Scope-bounded multistack pushdown systems: fixed-point, sequentialization, and tree-width

We present a novel fixed-point algorithm to solve reachability of multi-stack pushdown systems restricted to runs of bounded-scope. The followed approach is compositional, in the sense that the runs of the system are summarized by bounded-size interfaces. Moreover, it is suitable for a direct implementation and can be exploited to prove two new results. We give a sequentialization for this class of systems, i.e., for each such multi-stack pushdown system we construct an equivalent single-stack pushdown system that faithfully simulates the behaviour of each thread. We prove that the behaviour graphs (multiply nested words) for these systems have bounded three-width, and thus a number of decidability results can be derived from Courcelle’s theorem

Country-level correlates of e-cigarette use in the European Union

Objectives The aim of this study was to assess the relationship between the prevalence of e-cigarette use and country-level factors across 28 European countries. Methods The study objectives were addressed in an ecological design in which both exposures and outcomes were measured at the country level. Data from the Eurobarometer Report, the Eurostat database and the WHO observatory were analyzed. Bivariate and multivariate analyses were performed considering the rates of current and ever smokers of e-cigarettes as dependent variables, and socio-economic factors, health status and policies against tobacco as independent variables. Results Both the rate of current smokers and ever smokers of e-cigarette were positively associated to the offer of help to quit tobacco use (P\0.01; P = 0.04) and to the raise of taxes on tobacco (P = 0.01; P = 0.01). The warn on dangers of tobacco negatively correlated with the rate of e-cigarette current smokers. The rate of current e-cigarette smokers correlated with the rate of current smokers and with national Gross Domestic Product, while the rate of ever e-cigarette smokers did not correlate with any socio-economic factor. Conclusions Our analysis suggests that both policy and non-policy factors are associated with the geographical variability seen in the prevalence of e-cigarette use. Policies against the consumption of conventional tobacco products may lead to an increase of e-cigarette smokers

Relativity of representations in quantum mechanics

Only the position representation is used in introductory quantum mechanics and the momentum representation is not usually presented until advanced undergraduate courses. To emphasize the relativity of the representations of the abstract formulation of quantum mechanics, two examples of representations related to the operators aX+(1-a)P and (XP+PX)/2 are presented.Comment: 10 pages, no figures, accepted in Am.J.Phy