470 research outputs found
Solving non-perturbative flow equations
Non-perturbative exact flow equations describe the scale dependence of the
effective average action. We present a numerical solution for an approximate
form of the flow equation for the potential in a three-dimensional N-component
scalar field theory. The critical behaviour, with associated critical
exponents, can be inferred with good accuracy.Comment: Latex, 14 pages, 2 uuencoded figure
Interplay between network structure and self-organized criticality
We investigate, by numerical simulations, how the avalanche dynamics of the
Bak-Tang-Wiesenfeld (BTW) sandpile model can induce emergence of scale-free
(SF) networks and how this emerging structure affects dynamics of the system.
We also discuss how the observed phenomenon can be used to explain evolution of
scientific collaboration.Comment: 4 pages, 4 figure
Annealing schedule from population dynamics
We introduce a dynamical annealing schedule for population-based optimization
algorithms with mutation. On the basis of a statistical mechanics formulation
of the population dynamics, the mutation rate adapts to a value maximizing
expected rewards at each time step. Thereby, the mutation rate is eliminated as
a free parameter from the algorithm.Comment: 6 pages RevTeX, 4 figures PostScript; to be published in Phys. Rev.
Transport on weighted Networks: when correlations are independent of degree
Most real-world networks are weighted graphs with the weight of the edges
reflecting the relative importance of the connections. In this work, we study
non degree dependent correlations between edge weights, generalizing thus the
correlations beyond the degree dependent case. We propose a simple method to
introduce weight-weight correlations in topologically uncorrelated graphs. This
allows us to test different measures to discriminate between the different
correlation types and to quantify their intensity. We also discuss here the
effect of weight correlations on the transport properties of the networks,
showing that positive correlations dramatically improve transport. Finally, we
give two examples of real-world networks (social and transport graphs) in which
weight-weight correlations are present.Comment: 8 pages, 8 figure
Topological Evolution of Dynamical Networks: Global Criticality from Local Dynamics
We evolve network topology of an asymmetrically connected threshold network
by a simple local rewiring rule: quiet nodes grow links, active nodes lose
links. This leads to convergence of the average connectivity of the network
towards the critical value in the limit of large system size . How
this principle could generate self-organization in natural complex systems is
discussed for two examples: neural networks and regulatory networks in the
genome.Comment: 4 pages RevTeX, 4 figures PostScript, revised versio
Genetic algorithm dynamics on a rugged landscape
The genetic algorithm is an optimization procedure motivated by biological
evolution and is successfully applied to optimization problems in different
areas. A statistical mechanics model for its dynamics is proposed based on the
parent-child fitness correlation of the genetic operators, making it applicable
to general fitness landscapes. It is compared to a recent model based on a
maximum entropy ansatz. Finally it is applied to modeling the dynamics of a
genetic algorithm on the rugged fitness landscape of the NK model.Comment: 10 pages RevTeX, 4 figures PostScrip
Universal scaling of distances in complex networks
Universal scaling of distances between vertices of Erdos-Renyi random graphs,
scale-free Barabasi-Albert models, science collaboration networks, biological
networks, Internet Autonomous Systems and public transport networks are
observed. A mean distance between two nodes of degrees k_i and k_j equals to
=A-B log(k_i k_j). The scaling is valid over several decades. A simple
theory for the appearance of this scaling is presented. Parameters A and B
depend on the mean value of a node degree _nn calculated for the nearest
neighbors and on network clustering coefficients.Comment: 4 pages, 3 figures, 1 tabl
Thermodynamic forces, flows, and Onsager coefficients in complex networks
We present Onsager formalism applied to random networks with arbitrary degree
distribution. Using the well-known methods of non-equilibrium thermodynamics we
identify thermodynamic forces and their conjugated flows induced in networks as
a result of single node degree perturbation. The forces and the flows can be
understood as a response of the system to events, such as random removal of
nodes or intentional attacks on them. Finally, we show that cross effects (such
as thermodiffusion, or thermoelectric phenomena), in which one force may not
only give rise to its own corresponding flow, but to many other flows, can be
observed also in complex networks.Comment: 4 pages, 2 figure
The conduciveness of CA-rule graphs
Given two subsets A and B of nodes in a directed graph, the conduciveness of
the graph from A to B is the ratio representing how many of the edges outgoing
from nodes in A are incoming to nodes in B. When the graph's nodes stand for
the possible solutions to certain problems of combinatorial optimization,
choosing its edges appropriately has been shown to lead to conduciveness
properties that provide useful insight into the performance of algorithms to
solve those problems. Here we study the conduciveness of CA-rule graphs, that
is, graphs whose node set is the set of all CA rules given a cell's number of
possible states and neighborhood size. We consider several different edge sets
interconnecting these nodes, both deterministic and random ones, and derive
analytical expressions for the resulting graph's conduciveness toward rules
having a fixed number of non-quiescent entries. We demonstrate that one of the
random edge sets, characterized by allowing nodes to be sparsely interconnected
across any Hamming distance between the corresponding rules, has the potential
of providing reasonable conduciveness toward the desired rules. We conjecture
that this may lie at the bottom of the best strategies known to date for
discovering complex rules to solve specific problems, all of an evolutionary
nature
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