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 favour 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 modelled), 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 present some graph theory concepts, together with examples, and comparisons between the mean-field and simulations in Barab\'asi-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims. 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).Comment: 15 pages, 18 figures. To be submitted to Physical Revie

A Generalized Sznajd Model

In the last decade the Sznajd Model has been successfully employed in modeling some properties and scale features of both proportional and majority elections. We propose a new version of the Sznajd model with a generalized bounded confidence rule - a rule that limits the convincing capability of agents and that is essential to allow coexistence of opinions in the stationary state. With an appropriate choice of parameters it can be reduced to previous models. We solved this new model both in a mean-field approach (for an arbitrary number of opinions) and numerically in a Barabasi-Albert network (for three and four opinions), studying the transient and the possible stationary states. We built the phase portrait for the special cases of three and four opinions, defining the attractors and their basins of attraction. Through this analysis, we were able to understand and explain discrepancies between mean-field and simulation results obtained in previous works for the usual Sznajd Model with bounded confidence and three opinions. Both the dynamical system approach and our generalized bounded confidence rule are quite general and we think it can be useful to the understanding of other similar models.Comment: 19 pages with 8 figures. Submitted to Physical Review

Domestic Dogs In A Fragmented Landscape In The Brazilian Atlantic Forest: Abundance, Habitat Use And Caring By Owners.

This study aimed at estimating the population size and attitudes of residents towards caring for domestic dogs, through questionnaire surveys, as well as the frequency of these animals in different habitats (anthropic and forest patch), using scent stations. The study was conducted in a severely fragmented area of the Brazilian Atlantic Forest. A large number of unrestricted dogs was recorded, averaging 6.2 ind/km². These dogs have owners and are regularly fed. Dog records decreased from the anthropogenic matrix to the forest patch edge, which suggests that dogs act as an edge effect on forest patches. Encounters between domestic dog and wild animals can still be frequent in severely fragmented landscapes, mainly at the forest edges. However the fact that most dogs have an owner and are more frequent in the anthropic habitat suggests that their putative effects are less severe than expected for a carnivore of such abundance, but the reinforcement of responsible ownership is needed to further ameliorate such effects.70987-9

The occurrence of unpigmented mature oocytes in Hypsiboas (Anura: Hylidae)

The genus Hypsiboas is composed of 90 species distributed in Central and South America from Nicaragua to Argentina, as well as on Trinidad and Tobago (Frost 2014). Previous studies on the reproductive biology of species in this genus have reported that female mature oocytes or eggs generally have pigmented animal poles (Tab. 1), which has been generally suggested as a protection of the exposed embryos from solar radiation (Wells 2007).Fil: Nali, Renato C.. Universidade Estadual Paulista Julio de Mesquita Filho; BrasilFil: Faivovich, Julián. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; ArgentinaFil: Prado, Cynthia P. A.. Universidade Estadual Paulista Julio de Mesquita Filho; Brasi