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 Knotted graphs based on papers in

CMMP 2022   NumGrid 2020   MV 2017   CCIS 2016   IVAPP 2015  

Invariant-based formula for the linking number

linking line segments
  • Matthew Bright, Olga Anosova, Vitaliy Kurlin
  • A formula for the linking number in terms of isometry invariants of straight line segments
  • Computational Mathematics and Mathematical Physics, v.62(8), p.1217–1233, 2022.
  • PDF [17 pages, 1.9M]   url [official link]   url [early version]

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Asymptotic behaviour of the linking number

linking number surface
  • Matthew Bright, Olga Anosova, Vitaliy Kurlin
  • A proof of the invariant-based formula for the linking number and its asymptotic behaviour
  • Springer Lecture Notes in Computational Science and Engineering, v.143, p.37-60.
  • Presented at NumGrid 2020 : Numerical Geometry, Grid Generation, Scientific Computing
  • PDF [extended, 20 pages, 1.4M]   url [official link]   url [early version]

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Paper: Computing invariants of knotted graphs given by sequences of points in 3-dimensional Space.

knotted protein
  • Author : V. Kurlin.
  • Reference : in the Springer book of the series MV: Mathematics and Visualization, p. 349-363
    (post-proceedings of TopoInVis 2015: Topology-based Methods in Visualization.
  • PDF [14 pages, 0.9M]   Slides [pdf, 24 pages, 1.4M]  

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Paper: A linear time algorithm for embedding arbitrary knotted graphs into a 3-page book.

knotted neuron

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Paper: A linear time algorithm for visualizing knotted structures in 3 pages.

3-page embedding
  • Author : V. Kurlin.
  • Reference : Proc. IVAPP 2015: Information Visualization Theory and Applications, p. 5-16.
  • PDF [14 pages, 1.1M]   Slides [pdf, 16 pages, 1.6M]   bib [code, beta]   url [official link]

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