Directed Descriptors of Data

Studying data and mathematical models using the information of a partial or total order can be enlightening. We focus on two examples. The first is studying multidimensional time series data based on the order of local extrema with applications to biological network analysis. The second is studying directed paths in a Euclidean cubical complex that model concurrent programs. We can construct and compute directed descriptors in these two settings. I will discuss the theoretical foundations, implementations, and results behind these methods that draw from Topological Data Analysis (TDA) and Directed Topology.