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Integro-differential Equations and Hereditary Systems: From Functional and Analytical Methods to Wavelets, Neural Networks, and Fuzzy Kernels

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Abstract

This review is oriented to the works of authors who have substantially contributed to the research area of integro-differential equations and hereditary systems both from the fundamental theoretical viewpoint and in the sense of the constructing of analytic tools and computational procedures. Works reflecting functional results in the specified area and describing analytic research methods and numerical algorithms are presented. Modern trends in the area of integro-differential equations related to wavelets, neural networks, and the theory of fuzzy sets are considered.

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  1. Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44-2 Ul. Vavilova, Moscow, 119333, Russian Federation

    A. K. Gorshenin

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Andrey Konstantinovich Gorshenin. Born in 1986. Candidate of Science (PhD) in physics and mathematics (Probability theory and mathematical statistics, Lomonosov Moscow State University, 2011); associate professor (Mathematical modeling, numerical methods, and software systems, 2017); leading scientist, Institute of Informatics Problems, Computer Science and Control Federal Research Center of the Russian Academy of Sciences; senior scientist, P.P. Shirshov Institute of Oceanology of the Russian Academy of Sciences. Specialist degree with honors in applied mathematics and computer science (Faculty of Computational Mathematics and Cybernetics of Lomonosov Moscow State University, 2008). Fields of research interest: probability theory, mathematical statistics, computer sciences, modelling of real processes, EM algorithms, method of moving separation of mixtures of probability distributions, Big Data, data visualization, mathematical modelling, neural networks. Author of 120 research papers and textbooks, 55 certificates of state registration of computer programs. Academic Expert of the National Research University Higher School of Economics (Moscow, Russia), Expert of the Russian Academy of Sciences (Moscow, Russia), External Expert of the Foundation for Assistance to Small Innovative Enterprises (Moscow, Russia), Member of the Skolkovo Expert Panel (Moscow, Russia). Member of the editorial board of peer-reviewed journal “Systems and Means оf Informatics.” Member of the Coordination Council for Youth Affairs in the Sphere of Science and Education under the Presidential Council for Science and Education. Awards: Presidential Grant for Government Support of Young Russian Scientists (2014–2025), Russian Academy of Sciences Medal with the Prize for Young Scientists (2015), Scholarship of the President of the Russian Federation for Young Scientists and Postgraduates (2018–2020). Grant supervisor (Russian Foundation for Basic Research, Presidential Grant for Government Support of Young Russian Scientists).

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Gorshenin, A.K. Integro-differential Equations and Hereditary Systems: From Functional and Analytical Methods to Wavelets, Neural Networks, and Fuzzy Kernels. Pattern Recognit. Image Anal. 28, 462–467 (2018). https://doi.org/10.1134/S1054661818030070

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