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math.MG2024
Stability of Hypergraph Invariants and Transformations
Tom Needham, Ethan Semrad
Graphs are fundamental tools for modeling pairwise interactions in complex systems. However, many real-world systems involve multi-way interactions that cannot be fully captured by…
math.MG2024
Geometry of the Space of Partitioned Networks: A Unified Theoretical and Computational Framework
Stephen Y Zhang, Fangfei Lan, Youjia Zhou +4
Interactions and relations between objects may be pairwise or higher-order in nature, and so network-valued data are ubiquitous in the real world. The "space of networks", however,…
math.AT2024
Topological Optimal Transport for Geometric Cycle Matching
Stephen Y Zhang, Michael P H Stumpf, Tom Needham +1
Topological data analysis is a powerful tool for describing topological signatures in real world data. An important challenge in topological data analysis is matching significant t…