873 research outputs found

### 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

### 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

### Pulses of chaos synchronization in coupled map chains with delayed transmission

Pulses of synchronization in chaotic coupled map lattices are discussed in
the context of transmission of information. Synchronization and
desynchronization propagate along the chain with different velocities which are
calculated analytically from the spectrum of convective Lyapunov exponents.
Since the front of synchronization travels slower than the front of
desynchronization, the maximal possible chain length for which information can
be transmitted by modulating the first unit of the chain is bounded.Comment: 4 pages, 6 figures, updated version as published in PR

### Dynamics of Interacting Neural Networks

The dynamics of interacting perceptrons is solved analytically. For a
directed flow of information the system runs into a state which has a higher
symmetry than the topology of the model. A symmetry breaking phase transition
is found with increasing learning rate. In addition it is shown that a system
of interacting perceptrons which is trained on the history of its minority
decisions develops a good strategy for the problem of adaptive competition
known as the Bar Problem or Minority Game.Comment: 9 pages, 3 figures; typos corrected, content reorganize

### 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

### 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

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