Prof Vitaliy Kurlin: mathematics & computer science

Data Science theory and applications. Everything is possible!

E-mail: vitaliy.kurlin(at)gmail.com, University of Liverpool, UK

Project Periodic Geometry within a new area of Geometric Data Science based on papers in

IUCrJ 2024   SISC 2023   NeurIPS 2022   PRE 2022   MATCH 2022   DGMM 2021


Important definitions in crystallography

crystallographic packing

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Densest Crystallographic Group Packings

crystallographic packing
  • Milo Torda, John Goulermas, Roland Púček, Vitaliy Kurlin.
  • Entropic Trust Region for Densest Crystallographic Symmetry Group Packings.
  • SIAM Journal on Scientific Computing, 2023, v. 45 (4), p. B493-B522.
  • PDF [52 pages, 372K]   url [official link]

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Resolving the data ambiguity for periodic crystals

ambiguity of crystal representations

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Densest packings of regular polygons

patterns of densest packings of regular polygons
  • Milo Torda, John Y Goulermas, Vitaliy A Kurlin, Graeme M Day.
  • Densest plane group packings of regular polygons.
  • Physical Review E, v. 106 (5), 054603 (2022).
  • PDF [11 pages, 372K]   url [official link]   url [early version]

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Average Minimum Distances of periodic point sets

AMD of the square lattice AMD of the hexagonal lattice
  • Dan Widdowson, Marco M Mosca, Angeles Pulido, Andrew I Cooper, Vitaliy A Kurlin.
  • Average Minimum Distances of periodic point sets - foundational invariants for mapping all periodic crystals.
  • MATCH Communications in Mathematical and in Computer Chemistry, v.87(3), p.529-559, 2022.
  • PDF [31 pages, 2.6M]   url [official link]   url [early version]

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Crystal isosets are complete isometry invariants

isometry space of lattices
  • Olga Anosova, Vitaliy Kurlin.
  • An isometry classification of periodic point sets.
  • Lecture Notes in Computer Science (Proceedings of DGMM 2021 : Discrete Geometry and Mathematical Morphology), v.12708, p.229-241.
  • PDF [14 pages, 757K]   url [official link]  

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