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math.MG2026
The microscopic weighting on a metric space
Emily Roff, Simon Willerton
We introduce the microscopic weighting, a canonical signed measure of mass one that can be associated to almost any finite metric space. The microscopic weighting is obtained as th…
math.AT2026
Homotopy theories via the magnitude-path spectral sequence
Muriel Livernet, Emily Roff, Sarah Whitehouse
We introduce a family of homotopy theories for generalized metric spaces with natural number distances, via the magnitude-path spectral sequence (MPSS). The first page of the MPSS…
cs.SI2026
Coalgebraic analysis of social systems
Nima Motamed, Nina Otter, Emily Roff
The algebraic analysis of social systems, or algebraic social network analysis, refers to a collection of methods designed to extract information about the structure of a social sy…