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

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


Material property prediction by isometry invariants

Distance Distribution Graph for the table salt crystal

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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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Higher degree Voronoi domains of periodic point sets

higher degree Voronoi domains
  • Phil Smith, Vitaliy Kurlin.
  • A practical algorithm for degree-k Voronoi domains of three-dimensional periodic point sets.
  • Proceedings of ISVC 2022, Lecture Notes in Computer Science, v.13599, p.377-391.
  • PDF [14 pages, 2.1M]   url [official link]  

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Density functions of periodic sequences

density functions of a 3-point periodic sequence
  • Olga Anosova, Vitaliy Kurlin.
  • Density functions of periodic sequences.
  • Lecture Notes in Computer Science (Proceedings of DGMM 2022: Discrete Geometry and Mathematical Morphology), v.13493, p.395-408.
  • PDF [13 pages, 2M]   url [official link]   url [early version]

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Density functions of a periodic point set

offset at radius 0.25 offset at radius 0.55 offset at radius 0.75 offset at radius 0.55

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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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