Automatic sets of rational numbers

The notion of a k-automatic set of integers is well-studied. We develop a new notion - the k-automatic set of rational numbers - and prove basic properties of these sets, including closure properties and decidability.Comment: Previous version appeared in Proc. LATA 2012 conferenc

Cuba’s Communist Party would thrive under democracy, but only if it gives up power soon

Cuba has been under communist rule since Fidel Castro overthrew Fulgencio Batista in 1959. After many years of international isolation and a trade embargo begun in the 1960s, President Obama last year ‘normalised’ relations with the country, creating potential for an eventual transition to democracy. Here, James Loxton argues that the Cuban Communist Party would stand a good chance of thriving in a hypothetical democratic future as an ‘authoritarian successor party’ – but that this likelihood decreases the longer the regime clings to authoritarian contro

Impulsivity: four ways five factors are not basic to addiction

Several impulsivity-related models have been applied to understanding the vulnerability to addiction. While there is a growing consensus that impulsivity is multifaceted, debate continues as to the precise number of facets and, more critically, which are most relevant to explaining the addiction-risk profile. In many ways, the current debate mirrors that which took place in the personality literature in the early 1990s (e.g., Eysenck's 'Big Three' versus Costa and McCrae's 'Big Five'). Indeed, many elements of this debate are relevant to the current discussion of the role of impulsivity in addictive behavior. Specifically, 1) the use of factor analysis as an atheoretical 'truth-grinding machine'; 2) whether additional facets add explanatory power over fewer; 3) the delineation of specific neurocognitive pathways from each facet to addictive behaviors, and; 4) the relative merit of 'top-down' versus 'bottom-up' approaches to the understanding of impulsivity. Ultimately, the utility of any model of impulsivity and addiction lies in its heuristic value and ability to integrate evidence from different levels of analysis. Here, we make the case that theoretically-driven, bottom-up models proposing two factors deliver the optimal balance of explanatory power, parsimony, and integration of evidence. (C) 2014 Elsevier Ltd. All rights reserved

Differential Effects of Reward Drive and Rash Impulsivity on the Consumption of a Range of Hedonic Stimuli

Background and aims Impulsivity has consistently been associated with over-consumption and addiction. Recent research has reconceptualized impulsivity as a two-dimensional construct (Dawe, Gullo, & Loxton, 2004). This study explores the relationship of the two components of impulsivity, reward drive (RD) and rash impulsivity (RI), on a broad group of 23 hedonic consumption behaviors (e.g., gambling, substance use, eating, and media use). We tentatively grouped the behaviors into three descriptive classes: entertainment, foodstuffs, and illicit activities and substances. Results RD and RI positively predicted elevated levels of consumption in a community sample (N=5,391; 51% female), for the vast majority of the behaviors considered. However, the effect sizes for RD and RI varied significantly depending on the behavior; a pattern that appeared to be at least partially attributable to the class of consumption. Results support the view that RD is related more strongly to the consumption of products that provide social engagement or a sense of increased status; whereas RI better reflects an approach toward illicit or restricted products that are intensely rewarding with clear negative consequences. Discussion and conclusion Results support the utility of the two-factor model of impulsivity in explaining individual differences in patterns of hedonic consumption in the general population. We discuss findings in terms of strengthening current conceptualizations of RI and RD as having distinct implications with respect to health-related behaviors

A looped-functional approach for robust stability analysis of linear impulsive systems

A new functional-based approach is developed for the stability analysis of linear impulsive systems. The new method, which introduces looped-functionals, considers non-monotonic Lyapunov functions and leads to LMIs conditions devoid of exponential terms. This allows one to easily formulate dwell-times results, for both certain and uncertain systems. It is also shown that this approach may be applied to a wider class of impulsive systems than existing methods. Some examples, notably on sampled-data systems, illustrate the efficiency of the approach.Comment: 13 pages, 2 figures, Accepted at Systems & Control Letter

Complementary and alternative medicine for victims of intimate partner abuse: A systematic review of use and efficacy

Objectives. To examine: (i) the extent to which victims of intimate partner abuse (IPA) use complementary and alternative medicine (CAM) and (ii) the effects of CAM on their mental health. Methods. Medline, Scopus, and Web of Science were searched for studies measuring the extent of CAM use amongst victims of IPA and trials assessing the impact of CAM on mental health amongst this population. Risk of bias was assessed using the Cochrane collaboration tool. Results. No studies measuring the level of CAM use amongst IPA victims, and only three studies assessing the effect of CAM on the mental health of this population were identified. Two studies looked at yogic breathing, while one assessed the effect of music therapy. All three studies showed some beneficial effects; however, each had a small sample, brief intervention period, and no follow-up measurement and were considered to be at high risk of bias. Conclusions. The review found little evidence for the benefits of CAM for IPA victims. Findings suggest positive effects of music therapy and yogic breathing; however, methodological limitations mean that these results should be interpreted with caution. It is important that more research into the use and effects of CAM amongst this population are undertaken. © 2014 Luke Duffy et al

Characterizing Triviality of the Exponent Lattice of A Polynomial through Galois and Galois-Like Groups

The problem of computing \emph{the exponent lattice} which consists of all the multiplicative relations between the roots of a univariate polynomial has drawn much attention in the field of computer algebra. As is known, almost all irreducible polynomials with integer coefficients have only trivial exponent lattices. However, the algorithms in the literature have difficulty in proving such triviality for a generic polynomial. In this paper, the relations between the Galois group (respectively, \emph{the Galois-like groups}) and the triviality of the exponent lattice of a polynomial are investigated. The \bbbq\emph{-trivial} pairs, which are at the heart of the relations between the Galois group and the triviality of the exponent lattice of a polynomial, are characterized. An effective algorithm is developed to recognize these pairs. Based on this, a new algorithm is designed to prove the triviality of the exponent lattice of a generic irreducible polynomial, which considerably improves a state-of-the-art algorithm of the same type when the polynomial degree becomes larger. In addition, the concept of the Galois-like groups of a polynomial is introduced. Some properties of the Galois-like groups are proved and, more importantly, a sufficient and necessary condition is given for a polynomial (which is not necessarily irreducible) to have trivial exponent lattice.Comment: 19 pages,2 figure

Cyclotomic integers, fusion categories, and subfactors

Dimensions of objects in fusion categories are cyclotomic integers, hence number theoretic results have implications in the study of fusion categories and finite depth subfactors. We give two such applications. The first application is determining a complete list of numbers in the interval (2, 76/33) which can occur as the Frobenius-Perron dimension of an object in a fusion category. The smallest number on this list is realized in a new fusion category which is constructed in the appendix written by V. Ostrik, while the others are all realized by known examples. The second application proves that in any family of graphs obtained by adding a 2-valent tree to a fixed graph, either only finitely many graphs are principal graphs of subfactors or the family consists of the A_n or D_n Dynkin diagrams. This result is effective, and we apply it to several families arising in the classification of subfactors of index less then 5.Comment: 47 pages, with an appendix by Victor Ostri