One of the most challenging and fascinating problems of the theory of neural nets is that of asymptotic behavior, of how a system behaves as time proceeds. This is of particular relevance to many practical applications. Here we focus on association, generalization, and representation. We turn to the last topic first. The introductory chapter, "Global Analysis of Recurrent Neural Net works," by Andreas Herz presents an in-depth analysis of how to construct a Lyapunov function for various types of dynamics and neural coding. It includes a review of the recent work with John Hopfield on integrate-and fire neurons with local interactions. The chapter, "Receptive Fields and Maps in the Visual Cortex: Models of Ocular Dominance and Orientation Columns" by Ken Miller, explains how the primary visual cortex may asymptotically gain its specific structure through a self-organization process based on Hebbian learning. His argu ment since has been shown to be rather susceptible to generalization."

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 a complex device which compares and integrates incoming electrical signals and relays a nonlinear response to other neurons. The brain certainly exceeds in complexity any system which physicists have studied in the past. Nevertheless, there do exist many analogies of the brain to simpler physical systems. We have witnessed during the last decade some surprising contributions of physics to the study of the brain. The most significant parallel between biological brains and many physical systems is that both are made of many tightly interacting components.

This volume, with chapters by leading researchers in the field, is devoted to early vision and attention, that is, to the first stages of visual information processing. This state-of-the-art look at biological neural networks spans the many subfields, such as computational and experimental neuroscience; anatomy and physiology; visual information processing and scene segmentation; perception at illusory contours; control of visual attention; and paradigms for computing with spiking neurons.

Since the appearance of Vol. 1 of Models of Neural Networks in 1991, the theory of neural nets has focused on two paradigms: information coding through coherent firing of the neurons and functional feedback. Information coding through coherent neuronal firing exploits time as a cardinal degree of freedom. This capacity of a neural network rests on the fact that the neuronal action potential is a short, say 1 ms, spike, localized in space and time. Spatial as well as temporal correlations of activity may represent different states of a network. In particular, temporal correlations of activity may express that neurons process the same "object" of, for example, a visual scene by spiking at the very same time. The traditional description of a neural network through a firing rate, the famous S-shaped curve, presupposes a wide time window of, say, at least 100 ms. It thus fails to exploit the capacity to "bind" sets of coherently firing neurons for the purpose of both scene segmentation and figure-ground segregation. Feedback is a dominant feature of the structural organization of the brain. Recurrent neural networks have been studied extensively in the physical literature, starting with the ground breaking work of John Hop field (1982)."

With no effort we scan a scene by directing our gaze at specific objects, discerning them individually despite the background of other objects, contours, shadows, and changes in illumination. The process is partially intentional, partially automatic, and entirely amazing: no machine can accomplish this, but the simplest insect can. A single glance captures megabytes of data; we reduce this flood by singling out specific objects for attention. This volume, with chapters by leading researchers in the field, is devoted to early vision and attention, that is, to the first stages of visual information processing. John Hertz, who has extensive experience in both computational and experimental neuroscience, provides a theoretical introduction to neural modeling. John Van Opstal explains how the gaze is controlled and presents a novel theory incorporating recent experimental results. Klaus Funke and his colleagues describe the anatomy, physiology, functional relations, and ensuing response properties of the first stages in visual information processing; they provide one of the most comprehensive reviews available at the moment. Reinhard Eckhorn explains the underlying principles of scene segmentation. Esther Peterhans and her coworkers analyze a model of figure-ground segregation and brightness perception at illusory contours. Ernst Niebur and his collaborators indicate how visual attention can be controlled; Julian Eggert and Leo van Hemmen elucidate the feedback mechanism proper. Rob de Ruyter van Steveninck and Bill Bialek show how insects process visual information with impressive efficiency. Finally, Wolfgang Maass describes paradigms for computing with spiking neurons from the point of view of a computer scientist.

One of the most challenging and fascinating problems of the theory of neural nets is that of asymptotic behavior, of how a system behaves as time proceeds. This is of particular relevance to many practical applications. Here we focus on association, generalization, and representation. We turn to the last topic first. The introductory chapter, "Global Analysis of Recurrent Neural Net works," by Andreas Herz presents an in-depth analysis of how to construct a Lyapunov function for various types of dynamics and neural coding. It includes a review of the recent work with John Hopfield on integrate-and fire neurons with local interactions. The chapter, "Receptive Fields and Maps in the Visual Cortex: Models of Ocular Dominance and Orientation Columns" by Ken Miller, explains how the primary visual cortex may asymptotically gain its specific structure through a self-organization process based on Hebbian learning. His argu ment since has been shown to be rather susceptible to generalization."

Since the appearance of Vol. 1 of Models of Neural Networks in 1991, the theory of neural nets has focused on two paradigms: information coding through coherent firing of the neurons and functional feedback. Information coding through coherent neuronal firing exploits time as a cardinal degree of freedom. This capacity of a neural network rests on the fact that the neuronal action potential is a short, say 1 ms, spike, localized in space and time. Spatial as well as temporal correlations of activity may represent different states of a network. In particular, temporal correlations of activity may express that neurons process the same "object" of, for example, a visual scene by spiking at the very same time. The traditional description of a neural network through a firing rate, the famous S-shaped curve, presupposes a wide time window of, say, at least 100 ms. It thus fails to exploit the capacity to "bind" sets of coherently firing neurons for the purpose of both scene segmentation and figure-ground segregation. Feedback is a dominant feature of the structural organization of the brain. Recurrent neural networks have been studied extensively in the physical literature, starting with the ground breaking work of John Hop field (1982)."