Qualitative computation with neural nets: differential equations like examples

Abstract

Linear and non-linear local computation with self-programming facilities is the more used model of biological neural nets. The diversity, specificity and complexity of anatomo-physiological contacts (dendrite-dendrite, axon-axon, axon-dendrite,.) and the variety of local processes carried out by those contacts make one think of authentic subcellular microcomputation. To illustrate the enormous computational capacity asociated to a neuron we present the masks necessary to solve the more usual equations of classical physics (Newton, Diffusion,.) and compare with the dendritic field of a Purkinje cell. Size, form and symmetries in the anatomy of receptive fields are interpreted as responsable of specific spatio-temporal filtering, orientation and movement detection. Furthermore, there is experimental evidence of other algorithmic local functions which do not have an analytical counterpart and consequently are not considered in this paper.