1,929 research outputs found
Synchronization interfaces and overlapping communities in complex networks
We show that a complex network of phase oscillators may display interfaces
between domains (clusters) of synchronized oscillations. The emergence and
dynamics of these interfaces are studied in the general framework of
interacting phase oscillators composed of either dynamical domains (influenced
by different forcing processes), or structural domains (modular networks). The
obtained results allow to give a functional definition of overlapping
structures in modular networks, and suggest a practical method to identify
them. As a result, our algorithm could detect information on both single
overlapping nodes and overlapping clusters.Comment: 5 pages, 4 figure
Branching Transition of a Directed Polymer in Random Medium
A directed polymer is allowed to branch, with configurations determined by
global energy optimization and disorder. A finite size scaling analysis in 2D
shows that, if disorder makes branching more and more favorable, a critical
transition occurs from the linear scaling regime first studied by Huse and
Henley [Phys. Rev. Lett. 54, 2708 (1985)] to a fully branched, compact one. At
criticality clear evidence is obtained that the polymer branches at all scales
with dimension and roughness exponent satisfying , and energy fluctuation exponent , in terms of longitudinal distanceComment: REVTEX, 4 pages, 3 encapsulated eps figure
Stability of the replica symmetric solution for the information conveyed by by a neural network
The information that a pattern of firing in the output layer of a feedforward
network of threshold-linear neurons conveys about the network's inputs is
considered. A replica-symmetric solution is found to be stable for all but
small amounts of noise. The region of instability depends on the contribution
of the threshold and the sparseness: for distributed pattern distributions, the
unstable region extends to higher noise variances than for very sparse
distributions, for which it is almost nonexistant.Comment: 19 pages, LaTeX, 5 figures. Also available at
http://www.mrc-bbc.ox.ac.uk/~schultz/papers.html . Submitted to Phys. Rev. E
Minor change
Fronts dynamics in the presence of spatio-temporal structured noises
Front dynamics modeled by a reaction-diffusion equation are studied under the
influence of spatio-temporal structured noises. An effective deterministic
model is analytical derived where the noise parameters, intensity, correlation
time and correlation length appear explicitely. The different effects of these
parameters are discussed for the Ginzburg-Landau and Schl\"ogl models. We
obtain an analytical expression for the front velocity as a function of the
noise parameters. Numerical simulations results are in a good agreement with
the theoretical predictions.Comment: 11 pages, 6 figures; REVTEX; to be published in Phys.Rev.E, july 200
Multifractal Properties of Price Fluctuations of Stocks and Commodities
We analyze daily prices of 29 commodities and 2449 stocks, each over a period
of years. We find that the price fluctuations for commodities have
a significantly broader multifractal spectrum than for stocks. We also propose
that multifractal properties of both stocks and commodities can be attributed
mainly to the broad probability distribution of price fluctuations and
secondarily to their temporal organization. Furthermore, we propose that, for
commodities, stronger higher order correlations in price fluctuations result in
broader multifractal spectra.Comment: Published in Euro Physics Letters (14 pages, 5 figures
The mutual information of a stochastic binary channel: validity of the Replica Symmetry Ansatz
We calculate the mutual information (MI) of a two-layered neural network with
noiseless, continuous inputs and binary, stochastic outputs under several
assumptions on the synaptic efficiencies. The interesting regime corresponds to
the limit where the number of both input and output units is large but their
ratio is kept fixed at a value . We first present a solution for the MI
using the replica technique with a replica symmetric (RS) ansatz. Then we find
an exact solution for this quantity valid in a neighborhood of . An
analysis of this solution shows that the system must have a phase transition at
some finite value of . This transition shows a singularity in the third
derivative of the MI. As the RS solution turns out to be infinitely
differentiable, it could be regarded as a smooth approximation to the MI. This
is checked numerically in the validity domain of the exact solution.Comment: Latex, 29 pages, 2 Encapsulated Post Script figures. To appear in
Journal of Physics
Stochastic learning in a neural network with adapting synapses
We consider a neural network with adapting synapses whose dynamics can be
analitically computed. The model is made of neurons and each of them is
connected to input neurons chosen at random in the network. The synapses
are -states variables which evolve in time according to Stochastic Learning
rules; a parallel stochastic dynamics is assumed for neurons. Since the network
maintains the same dynamics whether it is engaged in computation or in learning
new memories, a very low probability of synaptic transitions is assumed. In the
limit with large and finite, the correlations of neurons and
synapses can be neglected and the dynamics can be analitically calculated by
flow equations for the macroscopic parameters of the system.Comment: 25 pages, LaTeX fil
Kinematic reduction of reaction-diffusion fronts with multiplicative noise: Derivation of stochastic sharp-interface equations
We study the dynamics of generic reaction-diffusion fronts, including pulses
and chemical waves, in the presence of multiplicative noise. We discuss the
connection between the reaction-diffusion Langevin-like field equations and the
kinematic (eikonal) description in terms of a stochastic moving-boundary or
sharp-interface approximation. We find that the effective noise is additive and
we relate its strength to the noise parameters in the original field equations,
to first order in noise strength, but including a partial resummation to all
orders which captures the singular dependence on the microscopic cutoff
associated to the spatial correlation of the noise. This dependence is
essential for a quantitative and qualitative understanding of fluctuating
fronts, affecting both scaling properties and nonuniversal quantities. Our
results predict phenomena such as the shift of the transition point between the
pushed and pulled regimes of front propagation, in terms of the noise
parameters, and the corresponding transition to a non-KPZ universality class.
We assess the quantitative validity of the results in several examples
including equilibrium fluctuations, kinetic roughening, and the noise-induced
pushed-pulled transition, which is predicted and observed for the first time.
The analytical predictions are successfully tested against rigorous results and
show excellent agreement with numerical simulations of reaction-diffusion field
equations with multiplicative noise.Comment: 17 pages, 6 figure
Replica symmetric evaluation of the information transfer in a two-layer network in presence of continuous+discrete stimuli
In a previous report we have evaluated analytically the mutual information
between the firing rates of N independent units and a set of multi-dimensional
continuous+discrete stimuli, for a finite population size and in the limit of
large noise. Here, we extend the analysis to the case of two interconnected
populations, where input units activate output ones via gaussian weights and a
threshold linear transfer function. We evaluate the information carried by a
population of M output units, again about continuous+discrete correlates. The
mutual information is evaluated solving saddle point equations under the
assumption of replica symmetry, a method which, by taking into account only the
term linear in N of the input information, is equivalent to assuming the noise
to be large. Within this limitation, we analyze the dependence of the
information on the ratio M/N, on the selectivity of the input units and on the
level of the output noise. We show analytically, and confirm numerically, that
in the limit of a linear transfer function and of a small ratio between output
and input noise, the output information approaches asymptotically the
information carried in input. Finally, we show that the information loss in
output does not depend much on the structure of the stimulus, whether purely
continuous, purely discrete or mixed, but only on the position of the threshold
nonlinearity, and on the ratio between input and output noise.Comment: 19 pages, 4 figure
Optimal static and dynamic recycling of defective binary devices
The binary Defect Combination Problem consists in finding a fully working
subset from a given ensemble of imperfect binary components. We determine the
typical properties of the model using methods of statistical mechanics, in
particular, the region in the parameter space where there is almost surely at
least one fully-working subset. Dynamic recycling of a flux of imperfect binary
components leads to zero wastage.Comment: 14 pages, 15 figure
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