Natural computation in the mesoscale dynamics of the brain

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Nature computes. From the complex branching growth of a tree to the processing of DNA, many natural processes and phenomena can be modelled, and understood, through the lens of computation.The primary drive behind this research program is the framing of the dynamics of natural systems in terms of computation. Once framed this way, we can bring to bear the mathematics of computation to model and understand natural processes. At the same time, the challenge of modelling natural systems extends the boundaries of known mathematics by forcing the development of new concepts and techniques.Within this broad research program, I propose to study the dynamics of large-scale networks in the human brain. We will collect neuroimaging data which, roughly, quantifies "neural activity" in spatially constrained regions of the brain. If we assign each region to a node, and draw a line between two nodes if the two regions have similar patterns of activity, we define a brain activity based graph. If, instead of a single graph, we build a series of graphs -- as neural relationships evolve in time -- we now have a dynamic graph. The "front end" of the proposed research is to develop optimal methods for inferring such dynamic graphs from neuroimaging data.Once the dynamic graphs have been generated, we can begin to look for patterns in how the graphs change over time. Patterns can be turned into (probabilistic) rules which compose a formal computing system which can then be analyzed using the tools of theoretical computer science. The anticipated outcomes of this program are the development of new models of natural computing and the application of these models to understanding the dynamics of the human brain.