Open Problems in Sheaves of Measured Data
Monday, May 21, 2018 - 3:15pm - 4:15pm
Emilie Purvine (Pacific Northwest National Laboratory)
When using sheaves to model real-world problems -- e.g., topological signal processing or information integration -- we must face up to the challenges that real data provide. In a sheaf-theoretical context, measured data, called assignments, are represented by members of objects in the data category. Assignments need not be sections, and indeed, as measured data, almost always require statistical descriptions and tolerances. Uncertainty can exist between disparate measurements generally, and even on the same observable, due to uncertainty, noise, or sensor malfunctions. As such, statistical and uncertainty quantification questions naturally arise when considering sheaves on measured data. In this talk we will introduce our recent research on sheaves of real world data – e.g., approximate sections and consistency radius, and discuss some key open problems in the area.