1,019 research outputs found
Limit cycles of a perceptron
An artificial neural network can be used to generate a series of numbers. A
boolean perceptron generates bit sequences with a periodic structure. The
corresponding spectrum of cycle lengths is investigated analytically and
numerically; it has similarities with properties of rational numbers.Comment: LaTeX and 4 postscript pages of figure
Synchronization of random walks with reflecting boundaries
Reflecting boundary conditions cause two one-dimensional random walks to
synchronize if a common direction is chosen in each step. The mean
synchronization time and its standard deviation are calculated analytically.
Both quantities are found to increase proportional to the square of the system
size. Additionally, the probability of synchronization in a given step is
analyzed, which converges to a geometric distribution for long synchronization
times. From this asymptotic behavior the number of steps required to
synchronize an ensemble of independent random walk pairs is deduced. Here the
synchronization time increases with the logarithm of the ensemble size. The
results of this model are compared to those observed in neural synchronization.Comment: 10 pages, 7 figures; introduction changed, typos correcte
Phase Transitions of Neural Networks
The cooperative behaviour of interacting neurons and synapses is studied
using models and methods from statistical physics. The competition between
training error and entropy may lead to discontinuous properties of the neural
network. This is demonstrated for a few examples: Perceptron, associative
memory, learning from examples, generalization, multilayer networks, structure
recognition, Bayesian estimate, on-line training, noise estimation and time
series generation.Comment: Plenary talk for MINERVA workshop on mesoscopics, fractals and neural
networks, Eilat, March 1997 Postscript Fil
Mutual learning in a tree parity machine and its application to cryptography
Mutual learning of a pair of tree parity machines with continuous and
discrete weight vectors is studied analytically. The analysis is based on a
mapping procedure that maps the mutual learning in tree parity machines onto
mutual learning in noisy perceptrons. The stationary solution of the mutual
learning in the case of continuous tree parity machines depends on the learning
rate where a phase transition from partial to full synchronization is observed.
In the discrete case the learning process is based on a finite increment and a
full synchronized state is achieved in a finite number of steps. The
synchronization of discrete parity machines is introduced in order to construct
an ephemeral key-exchange protocol. The dynamic learning of a third tree parity
machine (an attacker) that tries to imitate one of the two machines while the
two still update their weight vectors is also analyzed. In particular, the
synchronization times of the naive attacker and the flipping attacker recently
introduced in [1] are analyzed. All analytical results are found to be in good
agreement with simulation results
Training a perceptron by a bit sequence: Storage capacity
A perceptron is trained by a random bit sequence. In comparison to the
corresponding classification problem, the storage capacity decreases to
alpha_c=1.70\pm 0.02 due to correlations between input and output bits. The
numerical results are supported by a signal to noise analysis of Hebbian
weights.Comment: LaTeX, 13 pages incl. 4 figures and 1 tabl
Synchronization of unidirectional time delay chaotic networks and the greatest common divisor
We present the interplay between synchronization of unidirectional coupled
chaotic nodes with heterogeneous delays and the greatest common divisor (GCD)
of loops composing the oriented graph. In the weak chaos region and for GCD=1
the network is in chaotic zero-lag synchronization, whereas for GCD=m>1
synchronization of m-sublattices emerges. Complete synchronization can be
achieved when all chaotic nodes are influenced by an identical set of delays
and in particular for the limiting case of homogeneous delays. Results are
supported by simulations of chaotic systems, self-consistent and mixing
arguments, as well as analytical solutions of Bernoulli maps.Comment: 7 pages, 5 figure
Genetic attack on neural cryptography
Different scaling properties for the complexity of bidirectional
synchronization and unidirectional learning are essential for the security of
neural cryptography. Incrementing the synaptic depth of the networks increases
the synchronization time only polynomially, but the success of the geometric
attack is reduced exponentially and it clearly fails in the limit of infinite
synaptic depth. This method is improved by adding a genetic algorithm, which
selects the fittest neural networks. The probability of a successful genetic
attack is calculated for different model parameters using numerical
simulations. The results show that scaling laws observed in the case of other
attacks hold for the improved algorithm, too. The number of networks needed for
an effective attack grows exponentially with increasing synaptic depth. In
addition, finite-size effects caused by Hebbian and anti-Hebbian learning are
analyzed. These learning rules converge to the random walk rule if the synaptic
depth is small compared to the square root of the system size.Comment: 8 pages, 12 figures; section 5 amended, typos correcte
Evaporation and Step Edge Diffusion in MBE
Using kinetic Monte-Carlo simulations of a Solid-on-Solid model we
investigate the influence of step edge diffusion (SED) and evaporation on
Molecular Beam Epitaxy (MBE). Based on these investigations we propose two
strategies to optimize MBE-growth. The strategies are applicable in different
growth regimes: during layer-by-layer growth one can reduce the desorption rate
using a pulsed flux. In three-dimensional (3D) growth the SED can help to grow
large, smooth structures. For this purpose the flux has to be reduced with time
according to a power law.Comment: 5 pages, 2 figures, latex2e (packages: elsevier,psfig,latexsym
Critical behavior for mixed site-bond directed percolation
We study mixed site-bond directed percolation on 2D and 3D lattices by using
time-dependent simulations. Our results are compared with rigorous bounds
recently obtained by Liggett and by Katori and Tsukahara. The critical
fractions and of sites and bonds are extremely well
approximated by a relationship reported earlier for isotropic percolation,
, where and are the critical fractions in
pure site and bond directed percolation.Comment: 10 pages, figures available on request from [email protected]
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