Probability Seminar: Mark McDonnell

Although directed random graph models are frequently used in modeling the electrical activity of networks of cortical neurons, experimental results consistently reveal that the actual network topology is complex, and tends to be clustered locally. This suggests that the random network assumption is unrealistic and that when analysing population dynamics in cortical networks, it is necessary to employ directed network models that incorporate clustering.


In this seminar I shall describe simulation results that demonstrate that replacing random connectivity with clustered connectivity can induce instability in subsets of neurons, in terms of significantly increased firing rates. Moreover, it is shown that one specific network topology gives rise to slow bistable switching between low and high states.


The aim of presenting this seminar is not to describe finished mathematical work, but rather to seek collaboration or assistance with finding mathematical explanations that predict that clustered connectivity can lead to the bistable or unstable states observed in simulations.