1,021 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
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
Distribution of epicenters in the Olami-Feder-Christensen model
We show that the well established Olami-Feder-Christensen (OFC) model for the
dynamics of earthquakes is able to reproduce a new striking property of real
earthquake data. Recently, it has been pointed out by Abe and Suzuki that the
epicenters of earthquakes could be connected in order to generate a graph, with
properties of a scale-free network of the Barabasi-Albert type. However, only
the non conservative version of the Olami-Feder-Christensen model is able to
reproduce this behavior. The conservative version, instead, behaves like a
random graph. Besides indicating the robustness of the model to describe
earthquake dynamics, those findings reinforce that conservative and non
conservative versions of the OFC model are qualitatively different. Also, we
propose a completely new dynamical mechanism that, even without an explicit
rule of preferential attachment, generates a free scale network. The
preferential attachment is in this case a ``by-product'' of the long term
correlations associated with the self-organized critical state. The detailed
study of the properties of this network can reveal new aspects of the dynamics
of the OFC model, contributing to the understanding of self-organized
criticality in non conserving models.Comment: 7 pages, 7 figure
First results on light readout from the 1-ton ArDM liquid argon detector for dark matter searches
ArDM-1t is the prototype for a next generation WIMP detector measuring both
the scintillation light and the ionization charge from nuclear recoils in a
1-ton liquid argon target. The goal is to reach a minimum recoil energy of
30\,keVr to detect recoiling nuclei. In this paper we describe the experimental
concept and present results on the light detection system, tested for the first
time in ArDM on the surface at CERN. With a preliminary and incomplete set of
PMTs, the light yield at zero electric field is found to be between 0.3-0.5
phe/keVee depending on the position within the detector volume, confirming our
expectations based on smaller detector setups.Comment: 14 pages, 10 figures, v2 accepted for publication in JINS
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