are examined. The regions of system parameters and initial conditions leading to chaotic, synchronized and quasi-periodic are obtained. The condition for the pendulum to escape from the potential well V(q'» = ,(I - cos(q»' ) was also found. This is joint work with Wojciech Przystupa, Kazimierz Szabelski and Jerzy Warminski.

# Sharpening Occam's razor

Seth Lloyd, MIT slloyd@mit.edu

Abstract not available.

# Free Energy Minimization and Binary Decoding Tasks

David MacKay, University of Cambridge mackay@mrao.cam.ac.uk

I study the task of inferring a binary vector s given a noisy measurement of the vector [ = As mod 2, where A is an M x N binary matrix. This combinatorial problem can be attacked by replacing the unknown binary vector by a real vector of probabilities which are optimized by variational free energy minimization. The resulting algorithm shows great promise as a decoder for a novel class of error correcting codes. For references, see [51, 36J.

# The Shannon-McMillan theorem from the point of view of statistical mechanics

Anders Martin-Lof, University of Stockholm andersm I@insanus.matematik.su.se

Abstract not available, but see [53J. Anders provided a set of handwritten notes for this lecture. Copies are available from Jeremy Gunawardena upon request.

# Some Properties of the Generalized BFOS Tree Pruning Algorithm

Nader Moayeri, HP Labs Palo Alto moayeri@alvand.hpl.hp.com

We first show that the generalized BFOS algorithm is not optimal when it is used to design fixed-rate pruned tree-structured vector quantizers (TSVQ). A simple modification is made in the algorithm that makes it optimal. However, this modification has little effect on the (experimental) rate-distortion performance. An asymptotic analysis is presented that justifies the experimental results. It also suggests that in designing fixed-rate, variable-depth TSVQ's, one can get as good a rate-distortion performance with a greedy TSVQ design algorithm as with an optimal pruning of a large tree.