Disordered and Complex Systems: London, United Kingdom, 10-14 July 2000 / Edition 1

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Overview

This book arose from a conference on Disordered and Complex Systems held at Kings College, London. It takes a broad view of the topic, containing articles on glassy systems and neural networks, information geometry, quantum chaos, reaction-diffusion equations, and mathematical finance. Exciting common threads appear; to give just two examples: information geometry appears in neural network learning, quantum mechanics and interest rate theory, and systems of economic agents can show glassy features.

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Editorial Reviews

Booknews
Casting a wide meaning for the terms disorder and complexity in order to gather researchers from many disciplines, the meeting covered glassy systems and neural networks, information geometry, quantum dynamics and quantum chaos, reaction-diffusion equations, and new directions in mathematical finance. The 50 papers include such discussions as the glassy dynamics of a two-dimensional non- disordered spin model, dualistic properties of the manifold of quantum states, applying the statistical mechanics of random matrices to disordered metals, steady states and long-time asymptotics of solutions of Steater's models, and scaling and multiscaling in financial markets. There is no subject index. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9781563969836
  • Publisher: American Institute of Physics
  • Publication date: 3/1/2001
  • Series: AIP Conference Proceedings Series , #553
  • Edition description: 2001
  • Edition number: 1
  • Pages: 344
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.81 (d)

Table of Contents

Preface
Levy Statistics for Single Molecule Spectroscopy in Low Temperature Glass 3
Information Content of Neural Networks with Self Control and Variable Activity 11
Storage Capacity of the Tilinglike Learning Algorithm 17
Saddles on the Potential Energy Landscape of a Lennard-Jones Liquid 23
Glassy Dynamics of a Two-Dimensional Non-Disordered Spin Model 29
Proliferation Assisted Barrier Crossing and Population Dynamics 35
Vulcanization and the Random Solid State It Yields: A Statistical Mechanical Perspective 41
Optimal Capacity of Ashkin-Teller Neural Networks 49
Cluster Derivation of the Parisi Scheme for Disordered Systems 55
Statistical Mechanics Models for Jamming in Granular Media 61
Absence of Replica Symmetry Breaking in a Region of the Phase Diagram of the Ising Spin Glass 67
Stochastic Stability 73
Configurational Entropy and the One-Step RSB Scenario in Glasses 81
Public Key Cryptography and Error Correcting Codes as Ising Models 89
Statistical Physics of Adaptive Correlation of Agents in a Market 95
Random Field Ising Chains and Neural Networks with Synchronous Dynamics 101
Geometrical Methods in Learning Theory 109
Geometry of Neural Networks and Models with Singularities 117
Information Geometry and the Quantum Estimation Problem: The Phase-Space Connection 123
Monotone Metrics on Statistical Manifolds of Density Matrices by Geometry of Non-Commutative L[superscript 2]-Spaces 129
Infinite Dimensional Quantum Information Geometry 141
Dualistic Properties of the Manifold of Quantum States 147
One Real Hilbertian Info-Manifolds 153
New Ideas in Non-Parametric Estimation 159
The Uniqueness of the Chentsov Metric 165
Symmetry in Phase Space of a Chaotic System 173
A Topological Method for Studying Dynamical Systems in Classical Mechanics 179
Chaos and Gram's Matrix 185
Spectra of Random Matrices Close to Unitary and Scattering Theory for Discrete-Time Systems 191
Statistical Mechanics of Random Matrices: Application to Disordered Metals 197
Qualitative Properties of the Ground State in Nelson's Scalar Field Model: A Gibbs Measure-Based Approach 203
On the Application of Quantum L[subscript p]-Spaces 209
The l/r[superscript 2] Integrable System: A Universal Hamiltonian for "Complex" Level Dynamics 215
The Distribution of the Modes of Coupled Quartic Oscillators 223
Nonlinear Relation between Diffusion and Conductivity for Levy Flights 231
Steady States and Long Time Asymptotics of Solutions of Streater's Models 237
Scaling in Nonlinear Parabolic Equations: Applications to Debye System 243
Estimates for Fundamental Solutions of Parabolic Equations with Application to a Nonlinear Problem 249
A Note on Nonlocal Equations in Mathematical Physics 255
Risk Avalanches in Financial Markets 263
Hedging Contingent Claims on Defaultable Assets 269
Hyberbolic and Semi-Parametric Models in Finance 275
Applications of Information Geometry to Interest Rate Theory 281
Measures of Dependence for Multivariate Levy Distributions 289
Scaling and Multiscaling in Financial Markets 297
Diagrammatic Approach to Real Options 303
Instability of Implied Volatility, Fictitious Skews and Smiles, and the Hazards of Exotics: The Importance of the Inverse Function Theorem in Mathematical Finance 309
Valuation of Financial Models with Non-Linear State Spaces 315
Natural Hazard Metaphors for Financial Crises 321
Martingale Approach to Real Options 325
Author Index 331
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