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Page Iiii Margarita Kuzmina, Eduard Manykin, Evgeny Grichuk i i Margarita Kuzmina, Eduard Manykin, Evgeny Grichuk: Oscillatory Neural Networks — 2013/10/11 — 11:18 — page i i i Margarita Kuzmina, Eduard Manykin, Evgeny Grichuk Oscillatory Neural Networks i i i i i i Margarita Kuzmina, Eduard Manykin, Evgeny Grichuk: Oscillatory Neural Networks — 2013/10/11 — 11:18 — page ii i i i i i i i i Margarita Kuzmina, Eduard Manykin, Evgeny Grichuk: Oscillatory Neural Networks — 2013/10/11 — 11:18 — page iii i i Margarita Kuzmina, Eduard Manykin, Evgeny Grichuk Oscillatory Neural Networks | In Problems of Parallel Information Processing i i i i i i Margarita Kuzmina, Eduard Manykin, Evgeny Grichuk: Oscillatory Neural Networks — 2013/10/11 — 11:18 — page iv i i Mathematics Subject Classification 2010 68T45, 68T05, 68T40, 68T42, 93C10, 93C15, 93C40, 34H20 Physics and Astronomy Classification Scheme 2010 05.45.Xt, 87.10.-e, 87.18.Sn, 87.85.dq, 87.85.St, 42.65.-k, 42.30.Tz Authors Margarita Kuzmina, Ph. D. Russian Academy of Sciences Keldysh Institute of Applied Mathematics Miusskaya Sq. 4 125047 Moscow Russia [email protected] Prof. Dr. habil. Eduard Manykin National Research Center Kurchatov Institute Kurchatov Sq. 1 123182 Moscow Russia [email protected] Evgeny Grichuk, Ph. D. National Research Center Kurchatov Institute Kurchatov Sq. 1 123182 Moscow Russia [email protected] ISBN 978-3-11-026835-5 e-ISBN 978-3-11-026920-8 Library of Congress Cataloging-in-Publication Data A CIP catalog record for this book has been applied for at the Library of Congress. Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at http://dnb.dnb.de. © 2014 Walter de Gruyter GmbH, Berlin/Boston Cover image: Thinkstock/iStock Typesetting: le-tex publishing services GmbH, Leipzig Printing and binding: Hubert & Co. GmbH & Co. KG, Göttingen ♾Printed on acid-free paper Printed in Germany www.degruyter.com i i i i i i Margarita Kuzmina, Eduard Manykin, Evgeny Grichuk: Oscillatory Neural Networks — 2013/10/11 — 11:18 — page v i i Preface The last decade was marked by highly increased interest to the study of human brain functioning. Understanding of the human brain has been recently claimed as one of the greatest problems of 21st century science. An integrated brain understanding would offer great benefits for computational mathematics, medicine, and intellectual robotics dealing with creation of intelligent machines capable of thinking, learning, and demonstrating human reactions. Intentions to create a complex large-scale multilevel model of the human brain, based on physiologically accurate imitations of brain structure performance, were de­ clared repeatedly. In particular, in the frames of the famous interdisciplinary Blue Brain Project, started in 2005, a physiologically detailed rat brain neocortical column consisting of 1.2 × 106 neurons and 109 synapses was created in 2011. Another de­ tailed large-scale model of a mammalian brain thalamocortical system, comprising 1011 spiking neurons and almost 1015 synapses, was created in 2008 at the Neuro­ science Institute, San Diego, CA, USA. These achievements in computer modeling of the brain structures can naturally provide inspirations for new research in related ar­ eas, such as neuroinformatics, communication theory, neuroscience, medicine, and neurorobotics. Nowadays there is a variety of programs on creation of artificial brains for intelligent “android” robots emulating the human brain. The performance of cre­ ated artificial brains should be tested (and compared with the human brain perfor­ mance) in a representative set of tasks. The task of image recognition belongs to the simplest type of such tasks. The aspects of human consciousness should be tradition­ ally expertized using the so-called Alan Turing test, initiated in the early 1950s. There are claims, based particularly on quick growth trends of computer power, that the whole brain emulation using conventional computers could be done by 2025. Further extensive brain studies will definitely stimulate the development of new brain-inspired parallel adaptive computational algorithms. Neuromorphic methods of image and signal processing based on the brain visual cortex performance and its ac­ tivity-dependent plasticity are of particular interest. The scope of problems concern­ ing the brain memory also remains a challenging and interesting topic. Although it has been understood that the source of the brain memory consists in synaptic con­ nections change, the character of memory data representation in the brain (memory structure) continues to remain a big puzzle. The information processing in the brain is realized via spatiotemporal dynam­ ics of patterns of excitation in neuronal ensembles arising by means of neuron in­ teractions. Learning processes, equipped with the brain memory and self-organizing ability, modify the pattern structure and dynamics. A combination of analytical math­ ematical tools (such as approaches from statistical physics and information geome­ try) and the development of artificial neural networks (ANNs) models and associated learning algorithms constitute the theoretical background for the investigation of the i i i i i i Margarita Kuzmina, Eduard Manykin, Evgeny Grichuk: Oscillatory Neural Networks — 2013/10/11 — 11:18 — page vi i i vi |Preface brain structures functioning. The design of oscillatory neural networks, a special kind of ANN models, provides a valuable contribution into the elucidation of the basic prin­ ciples of the brain performance, because they allow us to study capabilities and limi­ tations of synchronization-based information processing. The book is devoted to the description and analysis of various oscillatory neural network models. Neuromorphic dynamical synchronization-based methods of infor­ mation processing can be developed based on oscillatory network models with con­ trollable synchronization. Besides, recurrent oscillatory networks of associative mem­ ory can be designed. The oscillatory associative memory networks, closely related to analogous networks of complex-valued neurons, possess better memory characteris­ tics compared with those inherent to recurrent associative memory networks of formal neurons, namely the higher memory storage capacity and poor extraneous memory. The book consists of six chapters. The introductory material in the first chapter briefly presents the necessary data on the human brain and outlines the basic types of ANN models, the widely used classical and modern learning algorithms for ANN, and the well-known models of oscillatory neural networks. A short overview of mod­ ern branches of ANN theory, such as complicated small-world networks, multi-agent systems, and cognitive dynamical systems, is given, and brief information about bio­ logically accurate large-scale computer models of the brain structures is also included into the first chapter. The second chapter concerns oscillatory network versions of recurrent associative memory networks (so-called attractor oscillatory networks). The computation proce­ dure executed by this type of networks is realized via network state relaxation into the vicinity of a stable attractor of network dynamics. The original result, obtained by the authors, related to the construction and analysis of associative memory networks of limit-cycle oscillators is presented. Chapter 2 also contains the most significant re­ sults of the macrodynamical approach for large-scale recurrent neural networks of as­ sociative memory, including the authors’ original results. A short review of the most important results on complex-valued neural networks of associative memory, closely related to oscillatory associative memory networks, is also included in the chapter. A series of oscillatory network models with synchronization-based performance are described in Chapter 3. In particular, the famous oscillatory network LEGION, the three-dimensional biologically plausible network model by Li imitating the brain vi­ sual cortex performance, and a three-dimensional oscillatory network model for im­ age processing tasks developed by the authors are included. Besides, the oscillatory network models for the separation of mixed sound fluxes and for odor recognition, ex­ ploiting versions of dynamical binding principle, and two models including modeling of visual attention are presented in the chapter. A neuromorphic oscillatory network model with controllable synchronization and self-organized performance, developed by the authors, for image processing tasks is described in Chapter 4. It is a spatially distributed network of limit-cycle oscillators lo­ calized at the nodes of a two-dimensional lattice isomorphic with an image pixel array. i i i i i i Margarita Kuzmina, Eduard Manykin, Evgeny Grichuk: Oscillatory Neural Networks — 2013/10/11 — 11:18 — page vii i i Preface | vii Single oscillator dynamics is tunable by the brightness value of the image pixel corre­ sponding to the oscillator. A number of network coupling principles were constructed for different image processing tasks. The model demonstrates a variety of capabili­ ties, such as brightness segmentation of real multipixel gray-level images, color image segmentation, selective image segmentation, and the simplest version of visual scene analysis – successive selection of spatially separated fragments of a visual scene. Chapter 5 contains information on the photon echo effect that interestingly
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