The recent decade has seen significant progress in our ability to analyse mathematically complex interaction processes on large finitely connected networks, with topologies tailored to mimic those of observed biological systems. The main methods are finite connectivity replica methods and generating functional analysis. In this project we explore the potential of this new analysis technology, supplemented by numerical simulations, to increase our understanding of instabilities in the brain, such as epilepsy, via a close collaboration between experts in experimental neuroscience (at the Institute of Psychiatry, Psychology and Neuroscience) and in mathematical biology (at the Institute for Mathematical and Molecular Biomedicine).
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