An Algorithmic Metatheorem for Directed Treewidth

The notion of directed treewidth was introduced by Johnson, Robertson, Seymour and Thomas [Journal of Combinatorial Theory, Series B, Vol 82, 2001] as a first step towards an algorithmic metatheory for digraphs. They showed that some NP-complete properties such as Hamiltonicity can be decided in polynomial time on digraphs of constant directed treewidth. Nevertheless, despite more than one decade of intensive research, the list of hard combinatorial problems that are known to be solvable in polynomial time when restricted to digraphs of constant directed treewidth has remained scarce. In this work we enrich this list by providing for the first time an algorithmic metatheorem connecting the monadic second order logic of graphs to directed treewidth. We show that most of the known positive algorithmic results for digraphs of constant directed treewidth can be reformulated in terms of our metatheorem. Additionally, we show how to use our metatheorem to provide polynomial time algorithms for two classes of combinatorial problems that have not yet been studied in the context of directed width measures. More precisely, for each fixed $k,w \in \mathbb{N}$, we show how to count in polynomial time on digraphs of directed treewidth $w$, the number of minimum spanning strong subgraphs that are the union of $k$ directed paths, and the number of maximal subgraphs that are the union of $k$ directed paths and satisfy a given minor closed property. To prove our metatheorem we devise two technical tools which we believe to be of independent interest. First, we introduce the notion of tree-zig-zag number of a digraph, a new directed width measure that is at most a constant times directed treewidth. Second, we introduce the notion of $z$-saturated tree slice language, a new formalism for the specification and manipulation of infinite sets of digraphs.Comment: 41 pages, 6 figures, Accepted to Discrete Applied Mathematic

Toward an ecological aesthetics: music as emergence

In this article we intend to suggest some ecological based principles to support the possibility of develop an ecological aesthetics. We consider that an ecological aesthetics is founded in concepts as “direct perception”, “acquisition of affordances and invariants”, “embodied embedded perception” and so on. Here we will purpose that can be possible explain especially soundscape music perception in terms of direct perception, working with perception of first hand (in a Gibsonian sense). We will present notions as embedded sound, detection of sonic affordances and invariants, and at the end we purpose an experience with perception/action paradigm to make soundscape music as emergence of a self-organized system

Classical Solutions of SU(3) Yang-Mills Theory and Heavy Quark Phenomenology

It is showed that potentials derived from classical solutions of the SU(3) Yang-Mills theory can provide confining potentials that reproduce the heavy quarkonium spectrum within the same level of precision as the Cornell potential.Comment: Talk given at Quark Confinement and the Hadron Spectrum VI 2004, 21-25 Sept, Ital

Infrared Gluon and Ghost Propagators from Lattice QCD. Results from large asymmetric lattices

We report on the infrared limit of the quenched lattice Landau gauge gluon and ghost propagators as well as the strong coupling constant computed from large asymmetric lattices. The infrared lattice propagators are compared with the pure power law solutions from Dyson-Schwinger equations (DSE). For the gluon propagator, the lattice data is compatible with the DSE solution. The preferred measured gluon exponent being $\sim 0.52$, favouring a null zero momentum propagator. The lattice ghost propagator shows finite volume effects and, for the volumes considered, the propagator does not follow a pure power law. Furthermore, the strong coupling constant is computed and its infrared behaviour investigated.Comment: Talk given at QNP06; final version with improved english, accepted for publication at EPJ

Juvenile substance use and effects of substance use disorder on incarceration and grade retention in a sample referred for court clinic mental health evaluation

A significant amount of adolescents are involved in the drug court system. Within a few of the systems are mental health clinics providing more specific services to youth introduced into the courts. At the Rhode Island Family Court, juveniles are referred for full mental health evaluations in the court mental health clinic. They are then referred for other services depending on the outcome of the evaluation. The purpose of this study is to provide a descriptive analysis of the drug use of these youth referred to the mental health clinic. Because little is known about the about the affects of a substance use disorder diagnosis on incarceration and grade repetition, an analysis was done to determine if any associations were present. After accounting for mental health diagnosis and demographic variables, an association between substance use disorder and incarceration within 3 months of the mental health evaluation was found. There was no significant association between a substance use disorder diagnosis and grade repetition in school

Where does inter-firm trust come from?

This research aims at understanding the manifestation of inter-firm trust in a given activity sector