Sergey Rashkovskiy
Publications:
Antipova E. S., Rashkovskiy S. A.
Autoassociative Hamming Neural Network
2021, Vol. 17, no. 2, pp. 175193
Abstract
An autoassociative neural network is suggested which is based on the calculation of Hamming
distances, while the principle of its operation is similar to that of the Hopfield neural network.
Using standard patterns as an example, we compare the efficiency of pattern recognition for the
autoassociative Hamming network and the Hopfield network. It is shown that the autoassociative
Hamming network successfully recognizes standard patterns with a degree of distortion up to
40% and more than 60%, while the Hopfield network ceases to recognize the same patterns with
a degree of distortion of more than 25% and less than 75%. A scheme of the autoassociative
Hamming neural network based on McCulloch – Pitts formal neurons is proposed. It is shown
that the autoassociative Hamming network can be considered as a dynamical system which has
attractors that correspond to the reference patterns. The Lyapunov function of this dynamical
system is found and the equations of its evolution are derived.

Rashkovskiy S. A.
Hamiltonian Thermodynamics
2020, Vol. 16, no. 4, pp. 557580
Abstract
It is believed that thermodynamic laws are associated with random processes occurring
in the system and, therefore, deterministic mechanical systems cannot be described within the
framework of the thermodynamic approach. In this paper, we show that thermodynamics (or,
more precisely, a thermodynamicallylike description) can be constructed even for deterministic
Hamiltonian systems, for example, systems with only one degree of freedom. We show that
for such systems it is possible to introduce analogs of thermal energy, temperature, entropy,
Helmholtz free energy, etc., which are related to each other by the usual thermodynamic relations.
For the Hamiltonian systems considered, the first and second laws of thermodynamics are
rigorously derived, which have the same form as in ordinary (molecular) thermodynamics. It is
shown that for Hamiltonian systems it is possible to introduce the concepts of a thermodynamic
state, a thermodynamic process, and thermodynamic cycles, in particular, the Carnot cycle,
which are described by the same relations as their usual thermodynamic analogs.
