remarks on the energy decay for nonlinear wave equations with nonlinear localized dissipative terms abstract we derive an energy decay estimate for solutions to the initial boundary value problem of a semilinear wave equation with a nonlinear localized dissipation to overcome a difficulty related to derivative loss mechanism we employ a loan method

reasoning from last conflict s in constraint programming constraint programming is a popular paradigm to deal with combinatorial problems in artificial intelligence backtracking algorithms applied to constraint networks are commonly used but suffer from thrashing i e the fact of repeatedly exploring similar subtrees during search an extensive literature has been devoted to prevent thrashing often classified into look ahead constraint propagation and search heuristics and look back intelligent backtracking and learning approaches in this paper we present an original look ahead approach that allows to guide backtrack search toward sources of conflicts and as a side effect to obtain a behavior similar to a backjumping technique the principle is the following after each conflict the last assigned variable is selected in priority so long as the constraint network cannot be made consistent this allows us to find following the current partial instantiation from the leaf to the root of the search tree the culprit decision that prevents the last variable from being assigned this way of reasoning can easily be grafted to many variations of backtracking algorithms and represents an original mechanism to reduce thrashing moreover we show that this approach can be generalized so as to collect a small set of incompatible variables that are together responsible for the last conflict experiments over a wide range of benchmarks demonstrate the effectiveness of this approach in both constraint satisfaction and automated artificial intelligence planning

handwritten numeral recognition using gradient and curvature of gray scale image abstract in this paper the authors study on the use of gradient and curvature of the gray scale character image to improve the accuracy of handwritten numeral recognition three procedures based on curvature coefficient bi quadratic interpolation and gradient vector interpolation are proposed for calculating the curvature of the equi gray scale curves of an input image then two procedures to compose a feature vector of the gradient and the curvature are described the efficiency of the feature vectors are tested by recognition experiments for the handwritten numeral database iptp cdrom1 and nist sd3 and sd7 the experimental results show the usefulness of the curvature feature and recognition rate of 99 49 and 98 25 which are one of the highest rates ever reported for these databases h kato et al technical report of ieice pru95 3 1995 p 17 r a wilkinson et al technical report nistir 4912 august 1992 j geist et al technical report nistir 5452 june 1994 are achieved respectively

regularized discriminant analysis abstract linear and quadratic discriminant analysis are considered in the small sample high dimensional setting alternatives to the usual maximum likelihood plug in estimates for the covariance matrices are proposed these alternatives are characterized by two parameters the values of which are customized to individual situations by jointly minimizing a sample based estimate of future misclassification risk computationally fast implementations are presented and the efficacy of the approach is examined through simulation studies and application to data these studies indicate that in many circumstances dramatic gains in classification accuracy can be achieved

modified quadratic discriminant functions and the application to chinese character recognition issues in the quadratic discriminant functions qdf are discussed and two types of modified quadratic disriminant functions mqdf1 mqdf2 which are less sensitive to the estimation error of the covariance matrices are proposed the mqdf1 is a function which employs a kind of a pseudo bayesian estimate of the covariance matrix instead of the maximum likelihood estimate ordinarily used in the qdf the mqdf2 is a variation of the mqdf1 to save the required computation time and storage two discriminant functions were applied to chinese character recognition to evaluate their effectiveness and remarkable improvement was observed in their performance

tractability preserving transformations of global cost functions graphical model processing is a central problem in artificial intelligence the optimization of the combined cost of a network of local cost functions federates a variety of famous problems including csp sat and max sat but also optimization in stochastic variants such as markov random fields and bayesian networks exact solving methods for these problems typically include branch and bound and local inference based bounds in this paper we are interested in understanding when and how dynamic programming based optimization can be used to efficiently enforce soft local consistencies on global cost functions defined as parameterized families of cost functions of unbounded arity enforcing local consistencies in cost function networks is performed by applying so called equivalence preserving transformations epts to the cost functions these epts may transform global cost functions and make them intractable to optimize we identify as tractable projection safe those global cost functions whose optimization is and remains tractable after applying the epts used for enforcing arc consistency we also provide new classes of cost functions that are tractable projection safe thanks to dynamic programming we show that dynamic programming can either be directly used inside filtering algorithms defining polynomially dag filterable cost functions or emulated by arc consistency filtering on a berge acyclic network of bounded arity cost functions defining berge acyclic network decomposable cost functions we give examples of such cost functions and we provide a systematic way to define decompositions from existing decomposable global constraints these two approaches to enforcing consistency in global cost functions are then embedded in a solver for extensive experiments that confirm the feasibility and efficiency of our proposal

covariance matrix estimation and classification with limited training data a new covariance matrix estimator useful for designing classifiers with limited training data is developed in experiments this estimator achieved higher classification accuracy than the sample covariance matrix and common covariance matrix estimates in about half of the experiments it achieved higher accuracy than regularized discriminant analysis but required much less computation

strong decay for wave equations with nonlinear nonmonotone damping thus the energy is nonincreasing and the term p represents damping here and always the ymbols i ii denote the norm on the sobolev space wk p o 1 the classical example p d u d a positive constant shows that under reasonable coercivity hypotheses concerning f any solution u u decays to zero exponentially with respect to the trong topology on the energy space hd o 1 x l o 1 this property is preserved even if tl d x with d 0 on a certain nonvoid subinterval i e 0 l see l 4 moreover the same is true if p d g u d as above and g is globally lipschitz and satisfies the growth condition g w w 2 const w2 wer 1 2 cf 3 in the case f 0 3 d x g ut g monotone the strong decay to zero follows from a variant of the lasalle invariance principle see 5 91 in some particular cases the speed of convergence is obtained lo

decay estimates for some semilinear damped hyperbolic problems let be a bounded open domain in rn g r r a non decreasing continuous function such that g 0 0 and h e lloc1 r l2 under suitable assumptions on g and h the rate of decay of the difference of two solutions is studied for some abstract evolution equations of the general form u lu g u h t x as t the results obtained by use of differential inequalities can be applied to the case of the semilinear wave equation u u delta u g text u t text h text in r times omega text u text 0 on r times partial omega in r u 0 onr for instance if g s c left s right p 1 s d left s right q 1 s with c d 0 and 1 p q n 2 q n 2 then if h in l infty r l 2 omega all solutions are bounded in the energy space for t 0 and if u v are two such solutions the energy norm of u t v t decays like t 1 p 1 as t

high accuracy handwritten chinese character recognition using lda based compound distances to improve the accuracy of handwritten chinese character recognition hccr we propose linear discriminant analysis lda based compound distances for discriminating similar characters the lda based method is an extension of previous compound mahalanobis function cmf which calculates a complementary distance on a one dimensional subspace discriminant vector for discriminating two classes and combines this complementary distance with a baseline quadratic classifier we use lda to estimate the discriminant vector for better discriminability and show that under restrictive assumptions the cmf is a special case of our lda based method further improvements can be obtained when the discriminant vector is estimated from higher dimensional feature spaces we evaluated the methods in experiments on the etl9b and casia databases using the modified quadratic discriminant function mqdf as baseline classifier the results demonstrate the superiority of lda based method over the cmf and the superiority of discriminant vector learning from high dimensional feature spaces compared to the mqdf the proposed method reduces the error rates by factors of over 26

solving weighted csp by maintaining arc consistency recently a general definition of arc consistency ac for soft constraint frameworks has been proposed by t schiex proc cp 2000 singapore 2000 pp 411 424 in this paper we specialize this definition to weighted csp and introduce two o ed3 enforcing algorithms then we refine the definition and introduce a stronger form of arc consistency ac along with two o n2d2 ed3 algorithms as in the csp case an important application of ac is to combine it with search we empirically demonstrate that a branch and bound algorithm that maintains either ac or ac is a state of the art general solver for weighted csp our experiments cover binary max csp and max sat problems

generalized quadratic discriminant analysis in linear discriminant analysis the assumption of equality of the dispersion matrices of different classes leads to a classification rule based on minimum mahalanobis distance from the class centres however without this assumption the resulting quadratic discriminant classifier involves in addition to the mahalanobis distances the ratio of the determinants of the dispersion matrices as a factor in fact it has been observed that for discriminating between populations with underlying elliptically symmetric distributions such classifiers also incorporate similar factors apart from the mahalanobis distances in this paper a nonparametric classification technique which generalizes discriminant analysis has been proposed the method of cross validation is used to make the technique adaptive to a given dataset an extensive simulation study is presented to illustrate the potential of the method finally through implementation on a number of real life data sets it has been demonstrated that the proposed generalized quadratic discriminant analysis gqda compares very favourably with other nonparametric methods and is computationally cost effective highlightsa nonparametric classification technique has been proposed it generalizes fisher s discriminant analysis cross validation is used to make the technique adaptive to given data found empirically to compare very favourably with other nonparametric methods computationally cost effective

handwritten numerical recognition based on multiple algorithms abstract in this paper the authors combine two algorithms for application to the recognition of unconstrained isolated handwritten numerals the first algorithm employs a modified quadratic discriminant function utilizing direction sensitive spatial features of the numeral image the second algorithm utilizes features derived from the profile of the character in a structural configuration to recognize the numerals while both algorithms yield very low error rates the authors combine the two algorithms in different ways to study the best polling strategy and realize very low error rates 0 2 or less and rejection rates below 4

reduction operations in fuzzy or valued constraint satisfaction in the constraint satisfaction problem csp knowledge about a relation on n variables is given in the form of constraints on subsets of the variables a solution to the csp is simply an instantiation of the n variables which satisfies all the constraints the fuzzy constraint satisfaction problem fcsp is a generalisation of the csp to the case in which the constraints are not categorical but represent preferences in the form of fuzzy sets the fcsp is then an optimisation problem in the space of all possible instantiations of the n variables it has potentially many more applications in real world problems than the csp when the aim is to maximise the value of the most violated constraint then the fcsp can be solved by solving a logarithmic number of csps fuzzy k consistency can even be established by an algorithm whose worst case complexity is identical to that of an optimal k consistency algorithm for csps when the operator used to aggregate constraint values is strictly monotonic as is the case in max csp for example the classic operation of arc consistency has to be completely redefined we show that an ordered version of arc consistency exists for all fcsps with a strictly monotonic aggregation operator and that in the case of max csp it can be established by an algorithm whose worst case complexity is identical to that of the optimal arc consistency algorithm for csps neighbourhood substitution in csps can be generalised to fuzzy neighbourhood substitution in fcsps whether the aggregation operator is strictly monotonic or idempotent we give an algorithm for applying fuzzy neighbourhood substitutions until convergence based on the corresponding algorithm for csps

the abstract cauchy problem for dissipative operators with respect to metric like functionals abstract this paper is devoted to a characterization of semigroups of lipschitz operators on a closed subset d of a banach space x and the abstract cauchy problem for an operator a in x satisfying the following condition there exists a proper lower semicontinuous functional from x into 0 such that the effective domain of is d a and such that lim n a x n a x in x for any x d a and any sequence x n in d a satisfying two conditions lim n x n x in x and lim sup n x n x the main result asserts that a semigroup of lipschitz operators on d can be generated by an operator a satisfying the above mentioned condition a dissipative condition with respect to a metric like functional and a subtangential condition the kirchhoff equations with acoustic boundary conditions are solved by the method based on the abstract result with the construction of suitable liapunov functionals and the use of a metric like functional on a suitable set

existence and decay of solutions of a viscoelastic equation with a nonlinear source abstract in a bounded domain we consider u tt u 0 t g t u d u u where 0 and g is a nonnegative and decaying function we prove a local existence theorem and show for certain initial data and suitable conditions on g and that this solution is global with energy which decays exponentially or polynomially depending on the rate of the decay of the relaxation function g

on the decay of solutions of some nonlinear dissipative wave equations in higher dimensions on etudie la propriete de decroissance des solutions des equations d onde dissipatives non lineaires de la forme 2 u t 2 u g u t f x t x t r avec les conditions u x o u 0 x u t x o u 1 x x et u x t 0 sur r ou est un domaine borne de r n avec une frontiere lisse et g v est une fonction du genre k v v k o o

affine transformation and 2d projection invariant k nn classification of handwritten characters via a new matching measure pattern recognition based on matching remains important because it is a fundamental technique it does not require a learning process and the result of matching provides intuitive and geometrical information wakahara et al proposed global affine transformation gat correlation matching which can compensate for affine transformations imposed on a pattern gat correlation matching with an acceleration method and a new matching measure called the nearest neighbor distance of equi gradient direction nndegd achieved high performance in experiments using the mnist database the gat matching measure was extended to a global projection transformation gpt matching measure to allow deformation by 2d projection transformations the purpose of this paper is threefold first we develop an acceleration method for gpt correlation matching second in order to improve recognition performance we apply the curvature of edges in strokes to the matching measure curvature is often used as a feature of characters however in this paper we use it as a weight in the nndegd third to investigate the performance of the proposed methods we apply them to image matching and recognition from the mnist and the iptp databases for k nearest neighbors k nn in the experiment with the mnist database the gpt correlation matching with the curvature weighted nndegd matching measure achieves the lowest error rate of 0 30 among k nn based methods highlightswe enhance k nn classification by affine and 2d projection invariant matchings we develop acceleration methods for those distortion tolerant matching techniques we propose a matching measure using similarity in direction and curvature of edges experiments using the mnist database show a very low error rate of 0 30 the source code used in the above mentioned experiments is uploaded

reduction of processing time for optimal and quadratic discriminant analyses a fast algorithm is presented for optimal discriminant analysis and quadratic discriminant analysis in this algorithm the discriminant function of an input feature vector for each category is calculated via a monotonically increasing sequence and when the sequence value exceeds a certain value then you can assert that the current category cannot be the classification result and omit the redundant calculation of the remaining terms for the category thus making the calculation faster applying this algorithm to the recognition experiment on handwritten characters we could reduce the processing time to 4 of the conventional simple method since both discriminant analyses assume the normal distribution of the features disnormality contained in real world data affects the accuracy of the two discriminant analyses we also compared the accuracy performances of the two discriminant analyses using real world data and artificial data

effects of sample size in classifier design the effect of finite sample size on parameter estimates and their subsequent use in a family of functions are discussed general and parameter specific expressions for the expected bias and variance of the functions are derived these expressions are then applied to the bhattacharyya distance and the analysis of the linear and quadratic classifiers providing insight into the relationship between the number of features and the number of training samples because of the functional form of the expressions an empirical approach is presented to enable asymptotic performance to be accurately estimated using a very small number of samples results were experimentally verified using artificial data in controlled cases and using real high dimensional data

periodic solution and decay for some nonlinear wave equations with sublinear dissipative terms on considere l existence d une solution periodique pour les equations d onde non lineaires a une dimension d espace de la forme u tt u xx x u t x u f x t sur i r u i 0 t r ou i est un intervalle sur r 0 et f x t une fonction periodique en t

discrimination with many variables abstract many statistical methods for discriminant analysis do not adapt well or easily to situations where the number of variables is large possibly even exceeding the number of cases in the training set we explore a variety of methods for providing robust identification of future samples in this situation we develop a range of flexible bayesian methods and primarily a new hierarchical covariance compromise method akin to regularized discriminant analysis although the methods are much more widely applicable the motivating problem was that of discriminating between groups of samples on the basis of their near infrared spectra here the ability of the bayesian methods to take account of continuity of the spectra may be beneficial the spectra may consist of absorbances or reflectances at as many as 1 000 wavelengths and yet there may be only tens or hundreds of training samples in which both sample spectrum and group identity are known such problems arise in the food and pharmaceutical industries

improvement of handwritten japanese character recognition using weighted direction code histogram several algorithms for preprocessing feature extraction pre classification and main classification are experimentally compared to improve the recognition accuracy of handwritten japanese character recognition the compared algorithms are three types of nonlinear normalization for the preprocessing the discriminant analysis and the principal component analysis for the feature extraction the minimum distance classifiers and the linear classifier for the high speed pre classification and modified bayes classifier and subspace method for the robust main classification the performance of the recognition algorithm is fully tested using the etl9b character database the recognition accuracy of 99 15 at the recognition speed of eight characters per second is achieved this accuracy is the best one ever reported for the database

energy decay of solutions to the cauchy problem for a nondissipative wave equation in this paper we consider energy decay for nondissipative wave equation in unbounded domain the usual energy is not decreasing we use an approach introduced by guesmia which leads to decay estimates known in the dissipative case when the integral inequalities method by komornik exact controllability and stabilization the multiplier method masson wiley paris 1994 cannot be applied due to the lack of dissipativity first we study the stability of a wave equation with a weak nonlinear dissipative term based on the equation u xu 2 x u t g u t h xu 0 in irn we consider the general case with a function h satisfying a smallness condition and we obtain decay of solutions under weak growth assumptions on the feedback function and without any control of the sign of the derivative of the energy related to the above equation in the second case we consider the case h u u we prove some precise decay estimates of equivalent energy

soft arc consistency revisited the valued constraint satisfaction problem vcsp is a generic optimization problem defined by a network of local cost functions defined over discrete variables it has applications in artificial intelligence operations research bioinformatics and has been used to tackle optimization problems in other graphical models including discrete markov random fields and bayesian networks the incremental lower bounds produced by local consistency filtering are used for pruning inside branch and bound search in this paper we extend the notion of arc consistency by allowing fractional weights and by allowing several arc consistency operations to be applied simultaneously over the rationals and allowing simultaneous operations we show that an optimal arc consistency closure can theoretically be determined in polynomial time by reduction to linear programming this defines optimal soft arc consistency osac to reach a more practical algorithm we show that the existence of a sequence of arc consistency operations which increases the lower bound can be detected by establishing arc consistency in a classical constraint satisfaction problem csp derived from the original cost function network this leads to a new soft arc consistency method called virtual arc consistency which produces improved lower bounds compared with previous techniques and which can solve submodular cost functions these algorithms have been implemented and evaluated on a variety of problems including two difficult frequency assignment problems which are solved to optimality for the first time our implementation is available in the open source toulbar2 platform

a nonlinear normalization method for handprinted kanji character recognition line density equalization abstract a nonlinear normalization method the line density equalization is proposed where a resampling is done so as to equate the product of a local line density and a variable sampling pitch consequently the line density in the space is homogenized the efficiency of utilization of the space is increased and a stable normalization is obtained for partially irregular shape variations the method was applied to handprinted kanji character recognition and its effectiveness has been demonstrated

global and periodic solutions for nonlinear wave equations with some localized nonlinear dissipation abstract we discuss the existence of global or periodic solutions to the nonlinear wave equation u tt u x u t x u f x t r r with the boundary condition u where is a bounded domain in rn x v is a function like x v a x g v with g v 0 and x u is a source term of power nonlinearity a x is assumed to be positive only in a neighborhood of a part of the boundary and the stability property is very delicate which makes the problem interesting

arc consistency for soft constraints the notion of arc consistency plays a central role in constraint satisfaction r dechter constraint processing morgan kaufmann san mateo ca 2003 it is known since the introduction of valued and semi ring constraint networks in 1995 that the notion of local consistency can be extended to constraint optimisation problems defined by soft constraint frameworks based on an idempotent cost combination operator this excludes non idempotent operators such as which define problems which are very important in practical applications such as max csp where the aim is to minimise the number of violated constraints in this paper we show that using a weak additional axiom satisfied by most existing soft constraints proposals it is possible to define a notion of soft arc consistency that extends the classical notion of arc consistency and this even in the case of non idempotent cost combination operators a polynomial time algorithm for enforcing this soft arc consistency exists and its space and time complexities are identical to that of enforcing arc consistency in csps when the cost combination operator is strictly monotonic for example max csp a directional version of arc consistency first introduced by m c cooper reduction operations in fuzzy or valued constraint satisfaction fuzzy sets and systems 134 3 2003 311 342 is potentially even stronger than the non directional version since it allows non local propagation of penalties we demonstrate the utility of directional arc consistency by showing that it not only solves soft constraint problems on trees but that it also implies a form of local optimality which we call arc irreducibility

existence of global classical solutions of the initial boundary value problem for some nonlinear wave equations in fact we shall assume a x u is strictly increasing in u and also impose a certain smallness condition on the initial data zq u and the forcing term f but it is weaker compared with earlier works see theorem 1 1 for a moment we assume further g x u u 3 0 for simplicity when n 1 the global existence of the smooth solutions for o l 0 2 is easily proved by a standard energy method cf strauss 121 nakao 7 when iv 2 we can also prove a similar result if b x o satisfies the conditions 8 x u du b 0

mini buckets a general scheme for bounded inference this article presents a class of approximation algorithms that extend the idea of bounded complexity inference inspired by successful constraint propagation algorithms to probabilistic inference and combinatorial optimization the idea is to bound the dimensionality of dependencies created by inference algorithms this yields a parameterized scheme called mini buckets that offers adjustable trade off between accuracy and efficiency the mini bucket approach to optimization problems such as finding the most probable explanation mpe in bayesian networks generates both an approximate solution and bounds on the solution quality we present empirical results demonstrating successful performance of the proposed approximation scheme for the mpe task both on randomly generated problems and on realistic domains such as medical diagnosis and probabilistic decoding

on the desirability of acyclic database schemes a class of database schemes called acychc was recently introduced it is shown that this class has a number of desirable properties in particular several desirable properties that have been studied by other researchers m very different terms are all shown to be eqmvalent to acydicity in addition several equivalent charactenzauons of the class m terms of graphs and hypergraphs are given and a smaple algorithm for determining acychclty is presented also given are several eqmvalent characterizations of those sets m of multivalued dependencies such that m is the set of murlvalued dependencies that are the consequences of a given join dependency several characterizations for a conflict free in the sense of lien set of muluvalued dependencies are provided

a new approach of stabilization of nondissipative distributed systems in this paper we propose a new approach to prove the nonlinear internal or boundary stabilization of certain nondissipative distributed systems the usual energy is not decreasing this approach leads to decay estimates known in the dissipative case when the integral inequalities method due to komornik exact controllability and stabilization the multiplier method masson paris john wiley chichester uk 1994 cannot be applied due to the lack of dissipativity first we study the stability of a semilinear wave equation with a nonlinear damping based on the equation u delta u h nabla u f u g u 0 we consider the general case with a function h satisfying a smallness condition and we obtain uniform decay of strong and weak solutions under weak growth assumptions on the feedback function and without any control of the sign of the derivative of the energy related with the above equation in the second part we consider the case h nabla u nabla phi cdot nabla u with phi in w 1 infty omega we prove some precise decay estimates exponential or polynomial of equivalent energy without any restriction on phi the same results will be proved in the case of boundary feedback finally we comment on some applications of our approach to certain nondissipative distributed systems some results of this paper were announced without proof in a guesmia c r acad sci paris ser i math 332 2001 pp 633 636

on solutions of the wave equation with a sublinear dissipative term the existence of periodic solution and a certain decay property for the nonlinear dissipative wave equation utt u ut f in r or r with the boundary condition u 0 are proved where is a bounded domain in rn and v is a sublinear function say v k0 v rv k0 0 0 r 1