24 citations · 81 across the 19 of their papers we have counts for
Showing 2021Show all
2 papers · 1 filter
math.GT2021
A statistical approach to knot confinement via persistent homology
Daniele Celoria, Barbara I. Mahler
In this paper we study how randomly generated knots occupy a volume of space using topological methods. To this end, we consider the evolution of the first homology of an immersed…
math.CO2021
Filtered simplicial homology, graph dissimilarity and überhomology
Daniele Celoria
We introduce a filtration on the simplicial homology of a finite simplicial complex X using bi-colourings of its vertices. This yields two dual homology theories closely related to…