global smooth solutions and exponential stability for a nonlinear beam in this paper we consider a dynamical system with boundary input and output describing the bending vibrations of a quasi linear beam where the nonlinearity comes from hooke s law first we derive an existence result for short time solutions of the system of equations then we show that the structure of the boundary input and output forces the system to admit global solutions at least when the initial data and the boundary input are small in a certain sense in particular we prove that the norm of the state of the system decays exponentially if the input becomes zero after a finite time the input being zero can be understood as a boundary feedback

control of wave processes with distributed controls supported on a subregion it is proved that solutions of one dimensional wave equations satisfying general boundary conditions at the ends of a bounded interval i can be exactly controlled to any finite energy state by means of distributed controls which vanish outside of any fixed nonempty subinterval of i an example is given which shows that no such general analogous result can hold in higher dimensions in this case for a spherical region those states are characterized which can be exactly controlled to zero by means of controls supported in an annulus within the region it is found that very strong controllability obtains when the controls are distributed near the boundary but that only rather weak controllability is possible with controls supported in an interior annulus applications of these results to boundary control problems in annular regions are also discussed

boundary stabilization of linear elastodynamic systems it is proved that an elastic medium which occupies a bounded region in three dimensional euclidean space can be uniformly stabilized by means of traction forces applied on a portion of the boundary

global smooth solutions and stabilization of nonlinear elastodynamic systems with locally distributed dissipation we consider the existence of global solutions of the nonlinear elastodynamic system with a locally distributed damping in a bounded domain we assume that the energy function satisfies the strong ellipticity condition at the zero equilibrium the local dissipation is in the form a x u where the nonnegative function a x is only positive on a small portion of the domain we show the existence of global smooth solutions when initial data are small in particular we obtain the exponential decay of the energy which implies the exponential stabilization of the system by internal feedback

global existence and nonexistence for nonlinear wave equations with damping and source terms we consider an initial boundary value problem for a nonlinear wave equation in one space dimension the nonlinearity features the damping term u m 1 u t and a source term of the form u p 1 u with m p 1 we show that whenever m p then local weak solutions are global on the other hand we prove that whenever p m and the initial energy is negative then local weak solutions cannot be global regardless of the size of the initial data

global identifiability of linear structural equation models structural equation models are multivariate statistical models that are defined by specifying noisy functional relationships among random variables we consider the classical case of linear relationships and additive gaussian noise terms we give a necessary and sufficient condition for global identifiability of the model in terms of a mixed graph encoding the linear structural equations and the correlation structure of the error terms global identifiability is understood to mean injectivity of the parametrization of the model and is fundamental in particular for applicability of standard statistical methodology

impact of imputation of missing values on classification error for discrete data numerous industrial and research databases include missing values it is not uncommon to encounter databases that have up to a half of the entries missing making it very difficult to mine them using data analysis methods that can work only with complete data a common way of dealing with this problem is to impute fill in the missing values this paper evaluates how the choice of different imputation methods affects the performance of classifiers that are subsequently used with the imputed data the experiments here focus on discrete data this paper studies the effect of missing data imputation using five single imputation methods a mean method a hot deck method a nai ve bayes method and the latter two methods with a recently proposed imputation framework and one multiple imputation method a polytomous regression based method on classification accuracy for six popular classifiers ripper c4 5 k nearest neighbor support vector machine with polynomial and rbf kernels and nai ve bayes on 15 datasets this experimental study shows that imputation with the tested methods on average improves classification accuracy when compared to classification without imputation although the results show that there is no universally best imputation method nai ve bayes imputation is shown to give the best results for the ripper classifier for datasets with high amount i e 40 and 50 of missing data polytomous regression imputation is shown to be the best for support vector machine classifier with polynomial kernel and the application of the imputation framework is shown to be superior for the support vector machine with rbf kernel and k nearest neighbor the analysis of the quality of the imputation with respect to varying amounts of missing data i e between 5 and 50 shows that all imputation methods except for the mean imputation improve classification error for data with more than 10 of missing data finally some classifiers such as c4 5 and nai ve bayes were found to be missing data resistant i e they can produce accurate classification in the presence of missing data while other classifiers such as k nearest neighbor svms and ripper benefit from the imputation

graphical methods for efficient likelihood inference in gaussian covariance models in graphical modelling a bi directed graph encodes marginal independences among random variables that are identified with the vertices of the graph we show how to transform a bi directed graph into a maximal ancestral graph that i represents the same independence structure as the original bi directed graph and ii minimizes the number of arrowheads among all ancestral graphs satisfying i here the number of arrowheads of an ancestral graph is the number of directed edges plus twice the number of bi directed edges in gaussian models this construction can be used for more efficient iterative maximization of the likelihood function and to determine when maximum likelihood estimates are equal to empirical counterparts

mixed problem for some semi linear wave equation with a nonhomogeneous condition on considere le probleme aux valeurs limites et initiales suivant u tt u xx u t sign u t 0 x t 0 1 0 t u x 0 t g t u 1 t 0 u x 0 u 0 x u t x 0 u 1 x avec 0 1 avec u 0 h 1 0 1 u 1 dans l 2 0 1 et g t dans l 2 0 t un theoreme d existence globale et d unicite est demontre

markov equivalence for ancestral graphs ancestral graphs can encode conditional independence relations that arise in directed acyclic graph dag models with latent and selection variables however for any ancestral graph there may be several other graphs to which it is markov equivalent we state and prove conditions under which two maximal ancestral graphs are markov equivalent to each other thereby extending analogous results for dags given by other authors these conditions lead to an algorithm for determining markov equivalence that runs in time that is polynomial in the number of vertices in the graph

a convergence theorem for the fuzzy subspace clustering fsc algorithm we establish the convergence of the fuzzy subspace clustering fsc algorithm by applying zangwill s convergence theorem we show that the iteration sequence produced by the fsc algorithm terminates at a point in the solution set s or there is a subsequence converging to a point in s in addition we present experimental results that illustrate the convergence properties of the fsc algorithm in various scenarios

energy methods for quasilinear hyperbolic initial boundary value problems applications to elastodynamics the aim of this paper is to show how energy methods can be used to establish local in time existence of smooth solutions to certain initial boundary value problems for systems of quasilinear hyperbolic partial differential equations our particular objective is to treat the equations of nonlinear elastodynamics

global smooth solutions for the quasilinear wave equation with boundary dissipation abstract we consider the existence of global solutions of the quasilinear wave equation with a boundary dissipation structure of an input output in high dimensions when initial data and boundary inputs are near a given equilibrium of the system our main tool is the geometrical analysis the main interest is to study the effect of the boundary dissipation structure on solutions of the quasilinear system we show that the existence of global solutions depends not only on this dissipation structure but also on a riemannian metric given by the coefficients and the equilibrium of the system some geometrical conditions on this riemannian metric are presented to guarantee the existence of global solutions in particular we prove that the norm of the state of the system decays exponentially if the input stops after a finite time which implies the exponential stabilization of the system by boundary feedback

global smooth solutions of the quasi linear wave equation with internal velocity feedback we study the existence of global smooth solutions for the quasi linear wave equation by an internal local damping when initial data are close to a given equilibrium our interest is in studying the structure of the damping region which guarantees the existence of global solutions our results show that the structure of the damping region depends on the geometric properties of a riemannian metric based on the coefficients and the equilibrium of the system some geometrical conditions are presented to obtain the damping region

fuzzy weighted c ordered means clustering algorithm abstract in real life data sets some attributes may have lower importance or even may be completely noninformative the subspace clustering algorithms have been proposed to handle this the soft subspace algorithms are vulnerable to noise and outliers the paper presents a novel algorithm that handles both various importance of attributes and outliers the proposed fuzzy weighted c ordered mean fwcom clustering algorithm elaborates clusters in soft subspaces in each cluster each attribute is assigned a weight from interval 0 1 each attribute has its individual weight importance in each cluster the proposed algorithm applies the ordering technique to effectively reduce the influence of outliers and noise the paper is accompanied by numerical experiments

a clustering algorithm for fuzzy model identification the fuzzy model proposed by takagi and sugeno can represent highly nonlinear systems and is widely used for the representation of fuzzy rules in this paper the model is firstly modified to make its identification easier based on the fuzzy c partition space four criteria are proposed for optimization of the model parameters following that a clustering algorithm composed of fuzzy c linear functions clustering and like fuzzy c means clustering is developed for minimizing the four criteria an identification scheme for rule s premise and consequence parameters is deduced from the clustering algorithm in succession finally four examples are demonstrated to verify the effectiveness of the proposed algorithm

rough subspace neuro fuzzy system the missing values can be an important obstacle and challenging problem in data analysis the paper presents the neuro fuzzy system that handles incomplete data the system is complete it can extract the fuzzy rule base from both complete and incomplete data and can elaborate answers for complete and incomplete data the second major feature of the system is the assignment of weights to attributes in fuzzy rules the weights are assigned locally each fuzzy rule has its own weights for attributes this feature may improve the precision of answers elaborated by the system and may reveal relations between attributes in the data set the paper is accompanied by experimental results the results show that the subspace technique is advantageous in handling data set with missing values the results also reveal that for approximation of complete data it is better to apply techniques without subspace approach

boundary observability controllability and stabilization of linear elastodynamic systems in 1988 lions obtained observability and exact controllability results for linear homogeneous isotropic elastodynamic systems siam rev 30 1988 pp 1 68 applying some new identities we extend his theorems to nonisotropic systems in 1991 lagnese obtained uniform stabilizability results for two dimensional linear homogeneous isotropic systems by applying a somewhat artificial feedback nonlinear anal 16 1991 pp 35 54 then he asked whether analogous results hold for a natural and physically implementable boundary feedback using some new identities and applying a method introduced in 1987 by zuazua and the second author j math pures appl 69 1990 pp 33 54 we give an affirmative answer to this question in all dimensions and also for nonisotropic systems moreover we obtain good decay estimates finally applying a recent general method of uniform stabilization we construct boundary feedbacks leading to arbitrarily large energy decay rates

joint response graphs and separation induced by triangular systems summary we consider joint probability distributions generated recursively in terms of univariate conditional distributions satisfying conditional independence restrictions the independences are captured by missing edges in a directed graph a matrix form of such a graph called the generating edge matrix is triangular so the distributions that are generated over such graphs are called triangular systems we study consequences of triangular systems after grouping or reordering of the variables for analyses as chain graph models i e for alternative recursive factorizations of the given density using joint conditional distributions for this we introduce families of linear triangular equations which do not require assumptions of distributional form the strength of the associations that are implied by such linear families for chain graph models is derived the edge matrices of chain graphs that are implied by any triangular system are obtained by appropriately transforming the generating edge matrix it is shown how induced independences and dependences can be studied by graphs by edge matrix calculations and via the properties of densities some ways of using the results are illustrated

trek separation for gaussian graphical models gaussian graphical models are semi algebraic subsets of the cone of positive definite covariance matrices submatrices with low rank correspond to generalizations of conditional independence constraints on collections of random variables we give a precise graph theoretic characterization of when submatrices of the covariance matrix have small rank for a general class of mixed graphs that includes directed acyclic and undirected graphs as special cases our new trek separation criterion generalizes the familiar d separation criterion proofs are based on the trek rule the resulting matrix factorizations and classical theorems of algebraic combinatorics on the expansions of determinants of path polynomials

global existence and global nonexistence of solutions of the cauchy problem for a nonlinearly damped wave equation abstract in this paper we consider the long time behavior of solutions of the initial value problem for semilinear wave equations of the form formula

weak asymptotic decay via a relaxed invariance principle for a wave equation with nonlinear non monotone damping this paper considers the problem of asymptotic decay as t of solutions of the wave equation u tt u a x u t u t x a bounded open connected set in n n 1 with smooth boundary u 0 on the nonlinear function is not assumed to be globally lipschitz continuous 0 y 2 y n 1 0 y 1 y 1 y n 1 0 for all y n 1 is not assumed to be monotone in y 1 under additional restrictions on the kernel of conditions are given which imply that u u t converges to 0 0 weakly in h h 1 0 l 2 as t the work generalises earlier results of dafermos and haraux where strong decay in h as t was obtained in the case y 1 y n 1 q y 1 q monotone on

computing maximum likelihood estimates in recursive linear models with correlated errors in recursive linear models the multivariate normal joint distribution of all variables exhibits a dependence structure induced by a recursive or acyclic system of linear structural equations these linear models have a long tradition and appear in seemingly unrelated regressions structural equation modelling and approaches to causal inference they are also related to gaussian graphical models via a classical representation known as a path diagram despite the models long history a number of problems remain open in this paper we address the problem of computing maximum likelihood estimates in the subclass of bow free recursive linear models the term bow free refers to the condition that the errors for variables i and j be uncorrelated if variable i occurs in the structural equation for variable j we introduce a new algorithm termed residual iterative conditional fitting ricf that can be implemented using only least squares computations in contrast to existing algorithms ricf has clear convergence properties and yields exact maximum likelihood estimates after the first iteration whenever the mle is available in closed form

stabilization of trajectories for some weakly damped hyperbolic equations in this paper we study the phenomenon of stabilization of trajectories for a wave equation in a bounded open domain endowed with a weak dissipative mechanism by stabilization we mean that the self oscillations induced by the wave equation are damped out asymptotically and so we are left when time tends to infinity either with an equilibrium if the system is autonomous or with a forced oscillation if the system was submitted to an exterior periodic or almost periodic excitation the common point between the two situations is the extinction of selfoscillations in the presence of a weak damping and it is extremely satisfactory to discover that the difficulty is overcome in both cases by the use of one simple and elegant idea due to c m dafermos and which appeared in s precisely in the study of some partially damped hyperbolic systems the paper is divided in four sections in section 1 we recall the idea of s which will be used in sections 2 and 3 in section 2 we generalize the result of s proposition 2 31 in a framework which allows the existence of nontrivial equilibria a simple example from continuum mechanics is given in section 3 we apply the same device to establish total damping in the sense of s for a wave equation with single valued damping term and almost periodic forcing the result which we obtain is not covered by the general theorems of 7 or 8 a simple example is studied in section 4 we give two counterexamples which show that the result of section 3 cannot be extended to the framework of weak solutions or to other boundary conditions in each specific case a careful analysis will be necessary the notation which is used throughout the text is the standard one with 145 0022 0396185 3 00

locally distributed control and damping for the conservative systems in this paper we note the equivalence between exact controllability and exponential stabilizability for an abstract conservative system with bounded control this enables us to establish a frequency domain characterization for the exact controllability uniform exponential decay property of second order elastic systems such as the wave equation and the petrovsky equation with locally distributed control damping a piecewise multiplier method for frequency domain is introduced for several classes of pdes on regions which are not necessarily smooth we obtain a sufficient condition for the subregion on which the application of control damping will yield the exact controllability uniform exponential decay property this result provides useful information for designing the location of controllers dampers for distributed systems with a law of conservation

building sugeno type models using fuzzy discretization and orthogonal parameter estimation techniques this paper develops a new approach to building sugeno type models the essential idea is to separate the premise identification from the consequence identification while these are mutually related in the previous methods a fuzzy discretization technique is suggested to determine the premise of the model and an orthogonal estimator is provided to identify the consequence of the model the orthogonal estimator can provide information about the model structure or which terms to include in the model and final parameter estimates in a very simple and efficient manner the well known gas furnace data of box and jenkins is used to illustrate the proposed modeling approach and to compare its performance with other statistical and fuzzy modeling approaches it shows that the performance of the new approach compares favorably with these existing techniques

ancestral graph markov models this paper introduces a class of graphical independence models that is closed under marginalization and conditioning but that contains all dag independence models this class of graphs called maximal ancestral graphs has two attractive features there is at most one edge between each pair of vertices every missing edge corresponds to an independence relation these features lead to a simple parameterization of the corresponding set of distributions in the gaussian case

learning high dimensional directed acyclic graphs with latent and selection variables we consider the problem of learning causal information between random variables in directed acyclic graphs dags when allowing arbitrarily many latent and selection variables the fci fast causal inference algorithm has been explicitly designed to infer conditional independence and causal information in such settings however fci is computationally infeasible for large graphs we therefore propose the new rfci algorithm which is much faster than fci in some situations the output of rfci is slightly less informative in particular with respect to conditional independence information however we prove that any causal information in the output of rfci is correct in the asymptotic limit we also define a class of graphs on which the outputs of fci and rfci are identical we prove consistency of fci and rfci in sparse high dimensional settings and demonstrate in simulations that the estimation performances of the algorithms are very similar all software is implemented in the r package pcalg

stabilization of the elastodynamic equations with a degenerate locally distributed dissipation we consider the dynamic elasticity equations with a locally distributed damping in a bounded domain the local dissipation of the form a x yt involves coefficients a that vanish on a negligible portion of the subset where the damping is effective using multiplier techniques interpolation inequalities and a judicious application of holder inequality we prove sharp energy decay estimates the results obtained generalize and improve on earlier works by nakao and the author in the framework of the ordinary wave equation

stabilization of the wave equation with localized nonlinear damping abstract we prove some decay estimates of the energy of the wave equation in a bounded domain the damping is nonlinear and is effective only in a neighborhood of a suitable subset of the boundary the method of proof is direct and is based on the multipliers technique on some integral inequalities due to haraux and komornik and on a judicious idea of conrad and rao

on the causal interpretation of acyclic mixed graphs under multivariate normality abstract in multivariate statistics acyclic mixed graphs with directed and bidirected edges are widely used for compact representation of dependence structures that can arise in the presence of hidden i e latent or unobserved variables indeed under multivariate normality every mixed graph corresponds to a set of covariance matrices that contains as a full dimensional subset the covariance matrices associated with a causally interpretable acyclic digraph this digraph generally has some of its nodes corresponding to hidden variables we seek to clarify for which mixed graphs there exists an acyclic digraph whose hidden variable model coincides with the mixed graph model restricting to the tractable setting of chain graphs and multivariate normality we show that decomposability of the bidirected part of the chain graph is necessary and sufficient for equality between the mixed graph model and some hidden variable model given by an acyclic digraph

implications of sharp trace regularity results on boundary stabilization of the system of linear elasticity abstract uniform exponential decay of solution is established for the elastodynamic system of elasticity using boundary feedback control energy dissipation is introduced via linear velocity feedbacks acting through a portion of the boundary as traction forces two primary goals are achieved first these results are proven without the imposition of strong geometric assumptions on the controlled portion of the boundary thus extending earlier work which required that the domain be star shaped second the feedback is only a function of velocity as opposed to also containing the tangential derivative of the displacement resulting in a physically viable feedback proof is based on the multiplier method and relies critically on sharp trace estimates for the tangential derivative of the displacement on the boundary as well as on unique continuation results for the corresponding static system