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The Primary Visual Cortex (V1) is the first region in the cortical pathway
in which visual information is processed by the brain. As the processing
in V1 is very elementary, this cortical region is a natural candidate
for> computational and mathematical modelling.
We
(with R. Shapley, M. Shelley, and J. Wielaard, PNAS 2000) have developed
a large-scale computational model of a local patch of an input layer of
V1, and used this model to investigate cortical mechanisms for orientation
selectivity. In this talk, I will (i) define "orientation selectivity'',
(ii) describe the construction and performance of our large-scale model,
and (iii) use asymptotic analysis to derive a coarse-grained reduction
of the large-scale model. This derivation of the reduced model follows
from a temporal scale separation which emerges from cortical activity
-- activity which places the neuronal network in a state of an overdamped
system. Finally, the reduced model will be used to identify cortical mechanisms
underlying orientation selectivity.
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