The Mathematics of Synaptic Noise

Abstract

The previous chapters of this book have focused mostly on studies assessing and characterizing synaptic noise under a variety of experimental conditions, and on evaluating its role in shaping neural dynamics through computational models. Although detailed biophysical models of neurons in vivo (see Sect. 4.2) remain, so far, out of reach for a mathematically more rigorous approach, the introduced simplified models (see Sects. 4.3 and 4.4), at least partially, allow for an analytical treatment. The latter can be used to complement experimental and computational studies and, therefore, provide a deeper understanding of neuronal dynamics under noisy conditions. Moreover, a mathematical treatment can also be used to provide unprecedented characterization of synaptic noise and how it affects spiking activity. This will be the subject of this and the forthcoming chapters.