36 citations · 177 across the 35 of their papers we have counts for
6 papers · 1 filter
A Proof of the Invariant Based Formula for the Linking Number and its Asymptotic Behaviour
Matt Bright, Olga Anosova, Vitaliy Kurlin
In 1833 Gauss defined the linking number of two disjoint curves in 3-space. For open curves this double integral over the parameterised curves is real-valued and invariant modulo r…
The asymptotic behaviour and a near linear time algorithm for isometry invariants of periodic sets
Daniel Widdowson, Marco Mosca, Angeles Pulido +2
The fundamental model of a periodic structure is a periodic point set up to rigid motion or isometry. Our recent paper in SoCG 2021 defined isometry invariants (density functions),…
Encoding and Topological Computation on Textiles
Matt Bright, Vitaliy Kurlin
A textile structure is a periodic arrangement of threads in the thickened plane. A topological classification of textile structures is harder than for classical knots and links tha…
The mergegram of a dendrogram and its stability
Yury Elkin, Vitaliy Kurlin
This paper extends the key concept of persistence within Topological Data Analysis (TDA) in a new direction. TDA quantifies topological shapes hidden in unorganized data such as cl…
A fast approximate skeleton with guarantees for any cloud of points in a Euclidean space
Yury Elkin, Di Liu, Vitaliy Kurlin
The tree reconstruction problem is to find an embedded straight-line tree that approximates a given cloud of unorganized points in up to a certain error. A practical…
Voronoi-based similarity distances between arbitrary crystal lattices
Marco Michele Mosca, Vitaliy Kurlin
This paper develops a new continuous approach to a similarity between periodic lattices of ideal crystals. Quantifying a similarity between crystal structures is needed to substant…