5,317 research outputs found
Dynamic mean-field and cavity methods for diluted Ising systems
We compare dynamic mean-field and dynamic cavity as methods to describe the
stationary states of dilute kinetic Ising models. We compute dynamic mean-field
theory by expanding in interaction strength to third order, and compare to the
exact dynamic mean-field theory for fully asymmetric networks. We show that in
diluted networks the dynamic cavity method generally predicts magnetizations of
individual spins better than both first order ("naive") and second order
("TAP") dynamic mean field theory
p>2 spin glasses with first order ferromagnetic transitions
We consider an infinite-range spherical p-spin glass model with an additional
r-spin ferromagnetic interaction, both statically using a replica analysis and
dynamically via a generating functional method. For r>2 we find that there are
first order transitions to ferromagnetic phases. For r<p there are two
ferromagnetic phases, one non-glassy replica symmetric and one exhibiting
glassy one-step replica symmetry breaking and aging, whereas for r>=p only the
replica symmetric phase exists.Comment: AMSLaTeX, 13 pages, 23 EPS figures ; one figure correcte
Response variability in balanced cortical networks
We study the spike statistics of neurons in a network with dynamically
balanced excitation and inhibition. Our model, intended to represent a generic
cortical column, comprises randomly connected excitatory and inhibitory leaky
integrate-and-fire neurons, driven by excitatory input from an external
population. The high connectivity permits a mean-field description in which
synaptic currents can be treated as Gaussian noise, the mean and
autocorrelation function of which are calculated self-consistently from the
firing statistics of single model neurons. Within this description, we find
that the irregularity of spike trains is controlled mainly by the strength of
the synapses relative to the difference between the firing threshold and the
post-firing reset level of the membrane potential. For moderately strong
synapses we find spike statistics very similar to those observed in primary
visual cortex.Comment: 22 pages, 7 figures, submitted to Neural Computatio
Entropy and typical properties of Nash equilibria in two-player games
We use techniques from the statistical mechanics of disordered systems to
analyse the properties of Nash equilibria of bimatrix games with large random
payoff matrices. By means of an annealed bound, we calculate their number and
analyse the properties of typical Nash equilibria, which are exponentially
dominant in number. We find that a randomly chosen equilibrium realizes almost
always equal payoffs to either player. This value and the fraction of
strategies played at an equilibrium point are calculated as a function of the
correlation between the two payoff matrices. The picture is complemented by the
calculation of the properties of Nash equilibria in pure strategies.Comment: 6 pages, was "Self averaging of Nash equilibria in two player games",
main section rewritten, some new results, for additional information see
http://itp.nat.uni-magdeburg.de/~jberg/games.htm
Hierarchical growing neural gas
“The original publication is available at www.springerlink.com”. Copyright Springer.This paper describes TreeGNG, a top-down unsupervised learning method that produces hierarchical classification schemes. TreeGNG is an extension to the Growing Neural Gas algorithm that maintains a time history of the learned topological mapping. TreeGNG is able to correct poor decisions made during the early phases of the construction of the tree, and provides the novel ability to influence the general shape and form of the learned hierarchy
Neural Relax
We present an algorithm for data preprocessing of an associative memory
inspired to an electrostatic problem that turns out to have intimate relations
with information maximization
Soliton-dynamical approach to a noisy Ginzburg-Landau model
We present a dynamical description and analysis of non-equilibrium
transitions in the noisy Ginzburg-Landau equation based on a canonical phase
space formulation. The transition pathways are characterized by nucleation and
subsequent propagation of domain walls or solitons. We also evaluate the
Arrhenius factor in terms of an associated action and find good agreement with
recent numerical optimization studies.Comment: 4 pages (revtex4), 3 figures (eps
The dynamics of quasi-isometric foliations
If the stable, center, and unstable foliations of a partially hyperbolic
system are quasi-isometric, the system has Global Product Structure. This
result also applies to Anosov systems and to other invariant splittings.
If a partially hyperbolic system on a manifold with abelian fundamental group
has quasi-isometric stable and unstable foliations, the center foliation is
without holonomy. If, further, the system has Global Product Structure, then
all center leaves are homeomorphic.Comment: 18 pages, 1 figur
Ionisation by quantised electromagnetic fields: The photoelectric effect
In this paper we explain the photoelectric effect in a variant of the
standard model of non relativistic quantum electrodynamics, which is in some
aspects more closely related to the physical picture, than the one studied in
[BKZ]: Now we can apply our results to an electron with more than one bound
state and to a larger class of electron-photon interactions. We will specify a
situation, where ionisation probability in second order is a weighted sum of
single photon terms. Furthermore we will see, that Einstein's equality
for the maximal kinetic energy of
the electron, energy of the photon and ionisation gap
is the crucial condition for these single photon terms to be nonzero.Comment: 59 pages, LATEX2
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