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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.

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