841 research outputs found
Functional Optimization in Complex Excitable Networks
We study the effect of varying wiring in excitable random networks in which
connection weights change with activity to mold local resistance or
facilitation due to fatigue. Dynamic attractors, corresponding to patterns of
activity, are then easily destabilized according to three main modes, including
one in which the activity shows chaotic hopping among the patterns. We describe
phase transitions to this regime, and show a monotonous dependence of critical
parameters on the heterogeneity of the wiring distribution. Such correlation
between topology and functionality implies, in particular, that tasks which
require unstable behavior --such as pattern recognition, family discrimination
and categorization-- can be most efficiently performed on highly heterogeneous
networks. It also follows a possible explanation for the abundance in nature of
scale--free network topologies.Comment: 7 pages, 3 figure
Systematic Series Expansions for Processes on Networks
We use series expansions to study dynamics of equilibrium and non-equilibrium
systems on networks. This analytical method enables us to include detailed
non-universal effects of the network structure. We show that even low order
calculations produce results which compare accurately to numerical simulation,
while the results can be systematically improved. We show that certain commonly
accepted analytical results for the critical point on networks with a broad
degree distribution need to be modified in certain cases due to
disassortativity; the present method is able to take into account the
assortativity at sufficiently high order, while previous results correspond to
leading and second order approximations in this method. Finally, we apply this
method to real-world data.Comment: 4 pages, 3 figure
Non-equilibrium Anisotropic Phases, Nucleation and Critical Behavior in a Driven Lennard-Jones Fluid
We describe short-time kinetic and steady-state properties of the
non--equilibrium phases, namely, solid, liquid and gas anisotropic phases in a
driven Lennard-Jones fluid. This is a computationally-convenient
two-dimensional model which exhibits a net current and striped structures at
low temperature, thus resembling many situations in nature. We here focus on
both critical behavior and details of the nucleation process. In spite of the
anisotropy of the late--time spinodal decomposition process, earlier nucleation
seems to proceed by Smoluchowski coagulation and Ostwald ripening, which are
known to account for nucleation in equilibrium, isotropic lattice systems and
actual fluids. On the other hand, a detailed analysis of the system critical
behavior rises some intriguing questions on the role of symmetries; this
concerns the computer and field-theoretical modeling of non-equilibrium fluids.Comment: 7 pages, 9 ps figures, to appear in PR
Probability distribution of the order parameter in the directed percolation universality class
The probability distributions of the order parameter for two models in the
directed percolation universality class were evaluated. Monte Carlo simulations
have been performed for the one-dimensional generalized contact process and the
Domany-Kinzel cellular automaton. In both cases, the density of active sites
was chosen as the order parameter. The criticality of those models was obtained
by solely using the corresponding probability distribution function. It has
been shown that the present method, which has been successfully employed in
treating equilibrium systems, is indeed also useful in the study of
nonequilibrium phase transitions.Comment: 6 pages, 4 figure
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