A survey of parallel execution strategies for transitive closure and logic programs

An important feature of database technology of the nineties is the use of parallelism for speeding up the execution of complex queries. This technology is being tested in several experimental database architectures and a few commercial systems for conventional select-project-join queries. In particular, hash-based fragmentation is used to distribute data to disks under the control of different processors in order to perform selections and joins in parallel. With the development of new query languages, and in particular with the definition of transitive closure queries and of more general logic programming queries, the new dimension of recursion has been added to query processing. Recursive queries are complex; at the same time, their regular structure is particularly suited for parallel execution, and parallelism may give a high efficiency gain. We survey the approaches to parallel execution of recursive queries that have been presented in the recent literature. We observe that research on parallel execution of recursive queries is separated into two distinct subareas, one focused on the transitive closure of Relational Algebra expressions, the other one focused on optimization of more general Datalog queries. Though the subareas seem radically different because of the approach and formalism used, they have many common features. This is not surprising, because most typical Datalog queries can be solved by means of the transitive closure of simple algebraic expressions. We first analyze the relationship between the transitive closure of expressions in Relational Algebra and Datalog programs. We then review sequential methods for evaluating transitive closure, distinguishing iterative and direct methods. We address the parallelization of these methods, by discussing various forms of parallelization. Data fragmentation plays an important role in obtaining parallel execution; we describe hash-based and semantic fragmentation. Finally, we consider Datalog queries, and present general methods for parallel rule execution; we recognize the similarities between these methods and the methods reviewed previously, when the former are applied to linear Datalog queries. We also provide a quantitative analysis that shows the impact of the initial data distribution on the performance of methods

Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame

Using the Cachazo-He-Yuan (CHY) formalism, we prove a recursive expansion of tree level single trace Einstein-Yang-Mills (EYM) amplitudes with arbitrary number of gluons and gravitons, which is valid for general spacetime dimensions and any helicity configurations. The recursion is written in terms of fewer-graviton EYM amplitudes and pure Yang-Mills (YM) amplitudes, which can be further carried out until we reach an expansion in terms of pure YM amplitudes in Kleiss-Kuijf (KK) basis. Our expansion then generates naturally a spanning tree structure rooted on gluons whose vertices are gravitons. We further propose a set of graph theoretical rules based on spanning trees that evaluate directly the pure YM expansion coefficients.Comment: 36 pages, 3 captioned figures; v2: more details added, revised and published versio

Recent Conceptual Consequences of Loop Quantum Gravity. Part II: Holistic Aspects

Based on the foundational aspects which have been discussed as consequences of ongoing research on loop quantum gravity in the first part of this paper, the holistic aspects of the latter are discussed in this second part, aiming at a consistent and systematic approach to eventually model a hierarchically ordered architecture of the world which is encompassing all of what there actually is. The idea is to clarify the explicit relationship between physics and philosophy on the one hand, and philosophy and the sciences in general, on the other. It is shown that the ontological determination of worldliness is practically identical with its epistemological determination so that the (scientific) activity of modelling and representing the world can be visualized itself as a (worldly) mode of being.Comment: 20 page

General Ramified Recurrence is Sound for Polynomial Time

Leivant's ramified recurrence is one of the earliest examples of an implicit characterization of the polytime functions as a subalgebra of the primitive recursive functions. Leivant's result, however, is originally stated and proved only for word algebras, i.e. free algebras whose constructors take at most one argument. This paper presents an extension of these results to ramified functions on any free algebras, provided the underlying terms are represented as graphs rather than trees, so that sharing of identical subterms can be exploited

First order convergence of matroids

The model theory based notion of the first order convergence unifies the notions of the left-convergence for dense structures and the Benjamini-Schramm convergence for sparse structures. It is known that every first order convergent sequence of graphs with bounded tree-depth can be represented by an analytic limit object called a limit modeling. We establish the matroid counterpart of this result: every first order convergent sequence of matroids with bounded branch-depth representable over a fixed finite field has a limit modeling, i.e., there exists an infinite matroid with the elements forming a probability space that has asymptotically the same first order properties. We show that neither of the bounded branch-depth assumption nor the representability assumption can be removed.Comment: Accepted to the European Journal of Combinatoric

Visual and computational analysis of structure-activity relationships in high-throughput screening data

Novel analytic methods are required to assimilate the large volumes of structural and bioassay data generated by combinatorial chemistry and high-throughput screening programmes in the pharmaceutical and agrochemical industries. This paper reviews recent work in visualisation and data mining that can be used to develop structure-activity relationships from such chemical/biological datasets