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2013
Impact Factor

    Sergey Rashkovskiy

    Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences

    Publications:

    Antipova E. S., Rashkovskiy S. A.
    Autoassociative Hamming Neural Network
    2021, Vol. 17, no. 2, pp.  175-193
    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.
    Keywords: autoassociative Hamming network, Hopfield network, iterative algorithm, pattern recognition, dynamical system, neurodynamics, attractors, stationary states
    Citation: Antipova E. S., Rashkovskiy S. A.,  Autoassociative Hamming Neural Network, Rus. J. Nonlin. Dyn., 2021, Vol. 17, no. 2, pp.  175-193
    DOI:10.20537/nd210204
    Rashkovskiy S. A.
    Hamiltonian Thermodynamics
    2020, Vol. 16, no. 4, pp.  557-580
    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 thermodynamically-like 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.
    Keywords: Hamiltonian system, adiabatic invariants, thermodynamics, temperature, heat, entropy, thermodynamic processes, the first and second laws of thermodynamics
    Citation: Rashkovskiy S. A.,  Hamiltonian Thermodynamics, Rus. J. Nonlin. Dyn., 2020, Vol. 16, no. 4, pp.  557-580
    DOI:10.20537/nd200403

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