1,108 research outputs found
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
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
Beyond the Colours: Discovering Hidden Diversity in the Nymphalidae of the Yucatan Peninsula in Mexico through DNA Barcoding
BACKGROUND: Recent studies have demonstrated the utility of DNA barcoding in the discovery of overlooked species and in the connection of immature and adult stages. In this study, we use DNA barcoding to examine diversity patterns in 121 species of Nymphalidae from the Yucatan Peninsula in Mexico. Our results suggest the presence of cryptic species in 8 of these 121 taxa. As well, the reference database derived from the analysis of adult specimens allowed the identification of nymphalid caterpillars providing new details on host plant use. METHODOLOGY/PRINCIPAL FINDINGS: We gathered DNA barcode sequences from 857 adult Nymphalidae representing 121 different species. This total includes four species (Adelpha iphiclus, Adelpha malea, Hamadryas iphtime and Taygetis laches) that were initially overlooked because of their close morphological similarity to other species. The barcode results showed that each of the 121 species possessed a diagnostic array of barcode sequences. In addition, there was evidence of cryptic taxa; seven species included two barcode clusters showing more than 2% sequence divergence while one species included three clusters. All 71 nymphalid caterpillars were identified to a species level by their sequence congruence to adult sequences. These caterpillars represented 16 species, and included Hamadryas julitta, an endemic species from the Yucatan Peninsula whose larval stages and host plant (Dalechampia schottii, also endemic to the Yucatan Peninsula) were previously unknown. CONCLUSIONS/SIGNIFICANCE: This investigation has revealed overlooked species in a well-studied museum collection of nymphalid butterflies and suggests that there is a substantial incidence of cryptic species that await full characterization. The utility of barcoding in the rapid identification of caterpillars also promises to accelerate the assembly of information on life histories, a particularly important advance for hyperdiverse tropical insect assemblages
On the robustness of scale invariance in SOC models
A random neighbor extremal stick-slip model is introduced. In the
thermodynamic limit, the distribution of states has a simple analytical form
and the mean avalanche size, as a function of the coupling parameter, is
exactly calculable. The system is critical only at a special point Jc in the
coupling parameter space. However, the critical region around this point, where
approximate scale invariance holds, is very large, suggesting a mechanism for
explaining the ubiquity of scale invariance in Nature.Comment: 6 pages, 4 figures; submitted to Physical Review E;
http://link.aps.org/doi/10.1103/PhysRevE.59.496
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