reduces acuity due to diffraction. Good "ballpark" estimates of facet size can be made by equating the diffraction limit to resolution with the Nyquist frequency of the sampling lattice. But other factors are involved such as photon shot noise, which fundamentally limits all visual processing. In the 1970's, Snyder et a , [72J, applied information theory to the compound eye, finding that maximizing information capacity gave reasonable estimates of design parameters. In this talk I extend the information-theoretic treatment by introducing the time domain. Basic questions such as "how fast should a photoreceptor respond as a function of light level and flight speed?" will be addressed, as will the use of moving natural images as a stimulus ensemble. Preliminary results suggest that information theory can provide a useful tool for understanding the tradeoffs and trends in compound eye design, both in the spatial and temporal domains. For references, see [64, 68J. This is joint work with S. B. Laughlin.

# Entropy estimates: measuring the information output of a source

Raymond Russell, Dublin Institute for Advanced Studies russell@stp.dias.ie

Abstract not available.

# On Tree Sources, Finite State Machines, and Time Reversal

Gadiel Seroussi, HP Labs Palo Alto seroussi@hpJ.hp.com

We investigate the effect of time reversal on tree models of finite-memory processes. This is motivated in part by the following simple question that arises in some data compression applications: when trying to compress a data string using a universal source modeler, can it make a difference whether we read the string from left to right or from right to left? We characterize the class of finite-memory two-sided tree processes, whose time-reversed versions also admit tree models. Given a tree model, we present a construction of the tree model corresponding to the reversed process, and we show that the number of states in the reversed tree might be, in the extreme case, quadratic in the number of states of the original tree. This answers the above motivating question in the affirmative. This is joint work with Marcelo Weinberger. For a reference, see [70J.

# Statistical physics and replica theory-neural networks; equilibrium and non-equilibrium

David Sherrington, Oxford University sherr@thphys.ox.ac.uk

Abstract not available, but see [16, 84J.

Maximum Quantum Entropy Richard Silver, Los Alamos National Laboratory