Dresden 2009 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 4: Statistical physics in biological systems II (joint session DY/BP)
DY 4.9: Talk
Monday, March 23, 2009, 16:30–16:45, HÜL 386
Pinwheel Crystallization in a Competitive Hebbian Model of Visual Cortical Development — •Wolfgang Keil1,2,3,4 and Fred Wolf1,2,3,4 — 1MPI for Dynamics and Self-Organization, Göttingen — 2BCCN, Göttingen — 3Georg-August-Universität, Fakultät für Physik, Göttingen — 4IMPRS, Göttingen
The spatially complex modular architecture of the mammalian primary visual cortex is believed to reflect the requirement to smoothly map a high dimensional space of visual stimulus features to an effectively two dimensional array of neurons. Competitive Hebbian models of cortical development have been widely used to numerically study the properties of such mappings, but no analytical results about their ground states have been obtained so far. A classical example of such dimension reducing mappings is the Elastic Network Model (EN), proposed by Durbin and Mitchison (Nature (343), pp. 644-647, 1990). Here we use a perturbative approach to compute the ground states of the dynamics of orientation preference maps within this model. We find different phases as a function of the lateral intracortical interactions and external stimulus distribution properties. However, in all parameter regimes, the grounds states of the Elastic Network Model are either stripe-like, or crystalline representation of visual features. We present a complete phase diagram of the model, summarizing pattern selection. Analytical predictions are confirmed by direct numerical simulations. Our results question previous studies concluding that the EN correctly reproduces the spatially aperiodic arrangement of visual cortical processing modules.