Soft computing is a consortium of computing methodologies that provide a foundation for the conception, design, and deployment of intelligent systems and aims to formalize the human ability to make rational decisions in an environment of uncertainty and imprecision. This book is based on a NATO Advanced Study Institute held in 1996 on soft computing and its applications. The distinguished contributors consider the principal constituents of soft computing, namely fuzzy logic, neurocomputing, genetic computing, and probabilistic reasoning, the relations between them, and their fusion in industrial applications. Two areas emphasized in the book are how to achieve a synergistic combination of the main constituents of soft computing and how the combination can be used to achieve a high Machine Intelligence Quotient.

Computational Intelligence: Soft Computing and Fuzzy-Neuro Integration with Applications

Visual space (VS) is a coherent self-organized dynamic complex that is structured into objects, backgrounds, and the self. As a concrete example of geometrical properties in VS, experimental results on parallel and (equi) distance alleys in a frameless VS were reviewed, and Luneburg's interpretation on the discrepancy between these 2 alleys was sketched with emphasis on the 2 hypotheses involved: VS is a Riemannian space of constant curvature (RCC) and the a priori assumed correspondence between VS and the physical space in which stimulus points are presented. Dissociating these 2 assumptions, the author tried to see to what extent the global structure of VS under natural conditions is in accordance with the hypothesis of RCC and to make explicit the logic underlying RCC. Several open questions about the geometry of VS per se have been enumerated.

A critical review of Luneburg's model with regard to global structure of visual space.

The visual cortex is a contact bundle

A one-dimensional random rough surface is modeled as a Gaussian noise signal. The effect of shadowing in the case of backscattering of waves from such a surface is studied in the geometric optic limit by analyzing the Gaussian noise signal in a digital computer. It is found that presently accepted theories for the shadowing effect are of doubtful validity.

Note on the effect of shadowing on the backscattering of waves from a random rough surface

The postnatal development of the human cerebral cortex

A basic Lie group derived earlier that describes the \"constancies\" of visual perception is extended to one more dimension to take into account the nonlinear flow of an afferent volley of nerve impulses through the layers of the visual cortex. One is then led, via the usual determination of the solutions of a Lagrange partial differential equation in terms of an associated Pfaffian system of ordinary differential equations, to a correspondence between neuron cell body, Lie group germ, and critical point of the system of ordinary differential equations governing the orbits. The local phase portraits of the latter bear a marked resemblance to one or the other of the neuron types defined by Sholl. Since \"brains are as different as faces\", the concept of structural stability plays an important role in analyzing the connectivity of the neural network. Finally, Lukasiewicz's theory of parentheses is used to obtain a graph-theoretic representation of the Jacobi identity, which then serves to explain the branching of neuronal processes (dendrites).

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The neuron as a Lie group germ and a Lie product

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William C. Hoffman

Papers

The neuron as a Lie group germ and a Lie product

Scattering of eletromagnetic waves from a random surface