Nonlinear analysis of orientation tuning: stationary properties of simple cells in V1

Thomas Wennekers

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Submission date: 28. Jan. 2000
Pages: 9
published in: Neurocomputing, 38 (2001), p. 439-444 
DOI number (of the published article): 10.1016/S0925-2312(01)00372-1
Bibtex

Abstract:
We present an approximate mathematical analysis of field models for orientation tuning. Excitatory and inhibitory cells are considered as separate fields with intrinsic as well as mutual Gaussian connectivity kernels. Qualitative properties of fixed point solutions of these equations are approximated for a whole class of nonlinear rate-functions that obey a power law above some threshold and that are zero below. Algebraic expressions for stationary firing rates and tuning widths are derived that can be solved numerically and also analytically in an approximate way. Results show that the only rate-function (from the class of functions under consideration) that leads to a linearly growing network response and a constant tuning width when the input intensity is varied is the rectilinear function.