first order intrinsic autoregressions and the de wijs process summary we discuss intrinsic autoregressions for a first order neighbourhood on a two dimensional rectangular lattice and give an exact formula for the variogram that extends known results to the asymmetric case we obtain a corresponding asymptotic expansion that is more accurate and more general than previous ones and use this to derive the de wijs variogram under appropriate averaging a result that can be interpreted as a two dimensional spatial analogue of brownian motion obtained as the limit of a random walk in one dimension this provides a bridge between geostatistics where the de wijs process was once the most popular formulation and markov random fields and also explains why statistical analysis using intrinsic autoregressions is usually robust to changes of scale we briefly describe corresponding calculations in the frequency domain including limiting results for higher order autoregressions the paper closes with some practical considerations including applications to irregularly spaced data

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

generalized monte carlo significance tests summary simple monte carlo significance testing has many applications particularly in the preliminary analysis of spatial data the method requires the value of the test statistic to be ranked among a random sample of values generated according to the null hypothesis however there are situations in which a sample of values can only be conveniently generated using a markov chain initiated by the observed data so that independence is violated this paper describes two methods that overcome the problem of dependence and allow exact tests to be carried out the methods are applied to the rasch model to the finite lattice ising model and to the testing of association between spatial processes power is discussed in a simple case

an h likelihood method for spatial mixed linear models based on intrinsic auto regressions summary we consider sparse spatial mixed linear models particularly those described by besag and higdon and develop an h likelihood method for their statistical inference the method proposed allows for singular precision matrices as it produces estimates that coincide with those from the residual maximum likelihood based on appropriate differencing of the data and has a novel approach to estimating precision parameters by a gamma linear model furthermore we generalize the h likelihood method to include continuum spatial variations by making explicit use of scaling limit connections between gaussian intrinsic markov random fields on regular arrays and the de wijs process keeping various applications of spatial mixed linear models in mind we devise a novel sparse conjugate gradient algorithm that allows us to achieve fast matrix free statistical computations we provide two applications the first is an extensive analysis of an agricultural variety trial that brings forward various new aspects of nearest neighbour adjustment such as effects on statistical analyses to changes of scale and use of implicit continuum spatial formulation the second application concerns an analysis of a large cotton field which gives a focus to matrix free computations the paper closes with some further considerations such as applications to irregularly spaced data use of the parametric bootstrap and some generalizations to the gaussian matern mixed effect models

a preconditioner for substructuring based on constrained energy minimization a preconditioner for substructuring based on constrained energy minimization concepts is presented the preconditioner is applicable to both structured and unstructured meshes and offers a straightforward approach for the iterative solution of second and fourth order structural mechanics problems the approach involves constraints associated with disjoint sets of nodes on substructure boundaries these constraints provide the means for preconditioning at both the substructure and global levels numerical examples are presented that demonstrate the good performance of the method in terms of iterations compute time and condition numbers of the preconditioned equations

thermodynamics and statistical analysis of gaussian random fields gaussian fields are considered as gibbsian fields thermodynamic functions are calculated for them and the variational principle is proved as an application we get an approximation of log likelihood and an information theoretic interpretation of the asymptotic behaviour of the maximum likelihood estimator for gaussian markov fields

a stabilized finite element method for generalized stationary incompressible flows abstract in this paper we describe a finite element formulation for the numerical solution of the stationary incompressible navier stokes equations including coriolis forces and the permeability of the medium the stabilized method is based on the algebraic version of the sub grid scale approach we first describe this technique for general systems of convection diffusion reaction equations and then we apply it to the linearized flow equations the important point is the design of the matrix of stabilization parameters that the method has this design is based on the identification of the stability problems of the galerkin method and a scaling of variables argument to determine which coefficients must be included in the stabilization matrix this together with the convergence analysis of the linearized problem leads to a simple expression for the stabilization parameters in the general situation considered in the paper the numerical analysis of the linearized problem also shows that the method has optimal convergence properties

parameter estimation for a stationary process on a d dimensional lattice summary we study asymptotic properties of various estimation procedures for a general stationary regular process on a d dimensional lattice differences between d 1 time series and d 2 spatial processes are pointed out we suppose that the process is observed on a set pn with cn points which tends to infinity with the same speed in all directions the relative edge effect is of order cn lid increasing with d this effect is without statistical importance if d 1 but is important if d 2 we give a lcn consistent asymptotically normal estimator of the underlying parameter the procedure being constructed by a modification of whittle s approximation to the log likelihood in the gaussian case this procedure is asymptotically efficient

master slave chaos synchronization criteria for the horizontal platform systems via linear state error feedback control global chaos synchronization of two identical non autonomous horizontal platform systems coupled by linear state error feedback controller is investigated the sufficient criteria for global chaos synchronization are deduced based on the stability theory of linear time varied systems and lyapunov s direct method of which the criteria related to general coupling matrix are first proved and applied to derive the ones related to some special coupling matrices in the examples the coupling strengths are designed by the obtained criteria and the appearances of chaos synchronization are verified it is analytically and numerically examined that the synchronization criteria based on lyapunov s direct method are sharper than the criteria based on the stability theory of linear time varied systems

spatial classification using fuzzy membership models in the usual statistical approach to spatial classification it is assumed that each pixel belongs to precisely one of a small number of known groups this framework is extended to include mixed pixel data then only a proportion of each pixel belongs to each group two models based on multivariate gaussian random fields are proposed to model this fuzzy membership process the problems of predicting the group membership and estimating the parameters are discussed some simulations are presented to study the properties of this approach and an example is given using landsat remote sensing data

mixed finite element methods for stationary incompressible magneto hydrodynamics a new mixed variational formulation of the equations of stationary incompressible magneto hydrodynamics is introduced and analyzed the formulation is based on curl conforming sobolev spaces for the magnetic variables and is shown to be well posed in possibly non convex lipschitz polyhedra a finite element approximation is proposed where the hydrodynamic unknowns are discretized by standard inf sup stable velocity pressure space pairs and the magnetic ones by a mixed approach using nedelec s elements of the first kind an error analysis is carried out that shows that the proposed finite element approximation leads to quasi optimal error bounds in the mesh size

wavelet variance analysis for random fields on a regular lattice there has been considerable recent interest in using wavelets to analyze time series and images that can be regarded as realizations of certain 1 d and 2 d stochastic processes on a regular lattice wavelets give rise to the concept of the wavelet variance or wavelet power spectrum which decomposes the variance of a stochastic process on a scale by scale basis the wavelet variance has been applied to a variety of time series and a statistical theory for estimators of this variance has been developed while there have been applications of the wavelet variance in the 2 d context in particular in works by unser in 1995 on wavelet based texture analysis for images and by lark and webster in 2004 on analysis of soil properties a formal statistical theory for such analysis has been lacking in this paper we develop the statistical theory by generalizing and extending some of the approaches developed for time series thus leading to a large sample theory for estimators of 2 d wavelet variances we apply our theory to simulated data from gaussian random fields with exponential covariances and from fractional brownian surfaces we demonstrate that the wavelet variance is potentially useful for texture discrimination we also use our methodology to analyze images of four types of clouds observed over the southeast pacific ocean

a nodal based finite element approximation of the maxwell problem suitable for singular solutions a new mixed finite element approximation of maxwell s problem is proposed its main features being that it is based on a novel augmented formulation of the continuous problem and the introduction of a mesh dependent stabilizing term which yields a very weak control on the divergence of the unknown the method is shown to be stable and convergent in the natural h rm mathbf curl 0 omega norm for this unknown in particular convergence also applies to singular solutions for which classical nodal based interpolations are known to suffer from spurious convergence upon mesh refinement

intrinsic autoregressions and related models on the two dimensional lattice summary stationary autoregressions on a two dimensional lattice are generalized to intrinsic models where only increments are assumed to be stationary prediction formulae and the asymptotic behaviour of the semivariogram are derived for parameter estimation we propose an approximate maximum likelihood estimator a generalization of whittle s estimator it is derived also for general intrinsic models

a finite element method for magnetohydrodynamics abstract this paper presents a finite element method for the solution of 3d incompressible magnetohydrodynamic mhd flows two important issues are thoroughly addressed first appropriate formulations for the magnetic governing equations and the corresponding weak variational forms are discussed the selected b q formulation is conservative in the sense that the local divergence free condition of the magnetic field is accounted for in the variational sense a galerkin least squares variational formulation is used allowing equal order approximations for all unknowns in the second issue a solution algorithm is developed for the solution of the coupled problem which is valid for both high and low magnetic reynolds numbers several numerical benchmark tests are carried out to assess the stability and accuracy of the finite element method and to test the behavior of the solution algorithm

on some pressure segregation methods of fractional step type for the finite element approximation of incompressible flow problems abstract in this paper we treat several aspects related to time integration methods for the incompressible navier stokes equations that allow to uncouple the calculation of the velocities and the pressure the first family of schemes consists of classical fractional step methods of which we discuss several possibilities for the pressure extrapolation and the time integration of first and second order the second family consists of schemes based on an explicit treatment of the pressure in the momentum equation followed by a poisson equation for the pressure it turns out that this staggered treatment of the velocity and the pressure is stable finally we present predictor corrector methods based on the above schemes that aim to converge to the solution of the monolithic time integration method apart from presenting these schemes and check its numerical performance we also present a complete set of stability results for the fractional step methods that are independent of the space stability of the velocity pressure interpolation that is of the classical inf sup condition

bayesian k space time reconstruction of mr spectroscopic imaging for enhanced resolution a k space time bayesian statistical reconstruction method k bayes is proposed for the reconstruction of metabolite images of the brain from proton 1 h magnetic resonance mr spectroscopic imaging mrsi data k bayes performs full spectral fitting of the data while incorporating structural anatomical spatial information through the prior distribution k bayes provides increased spatial resolution over conventional discrete fourier transform dft based methods by incorporating structural information from higher resolution coregistered and segmented structural mr images the structural information is incorporated via a markov random field mrf model that allows for differential levels of expected smoothness in metabolite levels within homogeneous tissue regions and across tissue boundaries by further combining the structural prior model with a k space time mrsi signal and noise model for a specific set of metabolites and based on knowledge from prior spectral simulations of metabolite signals the impact of artifacts generated by low resolution sampling is also reduced the posterior mode estimates are used to define the metabolite map reconstructions obtained via a generalized expectation maximization algorithm k bayes was tested using simulated and real mrsi datasets consisting of sets of k space time series the recorded free induction decays the results demonstrated that k bayes provided qualitative and quantitative improvement over dft methods

fully bayesian spline smoothing and intrinsic autoregressive priors summary there is a well known bayesian interpretation for function estimation by spline smoothing using a limit of proper normal priors the limiting prior and the conditional and intrinsic autoregressive priors popular for spatial modelling have a common form which we call partially informative normal we derive necessary and sufficient conditions for the propriety of the posterior for this class of partially informative normal priors with noninformative priors on the variance components a condition crucial for successful implementation of the gibbs sampler the results apply for fully bayesian smoothing

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

on the existence uniqueness and finite element approximation of solutions of the equations of stationary incompressible magnetohydrodynamics the authors consider the equations of stationary incompressible magneto hydrodynamics posed in a bounded domain in three dimensions and treat the full coupled system of equations with inhomogeneous boundary conditions under certain conditions on the data they show that the existence and uniqueness of the solution of a weak formulation of the equations can be guaranteed they discuss a finite element discretization of the equations and prove an optimal estimate for the error of the approximate solution

unconditionally stable operator splitting algorithms for the incompressible magnetohydrodynamics system discretized by a stabilized finite element formulation based on projections summary in this article we propose different splitting procedures for the transient incompressible magnetohydrodynamics mhd system that are unconditionally stable we consider two levels of splitting on one side we perform the segregation of the fluid pressure and magnetic pseudo pressure from the vectorial fields computation at the second level the fluid velocity and induction fields are also decoupled this way we transform a fully coupled indefinite multi physics system into a set of smaller definite ones clearly reducing the cpu cost with regard to the finite element approximation we stick to an unconditionally convergent stabilized finite element formulation because it introduces convection stabilization allows to circumvent inf sup conditions clearly simplifying implementation issues and is able to capture non smooth solutions of the magnetic subproblem however residual based finite element formulations are not suitable for segregation because they lose the skew symmetry of the off diagonal blocks therefore in this work we have proposed a novel term by term stabilization of the mhd system based on projections that is still unconditionally convergent copyright 2012 john wiley sons ltd

feti dp a dual primal unified feti method part i a faster alternative to the two level feti method the feti method and its two level extension feti 2 are two numerically scalable domain decomposition methods with lagrange multipliers for the iterative solution of second order solid mechanics and fourth order beam plate and shell structural problems respectively the feti 2 method distinguishes itself from the basic or one level feti method by a second set of lagrange multipliers that are introduced at the subdomain cross points to enforce at each iteration the exact continuity of a subset of the displacement field at these specific locations in this paper we present a dual primal formulation of the feti 2 concept that eliminates the need for that second set of lagrange multipliers and unifies all previously developed one level and two level feti algorithms into a single dual primal feti dp method we show that this new feti dp method is numerically scalable for both second order and fourth order problems we also show that it is more robust and more computationally efficient than existing feti solvers particularly when the number of subdomains and or processors is very large copyright 2001 john wiley sons ltd

bayesian analysis of agricultural field experiments the paper describes bayesian analysis for agricultural field experiments a topic that has received very little previous attention despite a vast frequentist literature adoption of the bayesian paradigm simplifies the interpretation of the results especially in ranking and selection also complex formulations can be analysed with comparative ease by using markov chain monte carlo methods a key ingredient in the approach is the need for spatial representations of the unobserved fertility patterns this is discussed in detail problems caused by outliers and by jumps in fertility are tackled via hierarchical f formulations that may find use in other contexts the paper includes three analyses of variety trials for yield and one example involving binary data none is entirely straightforward some numerical comparisons with frequentist analyses are made

multi scale orthogonal basis method for nonlinear fractional equations with fractional integral boundary value conditions abstract in this paper we investigate the multi scale orthogonal basis method for fractional integral boundary value problems we apply the newton iteration method to linearize the nonlinear problems and employees the idea of collocation method to determine the coefficients of multi scale orthogonal basis then the approximation solution is obtained the error estimation and stable analysis are presented in detailed the final numerical experiments verify that the accuracy of our method

an arbitrary lagrangian eulerian discretization of mhd on 3d unstructured grids abstract we present an arbitrary lagrangian eulerian ale discretization of the equations of resistive magnetohydrodynamics mhd on unstructured hexahedral grids the method is formulated using an operator split approach with three distinct phases electromagnetic diffusion lagrangian motion and eulerian advection the resistive magnetic induction equation is discretized using a compatible mixed finite element method with a second order accurate implicit time differencing scheme which preserves the divergence free nature of the magnetic field at each discrete time step electromagnetic force and heat terms are calculated and coupled to the hydrodynamic equations to compute the lagrangian motion of the conducting materials by virtue of the compatible discretization method used the invariants of lagrangian mhd motion are preserved in a discrete sense when the lagrangian motion of the mesh causes significant distortion that distortion is corrected with a relaxation of the mesh followed by a second order monotonic remap of the electromagnetic state variables the remap is equivalent to eulerian advection of the magnetic flux density with a fictitious mesh relaxation velocity the magnetic advection is performed using a novel variant of constrained transport ct that is valid for unstructured hexahedral grids with arbitrary mesh velocities the advection method maintains the divergence free nature of the magnetic field and is second order accurate in regions where the solution is sufficiently smooth for regions in which the magnetic field is discontinuous e g mhd shocks the method is limited using a novel variant of algebraic flux correction afc which is local extremum diminishing led and divergence preserving finally we verify each stage of the discretization via a set of numerical experiments

bayesian grid matching a method for locating distorted grid structures in images is presented the method is based on the theories of template matching and bayesian image restoration the grid is modeled as a deformable template prior knowledge of the grid is described through a markov random field mrf model which represents the spatial coordinates of the grid nodes knowledge of how grid nodes are depicted in the observed image is described through the observation model the prior consists of a node prior and an arc edge prior both modeled as gaussian mrfs the node prior models variations in the positions of grid nodes and the arc prior models variations in row and column spacing across the grid grid matching is done by placing an initial rough grid over the image and applying an ensemble annealing scheme to maximize the posterior distribution of the grid the method can be applied to noisy images with missing grid nodes and grid node artifacts and the method accommodates a wide range of grid distortions including large scale warping varying row column spacing as well as nonrigid random fluctuations of the grid nodes the methodology is demonstrated in two case studies concerning 1 localization of dna signals in hybridization filters and 2 localization of knit units in textile samples

on edge correction of conditional and intrinsic autoregressions summarythis paper discusses edge correction for a large class of conditional and intrinsic autoregressions on two dimensional finite regular arrays the proposed method includes a novel reparameterization retains the simple neighbourhood structure ensures the nonnegative definiteness of the precision matrix and enables scalable matrix free statistical computation the edge correction provides new insight into how higher order differencing enters into the precision matrix of a conditional autoregression

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

modeling cardiac pacemakers with relaxation oscillators abstract a modified van der pol oscillator model was designed in order to reproduce the time series of the action potential generated by a natural pacemaker of the heart i e the sa or the av node the main motivation was that the models published up to now were not altogether adequate for research on the heart based on either the classical van der pol oscillator or other nonlinear oscillators these models were interesting rather because of the physical phenomena that could be obtained chaos and synchronization however they were unable to simulate many important physiological features of true physiological action potentials we based our research on the experience of other groups which modeled neuronal oscillators there complex nonlinear oscillators were used whose most important feature was a certain topology of the phase space in our case we modified the phase space of the classical van der pol oscillator by adding two fixed points a saddle and a node in addition a damping term asymmetric with respect to the voltage was introduced introduction of these new features into the van der pol oscillator allowed to change the firing frequency of the pacemaker node without changing the length of the refractory period an important physiological detail we also show different ways of changing the pacemaker rhythm a comparison of the properties of the signal obtained from our model with the features of the action potentials measured by other groups is made

convergence analysis of the fem approximation of the first order projection method for incompressible flows with and without the inf sup condition in this paper we obtain convergence results for the fully discrete projection method for the numerical approximation of the incompressible navier stokes equations using a finite element approximation for the space discretization we consider two situations in the first one the analysis relies on the satisfaction of the inf sup condition for the velocity pressure finite element spaces after that we study a fully discrete fractional step method using a poisson equation for the pressure in this case the velocity pressure interpolations do not need to accomplish the inf sup condition and in fact we consider the case in which equal velocity pressure interpolation is used optimal convergence results in time and space have been obtained in both cases

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

a multiscale wavelet based test for isotropy of random fields on a regular lattice a test for isotropy of images modeled as stationary or intrinsically stationary random fields on a lattice is developed the test is based on the wavelet theory and can operate on the horizontal and vertical scale of choice or on any combination of scales scale is introduced through the wavelet variances sometimes called as the wavelet power spectrum which decompose the variance over different horizontal and vertical spatial scales the method is more general than existing tests for isotropy since it handles intrinsically stationary random fields as well as second order stationary fields the performance of the method is demonstrated on samples from different random fields and compared with three existing methods it is competitive with or outperforms existing methods since it consistently rejects close to the nominal level for isotropic fields while having a rejection rate for anisotropic fields comparable with the existing methods in the stationary case and superior in the intrinsic case as practical examples paper density images of handsheets and mammogram images are analyzed

nonlinear dynamics of the heartbeat i the av junction passive conduit or active oscillator under physiologic conditions the av junction is traditionally regarded as a passive conduit for the conduction of impulses from the atria to the ventricles an alternative view namely that subsidiary pacemakers play an active role in normal electrophysiologic dynamics during sinus rhythm has been suggested based on nonlinear models of cardiac oscillators a central problem has been the development of a simple but explicit mathematical model for coupled nonlinear oscillators relevant both to stable and perturbed cardiac dynamics we use equations describing an analog electrical circuit with an external d c voltage source v0 and two nonlinear oscillators with intrinsic frequencies in the ratio of 3 2 comparable to the sa node and av junction rates the oscillators are coupled by means of a resistor 1 1 sa av phase locking of the oscillators occurs over a critical range of v0 externally driving the sa oscillator at increasing rates results in 3 2 av wenckebach periodicity and a 2 1 av block these findings appear with no assumptions about conduction time or refractoriness this dynamical model is consistent with the new interpretation that normal sinus rhythm may represent 1 1 coupling of two or more active nonlinear oscillators and also accounts for the appearance of an av block with critical changes in a single parameter such as the pacing rate