559 research outputs found
Transient dynamics for sequence processing neural networks: effect of degree distributions
We derive a analytic evolution equation for overlap parameters including the
effect of degree distribution on the transient dynamics of sequence processing
neural networks. In the special case of globally coupled networks, the
precisely retrieved critical loading ratio is obtained,
where is the network size. In the presence of random networks, our
theoretical predictions agree quantitatively with the numerical experiments for
delta, binomial, and power-law degree distributions.Comment: 11 pages, 6 figure
Synchronization and directed percolation in coupled map lattices
We study a synchronization mechanism, based on one-way coupling of
all-or-nothing type, applied to coupled map lattices with several different
local rules. By analyzing the metric and the topological distance between the
two systems, we found two different regimes: a strong chaos phase in which the
transition has a directed percolation character and a weak chaos phase in which
the synchronization transition occurs abruptly. We are able to derive some
analytical approximations for the location of the transition point and the
critical properties of the system.
We propose to use the characteristics of this transition as indicators of the
spatial propagation of chaoticity.Comment: 12 pages + 12 figure
Fractal Dimensions of Confined Clusters in Two-Dimensional Directed Percolation
The fractal structure of directed percolation clusters, grown at the
percolation threshold inside parabolic-like systems, is studied in two
dimensions via Monte Carlo simulations. With a free surface at y=\pm Cx^k and a
dynamical exponent z, the surface shape is a relevant perturbation when k<1/z
and the fractal dimensions of the anisotropic clusters vary continuously with
k. Analytic expressions for these variations are obtained using a blob picture
approach.Comment: 6 pages, Plain TeX file, epsf, 3 postscript-figure
Secure exchange of information by synchronization of neural networks
A connection between the theory of neural networks and cryptography is
presented. A new phenomenon, namely synchronization of neural networks is
leading to a new method of exchange of secret messages. Numerical simulations
show that two artificial networks being trained by Hebbian learning rule on
their mutual outputs develop an antiparallel state of their synaptic weights.
The synchronized weights are used to construct an ephemeral key exchange
protocol for a secure transmission of secret data. It is shown that an opponent
who knows the protocol and all details of any transmission of the data has no
chance to decrypt the secret message, since tracking the weights is a hard
problem compared to synchronization. The complexity of the generation of the
secure channel is linear with the size of the network.Comment: 11 pages, 5 figure
Training a perceptron in a discrete weight space
On-line and batch learning of a perceptron in a discrete weight space, where
each weight can take different values, are examined analytically and
numerically. The learning algorithm is based on the training of the continuous
perceptron and prediction following the clipped weights. The learning is
described by a new set of order parameters, composed of the overlaps between
the teacher and the continuous/clipped students. Different scenarios are
examined among them on-line learning with discrete/continuous transfer
functions and off-line Hebb learning. The generalization error of the clipped
weights decays asymptotically as / in the case of on-line learning with binary/continuous activation
functions, respectively, where is the number of examples divided by N,
the size of the input vector and is a positive constant that decays
linearly with 1/L. For finite and , a perfect agreement between the
discrete student and the teacher is obtained for . A crossover to the generalization error ,
characterized continuous weights with binary output, is obtained for synaptic
depth .Comment: 10 pages, 5 figs., submitted to PR
Nonlocal mechanism for cluster synchronization in neural circuits
The interplay between the topology of cortical circuits and synchronized
activity modes in distinct cortical areas is a key enigma in neuroscience. We
present a new nonlocal mechanism governing the periodic activity mode: the
greatest common divisor (GCD) of network loops. For a stimulus to one node, the
network splits into GCD-clusters in which cluster neurons are in zero-lag
synchronization. For complex external stimuli, the number of clusters can be
any common divisor. The synchronized mode and the transients to synchronization
pinpoint the type of external stimuli. The findings, supported by an
information mixing argument and simulations of Hodgkin Huxley population
dynamic networks with unidirectional connectivity and synaptic noise, call for
reexamining sources of correlated activity in cortex and shorter information
processing time scales.Comment: 8 pges, 6 figure
On the Use of Finite-Size Scaling to Measure Spin-Glass Exponents
Finite-size scaling (FSS) is a standard technique for measuring scaling
exponents in spin glasses. Here we present a critique of this approach,
emphasizing the need for all length scales to be large compared to microscopic
scales. In particular we show that the replacement, in FSS analyses, of the
correlation length by its asymptotic scaling form can lead to apparently good
scaling collapses with the wrong values of the scaling exponents.Comment: RevTeX, 5 page
A lattice gas model of II-VI(001) semiconductor surfaces
We introduce an anisotropic two-dimensional lattice gas model of metal
terminated II-IV(001) seminconductor surfaces. Important properties of this
class of materials are represented by effective NN and NNN interactions, which
result in the competition of two vacancy structures on the surface. We
demonstrate that the experimentally observed c(2x2)-(2x1) transition of the
CdTe(001) surface can be understood as a phase transition in thermal
equilbrium. The model is studied by means of transfer matrix and Monte Carlo
techniques. The analysis shows that the small energy difference of the
competing reconstructions determines to a large extent the nature of the
different phases. Possible implications for further experimental research are
discussed.Comment: 7 pages, 2 figure
Dynamical Replica Theory for Disordered Spin Systems
We present a new method to solve the dynamics of disordered spin systems on
finite time-scales. It involves a closed driven diffusion equation for the
joint spin-field distribution, with time-dependent coefficients described by a
dynamical replica theory which, in the case of detailed balance, incorporates
equilibrium replica theory as a stationary state. The theory is exact in
various limits. We apply our theory to both the symmetric- and the
non-symmetric Sherrington-Kirkpatrick spin-glass, and show that it describes
the (numerical) experiments very well.Comment: 7 pages RevTex, 4 figures, for PR
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