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Modeling Brain Function
One of the most exciting and potentially rewarding areas of scientific research is the study of the principles and mechanisms underlying brain function. It is also of great promise to future generations of computers. A growing group of researchers, adapting knowledge and techniques from a wide range of scientific disciplines, have made substantial progress understanding memory, the learning process, and self organization by studying the properties of models of neural networks - idealized systems containing very large numbers of connected neurons, whose interactions give rise to the special qualities of the brain. This book introduces and explains the techniques brought from physics to the st...
Neural Networks
Neural Networks presents concepts of neural-network models and techniques of parallel distributed processing in a three-step approach: - A brief overview of the neural structure of the brain and the history of neural-network modeling introduces to associative memory, preceptrons, feature-sensitive networks, learning strategies, and practical applications. - The second part covers subjects like statistical physics of spin glasses, the mean-field theory of the Hopfield model, and the "space of interactions" approach to the storage capacity of neural networks. - The final part discusses nine programs with practical demonstrations of neural-network models. The software and source code in C are on a 3 1/2" MS-DOS diskette can be run with Microsoft, Borland, Turbo-C, or compatible compilers.
Statistical Physics and Economics
This systematic book covers in simple language the physical foundations of evolution equations, stochastic processes and generalized Master equations applied on complex economic systems, helping to understand the large variability of financial markets, trading and communications networks.
Methods and Models in Neurophysics
1. E. Marder, Experimenting with theory -- 2. A. Borysuk and J. Rinzel, Understanding neuronal dynamics by geometrical dissection of minimal models -- 3. D. Terman, Geometry singular perturbation analysis of neuronal dynamics -- 4. G. Mato, Theory of neural synchrony -- 5. M. Shelley, Some useful numerical techniques for simulating integrate-and-fire networks -- 6. D. Golomb, Propagation of pulses in cortical networks: the single-spike approximation -- 7. M. Tsodyks, Activity-dependent transmission in neocortical synapses -- 8. H. Sompolinsky and J. White, Theory of large recurrent networks: from spikes to behavior -- 9. C. van Vreeswijk, Irregular activity in large networks of neurons -- 10. N. Brunel, Network models of memory -- 11. P. Bressloff, Pattern formation in visual cortex -- 12. F. Wolf, Symmetry breaking and pattern selection in visual cortical development -- 13. A. Treves and Y. Roudi, On the evolution of the brain -- 14. E. Brown, Theory of point processes for neural syst ...
Statistical Mechanics of Neural Networks
This book highlights a comprehensive introduction to the fundamental statistical mechanics underneath the inner workings of neural networks. The book discusses in details important concepts and techniques including the cavity method, the mean-field theory, replica techniques, the Nishimori condition, variational methods, the dynamical mean-field theory, unsupervised learning, associative memory models, perceptron models, the chaos theory of recurrent neural networks, and eigen-spectrums of neural networks, walking new learners through the theories and must-have skillsets to understand and use neural networks. The book focuses on quantitative frameworks of neural network models where the underlying mechanisms can be precisely isolated by physics of mathematical beauty and theoretical predictions. It is a good reference for students, researchers, and practitioners in the area of neural networks.
Field Theory, The Renormalization Group, And Critical Phenomena: Graphs To Computers (3rd Edition)
This volume links field theory methods and concepts from particle physics with those in critical phenomena and statistical mechanics, the development starting from the latter point of view. Rigor and lengthy proofs are trimmed by using the phenomenological framework of graphs, power counting, etc., and field theoretic methods with emphasis on renormalization group techniques. Non-perturbative methods and numerical simulations are introduced in this new edition. Abundant references to research literature complement this matter-of-fact approach. The book introduces quantum field theory to those already grounded in the concepts of statistical mechanics and advanced quantum theory, with sufficient exercises in each chapter for use as a textbook in a one-semester graduate course.The following new chapters are included:I. Real Space MethodsII. Finite Size ScalingIII. Monte Carlo Methods. Numerical Field Theory
The Physics of Structure Formation
The formation and evolution of complex dynamical structures is one of the most exciting areas of nonlinear physics. Such pattern formation problems are common in practically all systems involving a large number of interacting components. Here, the basic problem is to understand how competing physical forces can shape stable geometries and to explain why nature prefers just these. Motivation for the intensive study of pattern formation phenomena during the past few years derives from an increasing appreciation of the remarkable diversity of behaviour encountered in nonlinear systems and of universal features shared by entire classes of nonlinear processes. As physics copes with ever more ambi...
The Self-Avoiding Walk
The self-avoiding walk is a mathematical model that has important applications in statistical mechanics and polymer science. In spite of its simple definition—a path on a lattice that does not visit the same site more than once—it is difficult to analyze mathematically. The Self-Avoiding Walk provides the first unified account of the known rigorous results for the self-avoiding walk, with particular emphasis on its critical behavior. Its goals are to give an account of the current mathematical understanding of the model, to indicate some of the applications of the concept in physics and in chemistry, and to give an introduction to some of the nonrigorous methods used in those fields. Top...
Models of Neural Networks I
One of the great intellectual challenges for the next few decades is the question of brain organization. What is the basic mechanism for storage of memory? What are the processes that serve as the interphase between the basically chemical processes of the body and the very specific and nonstatistical operations in the brain? Above all, how is concept formation achieved in the human brain? I wonder whether the spirit of the physics that will be involved in these studies will not be akin to that which moved the founders of the "rational foundation of thermodynamics". C. N. Yang! 10 The human brain is said to have roughly 10 neurons connected through about 14 10 synapses. Each neuron is itself ...
Computational Neuroscience
The thirty original contributions in this book provide a working definition of"computational neuroscience" as the area in which problems lie simultaneously within computerscience and neuroscience. They review this emerging field in historical and philosophical overviewsand in stimulating summaries of recent results. Leading researchers address the structure of thebrain and the computational problems associated with describing and understanding this structure atthe synaptic, neural, map, and system levels.The overview chapters discuss the early days of thefield, provide a philosophical analysis of the problems associated with confusion between brainmetaphor and brain theory, and take up the s...
