Dr Vitaliy Kurlin: mathematics & computer science

Data Science theory and applications. Everything is possible!

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

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

NeurIPS 2022   PRE 2022   MATCH 2022   ISVC 2022   DGMM 2022   SoCG 2021   DGMM 2021


Resolving the data ambiguity for periodic crystals

ambiguity of crystal representations
  • Dan Widdowson, Vitaliy Kurlin.
  • Resolving the data ambiguity for periodic crystals.
  • Advances in Neural Information Processing Systems (NeurIPS 2022), v.35.
  • PDF [14 pages, 1.1M]   url [early version, extended]  

Back to Top of this page | Back to Research & papers | Back to Home page

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.
  • PDF [11 pages, 370K]   url [official link]   url [early version]

Back to Top of this page | Back to Research & papers | Back to Home page

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 [24 pages, 2.6M]   url [official link]   url [early version]

Back to Top of this page | Back to Research & papers | Back to Home page

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.
  • PDF [14 pages, 2.1M]   url [official link]  

Back to Top of this page | Back to Research & papers | Back to Home page

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]

Back to Top of this page | Back to Research & papers | Back to Home page

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

Back to Top of this page | Back to Research & papers | Back to Home page

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]  

Back to Top of this page | Back to Research & papers | Back to Home page