modeling fractures and barriers as interfaces for flow in porous media we consider a fractured porous medium that is studied at a scale such that the fractures can be modeled individually models for flow in which the fractures are interfaces between subdomains are presented these models take into account interactions between the fractures and the surrounding porous medium existence and uniqueness of the solution to the model problem are proved error estimates show convergence as mathcal o max h d in the l2 norm where h is the mesh size and d the fracture width numerical experiments confirm the theoretical results

on conditional and intrinsic autoregressions summary gaussian conditional autoregressions have been widely used in spatial statistics and bayesian image analysis where they are intended to describe interactions between random variables at fixed sites in euclidean space the main appeal of these distributions is in the markovian interpretation of their full conditionals intrinsic autoregressions are limiting forms that retain the markov property despite being improper they can have advantages over the standard autoregressions both conceptually and in practice for example they often avoid difficulties in parameter estimation without apparent loss or exhibit appealing invariances as in texture analysis however on small arrays and in nonlattice applications both forms of autoregression can lead to undesirable second order characteristics either in the variables themselves or in contrasts among them this paper discusses standard and intrinsic autoregressions and describes how the problems that arise can be alleviated using dempster s 1972 algorithm or an appropriate modification the approach represents a partial synthesis of standard geostatistical and gaussian markov random field formulations some nonspatial applications are also mentioned

stable cell centered finite volume discretization for biot equations in this paper we discuss a new discretization for the biot equations the discretization treats the coupled system of deformation and flow directly as opposed to combining discretizations for the two separate subproblems the coupled discretization has the following key properties the combination of which is novel 1 the variables for the pressure and displacement are co located and are as sparse as possible e g one displacement vector and one scalar pressure per cell center 2 with locally computable restrictions on grid types the discretization is stable with respect to the limits of incompressible fluid and small time steps 3 no artificial stabilization term has been introduced furthermore due to the finite volume structure embedded in the discretization explicit local expressions for both momentum balancing forces and mass conservative fluid fluxes are available we prove stability of the proposed method with respect to all relevant limits together with consistency this proves conve

bayesian reconstructions from emission tomography data using a modified em algorithm a novel method of reconstruction from single photon emission computerized tomography data is proposed this method builds on the expectation maximization em approach to maximum likelihood reconstruction from emission tomography data but aims instead at maximum posterior probability estimation which takes account of prior belief about smoothness in the isotope concentration a novel modification to the em algorithm yields a practical method the method is illustrated by an application to data from brain scans

image estimation using doubly stochastic gaussian random field models the two dimensional 2 d doubly stochastic gaussian dsg model was introduced by one of the authors to provide a complete model for spatial filters which adapt to the local structure in an image signal here we present the optimal estimator and 2 d fixed lag smoother for this dsg model extending earlier work of ackerson and fu as the optimal estimator has an exponentially growing state space we investigate suboptimal estimators using both a tree and a decision directed method experimental results are presented

adaptive estimation of stationary gaussian fields we study the nonparametric covariance estimation of a stationary gaussian field x observed on a regular lattice in the time series setting some procedures like aic are proved to achieve optimal model selection among autoregressive models however there exists no such equivalent results of adaptivity in a spatial setting by considering collections of gaussian markov random fields gmrf as approximation sets for the distribution of x we introduce a novel model selection procedure for spatial fields for all neighborhoods m in a given collection mathcal m this procedure first amounts to computing a covariance estimator of x within the gmrfs of neighborhood m then it selects a neighborhood m by applying a penalization strategy the so defined method satisfies a nonasymptotic oracle type inequality if x is a gmrf the procedure is also minimax adaptive to the sparsity of its neighborhood more generally the procedure is adaptive to the rate of approximation of the true distribution by gmrfs with growing neighborhoods

a primal dual active set algorithm for three dimensional contact problems with coulomb friction in this paper efficient algorithms for contact problems with tresca and coulomb friction in three dimensions are presented and analyzed the numerical approximation is based on mortar methods for nonconforming meshes with dual lagrange multipliers using a nonsmooth complementarity function for the three dimensional friction conditions a primal dual active set algorithm is derived the method determines active contact and friction nodes and at the same time resolves the additional nonlinearity originating from sliding nodes no regularization and no penalization are applied and superlinear convergence can be observed locally in combination with a multigrid method it defines a robust and fast strategy for contact problems with tresca or coulomb friction the efficiency and flexibility of the method is illustrated by several numerical examples

finite volume methods for elasticity with weak symmetry we introduce a new cell centered finite volume discretization for elasticity with weakly enforced symmetry of the stress tensor the method is motivated by the need for robust discretization methods for deformation and flow in porous media and falls in the category of multi point stress approximations mpsa by enforcing symmetry weakly the resulting method has additional flexibility beyond previous mpsa methods this allows for a construction of a method which is applicable to all grid types and in particular the method amends a crucial shortcoming in previous mpsa methods for simplex grids by formulating the method as a discrete variational problem we prove convergence of the new method for a wide range of problems with conditions that can be verified at the time of discretization we present the first set of comprehensive numerical tests for the mpsa methods in three dimensions covering cartesian and simplex grids with both heterogeneous and nearly incompressible media the tests show that the new method consistently is second order convergent in displacement despite being lowest order with a rate that mostly is between 1 and 2 for stresses the results further show that the new method is more robust and computationally cheaper than previous mpsa methods

markov chain monte carlo convergence diagnostics a comparative review abstract a critical issue for users of markov chain monte carlo mcmc methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest research into methods of computing theoretical convergence bounds holds promise for the future but to date has yielded relatively little of practical use in applied work consequently most mcmc users address the convergence problem by applying diagnostic tools to the output produced by running their samplers after giving a brief overview of the area we provide an expository review of 13 convergence diagnostics describing the theoretical basis and practical implementation of each we then compare their performance in two simple models and conclude that all of the methods can fail to detect the sorts of convergence failure that they were designed to identify we thus recommend a combination of strategies aimed at evaluating and accelerating mcmc sampler convergence including ap

on a free boundary problem for thep laplacian abstract by a maximum principle we obtain radial symmetry of domain and weak solution to div du p 2du 0 on a starshaped ring 0 1 inrn with the overdetermined boundary conditionsu 1 and du c1uniformly a e asx 1 u 0 and du c0uniformly a e asx 0 c1 c0 0 1

maximum likelihood reconstruction for emission tomography previous models for emission tomography et do not distinguish the physics of et from that of transmission tomography we give a more accurate general mathematical model for et where an unknown emission density x y z generates and is to be reconstructed from the number of counts n d in each of d detector units d within the model we give an algorithm for determining an estimate of which maximizes the probability p n of observing the actual detector count data n over all possible densities let independent poisson variables n b with unknown means b b 1 b represent the number of unobserved emissions in each of b boxes pixels partitioning an object containing an emitter suppose each emission in box b is detected in detector unit d with probability p b d d 1 d with p b d a one step transition matrix assumed known we observe the total number n n d of emissions in each detector unit d and want to estimate the unknown b b 1 b for each the observed data n has probability or likelihood p n the em algorithm of mathematical statistics starts with an initial estimate 0 and gives the following simple iterative procedure for obtaining a new estimate new from an old estimate old to obtain k k 1 2 new b old b dd 1 n d p b d old b p b d b 1 b

inhomogeneous prior models for image reconstruction abstract over recent years the use of homogeneous gibbs prior models in image processing has become widely accepted there has been however much discussion over precisely which models are most appropriate for most applications the simplest gaussian model tends to oversmooth reconstructions so it has been rejected in favor of various edge preserving alternatives we claim that the problem is not with the gaussian family but rather with the assumption of homogeneity in this article we propose an inhomogeneous gaussian random field as a general prior model for many image processing applications the simplicity of the gaussian model allows rapid calculation and the flexibility of the spatially varying prior parameter allows varying degrees of spatial smoothing this approach is in the spirit of adaptive kernel density methods where only the choice of the variable window width is important the analysis of real single photon emission computed tomography data is used to illustrate the methods and simu

symmetric positive definite flux continuous full tensor finite volume schemes on unstructured cell centered triangular grids novel cell centered full tensor finite volume methods are presented for general unstructured grids in two spatial dimensions the numerical schemes are flux continuous and based on computing the transmissibilities in a local subcell transform space ensuring that local flux matrices are symmetric as a result the global discretization matrix is shown to be symmetric positive definite for any grid type a symmetric physical space method is also introduced and the symmetric methods are shown to be closely related discrete ellipticity conditions are derived for positive definiteness of the physical space and subcell space schemes computational examples are presented for unstructured triangular grids demonstrating good performance of the scheme the schemes are compared with the so called multipoint flux approximation mpfa o method i aavatsmark t barkve o boe and t mannseth siam j sci comput 19 1998 pp 1700 1716 good agreement between the methods is obtained but the new scheme shows improved behavior in challenging cases

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

hybrid finite element methods for the signorini problem we study three mixed linear finite element methods for the numerical simulation of the two dimensional signorini problem applying falk s lemma and saddle point theory to the resulting discrete mixed variational inequality allows us to state the convergence rate of each of them two of these finite elements provide optimal results under reasonable regularity assumptions on the signorini solution and the numerical investigation shows that the third method also provides optimal accuracy

bayesian estimation for homogeneous and inhomogeneous gaussian random fields this paper investigates bayesian estimation for gaussian markov random fields in particular a new class of compound model is proposed which describes the observed intensities using an inhomogeneous model and the degree of spatial variation described by a second random field the coupled markov random fields are used as prior distributions and combined with gaussian noise models to produce posterior distributions on which estimation is based all model parameters are estimated in a fully bayesian setting using the metropolis hasting algorithm the full posterior estimation procedures are illustrated and compared using various artificial examples for these examples the inhomogeneous model performs very favorably when compared to the homogeneous model allowing differential degrees of smoothing and varying local textures

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

constrained restoration and the recovery of discontinuities the linear image restoration problem is to recover an original brightness distribution x sup 0 given the blurred and noisy observations y kx sup 0 b where k and b represent the point spread function and measurement error respectively this problem is typical of ill conditioned inverse problems that frequently arise in low level computer vision a conventional method to stabilize the problem is to introduce a priori constraints on x sup 0 and design a cost functional h x over images x which is a weighted average of the prior constraints regularization term and posterior constraints data term the reconstruction is then the image x which minimizes h a prominent weakness in this approach especially with quadratic type stabilizers is the difficulty in recovering discontinuities the authors therefore examine prior smoothness constraints of a different form which permit the recovery of discontinuities without introducing auxiliary variables for marking the location of jumps and suspending the constraints in their vicinity in this sense discontinuities are addressed implicitly rather than explicitly

on two free boundary problems in potential theory in two dimensions this problem plays a role in the theory of nonlinear elasticity where the function u x may be interpreted as the stress function associated to an elasto plastic beam of cross section q c ox when g 1 the problem reduces to that of the elastic torsion of a hollow cylinder in which case our result is a natural extension of serrin s and weinberger s results 18 193 the corresponding classical boundary value problem i e with fixed 2 but

statistical mechanical approach to image processing the basic frameworks and techniques of the bayesian approach to image restoration are reviewed from the statistical mechanical point of view first a few basic notions in digital image processing are explained to convince the reader that statistical mechanics has a close formal similarity to this problem second the basic formulation of the statistical estimation from the observed degraded image by using the bayes formula is demonstrated the relationship between bayesian statistics and statistical mechanics is also listed particularly it is explained that some correlation inequalities on the nishimori line of the random spin model also play an important role in bayesian image restoration third the framework of bayesian image restoration for binary images by means of the ising model is reviewed some practical algorithms for binary image restoration are given by employing the mean field and the bethe approximations finally bayesian image restoration for a grey level image using the gaussian model is reviewed and the gaussian model is extended to a more practical probabilistic model by introducing the line state to treat the effects of edges the line state is also extended to quantized values

compound gauss markov random fields for image estimation algorithms for obtaining approximations to statistically optimal estimates for images modeled as compound gauss markov random fields are discussed the authors consider both the maximum a posteriori probability map estimate and the minimum mean squared error mmse estimate for image estimation and image restoration compound image models consist of several submodels having different characteristics along with an underlying structure model which govern transitions between these image submodels two different compound random field models are employed the doubly stochastic gaussian dsg random field and a compound gauss markov cgm random field the authors present map estimators for dsg and cgm random fields using simulated annealing a fast converging algorithm called deterministic relaxation which however converges to only a locally optimal map estimate is also presented as an alternative for reducing computational loading on sequential machines for comparison purposes the authors include results on the fixed lag smoothing mmse estimator for the dsg field and its suboptimal m algorithm approximation

stability and convergence of sequential methods for coupled flow and geomechanics fixed stress and fixed strain splits abstract we analyze stability and convergence of sequential implicit methods for coupled flow and geomechanics in which the flow problem is solved first we employ the von neumann and energy methods for linear and nonlinear problems respectively we consider two sequential methods with the generalized midpoint rule for tn where is the parameter of time discretization namely the fixed strain and fixed stress splits the von neumann method indicates that the fixed strain split is only conditionally stable and that its stability limit is a coupling strength less than unity if 0 5 on the other hand the fixed stress split is unconditionally stable when 0 5 the amplification factors of the fixed stress split are different from those of the undrained split and are identical to the fully coupled method unconditional stability of the fixed stress split is also obtained from the energy method for poroelastoplasticity we show that the fixed stress split is contractive and b stable when 0 5 we also estimate the convergence behaviors for the two sequential methods by the matrix based and spectral analyses for the backward euler method in time from the estimates the fixed strain split may not be convergent with a fixed number of iterations particularly around the stability limit even though it is stable the fixed stress split however is convergent for a fixed number of iterations showing better accuracy than the undrained split even when we cannot obtain the exact local bulk modulus or exact rock compressibility at the flow step a priori due to complex boundary conditions or the nonlinearity of the materials the fixed stress split can still provide stability and convergence by an appropriate estimation of the local bulk modulus such as the dimension based estimation by which the employed local bulk modulus is less stiff than the exact local bulk modulus we provide numerical examples supporting all the estimates of stability and convergence for the fixed strain and fixed stress splits

simple parallel hierarchical and relaxation algorithms for segmenting noncausal markovian random fields the modeling and segmentation of images by mrf s markov random fields is treated these are two dimensional noncausal markovian stochastic processes two conceptually new algorithms are presented for segmenting textured images into regions in each of which the data are modeled as one of c mrf s the algorithms are designed to operate in real time when implemented on new parallel computer architectures that can be built with present technology a doubly stochastic representation is used in image modeling here a gaussian mrf is used to model textures in visible light and infrared images and an autobinary or autoternary etc mrf to model a priori information about the local geometry of textured image regions for image segmentation the true texture class regions are treated either as a priori completely unknown or as a realization of a binary or ternary etc mrf in the former case image segmentation is realized as true maximum likelihood estimation in the latter case it is realized as true maximum a posteriori likelihood segmentation in addition to providing a mathematically correct means for introducing geometric structure the autobinary or ternary etc mrf can be used in a generative mode to generate image geometries and artificial images and such simulations constitute a very powerful tool for studying the effects of these models and the appropriate choice of model parameters the first segmentation algorithm is hierarchical and uses a pyramid like structure in new ways that exploit the mutual dependencies among disjoint pieces of a textured region

single image defogging by multiscale depth fusion restoration of fog images is important for the deweathering issue in computer vision the problem is ill posed and can be regularized within a bayesian context using a probabilistic fusion model this paper presents a multiscale depth fusion mdf method for defog from a single image a linear model representing the stochastic residual of nonlinear filtering is first proposed multiscale filtering results are probabilistically blended into a fused depth map based on the model the fusion is formulated as an energy minimization problem that incorporates spatial markov dependence an inhomogeneous laplacian markov random field for the multiscale fusion regularized with smoothing and edge preserving constraints is developed a nonconvex potential adaptive truncated laplacian is devised to account for spatially variant characteristics such as edge and depth discontinuity defog is solved by an alternate optimization algorithm searching for solutions of depth map by minimizing the nonconvex potential in the random field the mdf method is experimentally verified by real world fog images including cluttered depth scene that is challenging for defogging at finer details the fog free images are restored with improving contrast and vivid colors but without over saturation quantitative assessment of image quality is applied to compare various defog methods experimental results demonstrate that the accurate estimation of depth map by the proposed edge preserved multiscale fusion should recover high quality images with sharp details

numerical stabilization of biot s consolidation model by a perturbation on the flow equation in this paper a stabilized finite element scheme for the poroelasticity equations is proposed this method based on the perturbation of the flow equation allows us to use continuous piecewise linear approximation spaces for both displacements and pressure obtaining solutions without oscillations independently of the chosen discretization parameters the perturbation term depends on a parameter which is established in terms of the mesh size and the properties of the material in the one dimensional case this parameter is shown to be optimal some numerical experiments are presented indicating the efficiency of the proposed stabilization technique copyright 2008 john wiley sons ltd

a new two scale computational model for hydromechanical coupling in jointed rocks abstract we develop a new computational model to describe hydro mechanical coupling in fractured rocks composed of a linear poroelastic biot medium and nonlinear elastic joints with constitutive response governed by the barton bandis bb law the model aims at capturing increase in stiffness induced by fracture closure during fluid withdrawal the nonlinear hydro mechanical formulation is constructed within the framework of the discrete fracture model with flow and geomechanical sub systems coupled through a sequential iterative algorithm the internal contact constraint arising from non overlapping between opposite fracture faces is enforced through the weak fulfillment of the bb law such a constraint is captured within the framework of the augmented lagrangian formulation where the non linear mechanical interaction is enforced adopting successive approximations of the lagrange multiplier interpreted as the contact pressure in the joint supplemented by a penalty component associated with the rock stiffness furthermore adopting a traditional flow based upscaling method macroscopic permeabilities are numerically reconstructed with magnitude strongly dependent on the local stress state such a mechanical dependence of the homogenized properties is represented in a discrete manner through pseudo coupling tables with enormous potential to be explored within a preprocessing stage in reservoir simulators to compute multipliers relative to a chosen pre stressed reference state where input data is available numerical simulations are performed for some fracture arrangements illustrating the potential of the formulation proposed herein in bridging hydromechanical coupling at different scales in jointed rocks

bayesian methods applied to survey data from archeological magnetometry a model is presented for the interpretation of magnetometer data in terms of archeological features beneath the ground it describes the detector s response to the assemblage of buried features incorporating both a spread function and a statistical error process as well as appropriate prior beliefs about the nature of archeological features the problem is to estimate the magnetic susceptibility of the buried features at each horizontal location a monte carlo markov chain approach is used to estimate magnetic susceptibilities and all prior parameters this requires estimation of the normalization constant of the gibbs prior distribution the approach is illustrated with both simulated data and measurements from an archeological site in the latter case the reconstruction of the buried features corresponds well with the archeologist s observations during subsequent excavation

on stability and convergence of finite element approximations of biot s consolidation problem stability and convergence analysis of finite element approximations of biot s equations governing quasistatic consolidation of saturated porous media are discussed a family of decay functions parametrized by the number of time steps is derived for the fully discrete backward euler galerkin formulation showing that the pore pressure oscillations arising from an unstable approximation of the incompressibility constraint on the initial condition decay in time error estimates holding over the unbounded time domain for both semidiscrete and fully discrete formulations are presented and a post processing technique is employed to improve the pore pressure accuracy