Zobrazeno 1 - 10
of 43
pro vyhledávání: '"Moy, Michael"'
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
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
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
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
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
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
Akademický článek
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Autor:
Moy, Michael
Publikováno v:
Journal of Applied & Computational Topology; Dec2023, Vol. 7 Issue 4, p831-877, 47p
