On some methods in neuromathematics (or the development of mathematical methods for the description of structure and function in neurons)

Abstract

Success in exploring neural circuitry and its functions depends critically on the availability of data. This determines what kinds of questions can be asked and what analytical tools can most appropriately be used. Biophysical studies have relied heavily on statistics -e.g. as applied to neuronal spike trains- and differential equations and matrix algebra-e.g. as applied to the Hodgkin/Huxley axon and in modeling some networks. Some other approaches have been relatively neglected. These include the search for optimality criteria in relating structure and function and the decomposition of informational processes into simple units.

In this paper we describe how a particular optimaliy criterion has led to new insights and to the classifications of one type of neural cell; and we describe a new family of filters with interesting properties, which serve as simple information processing units and which can be concatenated to provide both high level and low level descriptions. Both methods were developed in connection with visual processing in the retina. But they can be extended with appropriate reformulations to other areas of the nervous system.