stability of peakons the peakons are peaked solitary wave solutions of a certain nonlinear dispersive equation that is a model in shallow water theory and the theory of hyperelastic rods we give a very simple proof of the orbital stability of the peakons in the h1 norm 2000 john wiley sons inc

fast dimension reduction for document classification based on imprecise spectrum analysis latent semantic indexing lsi with singular value decomposition svd is an effective dimension reduction method for document classification and other information analysis tasks the computational overhead of svd is known to be a bottleneck in dealing with large data sets and faster dimension reduction with competitive accuracy is desired in such a setting this paper presents imprecise spectrum analysis isa to carry out fast dimension reduction for document classification isa follows the one sided jacobi method for computing svd and simplifies its intensive orthogonality computation it uses a representative matrix composed of top k column vectors derived from the original feature vector space and reduces the dimension of a feature vector by computing its product with this representative matrix the paper provides an analysis to show the approximation error and the rationale behind such a dimension reduction method to further improve classification accuracy this paper also presents a feature selection method in building the initial feature matrix and augments the representative matrix by including centroid vectors our extensive experimental results show that isa is fast in handling large term document feature matrices while delivering better or competitive classification accuracy for the tested benchmarks compared to lsi with svd

sensitivity to evidence in gaussian bayesian networks using mutual information we introduce a methodology for sensitivity analysis of evidence variables in gaussian bayesian networks knowledge of the posterior probability distribution of the target variable in a bayesian network given a set of evidence is desirable however this evidence is not always determined in fact additional information might be requested to improve the solution in terms of reducing uncertainty in this study we develop a procedure based on shannon entropy and information theory measures that allows us to prioritize information according to its utility in yielding a better result some examples illustrate the concepts and methods introduced

the joint graphical lasso for inverse covariance estimation across multiple classes we consider the problem of estimating multiple related gaussian graphical models from a high dimensional data set with observations belonging to distinct classes we propose the joint graphical lasso which borrows strength across the classes in order to estimate multiple graphical models that share certain characteristics such as the locations or weights of nonzero edges our approach is based upon maximizing a penalized log likelihood we employ generalized fused lasso or group lasso penalties and implement a fast admm algorithm to solve the corresponding convex optimization problems the performance of the proposed method is illustrated through simulated and real data examples

dimensionality reduction for data of unknown cluster structure dimensionality reduction that preserves certain characteristics of data is needed for numerous reasons in this work we focus on data coming from a mixture of gaussian distributions and we propose a method that preserves the distinctness of the clustering structure although this structure is assumed to be yet unknown the rationale behind the method is the following i had one known the clusters classes within the data one could facilitate further analysis and reduce space dimensionality by projecting the data to the fisher s linear subspace which by definition best preserves the structure of the given classes ii under some reasonable assumptions this can be done albeit approximately without prior knowledge of the clusters classes in this paper we show how this approach works we present a method of preliminary data transformation that brings the directions of largest overall variability close to the directions of the best between class separation hence for the transformed data simple pca provides an approximation to the fisher s subspace we show that the transformation preserves the distinctness of the unknown structure in the data to a great extent

the quadrilateral mindlin plate elements using the spline interpolation bases abstract by the mindlin reissner plate theory the displacement and rotations x y are interpolated by independent functions for which only c 0 continuity condition is required the difficulty for constructing interpolation bases on the quadrilateral element without isoparametric transformation can be overcome by using the spline method in this paper two sets of spline interpolation bases are adopted to construct two quadrilateral spline mindlin plate elements qsmp1 and qsmp2 with 12 degrees of freedom the spline elements can be applied for both thick and thin plates and can converge for the very thin case numerical examples are discussed to show that the mindlin plate element combined with the spline interpolation bases can possess good accuracy

multiple graph regularized graph transduction via greedy gradient max cut abstract graph transduction methods have been widely adopted for label prediction under semi supervised settings to alleviate the relevant sensitivity to initial labels and graph construction processes recent studies have been aiming at developing robust graph transduction techniques in particular the graph transduction method via greedy gradient max cut ggmc that minimizes a cost function over a continuous classification function and a binary label variable has been successfully applied to a wide range of applications however this method predominately relies on the choice of a high quality single graph representation often leading to unstable performance due to selection bias to tackle this major drawback we leverage an ensemble learning framework into the ggmc method for exploiting the advantage of constructing and combining multiple graphs as opposed to performing constrained max cut on a single graph the proposed multiple graph greedy gradient max cut method mg ggmc simultaneously solves the label prediction and the true graph estimation problems specifically the true graph is approximated by a linear combination of a set of constructed graphs the coefficients of the linear combination are learned automatically by alternately minimizing a unified objective function in an iterative manner comparison studies with representative methods across various real world benchmarks conspicuously demonstrate the efficaciousness and the superiority of the proposed algorithm in standard evaluation metrics

nonparametric detection of signals by information theoretic criteria performance analysis and an improved estimator determining the number of sources from observed data is a fundamental problem in many scientific fields in this paper we consider the nonparametric setting and focus on the detection performance of two popular estimators based on information theoretic criteria the akaike information criterion aic and minimum description length mdl we present three contributions on this subject first we derive a new expression for the detection performance of the mdl estimator which exhibits a much closer fit to simulations in comparison to previous formulas second we present a random matrix theory viewpoint of the performance of the aic estimator including approximate analytical formulas for its overestimation probability finally we show that a small increase in the penalty term of aic leads to an estimator with a very good detection performance and a negligible overestimation probability

asymptotic geometry of multiple hypothesis testing we present a simple geometrical interpretation for the solution to the multiple hypothesis testing problem in the asymptotic limit under this interpretation the optimal decision rule is a nearest neighbor classifier on the probability simplex

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

simple and efficient nonparametric method for estimating the number of signals without eigendecomposition inspired by the computational simplicity and numerical stability of qr decomposition a nonparametric method for estimating the number of signals without eigendecomposition mense is proposed for the coherent narrowband signals impinging on a uniform linear array ula by exploiting the array geometry and its shift invariance property to decorrelate the coherency of signals through subarray averaging the number of signals is revealed in the rank of the qr upper trapezoidal factor of the autoproduct of a combined hankel matrix formed from the cross correlations between some sensor data since the infection of additive noise is defused signal detection capability is improved a new detection criterion is then formulated in terms of the row elements of the qr upper triangular factor when finite array data are available and the number of signals is determined as a value of the running index for which this ratio criterion is maximized where the qr decomposition with column pivoting is also used to improve detection performance the statistical analysis clarifies that the mense detection criterion is asymptotically consistent furthermore the proposed mense algorithm is robust against the array uncertainties including sensor gain and phase errors and mutual coupling and against the deviations from the spatial homogeneity of noise model the effectiveness of the mense is verified through numerical examples and the simulation results show that the mense is superior in detecting closely spaced signals with a small number of snapshots and or at relatively low signal to noise ratio snr

information theoretic limits of selecting binary graphical models in high dimensions the problem of graphical model selection is to estimate the graph structure of a markov random field given samples from it we analyze the information theoretic limitations of the problem of graph selection for binary markov random fields under high dimensional scaling in which the graph size and the number of edges k and or the maximal node degree d are allowed to increase to infinity as a function of the sample size n for pair wise binary markov random fields we derive both necessary and sufficient conditions for correct graph selection over the class gp k of graphs on vertices with at most k edges and over the class gp d of graphs on p vertices with maximum degree at most d for the class gp k we establish the existence of constants c and c such that if n c k2 log p similarly for the class gp d we exhibit constants c and c such that for n c d3 log p

linked interpolation for reissner mindlin plate elements part i a simple quadrilateral in most plate elements using the reissner mindlin assumptions the interpolations used for the lateral displacements w and the rotation involve the independent representation of each variable by its nodal values usually with identical interpolations to ensure a higher order of expansion for displacement w its representation is linked in the present paper with both sets of nodal variables conditions necessary for the use of such expansions are established here and the paper shows the development of a linear quadrilateral element q4bl whose performance and robustness are good although it possesses one singularity if only three degrees of freedom are prescribed in part ii we apply the identical formulation to develop a triangular element t3bl which performs equally well and is fully robust

global existence of solution to the camassa holm equation abstract in this paper we prove the result of global existence of solution to camassa holm equation under the assumption that v 0 u 0 u 0 has unique zero point and that v 0 is negative at in this situation v 0 clearly changes sign thus our result completes the picture described in ann scuola norm sup pisa cl sci 4 xxvi 1998 303 where the global existence of solutions is shown under the assumption that v 0 does not change sign we also give the sufficient and necessary condition of global existence of the solution when v 0 is odd with unique zero point

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

joint estimation of multiple graphical models gaussian graphical models explore dependence relationships between random variables through the estimation of the corresponding inverse covariance matrices in this paper we develop an estimator for such models appropriate for data from several graphical models that share the same variables and some of the dependence structure in this setting estimating a single graphical model would mask the underlying heterogeneity while estimating separate models for each category does not take advantage of the common structure we propose a method that jointly estimates the graphical models corresponding to the different categories present in the data aiming to preserve the common structure while allowing for differences between the categories this is achieved through a hierarchical penalty that targets the removal of common zeros in the inverse covariance matrices across categories we establish the asymptotic consistency and sparsity of the proposed estimator in the high dimensional case and illustrate its performance on a number of simulated networks an application to learning semantic connections between terms from webpages collected from computer science departments is included

detection tests for array processing in unknown correlated noise fields this paper introduces two eigenvalue based rules for estimating the number of signals impinging on an array of sensors along with a spatially correlated noise field the first rule called s is derived under the assumption that the noise spatial covariance is block diagonal or banded the assumption underlying the second detection rule named t is that the temporal correlation of the noise has a shorter length than that of the signals in both cases a matrix is built from the array output data covariances the smallest eigenvalue of which is equal to zero under the hypothesis that the source number is overestimated the sample distribution of the aforementioned smallest eigenvalue is derived and used to formulate the detection rules s and t both these rules are computationally quite simple additionally they can be used with a noncalibrated array the paper includes numerical examples that lend empirical support to the theoretical findings and illustrate the kind of performance that can be achieved by using the s and t detection rules

maximum likelihood discriminant analysis on the plane using a markovian model of spatial context abstract a method is presented for utilising spatial information in performing discriminant analysis on multivariate data at each point on a regular lattice as for example with landsat the spatial information is modelled as a particularly simple markov random field the discriminant analysis is based on the maximum likelihood method the results are compared with alternatives by monte carlo simulation and seem to be encouraging

local well posedness of a new integrable equation in this article we focus on the local in time well posedness of the cauchy problem for a new integrable equation we proved the local in time existence and uniqueness of the entropy solutions by using the method of the vanishing viscosity and l1 contraction property

a large deviation analysis of the maximum likelihood learning of markov tree structures the problem of maximum likelihood ml estimation of discrete tree structured distributions is considered chow and liu established that ml estimation reduces to the construction of a maximum weight spanning tree using the empirical mutual information quantities as the edge weights using the theory of large deviations we analyze the exponent associated with the error probability of the event that the ml estimate of the markov tree structure differs from the true tree structure given a set of independently drawn samples by exploiting the fact that the output of ml estimation is a tree we establish that the error exponent is equal to the exponential rate of decay of a single dominant crossover event we prove that in this dominant crossover event a non neighbor node pair replaces a true edge of the distribution that is along the path of edges in the true tree graph connecting the nodes in the non neighbor pair using ideas from euclidean information theory we then analyze the scenario of ml estimation in the very noisy learning regime and show that the error exponent can be approximated as a ratio which is interpreted as the signal to noise ratio snr for learning tree distributions we show via numerical experiments that in this regime our snr approximation is accurate

learning gaussian tree models analysis of error exponents and extremal structures the problem of learning tree structured gaussian graphical models from independent and identically distributed i i d samples is considered the influence of the tree structure and the parameters of the gaussian distribution on the learning rate as the number of samples increases is discussed specifically the error exponent corresponding to the event that the estimated tree structure differs from the actual unknown tree structure of the distribution is analyzed finding the error exponent reduces to a least squares problem in the very noisy learning regime in this regime it is shown that the extremal tree structure that minimizes the error exponent is the star for any fixed set of correlation coefficients on the edges of the tree if the magnitudes of all the correlation coefficients are less than 0 63 it is also shown that the tree structure that maximizes the error exponent is the markov chain in other words the star and the chain graphs represent the hardest and the easiest structures to learn in the class of tree structured gaussian graphical models this result can also be intuitively explained by correlation decay pairs of nodes which are far apart in terms of graph distance are unlikely to be mistaken as edges by the maximum likelihood estimator in the asymptotic regime

effects of element distortions on the performance of isoparametric elements we discuss the effects of element distortions on the performance of displacement based isoparametric quadrilateral finite elements suitable example problems for both the lagrangian and the serendipity types of elements are used to show numerically the effects of element distortions the effects of angular and curved edge distortions are evaluated analytically in terms of the abilities of the elements to represent exactly various polynomial displacement fields we then solve a plane stress problem adaptively to demonstrate the effect of element distortions on the accuracy of the stress distribution the conclusion is that the lagrangian elements are not affected by angular distortions and are therefore the more reliable elements for general use

on the weak solutions to a shallow water equation we obtain the existence of global in time weak solutions to the cauchy problem for a one dimensional shallow water equation that is formally integrable and can be obtained by approximating directly the hamiltonian for euler s equation in the shallow water regime the solution is obtained as a limit of viscous approximation the key elements in our analysis are some new a priori one sided supernorm and space time higher norm estimates on the first order derivatives 2000 john wiley sons inc

analysis of field experiments by least squares smoothing summary assuming a smooth trend plus independent error model for the environmental effects in the yields of a field plot experiment least squares smoothing methods are developed to estimate both the treatment effects and the unknown trend treatment estimates are closely related to those resulting from a generalized least squares analysis in which the covariance structure for the environmental effects has a particular form however the main emphases are on the accuracy of treatment estimates under a fixed smooth trend plus error model and the exploratory power of the basic method to isolate trend effects of unknown form although the detailed development is for the one dimensional case generalizations of the smoothness concept and extensions to two dimensions are also discussed application of the basic method is illustrated on three data sets and the results compared with other analyses

a new 8 node quadrilateral spline finite element by using bivariate quadratic splines on triangulated quadrangulations or fvs triangulations we construct a new 8 node quadrilateral element which reproduces polynomials of degree 2 and possesses second order completeness in cartesian coordinates the computation of derivatives integrals and products of the element shape functions can be simplified greatly by using their bezier coefficients on each triangle cell some appropriate examples are employed to evaluate the performance of the proposed element the numerical results show that the new spline element is superior to the standard 8 node isoparametric element and is comparable to some other 8 node quadrilateral elements

chernoff information between gaussian trees abstract in this paper we deal with gaussian graphical classifiaction problem we aim to provide a systematic study of the relationship between chernoff information and topological as well as algebraic properties of the corresponding gaussian graphs for the underlying graphical testing problems we first show the relationship between chernoff information and generalized eigenvalues of the associated covariance matrices it is then proved that chernoff information between two gaussian trees sharing certain local subtree structures can be transformed into that of two smaller trees in this way we provide a sequence of equivalent gaussian tree pairs in terms of chernoff information under our proposed grafting operations bottleneck gaussian trees namely gaussian trees connected by one such operation can thus be simplified into two 3 node gaussian trees thereafter we provide a thorough study about how chernoff information changes when small differences are accumulated into bigger ones via concatenated grafting operations as well as partial ordering in the end we propose an optimal linear dimension reduction method based on generalized eigenvalues for the purpose of classification which is proved to achieve maximum chernoff information among all linear transformations

a four node plate bending element based on mindlin reissner plate theory and a mixed interpolation this communication discusses a 4 node plate bending element for linear elastic analysis which is obtained as a special case from a general nonlinear continuum mechanics based 4 node shell element formulation the formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate and shell element

on the dimensions of bivariate spline spaces and the stability of the dimensions in this paper the dimensions of bivariate spline spaces are studied using the smoothing cofactor conformality method based on the analysis on the conformality condition at one interior vertex the stability or singularity to the contrary of the dimensions of general spline spaces is discussed in detail by the aid of directed partition some new results on dimensions are obtained with the corresponding constraints depending on the degree the smoothness order of the spline spaces and the structure of the partition as well

a statistical model for positron emission tomography abstract positron emission tomography pet still in its research stages is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner much as in x ray transmission tomography and other modes of computerized tomography the quality of the reconstructed image in pet is very sensitive to the mathematical algorithm to be used for reconstruction in this article we tailor a mathematical model to the physics of positron emissions and we use the model to describe the basic image reconstruction problem of pet as a standard problem in statistical estimation from incomplete data we describe various estimation procedures such as the maximum likelihood ml method using the em algorithm the method of moments and the least squares method a computer simulation of a pet experiment is then used to demonstrate the ml and the least squares reconstructions the main purposes of this article are to report on what we believe is an

graphical and recursive models for contingency tables summary we discuss two classes of models for contingency tables graphical and recursive models both of which arise from restrictions that are expressible as conditional independencies of variable pairs the first of these is a subclass of hierarchical log linear models each of its models can be represented by an undirected graph in the second class each model corresponds to a particular kind of a directed graph instead and can be characterized by a nontrivial factorization of the joint distribution in terms of response variables we derive decomposable or multiplicative models as the intersecting class this result has useful consequences for exploratory types of analysis as well as for the model interpretation we can give an aid for detecting well fitting decomposable models in a transformation of the observed contingency table and each decomposable model may be interpreted with the help of an undirected or directed graph

application of the quadrilateral area co ordinate method a new element for mindlin reissner plate the quadrilateral area co ordinate method is used to formulate a new quadrilateral element for mindlin reissner plate bending problem firstly an independent shear field is assumed based on the locking free timoshenko s beam formulae secondly a fourth order deflection field is assumed by introducing some generalized conforming conditions thirdly the rotation field is determined by the strain displacement relations furthermore a hybrid post processing procedure is suggested to improve the stress internal force solutions following this procedure a new 4 node 12 dof quadrilateral element named ac mq4 is successfully constructed since all formulations are expressed by the area co ordinates element ac mq4 presents some different but beneficial characters when compared with other usual models numerical examples show the new element is free of shear locking insensitive to mesh distortion and possesses excellent accuracy in the analysis of both thick and thin plates it has also been demonstrated that the area co ordinate method the generalized conforming condition method and the hybrid post processing procedure are efficient tools for developing simple effective and reliable finite element models copyright 2005 john wiley sons ltd

mse based regularization approach to direction estimation of coherent narrowband signals using linear prediction this paper addresses the problem of directions of arrival doas estimation of coherent narrowband signals impinging on a uniform linear array ula when the number of signals is unknown by using an overdetermined linear prediction lp model with a subarray scheme the doas of coherent signals can be estimated from the zeros of the corresponding prediction polynomial although the corrected least squares cls technique can be used to improve the accuracy of the lp parameters estimated from the noisy array data the inversion of the resulting matrix in the cls estimation is ill conditioned and then the cls estimation becomes unstable to combat this numerical instability we introduce multiple regularization parameters into the cls estimation and show that determining the number of coherent signals is closely related to the truncation of the eigenvalues an analytical expression of the mean square error mse of the estimated lp parameters is derived and it is clarified that the number of signals can be determined by comparing the optimal regularization parameters with the corresponding eigenvalues an iterative regularization algorithm is developed for estimating directions without any a priori knowledge where the number of coherent signals and the noise variance are estimated from the noise corrupted received data simultaneously