regularity criteria for the three dimensional ericksen leslie system in homogeneous besov spaces in this paper we establish some regularity criteria involving homogeneous besov spaces for both the simplified and the general three dimensional ericksen leslie system this improves many previous results and can be viewed as the ultimate optimal regularity criterion in the besov space framework

redundancy in logic i cnf propositional formulae a knowledge base is redundant if it contains parts that can be inferred from the rest of it we study some problems related to the redundancy of a cnf formula in particular any cnf formula can be made irredundant by deleting some of its clauses what results is an irredundant equivalent subset we study the complexity of problems related to irredundant equivalent subsets verification checking existence of an irredundant equivalent subset with a given size checking necessary and possible presence of clauses in irredundant equivalent subsets and uniqueness we also consider the problem of redundancy with different definitions of equivalence

node and element resequencing using the laplacian of a finite element graph part i general concepts and algorithm a finite element graph feg is defined here as a nodal graph g a dual graph g or a communication graph g associated with a generic finite element mesh the laplacian matrix l g l g or l g used for the study of spectral properties of an feg is constructed from usual vertex and edge connectivities of a graph an automatic algorithm based on spectral properties of an feg g g or g is proposed to reorder the nodes and or elements of the associated finite element mesh the new algorithm is called spectral peg resequencing sfr this algorithm uses global information in the graph it does not depend on a pseudoperipheral vertex in the resequencing process and it does not use any kind of level structure of the graph moreover the sfr algorithm is of special advantage in computing environments with vector and parallel processing capabilities nodes or elements in the mesh can be reordered depending on the use of an adequate graph representation associated with the mesh if g is used then the nodes in the mesh are properly reordered for achieving profile and wavefront reduction of the finite element stiffness matrix if either g or g is used then the elements in the mesh are suitably reordered for a finite element frontai solver a unified approach involving fegs and finite element concepts is presented conclusions are inferred and possible extensions of this research are pointed out in part ii of this work 1 the computational implementation of the sfr algorithm is described and several numerical examples are presented the examples emphasize important theoretical numerical and practical aspects of the new resequencing method

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

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

factoring matrices with a tree structured sparsity pattern abstract let a be a matrix whose sparsity pattern is a tree with maximal degree d max we show that if the columns of a are ordered using minimum degree on a a then factoring a using a sparse lu with partial pivoting algorithm generates only o d max n fill requires only o d max n operations and is much more stable than lu with partial pivoting on a general matrix we also propose an even more efficient and just as stable algorithm called sibling dominant pivoting this algorithm is a strict partial pivoting algorithm that modifies the column preordering locally to minimize fill and work it leads to only o n work and fill more conventional column pre ordering methods that are based usually implicitly on the sparsity pattern of a a are not as efficient as the approaches that we propose in this paper

multiphysics simulation of flow induced vibrations and aeroelasticity on parallel computing platforms abstract this article describes the application of multiphysics simulation on parallel computing platforms to model aeroelastic instabilities and flow induced vibrations multiphysics simulation is based on a single computational framework for the modeling of multiple interacting physical phenomena within the multiphysics framework the finite element treatment of fluids is based on the galerkin least squares gls method with discontinuity capturing operators the arbitrary lagrangian eulerian ale method is utilized to account for deformable fluid domains the finite element treatment of solids and structures is based on a three field variational principle fully coupled interaction constraints are enforced using the augmented lagrangian method the multiphysics architecture lends itself naturally to high performance parallel computing several applications are presented the importance of capturing the nonlinear effects and accounting for mesh movement is highlighted and the scalability of the software is illustrated

a study of the factorization fill in for a parallel implementation of the finite element method in this paper we investigate the additional storage overhead needed for a parallel implementation of finite element applications in particular we compare the storage requirements for the factorization of the sparse matrices that would occur on a parallel processor vs a uniprocessor this variation in storage results from the factorization fill in we address the question of whether the storage overhead is so large for parallel implementations that it imposes severe limitations on the problem size in contrast to the problems executed sequentially on a uniprocessor the storage requirements for the parallel implementation are based upon a new ordering scheme the combination mesh based scheme this scheme uses a domain decomposition method which attempts to balance the processors loads and decreases the interprocessor communication the storage requirements for the sequential implementation is based upon the minimum degree algorithm the difference between the two storage requirements corresponds to the storage overhead attributed to the parallel scheme experiments were conducted on regular and irregular 2 d and 3 d problems the meshes were decomposed into 2 256 subdomains which can be executed on 2 256 processors respectively the total storage requirements or fill in for most of the 2 d problems were less than a factor of two increase over the sequential execution in contrast large 3 d problems had zero increase in storage or fill in over the sequential execution the fill in was less for the parallel execution than the sequential execution thus we conclude that the storage overhead attributed to the use of parallel processors will not impose severe constraints on the problem size further for large 3 d applications the combination mesh based algorithm does better than minimum degree for reducing the fill in

a generalization of collapsible cases of circumscription abstract circumscription is a second order formula expressing the minimality of the extension of a particular predicate or set of predicates it was fashioned to capture the concept of nonmonotonic logic of human beings in some instances circumscription is equivalent to a first order formula we show that the known cases are special instances of a more general case

imf an incomplete multifrontal lu factorization for element structured sparse linear systems we propose an incomplete multifrontal lu factorization imf preconditioner that extends supernodal multifrontal methods to incomplete factorizations it can be used as a preconditioner in a krylov subspace method to solve large scale sparse linear systems with an element structure e g those arising from a finite element discretization of a partial differential equation the fact that the element matrices are dense is exploited to increase the computational performance and the robustness of the factorization through efficient partial pivoting imf is compared with the multilevel arms2 the level of fill in ilu and the threshold based ilutp preconditioners our experiments indicate that imf is competitive with arms2 on saddle point problems arising in the solution of the steady state navier stokes equation experiments with element structured matrices arising from structural engineering applications found in the university of florida sparse matrix collection illustrate the robustness of imf final

improving the run time and quality of nested dissection ordering when performing sparse matrix factorization the ordering of matrix rows and columns has a dramatic impact on the factorization time this paper describes an approach to the reordering problem that produces significantly better orderings than prior methods the algorithm is a hybrid of nested dissection and minimum degree ordering and combines an assortment of different algorithmic advances new or improved algorithms are described for graph compression multilevel partitioning and separator improvement when these techniques are combined the resulting orderings average 39 better than minimum degree over a suite of test matrices while requiring roughly 2 7 times the run time of liu s multiple minimum degree

using an interior point method for the master problem in a decomposition approach abstract we address some of the issues that arise when an interior point method is used to handle the master problem in a decomposition approach the main points concem the efficient exploitation of the special structure of the master problem to reduce the cost of a single interior point iteration the particular structure is the presence of gub constraints and the natural partitioning of the constraint matrix into blocks built of cuts generated by different subproblems the method can be used in a fairly general case i e in any decomposition approach whenever the master is solved by an interior point method in which the normal equations are used to compute orthogonal projections computational results demonstrate its advantages for one particular decomposition approach analytic center cutting plane method accpm is applied to solve large scale nonlinear multicommodity network flow problems up to 5000 arcs and 10000 commodities

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

on the static interaction of fluid and gas loaded multi chamber systems in large deformation finite element analysis abstract completing previous studies d berry h yang formulation and experimental verification of a pneumatic finite element int j numer methods engrg 39 1996 1097 1114 j bonet r d wood j mahaney p heywood finite element analysis of air supported membrane structures comput methods appl mech engrg 190 2000 579 595 t rumpel effiziente diskretisierung von statischen fluid struktur problemen bei grosen deformationen ph d thesis institut fur mechanik der universitat karlsruhe th 2003 t rumpel k schweizerhof volume dependent pressure loading and its influence on the stability of structures int j numer methods engrg 56 2003 211 238 t rumpel k schweizerhof hydrostatic fluid loading in non linear finite element analysis int j numer methods engrg 59 2004 849 870 on the deformation dependence of gas or fluid loadings with the assumption of finite gas and fluid volumes the current contribution focuses on the influence of modifications of the size and shape of a finite structure filled with combinations of gas and incompressible or compressible heavy fluid in contrast to the previous contributions berry and yang 1996 bonet et al 2000 rumpel 2003 rumpel and schweizerhof 2003 rumpel and schweizerhof 2004 where different finite element formulations for some specific load cases were derived this derivation provides a general formulation of a multi chamber system filled with gas and additional compressible heavy fluid by introducing two stiffness parameters it is possible to reduce the formulation to the pure pneumatic or hydrostatic load cases described in earlier works further on it will be shown how to manage the modification of the load cases during the loading process the linearization of the corresponding virtual work expression necessary for a newton type solution algorithm leads to additional terms for the volume dependence bonet et al 2000 rumpel 2003 rumpel and schweizerhof 2003 and the expected fully symmetric stiffness matrix the discretization of the solid structures with finite elements leads to standard stiffness matrix forms for the structures plus the so called load stiffness matrices k schweizerhof e ramm displacement dependent pressure loads in non linear finite element analyses comput struct 18 1984 1099 1114 and several dyadic rank updates depending on the type of filling for each filled structure part assuming that loaded surface segments are identical with the element surfaces a further focus is on a specific solution scheme exploiting the dyadic rank update structure some numerical examples show the effectiveness of the approach and the necessity to take the corresponding terms in the variational expression and in the linearization into account

why finite element discretizations can be factored by triangular hierarchical matrices although the asymptotic complexity of direct methods for the solution of large sparse finite element systems arising from second order elliptic partial differential operators is far from being optimal these methods are often preferred over modern iterative methods this is mainly due to their robustness in this article it is shown that an approximate lu decomposition exists which can be computed in the algebra of hierarchical matrices with almost linear complexity and with the same robustness as the classical lu decomposition low precision approximations may be used for preconditioning iterative solvers as a byproduct we prove that schur complements of stiffness matrices can be approximated with almost linear complexity

preconditioning techniques for large linear systems a survey this article surveys preconditioning techniques for the iterative solution of large linear systems with a focus on algebraic methods suitable for general sparse matrices covered topics include progress in incomplete factorization methods sparse approximate inverses reorderings parallelization issues and block and multilevel extensions some of the challenges ahead are also discussed an extensive bibliography completes the paper

an evaluation of limited memory sparse linear solvers for thermo mechanical applications we consider the performance of sparse linear solvers for problems that arise from thermo mechanical applications such problems have been solved using sparse direct schemes that enable robust solution at the expense of memory requirements that grow non linearly with the dimension of the coefficient matrix in this paper we consider a class of preconditioned iterative solvers as a limited memory alternative to direct solution schemes however such preconditioned iterative solvers typically exhibit complex trade offs between reliability and performance we therefore characterize such trade offs for systems from thermo mechanical problems by considering several preconditioning schemes including multilevel methods and those based on sparse approximate inversion and incomplete matrix factorization we provide an analysis of computational costs and memory requirements for model thermo mechanical problems indicating that certain incomplete factorization schemes can achieve good performance we also provide empirical evaluations that corroborate our analysis and indicate the relative effectiveness of different solution schemes our results indicate that our drop threshold incomplete cholesky preconditioning is more robust efficient and flexible than other popular preconditioning schemes in addition we propose preconditioner reuse to amortize preconditioner construction cost over a sequence of linear systems that arise from non linear solutions in a plastic regime copyright 2007 john wiley sons ltd

propositional circumscription and extended closed world reasoning are p p 2 complete abstract circumscription and the closed world assumption with its variants are well known nonmonotonic techniques for reasoning with incomplete knowledge their complexity in the propositional case has been studied in detail for fragments of propositional logic one open problem is whether the deduction problem for arbitrary propositional theories under the extended closed world assumption or under circumscription is p 2 complete i e complete for a class of the second level of the polynomial hierarchy we answer this question by proving these problems p 2 complete and we show how this result applies to other variants of closed world reasoning

an algebraic multilevel parallelizable preconditioner for large scale cfd problems abstract an efficient parallelizable preconditioner for solving large scale cfd problems is presented it is adapted to coarse grain parallelism and can be used for both shared and distributed memory parallel computers the proposed preconditioner consists of two independent approximations of the system matrix the first one is a block diagonal fully parallelizable approximation of the given system the second matrix is coarser than the original one and is built using algebraic multi grid methods the preconditioner is used to compute the steady solution of the compressible navier stokes equations for subsonic laminar flows on shared memory computers for a moderate number of processors the coupled two level preconditioner is robust and has a large potential for parallelism interesting savings in computational time for parallel computations are obtained when comparing the two level preconditioner with the well known incomplete gaussian factorization

the effect of ordering on preconditioned gmres algorithm for solving the compressible navier stokes equations we investigate the effect of the ordering of the blocks of unknowns on the rate of convergence of a preconditioned non linear gmres algorithm for solving the navier stokes equations for compressible flows using finite element methods on unstructured grids the gmres algorithm is preconditioned by an incomplete ldu block factorization of the jacobian matrix associated with the non linear problem to solve we examine a wide range of ordering methods including minimum degree reverse cuthill mckee and snake and consider preconditionings without fill in we show empirically that there can be a significant difference in the number of iterations required by the preconditioned non linear gmres method and suggest a criterion for choosing a good ordering algorithm according to the problem to solve we also consider the effect of orderings when an incomplete factorization which allows some fill in is performed we consider the effect of automatically controlling the sparsity of the incomplete factorization through the level of fill in finally following the principal ideas of non linear gmres algorithm we suggest other inexact newton methods

differentiation of matrix functionals using triangular factorization in various applications it is necessary to differentiate a matrix functional w a x where a x is a matrix depending on a parameter vector x usually the functional itself can be readily computed from a triangular factorization of a x this paper develops several methods that also use the triangular factorization to efficiently evaluate the first and second derivatives of the functional both the full and sparse matrix situations are considered there are similarities between these methods and algorithmic differentiation however the methodology developed here is explicit leading to new algorithms it is shown how the methods apply to several applications where the functional is a log determinant including spline smoothing covariance selection and restricted maximum likelihood

the average parallel complexity of cholesky factorization abstract we analyze the average parallel complexity of the solution of large sparse positive definite linear systems more precisely using probabilistic techniques we study the cholesky factorization with the application of the minimum degree algorithm main results are the estimation of the evolution of sparsity during the factorization and a characterization of the elimination tree in terms of depth and number of leaves we also conjecture that the number of parallel steps needed to perform the factorization is linear with respect to the matrix size

some computational aspects of circumscription the effects of circumscribing first order formulas are explored from a computational standpoint first extending work of v lifschitz it is shown that the circumscription of any existential first order formula is equivalent to a first order formula after this it is established that a set of universal horn clauses has a first order circumscription if and only if it is bounded when considered as a logic program thus it is undecidable to tell whether such formulas have first order circumscription finally it is shown that there arefirst order formulas whode circumscription has a conp complete model checking problem

sequential and parallel triangulating algorithms for elimination game and new insights on minimum degree elimination game is a well known algorithm that simulates gaussian elimination of matrices on graphs and it computes a triangulation of the input graph the number of fill edges in the computed triangulation is highly dependent on the order in which elimination game processes the vertices and in general the produced triangulations are neither minimum nor minimal in order to obtain a triangulation which is close to minimum the minimum degree heuristic is widely used in practice but until now little was known on the theoretical mechanisms involved in this paper we show some interesting properties of elimination game in particular that it is able to compute a partial minimal triangulation of the input graph regardless of the order in which the vertices are processed this results in a new algorithm to compute minimal triangulations that are sandwiched between the input graph and the triangulation resulting from elimination game one of the strengths of the new approach is that it is easily parallelizable and thus we are able to present the first parallel algorithm to compute such sandwiched minimal triangulations in addition the insight that we gain through elimination game is used to partly explain the good behavior of the minimum degree algorithm we also give a new algorithm for producing minimal triangulations that is able to use the minimum degree idea to a wider extent

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

some computational aspects of a group theoretic finite element approach to the buckling and postbuckling analyses of plates and shells of revolution abstract progress in the application of group theoretic methods to the nonlinear bifurcation analysis of symmetric structures has provided new hope in understanding the global postbuckling behavior of symmetric thin shell structures however what is still lacking in the computational mechanics community is a general purpose fe code with a group theoretic capability designed to take optimal advantage of existing symmetry this paper addresses some of the important issues associated with developing such a code the long term goal being to provide structural analysts with new numerical tools for doing careful global analyses of imperfection sensitive structures which may eventually lead to more accurate predictions of the maximum load carrying capacity of thin imperfection sensitive shell structures

computing circumscriptive databases i theory and algorithms abstract though circumscription was introduced by mccarthy over a decade ago there has been relatively little work on algorithms for computing circumscriptive databases in this paper we develop algorithms to compute the preferred models of circumscriptive databases at compile time using mixed integer linear programming techniques two advantages of this bottom up approach are that it makes efficient re use of previous computations and it provides much faster run time performance some other advantages of using linear programming to automate deduction at compile time are that its re optimization facilities elegantly accommodate database updates and also that it leads to a completely declarative formulation in which ordering of rules and literals in rule bodies plays no real role finally we plan to use a standard relational database system as our run time environment this should yield relatively fast run time processing and provide a more expressive query language in which aggregates and the like can be expressed easily

a logic for default reasoning the need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations it is this property which leads to the non monotonicity of any logic of defaults in this paper we propose a logic for default reasoning we then specialize our treatment to a very large class of commonly occuring defaults for this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover finally we provide criteria under which the revision of derived beliefs must be effected

exploiting special structure in semidefinite programming a survey of theory and applications abstract semidefinite programming sdp may be seen as a generalization of linear programming lp in particular one may extend interior point algorithms for lp to sdp but it has proven much more difficult to exploit structure in the sdp data during computation we survey three types of special structures in sdp data 1 a common chordal sparsity pattern of all the data matrices this structure arises in applications in graph theory and may also be used to deal with more general sparsity patterns in a heuristic way 2 low rank of all the data matrices this structure is common in sdp relaxations of combinatorial optimization problems and sdp approximations of polynomial optimization problems 3 the situation where the data matrices are invariant under the action of a permutation group or more generally where the data matrices belong to a low dimensional matrix algebra such problems arise in truss topology optimization particle physics coding theory computational geometry and graph theory we will give an overview of existing techniques to exploit these structures in the data most of the paper will be devoted to the third situation since it has received the least attention in the literature so far

the critical sobolev inequalities in besov spaces and regularity criterion to some semi linear evolution equations we show the critical sobolev inequalities in the besov spaces with the logarithmic form such as brezis gallouet wainger and beale kato majda as an application of those inequalities the regularity problem under the critical condition to the navier stokes equations the euler equations in mathbb r n and the gradient flow to the harmonic map to the sphere are discussed namely the serrin ohyama type regularity criteria are improved in the terms of the besov spaces

autoepistemic logic autoepistemic logic is one of the principal modes of nonmonotonic reasoning it unifies several other modes of nonmonotonic reasoning and has important application in logic programming in the paper a theory of autoepistemic logic is developed this paper starts with a brief survey of some of the previously known results then the nature of nonmonotonicity is studied by investigating how membership of autoepistemic statements in autoepistemic theories depends on the underlying objective theory a notion similar to set theoretic forcing is introduced expansions of autoepistemic theories are also investigated expansions serve as sets of consequences of an autoepistemic theory and they can also be used to define semantics for logic programs with negation theories that have expansions are characterized and a normal form that allows the description of all expansions of a theory is introduced our results imply algorithms to determine whether a theory has a unique expansion sufficient conditions stratification that imply existence of a unique expansion are discussed the definition of stratified theories is extended and under some additional assumptions efficient algorithms for testing whether a theory is stratified are proposed the theorem characterizing expansions is applied to two classes of theories k1 theories and ae programs in each case simple hypergraph characterization of expansions of theories from each of these classes is given finally connections with stable model semantics for logic programs with negation is discussed in particular it is proven that the problem of existence of stable models is np complete authors abstract

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

some consequences of non uniform conditions on uniform classes we obtain some results of the form if certain complexity classes satisfy a non uniform condition then some unlikely consequences follow more precisely 1 1 if the non uniform polynomial time hierarchy collapses at level i 0 i e ipoly ipoly then the meyer stockmeyer hierarchy collapses at level i 2 i e i 2 i 2 this strengthens a generalization of a result of karp and lipton 1980 2 2 if co np is conjunctively reducible to a sparse set then p np this generalizes a theorem of fortune 1979 3 3 if np is conjunctively and disjunctively reducible to a sparse np complete set then p np this is a partial generalization of a result of mahaney 1980 conjuctive and disjunctive reducibility were introduced by ladner lynch and selman 1975 4 4 if co np is reducible to a sparse set then np co np reducibility was introduced 5 by adleman and manders 1977

subspace iteration randomization and singular value problems a classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank the truncated singular value decomposition svd is known to provide the best such approximation for any given fixed rank however the svd is also known to be very costly to compute among the different approaches in the literature for computing low rank approximations randomized algorithms have attracted researchers attention recently due to their surprising reliability and computational efficiency in different application areas typically such algorithms are shown to compute with very high probability low rank approximations that are within a constant factor from optimal and are known to perform even better in many practical situations in this paper we present a novel error analysis that considers randomized algorithms within the subspace iteration framework and show with very high probability that highly accurate low rank approximations as well as singular values ca

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

applications of circumscription to formalizing common sense knowledge we present a new and more symmetric version of the circumscription method of nonmonotonic reasoning first described in mccarthy 1980 and some applications to formalizing common sense knowledge the applications in this paper are mostly based on minimizing the abnormality of different aspects of various entities included are nonmonotonic treatments of is a hierarchies the unique names hypothesis and the frame problem the new circumscription may be called formula circumscription to distinguish it from the previously defined domain circumscription and predicate circumscription a still more general formalism called prioritized circumscription is briefly explored

fully dynamic algorithm for chordal graphs with o 1 query time and o n 2 update time we propose dynamic algorithms and data structures for chordal graphs supporting the following operation determine if an edge can be added or removed from the graph while preserving the chordality in o 1 time we show that the complexity of the algorithms for updating the data structures when an edge is actually inserted or deleted is o n 2 where n is the number of vertices of the graph

regularity criteria for the strong solutions to the ericksen leslie system in r3 abstract in this paper we establish some regularity criteria for both the simplified and the general ericksen leslie system in r 3

stochastic preconditioning for diagonally dominant matrices this paper presents a new stochastic preconditioning approach for large sparse matrices for the class of matrices that are rowwise and columnwise irreducibly diagonally dominant we prove that an incomplete rm ldl t factorization in a symmetric case or an incomplete ldu factorization in an asymmetric case can be obtained from random walks and used as a preconditioner it is argued that our factor matrices have better quality i e better accuracy size trade offs than preconditioners produced by existing incomplete factorization methods therefore a resulting preconditioned krylov subspace iterative solver requires less computation than traditional methods to solve a set of linear equations with the same error tolerance the advantage increases for larger and denser matrices these claims are verified by numerical tests and we provide techniques that can potentially extend the theory to non diagonally dominant matrices

regularity criteria for the navier stokes landau lifshitz system abstract in this paper we study regularity criteria for the navier stokes landau lifshitz system using delicate estimates the regularity criteria for smooth solution of navier stokes landau lifshitz system in besov spaces and the multiplier spaces are obtained the navier stokes landau lifshitz system is coupled system of the navier stokes equation and landau lifshitz system our results generalize the related results for navier stokes equation and landau lifshitz system to our system

fast minimal triangulation algorithm using minimum degree criterion we propose an algorithm for minimal triangulation which using simple and efficient strategy subdivides the input graph in different almost non overlapping subgraphs using the technique of matrix multiplication for saturating the minimal separators we show that the partition of the graph can be computed in time o n a where n a is the time required by the binary matrix multiplication after saturating the minimal separators the same procedure is recursively applied on each subgraphs we also present a variant of the algorithm in which the minimum degree criterion is used in this way we obtain an algorithm that uses minimum degree criterion and at the same time produces a minimal triangulation thus shedding new light on the effectiveness of the minimum degree heuristics

on the relationship between circumscription and negation as failure abstract the aim of this paper is to investigate two powerful methods of handling negative information in logic based knowledge representation systems the logical minimization in the form of circumscription and the negation as failure rule formalized by various closures or completions of original theories we suggest a new more powerful form of the negation as failure rule and describe an important class of theories for which this form of negation as failure is equivalent to particular forms of circumscription these results establish a close relationship between the two important formalizations of nonmonotonic reasoning and provide a syntactic characterization of the corresponding circumscriptive theories this allows us to apply existing methods of deduction using various negation as failure rules to answering queries in a broad class of circumscriptive theories

an algorithm to compute circumscription abstract mccarthy s theory of circumscription appears to be the most powerful among various formalizations of nonmonotonic reasoning designed to handle incomplete and negative information in knowledge representation systems in this paper we describe a query answering algorithm for circumscriptive theories the closed world assumption cwa and its generalizations the generalized closed world assumption gcwa and the extended closed world assumption ecwa can be considered as special forms of circumscription consequently our algorithm also applies to answering queries in theories using the closed world assumption and its generalizations similarly since prioritized circumscription is equivalent to a conjunction of parallel circumscriptions our algorithm can be used to answer queries in theories circumscribed by prioritized circumscription

effective preconditioning through minimum degree ordering interleaved with incomplete factorization in this paper we study a kind of effective preconditioning technique which interleaves the incomplete cholesky ic factorization with an approximate minimum degree ordering an ic factorization algorithm derived from ikj version gaussian elimination is proposed and some details on implementation are presented then we discuss the ways to compute the degrees of the unnumbered nodes exactly and approximately using the concept of element absorbing when used in conjunction with conjugate gradient algorithm the new preconditioners usually lead to fast convergence the numerical experiments show that the interleaving of symbolic ordering and numerical ic factorization will generate better preconditioners than those generated by the ic factorization without ordering or with purely symbolic ordering ahead of the factorization

the evolution of the minimum degree ordering algorithm over the past fifteen years the implementation of the minimum degree algorithm has received much study and many important enhancements have been made to it this paper describes these various enhancements their historical development and some experiments showing how very effective they are in improving the execution time of the algorithm a shortcoming is also presented that exists in all of the widely used implementations of the algorithm namely that the quality of the ordering provided by the implementations is surprisingly sensitive to the initial ordering for example changing the input ordering can lead to an increase or decrease of as much as a factor of three in the cost of the subsequent numerical factorization this sensitivity is caused by the lack of an effective tie breaking strategy and the authors experiments illustrate the importance of developing such a strategy