hp dgfem for second order elliptic problems in polyhedra ii exponential convergence the goal of this paper is to establish exponential convergence of hp version interior penalty ip discontinuous galerkin dg finite element methods for the numerical approximation of linear second order elliptic boundary value problems with homogeneous dirichlet boundary conditions and piecewise analytic data in three dimensional polyhedral domains more precisely we shall analyze the convergence of the hp ip dg methods considered in d schotzau c schwab t p wihler siam j numer anal 51 2013 pp 1610 1633 based on axiparallel sigma geometric anisotropic meshes and bm s linear anisotropic polynomial degree distributions

similarity based classification of sequences using hidden markov models hidden markov models hmm are a widely used tool for sequence modelling in the sequence classification case the standard approach consists of training one hmm for each class and then using a standard bayesian classification rule in this paper we introduce a novel classification scheme for sequences based on hmms which is obtained by extending the recently proposed similarity based classification paradigm to hmm based classification in this approach each object is described by the vector of its similarities with respect to a predetermined set of other objects where these similarities are supported by hmms a central problem is the high dimensionality of resulting space and to deal with it three alternatives are investigated synthetic and real experiments show that the similarity based approach outperforms standard hmm classification schemes

toward a universal adaptive finite element strategy part 3 design of meshes abstract in this third paper in our series the issue of designing h p meshes which are optimal in some sense is addressed criteria for h p meshes are derived which are based on the idea of minimizing the estimated error over a mesh with a fixed number of degrees of freedom an optimization algorithm is developed based on these criteria and is applied to several model one dimensional and two dimensional elliptic boundary value problems numerical results indicate that the approach can lead to exponential rates of convergence

hp dgfem for second order elliptic problems in polyhedra i stability on geometric meshes we introduce and analyze hp version discontinuous galerkin dg finite element methods for the numerical approximation of linear second order elliptic boundary value problems in three dimensional polyhedral domains to resolve possible corner edge and corner edge singularities we consider hexahedral meshes that are geometrically and anisotropically refined toward the corresponding neighborhoods similarly the local polynomial degrees are increased linearly and possibly anisotropically away from singularities we design interior penalty hp dg methods and prove that they are well defined for problems with singular solutions and stable under the proposed hp refinements we establish abstract error bounds that will allow us to prove exponential rates of convergence in the second part of this work

2 d shape classification using hidden markov model the authors present a planar shape recognition approach based on the hidden markov model and autoregressive parameters this approach segments closed shapes to make classifications at a finer level the algorithm can tolerate a lot of shape contour perturbation and a moderate amount of occlusion an orientation scheme is described to make the overall classification insensitive to shape orientation excellent recognition results have been reported a distinct advantage of the approach is that the classifier does not have to be trained again when a new class of shapes is added

multi element generalized polynomial chaos for arbitrary probability measures we develop a multi element generalized polynomial chaos me gpc method for arbitrary probability measures and apply it to solve ordinary and partial differential equations with stochastic inputs given a stochastic input with an arbitrary probability measure its random space is decomposed into smaller elements subsequently in each element a new random variable with respect to a conditional probability density function pdf is defined and a set of orthogonal polynomials in terms of this random variable is constructed numerically then the generalized polynomial chaos gpc method is implemented element by element numerical experiments show that the cost for the construction of orthogonal polynomials is negligible compared to the total time cost efficiency and convergence of me gpc are studied numerically by considering some commonly used random variables me gpc provides an efficient and flexible approach to solving differential equations with random inputs especially for problems related to long term integration large perturbation and stochastic discontinuities

efficient preconditioning for the p version finite element method in two dimensions parallel preconditioners are formulated and analyzed for systems of equations arising from the p version finite element method applied to second order self adjoint elliptic boundary value problems in two dimensions by using new theoretical results for polynomial spaces it is proved that the condition number of the preconditioned system grows as log 2 p where p is the degree of the polynomial space numerical results are presented showing that the condition number indeed grows very slowly with p

polynomial degree robust a posteriori estimates in a unified setting for conforming nonconforming discontinuous galerkin and mixed discretizations we present equilibrated flux a posteriori error estimates in a unified setting for conforming nonconforming discontinuous galerkin and mixed finite element discretizations of the two dimensional poisson problem relying on the equilibration by the mixed finite element solution of patchwise neumann problems the estimates are guaranteed locally computable locally efficient and robust with respect to polynomial degree maximal local overestimation is guaranteed as well numerical experiments suggest asymptotic exactness for the incomplete interior penalty discontinuous galerkin scheme

tree approximation for hp adaptivity the hp adaptive approximation is formulated as an approximation problem on a full binary tree t where for each of the leaves delta an order p delta ge1 is assigned in such a way that the

a note on the design of hp adaptive finite element methods for elliptic partial differential equations we introduce an hp adaptive finite element algorithm based on a combination of reliable and efficient residual error indicators and a new hp extension control technique which assesses the local regularity of the underlying analytical solution on the basis of its local legendre series expansion numerical experiments confirm the robustness and reliability of the proposed algorithm

polygonal approximation of digital planar curves through vertex betweenness contour polygonal approximation is usually defined as a set of selected points which describes a polygon and best represents the original contour this paper presents a novel graph based approach to compute a polygonal approximation of a shape contour in a graph such points correspond to a high transitivity region of the graph we use the vertex betweenness to measure the importance of each vertice in a graph according to the number of shortest paths where each vertice occurs by selecting the vertices with higher vertex betweenness a polygon which retains the main characteristics of the contour is achieved by using benchmark curves a comparative experiment with other commonly used algorithms is presented results indicate that the proposed approach produced efficient and effective polygonal approximations for digital planar curves

adaptive mesh strategies for the spectral element method abstract an adaptive spectral element method has been developed for the efficient solution of time dependent partial differential equations adaptive mesh strategies that include resolution refinement and coarsening by three different methods are illustrated on solutions to the one dimensional viscous burgers equation and the two dimensional navier stokes equations for driven flow in a cavity sharp gradients singularities and regions of poor resolution are resolved optimally as they develop in time using error estimators which indicate the choice of refinement to be used the adaptive formulation presents significant increases in efficiency flexibility and general capabilities for high order spectral methods

on p robust saturation for hp afem for the poisson problem in two dimensions we consider the standard adaptive finite element loop solve estimate mark refine with estimate being implemented using the p robust equilibrated flux estimator and mark being drfler marking as a refinement strategy we employ p refinement we investigate the question by which amount the local polynomial degree on any marked patch has to be incremented in order to achieve a p independent error reduction we show that the analysis can be transferred from the patches to a reference triangle and therein we provide clear cut computational evidence that any increment proportional to the polynomial degree for any fixed proportionality constant yields the desired reduction the resulting adaptive method can be turned into an instance optimal hp adaptive method by the addition of a coarsening routine

review of shape representation and description techniques more and more images have been generated in digital form around the world there is a growing interest in 1nding images in large collections or from remote databases in order to 1nd an image the image has to be described or represented by certain features shape is an important visual feature of an image searching for images using shape features has attracted much attention there are many shape representation anddescription techniques in the literature in this paper we classify and review these important techniques we examine implementation procedures for each technique and discuss its advantages and disadvantages some recent research results are also included and discussed in this paper finally we identify some promising techniques for image retrieval according to standard principles

the h p and h p versions of the finite element methods in 1 dimension part iii the adaptive h p version abstract the paper is the third and final part in the series of three devoted to the detailed analysis of the three basic versions of the finite element method in one dimension the first part analyzed the p version and the second part concentrated on the h and h p version this paper analyzes a theoretical frame of the adaptive h p version and based on it the authors provide concrete algorithm for the one dimensional problem it is proven that in the case that the solution has x sub alpha type singularity the adaptive algorithm give an exponential rate of convergence very close to the optimal one analyzed in the second part of the paper additional keyword error analysis

adaptive finite element methods with convergence rates adaptive finite element methods for numerically solving elliptic equations are used often in practice only recently 12 17 have these methods been shown to converge however this convergence analysis says nothing about the rates of convergence of these methods and therefore does in principle not guarantee yet any numerical advantages of adaptive strategies versus non adaptive strategies the present paper modifies the adaptive method of morin nochetto and siebert 17 for solving the laplace equation with piecewise linear elements on domains in 2 by adding a coarsening step and proves that this new method has certain optimal convergence rates in the energy norm which is equivalent to the h1 norm namely it is shown that whenever s 0 and the solution u is such that for each n 1 it can be approximated to accuracy o n s in the energy norm by a continuous piecewise linear function on a triangulation with n cells using complete knowledge of u then the adaptive algorithm constructs an approximation of the same type with the same asymptotic accuracy while using only information gained during the computational process moreover the number of arithmetic computations in the proposed method is also of order o n for each n 1 the construction and analysis of this adaptive method relies on the theory of nonlinear approximation

an adaptive hp refinement strategy with computable guaranteed bound on the error reduction factor we propose a new practical adaptive refinement strategy for hp finite element approximations of elliptic problems following recent theoretical developments in polynomial degree robust a posteriori error analysis we solve two types of discrete local problems on vertex based patches the first type involves the solution on each patch of a mixed finite element problem with homogeneous neumann boundary conditions which leads to an mathbf h mathrm div omega conforming equilibrated flux this in turn yields a guaranteed upper bound on the error and serves to mark mesh vertices for refinement via dorfler s bulk chasing criterion the second type of local problems involves the solution on patches associated with marked vertices only of two separate primal finite element problems with homogeneous dirichlet boundary conditions which serve to decide between h p or hp refinement altogether we show that these ingredients lead to a computable guaranteed bound on the ratio of the errors between successive refinements error reduction factor in a series of numerical experiments featuring smooth and singular solutions we study the performance of the proposed hp adaptive strategy and observe exponential convergence rates we also investigate the accuracy of our bound on the reduction factor by evaluating the ratio of the predicted reduction factor relative to the true error reduction and we find that this ratio is in general quite close to the optimal value of one

shape retrieval based on dynamic programming we propose a shape matching algorithm for deformed shapes based on dynamic programming our algorithm is capable of grouping together segments at finer scales in order to come up with appropriate correspondences with segments at coarser scales we illustrate the effectiveness of our algorithm in retrieval of shapes by content on two different two dimensional 2 d datasets one of static hand gesture shapes and another of marine life shapes we also demonstrate the superiority of our approach over traditional approaches to shape matching and retrieval such as fourier descriptors and geometric and sequential moments our evaluation is based on human relevance judgments following a well established methodology from the information retrieval field

almost gorenstein rings abstract barucci and froberg 1997 2 introduced the notion of an almost gorenstein ring in the case of an analytically unramified local ring r m in this work we provide a framework that allows us to generalize this notion to include the analytically ramified case as a consequence for any cohen macaulay local ring r m of dimension one we solve in full generality the problem of determining when the endomorphism algebra m m is gorenstein we also provide characterizations for rings to be almost gorenstein in connection with the principle of idealization several examples are explored as well

toward a universal h p adaptive finite element strategy part 1 constrained approximation and data structure abstract this is the first of a series of papers devoted to the development of an adaptive finite element method to solve various boundary value problems arising in solid and fluid mechanics the paper deals with the general concepts of h p finite element methods constrained approximation and data structure and related issues several numerical examples illustrate the main ideas of the method

invariants of cohen macaulay rings associated to their canonical ideals abstract the purpose of this paper is to introduce new invariants of cohen macaulay local rings our focus is the class of cohen macaulay local rings that admit a canonical ideal attached to each such ring r with a canonical ideal c there are integers the type of r the reduction number of c that provide valuable metrics to express the deviation of r from being a gorenstein ring we enlarge this list with other integers the roots of r and several canonical degrees the latter are multiplicity based functions of the rees algebra of c

contraction and optimality properties of an adaptive legendre galerkin method the multi dimensional case we analyze the theoretical properties of an adaptive legendre galerkin method in the multidimensional case after the recent investigations for fourier galerkin methods in a periodic box and for legendre galerkin methods in the one dimensional setting the present study represents a further step towards a mathematically rigorous understanding of adaptive spectral hp hp discretizations of elliptic boundary value problems the main contribution of the paper is a careful construction of a multidimensional riesz basis in h 1 h1 based on a quasi orthonormalization procedure this allows us to design an adaptive algorithm to prove its convergence by a contraction argument and to discuss its optimality properties in the sense of non linear approximation theory in certain sparsity classes of gevrey type

toward a universal h p adaptive finite element strategy part 2 a posteriori error estimation abstract in this second paper of the series on h p adaptive finite element methods we present five different techniques for a posteriori error estimation of h p methods for linear elliptic boundary value problems the techniques are referred to as the residual estimation method the duality method the subdomain residual method a method based on interpolation theory and a post processing method the present study examines the theory and behavior of such techniques applied specifically to h p adaptive finite element methods several numerical examples illustrate the efficiency of the methods

adaptive energy minimisation for h p finite element methods this article is concerned with the numerical solution of convex variational problems more precisely we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in an adaptive manner specifically we outline a new approach in the context of h p adaptive finite element methods employed for the efficient numerical solution of linear and nonlinear second order boundary value problems numerical experiments are presented which highlight the practical performance of this new h p refinement technique for both one and two dimensional problems

equilibrated residual error estimates are p robust abstract equilibrated residual error estimators applied to high order finite elements are analyzed the estimators provide always a true upper bound for the energy error we prove that also the efficiency estimate is robust with respect to the polynomial degrees a complete theory is provided for tensor product elements in the case of simplicial elements the theorem was first based on a conjecture but the conjecture was quite recently proved by costabel and mcintosh m costabel a mcintosh on bogovskii and regularized poincare integral operators for de rham complexes on lipschitz domains irmar preprint 08 40 rennes august 2008 numerical evidence for the p robustness is provided

on hidden markov models and cyclic strings for shape recognition abstract shape descriptions and the corresponding matching techniques must be robust to noise and invariant to transformations for their use in recognition tasks most transformations are relatively easy to handle when contours are represented by strings however starting point invariance is difficult to achieve one interesting possibility is the use of cyclic strings which are strings that have no starting and final points we propose new methodologies to use hidden markov models to classify contours represented by cyclic strings experimental results show that our proposals outperform other methods in the literature

image clustering using local discriminant models and global integration in this paper we propose a new image clustering algorithm referred to as clustering using local discriminant models and global integration ldmgi to deal with the data points sampled from a nonlinear manifold for each data point we construct a local clique comprising this data point and its neighboring data points inspired by the fisher criterion we use a local discriminant model for each local clique to evaluate the clustering performance of samples within the local clique to obtain the clustering result we further propose a unified objective function to globally integrate the local models of all the local cliques with the unified objective function spectral relaxation and spectral rotation are used to obtain the binary cluster indicator matrix for all the samples we show that ldmgi shares a similar objective function with the spectral clustering sc algorithms e g normalized cut ncut in contrast to ncut in which the laplacian matrix is directly calculated based upon a gaussian function a new laplacian matrix is learnt in ldmgi by exploiting both manifold structure and local discriminant information we also prove that k means and discriminative k means diskmeans are both special cases of ldmgi extensive experiments on several benchmark image datasets demonstrate the effectiveness of ldmgi we observe in the experiments that ldmgi is more robust to algorithmic parameter when compared with ncut thus ldmgi is more appealing for the real image clustering applications in which the ground truth is generally not available for tuning algorithmic parameters

multi aspect target discrimination using hidden markov models and neural networks this paper presents a new multi aspect pattern classification method using hidden markov models hmms models are defined for each class with the probability found by each model determining class membership each hmm model is enhanced by the use of a multilayer perception mlp network to generate emission probabilities this hybrid system uses the mlp to find the probability of a state for an unknown pattern and the hmm to model the process underlying the state transitions a new batch gradient descent based method is introduced for optimal estimation of the transition and emission probabilities a prediction method in conjunction with hmm model is also presented that attempts to improve the computation of transition probabilities by using the previous states to predict the next state this method exploits the correlation information between consecutive aspects these algorithms are then implemented and benchmarked on a multi aspect underwater target classification problem using a realistic sonar data set collected in different bottom conditions

quasi optimal convergence rate for an adaptive finite element method we analyze the simplest and most standard adaptive finite element method afem with any polynomial degree for general second order linear symmetric elliptic operators as is customary in practice the afem marks exclusively according to the error estimator and performs a minimal element refinement without the interior node property we prove that the afem is a contraction for the sum of the energy error and the scaled error estimator between two consecutive adaptive loops this geometric decay is instrumental to derive the optimal cardinality of the afem we show that the afem yields a decay rate of the energy error plus oscillation in terms of the number of degrees of freedom as dictated by the best approximation for this combined nonlinear quantity

adaptive fourier galerkin methods we study the performance of adaptive fourier galerkin methods in a periodic box in r d with dimension d 1 these methods offer unlimited approximation power only restricted by solution and data regularity they are of intrinsic interest but are also a first step towards understanding adaptivity for the hp fem we examine two nonlinear approximation classes one classical corresponding to algebraic decay of fourier coefficients and another associated with exponential decay typical of spectral approximation we investigate the natural sparsity class for the operator range and find that the exponential class is not preserved thus in contrast with the algebraic class this entails a striking different behavior of the feasible residuals that lead to practical algorithms influencing the overall optimality the sparsity degradation for the exponential class is partially compensated with coarsening we present several feasible adaptive fourier algorithms prove their contraction properties and examine the cardinality of the activated sets the galerkin approximations at the end of each iteration are quasi optimal for both classes but inner loops or intermediate approximations are sub optimal for the exponential class

sparsifying the fisher linear discriminant by rotation many high dimensional classification techniques have been proposed in the literature based on sparse linear discriminant analysis lda to efficiently use them sparsity of linear classifiers is a prerequisite however this might not be readily available in many applications and rotations of data are required to create the needed sparsity in this paper we propose a family of rotations to create the required sparsity the basic idea is to use the principal components of the sample covariance matrix of the pooled samples and its variants to rotate the data first and to then apply an existing high dimensional classifier this rotate and solve procedure can be combined with any existing classifiers and is robust against the sparsity level of the true model we show that these rotations do create the sparsity needed for high dimensional classifications and provide theoretical understanding why such a rotation works empirically the effectiveness of the proposed method is demonstrated by a number of simulated and real data examples and the improvements of our method over some popular high dimensional classification rules are clearly shown

exponential convergence in h 1 of hp fem for gevrey regularity with isotropic singularities for functions u in h 1 omega in a bounded polytope omega subset mathbb r d d 1 2 3 with plane sides for d 2 3 which are gevrey regular in overline omega backslash mathscr s with point singularities concentrated at a set mathscr s subset overline omega consisting of a finite number of points in overline omega we prove exponential rates of convergence of hp version continuous galerkin finite element methods on affine families of regular simplicial meshes in omega the simplicial meshes are geometrically refined towards mathscr s but are otherwise unstructured

sally modules of canonical ideals in dimension one and 2 agl rings abstract the notion of 2 agl ring in dimension one which is a natural generalization of almost gorenstein local ring is posed in terms of the rank of sally modules of canonical ideals the basic theory is developed investigating also the case where the rings considered are numerical semigroup rings over fields examples are explored

nonparametric joint shape and feature priors for image segmentation in many image segmentation problems involving limited and low quality data employing statistical prior information about the shapes of the objects to be segmented can significantly improve the segmentation result however defining probability densities in the space of shapes is an open and challenging problem especially if the object to be segmented comes from a shape density involving multiple modes classes existing techniques in the literature estimate the underlying shape distribution by extending parzen density estimator to the space of shapes in these methods the evolving curve may converge to a shape from a wrong mode of the posterior density when the observed intensities provide very little information about the object boundaries in such scenarios employing both shape and class dependent discriminative feature priors can aid the segmentation process such features may involve e g intensity based textural or geometric information about the objects to be segmented in this paper we propose a segmentation algorithm that uses nonparametric joint shape and feature priors constructed by parzen density estimation we incorporate the learned joint shape and feature prior distribution into a maximum a posteriori estimation framework for segmentation the resulting optimization problem is solved using active contours we present experimental results on a variety of synthetic and real data sets from several fields involving multimodal shape densities experimental results demonstrate the potential of the proposed method

a gpu accelerated level set reinitialization for an adaptive discontinuous galerkin method gpu accelerated high order reconstruction of signed distance function of the level set method is studied the flow based reinitialization equation is discretized in space by using a nodal discontinuous galerkin method on adaptive unstructured grids artificial diffusion with a modal decay rate based regularity estimator is used to damp out high frequency solution components near kinks where mesh adaptivity is applied a two rate adams bashforth time integrator is developed to avoid time step restrictions resulting from artificial diffusion stabilization and local mesh refinement platform independence of the solver is achieved by using an extensible multi threading programming api that allows runtime selection of different computing devices gpu and cpu and threading interfaces cuda opencl and openmp overall a highly scalable numerical scheme that preserves the simplicity of the original level set method is obtained performance and accuracy of the method to construct signed distance function on highly disturbed initial data with smooth and non smooth interfaces are tested through distinct two and three dimensional problems

fast computation in adaptive tree approximation adaptive methods of approximation arise in many settings including numerical methods for pdes and image processing they can usually be described by a tree which records the adaptive decisions this paper is concerned with the fast computation of near optimal trees based on n adaptive decisions the best tree based on n adaptive decisions could be found by examining all such possibilities however this is exponential in n and could be numerically prohibitive the main result of this paper is to show that it is possible to find near optimal trees using computations linear in n

the h p and h p versions of the finite element method in 1 dimension part ii the error analysis of the h and h p versions the paper is the second in the series of three devoted to the detailed analysis of the three basic versions of the finite element method in one dimensional setting the first part 1 analyzed thep version the present one concentrates on theh andh p versions

a posteriori error estimation and adaptivity in hp virtual elements an explicit and computable error estimator for the hp version of the virtual element method vem together with lower and upper bounds with respect to the exact energy error is presented such error estimator is employed to provide following the approach of melenk and wohlmuth adv comput math 15 1 4 311 331 2001 hp adaptive mesh refinements for very general polygonal meshes in addition a novel vem hp clement quasi interpolant instrumental for the a posteriori error analysis is introduced the performances of the adaptive method are validated by a number of numerical experiments

data oscillation and convergence of adaptive fem data oscillation is intrinsic information missed by the averaging process associated with finite element methods fem regardless of quadrature ensuring a reduction rate of data oscillation together with an error reduction based on a posteriori error estimators we construct a simple and efficient adaptive fem for elliptic partial differential equations pdes with linear rate of convergence without any preliminary mesh adaptation nor explicit knowledge of constants any prescribed error tolerance is thus achieved in a finite number of steps a number of numerical experiments in two and three dimensions yield quasi optimal meshes along with a competitive performance

convergence and optimality of mathbf hp hp afem we design and analyze an adaptive hp finite element method mathbf hp hp afem in dimensions n 1 2 n 1 2 the algorithm consists of iterating two routines mathbf hp hp nearbest finds a near best hp approximation of the current discrete solution and data to a desired accuracy and reduce improves the discrete solution to a finer but comparable accuracy the former hinges on a recent algorithm by binev for adaptive hp approximation and acts as a coarsening step we prove convergence and instance optimality

flexible syntactic matching of curves and its application to automatic hierarchical classification of silhouettes curve matching is one instance of the fundamental correspondence problem our flexible algorithm is designed to match curves under substantial deformations and arbitrary large scaling and rigid transformations a syntactic representation is constructed for both curves and an edit transformation which maps one curve to the other is found using dynamic programming we present extensive experiments where we apply the algorithm to silhouette matching in these experiments we examine partial occlusion viewpoint variation articulation and class matching where silhouettes of similar objects are matched based on the qualitative syntactic matching we define a dissimilarity measure and we compute it for every pair of images in a database of 121 images we use this experiment to objectively evaluate our algorithm first we compare our results to those reported by others second we use the dissimilarity values in order to organize the image database into shape categories the veridical hierarchical organization stands as evidence to the quality of our matching and similarity estimation

a spectral element method for fluid dynamics laminar flow in a channel expansion a spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible navier stokes equations in the spectral element discretization the computational domain is broken into a series of elements and the velocity in each element is represented as a high order lagrangian interpolant through chebyshev collocation points the hyperbolic piece of the governing equations is then treated with an explicit collocation scheme while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle the implementation of the technique is demonstrated on a one dimensional inflow outflow advection diffusion equation and the method is then applied to laminar two dimensional separated flow in a channel expansion comparisons are made with experiment and previous numerical work

hidden markov model based weighted likelihood discriminant for 2 d shape classification the goal of this paper is to present a weighted likelihood discriminant for minimum error shape classification different from traditional maximum likelihood ml methods in which classification is based on probabilities from independent individual class models as is the case for general hidden markov model hmm methods proposed method utilizes information from all classes to minimize classification error the proposed approach uses a hmm for shape curvature as its 2 d shape descriptor we introduce a weighted likelihood discriminant function and present a minimum classification error strategy based on generalized probabilistic descent method we show comparative results obtained with our approach and classic ml classification with various hmm topologies alongside fourier descriptor and zernike moments based support vector machine classification for a variety of shapes

a convergent adaptive algorithm for poisson s equation we construct a converging adaptive algorithm for linear elements applied to poisson s equation in two space dimensions starting from a macro triangulation we describe how to construct an initial triangulation from a priori information then we use a posteriors error estimators to get a sequence of refined triangulation and approximate solutions it is proved that the error measured in the energy norm decreases at a constant rate in each step until a prescribed error bound is reached extension to higher order elements in two space dimension and numerical results are included

ulrich ideals and 2 agl rings abstract the notion of 2 almost gorenstein local ring 2 agl ring for short is a generalization of the notion of almost gorenstein local ring from the point of view of sally modules of canonical ideals in this paper for further developments of the theory we discuss three different topics on 2 agl rings the first one is to clarify the structure of minimal presentations of canonical ideals and the second one is the study of the question of when certain fiber products so called amalgamated duplications are 2 agl rings we also explore ulrich ideals in 2 agl rings mainly two generated ones

shape similarity measure based on correspondence of visual parts a cognitively motivated similarity measure is presented and its properties are analyzed with respect to retrieval of similar objects in image databases of silhouettes of 2d objects to reduce influence of digitization noise as well as segmentation errors the shapes are simplified by a novel process of digital curve evolution to compute our similarity measure we first establish the best possible correspondence of visual parts without explicitly computing the visual parts then the similarity between corresponding parts is computed and aggregated we applied our similarity measure to shape matching of object contours in various image databases and compared it to well known approaches in the literature the experimental results justify that our shape matching procedure gives an intuitive shape correspondence and is stable with respect to noise distortions

the h p adaptive finite element method for the numerical simulation of compressible flow an h p adaptive finite element method is presented for the numerical simulation of compressible fluid flow in addition to refining the mesh in regions where the estimated error is large the polynomial degree of the elements is increased it is shown that by using high order polynomials highly accurate approximations are obtained to a regularized form of the equations governing viscous compressible flow

spectral implementation of an adaptive moving mesh method for phase field equations phase field simulations have been extensively applied to modeling microstructure evolution during various materials processes however large scale simulations of three dimensional 3d microstructures are still computationally expensive among recent efforts to develop advanced numerical algorithms the semi implicit fourier spectral method is found to be particularly efficient for systems involving long range interactions as it is able to utilize the fast fourier transforms fft on uniform grids in this paper we report our recent progress in making grid points spatially adaptive in the physical domain via a moving mesh strategy while maintaining a uniform grid in the computational domain for the spectral implementation this approach not only provides more accurate treatment at the interfaces requiring higher resolution but also retains the numerical efficiency of the semi implicit fourier spectral method numerical examples using the new adaptive moving mesh semi implicit fourier spectral method are presented for both two and three space dimensional microstructure simulations and they are compared with those obtained by other methods by maintaining a similar accuracy the proposed method is shown to be far more efficient than the existing methods for microstructures with small ratios of interfacial widths to the domain size

axioms of adaptivity this paper aims first at a simultaneous axiomatic presentation of the proof of optimal convergence rates for adaptive finite element methods and second at some refinements of particular questions like the avoidance of discrete lower bounds inexact solvers inhomogeneous boundary data or the use of equivalent error estimators solely four axioms guarantee the optimality in terms of the error estimators compared to the state of the art in the temporary literature the improvements of this article can be summarized as follows first a general framework is presented which covers the existing literature on optimality of adaptive schemes the abstract analysis covers linear as well as nonlinear problems and is independent of the underlying finite element or boundary element method second efficiency of the error estimator is neither needed to prove convergence nor quasi optimal convergence behavior of the error estimator in this paper efficiency exclusively characterizes the approximation classes involved in terms of the best approximation error and data resolution and so the upper bound on the optimal marking parameters does not depend on the efficiency constant third some general quasi galerkin orthogonality is not only sufficient but also necessary for the r linear convergence of the error estimator which is a fundamental ingredient in the current quasi optimality analysis due to stevenson 2007 finally the general analysis allows for equivalent error estimators and inexact solvers as well as different non homogeneous and mixed boundary conditions

spectral element methods for large scale parallel navier stokes calculations abstract we analyze the computational complexity of a recently developed two level iteration scheme for spectral element solution of the time dependent incompressible navier stokes equations in complex domains we present several algorithmic advances which significantly enhance the scalability of this approach including implementation of an advanced combine operation for degrees of freedom on subdomain edges parallel solution of the fine grained coarse grid problem and implementation of local low order finite element preconditioners for the find grid problem timings on the 512 node intel delta machine show that the combined improvements lead to a fourfold reduction in navier stokes solution time for the particular case of a three dimensional boundary layer calculation consisting of one million degrees of freedom

deformation based curved shape representation in this paper we introduce a deformation based representation space for curved shapes in mathbb r n given an ordered set of points sampled from a curved shape the proposed method represents the set as an element of a finite dimensional matrix lie group variation due to scale and location are filtered in a preprocessing stage while shapes that vary only in rotation are identified by an equivalence relationship the use of a finite dimensional matrix lie group leads to a similarity metric with an explicit geodesic solution subsequently we discuss some of the properties of the metric and its relationship with a deformation by least action furthermore invariance to reparametrization or estimation of point correspondence between shapes is formulated as an estimation of sampling function thereafter two possible approaches are presented to solve the point correspondence estimation problem finally we propose an adaptation of k means clustering for shape analysis in the proposed representation space experimental results show that the proposed representation is robust to uninformative cues e g local shape perturbation and displacement in comparison to state of the art methods it achieves a high precision on the swedish and the flavia leaf datasets and a comparable result on mpeg 7 kimia99 and kimia216 datasets

dynamic refinement algorithms for spectral element methods abstract a numerical method is presented that combines high order domain decomposition and adaptive mesh refinement the spatial discretization is based on a nonconforming spectral element method meshes are generated by adaptive refinement of a quadtree using either local solution gradients or the local polynomial spectrum as a refinement criteria the method is applied to solve scalar test problems and to simulate the flow in a lid driven cavity at moderate reynolds numbers

links of prime ideals and their rees algebras abstract in a previous paper we exhibited the somewhat surprising property that most direct links of prime ideals in gorenstein rings are equimultiple ideals with reduction number 1 this led to the construction of large families of cohen macaulay rees algebras the first goal of this paper is to extend this result to arbitrary cohen macaulay rings the means of the proof are changed since one cannot depend so heavily on linkage theory we then study the structure of the rees algebra of these links more specifically we describe their canonical module in sufficient detail to be able to characterize self linked prime ideals in the last section multiplicity estimates for classes of such ideals are established

adjoint based h p adaptive discontinuous galerkin methods for the 2d compressible euler equations in this paper we investigate and present an adaptive discontinuous galerkin algorithm driven by an adjoint based error estimation technique for the inviscid compressible euler equations this approach requires the numerical approximations for the flow i e primal problem and the adjoint i e dual problem which corresponds to a particular simulation objective output of interest the convergence of these two problems is accelerated by an hp multigrid solver which makes use of an element gauss seidel smoother on each level of the multigrid sequence the error estimation of the output functional results in a spatial error distribution which is used to drive an adaptive refinement strategy which may include local mesh subdivision h refinement local modification of discretization orders p enrichment and the combination of both approaches known as hp refinement the selection between h and p refinement in the hp adaptation approach is made based on a smoothness indicator applied to the most recently available flow solution values numerical results for the inviscid compressible flow over an idealized four element airfoil geometry demonstrate that both pure h refinement and pure p enrichment algorithms achieve equivalent error reductions at each adaptation cycle compared to a uniform refinement approach but requiring fewer degrees of freedom the proposed hp adaptive refinement strategy is capable of obtaining exponential error convergence in terms of degrees of freedom and results in significant savings in computational cost a high speed flow test case is used to demonstrate the ability of the hp refinement approach for capturing strong shocks or discontinuities while improving functional accuracy