PhD, Imperial College of Science and Technology
929 E. 57th St.
Chicago, Illinois 60637
Jack Cowan, PhD
- Computational & Theoretical
My main research interest is to try to understand brain mechanisms. I use the techniques of modern statistical mechanics to investigate the effects of fluctuations and correlations on the nonlinear dynamics of large-scale brain activity. I am also interested in applying these techniques to chemical and biological network problems.
In another direction I am interested in information processing and computation in the brain, and have developed an approach that relies heavily on the intersection of nonlinear dynamics with symmetry groups, and geometrical and topological ideas. This approach can be applied to such topics as depth perception and the processing of color information in the visual brain.
Another but related area of interest is in geometrical hallucinations of form, texture, motion, depth and color. This requires the combination of many of the mathematical methods cited above, and is a source of many interesting mathematical problems.
Reliable Computation in the Presence of Noise, (with S. Winograd), MIT Press, 1963.
Excitatory and Inhibitory Interactions in Localized Populations of Model Neurons, (with H.R. Wilson), Biophysical Journal, 12, 1-24, 1972.
A Mathematical Theory of the Functional Dynamics of Cortical and Thalamic Nervous Tissue, (with H.R. Wilson), Kybernetik 13, 2, 55-80, 1973.
Transient Potentials in Neurons with Arbitrary Geometry, (with E.G. Butz), Biophysical Journal. 14, 9, 1974.
A Mathematical Theory of Visual Hallucination Patterns, (with G.B. Ermentrout), Biological Cybernetics 34, 137-150, 1979.
Geometric Visual Hallucinations, Euclidean Symmetry, and the Functional Architecture of Striate Cortex (with P. Bressloff, M. Golubitsky, P. Thomas and M.C. Wiener), Phil.Trans.Roy.Soc. (Lond) B, 356, 299-330, 2001.
Field Theoretic Approach to Fluctuation Effects in Neural Networks (with M.A. Buice), Phys. Rev. E, 051919, 2007.
Avalanches in a Stochastic Model of Spiking Neurons (with M.A. Benayoun, W.v.Drongelen, and E. Wallace), PLoS Computational Biology, 6, 7, e1000846, 2010.
Evolutionary constraints on visual cortex architecture from the dynamics of
hallucinations, (with T.C. Butler, M. Benayoun, E. Wallace, W. van Drongelen, and N.
Goldenfeld, PNAS, 109, 2, 606-609, 2012.
Self-organized criticality in a network of interacting neurons, (with J. Neuman, B.
Kiewiet, and W. van Drongelem), J. Stat. Mech. 04, P04030, 2013.