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Peter Grindrod CBE (University of Reading) 

We will consider the structure of dynamically evolving networks modelling information and activity moving across a very large set of vertices. We will adopt the "communicability" concept that generalizes that of centrality for static networks. We define the primary network structure within the whole as comprising of the most influential vertices (both as senders and receivers of dynamically sequenced activity). We apply these ideas to the analysis of evolving networks derived from fMRI scans of resting human brains, at the highest possible resolution, with vertices representing voxels. 

We present a methodology based on successive vertex knock-outs, up to a very small fraction of the whole primary network, that can characterize the nature of the primary network as being either relatively robust and lattice-like (with redundancies built in) or relatively fragile and tree-like (with sensitivities and few redundancies). For the fMRI scans of brains, we show that the estimation of such performance parameters is subject to less variability (due to sampling) than that observed across a very large (~1000) population of such scans. Hence the differences observed within the population are significant. The calculations, though sizable, can be cloud based. 

Since the knock-out testing is analogous to physical degradation of the brain due to failure of small groups to neurons (at least at a low level), we suggest that the differences in performance measures that are observed here may be an early clinical indicator of the brains' owners’ distinct future experiences of early onset cognitive decline.