modelling dependence within joint tail regions standard approaches for modelling dependence within joint tail regions are based on extreme value methods which assume max stability a particular form of joint tail dependence we develop joint tail models based on a broader class of dependence structure which provides a natural link between max stable models and weaker forms of dependence including independence and negative association this approach overcomes many of the problems that are encountered with standard methods and is the basis for a poisson process representation that generalizes existing bivariate results we apply the new techniques to simulated and environmental data and demonstrate the marked advantage that the new approach offers for joint tail extrapolation

is intractability of nonmonotonic reasoning a real drawback abstract several studies about computational complexity of nonmonotonic reasoning nmr showed that nonmonotonic inference is significantly harder than classical monotonic inference this contrasts with the general idea that nmr can be used to make knowledge representation and reasoning simpler not harder in this paper we show that to some extent nmr fulfills the representation goal in particular we prove that nonmonotonic formalisms such as circumscription and default logic allow for a much more compact and natural representation of propositional knowledge than propositional calculus proofs are based on a suitable definition of a compilable inference problem and on non uniform complexity classes some results about intractability of circumscription and default logic can therefore be interpreted as the price one has to pay for having such an extra compact representation on the other hand intractability of inference and compactness of representation are not equivalent notions we exhibit intractable nonmonotonic formalisms whose nonmonotonic assumptions are representable by few propositional formulae finally sometimes nmr really makes reasoning simpler we present prototypical scenarios where closed world reasoning and well founded semantics account for a faster complete and unsound approximation of classical reasoning

decay rates for inverses of band matrices spectral theory and classical approximation theory are used to give a new proof of the exponential decay of the entries of the inverse of band matrices the rate of decay of a 1 can be bounded in terms of the essential spectrum of aa for general a and in terms of the essential spectrum of a for positive definite a in the positive definite case the bound can be attained these results are used to establish the exponential decay for a class of generalized eigenvalue problems and to establish exponential decay for certain sparse but nonbanded matrices we also establish decay rates for certain generalized inverses

compiling propositional weighted bases in this paper we investigate the extent to which knowledge compilation can be used to improve model checking and inference from propositional weighted bases we first focus on the compilability issue for both problems deriving mainly non compilability results in the case preferences are subject to change then we present a general notion of c normal weighted base that is parametrized by a tractable class c for the clausal entailment problem we show how every weighted base can be turned compiled into a query equivalent c normal base whenever c is a complete class for propositional logic both negative and positive results are presented on the one hand complexity results are identified showing that the inference problem from a c normal weighted base is as difficult as in the general case when the prime implicates horn cover or renamable horn cover classes are targeted on the other hand we show that both the model checking and the clausal inference problem become tractable whenever dnnf normal bases are considered moreover we show that the set of all preferred models of a dnnf normal weighted base can be computed in time polynomial in the output size and as a consequence model checking is also tractable for such bases finally we sketch how our results can be used in model based diagnosis in order to compute the most likely diagnoses of a system

a general incomplete block matrix factorization method abstract a general method for incomplete factorization of m matrices in block matrix form is presented the method generalizes previous methods for pointwise incomplete factorization methods of varga 1960 of wo nicki 1973 and of meijerink and van der vorst 1977 as well as a method for tridiagonal block matrices also we present a new and more general result on the existence of so called modified incomplete factorizations which satisfy a generalized rowsum criterion

accuracy of preconditioned cg type methods for least squares problems abstract the conjugate gradient method with imgs an incomplete modified version of gram schmidt orthogonalization to obtain an incomplete orthogonal factorization preconditioner applied to the normal equations pcgls is often used as the basic iterative method to solve the linear least squares problems in this paper a detailed analysis is given for understanding the effect of rounding errors on imgs and determining the accuracy of computed solutions of pcgls with imgs for linear least squares problems in finite precision it is shown that for a consistent system the difference between the true residuals and the updated approximate residual vectors generated depends on the machine precision e on the maximum growth in norm of the iterates over their initial values the norm of the true solution and the condition number of r which is affected by the drop set in incomplete gram schmidt factorization similar results are obtained for the difference between the true and computed solution for inconsistent systems numerical tests are carried out to confirm the theoretical conclusions

on the rate of convergence of the preconditioned conjugate gradient method we derive new estimates for the rate of convergence of the conjugate gradient method by utilizing isolated eigenvalues of parts of the spectrum we present a new generalized version of an incomplete factorization method and compare the derived estimates of the number of iterations with the number actually found for some elliptic difference equations and for a similar problem with a model empirical distribution function

block incomplete factorization preconditioners for a symmetric block tridiagonal m matrix we propose new block incomplete factorization preconditioners for a symmetric block tridiagonal m matrix which can be computed in parallel and then theoretical properties for these block preconditioners are studied spectral properties of the transformed coefficient matrices with the block incomplete factorization preconditioners are also examined to see the convergence rate of the preconditioned cg pcg method lastly numerical results of the pcg using the block incomplete factorization preconditioners are compared with those of the pcg using a standard incomplete factorization preconditioner to see how effective the block incomplete factorization preconditioners are

a theory of diagnosis from first principles suppose one is given a description of a system together with an observation of the system s behaviour which conflicts with the way the system is meant to behave the diagnostic problem is to determine those components of the system which when assumed to be functioning abnormally will explain the discrepancy between the observed and correct system behaviour we propose a general theory for this problem the theory requires only that the system be described in a suitable logic moreover there are many such suitable logics e g first order temporal dynamic etc as a result the theory accommodates diagnostic reasoning in a wide variety of practical settings including digital and analogue circuits medicine and database updates the theory leads to an algorithm for computing all diagnoses and to various results concerning principles of measurement for discriminating among competing diagnoses finally the theory reveals close connections between diagnostic reasoning and nonmonotonic reasoning

on some versions of incomplete block matrix factorization iterative methods abstract various forms of preconditioning matrices for iterative acceleration methods are discussed the preconditioning is based on two versions of incomplete block matrix factorization

note about cardinality based circumscription abstract in a very interesting paper liberatore and schaerf showed how to express the leading proposals of belief revision using a circumscription in order to deal with one of the belief revision theories they had to introduce a new circumscription based on the cardinality instead of the classical set inclusion we give a few properties of this new circumscription in doing so we prove that in the finite case there is inter definability between ordinary circumscription and cardinality based circumscription we show why a technical result published in the initial paper cannot be true and we give a related result which is true instead where the respective roles of the varying or fixed propositions are reversed this result could help automatic computation we use the logical properties of circumscriptions and cardinality based circumscriptions in order to highlight the behavior of cardinality based circumscription and the importance of the fixed propositions this study allows a full description of the expressive power of cardinality based circumscription in the finite case and it provides some limitations in the infinite case

tail dependence measure for examining financial extreme co movements modeling and forecasting extreme co movements in financial market is important for conducting stress test in risk management asymptotic independence and asymptotic dependence behave drastically different in modeling such co movements for example the impact of extreme events is usually overestimated whenever asymptotic dependence is wrongly assumed on the other hand the impact is seriously underestimated whenever the data is misspecified as asymptotic independent therefore distinguishing between asymptotic independence dependence scenarios is very informative for any decision making and especially in risk management we investigate the properties of the limiting conditional kendall s tau which can be used to detect the presence of asymptotic independence dependence we also propose nonparametric estimation for this new measure and derive its asymptotic limit a simulation study shows good performances of the new measure and its combination with the coefficient of tail dependence proposed by ledford and tawn 1996 1997 finally applications to financial and insurance data are provided

reducing belief revision to circumscription and vice versa nonmonotonic formalisms and belief revision operators have been introduced as useful tools to describe and reason about evolving scenarios both approaches have been proven effective in a number of different situations however little is known about their relationship previous work by winslett has shown some correlations between a specific operator and circumscription in this paper we greatly extend winslett s work by establishing new relations between circumscription and a large number of belief revision operators this highlights similarities and differences between these formalisms furthermore these connections provide us with the possibility of importing results in one field into the other one

statistics for near independence in multivariate extreme values we propose a multivariate extreme value threshold model for joint tail estimation which overcomes the problems encountered with existing techniques when the variables are near independence we examine inference under the model and develop tests for independence of extremes of the marginal variables both when the thresholds are fixed and when they increase with the sample size motivated by results obtained from this model we give a new and widely applicable characterisation of dependence in the joint tail which includes existing models as special cases a new parameter which governs the form of dependence is of fundamental importance to this characterisation by estimating this parameter we develop a diagnostic test which assesses the applicability of bivariate extreme value joint tail models the methods are demonstrated through simulation and by analysing two previously published data sets

taking advantage of the potentialities of dynamically modified block incomplete factorizations recently modified block incomplete factorizations with dynamic diagonal perturbations have been introduced as preconditioning techniques to solve large linear systems and were successfully tested on isotropic and moderately anisotropic two dimensional partial differential equations pdes an analytic study is performed on the basis of improved versions of results published elsewhere displaying why dynamic methods should be preferred to standard block methods in particular the empirical observation that the optimal choice of the involved parameter does not significantly vary from one problem to another is theoretically confirmed it is also explained why in the case of strong anisotropy lack of attention when adding diagonal perturbations may result in very poor performance rules to surmount this inconvenience are discussed and tested on discretized two dimensional pdes

weighted approximations of tail copula processes with application to testing the bivariate extreme value condition consider n i i d random vectors on r 2 with unknown common distribution function f under a sharpening of the extreme value condition on f we derive a weighted ap proximation of the corresponding tail copula process then we construct a test to check whether the extreme value condition holds by comparing two estimators of the limiting extreme value dis tribution one obtained from the tail copula process and the other obtained by first estimating the spectral measure which is then used as a building block for the limiting extreme value distribu tion we derive the limiting distribution of the test statistic from the aforementioned weighted approximation this limiting distribution contains unknown functional parameters therefore we show that a version with estimated parameters converges weakly to the true limiting distribution based on this result the finite sample properties of our testing procedure are investigated through a simulation study a real data application is also presented

default reasoning from conditional knowledge bases complexity and tractable cases abstract conditional knowledge bases have been proposed as belief bases that include defeasible rules also called defaults of the form which informally read as generally if then such rules may have exceptions which can be handled in different ways a number of entailment semantics for conditional knowledge bases have been proposed in the literature however while the semantic properties and interrelationships of these formalisms are quite well understood about their computational properties only partial results are known so far in this paper we fill these gaps and first draw a precise picture of the complexity of default reasoning from conditional knowledge bases given a conditional knowledge base kb and a default does kb entail we classify the complexity of this problem for a number of well known approaches including goldszmidt et al s maximum entropy approach and geffner s conditional entailment where we consider the general propositional case as well as natural syntactic restrictions in particular to horn and literal horn conditional knowledge bases as we show the more sophisticated semantics for conditional knowledge bases are plagued with intractability in all these fragments we thus explore cases in which these semantics are tractable and find that most of them enjoy this property on feedback free horn conditional knowledge bases which constitute a new meaningful class of conditional knowledge bases furthermore we generalize previous tractability results from horn to q horn conditional knowledge bases which allow for a limited use of disjunction our results complement and extend previous results and contribute in refining the tractability intractability frontier of default reasoning from conditional knowledge bases they provide useful insight for developing efficient implementations

nonparametric estimation of global functionals and a measure of the explanatory power of covariates in regression in a nonparametric regression setting with multiple random predictor variables we give the asymptotic distributions of estimators of global integral functionals of the regression surface we apply the results to the problem of obtaining reliable estimators for the nonparametric coefficient of determination this coefficient which is also called pearson s correlation ratio gives the fraction of the total variability of a response that can be explained by a given set of covariates it can be used to construct measures of nonlinearity of regression and relative importance of subsets of regressors and to assess the validity of other model restrictions in addition to providing asymptotic results we propose several data based bandwidth selection rules and carry out a monte carlo simulation study of finite sample properties of these rules and associated estimators of explanatory power we also provide two real data examples

incomplete block matrix factorization preconditioning methods the ultimate answer abstract a considerable interest has been devoted to block matrix incomplete factorization preconditioning methods in recent time see 12 2 3 4 6 7 8 10 and 21 the purpose of this paper is to survey some of these results and to present new results showing how much more efficient and robust such methods can be as compared to other admittingly also efficient methods such as pointwise incomplete factorization preconditioning methods and multilevel methods with hierarchical basis functions both on scalar as well as on parallel or vectorizable computers

heuristics for planning with penalties and rewards formulated in logic and computed through circuits the automatic derivation of heuristic functions for guiding the search for plans is a fundamental technique in planning the type of heuristics that have been considered so far however deal only with simple planning models where costs are associated with actions but not with states in this work we address this limitation by formulating a more expressive planning model and a corresponding heuristic where preferences in the form of penalties and rewards are associated with fluents as well the heuristic that is a generalization of the well known delete relaxation heuristic is admissible informative but intractable exploiting a correspondence between heuristics and preferred models and a property of formulas compiled in d dnnf we show however that if a suitable relaxation of the domain expressed as the strong completion of a logic program with no time indices or horizon is compiled into d dnnf the heuristic can be computed for any search state in time that is linear in the size of the compiled representation this representation defines an evaluation network or circuit that maps states into heuristic values in linear time while this circuit may have exponential size in the worst case as for obdds this is not necessarily so we report empirical results discuss the application of the framework in settings where there are no goals but just preferences and illustrate the versatility of the account by developing a new heuristic that overcomes limitations of delete based relaxations through the use of valid but implicit plan constraints in particular for the traveling salesman problem the new heuristic captures the exact cost while the delete relaxation heuristic which is also exponential in the worst case captures only the minimum spanning tree lower bound

automated adaptive multilevel solver abstract this paper presents an automated adaptive multilevel solver for linear or linearized system of equations the multilevel aspect of the solver is aimed at securing an optimal rate of convergence while keeping the size of the coarsest problem sufficiently small to ensure that the direct portion of the solution does not dominate the total computational cost adaptivity in terms of a priori selection of the number of levels one or more and construction of the optimal multilevel preconditioner is the key to the robustness of the method the number of levels is selected on the basis of estimated conditioning sparsity of the factor and available memory the auxiliary coarse models if required are automatically constructed on the basis of spectral characteristics of individual aggregates groups of neighboring elements an obstacle test consisting of twenty industry and model problems was designed to i determine the optimal values of computational parameters and to ii compare the adaptive multilevel scheme with existing state of the art equation solvers including the multifrontal solver 17 with the mmd reordering scheme and the pcg solver with the nearly optimal modified incomplete cholesky factorization preconditioner

on approximate factorization methods for block matrices suitable for vector and parallel processors abstract some existence results for methods based on the approximate factorization of block matrices are proven these methods are based on recursive computations of diagonal block matrices and the approximation of their inverses to preserve sparsity we also discuss a recently proposed 1 inverse free factorization method and present some numerical tests for it

tree clustering for constraint networks research note abstract the paper offers a systematic way of regrouping constraints into hierarchical structures capable of supporting search without backtracking the method involves the formation and preprocessing of an acyclic database that permits a large variety of queries and local perturbations to be processed swiftly either by sequential backtrack free procedures or by distributed constraint propagation processes

analysis of incomplete matrix factorizations as multigrid smoothers for vector and parallel computers the cost of smoothing is usually a major expense in multigrid codes efficient vectorizable and parallelizable versions of incomplete blockmatrix factorization methods used as smoothers for multigrid methods are discussed in this paper the methods are particularly interesting for computers with parallel processors with pipelines because both multitasking with little overhead and vectorization can be achieved

on the eigenvalue distribution of a class of preconditioning methods a class of preconditioning methods depending on a relaxation parameter is presented for the solution of large linear systems of equationax b wherea is a symmetric positive definite matrix the methods are based on an incomplete factorization of the matrixa and include both pointwise and blockwise factorization we study the dependence of the rate of convergence of the preconditioned conjugate gradient method on the distribution of eigenvalues ofc 1a wherec is the preconditioning matrix we also show graphic representations of the eigenvalues and present numerical tests of the methods

semantical and computational aspects of horn approximations abstract selman and kautz proposed a method called horn approximation for speeding up inference in propositional knowledge bases their technique is based on the compilation of a propositional formula into a pair of horn formulae a horn greatest lower bound glb and a horn least upper bound lub in this paper we focus on glbs and address two questions that have been only marginally addressed so far 1 what is the semantics of the horn glbs 2 what is the exact complexity of finding them we obtain semantical as well as computational results the major semantical result is the set of minimal models of a propositional formula and the set of minimum models of its horn glbs are the same the major computational result is finding a horn glb of a propositional formula in cnf is np equivalent

the size of a revised knowledge base abstract in this paper we address a specific computational aspect of belief revision the size of the propositional formula obtained by means of the revision of a formula with a new one in particular we focus on the size of the smallest formula which is logically equivalent to the revised knowledge base the main result of this paper is that not all formalizations of belief revision are equal from this point of view for some of them we show that the revised knowledge base can be represented by a polynomial size formula we call these results compactability results on the other hand for other ones the revised knowledge base does not always admit a polynomial space representation unless the polynomial hierarchy collapses at a sufficiently low level non compactability results we also show that the time complexity of query answering for the revised knowledge base has definitely an impact on being able to represent the result of the revision compactly nevertheless formalisms with the same complexity may have different compactability properties we also study compactability properties for a weaker form of equivalence called query equivalence which allows to introduce new propositional symbols moreover we extend our analysis to the special case in which the new formula has constant size and to the case of sequences of revisions i e iterated belief revision a complete analysis along these four coordinates is shown

preprocessing of intractable problems some computationally hard problems e g deduction in logical knowledge bases are such that part of an instance is known well before the rest of it and remains the same for several subsequent instances of the problem in these cases it is useful to preprocess off line this known part so as to simplify the remaining on line problem in this paper we investigate such a technique in the context of intractable i e np hard problems recent results in the literature show that not all np hard problems behave in the same way for some of them preprocessing yields polynomial time on line simplified problems we call them compilable while for other ones their compilability implies some consequences that are considered unlikely our primary goal is to provide a sound methodology that can be used to either prove or disprove that a problem is compilable to this end we define new models of computation complexity classes and reductions we find complete problems for such classes completeness meaning they are the less likely to be compilable we also investigate preprocessing that does not yield polynomial time on line algorithms but generically decreases complexity this leads us to define hierarchies of compilability that are the analog of the polynomial hierarchy a detailed comparison of our framework to the idea of parameterized tractability shows the differences between the two approaches

guidelines for the usage of incomplete decompositions in solving sets of linear equations as they occur in practical problems abstract this paper presents incomplete decompositions for various types of matrices as they occur in the implicit discretisation of practical problems a review is given of methods for the usual five point discretisation of a self adjoint elliptic second order partial differential equation in two dimensions on a square the matrices which occur in this type of problem are symmetric m matrices of very regular structure the convergence behaviour of the different decompositions for this case is demonstrated by numerical experiments the paper also gives decompositions for the following type of matrices i symmetric m matrices of a different structure ii symmetric positive definite matrices iii non symmetric matrices

algorithmic bombardment for the iterative solution of linear systems a poly iterative approach many algorithms employing short recurrences have been developed for iteratively solving linear systems yet when the matrix is nonsymmetric or indefinite or both it is difficult to predict which method will perform best or indeed converge at all attempts have been made to classify the matrix properties for which a particular method will yield a satisfactory solution but luck still plays large role this report describes the implementation of a poly iterative solver here we apply three algorithms simultaneously to the system in the hope that at least one will converge to the solution while this approach has merit in a sequential computing environment it is even more valuable in a parallel environment by combining global communications the cost of three methods can be reduced to that of a single method

on compact representations of propositional circumscription we prove that unless the polynomial hierarchy collapses at the second level the size of a purely propositional representation of the circumscription circ t of a propositional formula t grows faster than any polynomial as the size of t increases we then analyze the significance of this result in the related field of closed world reasoning

on incomplete block factorization methods of generalized ssor type for h matrices abstract two types of modified incomplete block factorization methods are considered and the existence and convergence of the related splittings are established for h matrices this is done by studying in parallel the similar preconditioner for an m matrix a which satisfies a m a we show also for the m matrix case somewhat more general results for the type of preconditioners considered than previously found in the literature

the cluster index of regularly varying sequences with applications to limit theory for functions of multivariate markov chains we introduce the cluster index of a multivariate stationary sequence and characterize the index in terms of the spectral tail process this index plays a major role in limit theory for partial sums of sequences we illustrate the use of the cluster index by characterizing infinite variance stable limit distributions and precise large deviation results for sums of multivariate functions acting on a stationary markov chain under a drift condition

vectorizable preconditioners for elliptic difference equations in three space dimensions abstract until now research in vectorizable preconditioners has mainly focused on problems in two space dimensions employing all degrees of freedom we here present preconditioners for 3d matrices based on point line and plane factorizations both in vectorizable and for reasons of comparisons in recursive versions by a limit analysis and accompanying numerical tests of elliptic difference equations with anisotropy we find that methods based on line block factorizations are to be preferred in general among the vectorizable methods a line method where euler expansion of the factors of the pivot blocks is used is the most robust with respect to the problem parameters furthermore this method turns out to approach the best of the recursive methods in efficiency in terms of operation counts it has the added bonus of almost maximal vectorlength

preconditioning and two level multigrid methods of arbitrary degree of approximation let h be a mesh parameter corresponding to a finite element mesh for an elliptic problem we describe preconditioning methods for two level meshes which for most prob lems solved in practice behave as methods of optimal order in both storage and computa tional complexity namely per mesh point these numbers are bounded above by relatively small constants for all h ho where ho is small enough to cover all but excessively fine meshes we note that in practice multigrid methods are actually solved on a finite often even a fixed number of grid levels in which case also these methods are not asymptotically optimal as h 0 numerical tests indicate that the new methods are about as fast as the best implementations of multigrid methods applied on general problems variable coefficients general domains and boundary conditions for all but excessively fine meshes furthermore most of the latter methods have been implemented only for difference schemes of second order of accuracy whereas our methods are applicable to higher order approximations we claim that our scheme could be added fairly easily to many existing finite element codes 1 introduction consider the numerical solution of elliptic boundary value prob lems discretized by finite element methods we assume that the boundary is polygonal or consists of planes we note that in practical problems one often has a fine enough grid already after the definition of the boundary and the minimal number of vertices needed for a first coarse triangulation anyhow if not so in most cases one makes only a few steps of mesh refinement hence the power of multigrid methods their optimal order of computational complexity is most often not achieved fully because optimality requires a large number of recursively defined meshes for details see e g 4 and for further references see 7 hence one might as well consider other methods perhaps simpler and more effective on a fixed mesh but which are not asymptotically optimal here we shall describe a method which uses only a fixed mesh but for which one nevertheless achieves a low order of computational complexity and of seemingly optimal order except for from a practical viewpoint excessively small meshes to be more precise the computational cost per mesh point is bounded by clog n for n no where n is the number of mesh points no is large enough to cover most applications and c is small enough that the method is competitive with multigrid methods as is well known the latter need recursion and the usual smoothing followed by corrections of the solutions on the different mesh levels we claim that the new method is more suitable for implementation in existing finite element packages in fact most packages for the multigrid methods are only for second order difference methods