Spontaneous symmetry breaking and the formation of columnar structures in the primary visual cortex II --- Local organization of orientation modules

Details Spontaneous symmetry breaking and the formation of columnar structures in the primary visual cortex II --- Local organization of orientation modules Spontaneous symmetry breaking and the formation of columnar structures in the primary visual cortex II --- Local organization of orientation modules

1996-11-05

arxiv.org/abs/adap-org/9611002v1

Nonlinear Sciences

Adaptation and Self-Organizing Systems

36 pages Latex2.09 and eps figures. Needs epsf.sty, amssym.def, and Type1 TeX-fonts of BlueSky Res. for correct typo in graphi

Scientific paper

Self-organization of orientation-wheels observed in the visual cortex is discussed from the view point of topology. We argue in a generalized model of Kohonen's feature mappings that the existence of the orientation-wheels is a consequence of Riemann-Hurwitz formula from topology. In the same line, we estimate partition function of the model, and show that regardless of the total number N of the orientation-modules per hypercolumn the modules are self-organized, without fine-tuning of parameters, into definite number of orientation-wheels per hypercolumn if N is large.

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