Výsledky vyhledávání - "Moy, Michael"

Report

Autor: Adams, Henry, Lagoda, Evgeniya, Moy, Michael, Sadovek, Nikola, De Saha, Aditya

This article has two goals. First, we hope to give an accessible introduction to persistent equivariant cohomology. Given a topological group $G$ acting on a filtered space, persistent Borel equivariant cohomology measures not only the shape of the f

Externí odkaz: http://arxiv.org/abs/2408.17331

Zobrazit plný text záznamu

Report

Gromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips complexes

Autor: Adams, Henry, Bush, Johnathan, Clause, Nate, Frick, Florian, Gómez, Mario, Harrison, Michael, Jeffs, R. Amzi, Lagoda, Evgeniya, Lim, Sunhyuk, Mémoli, Facundo, Moy, Michael, Sadovek, Nikola, Superdock, Matt, Vargas, Daniel, Wang, Qingsong, Zhou, Ling

We explore emerging relationships between the Gromov-Hausdorff distance, Borsuk-Ulam theorems, and Vietoris-Rips simplicial complexes. The Gromov-Hausdorff distance between two metric spaces $X$ and $Y$ can be lower bounded by the distortion of (poss

Externí odkaz: http://arxiv.org/abs/2301.00246

Zobrazit plný text záznamu

Report

Vietoris-Rips Metric Thickenings of the Circle

Autor: Moy, Michael

Vietoris-Rips metric thickenings have previously been proposed as an alternate approach to understanding Vietoris-Rips simplicial complexes and their persistent homology. Recent work has shown that for totally bounded metric spaces, Vietoris-Rips met

Externí odkaz: http://arxiv.org/abs/2206.03539

Zobrazit plný text záznamu

Report

The Persistent Topology of Optimal Transport Based Metric Thickenings

Autor: Adams, Henry, Mémoli, Facundo, Moy, Michael, Wang, Qingsong

Publikováno v: Algebr. Geom. Topol. 24 (2024) 393-447

A metric thickening of a given metric space $X$ is any metric space admitting an isometric embedding of $X$. Thickenings have found use in applications of topology to data analysis, where one may approximate the shape of a dataset via the persistent

Externí odkaz: http://arxiv.org/abs/2109.15061

Zobrazit plný text záznamu

Report

Topology Applied to Machine Learning: From Global to Local

Autor: Adams, Henry, Moy, Michael

Through the use of examples, we explain one way in which applied topology has evolved since the birth of persistent homology in the early 2000s. The first applications of topology to data emphasized the global shape of a dataset, such as the three-ci

Externí odkaz: http://arxiv.org/abs/2103.05796

Zobrazit plný text záznamu

Report

Path Optimization Sheaves

Autor: Moy, Michael, Cardona, Robert, Green, Robert, Cleveland, Jacob, Hylton, Alan, Short, Robert

Motivated by efforts to incorporate sheaves into networking, we seek to reinterpret pathfinding algorithms in terms of cellular sheaves, using Dijkstra's algorithm as an example. We construct sheaves on a graph with distinguished source and sink vert

Externí odkaz: http://arxiv.org/abs/2012.05974

Zobrazit plný text záznamu