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

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

Diversity of N2-fixing cyanobacteria from Andalusian paddy fields and analysis of their potential as bioinoculants

The marshes of the Guadalquivir River contain the largest area of rice cultivation in Spain, where more than 40,000 ha are used every year for rice production. These wetland areas provide a perfect place for rice cultivation, and represent a unique aquaticterrestrial habitat that hold more wintering waterfowl than any other European wetland. Paddies require large amounts nitrogen and phosphorus for their growth, development and production. Though, flooded conditions used for rice cultivation drastically diminish efficiency inorganic nitrogen fertilizers, being only 30–40% used by the plant, and in some cases even less. Large amounts of nitrogen fertilizers are dissolved in the surface water and lost, causing environmental pollution and health problems due to losses through N2O and NO volatilization, denitrification, and leaching (Ishii et al., 2011)

The Network of Epicenters of the Olami-Feder-Christensen Model of Earthquakes

We study the dynamics of the Olami-Feder-Christensen (OFC) model of earthquakes, focusing on the behavior of sequences of epicenters regarded as a growing complex network. Besides making a detailed and quantitative study of the effects of the borders (the occurrence of epicenters is dominated by a strong border effect which does not scale with system size), we examine the degree distribution and the degree correlation of the graph. We detect sharp differences between the conservative and nonconservative regimes of the model. Removing border effects, the conservative regime exhibits a Poisson-like degree statistics and is uncorrelated, while the nonconservative has a broad power-law-like distribution of degrees (if the smallest events are ignored), which reproduces the observed behavior of real earthquakes. In this regime the graph has also a unusually strong degree correlation among the vertices with higher degree, which is the result of the existence of temporary attractors for the dynamics: as the system evolves, the epicenters concentrate increasingly on fewer sites, exhibiting strong synchronization, but eventually spread again over the lattice after a series of sufficiently large earthquakes. We propose an analytical description of the dynamics of this growing network, considering a Markov process network with hidden variables, which is able to account for the mentioned properties.Comment: 9 pages, 10 figures. Smaller number of figures, and minor text corrections and modifications. For version with full resolution images see http://fig.if.usp.br/~tpeixoto/cond-mat-0602244.pd

Thickness of the buccal bone wall and root angulation in the maxilla and mandible: an approach to cone beam computed tomography

Background: The objective of this paper is to anatomically describe the bone morphology in the maxillary and mandibular tooth areas, which might help in planning post-extraction implants. Methods: CBCT images (Planmeca ProMax 3D) of 403 teeth (208 upper teeth and 195 lower teeth) were obtained from 49 patients referred to the Dental School of Seville from January to December 2014. The thickness of the facial wall was measured at the crest, point A, 4mm below, point B, and at the apex, point C. The second parameter was the angle formed between the dental axis and the axis of the basal bone. Results: A total of 403 teeth were measured. In the maxilla, 89.4% of incisors, 93.94% of canines, 78% of premolars and 70.5% of molars had a buccal bone wall thickness less than the ideal 2mm. In the mandible, 73.5% of incisors, 49% of canines, 64% of premolars and 53% of molars had <1mm buccal bone thickness as measured at point B. The mean angulation in the maxilla was 11.67±6.37° for incisors, 16.88±7.93° for canines, 13.93±8.6° for premolars, and 9.89±4.8° for molars. In the mandible, the mean values were 10.63±8.76° for incisors, 10.98±7.36° for canines, 10.54±5.82° for premolars and 16.19±11.22° for molars. Conclusions: The high incidence of a buccal wall thickness of less than 2mm in over 80% of the assessed sites indicates the need for additional regeneration procedures, and several locations may also require custom abutments to solve the angulation problems for screw-retained crowns