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StATISTICAL MECHANICS AND ITS APPLICATIONS TO COMPLEX PROBLEMS IN PHYSICS ENGINEERING AND BIOLOGY

Objective


Neural networks are a major are of investigation but within their general remit covered many aspects: recurrent and feed forward architectures, synaptic and more general local rules, discrete and analogue neurons, discrete and analogue neurons, discrete and analogue synapses, unrestricted and bounded synapses, deterministic and stochastic dynamics, systems with and without detailed balance, systems with and without correlations between patterns, systems for static images and for sequences for retrieval and optimal training with and without training noise.
Spin glasses and analogues systems including dilutely connected spin glasses have been studied along with the related problem of the optimal partitioning of random graphics.
A layered net simulator which runs on transputer arrays has been developed and used to identify rock strata from well log data.
The UPSTART logarithm was discovered.
Replica symmetry techniques have been used to explore learning in a noisy linear perception trained with noisy data and to calculate the effects of finite word length (ie finite accuracy or dynamic range in synapes).

The Wentzel-Kramers-Brillouin (WKB) method has been employed for a direct calculation of the adiabatic limit and for a systematic inclusion of nonadiabatic corrections. A simple method has been provided for the calculation of adiabatic phases and for the inclusion of nonadiabatic corrections. Quantum spin-1 systems have been studied using a flexible semiclassical theory which predicts the occurrence of a nematic and a semiordered phase in addition to the usual ferromagnetism and antiferromagnetism, a subject of current interest in connection with theories of high critical temperature superconductors. Quantum spin-1 chains with strong planar anisotropy are studied using both semiclassical methods and strong coupling methods. A t-J model has been studied in terms of phase separation, magnetic fluctuations and dynamics of spin and charge fluctuations. Other topics studied include: dynamics of vortices, infrared anomalies, quantum precolation, photonic gaps and localization of classical waves in a random medium.

Correlated fermions have been studied using different techniques including mean field theories, variational calculations, exact numerical diagonalization and quantum Monte Carlo. Classical statistical mechanics has been applied to a 1-dimensional kinetic Ising model and the chiral Potts model. The infinite V Hubbard model has been investigated. Work has been done on the generalized flux phases in the t-J model including superconductivity, the Faraday effect and optical absorption. Noncommutative geometry methods have been applied in condensed matter physics.

Methods for solving classical mean field random site spin glass models have been extended to the quantum regime. Phase diagrams for a mean field quantum X Y model in a random field and for a quantum generalization of the van Hemmen model were computed to illustrate the working of the general theory. Properties of the adiabatically cooled SK spin glass in the vicinity of the transition temperature were investigated within a dynamical mean field approach. The N-dependent spectrum of relaxation times and the time dependent distribution of local fields were both computed using a Fokker-Planck type equation.
Within a dynamic mean field theory transients and basins of attraction in attractor neural networks were computed. The static limit of this theory corresponds to a replica symmetric treatment. Other topics studied included sequences, low activity patterns, hierarchically organized patterns, graded response meurons and dynamics of learning.

The main activity in the field of simulated annealing has been devoted to a theoretical and experimental investigation of parallel simulated annealing. Simulated annealing, an extremely valuable optimization tool, is often too slow for routine use, so that the implementation of this algorithm on relatively inexpensive parallel machines is an attractive solution. The parallel scheme which has been produced is problem independent.
In the field of neural networks the following results have been achieved: the design of a transputer based neurocomputer with the implementation of the Hopfield model and of the back propagation training of feedforward nets; the design and implementation of a special purpose chip implementing a 64-neuron Hopfield network with on chip training; the design and implementation of a very fast special purpose chip for the automatic classification of handwritten digits; and a general conceptual framework encompassing both the training of feedback neural networks and the adaptation of recursive filters leading to new powerful algorithms.

Statistical physics of disordered systems is being developed. The mean field theory of spin plasses receives application both in the study of realistic spin glasses and in other fields. The use of spin glass ideas and techniques has been applied to directed polymers in random media, the random field Ising model and the pinning of vortex lines in superconductors.
Statistical physics of combinational optimization problems has been studied.
Both attractor neural network models and feedforward models have been investigated and several useful algorithms have been developed.
Statistical mechanics has recently been developed in the context of disordered systems to compute the performance of certain error correcting codes.

The behaviour of a real brain after a lesion has been compared with that of a neural network after damage and it was found that the 2 systems behave in a similar fashion.
Extensive numerical simulations have been done in 3 dimensions on SK spin glass models and the predictions of the broken replica theory are found to be in qualitative agreement with the numerical data.
In spin glasses some problems have been studied connected to replica symmetry breaking and its consequences.
Direct polymers have been the subject of an extensive investigation using the replica method in high dimensions where replica symmetry is broken. Heteropolymer folding has also been studied using the replica approach and replica symmetry breaking.

Funding Scheme

CSC - Cost-sharing contracts

Coordinator

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Address
University Offices, Wellington Square
Oxford
United Kingdom

Participants (7)

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE
France
Address
Avenue Des Martyrs 25
38042 Grenoble
Centre National de la Recherche Scientifique (CNRS)
France
Address
24 Rue Lhomond
75231 Paris
ECOLE SUPERIEURE DE PHYSIQUE ET CHIMIE INDUSTRIELLES DE LA VILLE DE PARIS
France
Address
Rue Vauquelin 10
Paris
Foundation for Research and Technology-Hellas
Greece
Address

71110 Heraklion-crete
IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY AND MEDICINE
United Kingdom
Address
South Kensington Campus
London
RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG
Germany
Address
Seminarstrasse 2
69117 Heidelberg
UNIVERSITÀ DEGLI STUDI DI ROMA TOR VERGATA
Italy
Address
Via Della Ricerca Scientifica, 1 Edificio Sogene
00133 Roma