This is a ongoing project with Hangzhi Wang in Cambridge.

Motivation

Within the field of systems neuroscience, many models compete. But there is no single metric for which model is best. The Hodgkin-Huxley model is considered the best model for single neuron descriptions, but it is complicated. The Leaky-integrate-and-fire model is sleaker but ignores many details. The Self-organised-criticality models reduce neurons to spatially related three-state models. Branching models simplify single neurons to on/off signals without spatial relation. The Wilson-Cowan model smears out single neurons and describes excitation and inhibition as continuous functions. There are many other models with other advantages, simplifications and range of phenomena.

But how are they related? Is there a derivation from more microscopic ones to more macroscopic ones? Is rigorous coarse-graining possible? This project tries to answer these questions.