Tuple-Generating Dependencies Capture Complex Values

We formalise a variant of Datalog that allows complex values constructed by nesting elements of the input database in sets and tuples. We study its complexity and give a translation into sets of tuple-generating dependencies (TGDs) for which the standard chase terminates on any input database. We identify a fragment for which reasoning is tractable. As membership is undecidable for this fragment, we develop decidable sufficient conditions

Structure constants of short operators in planar N=4\mathcal{N}=4 SYM theory

We present an integrability-based conjecture for the three-point functions of single-trace operators in planar $\mathcal{N}=4$ super-Yang-Mills theory at finite coupling, in the case where two operators are protected. Our proposal is based on the hexagon representation for structure constants of long operators, which we complete to incorporate operators of any length using data from the TBA/QSC formalism. We perform various tests of our conjecture, at weak and strong coupling, finding agreement with the gauge theory through 5 loops for the shortest three-point function and with string theory in the classical limit.Comment: 6 pages, 4 figures, 1 appendi

Deciding Second-order Logics using Database Evaluation Techniques

We outline a novel technique that maps the satisfiability problems of second-order logics, in particular WSnS (weak monadic second-order logic with n successors), S1S (monadic second-order logic with one successor), and of μ-calculus, to the problem of query evaluation of Complex-value Datalog queries. In this dissertation, we propose techniques that use database evaluation and optimization techniques for automata-based decision procedures for the above logics. We show how the use of advanced implementation techniques for Deductive databases and for Logic Programs, in particular the use of tabling, yields a considerable improvement in performance over more traditional approaches. We also explore various optimizations of the proposed technique, in particular we consider variants of tabling and goal reordering. We then show that the decision problem for S1S can be mapped to the problem of query evaluation of Complex-value Datalog queries. We explore optimizations that can be applied to various types of formulas. Last, we propose analogous techniques that allow us to approach μ-calculus satisfiability problem in an incremental fashion and without the need for re-computation. In addition, we outline a top-down evaluation technique to drive our incremental procedure and propose heuristics that guide the problem partitioning to reduce the size of the problems that need to be solved

AN EXAMINATION OF MANAGERIAL STRATEGIES FOR INCREASING INFORMATION TECHNOLOGY PENETRATION IN ORGANIZATIONS

This paper describes an empirical study comparing two competing perspectives for explaining information technology (IT) penetration in organizations. IT penetration is defined as the extent to which IT is embedded within an organization\u27s strategic, managerial, and operational work systems. With the first perspective, IT penetration is hypothesized to be related to the implementation of a comprehensive set of management processes for the information systems (IS) function. With the second perspective, IT penetration is hypothesized to be related to the effectiveness of IT-related interactions among an organization\u27s managers, To strengthen the study\u27s research design, the hypotheses are examined separately across two samples of organizations. Senior ]S executives completed the study\u27s research instrument. Respondents in the first sample represented 132 large organizations across a variety of industries, while the respondents in the second sample represented 44 business units within a large, high teChnology firm. IT penetration and IT-related managerial interactions were measured at a subunit level, while IS management processes were measured at an organizational level. The study\u27s findings supported the research hypotheses. *The authors wish to thank Omar El Sawy and anonymous reviewers for their helpful comments on earlier drafts of this paper

Set Unification

The unification problem in algebras capable of describing sets has been tackled, directly or indirectly, by many researchers and it finds important applications in various research areas--e.g., deductive databases, theorem proving, static analysis, rapid software prototyping. The various solutions proposed are spread across a large literature. In this paper we provide a uniform presentation of unification of sets, formalizing it at the level of set theory. We address the problem of deciding existence of solutions at an abstract level. This provides also the ability to classify different types of set unification problems. Unification algorithms are uniformly proposed to solve the unification problem in each of such classes. The algorithms presented are partly drawn from the literature--and properly revisited and analyzed--and partly novel proposals. In particular, we present a new goal-driven algorithm for general ACI1 unification and a new simpler algorithm for general (Ab)(Cl) unification.Comment: 58 pages, 9 figures, 1 table. To appear in Theory and Practice of Logic Programming (TPLP

Analysis of comet rotation through modeling of features in the coma

An integral field unit fiber array spectrograph was used to observe the emission spectra of radical species (C2, C3, CH, CN, and NH2) in multiple comets. The resultant azimuthal and radial division maps produced from the reduced data provide a unique method of analyzing features with these radicals in the comae, as well as how they behave over time. A Monte Carlo model was developed in order to simulate the behavior of particles from the outer nucleus and coma of each comet depending on various parameters including rotational period, outflow velocity, and active area location. The results from the model were used to constrain the physical parameters of three comets: 10P/Tempel 2, C/2009 P1 (Garradd), and 168P/Hergenrother

The QCD phase diagram in the space of imaginary chemical potential via 't Hooft anomalies

The QCD phase diagram in the space of temperature and imaginary baryon chemical potential has been an interesting subject in numerical lattice QCD simulations because of the absence of the sign problem and its deep structure related to confinement/deconfinement. We study constraints on the phase diagram by using an 't Hooft anomaly. The relevant anomaly is an anomaly in the space of imaginary chemical potential. We compute it in the UV, and discuss how it is matched by the pion effective field theory at low temperatures. Then we study implications of the anomaly to the phase diagram. There must be a line of phase transition studied in the past by Roberge and Weiss such that the expectation value of the Polyakov loop is not smooth when we cross the line. Moreover, if the greatest common divisor of the color and flavor numbers is greater than one, the phase transition across the Roberge-Weiss line must be either a first order phase transition, or a second order phase transition described by a nontrivial interacting three-dimensional CFT.Comment: 28 pages, 6 figure

Quantum lattice models that preserve continuous translation symmetry

Bandlimited approaches to quantum field theory offer the tantalizing possibility of working with fields that are simultaneously both continuous and discrete via the Shannon Sampling Theorem from signal processing. Conflicting assumptions in general relativity and quantum field theory motivate the use of such an appealing analytical tool that could thread the needle to meet both requirements. Bandlimited continuous quantum fields are isomorphic to lattice theories, yet without requiring a fixed lattice. Any lattice with a required minimum spacing can be used. This is an isomorphism that avoids taking the limit of the lattice spacing going to zero. In this work, we explore the consequences of this isomorphism, including the emergence of effectively continuous symmetries in quantum lattice theories. One obtains conserved lattice observables for these continuous symmetries, as well as a duality of locality from the two perspectives. We expect this work and its extensions to provide useful tools for considering numerical lattice models of continuous quantum fields arising from the availability of discreteness without a fixed lattice, as well as offering new insights into emergent continuous symmetries in lattice models and possible laboratory demonstrations of these phenomena.Comment: 16 pages, 5 figure

Insights into the chemical composition of the metal-poor Milky Way halo globular cluster NGC 6426

We present our detailed spectroscopic analysis of the chemical composition of four red giant stars in the halo globular cluster NGC 6426. We obtained high-resolution spectra using the Magellan2/MIKE spectrograph, from which we derived equivalent widths and subsequently computed abundances of 24 species of 22 chemical elements. For the purpose of measuring equivalent widths, we developed a new semi-automated tool, called EWCODE. We report a mean Fe content of [Fe/H] =−2.34 ± 0.05 dex (stat.) in accordance with previous studies. At a mean α-abundance of [(Mg, Si, Ca)/3 Fe] = 0.39 ± 0.03 dex, NGC 6426 falls on the trend drawn by the Milky Way halo and other globular clusters at comparably low metallicities. The distribution of the lighter α-elements as well as the enhanced ratio [Zn/Fe] = 0.39 dex could originate from hypernova enrichment of the pre-cluster medium. We find tentative evidence for a spread in the elements Mg, Si, and Zn, indicating an enrichment scenario, where ejecta of evolved massive stars of a slightly older population have polluted a newly born younger one. The heavy element abundances in this cluster fit well into the picture of metal-poor globular clusters, which in that respect appear to be remarkably homogeneous. The pattern of the neutron-capture elements heavier than Zn points toward an enrichment history governed by the r-process with little, if any, sign of s-process contributions. This finding is supported by the striking similarity of our program stars to the metal-poor field star HD 108317