4 research outputs found

    Coordinated optimization of visual cortical maps (II) Numerical studies

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    It is an attractive hypothesis that the spatial structure of visual cortical architecture can be explained by the coordinated optimization of multiple visual cortical maps representing orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we defined a class of analytically tractable coordinated optimization models and solved representative examples in which a spatially complex organization of the orientation preference map is induced by inter-map interactions. We found that attractor solutions near symmetry breaking threshold predict a highly ordered map layout and require a substantial OD bias for OP pinwheel stabilization. Here we examine in numerical simulations whether such models exhibit biologically more realistic spatially irregular solutions at a finite distance from threshold and when transients towards attractor states are considered. We also examine whether model behavior qualitatively changes when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. Our numerical results support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the spatially irregular architecture of the visual cortex. We discuss several alternative scenarios and additional factors that may improve the agreement between model solutions and biological observations.Comment: 55 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1102.335

    Traveling–stripe forcing of oblique rolls in anisotropic systems

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    The effects of a traveling, spatially periodic forcing are investigated in a system with axial anisotropy, where oblique stripe patterns occur at threshold in the unforced case and where the forcing wavenumber and the wavenumber of stripes are close to a 2:1 resonance. The forcing induces an interaction between the two degenerate oblique stripe orientations and for larger forcing amplitudes rectangular patterns are induced, which are dragged in phase by the forcing. With increasing forcing velocity a transition from a locked rectangular pattern to an unlocked superposition of a rectangular and oblique stripe pattern takes place. In this transition regime, especially when the ratio between the wavenumber of the forcing and that of the pattern deviates from the 2:1 ratio, surprisingly stable or long living complex patterns, such as zig–zag patterns and patterns including domain walls are found. Even more surprising is the observation, that such coherent structures propagate faster than the stripe forcing. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2004