MCB111: Mathematics in Biology (Fall 2019)


week 01:

Introduction to Information Theory

Q1

This is mostly a computational question, you get familiar with some coding, and also on how to sample from any probability distribution.

Q2

Consider a system of 3 neurons that are all interconnected. We are going to assume that each neuron has two states +1 for firing and -1 for not firing.

Your experimental design allows you only to measure two neurons simultaneously (but not three at the time unfortunately), and what you can obtain is the averages of those pair measurements

Obviously, these averages are symmetric so we only need to consider the three cases above, as , etc..

\begin{equation} P(n_1, n_2, n_3) \end{equation}

that describes state of the three neurons, if you impose the average correlations that you have observed.

If you need some inspiration, you can look into this paper Schneidman E, Still S, Berry MJ, Sergev R, Bialek W (2006) Weak pairwise correlations imply strongly correlated network states in a neural population.