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Influence of the Inhibition Schema

Variations of the shape of the inhibitory kernel allow both (1) to assess the structural specificity of inhibition schemata, and (2) to account for the observed variability in the two-dimensional spatial organization of simple cell RFs. Structural specificity is related to the anisotropic character of the inhibitory kernel. Increasing the angle within which the recipient cell gets its inhibition, the connection schema loses its specificity, until, as approaches , inhibition arises from an annulus around the center cell (see figure 5a, according to a ``circular inhibition'' schema [123]. We verified, see figure 6a, [92] that notwithstanding the isotropic and non-specific character of ``circular inhibition'' schema, the resulting RFs still have specific and anisotropic appearance, as pointed out in the recent study of Wörgötter and his colleagues [123]. In addition, for this type of inhibition, we observed that the central excitatory subregion is often surrounded by an inhibitory ring of variable strength which provides RF with a certain amount of end-stopping (i.e., sensitivity to the length of the stimulus), that is a very common property of cells in the visual cortex [9,28].



Figure 5: (click on the image to view a larger version) Schematic representation of various inhibitory schemata. (a) circular inhibition; (b) anisotropic non-clustered inhibition; (c) asymmetric clustered inhibition, ; (d) slant (tilted) clustered inhibition.


Figure 6: (click on the image to view a larger version) The resulting 2-D RF profiles together with their contour levels for a cell in an iso-orientation domain subjected to the corresponding inhibitory schemata in figure 5. The strength of inhibition b is fixed to 0.5.

Also in the case of ``circular inhibition'', long-range clustered connections play a decisive role in endowing the resulting RF its periodic appearance. To probe further into the function of long-range inhibition, we conducted simulations with uniformly distributed inhibitory couplings that have no skips and drop off uniformly with distance. The results showed that non-clustered inhibition schemata, as the one depicted in figure 5b, slightly improve feature sensitivity of the resulting RF, providing it with two weak inhibitory sidebands, but fail in generating periodic RFs, even for high values of b and when inhibition occurs along a preferred direction (see figure 6b).

Real simple cell RFs present a broad variability of symmetry relationships among field subregions [24,26,27,40,61,62,93] that can be emulated only by introducing asymmetric or skewed inhibition kernels. By example, if , inhibitory effect is spatially unbalanced (see figure 5c) and the resulting RFs exhibit still a periodical structure with continuous phase shifts related to the ratio . In figure 6c a RF with quasi-odd symmetry is shown. Further realistic asymmetric behaviors, such as cartesian non-separability (see figure 6d) [61], can arise from inhibitory connections that do not extend exactly along the direction orthogonal to the orientation preference of the cell (see figure 5d) or from the joint effect of asymmetries in the inhibitory kernel and in the underlaying orientation map.

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