11 citations · 54 across the 16 of their papers we have counts for
17 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…
The importance of definitions in crystallography
Olga Anosova, Vitaliy Kurlin, Marjorie Senechal
This paper was motivated by the articles "Same or different - that is the question" in CrystEngComm (July 2020) and "Change to the definition of a crystal" in the IUCr newsletter (…
Accelerating Material Property Prediction using Generically Complete Isometry Invariants
Jonathan Balasingham, Viktor Zamaraev, Vitaliy Kurlin
Periodic material or crystal property prediction using machine learning has grown popular in recent years as it provides a computationally efficient replacement for classical simul…
Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants with no False Negatives and no False Positives
Daniel Widdowson, Vitaliy Kurlin
Rigid structures such as cars or any other solid objects are often represented by finite clouds of unlabeled points. The most natural equivalence on these point clouds is rigid mot…
Density functions of periodic sequences of continuous events
Olga Anosova, Vitaliy Kurlin
Periodic Geometry studies isometry invariants of periodic point sets that are also continuous under perturbations. The motivations come from periodic crystals whose structures are…
Counterexamples expose gaps in the proof of time complexity for cover trees introduced in 2006
Yury Elkin, Vitaliy Kurlin
This paper is motivated by the k-nearest neighbors search: given an arbitrary metric space, and its finite subsets (a reference set R and a query set Q), design a fast algorithm to…
Densest plane group packings of regular polygons
Miloslav Torda, John Y. Goulermas, Vitaliy Kurlin +1
Packings of regular convex polygons (-gons) that are sufficiently dense have been studied extensively in the context of modeling physical and biological systems as well as discr…
Density functions of periodic sequences
Olga Anosova, Vitaliy Kurlin
Periodic point sets model all solid crystalline materials whose structures are determined in a rigid form and should be studied up to rigid motion or isometry preserving inter-poin…
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…
Entropic trust region for densest crystallographic symmetry group packings
Miloslav Torda, John Y. Goulermas, Roland Púček +1
Molecular crystal structure prediction (CSP) seeks the most stable periodic structure given the chemical composition of a molecule and pressure-temperature conditions. Modern CSP s…
Paired compressed cover trees guarantee a near linear parametrized complexity for all -nearest neighbors search in an arbitrary metric space
Yury Elkin, Vitaliy Kurlin
This paper studies the important problem of finding all -nearest neighbors to points of a query set in another reference set within any metric space. Our previous work d…
A new near-linear time algorithm for k-nearest neighbor search using a compressed cover tree
Yury Elkin, Vitaliy Kurlin
Given a reference set of points and a query set of points in a metric space, this paper studies an important problem of finding -nearest neighbors of every point…
Geographic-style maps for 2-dimensional lattices
Matthew Bright, Andrew I Cooper, Vitaliy Kurlin
This paper develops geographic-style maps containing 2D lattices in all known crystals parameterised by recent complete invariants. Motivated by rigid crystal structures, lattices…
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…