Introduction

The preceding chapter dealt with methods for calculating the probability of finding synaptic contacts between neurons. In this chapter we assume that such contacts exist and create a certain network. This chapter develops methods for computing the input-output relations of a network from its structure.

Chapters 2 and 3 provide the material essential for analyzing small cortical networks. It is asumed that one can experimentally observe the input-output relation of a cortical network. Then, with the insight gained from studying Chapter 3, one can surmise the structure of cortical networks that might generate the observed relation. Finally, using the methods described in Chapter 2, one can determine which of the possible networks is most likely to exist in the brain. Chapters 6 and 7 will illustrate an important example of the use of such considerations.

This chapter derives quantitative descriptions of the way in which a spike train arriving at a neural network is modified and converted into an output spike train. The reader should be aware that this assignment is very ambitious and can be only partially achieved. Specifically, we could arrive at formulas that would hold true for spike trains in which the spikes did not follow each other too closely (we would, of course, have to define what “too closely” means).