6 papers
The strength of a geometric simplex
Olga Anosova, Vitaliy Kurlin
The basic input for many real objects is a finite cloud of unordered points. The strongest equivalence between objects in practice is rigid motion in a Euclidean space. A recent po…
Continuous invariant-based asymmetries of periodic crystals quantify deviations from higher symmetry
Surya Majumder, Daniel Widdowson, Yury Elkin +4
Ideal symmetry is known to break down under almost any noise. One measure of asymmetry in a periodic crystal is the relative multiplicity Z' of geometrically non-equivalent units.…
Computing the bridge length: the key ingredient in a continuous isometry classification of periodic point sets
Jonathan McManus, Vitaliy Kurlin
The fundamental model of any periodic crystal is a periodic set of points at all atomic centres. Since crystal structures are determined in a rigid form, their strongest equivalenc…
Complete and bi-continuous invariant of protein backbones under rigid motion
Olga Anosova, Alexey Gorelov, William Jeffcott +2
Proteins are large biomolecules that regulate all living organisms and consist of one or several chains. The primary structure of a protein chain is a sequence of amino acid residu…
Pointwise Distance Distributions for detecting near-duplicates in large materials databases
Daniel Widdowson, Vitaliy Kurlin
Many real objects are modeled as discrete sets of points, such as corners or other salient features. For our main applications in chemistry, points represent atomic centers in a mo…
Recognition of near-duplicate periodic patterns by continuous metrics with approximation guarantees
Olga Anosova, Daniel Widdowson, Vitaliy Kurlin
This paper rigorously solves the challenging problem of recognizing periodic patterns under rigid motion in Euclidean geometry. The 3-dimensional case is practically important for…