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

Selected 10 papers in top journals and conferences

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All papers by research topics and chronologically : Google scholar, arXiv, MathSciNet

2024   2023   2022   2021   2020   2019   2016-2018   2011-2015   2008-2010   2005-2007   2001-2004   1999-2000

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2024   CGD   IUCrJ   APCT   SR   MATCH   IMMI   RCR  

208 carbon allotropes on a map of the CSD
  • Dan Widdowson, Vitaliy Kurlin.
  • Continuous invariant-based maps of the Cambridge Structural Database.
  • Crystal Growth & Design (2024), to appear.
  • pdf [extended, 35 pages]   PDF [project page]   url [reference]
ambiguity of periodic point sets
point cloud with trivial 1D persistence
geometric descriptors of crystals
  • Jonathan Balasingham, Viktor Zamaraev, Vitaliy Kurlin.
  • Accelerating Material Property Prediction using Generically Complete Isometry Invariants.
  • Scientific Reports, v.14 (10132), 2024.
  • pdf [11 pages, 1.5M]   PDF [project page]   url [reference]
triangle vs square
  • Vitaliy Kurlin.
  • Polynomial-time algorithms for continuous metrics on atomic clouds of unordered points.
  • MATCH Communications in Mathematical and in Computer Chemistry, v.91 (2024), p.79-108.
  • url [30 pages, 1M]   PDF [project page]   url [reference]
Distance Distribution Graph for the table salt crystal
stress vs strain for plastics
  • Philip Smith, Andy McLauchlin, Tom Franklin, Peiyao Yan, Emily Cunliffe, Tom Hasell, Vitaliy A Kurlin, Colin Kerr, Jonathan Attwood, Michael P Shaver, Tom O McDonald.
  • A data-driven analysis of HDPE post-consumer recyclate for sustainable bottle packaging.
  • Resources, Conservation and Recycling, v.205 (2024), 107538.
  • pdf [11 pages]   PDF [project page]   url [reference]

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2023   ICML   CVPR   Chirality   DiD   JMIV   SISC   ACA   npjCM  

cover trees
  • Yury Elkin, Vitaliy Kurlin.
  • A new near-linear time algorithm for k-nearest neighbor search using a compressed cover tree.
  • ICML 2023 (International Conference on Machine Learning), p. 9267-9311. Top 20 publication venue across all subjects including Nature and Science.
  • url [45 pages, 615K]   PDF [project page]   url [reference]
non-isometric 4-point clouds
  • Dan Widdowson, Vitaliy Kurlin.   Video (8 min)   Poster (pdf)
  • Recognizing rigid patterns of unlabeled point clouds by complete and continuous isometry invariants with no false negatives and no false positives.
  • Proceedings of CVPR 2023 (Computer Vision and Pattern Recognition), 1275-1284. Top 4 publication venue across all subjects including Nature and Science.
    Extended version of section 3 for metric spaces: url [latest pdf]
    Extended version of section 4 for Euclidean spaces: url [latest pdf]
  • PDF [10 pages, 1.4M]   PDF [project page]   url [reference]
root chiral distance projective chiral distance
structural distance based on geometric invariants
  • Daniel Schwalbe-Koda, Dan Widdowson, Tuan Anh Pham, Vitaliy Kurlin.
  • Inorganic synthesis-structure maps in zeolites with machine learning and crystallographic distances.
  • Digital Discovery, v.2(6), p.1911-1924 (2023), doi:10.1039/D3DD00134B.
  • url [30 pages, 1M]   PDF [project page]   url [reference]
density functions of a 4-point periodic sequence
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 [accepted version, 52 pages, 21M]   web [project page]   url [reference]
map of 2D lattices from CSD crystals
room temperature conductivities
  • C.Hargreaves, M.Gaultois, L.Daniels, E.Watts, V.Kurlin, M.Moran, Y.Dang, R.Morris, A.Morscher, K.Thompson, M.Wright, B.Prasad, F.Blanc, C.Collins, C.Crawford, B.Duff, J.Evans, J.Gamon, G.Han, B.Leube, H.Niu, A.Perez, A.Robinson, O.Rogan, P.Sharp, E.Shoko, M.Sonni, W.Thomas, A.Vasylenko, L.Wang, M.Rosseinsky, M.Dyer.
  • A Database of Experimentally Measured Lithium Solid Electrolyte Conductivities Evaluated with Machine Learning. npj Computational Materials, v.9, 9 (2023).

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2022   FoCM   NeurIPS   PRE   JACS   MATCH   DiD   ISVC   DGMM   DAMDID   TopoInVis   CMMP   BDA  

quotient square of all 2D lattices
ambiguity of crystal representations
patterns of densest packings of regular polygons
  • Milo Torda, John Goulermas, Vitaliy Kurlin, Graeme Day.
  • Densest plane group packings of regular polygons.
  • Physical Review E, v. 106 (5), 054603.
  • PDF [13 pages, 372K]   PDF [project page]   url [reference]
invariants help discover materials
  • Qiang Zhu, Jay Johal, Dan Widdowson, Zhongfu Pang, Boyu Li, Christopher M Kane, Vitaliy A Kurlin, Graeme M Day, Marc Little, Andrew I Cooper.
  • Analogy Powered by Prediction and Structural Invariants: Computationally-Led Discovery of a Mesoporous Hydrogen-Bonded Organic Cage Crystal.
  • JACS (J Amer. Chem. Society), 2022, 144, 22, 9893–9901.
  • PDF [9 pages, 3M]   PDF [project page]   url [reference]
AMD of the square lattice AMD of the hexagonal lattice
  • Dan Widdowson, Marco M Mosca, Angeles Pulido, Andrew I Cooper, Vitaliy 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]   PDF [project page]   url [reference]
Minimum Spanning Tree of co-crystals
  • Aikaterini Vriza, Ioana Sovago, Dan Widdowson, Peter Wood, Vitaliy Kurlin, Matthew Dyer.
  • Molecular Set Transformer: Attending to the co-crystals in the Cambridge Structural Database.
  • Digital Discovery, v.1 (2022), p.834-850.
  • PDF [17 pages, 3.8M]   PDF [project page]   url [reference]
higher degree Voronoi domains
  • Phil Smith, Vitaliy Kurlin.
  • A practical algorithm for degree-k Voronoi domains of three-dimensional periodic point sets.
  • Lecture Notes in Computer Science (Proceedings of ISVC 2022), v.13599, p.377-391.
  • PDF [14 pages, 2.1M]   PDF [project page]   url [reference]
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]   PDF [project page]   url [reference]
energy continuous in AMD invariants
  • Jakob Ropers, Marco Mosca, Olga Anosova, Vitaliy Kurlin, Andrew Cooper.
  • Fast predictions of lattice energies by continuous isometry invariants of crystal structures.
  • Proceedings of DAMDID : Data Analytics and Management in Data Intensive Domains, p.178–192.
  • url [early version]   PDF [project page]   url [reference]
cover trees
  • Yury Elkin, Vitaliy Kurlin.
  • Counterexamples expose gaps in the proof of time complexity for cover trees introduced in 2006.
  • Proceedings of TopoInVis 2022 : IEEE Workshop on Topological Data Analysis and Visualization, p.9-17.
  • PDF [9 pages, 240K]   PDF [project page]   url [reference]
linking line segments
atmospheric river
  • Grzegorz Muszynski, Vitaliy Kurlin, Dmitriy Morozov, Michael Wehner, Karthik Kashinath, Prabhat Ram
  • Topological Methods for Pattern Detection in Climate Data.
  • Big Data Analytics in Earth, Atmospheric and Ocean Sciences, p. 227-242, Wiley.
  • web [project page]   bib [reference]   url [official link]

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2021   Mathematics   DGMM   PR   SoCG   CS   NumGrid   ICPR  

recognition rates
  • Yury Elkin, Vitaliy Kurlin.
  • Isometry invariant shape recognition of projectively perturbed point clouds by the mergegram extending 0D persistence.
  • Mathematics, 2021, 9(17), 2121.
  • PDF [17 pages, 1.5M]   PDF [project page]   url [reference]
space of isometry classes
HoPeS on 10 points 1D persistence of 10 points
  • Phil Smith, Vitaliy Kurlin.
  • Skeletonisation algorithms with theoretical guarantees for unorganised point clouds with high levels of noise.
  • Pattern Recognition, v.115 (2021), 107902.
  • PDF [extended, 48 pages, 7.6M]   PDF [project page]   url [reference]
offset at radius 0.25 offset at radius 0.55 offset at radius 0.75 offset at radius 0.55
1-class-classification
  • Aikaterini Vriza, Angelos Canaj, Rebecca Vismara, Laurence Cook, Troy Manning, Michael Gaultois, Peter Wood, Vitaliy Kurlin, Neil Berry, Matthew Dyer and Matthew Rosseinsky.
  • One class classification as a practical approach for accelerating π-π co-crystal discovery.
  • Chemical Science, v.12 (2021), p.1702-1719.
  • PDF [18 pages, 2.7M]   PDF [project page]   url [reference]
linking number surface
world regions
  • G. Muszynski, Prabhat, J. Balewski, K. Kashinath, M. Wehner, V. Kurlin.
  • Atmospheric Blocking Pattern Recognition in Global Climate Model Simulation Data.
  • Proceedings of ICPR : International Conference on Pattern Recognition.
  • PDF [8 pages, 5.9M]   web [project page]   bib [reference]  

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2020   CM   MFCS   CaG   CRaT   PRL   VISAPP   GECCO  

earth-mover's-distance earth-mover's-distance
  • Cameron Hargreaves, Matthew Dyer, Michael Gaultois, Vitaliy Kurlin, Matthew Rosseinsky.
  • The Earth Mover’s Distance as a Metric for the Space of Inorganic Compositions.
  • Chemistry of Materials, volume 32 (24), p.10610-10620 (December 2020).
  • PDF [11 pages, 3.5M]   PDF [project page]   url [reference]
textile structure
ambiguous cells of a lattice
Persistence-based mesh
polygonal mesh of a vortex image
  • Arshad Siddiqui, Vitaliy Kurlin.
  • Polygonal Meshes of Noisy Images based on a new Thinning Algorithm with Theoretical Guarantees.
  • Proceedings of VISAPP 2020 (International Conference on Computer Vision Theory and Applications).
  • PDF [10 pages, 16M]   web [project page]   bib [reference]   url [official link]
Conditional Linear Integer Arithmetic
  • Thomas Welsch, Vitaliy Kurlin.
  • Synthesis through Unification Genetic Programming.
  • Proceedings of GECCO : Genetic and Evolutionary Computation Conference.
  • PDF [8 pages, 414K]   url [official link]

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2019   JGRA   AAM   TopoInVis   ISVC   GMD   AIAA   CTIC  

impact of Atmospheric Rivers
  • Jonathan Rutz et al.
  • The Atmospheric River Tracking Method Intercomparison Project (ARTMIP): Quantifying Uncertainties in Atmospheric River Climatology.
  • Journal of Geophysical Research: Atmospheres, v. 124 (24), 2019, p. 13777-13802.
  • PDF [50 pages, 5.5M]   web [project page]   bib [reference]
2D HoPeS
  • Sara Kalisnik, Vitaliy Kurlin, Davorin Lesnik.
  • A higher-dimensional Homologically Persistent Skeleton.
  • Advances in Applied Mathematics, v.102 (2019), p.113-142.
  • PDF [30 pages, 1M]   web [project page]   bib [reference]

RIMe superpixels
Atmospheric River detection
  • Grzegorz Muszynski, Karthik Kashinath, Vitaliy Kurlin, Michael Wehner, Prabhat
  • Topological Data Analysis and Machine Learning for Recognizing Atmospheric River Patterns in Large Climate Datasets.
  • Geoscientific Model Development, v. 12, p. 613-628, 2019.
  • PDF [24 pages, 7.4M]   web [project page]   bib [reference]   url [official link]
vortex_skeleton
  • Naohiko Ban, Wataru Yamazaki, Vitaliy Kurlin.
  • Development of a Reconstruction Method for Major Vortex Structure around Tandem Flapping Wing Object via Vortex Trajectory Method.
  • American Institute of Aeronautics and Astronautics SciTech Forum (2019).
  • PDF [37 pages, 7.2M]   web [project page]   bib [reference]   url [official link]
persistence segments

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2018   GMD   CI

Atmospheric Rivers
  • Jonathan Rutz et al.
  • The Atmospheric River Tracking Method Intercomparison Project (ARTMIP): project goals and experimental design.
  • Geoscientific Model Development, v. 11, 2455-2474, 2018.
  • PDF [20 pages, 5.3M]   web [project page]   bib [reference]
multivariate climate data

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2017   EMMCVPR   JEI   MathVis  

mesh reconstruction
  • Vitaliy Kurlin, Donald Harvey.
  • Superpixels Optimized by Color and Shape (SOCS).
  • Proceedings of EMMCVPR 2017 (Energy Minimization Methods in Computer Vision and Pattern Recognition), LNCS 10746, p. 297-311, Springer.
  • PDF [14 pages, 4.9M]   web [project page]   bib [reference]
Voronoi vs CCM
knotted protein

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2016   ISVC   PRL   CCIS

mesh reconstruction
  • Jeremy Forsythe, Vitaliy Kurlin, Andrew Fitzgibbon.
  • Resolution-independent superpixels based on convex constrained meshes without small angles.
  • Proceedings of ISVC 2016: International Symposium on Visual Computing.
  • Lecture Notes in Computer Science, v. 10072, p. 223-233.
  • PDF [extended, 20 pages, 3.7M]   web [project page]   bib [reference]
original image noisy input segmentation
  • Vitaliy Kurlin.
  • A fast persistence-based segmentation of noisy 2D clouds with provable guarantees.
  • Pattern Recognition Letters, v. 83 (2016), p. 3-12.
  • PDF [full version: 16 pages, 4.2M]   web [project page]   bib [reference]   url [official]
knotted neuron

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2015   CGF   CAIP   CCCG   IVAPP

cloud   skeleton
  • Vitaliy Kurlin.
  • A one-dimensional Homologically Persistent Skeleton of a point cloud in any metric space.
  • Computer Graphics Forum, v. 34, no. 5 (2015), p. 253-262.
  • A special issue devoted to SGP 2015: Eurographics Symposium on Geometry Processing.
  • PDF [extended, 14 pages, 3.2M]   web [project page]   bib [reference]
noisy scan reconstruction
  • Vitaliy Kurlin.
  • A Homologically Persistent Skeleton is a fast and robust descriptor of interest points in 2D images.
  • Lecture Notes in Computer Science, v. 9256 (2015), p. 606-617.
  • (Proceedings of CAIP 2015: Computer Analysis of Images and Patterns).
  • PDF [12 pages, 1.2M]   web [project page]   bib [reference]   url [official link]
disk packing
  • Herbert Edelsbrunner, Mabel Iglesias-Ham, Vitaliy Kurlin.
  • Relaxed disk packing.
  • Proceedings of CCCG 2015: Canadian Conference on Computational Geometry, p.128-135.
  • PDF [8 pages, 390K]   web [project page]   bib [reference]  
a 3-page embedding of a Hopf graph
  • Vitaliy Kurlin.
  • A linear time algorithm for visualizing knotted structures in 3 pages.
  • Proceedings of IVAPP 2015: Information Visualization Theory and Applications, p. 5-16.
  • PDF [12 pages, 2.5M]   web [project page]   bib [reference]   url [official link]

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2014   CVPR   CTIC   ICRoM

count holes in a cloud
  • Vitaliy Kurlin.
  • A fast and robust algorithm to count topologically persistent holes in noisy clouds.
  • Proceedings of CVPR 2014: Computer Vision and Pattern Recognition, p. 1458-1463
    (top conference in Computer Science, the highest h-index conference in any field).
  • pdf [extended: 10 pages, 1.6M]   web [project page]   bib [reference]
noisy input automatic output
  • Vitaliy Kurlin.
  • Auto-completion of contours in sketches, maps and sparse 2D images based on persistence.
  • Proceedings of workshop CTIC (Computational Topology in Image Context) at SYNASC 2014
  • (Symposium on Symbolic and Numeric Algorithms for Scientific Computing), p. 594-601.
  • PDF [8 pages, 1.1M]   web [project page]   bib [reference]   bib [code: beta-version]
round robots in a metric graph
  • Vitaliy Kurlin, Marjan Safi-Samghabadi.
  • Computing a skeleton of the configuration space of 2 round robots on a metric graph.
  • Proceedings of ICRoM 2014: International Conference on Robotics and Mechatronics, p. 723-729.
  • PDF [7 pages, 370K]   Slides [pdf, 32 pages, 1.6M]   url [official link]

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2013   JAPS   Image-A

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2012   HHA

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2008 - 2010 : singularity theory applied to knots and links

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2005 - 2007 : postdoctoral work in non-commutative algebra

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2001 - 2004 : PhD work about classifications of embedded graphs

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1999 - 2000 : MSc work about link invariants and basic embeddings

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Invited lectures at international conferences

2024 | 2023 | 2022 | 2020-2021 | 2019 | 2017-2018 | 2016 | 2015 | 2011-2014 | 2007-2010 | 2005-2006 | 1999-2004

Videos of past talks, see also the most recent videos

Oral presentations in 2024

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Oral presentations in 2023

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Oral presentations in 2022

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Oral presentations in 2020-2021

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Oral presentations in 2019

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Oral presentations in 2017-2018

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Oral presentations in 2016

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Oral presentations in 2015

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Oral presentations in 2011-2014

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Oral presentations in 2007-2010

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Oral presentations in 2005-2006

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Oral presentations in 1999-2004

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Smaller research grants, see also larger awards

Liverpool logo Faculty summer bursaries (value 2×1K GBP) at the University of Liverpool for 2nd year undergraduates Cristian Badoi and Wenkai Zhang (2019).
LMS logo Since 2017 the organiser of the network Applied Geometry and Topology covering 3 meetings per year at the Universities of Liverpool, Queen Mary (G.Bianconi, M.Farber) and Southampton (J.Brodzki, J.Grbić), funded by the London Mathematical Society (total value 7.2K GBP in 2017-2022).
EPSRC logo EPSRC vacation bursaries (value 2×2.7K GBP) at the University of Liverpool for 2nd year undergraduates Simon Hirst (2017) and Gee Jack (2018).
LMS logo Summer bursary of the London Mathematical Society for Philip Smith (value 1.1K GBP) to work on the project Superpixel meshes for faster image and video processing in August - September 2016, closely related to the collaboration with Microsoft Research Cambridge.
IAS image Christopherson/Knott fellowship at Institute of Advanced Study (left after moving to Liverpool, UK). Title : Optimal meshes of superpixels for faster image processing (7.5K GBP 3-month teaching replacement).
Alan Turing Institute logo Conference grant (3K GBP, jointly with M.Grinfeld and M.Haw) to run the ATI strategic workshop on 14 March 2016 : Topological Data Analysis in Materials Science and Engineering.
LMS logo Travel grant of the London Mathematical Society to give the contributed 20-min talk Topological Computer Vision in the section Mathematical Image and Signal Processing at 7ECM (European Congress of Mathematicians) at TU Berlin on 18-22 July 2016.
ESF logo Travel grant (1.7K Euros) by the ACAT (Applied and Computational Algebraic Topology) network of ESF (European Science Foundation) to visit IST Austria (March 2015).
EC logo INTAS PhD Fellowship (10K Euros) at Moscow State University, March 2001 - February 2003, covered research collaboration at Universities of Montpellier II, Liverpool, Dijon, Toulouse III, Paris VII.

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Co-authors in the alphabetical order (last updated in 2016)

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