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Table of Contents


Preface

Neural network refers to a multifaceted representation of neural activity constituted by the essence of neurobiology, the framework of cognitive science, the art of computation, the physics of statistical mechanics, and the concepts of cybernetics. Inputs from these diverse disciplines have widened the scope of neural network modeling with the emergence of artificial neural networks and their engineering applications to pattern recognition and adaptive systems which mimic the biological neural complex in being “trained to learn from examples”.

Neurobiology which enclaves the global aspects of anatomy, physiology, and biochemistry of the neural complex both at microscopic (cellular) levels and at macroscopic structures of brain and nervous system constitutes the primary base upon which the theory and modeling of neural networks have been developed traditionally. The imminence of such neural models refers to the issues related to understanding the brain functions and the inherent (as well as intriguing) self-adaptive control abilities of the nervous system as dictated by the neurons.

The cognitive and learning features of neural function attracted psychologists to probe into the intricacies of the neural system in conjunction with similar efforts of neurobiologists. In this framework, philosophical viewpoints on neural networks have also been posed concurrently to query whether machines could be designed to perform cognitive functions akin to living systems.

Computer science vis-a-vis neural modeling stemmed from the underlying computational and memory capabilities of interconnected neural units and is concerned with the development of so-called artificial neural networks which mimic the functional characteristics of the web of real neurons and offer computational models inspired by an analogy with the neural network of the human brain.

Since the neuronal structure has been identified as a system of interconnected units with a collective behavior, physicists could extend the concepts of statistical mechanics to the neural complex with the related spin-glass theory which describes the interactions and collective attributes of magnetic spins at the atomic and/or molecular level.

Yet another phenomenological consideration of the complex neural network permits modeling in the framework of cybernetic* which is essentially “a science of optimal control over complex processes and systems”.


* The concepts of cybernetics adopted in this book refer to the global self-organizing aspects of neural networks which experience optimal reaction to an external stimulus and are not just restricted to or exclusively address the so-called cybernetic networks with maximally asymmetric feed-forward characteristics as conceived by Müller and Reinhardt [1].

Thus, modeling neural networks has different perspectives. It has different images as we view them through the vagaries of natural and physical sciences. Such latitudes of visualizing the neural complex and the associated functions have facilitated in the past the emergence of distinct models in each of the aforesaid disciplines. All these models are, however, based on the following common characteristics of real neurons and their artificial counterparts:

  A neural network model represents an analogy of the human brain and the associated neural complex — that is, the neural network is essentially a neuromorphic configuration.
  The performance of a neural network model is equitable to real neurons in terms of being a densely interconnected system of simple processing units (cells).
  The basic paradigm of the neural computing model corresponds to a distributed massive parallelism.
  Such a model bears associative memory capabilities and relies on learning through adaptation of connection strengths between the processing units.
  Neural network models have the memory distributed totally over the network (via connection strengths) facilitating massively parallel executions. As a result of this massive distribution of computational capabilities, the so-called von Neumann bottleneck is circumvented.
  Neural network vis-a-vis real neural complex refers to a connectionist model — that is, the performance of the network through connections is more significant than the computational dynamics of individual units (processors) themselves.

The present and the past decades have seen a wealth of published literature on neural networks and their modelings. Of these, the books in general emphasize the biological views and cognitive features of neural complex and engineering aspects of developing computational systems and intelligent processing techniques on the basis of depicting the nonlinear, adaptive, and parallel processing considerations identical to real neuron activities supplemented by the associated microelectronics and information sciences.

The physical considerations in modeling the collective activities of the neural complex via statistical mechanics have appeared largely as sections of books or as collections of conference papers. Notwithstanding the fact that such physical models fortify the biological, cognitive, and information-science perspectives on the neural complex and augment a better understanding of underlying principles, dedicated books covering the salient aspects of bridging the concepts of physics (or statistical mechanics) and neural activity are rather sparse.

Another lacuna in the neural network literature is the nonexistence of pertinent studies relating the neural activities and the principles of cybernetics, though it has been well recognized that cybernetics is a “science which fights randomness, emphasizing the idea of control counteracting disorganization and destruction caused by diverse random factors”. The central theme of cybernetics thus being the process automation of self-control in complex automata (in the modern sense), aptly applies to the neuronal activities as well. (In a restricted sense, a term cybernetic network had been proposed by Müller and Reinhardt [1] to represent just the feed-forward networks with anisotropic [or maximally unidirectional], asymmetric synaptic connections. However, it is stressed here that such cybernetic networks are only subsets of the global interconnected units which are more generally governed by the self-organizing optimal control or reaction to an external stimulus.)

This book attempts to fill the niche in the literature by portraying the concepts of statistical mechanics and cybernetics as bases for neural network modeling cohesively. It is intended to bring together the scientists who boned up on mathematical neurobiology and engineers who design the intelligent automata on the basis of collection, conversion, transmission, storage, and retrieval of information embodied by the concepts of neural networks to understand the physics of collective behavior pertinent to neural elements and the self-control aspects of neurocybernetics.

Further, understanding the complex activities of communication and control pertinent to neural networks as conceived in this book penetrates into the concept of “organizing an object (the lowering of its entropy) ... by applying the methods of cybernetics ...”. This represents a newer approach of viewing through the classical looking mirror of the neural complex and seeing the image of future information processing and complex man-made automata with clarity sans haziness.

As mentioned earlier, the excellent bibliography that prevails in the archival literature on neuronal activity and the neural network emphasizes mostly the biological aspects, cognitive perspectives, network considerations and computational abilities of the neural system. In contrast, this book is intended to outline the statistical mechanics considerations and cybernetic view points pertinent to the neurophysiological complex cohesively with the associated concourse of stochastical events and phenomena. The neurological system is a complex domain where interactive episodes are inevitable. The physics of interaction, therefore, dominates and is encountered in the random entity of neuronal microcosm. Further, the question of symmetry (or asymmetry?) that blends with the randomness of neural assembly is viewed in this book vis-a-vis the disorganizing effect of chance (of events) counteracted by the organizing influence of self-controlling neurocellular automata.

To comprehend and summarize the pertinent details, this book is written and organized in eight chapters:

Chapter 1: Introduction
Chapter 2: Neural and Brain Complex
Chapter 3: Concepts of Mathematical Neurobiology
Chapter 4: Pseudo-Thermodynamics of Neural Activity
Chapter 5: The Physics of Neural Activity: A Statistical Mechanics Perspective
Chapter 6: Stochastical Dynamics of the Neural Complex
Chapter 7: Neural Field Theory: Quasiparticle Dynamics and Wave Mechanics Analogies of Neural Networks
Chapter 8: Informatic Aspects of Neurocybernetics

The topics addressed in Chapters 1 through 3 are introductory considerations on neuronal activity and neural networks while the subsequent chapters outline the stochastical aspects with the associated mathematics, physics, and biological details concerning the neural system. The theoretical perspectives and explanatory projections presented thereof are somewhat unorthodox in that they portray newer considerations and battle with certain conventional dogma pursued hitherto in the visualization of neuronal interactions. Some novel features of this work are:

  A cohesive treatment of neural biology and physicomathematical considerations in neurostochastical perspectives.
  A critical appraisal of the interaction physics pertinent to magnetic spins, applied as an analogy of neuronal interactions; and searching for alternative interaction model(s) to represent the interactive neurocellular information traffic and entropy considerations.
  An integrated effort to apply the concepts of physics such as wave mechanics and particle dynamics for an analogous representation and modeling the neural activity.
  Viewing the complex cellular automata as a self-controlling organization representing a system of cybernetics.
  Analyzing the informatic aspects of the neurocybernetic complex.

This book is intended as a supplement and as a self-study guide to those who have the desire to understand the physical reasonings behind neurocellular activities and pursue advanced research in theoretical modeling of neuronal activity and neural network architecture. This book could be adopted for a graduate level course on neural network modeling with an introductory course on the neural network as the prerequisite.

If the reader wishes to communicate with the authors, he/she may send the communication to the publishers, who will forward it to the authors.

Boca Raton P.S. Neelakanta
1994 D. De Groff


Table of Contents

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