## The Legacy of Norbert Wiener: A Centennial Symposium: A Centennial Symposium in Honor of the 100th Anniversary of Norbert Wiener's Birth, October 8-14, 1994, Massachusetts Institute of Technology, Cambridge, MassachusettsThis 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: BLFourier integral operators with complex phase (a contemporary successor to the Paley-Wiener theory) BLstatistical aspects of quantum mechanics and of liquid crystals BLfinancial markets, including the new trading strategies for options based on Wiener processes BLstatistical methods of genetic research BLmodels 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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### Contents

3 | |

The rise and fall of cybernetics in the US and the USSR | 21 |

Reminiscences of Norbert Wiener | 31 |

Speech by Fagi Levinson | 33 |

Some memories of Norbert Wiener | 37 |

Pictures | 43 |

Scientific Articles | 51 |

Gibbs measures quasiperiodic solutions and nonlnear partial differential equations | 53 |

A nonrandom walk down Wall Street | 149 |

Filtered Wiener space versus abstract Wiener space | 185 |

Unsolved problems connected with the Wiener criterion | 199 |

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 | 273 |

Wieners Tauberian theorem | 65 |

The role of PaleyWiener theory in partial differential equations | 71 |

PaleyWiener on manifolds | 85 |

Norbert Wiener and the development of mathematical engineering | 93 |

Mathematics and function | 117 |

Using probabilistic models and algorithms to map genes and genomes | 137 |

The risk management revolution | 313 |

Complex noncommutative infinite dimensional analysis and FermionBoson interactions | 329 |

Complex integral transforms diffraction resonances and phase space tunneling | 355 |

Scaling the free field and statistical mechanics | 373 |

WienerHopf integral equations | 391 |

### Common terms and phrases

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