Connections between the Sznajd model with general confidence rules and graph theory

The Sznajd model is a sociophysics model that is used to model opinion propagation and consensus formation in societies. Its main feature is that its rules favor bigger groups of agreeing people. In a previous work, we generalized the bounded confidence rule in order to model biases and prejudices in discrete opinion models. In that work, we applied this modification to the Sznajd model and presented some preliminary results. The present work extends what we did in that paper. We present results linking many of the properties of the mean-field fixed points, with only a few qualitative aspects of the confidence rule (the biases and prejudices modeled), finding an interesting connection with graph theory problems. More precisely, we link the existence of fixed points with the notion of strongly connected graphs and the stability of fixed points with the problem of finding the maximal independent sets of a graph. We state these results and present comparisons between the mean field and simulations in Barabasi-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims and some graph theory concepts, together with examples. We also show that there is no qualitative difference in the mean-field results if we require that a group of size q > 2, instead of a pair, of agreeing agents be formed before they attempt to convince other sites (for the mean field, this would coincide with the q-voter model).

Gender differences in drinking patterns and alcohol-related problems in a community sample in Sao Paulo, Brazil

OBJECTIVE: To investigate drinking patterns and gender differences in alcohol-related problems in a Brazilian population, with an emphasis on the frequency of heavy drinking. METHODS: A cross-sectional study was conducted with a probability adult household sample (n = 1,464) in the city of Sao Paulo, Brazil. Alcohol intake and ICD-10 psychopathology diagnoses were assessed with the Composite International Diagnostic Interview 1.1. The analyses focused on the prevalence and determinants of 12-month non-heavy drinking, heavy episodic drinking (4-5 drinks per occasion), and heavy and frequent drinking (heavy drinking at least 3 times/week), as well as associated alcohol-related problems according to drinking patterns and gender. RESULTS: Nearly 22% (32.4% women, 8.7% men) of the subjects were lifetime abstainers, 60.3% were non-heavy drinkers, and 17.5% reported heavy drinking in a 12-month period (26.3% men, 10.9% women). Subjects with the highest frequency of heavy drinking reported the most problems. Among subjects who did not engage in heavy drinking, men reported more problems than did women. A gender convergence in the amount of problems was observed when considering heavy drinking patterns. Heavy and frequent drinkers were twice as likely as abstainers to present lifetime depressive disorders. Lifetime nicotine dependence was associated with all drinking patterns. Heavy and frequent drinking was not restricted to young ages. CONCLUSIONS: Heavy and frequent episodic drinking was strongly associated with problems in a community sample from the largest city in Latin America. Prevention policies should target this drinking pattern, independent of age or gender. These findings warrant continued research on risky drinking behavior, particularly among persistent heavy drinkers at the non-dependent level.