J.G. Taylor – författare

The subject of Neural Networks is being seen to be coming of age, after its initial inception 50 years ago in the seminal work of McCulloch and Pitts. It is proving to be valuable in a wide range of academic disciplines and in important applications in industrial and business tasks. The progress being made in each approach is considerable. Nevertheless, both stand in need of a theoretical framework of explanation to underpin their usage and to allow the progress being made to be put on a firmer footing.This book aims to strengthen the foundations in its presentation of mathematical approaches to neural networks. It is through these that a suitable explanatory framework is expected to be found. The approaches span a broad range, from single neuron details to numerical analysis, functional analysis and dynamical systems theory. Each of these avenues provides its own insights into the way neural networks can be understood, both for artificial ones and simplified simulations. As a whole, the publication underlines the importance of the ever-deepening mathematical understanding of neural networks.

This book is the product of a 15-month intensive investigation of the European artificial network scene, together with a view of the broader framework of the subject in a world context. It could not have been completed in such a remarkably short time, and so effectively, without the dedicated efforts of Louise Turner, the DEANNA secretary, and Geoff Chappell, the DEANNA researcher, at the Centre for Neural Networks, King''s College, London. I would like to take this opportunity to thank them for their heroic efforts. I would also like to thank my colleagues in the Centre and in the Mathematics Department, especially Mark Plumbley, Michael Reiss and Trevor Clarkson for all their help and encouragement, Denise Gorse of University College London, for allowing use of her lecture notes as a basis for the tutorial and the DEANNA partners for the part they played. Finally I would like to acknowledge the European Community support, and especially Mike Coyle for his trenchant comments during the carrying out of the work. March 1993 J. G. Taylor CONTENTS PART I: SETTING THE SCENE Chapter 1: DEANNA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 . 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . 2 The Geographical Dimension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 1. 3 The Industrial Dimension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1 . 4 The Plan for Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . 6 Chapter 2: Neural Net Demonstrators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2. 1 The Status of Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2. 2 Reasons for the Employment of Neural Networks . . . . . . . . . . . . . . . . . . . 9 2. 3 Neural Network Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2. 4 Areas of Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2. 5 Typical Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

This volume contains the papers from the first British Neural Network Society meeting held at Queen Elizabeth Hall, King''s College, London on 18--20 April 1990. The meeting was sponsored by the London Mathemati­ cal Society. The papers include introductory tutorial lectures, invited, and contributed papers. The invited contributions were given by experts from the United States, Finland, Denmark, Germany and the United Kingdom. The majority of the contributed papers came from workers in the United Kingdom. The first day was devoted to tutorials. Professor Stephen Grossberg was a guest speaker on the first day giving a thorough introduction to his Adaptive Resonance Theory of neural networks. Subsequent tutorials on the first day covered dynamical systems and neural networks, realistic neural modelling, pattern recognition using neural networks, and a review of hardware for neural network simulations. The contributed papers, given on the second day, demonstrated the breadth of interests of workers in the field. They covered topics in pattern recognition, multi-layer feedforward neural networks, network dynamics, memory and learning. The ordering of the papers in this volume is as they were given at the meeting. On the final day talks were given by Professor Kohonen (on self organising maps), Professor Kurten (on the dynamics of random and structured nets) and Professor Cotterill (on modelling the visual cortex). Dr A. Mayes presented a paper on various models for amnesia. The editors have taken the opportunity to include a paper of their own which was not presented at the meeting.

This volume consists of proceedings of the one-day conference on "Coupled Oscillating Neurons" held at King''s College, London on December 13th, 1990. The subject is currently of increasing interest to neurophysiologists, neural network researchers, applied mathematicians and physicists. The papers attempt to cover the major areas of the subject, as the titles indicate. It is hoped that the appearance of the papers (some of which have been updated since their original presentation) indicates why the subject is becoming of great excitement. A better understanding of coupled oscillating neurons may well hold the key to a clearer appreciation of the manner in which neural networks composed of such elements can control complex behaviour from the heart to consciousness. December 1991 J.G. Taylor King''s College, London C.L.T. Mannion CONTENTS Contributors....... ..................... .......... .......................... .................... ix Introduction to Nonlinear Oscillators I. Stewart ....................................................................................... . Identical Oscillator Networks with Symmetry P.B. Ashwin .................................................................................... 21 Bifurcating Neurones AV. Holden, J. Hyde, M.A Muhamad, H.G. Zhang....................... 41 A Model for Low Threshold Oscillations in Neurons J.L. Hindmarsh, R.M. Rose ............................................................ 81 Information Processing by Oscillating Neurons C.L. T. Mannion, J.G. Taylor ........................................................... 100 Gamma Oscillations, Association and Consciousness R.M.J. Cotterill, C. Nielsen ............................................................. 117 Modelling of Cardiac Rhythm: From Single Celis toMassive Networks D. Noble, J. C. Denyer, H.F. Brown, R. Winslow, A Kimball .......... 1 32 CONTRIBUTORS Ashwin, P.B. Mathematics Institute, University of Warwick, Coventry, CV4 7 AL, UK Brown, H.F.

Neural Network Dynamics is the latest volume in the Perspectives in Neural Computing series. It contains papers presented at the 1991 Workshop on Complex Dynamics in Neural Networks, held at IIASS in Vietri, Italy. The workshop encompassed a wide range of topics in which neural networks play a fundamental role, and aimed to bridge the gap between neural computation and computational neuroscience. The papers - which have been updated where necessary to include new results - are divided into four sections, covering the foundations of neural network dynamics, oscillatory neural networks, as well as scientific and biological applications of neural networks. Among the topics discussed are: A general analysis of neural network activity; Descriptions of various network architectures and nodes; Correlated neuronal firing; A theoretical framework for analyzing the behaviour of real and simulated neuronal networks; The structural properties of proteins; Nuclear phenomenology; Resonance searches in high energy physics; The investigation of information storage; Visual cortical architecture; Visual processing. Neural Network Dynamics is the first volume to cover neural networks and computational neuroscience in such detail. Although it is primarily aimed at researchers and postgraduate students in the above disciplines, it will also be of interest to researchers in electrical engineering, medicine, psychology and philosophy.

Neural Network Applications contains the 12 papers presented at the second British Neural Network Society Meeting (NCM ''91) held at King''s College London on 1st October 1991. The meeting was sponsored by the Centre for Neural Networks, King''s College, and the British Neural Network Society, and was also part of the DEANNA ESPRIT programme. The papers reflect the wide spectrum of neural network applications that are currently being attempted in industry and medicine. They cover medical diagnosis, robotics, plant control, machine learning, and visual inspection, as well as more general discussions on net learning and knowledge representation. The breadth and depth of coverage is a sign of the health of the subject, as well as indicating the importance of neural network developments in industry and the manner in which the applications are progressing. Among the actual topics covered are: Learning algorithms - theory and practice; A review of medical diagnostic applications of neural networks; Simulated ultrasound tomographic imaging of defects; Linear quadtrees for neural network based position invariant pattern recognition; The pRTAM as a hardware-realisable neuron; The cognitive modalities ("CM") system of knowledge representation - the DNA of neural networks? This volume provides valuable reading for all those attempting to apply neural networks, as well as those entering the field, including researchers and postgraduate students in computational neuroscience, neurobiology, electrical engineering, computer science, mathematics, and medicine.

This volume contains the papers from the first British Neural Network Society meeting held at Queen Elizabeth Hall, King's College, London on 18--20 April 1990. The meeting was sponsored by the London Mathemati­ cal Society. The papers include introductory tutorial lectures, invited, and contributed papers. The invited contributions were given by experts from the United States, Finland, Denmark, Germany and the United Kingdom. The majority of the contributed papers came from workers in the United Kingdom. The first day was devoted to tutorials. Professor Stephen Grossberg was a guest speaker on the first day giving a thorough introduction to his Adaptive Resonance Theory of neural networks. Subsequent tutorials on the first day covered dynamical systems and neural networks, realistic neural modelling, pattern recognition using neural networks, and a review of hardware for neural network simulations. The contributed papers, given on the second day, demonstrated the breadth of interests of workers in the field. They covered topics in pattern recognition, multi-layer feedforward neural networks, network dynamics, memory and learning. The ordering of the papers in this volume is as they were given at the meeting. On the final day talks were given by Professor Kohonen (on self organising maps), Professor Kurten (on the dynamics of random and structured nets) and Professor Cotterill (on modelling the visual cortex). Dr A. Mayes presented a paper on various models for amnesia. The editors have taken the opportunity to include a paper of their own which was not presented at the meeting.

This volume consists of proceedings of the one-day conference on "Coupled Oscillating Neurons" held at King's College, London on December 13th, 1990. The subject is currently of increasing interest to neurophysiologists, neural network researchers, applied mathematicians and physicists. The papers attempt to cover the major areas of the subject, as the titles indicate. It is hoped that the appearance of the papers (some of which have been updated since their original presentation) indicates why the subject is becoming of great excitement. A better understanding of coupled oscillating neurons may well hold the key to a clearer appreciation of the manner in which neural networks composed of such elements can control complex behaviour from the heart to consciousness. December 1991 J.G. Taylor King's College, London C.L.T. Mannion CONTENTS Contributors....... ..................... .......... .......................... .................... ix Introduction to Nonlinear Oscillators I. Stewart ....................................................................................... . Identical Oscillator Networks with Symmetry P.B. Ashwin .................................................................................... 21 Bifurcating Neurones AV. Holden, J. Hyde, M.A Muhamad, H.G. Zhang....................... 41 A Model for Low Threshold Oscillations in Neurons J.L. Hindmarsh, R.M. Rose ............................................................ 81 Information Processing by Oscillating Neurons C.L. T. Mannion, J.G. Taylor ........................................................... 100 Gamma Oscillations, Association and Consciousness R.M.J. Cotterill, C. Nielsen ............................................................. 117 Modelling of Cardiac Rhythm: From Single Celis toMassive Networks D. Noble, J. C. Denyer, H.F. Brown, R. Winslow, A Kimball .......... 1 32 CONTRIBUTORS Ashwin, P.B. Mathematics Institute, University of Warwick, Coventry, CV4 7 AL, UK Brown, H.F.

Neural Network Dynamics is the latest volume in the Perspectives in Neural Computing series. It contains papers presented at the 1991 Workshop on Complex Dynamics in Neural Networks, held at IIASS in Vietri, Italy. The workshop encompassed a wide range of topics in which neural networks play a fundamental role, and aimed to bridge the gap between neural computation and computational neuroscience. The papers - which have been updated where necessary to include new results - are divided into four sections, covering the foundations of neural network dynamics, oscillatory neural networks, as well as scientific and biological applications of neural networks. Among the topics discussed are: A general analysis of neural network activity; Descriptions of various network architectures and nodes; Correlated neuronal firing; A theoretical framework for analyzing the behaviour of real and simulated neuronal networks; The structural properties of proteins; Nuclear phenomenology; Resonance searches in high energy physics; The investigation of information storage; Visual cortical architecture; Visual processing. Neural Network Dynamics is the first volume to cover neural networks and computational neuroscience in such detail. Although it is primarily aimed at researchers and postgraduate students in the above disciplines, it will also be of interest to researchers in electrical engineering, medicine, psychology and philosophy.

Neural Network Applications contains the 12 papers presented at the second British Neural Network Society Meeting (NCM '91) held at King's College London on 1st October 1991. The meeting was sponsored by the Centre for Neural Networks, King's College, and the British Neural Network Society, and was also part of the DEANNA ESPRIT programme. The papers reflect the wide spectrum of neural network applications that are currently being attempted in industry and medicine. They cover medical diagnosis, robotics, plant control, machine learning, and visual inspection, as well as more general discussions on net learning and knowledge representation. The breadth and depth of coverage is a sign of the health of the subject, as well as indicating the importance of neural network developments in industry and the manner in which the applications are progressing. Among the actual topics covered are: Learning algorithms - theory and practice; A review of medical diagnostic applications of neural networks; Simulated ultrasound tomographic imaging of defects; Linear quadtrees for neural network based position invariant pattern recognition; The pRTAM as a hardware-realisable neuron; The cognitive modalities ("CM") system of knowledge representation - the DNA of neural networks? This volume provides valuable reading for all those attempting to apply neural networks, as well as those entering the field, including researchers and postgraduate students in computational neuroscience, neurobiology, electrical engineering, computer science, mathematics, and medicine.