efficient arnoldi type algorithms for rational eigenvalue problems arising in fluid solid systems we develop and analyze efficient methods for computing damped vibration modes of an acoustic fluid confined in a cavity with absorbing walls capable of dissipating acoustic energy the discretization in terms of pressure nodal finite elements gives rise to a rational eigenvalue problem numerical evidence shows that there are no spurious eigenmodes for such discretization and also confirms that the discretization based on nodal pressures is much more efficient than that based on raviart thomas finite elements for the displacement field the trimmed linearization method is used to linearize the associated rational eigenvalue problem into a generalized eigenvalue problem gep of the form ax lbx for solving the gep we apply arnoldi algorithm to two different types of single matrices b 1a and ab 1 numerical accuracy shows that the application of arnoldi on ab 1 is better than that on b 1a

semidiscrete finite element approximations of a linear fluid structure interaction problem semidiscrete finite element approximations of a linear fluid structure interaction problem are studied first results concerning a divergence free weak formulation of the interaction problem are reviewed next semidiscrete finite element approximations are defined and the existence of finite element solutions is proved with the help of an auxiliary discretely divergence free formulation a discrete inf sup condition is verified and the existence of a finite element pressure is established strong a priori estimates for the finite element solutions are also derived then by passing to the limit in the finite element approximations the existence of a strong solution is demonstrated and semidiscrete error estimates are obtained

bounds on the joint and generalized spectral radius of the hadamard geometric mean of bounded sets of positive kernel operators abstract let 1 m be bounded sets of positive kernel operators on a banach function space l we prove that for the generalized spectral radius and the joint spectral radius the inequalities 1 1 m m 1 m 1 2 m 1 m 1 1 m m 1 m 1 2 m 1 m hold where 1 1 m m 1 m denotes the hadamard schur geometric mean of the sets 1 m

a riemannian approach to graph embedding in this paper we make use of the relationship between the laplace beltrami operator and the graph laplacian for the purposes of embedding a graph onto a riemannian manifold to embark on this study we review some of the basics of riemannian geometry and explain the relationship between the laplace beltrami operator and the graph laplacian using the properties of jacobi fields we show how to compute an edge weight matrix in which the elements reflect the sectional curvatures associated with the geodesic paths on the manifold between nodes for the particular case of a constant sectional curvature surface we use the kruskal coordinates to compute edge weights that are proportional to the geodesic distance between points we use the resulting edge weight matrix to embed the nodes of the graph onto a riemannian manifold to do this we develop a method that can be used to perform double centring on the laplacian matrix computed from the edge weights the embedding coordinates are given by the eigenvectors of the centred laplacian with the set of embedding coordinates at hand a number of graph manipulation tasks can be performed in this paper we are primarily interested in graph matching we recast the graph matching problem as that of aligning pairs of manifolds subject to a geometric transformation we show that this transformation is pro crustean in nature we illustrate the utility of the method on image matching using the coil database

the locally weighted bag of words framework for document representation the popular bag of words assumption represents a document as a histogram of word occurrences while computationally efficient such a representation is unable to maintain any sequential information we present an effective sequential document representation that goes beyond the bag of words representation and its n gram extensions this representation uses local smoothing to embed documents as smooth curves in the multinomial simplex thereby preserving valuable sequential information in contrast to bag of words or n grams the new representation is able to robustly capture medium and long range sequential trends in the document we discuss the representation and its geometric properties and demonstrate its applicability for various text processing tasks

geometry based symbolic approximation for fast sequence matching on manifolds in this paper we consider the problem of fast and efficient indexing techniques for sequences evolving in non euclidean spaces this problem has several applications in the areas of human activity analysis where there is a need to perform fast search and recognition in very high dimensional spaces the problem is made more challenging when representations such as landmarks contours and human skeletons etc are naturally studied in a non euclidean setting where even simple operations are much more computationally intensive than their euclidean counterparts we propose a geometry and data adaptive symbolic framework that is shown to enable the deployment of fast and accurate algorithms for activity recognition dynamic texture recognition motif discovery toward this end we present generalizations of key concepts of piece wise aggregation and symbolic approximation for the case of non euclidean manifolds we show that one can replace expensive geodesic computations with much faster symbolic computations with little loss of accuracy in activity recognition and discovery applications the framework is general enough to work across both euclidean and non euclidean spaces depending on appropriate feature representations without compromising on the ultra low bandwidth high speed and high accuracy the proposed methods are ideally suited for real time systems and low complexity scenarios

the variational iteration method an efficient scheme for handling fractional partial differential equations in fluid mechanics variational iteration method has been used to handle linear and nonlinear differential equations the main property of the method lies in its flexibility and ability to solve nonlinear equations accurately and conveniently in this work a general framework of the variational iteration method is presented for analytical treatment of fractional partial differential equations in fluid mechanics the fractional derivatives are described in the caputo sense numerical illustrations that include the fractional wave equation fractional burgers equation fractional kdv equation fractional klein gordon equation and fractional boussinesq like equation are investigated to show the pertinent features of the technique comparison of the results obtained by the variational iteration method with those obtained by adomian decomposition method reveals that the first method is very effective and convenient the basic idea described in this paper is expected to be further employed to solve other similar linear and nonlinear problems in fractional calculus

the fractional diffusion equation in one space and in one time dimension a diffusion equation is solved where the first time derivative is replaced by the fractional time derivative 0 1 the solution is given in closed form in terms of fox functions

fine fisher information nonparametric embedding we consider the problems of clustering classification and visualization of high dimensional data when no straightforward euclidean representation exists in this paper we propose using the properties of information geometry and statistical manifolds in order to define similarities between data sets using the fisher information distance we will show that this metric can be approximated using entirely nonparametric methods as the parameterization and geometry of the manifold is generally unknown furthermore by using multidimensional scaling methods we are able to reconstruct the statistical manifold in a low dimensional euclidean space enabling effective learning on the data as a whole we refer to our framework as fisher information nonparametric embedding fine and illustrate its uses on practical problems including a biomedical application and document classification

eigenvalue approximation by mixed and hybrid methods note univ maryland dept math college pk md 20742 ecole polytech ctr math appl f 91128 palaiseau france univ paris 6 f 75230 paris 05 france mercier b cea limeil f 94190 villeneuve france isi document delivery no lq584times cited 29cited reference count 44 reference asn article 1981 005doi 10 2307 2007651 record created on 2006 08 24 modified on 2017 05 12

similarity preserving principal curve an optimal 1 d feature extractor for data representation this paper discusses the problem of what kind of learning model is suitable for the tasks of feature extraction for data representation and suggests two evaluation criteria for nonlinear feature extractors reconstruction error minimization and similarity preservation based on the suggested evaluation criteria a new type of principal curve similarity preserving principal curve sppc is proposed sppcs minimize the reconstruction error under the condition that the similarity between similar samples are preserved in the extracted features thus giving researchers effective and reliable cognition of the inner structure of data sets the existence and properties of sppcs are analyzed a practical learning algorithm is proposed and high dimensional extensions of sppcs are also discussed experimental results show the virtues of sppcs in preserving inner structures of data sets and discovering manifolds with high nonlinearity

fractional wave equation with a frictional memory kernel of mittag leffler type abstract in this paper we give an analytical treatment of a fractional wave equation with caputo time fractional derivative and frictional memory kernel of mittag leffler type this problem generalizes a recently solved problem 62 of a wave equation for a vibrating string in presence of a fractional friction with power law memory kernel such equations can be used in the context of modeling processes in complex and viscoelastic media

diffusion kernels on statistical manifolds a family of kernels for statistical learning is introduced that exploits the geometric structure of statistical models the kernels are based on the heat equation on the riemannian manifold defined by the fisher information metric associated with a statistical family and generalize the gaussian kernel of euclidean space as an important special case kernels based on the geometry of multinomial families are derived leading to kernel based learning algorithms that apply naturally to discrete data bounds on covering numbers and rademacher averages for the kernels are proved using bounds on the eigenvalues of the laplacian on riemannian manifolds experimental results are presented for document classification for which the use of multinomial geometry is natural and well motivated and improvements are obtained over the standard use of gaussian or linear kernels which have been the standard for text classification

depth based complexity traces of graphs in this paper we aim to characterize graphs in terms of a structural measure of complexity our idea is to decompose a graph into layered substructures of increasing size and then to measure the information content of these substructures to locate dominant substructures within a graph we commence by identifying a centroid vertex which has the minimum shortest path length variance to the remaining vertices for each graph a family of centroid expansion subgraphs is derived from the centroid vertex in order to capture dominant structural characteristics of the graph since the centroid vertex is identified through a global analysis of the shortest path length distribution the expansion subgraphs provide a fine representation of a graph structure we then show how to characterize graphs using depth based complexity traces here we explore two different strategies the first strategy is to measure how the entropies on the centroid expansion subgraphs vary with the increasing size of the subgraphs the second strategy is to measure how the entropy differences vary with the increasing size of the subgraphs we perform graph classification in the principal component space of the complexity trace vectors experiments on graph datasets abstracted from some bioinformatics and computer vision databases demonstrate the effectiveness and efficiency of the proposed graph complexity traces our methods are competitive to state of the art methods highlightswe identify a centroid vertex of a graph through its shortest path matrix we establish a family of expansion subgraphs of a graph from its centroid vertex we construct depth based complexity traces of a graph on its expansion subgraphs we evaluate the performance of our complexity traces on standard graph datasets we demonstrate the effectiveness and efficiency of the graph complexity traces

proto value functions a laplacian framework for learning representation and control in markov decision processes this paper introduces a novel spectral framework for solving markov decision processes mdps by jointly learning representations and optimal policies the major components of the framework described in this paper include i a general scheme for constructing representations or basis functions by diagonalizing symmetric diffusion operators ii a specific instantiation of this approach where global basis functions called proto value functions pvfs are formed using the eigenvectors of the graph laplacian on an undirected graph formed from state transitions induced by the mdp iii a three phased procedure called representation policy iteration comprising of a sample collection phase a representation learning phase that constructs basis functions from samples and a final parameter estimation phase that determines an approximately optimal policy within the linear subspace spanned by the current basis functions iv a specific instantiation of the rpi framework using least squares policy iteration lspi as the parameter estimation method v several strategies for scaling the proposed approach to large discrete and continuous state spaces including the nystrom extension for out of sample interpolation of eigenfunctions and the use of kronecker sum factorization to construct compact eigenfunctions in product spaces such as factored mdps vi finally a series of illustrative discrete and continuous control tasks which both illustrate the concepts and provide a benchmark for evaluating the proposed approach many challenges remain to be addressed in scaling the proposed framework to large mdps and several elaboration of the proposed framework are briefly summarized at the end

approximate solutions for boundary value problems of time fractional wave equation in this article we implement relatively a new analytical technique the adomian decomposition method for solving the boundary value problems of time fractional wave equation the fractional derivative is described in the caputo sense the decomposition method is used to construct analytical approximate solutions of time fractional wave equation subject to specified boundary conditions the solutions are calculated in the form of a convergent series with easily computable components some examples are given the results reveal that the adomian method is very effective and convenient

finite element analysis of a quadratic eigenvalue problem arising in dissipative acoustics a quadratic eigenvalue problem arising in the determination of the vibration modes of an acoustic fluid contained in a cavity with absorbing walls is considered the problem is shown to be equivalent to the spectral problem for a noncompact operator and a thorough spectral characterization is given a numerical discretization based on raviart thomas finite elements is analyzed the method is proved to be free of spurious modes and to converge with optimal order implementation issues and numerical experiments confirming the theoretical results are reported

series solutions of time fractional host parasitoid systems in this paper adomian s decomposition method adm has been used for solving time fractional host parasitoid system the derivatives are understood in the caputo sense the reason of using fractional order differential equations fod is that fod are naturally related to systems with memory which exists in most biological systems also they are closely related to fractals which are abundant in biological systems numerical example justifies the proposed scheme

finite element vibration analysis of fluid solid systems without spurious modes this paper deals with the finite element approximation of the vibration modes of a problem with fluid structure interaction displacement variables are used for both the fluid and the solid to avoid the typical spurious modes of this formulation we introduce a nonconforming discretization error estimates for the approximation of eigenvalues and eigenvectors are given

wright functions as scale invariant solutions of the diffusion wave equation the time fractional diffusion wave equation is obtained from the classical diffusion or wave equation by replacing the first or second order time derivative by a fractional derivative of order 0 2 using the similarity method and the method of the laplace transform it is shown that the scale invariant solutions of the mixed problem of signalling type for the time fractional diffusion wave equation are given in terms of the wright function in the case 0 1 and in terms of the generalized wright function in the case 1 2 the reduced equation for the scale invariant solutions is given in terms of the caputo type modification of the

a novel framework for learning geometry aware kernels the data from real world usually have nonlinear geometric structure which are often assumed to lie on or close to a low dimensional manifold in a high dimensional space how to detect this nonlinear geometric structure of the data is important for the learning algorithms recently there has been a surge of interest in utilizing kernels 1 to exploit the manifold structure of the data such kernels are called geometry aware kernels and are widely used in the machine learning algorithms the performance of these algorithms critically relies on the choice of the geometry aware kernels intuitively a good geometry aware kernel should utilize additional information other than the geometric information in many applications it is required to compute the out of sample data directly however most of the geometry aware kernel methods are restricted to the available data given beforehand with no straightforward extension for out of sample data in this paper we propose a framework for more general geometry aware kernel learning the proposed framework integrates multiple sources of information and enables us to develop flexible and effective kernel matrices then we theoretically show how the learned kernel matrices are extended to the corresponding kernel functions in which the out of sample data can be computed directly under our framework a novel family of geometry aware kernels is developed especially some existing geometry aware kernels can be viewed as instances of our framework the performance of the kernels is evaluated on dimensionality reduction classification and clustering tasks the empirical results show that our kernels significantly improve the performance 1 kernel refers to kernel function or kernel matrix which should be understood from the context

spectral approximation of variationally posed eigenvalue problems by nonconforming methods this paper deals with the nonconforming spectral approximation of variationally posed eigenvalue problems it is an extension to more general situations of known previous results about nonconforming methods as an application of the present theory convergence and optimal order error estimates are proved for the lowest order crouzeix raviart approximation of the eigenpairs of two representative second order elliptical operators

effect of bacterial memory dependent growth by using fractional derivatives reaction diffusion chemotactic model in this paper numerical solutions of a reaction diffusion chemotactic model of fractional orders for bacterial growth will be present a new solution is constructed in power series the fractional derivatives are described in the caputo sense we compare the experimental result obtained with those obtained by simulation of the chemotactic model without fractional derivatives the results show that the solution continuously depends on the time fractional derivative the resulting solutions spread faster than the classical solutions and may exhibit asymmetry depending on the fractional derivative used we present results of numerical simulations to illustrate the method and investigate properties of numerical solutions the adomian s decomposition method adm is used to find the approximate solution of fractional reaction diffusion chemotactic model numerical results show that the approach is easy to implement and accurate when applied to partial differential equations of fractional order

numerical steady state and hopf bifurcation analysis on the diffusive nicholson s blowflies equation1research partially supported by natural sciences and engineering research council of canada 1 for the dirichlet boundary value problem of the diffusive nicholson s blowflies equation it was shown in ref 17 that in a certain range of the parameter space there is a unique positive steady state solution in this paper we propose a scheme to compute this steady state numerically in addition we describe an iterative procedure to locate the critical values of the delay where a hopf bifurcation of time periodic solutions takes place near the steady state some numerical simulations of both schemes are given

finite element analysis of compressible and incompressible fluid solid systems this paper deals with a finite element method to solve interior fluid structure vibration problems valid for compressible and incompressible fluids it is based on a displacement formulation for both the fluid and the solid the pressure of the fluid is also used as a variable for the theoretical analysis yielding a well posed mixed linear eigenvalue problem lowest order triangular raviart thomas elements are used for the fluid and classical piece wise linear elements for the solid transmission conditions at the fluid solid interface are taken into account in a weak sense yielding a nonconforming discretization the method does not present spurious or circulation modes for nonzero frequencies convergence is proved and error estimates independent of the acoustic speed are given for incompressible fluids a convenient equivalent stream function formulation and a post process to compute the pressure are introduced

a posteriori error estimates in finite element acoustic analysis we present an a posteriori error estimator for the approximations of the acoustic vibration modes obtained by a finite element method which does not present spurious or circulation modes for non zero frequencies we prove that the proposed estimator is equivalent to the error in the approximation of the eigenvectors up to higher order terms with constants independent of the eigenvalues numerical results for some test examples are presented which show the good behavior of the estimator when it is used as local error indicator for adaptive refinement

nonextensive information theoretic kernels on measures positive definite kernels on probability measures have been recently applied to classification problems involving text images and other types of structured data some of these kernels are related to classic information theoretic quantities such as shannon s mutual information and the jensen shannon js divergence meanwhile there have been recent advances in nonextensive generalizations of shannon s information theory this paper bridges these two trends by introducing nonextensive information theoretic kernels on probability measures based on new js type divergences these new divergences result from extending the the two building blocks of the classical js divergence convexity and shannon s entropy the notion of convexity is extended to the wider concept of q convexity for which we prove a jensen q inequality based on this inequality we introduce jensen tsallis jt q differences a nonextensive generalization of the js divergence and define a k th order jt q difference between stochastic processes we then define a new family of nonextensive mutual information kernels which allow weights to be assigned to their arguments and which includes the boolean js and linear kernels as particular cases nonextensive string kernels are also defined that generalize the p spectrum kernel we illustrate the performance of these kernels on text categorization tasks in which documents are modeled both as bags of words and as sequences of characters

solving systems of fractional differential equations using differential transform method this paper presents approximate analytical solutions for systems of fractional differential equations using the differential transform method the fractional derivatives are described in the caputo sense the application of differential transform method developed for differential equations of integer order is extended to derive approximate analytical solutions of systems of fractional differential equations the solutions of our model equations are calculated in the form of convergent series with easily computable components some examples are solved as illustrations using symbolic computation the numerical results show that the approach is easy to implement and accurate when applied to systems of fractional differential equations the method introduces a promising tool for solving many linear and nonlinear fractional differential equations

covering numbers for support vector machines support vector sv machines are linear classifiers that use the maximum margin hyperplane in a feature space defined by a kernel function previously the only bounds on the generalization performance of sv machines within valiant s probably approximately correct framework took no account of the kernel used except in its effect on the margin and radius it has been shown that one can bound the relevant covering numbers using tools from functional analysis in this paper we show that the resulting bound can be greatly simplified the new bound involves the eigenvalues of the integral operator induced by the kernel it shows that the effective dimension depends on the rate of decay of these eigenvalues we present an explicit calculation of covering numbers for an sv machine using a gaussian kernel which is significantly better than that implied by previous results

finite element analysis of the vibration problem of a plate coupled with a fluid we consider the approximation of the vibration modes of an elastic plate in contact with a compressible fluid the plate is modelled by reissner mindlin equations while the fluid is described in terms of displacement variables this formulation leads to a symmetric eigenvalue problem reissner mindlin equations are discretized by a mixed method the equations for the fluid with raviart thomas elements and a non conforming coupling is used on the interface in order to prove that the method is locking free we consider a family of problems one for each thickness t 0 and introduce appropriate scalings for the physical parameters so that these problems attain a limit when t to 0 we prove that spurious eigenvalues do not arise with this discretization and we obtain optimal order error estimates for the eigenvalues and eigenvectors valid uniformly on the thickness parameter t finally we present numerical results confirming the good performance of the method

new ideas for proving convergence of decomposition methods in this paper we give new formulae which calculate easily the adomian s polynomials used in decomposition methods then the proof of convergence of the adomian s technique becomes almost obvious by using a weak hypothesis on the nonlinear operator of the functional equation

accurate pressure post process of a finite element method for elastoacoustics this paper deals with a post process to obtain a more accurate approximation of the fluid pressure from a finite element computation of the vibration modes of a fluid structure coupled system the underlying finite element method based on a displacement formulation for both media consists of using raviart thomas elements for the fluid combined with standard continuous elements for the solid an easy to compute post process of the pressure is derived the relation between this post process and an alternative finite element approximation of the problem based on discretizing the fluid pressure by enriched crouzeix raviart elements is studied higher order estimates for the l2 norm of the post processed pressure are proved by exploiting this relation as a by product higher order l2 estimates for the solid displacements obtained with the original method are also proved

eigenfunctions of the edge based laplacian on a graph abstract in this paper we analyze the eigenfunctions of the edge based laplacian on a graph and the relationship of these functions to random walks on the graph we commence by discussing the set of eigenfunctions supported at the vertices and demonstrate the relationship of these eigenfunctions to the classical random walk on the graph then from an analysis of functions supported only on the interior of edges we develop a method for explicitly calculating the edge interior eigenfunctions of the edge based laplacian this reveals a connection between the edge based laplacian and the adjacency matrix of backtrackless random walk on the graph the edge based eigenfunctions therefore correspond to some eigenfunctions of the normalized hashimoto matrix

a new modification of the adomian decomposition method for linear and nonlinear operators in this paper we present an efficient modification of the adomian decomposition method that will facilitate the calculations we then conduct a comparative study between the new modification and the modified decomposition method the study is conducted through illustrative examples the new modification introduces a promising tool for many linear and nonlinear models

recent advances in graph based pattern recognition with applications in document analysis graphs are a powerful and popular representation formalism in pattern recognition particularly in the field of document analysis they have found widespread application from the formal point of view however graphs are quite limited in the sense that the majority of mathematical operations needed to build common algorithms such as classifiers or clustering schemes are not defined consequently we observe a severe lack of algorithmic procedures that can directly be applied to graphs there exists recent work however aimed at overcoming these limitations the present paper first provides a review of the use of graph representations in document analysis then we discuss a number of novel approaches suitable for making tools from statistical pattern recognition available to graphs these novel approaches include graph kernels and graph embedding with several experiments using different data sets from the field of document analysis we show that the new methods have great potential to outperform traditional procedures applied to graph representations

analytical approximate solutions for nonlinear fractional differential equations we consider a class of nonlinear fractional differential equations fdes based on the caputo fractional derivative and by extending the application of the adomian decomposition method we derive an analytical solution in the form of a series with easily computable terms for linear equations the method gives exact solution and for non linear equations it provides an approximate solution with good accuracy several examples are discussed

on the performance of kernel classes we present sharp bounds on the localized rademacher averages of the unit ball in a reproducing kernel hilbert space in terms of the eigenvalues of the integral operator associated with the kernel we use this result to estimate the performance of the empirical minimization algorithm when the base class is the unit ball of the reproducing kernel hilbert space

graph characteristics from the heat kernel trace graph structures have been proved important in high level vision since they can be used to represent structural and relational arrangements of objects in a scene one of the problems that arises in the analysis of structural abstractions of objects is graph clustering in this paper we explore how permutation invariants computed from the trace of the heat kernel can be used to characterize graphs for the purposes of measuring similarity and clustering the heat kernel is the solution of the heat equation and is a compact representation of the path length distribution on a graph the trace of the heat kernel is given by the sum of the laplacian eigenvalues exponentiated with time we explore three different approaches to characterizing the heat kernel trace as a function of time our first characterization is based on the zeta function which from the mellin transform is the moment generating function of the heat kernel trace our second characterization is unary and is found by computing the derivative of the zeta function at the origin the third characterization is derived from the heat content i e the sum of the elements of the heat kernel we show how the heat content can be expanded as a power series in time and the coefficients of the series can be computed using the laplacian spectrum we explore the use of these characterizations as a means of representing graph structure for the purposes of clustering and compare them with the use of the laplacian spectrum experiments with the synthetic and real world databases reveal that each of the three proposed invariants is effective and outperforms the traditional laplacian spectrum moreover the heat content invariants appear to consistently give the best results in both synthetic sensitivity studies and on real world object recognition problems

a virtual element method for the acoustic vibration problem we analyze in this paper a virtual element approximation for the acoustic vibration problem we consider a variational formulation relying only on the fluid displacement and propose a discretization by means of mathrm h mathrm div h div virtual elements with vanishing rotor under standard assumptions on the meshes we show that the resulting scheme provides a correct approximation of the spectrum and prove optimal order error estimates with this end we prove approximation properties of the proposed virtual elements we also report some numerical tests supporting our theoretical results

vibration analysis of fluid solid systems using a finite element displacement formulation this report presents a finite element solution for the vibration interaction between an inviscid fluid and a solid the equation of motion governing the inviscid fluid is expressed in terms of the displacements reduced integration is used when computing the element stiffness matrix contributed by the fluid in addition a projection is used on the element mass matrix in order to remove the spurious modes which result from the use of reduced integration

a partially linear framework for massive heterogeneous data we consider a partially linear framework for modelling massive heterogeneous data the major goal is to extract common features across all sub populations while exploring heterogeneity of each sub population in particular we propose an aggregation type estimator for the commonality parameter that possesses the non asymptotic minimax optimal bound and asymptotic distribution as if there were no heterogeneity this oracular result holds when the number of sub populations does not grow too fast a plug in estimator for the heterogeneity parameter is further constructed and shown to possess the asymptotic distribution as if the commonality information were available we also test the heterogeneity among a large number of sub populations all the above results require to regularize each sub estimation as though it had the entire sample size our general theory applies to the divide and conquer approach that is often used to deal with massive homogeneous data a technical by product of this paper is the statistical inferences for the general kernel ridge regression thorough numerical results are also provided to back up our theory

kernels degrees of freedom and power properties of quadratic distance goodness of fit tests in this article we study the power properties of quadratic distance based goodness of fit tests first we introduce the concept of a root kernel and discuss the considerations that enter the selection of this kernel we derive an easy to use normal approximation to the power of quadratic distance goodness of fit tests and base the construction of a noncentrality index an analogue of the traditional noncentrality parameter on it this leads to a method akin to the neyman pearson lemma for constructing optimal kernels for specific alternatives we then introduce a midpower analysis as a device for choosing optimal degrees of freedom for a family of alternatives of interest finally we introduce a new diffusion kernel called the pearson normal kernel and study the extent to which the normal approximation to the power of tests based on this kernel is valid supplementary materials for this article are available online

a comparison between adomian decomposition method and taylor series method in the series solutions in this work we will compare the performance of the adomian decomposition method and the taylor series method applied to the solution of linear and nonlinear ordinary differential equations the comparison shows that the decomposition method is reliable efficient and easy to use from a computational viewpoint although the two methods provide the solution in an infinite series the decomposition method provides a fast convergent series of easily computable components and eliminates cumbersome computational work needed by taylor series method

application of legendre wavelets for solving fractional differential equations in this paper we develop a framework to obtain approximate numerical solutions to ordinary differential equations odes involving fractional order derivatives using legendre wavelet approximations the properties of legendre wavelets are first presented these properties are then utilized to reduce the fractional ordinary differential equations fodes to the solution of algebraic equations illustrative examples are included to demonstrate the validity and applicability of the technique results show that this technique can solve the linear and nonlinear fractional ordinary differential equations with negligible error compared to the exact solution

the order of convergence of eigenfrequencies in finite element approximations of fluid structure interaction problems in this paper we prove a double order for the convergence of eigenfrequencies in fluid structure vibration problems we improve estimates given recently for compressible and incompressible fluids to do this we extend classical results on finite element spectral approximation to nonconforming methods for noncompact operators

finite element approximation of spectral acoustic problems on curved domains this paper deals with the finite element approximation of the displacement formulation of the spectral acoustic problem on a curved non convex two dimensional domain convergence and error estimates are proved for raviart thomas elements on a discrete polygonal domain h inline equation in the framework of the abstract spectral approximation theory similar results have been previously proved only for polygonal domains numerical tests confirming the theoretical results are reported

numerical approach to differential equations of fractional order in this paper the variational iteration method and the adomian decomposition method are implemented to give approximate solutions for linear and nonlinear systems of differential equations of fractional order the two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of differential equations in these schemes the solution takes the form of a convergent series with easily computable components this paper presents a numerical comparison between the two methods for solving systems of fractional differential equations numerical results show that the two approaches are easy to implement and accurate when applied to differential equations of fractional order

a weighted numerical algorithm for two and three dimensional two sided space fractional wave equations a weighed numerical scheme that can effectively solve the fractional wave equation in a finite domain is provided we focus on detailedly discussing the two and three dimensional two sided space fractional wave equations with homogeneous boundary conditions a second order finite difference scheme is used to discretize the space fractional derivative and the time derivative additionally the numerical results confirm that the weighted numerical algorithm is convergent with second order accuracy in both space and time directions for the homogeneous boundary fractional problems

the exact solution of certain differential equations of fractional order by using operational calculus abstract in the present paper the authors first develop an operational calculus for the familiar riemann liouville fractional differential operator this operational calculus is then used here to solve a cauchy boundary value problem for a certain linear equation involving the riemann liouville fractional derivatives relevant connections are also indicated with the special cases of the equation which were solved earlier by using other methods

a new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations in this article the homotopy perturbation method proposed by j h he is adopted for solving linear fractional partial differential equations the fractional derivatives are described in the caputo sense comparison of the results obtained by the homotopy perturbation method with those obtained by the variational iteration method reveals that the present methods are very effective and convenient

finite element computation of the vibration modes of a fluid solid system abstract in this paper we solve the interior elastoacoustic problem by a finite element method which does not present spurious or circulation modes for nonzero frequencies it consists of classical triangular lagrangian elements for the solid and lowest order triangular raviart thomas elements for the fluid transmission conditions at the fluid solid interface are taken into account in a weak sense numerical results for some test examples are presented which show the good performance of the proposed methodology

local rademacher complexities we propose new bounds on the error of learning algorithms in terms of a data dependent notion of complexity the estimates we establish give optimal rates and are based on a local and empirical version of rademacher averages in the sense that the rademacher averages are computed from the data on a subset of functions with small empirical error we present some applications to classification and prediction with convex function classes and with kernel classes in particular

spatial and anatomical regularization of svm a general framework for neuroimaging data this paper presents a framework to introduce spatial and anatomical priors in svm for brain image analysis based on regularization operators a notion of proximity based on prior anatomical knowledge between the image points is defined by a graph e g brain connectivity graph or a metric e g fisher metric on statistical manifolds a regularization operator is then defined from the graph laplacian in the discrete case or from the laplace beltrami operator in the continuous case the regularization operator is then introduced into the svm which exponentially penalizes high frequency components with respect to the graph or to the metric and thus constrains the classification function to be smooth with respect to the prior it yields a new svm optimization problem whose kernel is a heat kernel on graphs or on manifolds we then present different types of priors and provide efficient computations of the gram matrix the proposed framework is finally applied to the classification of brain magnetic resonance mr images based on gray matter gm concentration maps and cortical thickness measures from 137 patients with alzheimer s disease ad and 162 elderly controls the results demonstrate that the proposed classifier generates less noisy and consequently more interpretable feature maps with high classification performances

a novel method for nonlinear fractional partial differential equations combination of dtm and generalized taylor s formula in this article a novel numerical method is proposed for nonlinear partial differential equations with space and time fractional derivatives this method is based on the two dimensional differential transform method dtm and generalized taylor s formula the fractional derivatives are considered in the caputo sense several illustrative examples are given to demonstrate the effectiveness of the present method results obtained using the scheme presented here agree well with the analytical solutions and the numerical results presented elsewhere results also show that the numerical scheme is very effective and convenient for solving nonlinear partial differential equations of fractional order

learning pullback hmm distances recent work in action recognition has exposed the limitations of methods which directly classify local features extracted from spatio temporal video volumes in opposition encoding the actions dynamics via generative dynamical models has a number of attractive features however using all purpose distances for their classification does not necessarily deliver good results we propose a general framework for learning distance functions for generative dynamical models given a training set of labelled videos the optimal distance function is selected among a family of pullback ones induced by a parametrised automorphism of the space of models we focus here on hidden markov models and their model space and design an appropriate automorphism there experimental results are presented which show how pullback learning greatly improves action recognition performances with respect to base distances