1,085 research outputs found
A Monte Carlo Renormalization Group Approach to the Bak-Sneppen model
A recent renormalization group approach to a modified Bak-Sneppen model is
discussed. We propose a self-consistency condition for the blocking scheme to
be essential for a successful RG-method applied to self-organized criticality.
A new method realizing the RG-approach to the Bak-Sneppen model is presented.
It is based on the Monte-Carlo importance sampling idea. The new technique
performs much faster than the original proposal. Using this technique we
cross-check and improve previous results.Comment: 11 pages, REVTex, 2 Postscript figures include
On the High-dimensional Bak-Sneppen model
We report on extensive numerical simulations on the Bak-Sneppen model in high
dimensions. We uncover a very rich behavior as a function of dimensionality.
For d>2 the avalanche cluster becomes fractal and for d \ge 4 the process
becomes transient. Finally the exponents reach their mean field values for
d=d_c=8, which is then the upper critical dimension of the Bak Sneppen model.Comment: 4 pages, 3 eps figure
Collaboration in Social Networks
The very notion of social network implies that linked individuals interact
repeatedly with each other. This allows them not only to learn successful
strategies and adapt to them, but also to condition their own behavior on the
behavior of others, in a strategic forward looking manner. Game theory of
repeated games shows that these circumstances are conducive to the emergence of
collaboration in simple games of two players. We investigate the extension of
this concept to the case where players are engaged in a local contribution game
and show that rationality and credibility of threats identify a class of Nash
equilibria -- that we call "collaborative equilibria" -- that have a precise
interpretation in terms of sub-graphs of the social network. For large network
games, the number of such equilibria is exponentially large in the number of
players. When incentives to defect are small, equilibria are supported by local
structures whereas when incentives exceed a threshold they acquire a non-local
nature, which requires a "critical mass" of more than a given fraction of the
players to collaborate. Therefore, when incentives are high, an individual
deviation typically causes the collapse of collaboration across the whole
system. At the same time, higher incentives to defect typically support
equilibria with a higher density of collaborators. The resulting picture
conforms with several results in sociology and in the experimental literature
on game theory, such as the prevalence of collaboration in denser groups and in
the structural hubs of sparse networks
Criticality and finite size effects in a simple realistic model of stock market
We discuss a simple model based on the Minority Game which reproduces the
main stylized facts of anomalous fluctuations in finance. We present the
analytic solution of the model in the thermodynamic limit and show that
stylized facts arise only close to a line of critical points with non-trivial
properties. By a simple argument, we show that, in Minority Games, the
emergence of critical fluctuations close to the phase transition is governed by
the interplay between the signal to noise ratio and the system size. These
results provide a clear and consistent picture of financial markets as critical
systems.Comment: 4 pages, 4 figure
Critical exponents of the anisotropic Bak-Sneppen model
We analyze the behavior of spatially anisotropic Bak-Sneppen model. We
demonstrate that a nontrivial relation between critical exponents tau and
mu=d/D, recently derived for the isotropic Bak-Sneppen model, holds for its
anisotropic version as well. For one-dimensional anisotropic Bak-Sneppen model
we derive a novel exact equation for the distribution of avalanche spatial
sizes, and extract the value gamma=2 for one of the critical exponents of the
model. Other critical exponents are then determined from previously known
exponent relations. Our results are in excellent agreement with Monte Carlo
simulations of the model as well as with direct numerical integration of the
new equation.Comment: 8 pages, three figures included with psfig, some rewriting, + extra
figure and table of exponent
Laplacian Fractal Growth in Media with Quenched Disorder
We analyze the combined effect of a Laplacian field and quenched disorder for
the generation of fractal structures with a study, both numerical and
theoretical, of the quenched dielectric breakdown model (QDBM). The growth
dynamics is shown to evolve from the avalanches of invasion percolation (IP) to
the smooth growth of Laplacian fractals, i. e. diffusion limited aggregation
(DLA) and the dielectric breakdown model (DBM). The fractal dimension is
strongly reduced with respect to both DBM and IP, due to the combined effect of
memory and field screening. This implies a specific relation between the
fractal dimension of the breakdown structures (dielectric or mechanical) and
the microscopic properties of disordered materials.Comment: 11 pages Latex (revtex), 3 postscript figures included. Submitted to
PR
Expansion Around the Mean-Field Solution of the Bak-Sneppen Model
We study a recently proposed equation for the avalanche distribution in the
Bak-Sneppen model. We demonstrate that this equation indirectly relates
,the exponent for the power law distribution of avalanche sizes, to ,
the fractal dimension of an avalanche cluster.We compute this relation
numerically and approximate it analytically up to the second order of expansion
around the mean field exponents. Our results are consistent with Monte Carlo
simulations of Bak-Sneppen model in one and two dimensions.Comment: 5 pages, 2 ps-figures iclude
Nonequilibrium phase transition in a model for social influence
We present extensive numerical simulations of the Axelrod's model for social
influence, aimed at understanding the formation of cultural domains. This is a
nonequilibrium model with short range interactions and a remarkably rich
dynamical behavior. We study the phase diagram of the model and uncover a
nonequilibrium phase transition separating an ordered (culturally polarized)
phase from a disordered (culturally fragmented) one. The nature of the phase
transition can be continuous or discontinuous depending on the model
parameters. At the transition, the size of cultural regions is power-law
distributed.Comment: 5 pages, 4 figure
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