Mathematical Psychology and Psychophysiology

By Stephen Grossberg | Go to book overview

Preface

Understanding the mind and its neural substrates has long been one of the most challenging and important scientific problems confronting humanity. Experimental and theoretical progress in this area has recently accelerated to the point that our knowledge of brain processes is undergoing a revolutionary transformation. This volume contains articles by the invited speakers at a joint AMS-SIAM Symposium on Mathematical Psychology and Psychophysiology in Philadelphia on April 15-16, 1980 at which several of the theoretical approaches to this area were reviewed.

The articles include contributions to a variety of topics and employ a variety of mathematical tools to explicate these topics. The topics include studies of development, perception, learning, cognition, information processing, psychophysiology, and measurement. Their mathematical substrates include algebraic, stochastic, and dynamical system models and theorems. Despite this diversity, the reader can discover an underlying coherence among the papers. Various concepts and formal laws reoccur in several different subjects. Distinct mathematical tools often probe different levels of the same underlying physical mechanisms.

N. Graham describes the Fourier approach to spatial vision. G. Iverson and M. Pavel discuss an invariance law in psychoacoustics. W. Freeman considers psychophysiological substrates of olfactory coding. D. Willshaw and C. von der Malsburg review a model of retinotectal development.

G. Carpenter analyzes the signal patterns of normal and abnormal nerve cells. S. Geman describes theorems concerning the approximation of stochastic differential equations by deterministic differential equations, and uses these theorems to analyze models of pattern learning and discrimination. S. Grossberg's first article discusses adaptive resonances and competitive dynamics in developmental, perceptual, and cognitive examples, and introduces a new explanation of how depth, brightness, spatial frequency, and filling-in visual computations are related. S. Grossberg's second article analyzes schedule interactions and behavioral contrast as examples of psychophysiological principles.

M. F. Norman's first article discusses some relationships between fitness and genetic mechanisms in a sociobiological context. M. F. Norman's second article describes a stochastic limit theorem whose proof is psychologically motivated.

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