Showing papers on "Completeness (order theory) published in 1996"

Mining quantitative association rules in large relational tables

Abstract: We introduce the problem of mining association rules in large relational tables containing both quantitative and categorical attributes. An example of such an association might be "10% of married people between age 50 and 60 have at least 2 cars". We deal with quantitative attributes by fine-partitioning the values of the attribute and then combining adjacent partitions as necessary. We introduce measures of partial completeness which quantify the information lost due to partitioning. A direct application of this technique can generate too many similar rules. We tackle this problem by using a "greater-than-expected-value" interest measure to identify the interesting rules in the output. We give an algorithm for mining such quantitative association rules. Finally, we describe the results of using this approach on a real-life dataset.

Can Quantum-Mechanical Description of Physical Reality be Considered Complete?

Abstract: Phys. Rev. 48 (1935) 696–702 (Received July 13, 1935) It is shown that a certain “criterion of physical reality” formulated in a recent article with the above title by A. Einstein, B. Podolsky and N. Rosen contains an essential ambiguity when it is applied to quantum phenomena. In this connection a viewpoint termed “complementarity” is explained from which quantum-mechanical description of physical phenomena would seem to fulfill, within its scope, all rational demands of completeness.

Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function

Abstract: Recall that a subset of R is called semi-algebraic if it can be represented as a (finite) boolean combination of sets of the form {~ α ∈ R : p(~ α) = 0}, {~ α ∈ R : q(~ α) > 0} where p(~x), q(~x) are n-variable polynomials with real coefficients. A map from R to R is called semi-algebraic if its graph, considered as a subset of R, is so. The geometry of such sets and maps (“semi-algebraic geometry”) is now a widely studied and flourishing subject that owes much to the foundational work in the 1930s of the logician Alfred Tarski. He proved ([11]) that the image of a semi-algebraic set under a semi-algebraic map is semi-algebraic. (A familiar simple instance: the image of {〈a, b, c, x〉 ∈ R : a 6= 0 and ax +bx+c = 0} under the projection map R×R→ R is {〈a, b, c〉 ∈ R : a 6= 0 and b−4ac ≥ 0}.) Tarski’s result implies that the class of semi-algebraic sets is closed under firstorder logical definability (where, as well as boolean operations, the quantifiers “∃x ∈ R . . . ” and “∀x ∈ R . . . ” are allowed) and for this reason it is known to logicians as “quantifier elimination for the ordered ring structure on R”. Immediate consequences are the facts that the closure, interior and boundary of a semialgebraic set are semi-algebraic. It is also the basis for many inductive arguments in semi-algebraic geometry where a desired property of a given semi-algebraic set is inferred from the same property of projections of the set into lower dimensions. For example, the fact (due to Hironaka) that any bounded semi-algebraic set can be triangulated is proved this way. In the 1960s the analytic geometer Lojasiewicz extended the above theory to the analytic context ([8]). The definition of a semi-analytic subset of R is the same as above except that for the basic sets the p(~x)’s and q(~x)’s are allowed to be analytic functions and we only insist that the boolean representations work locally around each point of R (allowing different representations around different points). It is also necessary to restrict the maps to be proper (with semi-analytic graph). With this restriction it is true that the image of a semi-analytic set, known as a sub-analytic set, is semi-analytic provided that the target space is either R or R. Counterexamples have been known since the beginning of this century for maps to R for m ≥ 3. (They are due to Osgood, see [8].) However, the situation was clarified in 1968 by Gabrielov ([5]) who showed that the class of sub-analytic sets

Kleene Algebra with Tests: Completeness and Decidability

Abstract: Kleene algebras with tests provide a rigorous framework for equational specification and verification They have been used successfully in basic safety analysis, source-to-source program transformation, and concurrency control We prove the completeness of the equational theory of Kleene algebra with tests and *-continuous Kleene algebra with tests over language-theoretic and relational models We also show decidability Cohen''s reduction of Kleene algebra with hypotheses of the form $r=0$ to Kleene algebra without hypotheses is simplified and extended to handle Kleene algebras with tests

Unification via Explicit Substitutions: The Case of Higher-Order Patterns.

Abstract: In [6] we have proposed a general higher-order unification method using a theory of explicit substitutions and we have proved its completeness. In this paper, we investigate the case of higher-order patterns as introduced by Miller. We show that our general algorithm specializes in a very convenient way to patterns. We also sketch an efficient implementation of the abstract algorithm and its generalization to constraint simplification, which has yielded good experimental results at the core of a higher-order constraint logic programming language.

Basic Model Theory

Abstract: Introduction 1. Basic notions 2. Relations between models 3. Ehrenfeucht-Fraisse games 4. Constructing models Appendix A. Deduction and completeness Appendix B. Set theory Bibliography Name index Subject index Notation.

NP Completeness of Kauffman's N-k Model, A Tuneable Rugged Fitness Landscape

Abstract: The concept of a "fitness landscape," a picturesque term for a mapping of the vertices of a finite graph to the real numbers, has arisen in several fields, including evolutionary theory The computational complexity of two, qualitatively similar versions of a particularly simple fitness landscape are shown to differ considerably In one version, the question "Is the global optimum greater than a given value V?" is shown to be answerable in polynominal time by presenting an efficient algorithm that actually computes the optimum The corresponding problem for the other version of the landscape is shown to be NP complete The NP completeness of the latter problem leads to some speculations on why P not equal to NP Key words rugged fitness landscape, n-k model

On the Complexity of Random Strings (Extended Abstract)

Abstract: We show that the set R of Kolmogorov random strings is truth-table complete. This improves the previously known Turing completeness of R and shows how the halting problem can be encoded into the distribution of random strings rather than using the time complexity of non-random strings. As an application we obtain that Post's simple set is truth-table complete in every Kolmogorov numbering. We also show that the truth-table completeness of R cannot be generalized to size-complexity with respect to arbitrary acceptable numberings. In addition we note that R is not frequency computable.

Proof systems for message-passing process algebras

Abstract: We give sound and complete proof systems for a variety of bisimulation based equivalences over a message-passing process algebra. The process algebra is a generalisation of pureCCS where the actions consist of receiving and sending messages or data on communication channels; the standard prefixing operatora.p is replaced by the two operatorsc?x.p andc!e.p and in addition messages can be tested by a conditional construct. The various proof systems are parameterised on auxiliary proof systems for deciding on equalities or more general boolean identities over the expression language for data. The completeness of these proof systems are thus relative to the completeness of the auxiliary proof systems.

Mathematical theory of elastic structures

Abstract: The book covers three main topics: the classical theory of linear elasticity, the mathematical theory of composite elastic structures, as an application of the theory of elliptic equations on composite manifolds developed by the first author, and the finite element method for solving elastic structural problems. The authors treat these topics within the framework of a unified theory. The book carries on a theoretical discussion on the mathematical basis of the principle of minimum potential theory. The emphasis is on the accuracy and completeness of the mathematical formulation of elastic structural problems. The book will be useful to applied mathematicians, engineers and graduate students. It may also serve as a course in elasticity for undergraduate students in applied sciences.

Axiomatizing Prefix Iteration with Silent Steps

Abstract: Prefix iteration is a variation on the original binary version of the Kleene star operationP*Q, obtained by restricting the first argument to be an atomic action The interaction of prefix iteration with silent steps is studied in the setting of Milner's basic CCS Complete equational axiomatizations are given for four notions of behavioural congruence over basic CCS with prefix iteration, viz, branching congruence,?-congruence, delay congruence, and weak congruence The completeness proofs for?-, delay, and weak congruence are obtained by reduction to the completeness theorem for branching congruence It is also argued that the use of the completeness result for branching congruence in obtaining the completeness result for weak congruence leads to a considerable simplification with respect to the only direct proof presented in the literature The preliminaries and the completeness proofs focus on open terms, ie, terms that may contain process variables As a by-product, the?-completeness of the axiomatizations is obtained, as well as their completeness for closed terms

The asymptotic completeness of inertial manifolds

Abstract: An investigation of the asymptotic completeness property for inertial manifolds leads to the concept of `flow-normal hyperbolicity', which is more natural in this case than the traditional form of normal hyperbolicity derived from the linearized flow near the manifold. An example shows that without flow-normal hyperbolicity asymptotic completeness cannot be guaranteed. The analysis also yields a new result on the asymptotic equivalence of ordinary differential equations.

On Wigner's theorem: Remarks, complements, comments, and corollaries

Abstract: In this paper we present a unified treatment of Wigner's unitarity-antiunitarity theorem simultaneously in the real and the complex case. Its elementary nature, emphasized by V. Bargmann in 1964, is underlined here by removing unnecessary hypotheses, the most important being the completeness of the inner product spaces involved. At the end, we shall obtain connections to some recent results in geometry.

Octonionic Quantum Mechanics and Complex Geometry

Abstract: The use of complex geometry allows us to obtain a consistent formulation of octonionic quantum mechanics (OQM) In our octonionic formulation we solve the hermiticity problem and define an appropriate momentum operator within OQM The nonextendability of the completeness relation and the norm conservation is also discussed in detail

Linear Algebra Problem Book

Abstract: Linear Algebra Problem Book can be either the main course or the dessert for someone who needs linear algebra—and nowadays that means every user of mathematics. It can be used as the basis of either an official course or a program of private study. If used as a course, the book can stand by itself, or if so desired, it can be stirred in with a standard linear algebra course as the seasoning that provides the interest, the challenge, and the motivation that is needed by experienced scholars as much as by beginning students. The best way to learn is to do, and the purpose of this book is to get the reader to DO linear algebra. The approach is Socratic: first ask a question, then give a hint (if necessary), then, finally, for security and completeness, provide the detailed answer.

Gamma-Accurate Failure Detectors

Abstract: The knowledge about failures needed to solve distributed agreement problems can be expressed in terms of completeness and accuracy properties of failure detectors introduced by Chandra and Toueg. The accuracy properties they have considered restrict the false suspicions that can be made by all the processes in the system. In this paper, we define “Γ-accurate” failure detectors, whose accuracy properties (only) restrict the false suspicions that can be made by a subset Γ of the processes. We discuss the relations between the classes of Γ-accurate failure detectors, and the classes of failure detectors defined by Chandra and Toueg. Then we point out the impact of these relations on the solvability of agreement problems.

Solutions of the elliptic qKZB equations and Bethe ansatz I

Abstract: We give an integral representation for solutions of the elliptic quantum Knizhnik-Zamolodchikov-Bernard difference equations, in the case of sl(2). The result is based on a geometric construction of highest weight representations of the elliptic quantum group associated to sl(2). We also obtain Bethe ansatz eigenfunctions for the corresponding integrable systems of difference operators, and prove their completeness in some cases.

Solutions of the elliptic qKZB equations and Bethe ansatz I

Abstract: We give an integral representation for solutions of the elliptic quantum Knizhnik-Zamolodchikov-Bernard difference equations, in the case of sl(2). The result is based on a geometric construction of highest weight representations of the elliptic quantum group associated to sl(2). We also obtain Bethe ansatz eigenfunctions for the corresponding integrable systems of difference operators, and prove their completeness in some cases.

Asymptotic completeness for long-range many-particle systems with Stark effect. II

Abstract: We prove the existence and the asymptotic completeness of the Dollard-type modified wave operators for many-particle Stark Hamiltonians with long-range potentials

Equational Properties of Iteration in Algebraically Complete Categories

Abstract: The main result is the following completeness theorem: If the fixed point operation over a category is defined by initiality, then the equations satisfied by the fixed point operation are exactly those of iteration theories. Thus, in such categories, the equational axioms of iteration theories provide a sound and complete axiomatization of the equational properties of the fixed point operation.

Completeness in discrete-time process algebra

Abstract: We prove soundness and completeness for some ACP-style concrete, relative-time, discrete-time process algebras. We treat non-delayable actions, delayable actions, and immediate deadlock. Basic process algebras are examined extensively, and also some concurrent process algebras are considered. We conclude with ACPdrt, which combines all described features in one theory. 1991 Mathematics Subject Classification: 68Q10, 68Q22, 68Q55. 1991 CR Categories: D.1.3, D.3.1, F.1.2, F.3.2.

Asymptotic completeness for N-body Stark Hamiltonians

Abstract: We prove asymptotic completeness for short- and long-rangeN-body Stark Hamiltonians with local singularities of at most Coulomb type. Our results include the usual models for atoms and molecules.