Preface

PART I: GLASSY SYSTEMS AND NEURAL NETWORKS

Levy Statistics for Single Molecule Spectroscopy in Low Temperature Glass

E. Barkai

R. J. Silbey

G. Zumofen

Information Content of Neural Networks with Self Control and Variable Activity

D. Bolle

S. I. Amari

D. R. C. Dominguez Carreta

G. Massolo

Storage Capacity of the Tilinglike Learning Algorithm

A. Buhot

M. B. Gordon

Saddles on the Potential Energy Landscape of a Lennard-Jones Liquid

K. Broderix

K. K. Bhattacharya

A. Cavagna

A. Zippelius

I. Giardina

Glassy Dynamics of a Two-Dimensional Non-Disordered Spin Model

J. P. Garrahan

M. E. J. Newman

Proliferation Assisted Barrier Crossing and Population Dynamics

I. Giardina

J.-P. Bouchaud

M. Mezard

Vulcanization and the Random Solid State It Yields: A Statistical Mechanical Perspective

P. M. Goldbart

W. Peng

Optimal Capacity of Ashkin-Teller Neural Networks

P. Kozlowski

D. Bolle

Cluster Derivation of the Parisi Scheme for Disordered Systems

A. C. C. Coolen

J. van Mourik

Statistical Mechanics Models for Jamming in Granular Media

M. Nicodemi

Absence of Replica Symmetry Breaking in a Region of the Phase Diagram of the Ising Spin Glass

H. Nishimori

D. Sherrington

Stochastic Stability

G. Parisi

Configurational Entropy and the One-Step RSB Scenario in Glasses

A. Crisanti

F. Ritort

Public Key Cryptography and Error Correcting Codes as Ising Models

D. Saad

Y. Kabashima

T. Murayama

Statistical Physics of Adaptive Correlation of Agents in a Market

D. Sherrington

J. P. Garrahan

E. Moro

Random Field Ising Chains and Neural Networks with Synchronous Dynamics

N. S. Skantzos

A. C. C. Coolen

PART II: INFORMATION GEOMETRY

Geometrical Methods in Learning Theory

G. Burdet

P. Combe

H. Nencka

Geometry of Neural Networks and Models with Singularities

K. Fukumizu

Information Geometry and the Quantum Estimation Problem: The Phase-Space Connection

D. P. K. Ghikas

Monotone Metrics on Statistical Manifolds of Density Matrices by Geometry of Non-Commutative L2-Spaces

P. Gibilisco

T. Isola

Infinite Dimensional Quantum Information Geometry

M. R. Grasselli

Dualistic Properties of the Manifold of Quantum States

A. Jencova

On Real Hilbertian Info-Manifolds

G. Burdet

P. Combe

H. Nencka

New Ideas in Non-Parametric Estimation

G. Pistone

The Uniqueness of the Chentsov Metric

M. R. Grasselli

R. F. Streater

PART III: QUANTUM DYNAMICS AND QUANTUM CHAOS

Symmetry in Phase Space of a Chaotic System

B. Aneva

A Topological Method for Studying Dynamical Systems in Classical Mechanics

V. L. Cartas

Chaos and Gram's Matrix

M. De Cock

Spectra of Random Matrices Close to Unitary and Scattering Theory for Discrete-Time Systems

Y. V. Fyodorov

Statistical Mechanics of Random Matrices: Application to Disordered Metals

H. Hasegawa

Qualitative Properties of the Ground State in Nelson's Scalar Field Model: A Gibbs Measure-Based Approach

J. Lorinczi

On the Application of Quantum Lp-Spaces

A. W. Majewski

The 1/r2 Integrable System: A Universal Hamiltonian for ``Complex'' Level Dynamics

P. Shukla

The Distribution of the Modes of Coupled Quartic Oscillators

M. Tomiya

N. Yoshinaga

PART IV: REACTION-DIFFUSION EQUATIONS

Nonlinear Relation between Diffusion and Conductivity for Levy Flights

V. E. Arkhincheev

Steady States and Long Time Asymptotics of Solutions of Streater's Models

P. Biler

Scaling in Nonlinear Parabolic Equations: Applications to Debye System

G. Karch

Estimates for Fundamental Solutions of Parabolic Equations with Application to a Nonlinear Problem

V. Kondratiev

V. Liskevich

Z. Sobol

A Note on Nonlocal Equations in Mathematical Physics

T. Nadzieja

PART V: NEW DIRECTIONS IN MATHEMATICAL FINANCE

Risk Avalanches in Financial Markets

P. Balland

Hedging Contingent Claims on Defaultable Assets

J. G. B. Beumee

Hyberbolic and Semi-Parametric Models in Finance

N. H. Bingham

R. Kiesel

Applications of Information Geometry to Interest Rate Theory

D. C. Brody

L. P. Hughston

Measures of Dependence for Multivariate Levy Distributions

J. Boland

T. R. Hurd

M. Pivato

L. Seco

Scaling and Multiscaling in Financial Markets

G. Iori

Diagrammatic Approach to Real Options

S. Leppard

Instability of Implied Volatility, Fictitious Skews and Smiles, and the Hazards of Exotics: The Importance of the Inverse Function Theorem in Mathematical Finance

W. T. Shaw

Valuation of Financial Models with Non-Linear State Spaces

N. Webber

Natural Hazard Metaphors for Financial Crises

G. Woo

Martingale Approach to Real Options

L. P. Hughston

M. Zervos

Author Index