4 citations · 4 across the 1 of their papers we have counts for
4 papers
The (homological) persistence of gerrymandering
Moon Duchin, Tom Needham, Thomas Weighill
We apply persistent homology, the dominant tool from the field of topological data analysis, to study electoral redistricting. Our method combines the geographic information from a…
The Weighted Euler Curve Transform for Shape and Image Analysis
Qitong Jiang, Sebastian Kurtek, Tom Needham
The Euler Curve Transform (ECT) of Turner et al.\ is a complete invariant of an embedded simplicial complex, which is amenable to statistical analysis. We generalize the ECT to pro…
Gromov-Wasserstein Averaging in a Riemannian Framework
Samir Chowdhury, Tom Needham
We introduce a theoretical framework for performing statistical tasks---including, but not limited to, averaging and principal component analysis---on the space of (possibly asymme…
Knot types of generalized Kirchhoff rods
Tom Needham
Kirchhoff energy is a classical functional on the space of arclength-parameterized framed curves whose critical points approximate configurations of springy elastic rods. We introd…