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Thursday 24 March
2005 |
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16:00 |
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Fourth Floor Seminar
Room (409) Alexandra House, 17 Queen Square, LONDON
Spontaneous pattern formation in large scale brain activity: what visual migraines and hallucinations tell us about the brain
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In 1952 Turing's paper on the chemical basis of
morphogenesis initiated an important approach to the mathematical analysis
of spontaneous pattern formation. In 1973 Wilson and Cowan introduced a
similar formulation in nets of interacting neurons and in 1979 Ermentrout
and Cowan developed the mathematical analysis of such nets using local
bifurcation theory and symmetry groups. Bressloff, Cowan, Golubitsky, Thomas
and Wiener further developed this approach to characterize and analyze some
of the circuitry of the primate visual cortex. The symmetry group used was
the Euclidean group in the plane, E(2), under a novel rotation action. Such
an action is related to the fact that the visual cortex is a network of
oriented edge detectors. However it is clear that much more than the
orientation of a local edge is detected in the visual cortex: movement,
texture and surface information, color and depth, for example. In this talk
I will describe a new approach that allows the incorporation of some of the
above features into a comprehensive account of the origins of visual
migraines and hallucinations.
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