Toroidal Coordinates: Decorrelating Circular Coordinates With Lattice Reduction

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.

Representations of Energy Landscapes by Sublevelset Persistent Homology: An Example With n-Alkanes

1 code implementation • 2 Nov 2020 • Joshua Mirth, Yanqin Zhai, Johnathan Bush, Enrique G Alvarado, Howie Jordan, Mark Heim, Bala Krishnamoorthy, Markus Pflaum, Aurora Clark, Y Z, Henry Adams

Encoding the complex features of an energy landscape is a challenging task, and often chemists pursue the most salient features (minima and barriers) along a highly reduced space, i. e. 2- or 3-dimensions.

Chemical Physics Mathematical Physics Algebraic Topology Mathematical Physics

A torus model for optical flow

1 code implementation • 9 Nov 2018 • Henry Adams, Johnathan Bush, Brittany Carr, Lara Kassab, Joshua Mirth

We propose a torus model for high-contrast patches of optical flow.

Optical Flow Estimation