3,099 research outputs found
Magic number 7 2 in networks of threshold dynamics
Information processing by random feed-forward networks consisting of units
with sigmoidal input-output response is studied by focusing on the dependence
of its outputs on the number of parallel paths M. It is found that the system
leads to a combination of on/off outputs when , while for , chaotic dynamics arises, resulting in a continuous distribution of
outputs. This universality of the critical number is explained by
combinatorial explosion, i.e., dominance of factorial over exponential
increase. Relevance of the result to the psychological magic number
is briefly discussed.Comment: 6 pages, 5 figure
Avalanches in self-organized critical neural networks: A minimal model for the neural SOC universality class
The brain keeps its overall dynamics in a corridor of intermediate activity
and it has been a long standing question what possible mechanism could achieve
this task. Mechanisms from the field of statistical physics have long been
suggesting that this homeostasis of brain activity could occur even without a
central regulator, via self-organization on the level of neurons and their
interactions, alone. Such physical mechanisms from the class of self-organized
criticality exhibit characteristic dynamical signatures, similar to seismic
activity related to earthquakes. Measurements of cortex rest activity showed
first signs of dynamical signatures potentially pointing to self-organized
critical dynamics in the brain. Indeed, recent more accurate measurements
allowed for a detailed comparison with scaling theory of non-equilibrium
critical phenomena, proving the existence of criticality in cortex dynamics. We
here compare this new evaluation of cortex activity data to the predictions of
the earliest physics spin model of self-organized critical neural networks. We
find that the model matches with the recent experimental data and its
interpretation in terms of dynamical signatures for criticality in the brain.
The combination of signatures for criticality, power law distributions of
avalanche sizes and durations, as well as a specific scaling relationship
between anomalous exponents, defines a universality class characteristic of the
particular critical phenomenon observed in the neural experiments. The spin
model is a candidate for a minimal model of a self-organized critical adaptive
network for the universality class of neural criticality. As a prototype model,
it provides the background for models that include more biological details, yet
share the same universality class characteristic of the homeostasis of activity
in the brain.Comment: 17 pages, 5 figure
Influence of Refractory Periods in the Hopfield model
We study both analytically and numerically the effects of including
refractory periods in the Hopfield model for associative memory. These periods
are introduced in the dynamics of the network as thresholds that depend on the
state of the neuron at the previous time. Both the retrieval properties and the
dynamical behaviour are analyzed.Comment: Revtex, 7 pages, 7 figure
Critical Line in Random Threshold Networks with Inhomogeneous Thresholds
We calculate analytically the critical connectivity of Random Threshold
Networks (RTN) for homogeneous and inhomogeneous thresholds, and confirm the
results by numerical simulations. We find a super-linear increase of with
the (average) absolute threshold , which approaches for large , and show that this asymptotic scaling is
universal for RTN with Poissonian distributed connectivity and threshold
distributions with a variance that grows slower than . Interestingly, we
find that inhomogeneous distribution of thresholds leads to increased
propagation of perturbations for sparsely connected networks, while for densely
connected networks damage is reduced; the cross-over point yields a novel,
characteristic connectivity , that has no counterpart in Boolean networks.
Last, local correlations between node thresholds and in-degree are introduced.
Here, numerical simulations show that even weak (anti-)correlations can lead to
a transition from ordered to chaotic dynamics, and vice versa. It is shown that
the naive mean-field assumption typical for the annealed approximation leads to
false predictions in this case, since correlations between thresholds and
out-degree that emerge as a side-effect strongly modify damage propagation
behavior.Comment: 18 figures, 17 pages revte
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