4 papers · 1 filter
The Singular Source of Vineyard Monodromy
Erin W. Chambers, Christopher Fillmore, Shankha Shubhra Mukherjee +3
Vineyards, or time-varying families of persistence diagrams, are widely used in topological data analysis (TDA) pipelines to track how topological features change and evolve as a p…
Braiding vineyards
Erin Chambers, Christopher Fillmore, Elizabeth Stephenson +1
In this work, we introduce and study what we believe is an intriguing and, to the best of our knowledge, previously unknown connection between two areas in computational topology,…
Counting Equilibria of the Electrostatic Potential
Herbert Edelsbrunner, Christopher Fillmore, Gonçalo Oliveira
In 1873, James C. Maxwell conjectured that the electric field generated by point charges in generic position has at most isolated zeroes. The first (non-optimal) uppe…
Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of Euclidean spaces and of Riemannian manifolds
Dominique Attali, Hana Dal Poz KouÅimská, Christopher Fillmore +4
In this article we extend and strengthen the seminal work by Niyogi, Smale, and Weinberger on the learning of the homotopy type from a sample of an underlying space. In their work,…