian pyramid of the signal we analyze possibilities to avoid gibbs like artifacts for multiscale haar wavelet shrinkage by scaling the thresholds finally we present experiments where hybrid methods are designed that combine the advantages of wavelets and pde variational approaches these methods are based on iterated shift invariant wavelet shrinkage at multiple scales with scaled thresholds

on explosions of solutions to a system of partial differential equations modelling chemotaxis a system of partial differential equations modelling chemotactic aggregation is analysed keller segel model conditions on the system of paramaters are given implying global existence of smooth solutions in two space dimensions and radially symmetric situations explosion of the bacteria concentration in finite time is shown for a class of initial values

oblique shock wave boundary layer interaction using near wall reynolds stress models a synthesis is presented of the predictive capability of a family of near wall wall normal free reynolds stress models which are completely independent of wall topology i e of the distance fromthe wall and the normal to thewall orientation for oblique shock wave turbulent boundary layer interactions for the purpose of comparison results are also presented using a standard low turbulence reynolds number k e closure and a reynolds stress model that uses geometric wall normals and wall distances studied shock wave mach numbers are in the range msw 2 85 2 9 and incoming boundary layer thickness reynolds numbers are in the range re 0 1 2 106 computations were carefully checked for grid convergence comparison with measurements shows satisfactory agreement improving on results obtained using a k e model and highlights the relative importance of redistribution and diffusion closures indicating directions for future modeling work

digital image restoration using spatial interaction models this paper is concerned with developing fast nonrecursive algorithms for the minimum mean squared error restoration of degraded images the degradation is assumed to be due to a space invariant periodic nonseparable known point spread function and additive white noise our basic approach is to represent the images by a class of spatial interaction models namely the simultaneous autoregressve models and the conditional markov models defined on toroidal lattices and develop minimum mean squared error restoration algorithms using these models the restoration algorithms are optimal if the parameters characterizing the interaction models are exactly known however in practice the parameters are estimated from the images by using spatial interaction models we develop restoration algorithms that do not require the availability of the original image or its prototype the specific structure of the underlying lattice enables the implementation of the filters using fast fourier transform fft computations several restoration examples are given

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

global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening abstract this paper deals with nonnegative solutions of the neumann initial boundary value problem for the parabolic chemotaxis system u t u u v u u 2 x t 0 v t v v u x t 0 in bounded convex domains r n n 1 with smooth boundary it is shown that if the ratio is sufficiently large then the unique nontrivial spatially homogeneous equilibrium given by u v 1 is globally asymptotically stable in the sense that for any choice of suitably regular nonnegative initial data u 0 v 0 such that u 0 0 the above problem possesses a uniquely determined global classical solution u v with u v t 0 u 0 v 0 which satisfies u t 1 l 0 and v t 1 l 0 as t

segmentation given partial grouping constraints we consider data clustering problems where partial grouping is known a priori we formulate such biased grouping problems as a constrained optimization problem where structural properties of the data define the goodness of a grouping and partial grouping cues define the feasibility of a grouping we enforce grouping smoothness and fairness on labeled data points so that sparse partial grouping information can be effectively propagated to the unlabeled data considering the normalized cuts criterion in particular our formulation leads to a constrained eigenvalue problem by generalizing the rayleigh ritz theorem to projected matrices we find the global optimum in the relaxed continuous domain by eigendecomposition from which a near global optimum to the discrete labeling problem can be obtained effectively we apply our method to real image segmentation problems where partial grouping priors can often be derived based on a crude spatial attentional map that binds places with common salient features or focuses on expected object locations we demonstrate not only that it is possible to integrate both image structures and priors in a single grouping process but also that objects can be segregated from the background without specific object knowledge

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

markov random field texture models we consider a texture to be a stochastic possibly periodic two dimensional image field a texture model is a mathematical procedure capable of producing and describing a textured image we explore the use of markov random fields as texture models the binomial model where each point in the texture has a binomial distribution with parameter controlled by its neighbors and number of tries equal to the number of gray levels was taken to be the basic model for the analysis a method of generating samples from the binomial model is given followed by a theoretical and practical analysis of the method s convergence examples show how the parameters of the markov random field control the strength and direction of the clustering in the image the power of the binomial model to produce blurry sharp line like and blob like textures is demonstrated natural texture samples were digitized and their parameters were estimated under the markov random field model a hypothesis test was used for an objective assessment of goodness of fit under the markov random field model overall microtextures fit the model well the estimated parameters of the natural textures were used as input to the generation procedure the synthetic microtextures closely resembled their real counterparts while the regular and inhomogeneous textures did not

genetic algorithms for ambiguous labelling problems abstract consistent labelling problems frequently have more than one solution most work in the field has aimed at disambiguating early in the interpretation process using only local evidence this paper starts with a review of the literature on labelling problems and ambiguity based on this review we propose a strategy for simultaneously extracting multiple related solutions to the consistent labelling problem in a preliminary experimental study we show that an appropriately modified genetic algorithm is a robust tool for finding multiple solutions to the consistent labelling problem these solutions are related by common labellings of the most strongly constrained junctions we have proposed three run time measures of algorithm performance the maximum fitness of the genetic algorithm s population its shannon entropy and the total hamming distance between its distinct members the results to date indicate that when the shannon entropy falls below a certain threshold new solutions are unlikely to emerge and that most of the diversity in the population disappears within the first few generations

convergence theorems for quantum annealing we prove several theorems to give sufficient conditions for convergence of quantum annealing which is a protocol to solve generic optimization problems by quantum dynamics in particular the property of strong ergodicity is proved for the path integral monte carlo implementation of quantum annealing for the transverse ising model under a power decay of the transverse field this result is to be compared with the much slower inverse log decay of temperature in the conventional simulated annealing similar results are proved for the green s function monte carlo approach optimization problems in continuous space of particle configurations are also discussed

on a quasilinear parabolic elliptic chemotaxis system with logistic source abstract this paper deals with a quasilinear parabolic elliptic chemotaxis system with logistic source under homogeneous neumann boundary conditions in a smooth bounded domain for the case of positive diffusion function it is shown that the corresponding initial boundary value problem possesses a unique global classical solution which is uniformly bounded moreover if the diffusion function is zero at some point or a positive diffusion function and the logistic damping effect is rather mild we proved that the weak solutions are global existence finally it is asserted that the solutions approach constant equilibria in the large time for a specific case of the logistic source

the measure on the original space from a product measure abstract the measurability problems can arise in gaussian and empirical processes underlying nonparametric and semiparametric problems critical in modern statistics and machine learning the usual applications are high dimensional data in random fields to ensure the validity of recovering a true original complex object from its observed images treated in a product space that appears in existing high dimensional data applications widely arising in physical biological and social sciences and engineering we begin with the results on the algebra of the original space induced by a given map f t mapping from to a product measure space t f t t we study the certain measurability issues on with the induced measure from the image measure t of the product space by establishing the outer measure restricted to the trace algebra we further investigate the measure on under the map f t to obtain the conditions for the identifiability equality t f t 1 to hold so that a practical and rigorous foundation is provided for the nontrivial applications to work meaningfully

iterative reweighted total generalized variation based poisson noise removal model total generalized variation tgv regularization model is one of the most effective methods for denoising and eliminating staircase effect however the tgv regularization model tends to blur edges as the existence of high order derivative in order to avoid the staircase effect while alleviating the edge blurring an iterative reweighted tgv based poisson noise removal model is presented under the assumption that each pixel of noisy image follows a poisson distribution the weight function incorporated in the tgv regularization term is derived from the expectation maximization em algorithm we design a new iterative weighted primal dual algorithm which is an improvement of the classic iterative reweighted algorithm numerical experimental results show the better performance of our model in removing noise effectively while preserving edges and eliminating staircase effect

boundedness vs blow up in a chemotaxis system abstract we determine the critical blow up exponent for a keller segel type chemotaxis model where the chemotactic sensitivity equals some nonlinear function of the particle density assuming some growth conditions for the chemotactic sensitivity function we establish an a priori estimate for the solution of the problem considered and conclude the global existence and boundedness of the solution furthermore we prove the existence of solutions that become unbounded in finite or infinite time in that situation where this a priori estimate fails

phase unwrapping of mr phase images using poisson equation the authors have developed a technique based on a solution of the poisson equation to unwrap the phase in magnetic resonance mr phase images the method is based on the assumption that the magnitude of the inter pixel phase change is less than spl pi per pixel therefore the authors obtain an estimate of the phase gradient by wrapping the gradient of the original phase image the problem is then to obtain the absolute phase given the estimate of the phase gradient the least squares ls solution to this problem is shown to be a solution of the poisson equation allowing the use of fast poisson solvers the absolute phase is then obtained by mapping the ls phase to the nearest multiple of 2 k from the measured phase the proposed technique is evaluated using mr phase images and is proven to be robust in the presence of noise an application of the proposed method to the 3 point dixon technique for water and fat separation is demonstrated

object based estimation of dense motion fields motion estimation belongs to key techniques in image sequence processing segmentation of the motion fields such that ideally each independently moving object uniquely corresponds to one region is one of the essential elements in object based image processing this paper is concerned with unsupervised simultaneous estimation of dense motion fields and their segmentations it is based on a stochastic model relating image intensities to motion information based on the analysis of natural images a region based model of motion compensated prediction error is proposed in each region the error is modeled by a white stationary generalized gaussian random process the motion field and its segmentation are themselves modeled by a compound gibbs markov random field accounting for statistical bindings in spatial direction and along the direction of motion trajectories the a posteriori distribution of the motion field for a given image sequence is formulated as an objective function such that its maximization results in the map estimate a deterministic multiscale relaxation technique with regular structure is employed for optimization of the objective function simulation results are in a good agreement with human perception for both the motion fields and their segmentations

3 d contextual bayesian classifiers we extend a series of multivariate bayesian two dimensional 2 d contextual classifiers to three dimensional 3 d by specifying a simultaneous gaussian distribution for the feature vectors as well as a prior distribution of the class variables of a pixel and its six nearest 3 d neighbors

bayesian lasso for semiparametric structural equation models there has been great interest in developing nonlinear structural equation models and associated statistical inference procedures including estimation and model selection methods in this paper a general semiparametric structural equation model ssem is developed in which the structural equation is composed of nonparametric functions of exogenous latent variables and fixed covariates on a set of latent endogenous variables a basis representation is used to approximate these nonparametric functions in the structural equation and the bayesian lasso method coupled with a markov chain monte carlo mcmc algorithm is used for simultaneous estimation and model selection the proposed method is illustrated using a simulation study and data from the affective dynamics and individual differences adid study results demonstrate that our method can accurately estimate the unknown parameters and correctly identify the true underlying model

the indian buffet process an introduction and review the indian buffet process is a stochastic process defining a probability distribution over equivalence classes of sparse binary matrices with a finite number of rows and an unbounded number of columns this distribution is suitable for use as a prior in probabilistic models that represent objects using a potentially infinite array of features or that involve bipartite graphs in which the size of at least one class of nodes is unknown we give a detailed derivation of this distribution and illustrate its use as a prior in an infinite latent feature model we then review recent applications of the indian buffet process in machine learning discuss its extensions and summarize its connections to other stochastic processes

global existence and asymptotic behavior of classical solutions to a parabolic elliptic chemotaxis system with logistic source on rn in the current paper we consider the following parabolic elliptic semilinear keller segel model on rnrn ut u u v au bu2 x rn t 0 0 i v u x rn t 0 where 0 a 0 b 0 are constant real numbers and n is a positive integer we first prove the local existence and uniqueness of classical solutions u x t u0 v x t u0 u x t u0 v x t u0 with u x 0 u0 u0 x u x 0 u0 u0 x for various initial functions u0 x u0 x next under some conditions on the constants a b a b and the dimension n we prove the global existence and boundedness of classical solutions u x t u0 v x t u0 u x t u0 v x t u0 for given initial functions u0 x u0 x finally we investigate the asymptotic behavior of the global solutions with strictly positive initial functions or nonnegative compactly supported initial functions under some conditions on the constants a b a b and the dimension n we show that for every strictly positive initial function u0 u0 limt supx rn u x t u0 ab v x t u0 ab 0 and that for every nonnegative initial function u0 u0 with non empty and compact support supp u0 supp u0 there are 0 clow u0 cup u0 such that limt sup x ct u x t u0 ab v x t u0 ab 0 0 c clow u0 and limt sup x ct u x t u0 v x t u0 0 c cup u0

segmentation based on fusion of range and intensity images using robust trimmed methods abstract this paper proposes a segmentation algorithm based on fusion of range and intensity images using robust trimmed methods based on the bayesian theory a priori knowledge is represented using the markov random field mrf a maximum a posteriori map estimator is constructed using the edge features extracted from both range and intensity images objects are represented by a number of local planar surfaces in range images and the parametric space for surface representation is constructed with the surface parameters estimated pixel by pixel based on the least trimmed squares lts method whereas in intensity images the trimmed variance is adopted as the feature for edge extraction a final edge map is obtained by the map estimator that is constructed using the likelihood functions based on the edge information obtained from range and intensity images finally an image is segmented using the fused edge map computer simulation results show that our new segmentation algorithm effectively segments test images independent of shadow noise and lighting environment

convergence of simulated annealing using the generalized transition probability we prove weak ergodicity of the inhomogeneous markov process generated by the generalized transition probability of tsallis and stariolo under power law decay of the temperature we thus have a mathematical foundation to conjecture convergence of simulated annealing processes with the generalized transition probability to the minimum of the cost function an explicitly solvable example in one dimension is analyzed in which the generalized transition probability leads to a fast convergence of the cost function to the optimal value we also investigate how far our arguments depend upon the specific form of the generalized transition probability proposed by tsallis and stariolo it is shown that a few requirements on analyticity of the transition probability are sufficient to assure fast convergence in the case of the solvable model in one dimension

convergence analysis of reweighted sum product algorithms markov random fields are designed to represent structured dependencies among large collections of random variables and are well suited to capture the structure of real world signals many fundamental tasks in signal processing e g smoothing denoising segmentation etc require efficient methods for computing approximate marginal probabilities over subsets of nodes in the graph the marginalization problem though solvable in linear time for graphs without cycles is computationally intractable for general graphs with cycles this intractability motivates the use of approximate ldquomessage passingrdquo algorithms this paper studies the convergence and stability properties of the family of reweighted sum product algorithms a generalization of the widely used sum product or belief propagation algorithm in which messages are adjusted with graph dependent weights for pairwise markov random fields we derive various conditions that are sufficient to ensure convergence and also provide bounds on the geometric convergence rates when specialized to the ordinary sum product algorithm these results provide strengthening of previous analyses we prove that some of our conditions are necessary and sufficient for subclasses of homogeneous models but not for general models the experimental simulations on various classes of graphs validate our theoretical results

high speed turbulent separated flows consistency of mathematical models and flow physics a large fraction of the experimental database used for validation of computational fluid dynamics cfd predictions of shock induced turbulent separated flows consists of time averaged measurements if meaningful conclusions are to be drawn from comparisons of these time averaged data with computations it is important to understand how the data are generated physically this can be difficult and time consuming but is an essential element in the selection of an appropriate mathematical model for the computation for the separated compression ramp interaction which is widely used as a cfd test case global unsteadiness is a dominant phenomenon without modeling the unsteadiness accurate predictions of the time averaged wall pressure outgoing velocity profiles and other parameters will likely remain elusive irrespective of the turbulence model

estimation and choice of neighbors in spatial interaction models of images some aspects of statistical inference for a class of spatial interaction models for finite images are presented primarily the simultaneous autoregressive sar models and conditional markov cm models each of these models is characterized by a set of neighbors a set of coefficients and a noise sequence of specified characteristics we are concerned with two problems the estimation of the unknown parameters in both sar and cm models and the choice of an appropriate model from a class of such competing models assuming gaussian distributed variables we discuss maximum likelihood ml estimation methods in general the ml scheme leads to nonlinear optimization problems to avoid excessive computation an iterative scheme is given for sar models which gives approximate ml estimates in the gaussian case and reasonably good estimates in some non gaussian situations as well likewise for cm models an easily computable consistent estimate is given the asymptotic mean squared error mse of this estimate for a four neighbor cm model is shown tn be substantially less than the mse of the popular coding estimate asymptotically consistent decision rules are given for choosing an appropriate sar or cm model the usefulness of the estimation scheme and the decision rule for the choice of neighbors is illustrated by using synthetic patterns synthetic patterns obeying known sar and cm models are generated and the models corresponding to true and several competing neighbor sets are fitted the estimation scheme yields estimates close to the parameters of the true models and the decision rule for the choice of neighbors picks up the true model from the class of competing models

rigid body segmentation and shape description from dense optical flow under weak perspective we present an algorithm for identifying and tracking independently moving rigid objects from optical flow some previous attempts at segmentation via optical flow have focused on finding discontinuities in the flow field while discontinuities do indicate a change in scene depth they do not in general signal a boundary between two separate objects the proposed method uses the fact that each independently moving object has a unique epipolar constraint associated with its motion thus motion discontinuities based on self occlusion can be distinguished from those due to separate objects the use of epipolar geometry allows for the determination of individual motion parameters for each object as well as the recovery of relative depth for each point on the object the algorithm assumes an affine camera where perspective effects are limited to changes in overall scale no camera calibration parameters are required a kalman filter based approach is used for tracking motion parameters with time

an integrated approach for scene understanding based on markov random field model in this paper we propose a markov random field model based approach as a unified and systematic way for modeling encoding and applying scene knowledge to the image understanding problem in our proposed scheme we formulate the image segmentation and interpretation problem as an integrated scheme and solve it through a general optimization algorithm more specifically the image is first segmented into a set of disjoint regions by a conventional region based segmentation technique which operates on image pixels and a region adjacency graph rag is then constructed from the resulting segmented regions based on the spatial adjacencies between regions our scheme then proceeds on the rag by defining the region merging and labeling problem based on the mrf models in the mrf model we specify the a priori knowledge about the optimal segmentation and interpretation in the form of clique functions and those clique functions are incorporated into the energy function to be minimized by a general optimization technique in the proposed scheme the image segmentation and interpretation processes cooperate in the simultaneous optimization process such that the erroneous segmentation and misinterpretation due to incomplete knowledge about each problem domain can be compensately recovered by continuous estimation of the single unified energy function we exploit the proposed scheme to segment and interpret natural outdoor scene images

singularity patterns in a chemotaxis model the authors study a chemotactic model under certain assumptions and obtain the existence of a class of solutions which blow up at the center of an open disc in finite time such a finite time blow up of solutions implies chemotactic collapse namely concentration of species to form sporae the model studied is the limiting case of a basic chemotactic model when diffusion of the chemical approaches infinity which has the form ut u u v 0 v u 1 on r2 where is an open disc with no flux homogeneous neumann boundary conditions the initial conditions are continuous functions u x 0 u0 x 0 v x 0 v0 x 0 for x under these conditions the authors prove there exists a radially symmetric solution u r t which blows up at r 0 t t a specific description of such a solution is presented the authors also discuss the strong similarity between the chemotactic model they study and the classical stefan problem

relation between optimal nonlinearity and non gaussian noise enhancing a weak signal in a nonlinear system in the study of stochastic resonance it is often mentioned that nonlinearity can enhance a weak signal embedded in noise in order to give a systematic proof of the signal enhancement in nonlinear systems we derive an optimal nonlinearity that maximizes a signal to noise ratio snr the obtained optimal nonlinearity yields the maximum unbiased signal estimation performance which is known in the context of information theory it is found that a linear system is optimal for a gaussian noise but for a non gaussian noise there exist nonlinear systems that can achieve an snr higher than that obtained from linear systems this analysis refers to a system subjected to an additive non gaussian noise with a small signal input

bayes inference in the tobit censored regression model we consider the bayes estimation of the tobit censored regression model with normally distributed errors a simple condition for the existence of posterior moments is provided suitable versions of monte carlo procedures based on symmetric multivariate t distributions and laplacian approximations in a certain parametrization are developed and illustrated ideas involving data augmentation and gibbs sampling cf tanner and wong 1987 and gelfand and smith 1990 are also developed the methods are compared in two examples with diffuse priors and various combinations of sample sizes and degrees of censoring

selecting the number of classes under latent class regression a factor analytic analogue recently the regression extension of latent class analysis rlca model has received much attention in the field of medical research the basic rlca model summarizes shared features of measured multiple indicators as an underlying categorical variable and incorporates the covariate information in modeling both latent class membership and multiple indicators themselves to reduce complexity and enhance interpretability one usually fixes the number of classes in a given rlca often goodness of fit methods comparing various estimated models are used as a criterion to select the number of classes in this paper we propose a new method that is based on an analogous method used in factor analysis and does not require repeated fitting two ideas with application to many settings other than ours are synthesized in deriving the method a connection between latent class models and factor analysis and techniques of covariate marginalization and elimination a monte carlo simulation study is presented to evaluate the behavior of the selection procedure and compare to alternative approaches data from a study of how measured visual impairments affect older persons functioning are used for illustration

the effect of source amplitude and phase in matched field source localization traditional matched field processing is typically employed for localization of a source with unknown amplitude and phase at transmission the spectral information of the source is estimated via maximum likelihood and is used for localization with the bartlett processor maximum a posteriori estimation of the spectrum of the source is here proposed along with the estimation of source location and noise variance where the joint posterior probability distribution of all parameters is computed with gibbs sampling it is shown that the proposed method has a higher probability of correct localization than the traditional approach

voxel based bayesian lesion symptom mapping most existing voxel based lesion symptom mapping methods are based on the same statistical foundation null hypothesis significance testing nhst the two major limitations of these methods are the inability to infer that there is no difference in lesion proportions and a requirement for multiple comparison correction we propose a bayesian approach that directly models the posterior distribution of lesion proportion difference and makes decisions based on inference on this posterior distribution compared to nhst based approaches our bayesian approach yields inference results with clearer semantics and does not require multiple comparison correction we evaluated our bayesian method using simulated data and data from a study of acute ischemic left hemispheric stroke results of both experiments indicate that the bayesian approach is sensitive in detecting regions that characterize group differences

combining monte carlo and mean field like methods for inference in hidden markov random fields issues involving missing data are typical settings where exact inference is not tractable as soon as nontrivial interactions occur between the missing variables approximations are required and most of them are based either on simulation methods or on deterministic variational methods while variational methods provide fast and reasonable approximate estimates in many scenarios simulation methods offer more consideration of important theoretical issues such as accuracy of the approximation and convergence of the algorithms but at a much higher computational cost in this work we propose a new class of algorithms that combine the main features and advantages of both simulation and deterministic methods and consider applications to inference in hidden markov random fields hmrfs these algorithms can be viewed as stochastic perturbations of variational expectation maximization vem algorithms which are not tractable for hmrf we focus more specifically on one of these perturbations and we prove their almost sure convergence to the same limit set as the limit set of vem in addition experiments on synthetic and real world images show that the algorithm performance is very close and sometimes better than that of other existing simulation based and variational em like algorithms

supersonic compression corner applications of a multiscale model for turbulent flows the new multiscale model for turbulent flows developed by wilcox has been sujected to a continuing series of rigorous applications including shock induced boundary layer separation to test its accuracy in simulating complex flow phenomena while previous applications have been inconclusive regarding superiority of the multiscale model over two equation models results obtained demonstrate a marked improvement in predictive accuracy for flows which include boundary layer separation