56 research outputs found
Dynamical properties of the Landau-Ginzburg model with long-range correlated quenched impurities
We investigate the critical dynamics of the time-dependent Landau-Ginzburg
model with non conserved n-component order parameter (Model A) in the presence
of long-range correlated quenched impurities. We use a special kind of
long-range correlations, previously introduced by Weinrib and Halperin. Using a
double expansion in \epsilon and \delta we calculate the critical exponent z up
to second order on the small parameters. We show that the quenched impurities
of this kind affect the critical dynamics already in first order of \epsilon
and \delta, leading to a relevant correction for the mean field value of the
exponent zComment: 7 pages, REVTEX, to be published in Phys. Rev.
A perturbative approach to non-linearities in the information carried by a two layer neural network
We evaluate the mutual information between the input and the output of a two
layer network in the case of a noisy and non-linear analogue channel. In the
case where the non-linearity is small with respect to the variability in the
noise, we derive an exact expression for the contribution to the mutual
information given by the non-linear term in first order of perturbation theory.
Finally we show how the calculation can be simplified by means of a
diagrammatic expansion. Our results suggest that the use of perturbation
theories applied to neural systems might give an insight on the contribution of
non-linearities to the information transmission and in general to the neuronal
dynamics.Comment: Accepted as a preprint of ICTP, Triest
A diagrammatic approach to study the information transfer in weakly non-linear channels
In a recent work we have introduced a novel approach to study the effect of
weak non-linearities in the transfer function on the information transmitted by
an analogue channel, by means of a perturbative diagrammatic expansion. We
extend here the analysis to all orders in perturbation theory, which allows us
to release any constraint concerning the magnitude of the expansion parameter
and to establish the rules to calculate easily the contribution at any order.
As an example we explicitly compute the information up to the second order in
the non-linearity, in presence of random gaussian connectivities and in the
limit when the output noise is not small. We analyze the first and second order
contributions to the mutual information as a function of the non-linearity and
of the number of output units. We believe that an extensive application of our
method via the analysis of the different contributions at distinct orders might
be able to fill a gap between well known analytical results obtained for linear
channels and the non trivial treatments which are required to study highly
non-linear channels.Comment: 17 pages, 3 figure
Time evolution of the extremely diluted Blume-Emery-Griffiths neural network
The time evolution of the extremely diluted Blume-Emery-Griffiths neural
network model is studied, and a detailed equilibrium phase diagram is obtained
exhibiting pattern retrieval, fluctuation retrieval and self-sustained activity
phases. It is shown that saddle-point solutions associated with fluctuation
overlaps slow down considerably the flow of the network states towards the
retrieval fixed points. A comparison of the performance with other three-state
networks is also presented.Comment: 8 pages, 5 figure
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