Title: Topological Data Analysis of Continuum Percolation with Disks
Authors: Leo Speidel, Heather A. Harrington, S. Jonathan Chapman, and Mason A. Porter
Abstract: We study continuum percolation with disks, a variant of continuum percolation in two-dimensional Euclidean space, by applying tools from topological data analysis. We interpret each realization of continuum percolation with disks as a topological subspace of [0,1]^2 and investigate its topological features across many realizations. Specifically, we apply persistent homology to investigate topological changes as we vary the number and radius of disks, and we observe evidence that the longest persisting invariant is born at or near the percolation transition.
And to give a story, or at least the hint of the interesting relationship that I sometimes have with typesetters and editors, here is a note that I received from them while we were working on the galley proofs.
Update (8/05/18): A nice way of phrasing things is that we're in a nonassociative situation, and hyphens are a great tool to indicate exactly (and tersely) where the parentheses should be to group terms in a way that renders their meaning unambiguous. (And, naturally, if somebody makes a change in my text that I don't like, my immediate desire is to change it back.)
