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Two neural networks that are trained on their mutual output synchronize to an identical time dependant weight vector. This novel phenomenon can be used for creation of a secure cryptographic secret-key using a public channel. Several models for this cryptographic system have been suggested, and have been tested for their security under different(More)
— Finding the entropy rate of Hidden Markov Processes is an active research topic, of both theoretical and practical importance. A recently used approach is studying the asymptotic behavior of the entropy rate in various regimes. In this paper we generalize and prove a previous conjecture relating the entropy rate to entropies of finite systems. Building on(More)
—Discrete-input two-dimensional (2-D) Gaussian channels with memory represent an important class of systems, which appears extensively in communications and storage. In spite of their widespread use, the workings of 2-D channels are still very much unknown. In this work, we try to explore their properties from the perspective of estimation theory and(More)
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(More)
— A recent result presented the expansion for the entropy rate of a Hidden Markov Process (HMP) as a power series in the noise variable ǫ. The coefficients of the expansion around the noiseless (ǫ = 0) limit were calculated up to 11th order, using a conjecture that relates the entropy rate of a HMP to the entropy of a process of finite length (which is(More)
A contact map is a simple representation of the structure of proteins and other chain-like macro-molecules. This representation is quite amenable to numerical studies of folding. We show that the number of contact maps corresponding to the possible configurations of a polypeptide chain of N amino acids, represented by (N − 1)-step self avoiding walks on a(More)
We calculate the Shannon entropy rate of a binary Hidden Markov Process (HMP), of given transition rate and noise (emission), as a series expansion in. The first two orders are calculated exactly. We then evaluate, for finite histories, simple upper-bounds of Cover and Thomas. Surprisingly, we find that for a fixed order k and history of n steps, the bounds(More)
We study chaotic synchronization in networks with time-delayed coupling. We introduce the notion of strong and weak chaos, distinguished by the scaling properties of the maximum Lyapunov exponent within the synchronization manifold for large delay times, and relate this to the condition for stable or unstable chaotic synchronization, respectively. In(More)