ABSTRACT
The goal of this paper is a model of the dendritic net that: (1) is mathematically tractable, (2) is reasonably true to the biology, and (3) illuminates information processing in the neuropil. First I discuss some general principles of mathematical modeling in a biological context that are relevant to the use of linearity and orthogonality in our models. Next I discuss the hypothesis that the dendritic net can be viewed as a linear field computer. Then I discuss the approximations involved in analyzing it as a dynamic, lumped-parameter, linear system. Within this basically linear framework I then present: (1) the self-organization of matched filters and of associative memories; (2) the dendritic computation of Gabor and other nonorthogonal representations; and (3) the possible effects of reverse current flow in neurons.
