1 citations · 1 across the 3 of their papers we have counts for
8 papers
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…
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…
Bigraded path homology and the magnitude-path spectral sequence
Richard Hepworth, Emily Roff
Two important invariants of directed graphs, namely magnitude homology and path homology, have recently been shown to be intimately connected: there is a 'magnitude-path spectral s…
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…
The small-scale limit of magnitude and the one-point property
Emily Roff, Masahiko Yoshinaga
The magnitude of a metric space is a real-valued function whose parameter controls the scale of the metric. A metric space is said to have the one-point property if its magnitude c…
The reachability homology of a directed graph
Richard Hepworth, Emily Roff
The last decade has seen the development of path homology and magnitude homology -- two homology theories of directed graphs, each satisfying classic properties such as Kunneth and…