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

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

by Peter Sollich, A.C.C. Coolen, L.P. Hughston, R.F. Streater
     
 

ISBN-10: 1563969831

ISBN-13: 9781563969836

Pub. Date: 03/01/2001

Publisher: American Institute of Physics

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

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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.

Product Details

ISBN-13:
9781563969836
Publisher:
American Institute of Physics
Publication date:
03/01/2001
Series:
AIP Conference Proceedings Series, #553
Edition description:
2001
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 Glass3
Information Content of Neural Networks with Self Control and Variable Activity11
Storage Capacity of the Tilinglike Learning Algorithm17
Saddles on the Potential Energy Landscape of a Lennard-Jones Liquid23
Glassy Dynamics of a Two-Dimensional Non-Disordered Spin Model29
Proliferation Assisted Barrier Crossing and Population Dynamics35
Vulcanization and the Random Solid State It Yields: A Statistical Mechanical Perspective41
Optimal Capacity of Ashkin-Teller Neural Networks49
Cluster Derivation of the Parisi Scheme for Disordered Systems55
Statistical Mechanics Models for Jamming in Granular Media61
Absence of Replica Symmetry Breaking in a Region of the Phase Diagram of the Ising Spin Glass67
Stochastic Stability73
Configurational Entropy and the One-Step RSB Scenario in Glasses81
Public Key Cryptography and Error Correcting Codes as Ising Models89
Statistical Physics of Adaptive Correlation of Agents in a Market95
Random Field Ising Chains and Neural Networks with Synchronous Dynamics101
Geometrical Methods in Learning Theory109
Geometry of Neural Networks and Models with Singularities117
Information Geometry and the Quantum Estimation Problem: The Phase-Space Connection123
Monotone Metrics on Statistical Manifolds of Density Matrices by Geometry of Non-Commutative L[superscript 2]-Spaces129
Infinite Dimensional Quantum Information Geometry141
Dualistic Properties of the Manifold of Quantum States147
One Real Hilbertian Info-Manifolds153
New Ideas in Non-Parametric Estimation159
The Uniqueness of the Chentsov Metric165
Symmetry in Phase Space of a Chaotic System173
A Topological Method for Studying Dynamical Systems in Classical Mechanics179
Chaos and Gram's Matrix185
Spectra of Random Matrices Close to Unitary and Scattering Theory for Discrete-Time Systems191
Statistical Mechanics of Random Matrices: Application to Disordered Metals197
Qualitative Properties of the Ground State in Nelson's Scalar Field Model: A Gibbs Measure-Based Approach203
On the Application of Quantum L[subscript p]-Spaces209
The l/r[superscript 2] Integrable System: A Universal Hamiltonian for "Complex" Level Dynamics215
The Distribution of the Modes of Coupled Quartic Oscillators223
Nonlinear Relation between Diffusion and Conductivity for Levy Flights231
Steady States and Long Time Asymptotics of Solutions of Streater's Models237
Scaling in Nonlinear Parabolic Equations: Applications to Debye System243
Estimates for Fundamental Solutions of Parabolic Equations with Application to a Nonlinear Problem249
A Note on Nonlocal Equations in Mathematical Physics255
Risk Avalanches in Financial Markets263
Hedging Contingent Claims on Defaultable Assets269
Hyberbolic and Semi-Parametric Models in Finance275
Applications of Information Geometry to Interest Rate Theory281
Measures of Dependence for Multivariate Levy Distributions289
Scaling and Multiscaling in Financial Markets297
Diagrammatic Approach to Real Options303
Instability of Implied Volatility, Fictitious Skews and Smiles, and the Hazards of Exotics: The Importance of the Inverse Function Theorem in Mathematical Finance309
Valuation of Financial Models with Non-Linear State Spaces315
Natural Hazard Metaphors for Financial Crises321
Martingale Approach to Real Options325
Author Index331

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