Gerald S. Guralnik, Ph.D. - US grants

A new approach known as the Source Galerkin method for Quantum Field Theory will be pursued. Source Galerkin, unlike current Monte Carlo based techniques, explicitly uses spacetime and internal symmetries of a system to pose the problem of solution so as to allow considerable analytic input. The complexity of this requires one to use computer algebra to generate the equations coded for computation on Cray's and CM-2's. Results have been sensationally good with many orders of magnitude improvement in speed and accuracy compared to Monte Carlo. Source Galerkin has the property that fermions and bosons can be treated (aside from commutation) in a symmetric manner. It is not necessary to solve a fermion problem exactly for any given boson configuration as with Monte Carlo. Consequently, problems involving dynamical fermions are no harder than those with bosons. Problems of physical significance will be analyzed with Source Galerkin methods during this research. We expect to examine Hubbard models for high temperature superconductivity without a "sign problem". We anticipate obtaining valid dynamical results in Lattice QCD. While it is certain that teraflop technology will still allow only a limited class of results for conventional QCD, it is possible that these new ideas will allow us to obtain predictive and valid QCD results.

IBN-9720320 PI: ANDERSON This project is being funded through the Learning & Intelligent Systems Initiative. This study investigates functional interactions among groups of neurons (nerve cells) in the brain. The cerebral cortex of the brain is a dynamic ensemble of groups of neurons with activities that coalesce and dissolve in the performance of particular tasks. A computational model called 'network of networks' describes the operation of computations based on neurons interacting in intermediate groupings, in the size range between single neurons (only one computing element) and entire brain regions (to hundreds of millions of computing elements). In the intermediate scale groupings, the model makes predictions about the behavior of both its component single neurons and the overall nature of the cortical computation, manifested as behavior and perception. Experimental tests utilize the mammalian visual system because so much is known about cortical processing of visual information at the level of single neurons, and also there is a large body of related experimental results for visual perception. There are three inter-related parts to this project. 1) Computer simulations and mathematical analysis further develop the 'network of networks' model itself. 2) Simultaneous activity of multiple neurons in visual areas are recorded physiologically to examine long-range transfer of information across visual cortex, of the type suggested by the model. 3) Analyses of previously obtained psychophysical behavioral data from human subjects are combined with computer simulations to try to understand the surprising effectiveness of silhouettes in object recognition, and to provide a test system for the network model. Results will have an impact because of the importance of linking cognition with neuroscience to understand mechanisms that underlie learning and perception, and because understanding how the brain handles complex computations will provide insights for the design of artificia l recognition and decision-making systems.