Identifying dynamics of networks

The classical theory of nonlinear dynamics exhibits wonderfully rich and exotic structures. I will argue that as we move to an era of data driven dynamics it offers too many riches. Stated differently, if we only have finite data at our disposal we need a simpler theory of dynamics. I will present such a theory based on combinatorics and algebraic topology. After describing the theory, I will apply it to the analysis of dynamics of networks.

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