image thresholding based on the em algorithm and the generalized gaussian distribution in this paper a novel parametric and global image histogram thresholding method is presented it is based on the estimation of the statistical parameters of object and background classes by the expectation maximization em algorithm under the assumption that these two classes follow a generalized gaussian gg distribution the adoption of such a statistical model as an alternative to the more common gaussian model is motivated by its attractive capability to approximate a broad variety of statistical behaviors with a small number of parameters since the quality of the solution provided by the iterative em algorithm is strongly affected by initial conditions which if inappropriately set may lead to unreliable estimation a robust initialization strategy based on genetic algorithms gas is proposed experimental results obtained on simulated and real images confirm the effectiveness of the proposed method

a small stencil and extremum preserving scheme for anisotropic diffusion problems on arbitrary 2d and 3d meshes in this paper a nonlinear extremum preserving scheme for the heterogeneous and anisotropic diffusion problems is proposed on general 2d and 3d meshes through a certain linearity preserving approach the so called harmonic averaging points located at the interface of heterogeneity are employed to define the auxiliary unknowns this new scheme is locally conservative has only cell centered unknowns and possesses a small stencil which is five point on the structured quadrilateral meshes and seven point on the structured hexahedral meshes the stability result in h 1 norm is obtained under quite general assumptions numerical results show that our scheme is robust and extremum preserving and the optimal convergence rates are verified on general distorted meshes in case that the diffusion tensor is taken to be anisotropic at times discontinuous

a finite volume element scheme with a monotonicity correction for anisotropic diffusion problems on general quadrilateral meshes abstract we construct a finite volume element scheme with a monotonicity correction for anisotropic diffusion problems on general quadrilateral meshes where the strict convexity restriction on the meshes is removed the main contributions of this paper include three aspects firstly the classical finite volume element c fve method is extended to severely distorted quadrilateral meshes even with concave cells by virtue of a new overlapping dual partition and a new gradient approximation in fact the choice of this dual partition and gradient approximation is also conducive to the construction of a monotone scheme secondly a new monotonicity correction is suggested based on which we obtain a monotone finite volume element m fve method the resulting m fve method still keeps the local conservation and is easy for implementation finally we analyze theoretically the truncation error and the monotonicity for this scheme besides the existence of a solution to this nonlinear scheme is proved by applying the brouwer s fixed point theorem numerical results demonstrate that the m fve method has the approximate second order accuracy and preserves well the positivity of the solution for both isotropic and anisotropic diffusion problems on severely distorted quadrilateral meshes

local limit theorems for free groups in this paper we obtain a local limit theorem for elements of a free group g under the abelianization map cdot g to g g g this is obtained via an analysis involving subshifts of finite type where we obtain a result of independent interest the case of fundamental groups of compact surfaces of genus geq 2 is also discussed

automatic histogram threshold using fuzzy measures in this paper an automatic histogram threshold approach based on a fuzziness measure is presented this work is an improvement of an existing method using fuzzy logic concepts the problems involved in finding the minimum of a criterion function are avoided similarity between gray levels is the key to find an optimal threshold two initial regions of gray levels located at the boundaries of the histogram are defined then using an index of fuzziness a similarity process is started to find the threshold point a significant contrast between objects and background is assumed previous histogram equalization is used in small contrast images no prior knowledge of the image is required

extrapolation methods for vector sequences this is an expository paper that describes and compares five methods for extrapolating to the limit or anti limit of a vector sequence without explicit knowledge of the sequence generator the methods are the minimal polynomial extrapolation mpe studied by cabay and jackson mesina and skelboe the reduced rank extrapolation rre of eddy which we show to be equivalent to mesina s version of mpe the vector and scalar versions of the epsilon algorithm vea sea introduced by wynn and extended by brezinski and gekeler and the topological epsilon algorithm tea of brezinski we cover the derivation and error analysis of iterated versions of the algorithms as applied to both linear and nonlinear problems and we show why these versions tend to converge quadratically we also present samples from extensive numerical testing that has led us to the following conclusions a tea in spite of its role as a theoretical link between the polynomial type and the epsilon type methods has no practical appl

a comparative study on methods for convergence acceleration of iterative vector sequences we discuss several methods for accelerating the convergence of the iterative solution of nonlinear equation systems commonly in use and point to interrelations between them in particular we investigate two of the most sophisticated schemes namely the anderson mixing and the broyden update both generalized to the consideration of arbitrarily many previous iterations for the broyden method we give a new derivation which is much simpler than that recently proposed by vanderbilt and louie we show that if the additional parameters invented by these authors in order to increase flexibility are used to optimize the convergence of the iteration process they in fact cancel out in addition we prove that in this optimal case the anderson mixing and the broyden update as applied to the inverse jacobian are fully identical thus we come to the conclusion that neither of these schemes is superior moreover we show that broyden update of the inverse jacobian is superior to updating the jacobian itself finally we propose an extension of the anderson mixing which avoids the numerical difficulties all these methods are faced with

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

conjugacy growth of commutators abstract for the free group f r on r 1 generators respectively the free product g 1 g 2 of two nontrivial finite groups g 1 and g 2 we obtain the asymptotic for the number of conjugacy classes of commutators in f r respectively g 1 g 2 with a given word length in a fixed set of free generators respectively the set of generators given by the nontrivial elements of g 1 and g 2 our result is proven by using the classification of commutators in free groups and in free products by wicks and builds on the works of rivin and sharp who asymptotically counted the conjugacy classes of commutator subgroup elements in f r with a given word length

nonlinear krylov and moving nodes in the method of lines we report on some successes and problem areas in the method of lines from our work with moving node finite element methods first we report on our nonlinear krylov accelerator for the modified newton s method on the nonlinear equations of our stiff ode solver since 1990 it has been robust simple cheap and automatic on all our moving node computations we publicize further trials with it here because it should be of great general usefulness to all those solving evolutionary equations second we discuss the need for reliable automatic choice of spatially variable time steps third we discuss the need for robust and efficient iterative solvers for the difficult linearized equations jx b of our stiff ode solver here the 1997 thesis of zulu xaba has made significant progress

new neutrosophic approach to image segmentation neutrosophic set ns a part of neutrosophy theory studies the origin nature and scope of neutralities as well as their interactions with different ideational spectra ns is a formal framework that has been recently proposed however ns needs to be specified from a technical point of view for a given application or field we apply ns after defining some concepts and operations for image segmentation the image is transformed into the ns domain which is described using three membership sets t i and f the entropy in ns is defined and employed to evaluate the indeterminacy two operations a mean and b enhancement operations are proposed to reduce the set indeterminacy finally the proposed method is employed to perform image segmentation using a c means clustering we have conducted experiments on a variety of images the experimental results demonstrate that the proposed approach can segment the images automatically and effectively especially it can segment the clean images and the images having noise with different noise levels

the finite volume scheme preserving extremum principle for diffusion equations on polygonal meshes we construct a new nonlinear finite volume scheme for diffusion equation on polygonal meshes and prove that the scheme satisfies the discrete extremum principle our scheme is locally conservative and has only cell centered unknowns numerical results are presented to show how our scheme works for preserving discrete extremum principle and positivity on various distorted meshes

a surface approximation method for image and video correspondences although finding correspondences between similar images is an important problem in image processing the existing algorithms cannot find accurate and dense correspondences in images with significant changes in lighting transformation or with the non rigid objects this paper proposes a novel method for finding accurate and dense correspondences between images even in these difficult situations starting with the non rigid dense correspondence algorithm 1 to generate an initial correspondence map we propose a new geometric filter that uses cubic b spline surfaces to approximate the correspondence mapping functions for shared objects in both images thereby eliminating outliers and noise we then propose an iterative algorithm which enlarges the region containing valid correspondences compared with the existing methods our method is more robust to significant changes in lighting color or viewpoint furthermore we demonstrate how to extend our surface approximation method to video editing by first generating a reliable correspondence map between a given source frame and each frame of a video the user can then edit the source frame and the changes are automatically propagated through the entire video using the correspondence map to evaluate our approach we examine applications of unsupervised image recognition and video texture editing and show that our algorithm produces better results than those from state of the art approaches

krylov subspace acceleration of nonlinear multigrid with application to recirculating flows this paper deals with the combination of two solution methods multigrid and gmres siam j sci comput 14 1993 pp 856 869 the generality and parallelizabili nonlinear pdes as the preconditioner for a nonlinear krylov subspace method we use the full approximation storage fas scheme math comp 31 1977 pp 333 390 a nonlinear multigrid method the nonlinear krylov acceleration is applied also on coarse grids so that recirculating incompressible flow problems discretized with a higher order upwind scheme can be solved efficiently

image segmentation by histogram thresholding using fuzzy sets methods for histogram thresholding based on the minimization of a threshold dependent criterion function might not work well for images having multimodal histograms we propose an approach to threshold the histogram according to the similarity between gray levels such a similarity is assessed through a fuzzy measure in this way we overcome the local minima that affect most of the conventional methods the experimental results demonstrate the effectiveness of the proposed approach for both bimodal and multimodal histograms

measuring fuzzy uncertainty first this paper reviews several well known measures of fuzziness for discrete fuzzy sets then new multiplicative and additive classes are defined we show that each class satisfies five well known axioms for fuzziness measures and demonstrate that several existing measures are relatives of these classes the multiplicative class is based on nonnegative monotone increasing concave functions the additive class requires only nonnegative concave functions some relationships between several existing and the new measures are established and some new properties are derived the relative merits and drawbacks of different measures for applications are discussed a weighted fuzzy entropy which is flexible enough to incorporate subjectiveness in the measure of fuzziness is also introduced finally we comment on the construction of measures that may assess all of the uncertainties associated with a physical system

generalized bounded variation and applications to piecewise monotonic transformations we prove the quasi compactness of the perron frobenius operator of piecewise monotonic transformations when the inverse of the derivative is holder continuous or more generally of bounded p variation

anderson acceleration for fixed point iterations this paper concerns an acceleration method for fixed point iterations that originated in work of d g anderson j assoc comput mach 12 1965 pp 547 560 which we accordingly call anderson acceleration here this method has enjoyed considerable success and wide usage in electronic structure computations where it is known as anderson mixing however it seems to have been untried or underexploited in many other important applications moreover while other acceleration methods have been extensively studied by the mathematics and numerical analysis communities this method has received relatively little attention from these communities over the years a recent paper by h fang and y saad numer linear algebra appl 16 2009 pp 197 221 has clarified a remarkable relationship of anderson acceleration to quasi newton secant updating methods and extended it to define a broader anderson family of acceleration methods in this paper our goals are to shed additional light on anderson acceleration and to draw further attention to its usefulness as a general tool we first show that on linear problems anderson acceleration without truncation is essentially equivalent in a certain sense to the generalized minimal residual gmres method we also show that the type 1 variant in the fang saad anderson family is similarly essentially equivalent to the arnoldi full orthogonalization method we then discuss practical considerations for implementing anderson acceleration and illustrate its performance through numerical experiments involving a variety of applications

analytic models and ambiguity of context free languages we establish that several classical context free languages are inherently ambiguous by proving that their counting generating functions when considered as analytic functions exhibit some characteristic form of transcendental behaviour to that purpose we survey some general results on elementary analytic properties and enumerative uses of algebraic functions in relation to formal languages in particular the paper contains a general density theorem for unambiguous context free languages

matrix group integrals surfaces and mapping class groups i u n since the 1970 s physicists and mathematicians who study random matrices in the gue or goe models are aware of intriguing connections between integrals of such random matrices and enumeration of graphs on surfaces we establish a new aspect of this theory for random matrices sampled from the group u n of unitary matrices more concretely we study measures induced by free words on u n let fr be the free group on r generators to sample a random element from u n according to the measure induced by w fr one substitutes the r letters in w by r independent haar random elements from u n the main theme of this paper is that every moment of this measure is determined by families of pairs f where is an orientable surface with boundary and f is a map from to the bouquet ofr circles which sends the boundary components of to powers of w a crucial role is then played by euler characteristics of subgroups of the mapping class group of as corollaries we obtain asymptotic bounds on the moments we show that the measure on u n bears information about the number of solutions to the equation u1 v1 ug vg w in the free group and deduce that one can hear the stable commutator length of a word through its unitary word measures

mixed finite elements for elliptic problems with tensor coefficients as cell centered finite differences we present an expanded mixed finite element approximation of second order elliptic problems containing a tensor coefficient the mixed method is expanded in the sense that three variables are explicitly approximated namely the scalar unknown the negative of its gradient and its flux the tensor coefficient times the negative gradient the resulting linear system is a saddle point problem in the case of the lowest order raviart thomas elements on rectangular parallelepipeds we approximate this expanded mixed method by incorporating certain quadrature rules this enables us to write the system as a simple cell centered finite difference method requiring the solution of a sparse positive semidefinite linear system for the scalar unknown for a general tensor coefficient the sparsity pattern for the scalar unknown is a 9 point stencil in two dimensions and 19 points in three dimensions existing theory shows that the expanded mixed method gives optimal order approximations in the l 2 and h s norms and superconvergence is obtained between the l 2 projection of the scalar variable and its approximation we show that these rates of convergence are retained for the finite difference method if h denotes the maximal mesh spacing then the optimal rate is o h the superconvergence rate o h 2 is obtained for the scalar unknown and rate o h 3 2 for its gradient and flux in certain discrete norms moreover the full o h 2 is obtained in the strict interior of the domain computational results illustrate these theoretical results

enhanced cell centered finite differences for elliptic equations on general geometry we present an expanded mixed finite element method for solving second order elliptic partial differential equations on geometrically general domains for the lowest order raviart thomas approximating spaces we use quadrature rules to reduce the method to cell centered finite differences possibly enhanced with some face centered pressures this substantially reduces the computational complexity of the problem to a symmetric positive definite system for essentially only as many unknowns as elements our new method handles general shape elements triangles quadrilaterals and hexahedra and full tensor coefficients while the standard mixed formulation reduces to finite differences only in special cases with rectangular elements as in other mixed methods we maintain the local approximation of the divergence i e local mass conservation in contrast galerkin finite element methods facilitate general element shapes at the cost of achieving only global mass conservation our method is shown to be as accurate as the standard mixed method for a large class of smooth meshes on nonsmooth meshes or with nonsmooth coefficients one can add lagrange multiplier pressure unknowns on certain element edges or faces this enhanced cell centered procedure recovers full accuracy with little additional cost if the coefficients or mesh geometry are piecewise smooth theoretical error estimates and numerical examples are given illustrating the accuracy and efficiency of the methods

krylov subspace methods for solving large unsymmetric linear systems some algorithms based upon a projection process onto the krylov subspace k sub m span r sub 0 ar sub 0 a sup m 1 r sub 0 are developed generalizing the method of conjugate gradients to unsymmetric systems these methods are extensions of arnoldi s algorithm for solving eigenvalue problems the convergence is analyzed in terms of the distance of the solution to the subspace k sub m and some error bounds are established showing in particular a similarity with the conjugate gradient method for symmetric matrices when the eigenvalues are real several numerical experiments are described and discussed

monotone finite volume schemes for diffusion equations on unstructured triangular and shape regular polygonal meshes we consider a non linear finite volume fv scheme for stationary diffusion equation we prove that the scheme is monotone i e it preserves positivity of analytical solutions on arbitrary triangular meshes for strongly anisotropic and heterogeneous full tensor coefficients the scheme is extended to regular star shaped polygonal meshes and isotropic heterogeneous coefficients

a vertex centered and positivity preserving scheme for anisotropic diffusion problems on arbitrary polygonal grids abstract we suggest a new positivity preserving finite volume scheme for anisotropic diffusion problems on arbitrary polygonal grids the scheme has vertex centered edge midpoint and cell centered unknowns the vertex centered unknowns are primary and have finite volume equations associated with them the edge midpoint and cell centered unknowns are treated as auxiliary ones and are interpolated by the primary unknowns which makes the final scheme a pure vertex centered one unlike most existing positivity preserving schemes the construction of the scheme is based on a special nonlinear two point flux approximation that has a fixed stencil and does not require the convex decomposition of the co normal in order to solve efficiently the nonlinear systems resulting from the nonlinear scheme picard method and its anderson acceleration are discussed numerical experiments demonstrate the second order accuracy and well positivity of the solution for heterogeneous and anisotropic problems on severely distorted grids the high efficiency of the anderson acceleration is also shown on reduction of the number of nonlinear iterations moreover the proposed scheme does not have the so called numerical heat barrier issue suffered by most existing cell centered and hybrid schemes however further improvements have to be made if the solution is very close to the machine precision and the mesh distortion is very severe

some results about vector extrapolation methods and related fixed point iterations abstract in this work we consider polynomial extrapolation methods for vector sequences we give a unified presentation of these methods and a new recursive algorithm for the implementation of the modified minimal polynomial extrapolation mmpe method properties operation counts and storage requirements of the algorithm will be given the second part of the work is devoted to the application of these methods for solving systems of nonlinear equations a sufficient condition for quadratic convergence is given

orientation selection using modified fcm for competitive code based palmprint recognition coding based methods are among the most promising palmprint recognition methods because of their small feature size fast matching speed and high verification accuracy the competitive coding scheme one representative coding based method first convolves the palmprint image with a bank of gabor filters with different orientations and then encodes the dominant orientation into its bitwise representation despite the effectiveness of competitive coding few investigations have been given to study the influence of the number of gabor filters and the orientation of each gabor filter in this paper based on the statistical orientation distribution and the orientation separation characteristics we propose a modified fuzzy c means cluster algorithm to determine the orientation of each gabor filter since the statistical orientation distribution is based on a set of real palmprint images the proposed method is more suitable for palmprint recognition experimental results indicate that the proposed method achieves higher verification accuracy while compared with that of the original competitive coding scheme and several state of the art methods such as ordinal measure and rloc considering both the computational complexity and the verification accuracy competitive code with six orientations would be the optimal choice for palmprint recognition

monotone finite volume schemes for diffusion equations on polygonal meshes we construct a nonlinear finite volume fv scheme for diffusion equation on star shaped polygonal meshes and prove that the scheme is monotone i e it preserves positivity of analytical solutions for strongly anisotropic and heterogeneous full tensor coefficients our scheme has only cell centered unknowns and it treats material discontinuities rigorously and offers an explicit expression for the normal flux numerical results are presented to show how our scheme works for preserving positivity on various distorted meshes for both smooth and non smooth highly anisotropic solutions and numerical results show that our scheme appears to be approximate second order accuracy for the solution and first order accuracy for the flux

an improved monotone finite volume scheme for diffusion equation on polygonal meshes we construct a new nonlinear monotone finite volume scheme for diffusion equation on polygonal meshes the new scheme uses the cell edge unknowns instead of cell vertex unknowns as the auxiliary unknowns in order to improve the accuracy of monotone scheme our scheme is locally conservative and has only cell centered unknowns numerical results are presented to show how our scheme works for preserving positivity on various distorted meshes specially numerical results show that the new scheme is robust and more accurate than the existing monotone scheme on some kinds of meshes

symbolic dynamics for geodesic floes the subject of symbolic dynamics is of central importance in the modern theory of dynamical systems the use of symbolic sequences to study dynamical properties of geodesies originates in the work of koebe 21 22 and morse 24 25 and is already foreshadowed in hadamard 15 and jordan 19 the method of koebe and of morse is to code a geodesic on a surface m of negative curvature by recording the order in which it traverses a given set of labelled curves on m the treatment of morse allows variable curvature but assumes at least two boundary components whereas koebe assumes constant curvature but allows infinite connectivity and nonorientability and treats the more difficult case of a closed surface this last case is handled by recording crossings of a fixed pants decomposition anticipating the thurston parameterization of simple curves as described in 11 both koebe and morse used their codings to demonstrate the existence of countably many closed geodesies and of everywhere dense transitive geodesies morse further constructed the first nonsynthetic example of a recurrent nonperiodic discontinuous motion in modern terminology a minimal nowhere dense set later 26 morse treated the special closed surfaces of genus g associated to tesselations of the disc d by regular 4 gons each edge of a region in such a tesselation may be labelled by the isometry which glues it to another side of the same region in forming the quotient sin face m the set of isometries appearing as labels generate tti m thus any geodesic is coded as a doubly infinite sequence of generators of iri m the same method applies quite generally to tesselations associated to any fuchsian group we call the sequences thus obtained cutting sequences and refer to generating sets of this kind as geometric the difficulty of course is to determine precisely the class of sequences which occur for a surface with boundary one obtains exactly reduced sequences in the generators in generalthe problem4s gompligated1 henge the difficulties encountered in 26 see also theorem 3 below there is another method of coding geodesies using certain boundary expansions for points at infinity in the universal cover of m for the modular surface h sl 2 2 the appropriate expansions are continued fractions and for the symmetrical genus g surfaces above they are the nielsen boundary expansions of 27

svd based initialization a head start for nonnegative matrix factorization we describe nonnegative double singular value decomposition nndsvd a new method designed to enhance the initialization stage of nonnegative matrix factorization nmf nndsvd can readily be combined with existing nmf algorithms the basic algorithm contains no randomization and is based on two svd processes one approximating the data matrix the other approximating positive sections of the resulting partial svd factors utilizing an algebraic property of unit rank matrices simple practical variants for nmf with dense factors are described nndsvd is also well suited to initialize nmf algorithms with sparse factors many numerical examples suggest that nndsvd leads to rapid reduction of the approximation error of many nmf algorithms

interpolation based second order monotone finite volume schemes for anisotropic diffusion equations on general grids we propose two interpolation based monotone schemes for the anisotropic diffusion problems on unstructured polygonal meshes through the linearity preserving approach the new schemes are characterized by their nonlinear two point flux approximation which is different from the existing ones and has no constraint on the associated interpolation algorithm for auxiliary unknowns thanks to the new nonlinear two point flux formulation it is no longer required that the interpolation algorithm should be a positivity preserving one the first scheme employs vertex unknowns as the auxiliary ones and a second order but not positivity preserving interpolation algorithm is utilized the second scheme uses the so called harmonic averaging points located on cell edges to define the auxiliary unknowns and a second order positivity preserving interpolation method is employed both schemes have nearly the same convergence rates as compared with their related second order linear schemes numerical results demonstrate that the new schemes are monotone and have the second order accuracy for the solution and first order for its gradient on severely distorted meshes

anderson acceleration for nonlinear finite volume scheme for advection diffusion problems we consider the solution of systems of nonlinear algebraic equations that appear in a positivity preserving finite volume scheme for steady state advection diffusion equations we propose and analyze numerically an efficient strategy for accelerating the picard method when it is applied to these systems the strategy is based on the anderson acceleration and the adaptive inexact solution of linear systems we demonstrate its numerical robustness for three black box preconditioners

a decoupled and positivity preserving discrete duality finite volume scheme for anisotropic diffusion problems on general polygonal meshes abstract we suggest a new positivity preserving discrete duality finite volume ddfv scheme for anisotropic diffusion problems on general polygonal meshes like existing ddfv schemes this scheme is built on the primary and dual meshes and has finite volume fv equations for both vertex and cell centered unknowns the transpose of the coefficient matrix for the fv equations of the cell centered unknowns is an m matrix while that for the vertex unknowns is not an m matrix but a symmetric and positive definite matrix by employing a certain truncation technique for the vertex unknowns the positivity preserving property for both categories of unknowns is guaranteed local conservation is strictly maintained for the cell centered unknowns and conditionally maintained for the vertex unknowns since the fv equations of the vertex unknowns can be solved independently the two sets of fv equations are decoupled in contrast to existing nonlinear positivity preserving schemes the new scheme requires no nonlinear iterations for linear problems for nonlinear problems the positivity preserving mechanism of the new scheme is decoupled from its nonlinear iteration so that any nonlinear solver can be adopted moreover the positivity of the discrete solution is proved and the well posedness is analyzed rigorously for linear problems in numerical experiments the new scheme is examined extensively and compared with two positivity preserving cell centered schemes and a nonlinear ddfv scheme numerical results show that the present ddfv scheme achieves second order accuracy and preserves the positivity of the solution for heterogeneous and anisotropic problems on severely distorted grids the high efficiency of the scheme is also demonstrated by the comparison of computation time and number of nonlinear iterations

monotonicity of control volume methods robustness of numerical methods for multiphase flow problems in porous media is important for development of methods to be used in a wide range of applications here we discuss monotonicity for a simplified problem of single phase flow but where the simulation grids and media are allowed to be general posing challenges to control volume methods we discuss discrete formulations of the maximum principle and derive sufficient criteria for discrete monotonicity for arbitrary nine point control volume discretizations for conforming quadrilateral grids in 2d these criteria are less restrictive than the m matrix property it is shown that it is impossible to construct nine point methods which unconditionally satisfy the monotonicity criteria when the discretization satisfies local conservation and exact reproduction of linear potential fields numerical examples are presented which show the validity of the criteria for monotonicity further the impact of nonmonotonicity is studied different behavior for different discretization methods is illuminated and simple ideas are presented for improvement in terms of monotonicity

design and application of a gradient weighted moving finite element code ii in two dimensions in part i the authors reported on the design of a robust and versatile gradient weighted moving finite element gwmfe code in one dimension and on its application to a variety of pdes and pde systems this companion paper does the same for the two dimensional 2d case these moving node methods are especially suited to problems which develop sharp moving fronts especially problems where one needs to resolve the fine scale structure of the fronts the many potential pitfalls in the design of gwmfe codes and the special features of the implicit one dimensional 1d and 2d codes which contribute to their robustness and efficiency are discussed at length in part i this paper concentrates on issues unique to the 2d case brief explanations are given of the variational interpretation of gwmfe the geometrical mechanical interpretation simplified regularization terms and the treatment of systems a catalog of inner products which occur in gwmfe is given with particular attention paid to those involving second order operators after presenting an example of the 2d phenomenon of grid collapse and discussing the need for long time regularization the paper reports on the application of the 2d code to several nontrivial problems nonlinear arsenic diffusion in the manufacture of semiconductors the drift diffusion equations for semiconductor device simulation the buckley leverett black oil equations for reservoir simulation and the motion of surfaces by mean curvature

stable commutator length in baumslag solitar groups and quasimorphisms for tree actions this paper has two parts on baumslag solitar groups and on general g trees in the first part we establish bounds for stable commutator length scl in baumslag solitar groups for a certain class of elements we further show that scl is computable and takes rational values we also determine exactly which of these elements admit extremal surfaces in the second part we establish a universal lower bound of 1 12 for scl of suitable elements of any group acting on a tree this is achieved by constructing efficient quasimorphisms calculations in the group bs 2 3 show that this is the best possible universal bound thus answering a question of calegari and fujiwara we also establish scl bounds for acylindrical tree actions returning to baumslag solitar groups we show that their scl spectra have a uniform gap no element has scl in the interval 0 1 12

accelerating with rank one updates abstract consider the iteration xk 1 xk h b axk for solving ax b a is n x n nonsingular we discuss rank one updates to improve h as an approximation to a 1 during the iteration the update kills and reduces singular values of i ah and thus speeds up the convergence the algorithm terminates after at most n sweeps and if all n sweeps are needed then a 1 has been computed

relative growth series in some hyperbolic groups we study certain groups of isometries of hyperbolic space including certain hyperbolic coxeter groups and normal subgroups with quotient z 1 we show that the associated relative growth series are not rational this extends results obtained by grigorchuk and de la harpe for free groups and pollicott and the author for surface groups

surface subgroups from linear programming we show that a random endomorphism of a free group gives rise to an hnn extension which contains a closed surface subgroup with probability one a special case is the hnn extension associated to the endomorphism of a rank 2 free group considered by sapir sending a to ab and b to ba we further show that a group obtained by doubling a free group along any collection of subgroups of arbitrary rank has the property that every rational 2 dimensional homology class is virtually represented by surface subgroups and the unit ball in the gromov norm is a finite sided rational polyhedron these results are obtained by a mixture of combinatorial geometric and linear programming techniques we obtain other related results of a more technical nature concerning stable commutator length in free groups especially concerning the structure of the space of so called counting quasimorphisms

scl in graphs of groups let g be a group acting on a tree with cyclic edge and vertex stabilizers then stable commutator length scl is rational in g furthermore scl varies predictably and converges to rational limits in so called surgery families this is a homological analog of the phenomenon of geometric convergence in hyperbolic dehn surgery

vector extrapolation methods applications and numerical comparison the present paper is a survey of the most popular vector extrapolation methods such as the reduced rank extrapolation rre the minimal polynomial extrapolation mpe the modified minimal polynomial extrapolation mmpe the vector e algorithm vea and the topological e algorithm tea using projectors we derive a different interpretation of these methods and give some theoretical results the second aim of this work is to give a numerical comparison of the vector extrapolation methods above when they are used for practical large problems such as linear and nonlinear systems of equations

the mimetic finite difference method for elliptic and parabolic problems with a staggered discretization of diffusion coefficient numerical schemes for nonlinear parabolic equations based on the harmonic averaging of cell centered diffusion coefficients break down when some of these coefficients go to zero or their ratio grows to tackle this problem we propose new mimetic finite difference schemes that use a staggered discretization of the diffusion coefficient the primary mimetic operator approximates div k the derived dual mimetic operator approximates the new mimetic schemes preserve symmetry and positive definiteness of the continuum problem which allows us to use algebraic solvers with optimal complexity we perform detailed numerical analysis of the new schemes for linear elliptic problems and a specially designed linear parabolic problem that has solution dynamics typical for nonlinear problems we show that the new schemes are competitive with the state of the art schemes for steady state problems but provide much more accurate solution dynamics for the transient problem

numerical artifacts in the generalized porous medium equation why harmonic averaging itself is not to blame abstract the degenerate parabolic generalized porous medium equation gpme poses numerical challenges due to self sharpening and its sharp corner solutions for these problems we show results for two subclasses of the gpme with differentiable k p with respect to p namely the porous medium equation pme and the superslow diffusion equation spurious temporal oscillations and nonphysical locking and lagging have been reported in the literature these issues have been attributed to harmonic averaging of the coefficient k p for small p and arithmetic averaging has been suggested as an alternative we show that harmonic averaging is not solely responsible and that an improved discretization can mitigate these issues here we investigate the causes of these numerical artifacts using modified equation analysis the modified equation framework can be used for any type of discretization we show results for the second order finite volume method the observed problems with harmonic averaging can be traced to two leading error terms in its modified equation this is also illustrated numerically through a modified harmonic method mhm that can locally modify the critical terms to remove the aforementioned numerical artifacts

convergence theorems for least change secant update methods the purpose of this paper is to present a convergence analysis of least change secant methods in which part of the derivative matrix being approximated is computed by other means the theorems and proofs given here can be viewed as generalizations of those given by broyden dennis more j inst math appl 12 1973 pp 223 246 and by dennis more math comp 28 1974 pp 549 560 the analysis is done in the orthogonal projection setting of dennis schnabel siam rev 21 1980 pp 443 459 and many readers might feel that it is easier to understand the theorems here readily imply local and q superlinear convergence of all the standard methods in addition to proving these results for the first time for the sparse symmetric method of marwil and toint and the nonlinear least squares method of dennis gay welsch

entropy and drift in word hyperbolic groups the fundamental inequality of guivarc h relates the entropy and the drift of random walks on groups it is strict if and only if the random walk does not behave like the uniform measure on balls we prove that in any nonelementary hyperbolic group which is not virtually free endowed with a word distance the fundamental inequality is strict for symmetric measures with finite support uniformly for measures with a given support this answers a conjecture of s lalley for admissible measures this is proved using previous results of ancona and blachere haissinsky mathieu for non admissible measures this follows from a counting result interesting in its own right we show that in any infinite index subgroup the number of non distorted points is exponentially small the uniformity is obtained by studying the behavior of measures that degenerate towards a measure supported on an elementary subgroup

histogram thresholding using fuzzy and rough measures of association error this paper presents a novel histogram thresholding methodology using fuzzy and rough set theories the strength of the proposed methodology lies in the fact that it does not make any prior assumptions about the histogram unlike many existing techniques for bilevel thresholding every element of the histogram is associated with one of the two regions by comparing the corresponding errors of association the regions are considered ambiguous in nature and hence the error measures are based on the fuzziness or roughness of the regions multilevel thresholding is carried out using the proposed bilevel thresholding method in a tree structured algorithm segmentation object background separation and edge extraction are performed using the proposed methodology a quantitative index to evaluate image segmentation performance is also proposed using the median of absolute deviation from median measure which is a robust estimator of scale extensive experimental results are given to demonstrate the effectiveness of the proposed methods in terms of both qualitative and quantitative measures

on the color image segmentation algorithm based on the thresholding and the fuzzy c means techniques abstract in this paper a segmentation algorithm for color images based on the thresholding and the fuzzy c means fcm techniques is presented the scale space filter is used as a tool for analyzing the histograms of three color components the methodology uses a coarse fine concept to reduce the computational burden required for the fcm the coarse segmentation attempts to segment coarsely using the thresholding technique while the fine segmentation assigns the pixels which remain unclassified after the coarse segmentation to the closest class using the fcm attempts also have been made to compare the performance of the proposed algorithm with other existing algorithms ohlander s rosenfeld s and bezdek s intensive computer simulation has been performed and the results are discussed in this paper the simulation results indicate that the proposed algorithm yields the most accurate segmented image on the color coordinate proposed by ohta et al while requiring a reasonable amount of computational effort

random equations in nilpotent groups abstract in this paper we study satisfiability of random equations in an infinite finitely generated nilpotent group g let sat g k be the set of all satisfiable equations over g in k variables for a free abelian group a m of rank m we show that the asymptotic density sat a m k of the set sat a m k in the whole space of all equations in k variables over g is equal to 0 for k 1 and is equal to k m k for k 2 more generally if g is a finitely generated nilpotent infinite group then again the asymptotic density of the set sat g 1 is 0 for k 2 we give robust estimates for the upper and lower asymptotic densities of the set sat g k namely we prove that these densities lie in the interval from 1 t g k h g k to k m k where h g is the hirsch length of g t g is the order of lower central torsion of g and m is the torsion free rank hirsch length of the abelianization of g this allows one to describe the asymptotic behavior of the set sat g k for different parameters k m h g t g

stable commutator length is rational in free groups for any group there is a natural pseudo norm on the vector space b h 1 of real homogenized group 1 boundaries called the stable commutator length norm this norm is closely related to and can be thought of as a relative version of the gromov pseudo norm on ordinary homology we show that for a free group the unit ball of this pseudo norm is a rational polyhedron it follows that the stable commutator length in free groups takes on only rational values moreover every element of the commutator subgroup of a free group rationally bounds an injective map of a surface group the proof of these facts yields an algorithm to compute the stable commutator length in free groups using this algorithm we answer a well known question of bavard in the negative constructing explicit examples of elements in free groups whose stable commutator length is not a half integer

acceleration of the schwarz method for elliptic problems in this paper we present a family of domain decomposition methods based on aitken like acceleration of the schwarz method which is an iterative procedure with linear rate of convergence this paper is a generalization of our method first introduced in 2000 that was restricted to cartesian grids we consider the finite volume fv approximation on general quadrangle meshes introduced by faille in 1992 we first present the so called aitken schwarz procedure for a linear differential operator this solver is a direct solver but its computational cost in the general case might be prohibitive second we introduce the steffensen schwarz variant which is an iterative domain decomposition solver that can be applied to linear and nonlinear problems we show that this iterative solver has reasonable numerical efficiency and can be applied successfully to several classes of linear and nonlinear elliptic problems however the salient feature of our method is that our algorithm has high tolerance for slow networks in the context of distributed parallel computing and is attractive to use with computer architectures for which performance is limited by the memory bandwidth rather than the flop performance of the cpu this is currently the case for most parallel computers using risc processor architecture such as beowulf systems

random walks with internal degrees of freedom between two absorbing barriers consider a random walk with a finite number of internal degrees of freedom and with zero drift by using a functional analytic approach based on the spectral theory of matrix polynomials the asymptotics of the first hitting probabilities is obtained when the distance of the barriers tends to infinity

the growth of free products abstract we improve estimates for the exponential growth rates of free products with or without amalgamation hnn extensions one relator groups and groups of positive deficiency some examples of groups for which the growth rates are realized are given

analysis of some vector extrapolation methods for solving systems of linear equations in this paper we consider some vector extrapolation methods for solving nonsymmetric systems of linear equations when applied to sequences generated linearly these methods namely the minimal polynomial extrapolation mpe and the reduced rank extrapolation rre are krylov subspaces methods and are respectively equivalent to the method of arnoldi and to the gcr and gmres by considering the geometrical aspect of these methods we derive new expressions for their residual norms and give a relationship between them this allows us to compare the two methods using this new approach we will show that for nonsingular skew symmetric matrices the gmres stagnates every two iterations and the restarted version gmres m m ge 2 is always convergent finally the incomplete forms are considered and some convergence results are given