1 code implementation • 19 Sep 2023 • Andrew Lee, Harlin Lee, Jose A. Perea, Nikolas Schonsheck, Madeleine Weinstein
Then, we define a continuous and $O(k)$-equivariant map $\pi_\alpha$ that acts as a ``closest point operator'' to project the data onto the image of $V_k(\mathbb{R}^n)$ in $V_k(\mathbb{R}^N)$ under the embedding determined by $\alpha$, while minimizing distortion.
no code implementations • 14 Dec 2022 • Luis Scoccola, Hitesh Gakhar, Johnathan Bush, Nikolas Schonsheck, Tatum Rask, Ling Zhou, Jose A. Perea
The circular coordinates algorithm of de Silva, Morozov, and Vejdemo-Johansson takes as input a dataset together with a cohomology class representing a $1$-dimensional hole in the data; the output is a map from the data into the circle that captures this hole, and that is of minimum energy in a suitable sense.
no code implementations • 18 Dec 2020 • Crichton Ogle, Nikolas Schonsheck
The completion tower of a nonunital commutative ring is a classical construction in commutative algebra.
Algebraic Topology 55P43, 55P48, 55P60, 55U35, 18G55