Superposition Models

Abstract

Many kinds of neurons have a large number of synapses. Since at each synapse there is an incident impulse sequence, in effect a number of point processes are superposed at the membrane, leading to a composite point process. Neuron models based on such superposition of point processes have been proposed in the literature. In this chapter, some of these models are discussed. Before the models are introduced, the basic theory of superposition of point processes is presented. Section 4.1 deals with renewal processes, and in Section 4.2 the limiting behaviour of a large number of stationary regular point processes that are superposed is considered. The subject of superposition is fairly advanced, but here only some basic concepts and results are presented. The treatment follows for the greater part Cox (1962) and Khintchine (1960). Section 4.3 discusses some models based on superposition.