Directed Descriptors of Data
Talk by Robin Belton (Mathematical Sciences, MSU)
11/24/2020 11:10am-12:00pm WebEx Meeting
Abstract: Studying data using the information of a partial order can be enlightening. We focus on two examples. The first is studying time series data based on the order of local extrema. This can help us compare different genomic time series. The second is studying directed paths in a Euclidean cubical complex that model concurrent programs. The directed paths provide us information about program executions. We can construct and compute directed descriptors that capture the data in these two settings. I will discuss the theoretical foundations behind these directed descriptor constructions. They draw from Topological Data Analysis (TDA) and Directed Topology. I will also talk about algorithms and implementations for computing these descriptors. I will end by proposing several future directions for this work that I plan to complete in my remaining time as a graduate student. They involve more computational implementations, simplifying directed descriptors, and applying descriptors to study the disease evolution of malaria.