[Legacy Report] Nonlinear Dynamics, High Dimensional Data, and Persistent Homology
It is almost cliche at this point to note that high dimensional data is being collected from experiments or generated through numerical simulation at an unprecedented rate and that this rate will continue rising extremely rapidly for the foreseeable future. Our interest is in data associated with nonlinear dynamics. The focus of this talk is on our efforts to use topological tools to characterize and classify high dimensional nonlinear time series associated with processes that exhibit complex spatiotemporal patterns. The long term goal is to develop robust efficient techniques for comparing experimental work against numerical simulation. I will introduce the necessary mathematical theory and provide examples arising from fluid flow and dense granular media.
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- Teaneck, New Jersey
- United States
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- Co-sponsored by C16 and School of Computer Sciences and Engineering, FDU