3 citations · 7 across the 6 of their papers we have counts for
8 papers
Dowker's theorem for higher-order relations
Vin de Silva, Chad Giusti, Vladimir Itskov +5
Given a relation between two sets, Dowker's Theorem (1952) states that the homology groups of two associated simplicial complexes, now known as Dowker comp…
-Equivariant Dimensionality Reduction on Stiefel Manifolds
Andrew Lee, Harlin Lee, Jose A. Perea +2
Many real-world datasets live on high-dimensional Stiefel and Grassmannian manifolds, and respectively, and benefit from projection onto l…
Toroidal Coordinates: Decorrelating Circular Coordinates With Lattice Reduction
Luis Scoccola, Hitesh Gakhar, Johnathan Bush +4
The circular coordinates algorithm of de Silva, Morozov, and Vejdemo-Johansson takes as input a dataset together with a cohomology class representing a -dimensional hole in the…
Spherical Coordinates from Persistent Cohomology
Nikolas C. Schonsheck, Stefan C. Schonsheck
We describe a method to obtain spherical parameterizations of arbitrary data through the use of persistent cohomology and variational optimization. We begin by computing the second…
On the chromatic localization of the homotopy completion tower for -algebras
Crichton Ogle, Nikolas Schonsheck
The completion tower of a nonunital commutative ring is a classical construction in commutative algebra. In the setting of structured ring spectra as modeled by algebras over a spe…
TQ-completion and the Taylor tower of the identity functor
Nikolas Schonsheck
The goal of this short paper is to study the convergence of the Taylor tower of the identity functor in the context of operadic algebras in spectra. Specifically, we show that if $…
Fibration theorems for TQ-completion of structured ring spectra
Nikolas Schonsheck
The aim of this short paper is to establish a spectral algebra analog of the Bousfield-Kan "fibration lemma" under appropriate conditions. We work in the context of algebraic struc…
On the cop number of generalized Petersen graphs
Taylor Ball, Robert W. Bell, Jonathan Guzman +2
We show that the cop number of every generalized Petersen graph is at most 4. The strategy is to play a modified game of cops and robbers on an infinite cyclic covering space where…