Dresden 2006 – scientific programme

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SYSS: Structure Formation and Self-Organization in non-equilibrium Systems

SYSS 3: Structure Formation and Self-Organization in non-equilibrium Systems - Poster

SYSS 3.9: Poster

Thursday, March 30, 2006, 16:00–18:00, P1

Pattern Formation in the Visual Cortex: Breaking Permutation Symmetry — •Lars Reichl, Matthias Kaschube, and Fred Wolf — Max-Planck-Institut für Dynamik und Selbstorganisation, Bunsenstrasse 10, D- 37073 Göttingen and Bernstein Center for Computational Neuroscience Göttingen

Neurons in the visual cortex are selective to the orientation of a stimulus. Neighboring neurons tend to have similar orientation preferences except at singularities (pinwheel centers) around which all orientations are represented. These properties are captured in a two dimensional orientation preference map (OPM). The formation of such an OPM can be modeled by a Swift-Hohenberg equation including local and nonlocal cubic interaction terms [1]. These interaction terms possess a permutation symmetry which implies that in the leading order of a perturbative expansion there is a set of attractors (planforms) which are energetically degenerate. The pinwheel density varies across different planform solutions. We show that due to higher order corrections planforms with the lowest pinwheel density also have the lowest energy. However OPM with such low pinwheel densities have not been observed experimentally. Therefore we introduce a cubic interaction term that breaks the permutation symmetry and thus energetically favors a planform already at leading order. We use a gradient interaction that selects planforms with a high pinwheel density. In a large parameter range these planforms are preferred even if higher order corrections are considered.

[1] F. Wolf, Les Houches Lecture Notes 2005