1 citations · 2 across the 9 of their papers we have counts for
10 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…
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…
Is magnitude 'generically continuous' for finite metric spaces?
Hirokazu Katsumasa, Emily Roff, Masahiko Yoshinaga
Magnitude is a real-valued invariant of metric spaces which, in the finite setting, can be understood as recording the 'effective number of points' in a space as the scale of the m…
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…
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…
Iterated magnitude homology
Emily Roff
Magnitude homology is an invariant of enriched categories which generalizes ordinary categorical homology -- the homology of the classifying space of a small category. The classify…
Magnitude, homology, and the Whitney twist
Emily Roff
Magnitude is a numerical invariant of metric spaces and graphs, analogous, in a precise sense, to Euler characteristic. Magnitude homology is an algebraic invariant constructed to…
The maximum entropy of a metric space
Tom Leinster, Emily Roff
We define a one-parameter family of entropies, each assigning a real number to any probability measure on a compact metric space (or, more generally, a compact Hausdorff space with…