Zobrazeno 1 - 10
of 2 222
pro vyhledávání: '"GILLESPIE, PATRICK"'
Equipping graph neural networks with a convolution operation defined in terms of a cellular sheaf offers advantages for learning expressive representations of heterophilic graph data. The most flexible approach to constructing the sheaf is to learn i
Externí odkaz:
http://arxiv.org/abs/2410.09590
Autor:
Gillespie, Patrick
Characterizing the homotopy types of the Vietoris--Rips complexes of a metric space $X$ is in general a difficult problem. The Vietoris--Rips metric thickening, a metric space analogue of the Vietoris--Rips complex, was introduced as a potentially mo
Externí odkaz:
http://arxiv.org/abs/2303.01019
Autor:
Brazas, Jeremy, Gillespie, Patrick
In this paper, we analyze the fundamental group $\pi_1(\Sigma X,\overline{x_0})$ of the reduced suspension $\Sigma X$ where $(X,x_0)$ is an arbitrary based Hausdorff space. We show that $\pi_1(\Sigma X,\overline{x_0})$ is canonically isomorphic to a
Externí odkaz:
http://arxiv.org/abs/2211.10499
Autor:
Gillespie, Patrick
In this note we show that a particular homological nerve theorem, which was originally proved for a finite cover of a simplicial complex by subcomplexes, also holds for an open cover of an arbitrary topological space. The motivation for this is to af
Externí odkaz:
http://arxiv.org/abs/2210.00388
Autor:
Story, Brittany, Gillespie, Patrick, Derryberry, Graham, Derryberry, Elizabeth, Fefferman, Nina, Maroulas, Vasileios
Publikováno v:
In Ecological Informatics September 2024 82
Autor:
Brazas, Jeremy, Gillespie, Patrick
The well-known Eckmann-Hilton Principle may be applied to prove that fundamental groups of $H$-spaces are commutative. In this paper, we identify an infinitary analogue of the Eckmann-Hilton Principle that applies to fundamental groups of all topolog
Externí odkaz:
http://arxiv.org/abs/2001.09500
Akademický článek
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Autor:
Lancaster, Makayla S., Kim, Byungwook, Doud, Emma H., Tate, Mason D., Sharify, Ahmad D., Gao, Hongyu, Chen, Duojiao, Simpson, Ed, Gillespie, Patrick, Chu, Xiaona, Miller, Marcus J., Wang, Yue, Liu, Yunlong, Mosley, Amber L., Kim, Jungsu, Graham, Brett H.
Publikováno v:
In Cell Reports 31 October 2023 42(10)
Autor:
Brazas, Jeremy, Gillespie, Patrick
Publikováno v:
In Topology and its Applications 1 August 2022 317
Autor:
Lancaster, Makayla S., Hafen, Paul, Law, Andrew S., Matias, Catalina, Meyer, Timothy, Fischer, Kathryn, Miller, Marcus, Hao, Chunhai, Gillespie, Patrick, McKinzie, David, Brault, Jeffrey J., Graham, Brett H.
Publikováno v:
Journal of Cachexia, Sarcopenia & Muscle; Dec2024, Vol. 15 Issue 6, p2729-2742, 14p