The Legacy of Norbert Wiener: A Centennial Symposium

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Brand new. We distribute directly for the publisher. This book contains lectures presented at the MIT symposium on the 100th anniversary of Norbert Wiener's birth held in October ... 1994. The topics reflect Wiener's main interests while emphasizing current developments.In addition to lectures dealing directly with problems on which Wiener worked, such as potential theory, harmonic analysis, Wiener-Hopf theory, and Paley-Wiener theory, the book discusses the following topics: * Fourier integral operators with complex phase (a contemporary successor to the Paley-Wiener theory) * statistical aspects of quantum mechanics and of liquid crystals * financial markets, including the new trading strategies for options based on Wiener processes * statistical methods of genetic research * models of the nervous system, pattern recognition, and the nature of intelligenceThe volume includes reviews on Norbert Wiener's contributions from historical and current perspectives.This book gives mathematical researchers an overview of new mathematical problems presented by other areas and gives researchers in other fields a broad overview of the ways in which advanced mathematics might be useful to them. Read more Show Less

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Brand new. We distribute directly for the publisher. This book contains lectures presented at the MIT symposium on the 100th anniversary of Norbert Wiener's birth held in October ... 1994. The topics reflect Wiener's main interests while emphasizing current developments.In addition to lectures dealing directly with problems on which Wiener worked, such as potential theory, harmonic analysis, Wiener-Hopf theory, and Paley-Wiener theory, the book discusses the following topics: * Fourier integral operators with complex phase (a contemporary successor to the Paley-Wiener theory) * statistical aspects of quantum mechanics and of liquid crystals * financial markets, including the new trading strategies for options based on Wiener processes * statistical methods of genetic research * models of the nervous system, pattern recognition, and the nature of intelligenceThe volume includes reviews on Norbert Wiener's contributions from historical and current perspectives.This book gives mathematical researchers an overview of new mathematical problems presented by other areas and gives researchers in other fields a broad overview of the ways in which advanced mathematics might be useful to them. Read more Show Less

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Overview

This book contains lectures presented at the MIT symposium on the 100th anniversary of Norbert Wiener's birth held in October 1994. The topics reflect Wiener's main interests while emphasizing current developments. In addition to lectures dealing directly with problems on which Wiener worked, such as potential theory, harmonic analysis, Wiener-Hopf theory, and Paley-Wiener theory, the book discusses the following topics: Fourier integral operators with complex phase (a contemporary successor to the Paley-Wiener theory) statistical aspects of quantum mechanics and of liquid crystals financial markets, including the new trading strategies for options based on Wiener processes statistical methods of genetic research models of the nervous system, pattern recognition, and the nature of intelligence The volume includes reviews on Norbert Wiener's contributions from historical and current perspectives. This book gives mathematical researchers an overview of new mathematical problems presented by other areas and gives researchers in other fields a broad overview of the ways in which advanced mathematics might be useful to them.

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Editorial Reviews

Booknews
Comprises the proceedings of the October 1994 symposium held at MIT in honor of the 100th anniversary of the birth of Norbert Wiener, a mathematician whose forays into physics, engineering, and biology changed the course of mathematical research. In addition to lectures dealing directly with problems on which Wiener worked, such as potential theory, harmonic analysis, Wiener-Hopf theory, and Palen-Wiener theory, the volume discusses Fourier integral operators with complex phase; statistical aspects of quantum mechanics and of liquid crystals; financial markets, including the new trading strategies for options based on Wiener processes; statistical methods of genetic research; and models of the nervous system, pattern recognition, and the nature of intelligence. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

Table of Contents

Preface
Program
Acknowledgments
Biographical and Historical Remarks 1
Norbert Wiener 3
The rise and fall of cybernetics in the US and the USSR 21
Reminiscences of Norbert Wiener 31
Speech 33
Some memories of Norbert Wiener 37
Pictures 43
Scientific Articles 51
Gibbs measures, quasi-periodic solutions and nonlinear partial differential equations 53
Wiener's Tauberian theorem 65
The role of Paley-Wiener theory in partial differential equations 71
Paley-Wiener on manifolds 85
Norbert Wiener and the development of mathematical engineering 93
Oscillating networks of Neurons: Mathematics and function 117
Mapping heredity: Using probabilistic models and algorithms to map genes and genomes 137
A non-random walk down Wall Street 149
Filtered Wiener space versus abstract Wiener space 185
Unsolved problems connected with the Wiener criterion 199
On the role of the Wiener process in finance theory and practice: The case of replicating portfolios 209
Inference, learning, and recognition 223
Issues in the mathematical modeling of cortical functioning and thought 235
Polymer braids and iterated Moire maps 261
Networks that learn and how the brain works 275
The risk management revolution 313
Complex noncommutative infinite dimensional analysis and Fermion-Boson interactions 329
Complex integral transforms, diffraction, resonances and phase space tunneling 355
Scaling, the free field and statistical mechanics 373
Wiener-Hopf integral equations 391
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