Optimizing Cortical Mappings

"Topographic" mappings occur frequently in the brain. A popular approach to understanding the structure of such mappings is to map points representing input features in a space of a few dimensions to points in a 2 dimensional space using some selforganizing algorithm. We argue that a more general approach may be useful, where similarities between features are not constrained to be geometric distances, and the objective function for topographic matching is chosen explicitly rather than being specified implicitly by the self-organizing algorithm. We investigate analytically an example of this more general approach applied to the structure of interdigitated mappings, such as the pattern of ocular dominance columns in primary visual cortex. 1 INTRODUCTION A prevalent feature of mappings in the brain is that they are often "topographic". In the most straightforward case this simply means that neighbouring points on a two-dimensional sheet (e.g. the retina) are mapped to neighbouring points in a more central two-dimensional structure (e.g. the optic tectum). However a more complex case, still often referred to as topographic, is the mapping from an abstract space of features (e.g.