Spike Train Statistics from Empirical Facts to Theory: The Case of the Retina - Modeling in Computational Biology and Biomedicine - page 252

brain via the optical nerve), independent signal-encoders or are neural correlations
important for coding a visual scene, and how to interpret them?

8.1.1 Chapter Overview

Public

This chapter addresses to readers having a master degree in Mathematics, Physics
or Biology.

Outline

In this chapter, we present a state of the art about neural coding in the retina
considered from the point of view of statistical physics and probability theory. As a
consequence, this chapter contains both recent biological results and mathematical
developments. The chapter is organized as follows. In Sect. 8.2 we introduce the
current challenge of unraveling the neural code via spike trains statistics analysis.
Such an analysis requires elaborated mathematical tools introduced in Sect. 8.3 .
We mainly focus on the so-called Gibbs distributions. This concept comes from
statistical physics but our presentation departs from the classical physics courses
since it is based on transition probabilities of Markov process. This way, as we show,
allows to handle non-stationary dynamics, and is adapted to statistical analysis, of
data as well as neural networks models. As an illustration, we present, in Sect. 8.4 ,
two “success stories” where spike train statistics analysis has allowed to make a
step further in our understanding of information encoding by the retina. In the same
section, we also present an example of a rigorous spike train analysis in a neural
network and compare the spike trains probability distribution to the models currently
used on the experimental side.

8.2 Unraveling the Neural Code in the Retina via Spike Train

Statistics Analysis

8.2.1 Retina Structure and Functions

8.2.1.1 Retina Structure

The vertebrate retina is a tightly packed neural tissue, exhibiting a rich diversity
of neurons. It is structured in three cells nuclei layers and two plexiform synaptic