Weakly connected neural networks
Weakly connected neural networks
What geometric visual hallucinations tell us about the visual cortex
Neural Computation
Pre-attentive segmentation in the primary visual cortex
Pre-attentive segmentation in the primary visual cortex
Hallucinogen persisting perception disorder in neuronal networks with adaptation
Journal of Computational Neuroscience
Neural field model of binocular rivalry waves
Journal of Computational Neuroscience
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A mathematical theory of interacting hypercolumns in primary visual cortex (V1) is presented that incorporates details concerning the anisotropic nature of long-range lateral connections. Each hypercolumn is modeled as a ring of interacting excitatory and inhibitory neural populations with orientation preferences over the range 0 to 180 degrees. Analytical methods from bifurcation theory are used to derive nonlinear equations for the amplitude and phase of the population tuning curves in which the effective lateral interactions are linear in the amplitudes. These amplitude equations describe how mutual interactions between hypercolumns via lateral connections modify the response of each hypercolumn to modulated inputs from the lateral geniculate nucleus; such interactions form the basis of contextual effects. The coupled ring model is shown to reproduce a number of orientation-dependent and contrast-dependent features observed in center-surround experiments. A major prediction of the model is that the anisotropy in lateral connections results in a nonuniform modulatory effect of the surround that is correlated with the orientation of the center.