Coherent states of the Euclidean group and activation regions of primary visual cortex

2011/11/02 by Davide Barbieri, Barbieri, Davide, Giovanna Citti +5
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Data Analysis #FOS: Biological sciences #FOS: Mathematics #FOS: Physical sciences #Group Theory (math.GR) #Neurons and Cognition (q-bio.NC) #Representation Theory (math.RT) #Statistics and Probability (physics.data-an) #math.GR #math.RT #physics.data-an #q-bio.NC

paper · pdf · doi:10.48550/arxiv.1111.0669

arxiv created 2011/11/02 · arxiv updated 2011/11/04

Abstract

The uncertainty principle of SE(2) allows to construct a coherent states transform that is strictly related to the Bargmann transform for the second Heisenberg group H2. The corresponding target space is characterized constructively and related to the almost complex structure of SE(2) as a contact manifold. Such a coherent state transform provides a model for neural activity maps in the primary visual cortex, that are then described in terms of minimal uncertainty states. The results of the model are compared with the experimental measurements.

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