Dr Vitaliy Kurlin: mathematics & computer science

We are looking for motivated MSc and PhD students and postdocs with strong C++ or Python skills to work on exciting projects in Geometric and Topological Data Science with real-life applications to Materials Science. Please e-mail vitaliy(dot)kurlin(at)gmail(dot)com if you are interested and would like to join our Data Science group.

Potential projects for PhD, MSc and undergraduates: join us

• The projects are for students of the University of Liverpool from summer 2020, but can be considered by external interns.
• Crystal project : Interactive visualisations of large crystal datasets.
  Solid crystals underpin many technological advances from solid-state batteries to safer crystalline drugs. However, materials discovery still relies on trial-and-error through manual choices or random simulations. The state-of-the-art approach to materials discovery is Crystal Structure Prediction (CSP), which optimises geometric arrangements of given atoms pr molecules on supercomputers. A typical CSP output consists of thousands or even millions of predicted crystals, though only a few crystals can be really synthesised. This embarrassment of over-prediction remains unresolved because there was no reliable method to continuously quantify similarities between nearly identical crystals. The recent Introduction to Periodic Geometry has defined the invariant isoset, which completely and continuously classifies all periodic point sets up to isoemtry or rigid motion, hence will play the role of a DNA code or a materials genome for crystals. Here is the earlier 30-min video introduction. The project aims to implement an interactive software tool based on the TreeMap to visualise any dataset of crystals in a hierarchical way. The input crystal data is first transformed into an invariant form and then presented by a few big clusters, which can be later zoomed in for a more detailed exploration.
• Mapping project : A low-dimensional map of high-dimensional data.
  The aim is to design and implement new algorithms for mapping high-dimensional data in a justifiable way. Most algorithms for visualising data in low dimensions have no underlying theory and involve too many manually chosen parameters that make an output unstable under perturbations of original data. The project will combine the rigorous approaches HoPeS and TreeMap from Geometric and Topological Data Analysis to produce a theoretically justified skeleton on given points given only by pairwise distances. The next or parallel direction is to design and implement a practical algorithm to draw in 2D or 3D a graph without intersections and with specified edge-lengths, potentially with restrictions on triangular cycles. We collaborate with the world-leading materials scientists Prof Andy Cooper FRS and Prof Matt Rosseinsky FRS, whose groups provide us with real and simulated data in the Liverpool Materials Innovation Factory.
• Plastic project : Data science and machine learning for plastic waste reduction.
  Most plastic materials are not really recycled, because the `secondary' plastic has poor performance properties in comparision with `virgin' plastic used (for example) in crack-resistant milk bottles. Any plastic material is an amorphous solid made of polymer molecules. Such a material can be modelled as a fintie set of points representing atoms or molecules in a big box with periodic boundary conditions. The recent paper on Average Minimum Distances introduced fast distance-based invariants of periodic points sets. The first aim is to develop Data Science or Machine Learning methods to predict mechanical properties of plastic from its invariants above. This project will be a part of a nearly £1M grant Understanding the quality-performance linkage for packaging led by Dr Thomas McDonald in Liverpool Chemistry.
• Expected skills for all the projects above.
  This research direction is suitable for a student who is dreaming about a PhD with a practical impact. The project will require strong programming skills, preferably Python, C++ or sometimes R. Communication skills will be needed to collaborate with a PhD student working in the same area. Other potentially useful skills are linear algebra and computational geometry. Depending on progress, there is a potential for a joint publications of research results.
• Publications based on past MSc or final year projects (all co-authored with former students):
  CaG 2020, VISAPP 2020, TopoInVis 2019, EMMCVPR 2017, JEI 2017, ISVC 2016, CCIS 2016.
• How to apply for one of the projects above.
  External candidates are welcome to follow the advice in the post how to join the research group. For internal candidates (final year and MSc students at the University of Liverpool), the first step is to e-mail Dr Vitaliy Kurlin a CV or a brief description of your past programming projects. The second step will involve solving programming exercises on basic geometry and working with software libraries. After that I would be happy to meet for a 15-min discussion. Thank you.

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Past members of the group in Data Science theory and applications

Dr Grzegorz Muszynski was supervised in April 2017 - January 2021 by Dr Vitaliy Kurlin (80%) and Dr Michael Wehner (Lawrence Berkeley National lab, US). In August 2017 his Intel-funded project was announced in the university news and created the Intel Parallel Computing Center at Liverpool. PhD : Pattern Recognition for Weather Phenomena in Climate Data (79M pdf). In 2020 Grzegorz started a permanent Data Science job in the AI lab of the British Antarctic Survey in Cambridge, UK. Publications : ICPR 2021, PRL 2020, GMD 2019, JGRA 2019, CTIC 2019, GMD 2018, CI 2018.

• Short-term project students in 2019-20: Jiahui An (2nd year), Cristian Badoi (4th year), Aaron Butterworth (4th year), Daniel Gardam (4th year), Yuzhao Chen (2nd year), Niko Theofilis (MSc), Chengzhe Li (3rd year), Yuanbang Liang (3rd year), Henan Liu (3rd year), Yulan Liu (3rd year), Jonathan McManus (summer project), Yifu Qian (3rd year), Musah Shaibu (MSc), Yuhao Wan (3rd year), Daniel Widdowson (MSc), Yuqing Yang (2nd year), Wenkai Zhang (3rd year).
• Short-term project students in 2018-19: Cristian Badoi (3rd year), Samuel Ball (4th year), Ruilin Han (3rd year), Yuhao Hua (3rd year), Di Liu (3rd year), Kristian Rowan (3rd year), Wenkai Zhang (2nd year), Yijia Zhao (3rd year).
• Short-term project students in 2017-18 (various periods from 8 weeks to 8 months): Abid Abdul (2nd year), Alex Bagnall (3rd year), Naohiko Ban (visiting PhD), Jacob Bracken (3rd year), Matthew Bright (MSc), Gemma Cook (MSc), Cameron Hargreaves (MSc), Di Liu (2nd year), Jingyi Lu (3rd year), Asim Munshi (graduate intern), Andrew Parry (3rd year), Antoine Rohmer (2nd year), Arshad Siddiqui (self-funded intern), Eris Tricker (graduate intern), Thomas Welsch (MSc).
• Summer students in 2017 : Graham Briggs (MSc), Jason Brewer (MSc), Sandra Garcia (MSc), Yuyao Wang (MSc), Zijian Li (MSc), Simon Hirst (EPSRC), Aviral Srivastava (self-funded intern), Falgun Patel (self-funded intern).
• Summer students in 2016 : David Torkington (MSc), Cheng Shen (MSc), Phil Smith (LMS), Aryaman Patel (intern on site).
• Mr Christopher Smithers : PhD supervised in 2015-2016 before moving to Liverpool, funded by the Leverhulme Trust.
• Dr Alexey Chernov : postdoc on the EPSRC grant in 2011-2012, now a Senior Lecturer in Statistics at Brighton University.
• Dr Marjan Safi-Samghabadi : PhD in Topological Robotics completed in 2009 - 2013, now a computer programmer.

Past student projects and highlighted achievements

• 2021 : PhD student Mr Grzegorz Muszynski was funded by Intel and Berkeley lab, defended his PhD "Pattern Recognition for Weather Phenomena in Climate Data" contributing to the high-profile publications JGRA 2019, GMD 2019, GMD 2018.
• 2018 : MSc student Dr Matthew Bright has completed an excellent MSc thesis whose results are published in CaG 2020.
• 2018 : intern student Mr Arshad Siddiqui has worked for 6 months in our group and published results in VISAPP 2020.
• 2018 : MSc student Mr Thomas Welsch has solved a Computer Vision problem for Unilever, which has co-funded his PhD.
• 2016 : Year 4 student Donald Harvey has completed the brilliant project Coarse-to-fine superpixel segmentation with a fast adaptive energy-based initialisation leading to the joint paper Superpixels Optimized by Color and Shape.
• 2016 : Year 4 student Jeremy Forsythe has completed the excellent project Convex Constrained Meshes: a new method to generate resolution-independent superpixels leading to the joint paper with Microsoft, see the journal version.
• 2013 : PhD student Ms Marjan Safi-Samghabadi has successfully completed her MSc (June 2009) and PhD (June 2013) in Topological Robotics under my supervision. Here is the joint paper based on her PhD.
• 2011 : The projects of Mr Caspar De Haes (Map Colouring) and Mr Chris Palmer (Topological Robotics) were ranked the 2nd and 4th best year 4 projects in the department.
• MSc dissertations (3 months in the summer):
  • Mr Daniel Widdowson : Consideration of a new similarity measure for periodic sets (2020)
  • Mr Nikolaos Mariano Theofilis Sobrino : On Knot Theory in Python (2020)
  • Mr Musah Shaibu : A classification of periodic knots and linked networks (2020)
  • Mr Cameron Hargreaves : machine learning techniques for similarity of crystals (2018)
  • Mr Matthew Bright : A new combinatorial description of 2-periodic structures (2018)
  • Mr Thomas Welsch : Helping a robot to see a correctly placed piece of cloth (2018)
  • Ms Gemma Cook : Visualising shapes of high-dimensional datasets (2018)
  • Mr Graham Briggs : Exploratory geometric data analysis of crystals (2017)
  • Mr Jason Brewer : Creating a geospatial macro level feature database (2017)
  • Ms Sandra Garcia : Creating a geospatial macro level feature database (2017)
  • Ms Yuyao Wang : Automatic data analysis for atomistic simulations (2017)
  • Mr Cheng Shen : Data skeletonization via alpha-Reeb graphs (2016)
  • Mr David Torkington : Testing the Mapper skeletonisation algorithm (2016)
  • Mr Christopher Smithers : A linear time algorithm for embedding knotted graphs in 3 pages (2015)
  • Ms Marjan Safi-Samghabadi : Configuration spaces of graphs (2009)
  • Mrs Suad Al-khmas : Virtual knots and knotted graphs (2008)
• Topological Data Analysis : final year projects
  • Mr Christopher Parkinson: Klein bottle model for a cloud of small patches from colour images (2016, year 4)
  • Mr Lewin Strauss: The skeletonisation problem in high dimensions (2016, year 4)
• Topological Robotics : final year projects
  • Mr Sam Bullen: Topological Complexity of Robot Motion Planning (2013, year 4)
  • Ms Alison Champernowne: Straightening a Robot Arm in the Plane (2013, year 4)
  • Mr Nathan Edwards: Euler Characteristic of Configuration Spaces (2013, year 4)
  • Mr Chris Guard: Locked Polygonal Linkages in 3-dimensional Space (2013, year 4)
  • Mr Martin Smith: Homotopy Types of Configuration Spaces of Graphs (2012, year 4)
  • Ms Emily Weir: Connectivity Algorithms for Configuration Spaces (2012, year 4)
  • Mr Chris Walker: Topological Complexity of Configuration Spaces (2011, year 4).
• Map Colouring : final year projects
  • Ms Katriina Nichols (2010, year 4)
  • Ms Camilla Banks (2009, year 3).

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Seminar of the group in Data Science theory and applications

The seminar is now online, usually on Fridays between 13.30-15.00 UK time.

Reverse chronological order : 2020-21 | 2019-20 | 2018-19 | 2017-18

Group seminars in the academic year 2020-2021

• 16 April 2021. Jonathan McManus. Introduction to Isosets and Minimum Quotient Graphs.
• 7 April 2021. Matt Bright. Introduction to Periodic Topology for Textiles and Crystals.
• 31 March 2021. Milo Torda. Geometry of the n-torus stochastic trust region method for materials discovery.
• 26 March 2021 (joint with the MIF++ seminar). Phil Smith. The density fingerprint of a periodic point set.
• 12 March 2021. Marco Mosca. Voronoi based invariants for clustering datasets of crystal structures.
• 5 March 2021. Dan Widdowson. TMap: visualising big, high-dimensional data with minimum spanning trees.
• 26 February 2021. Matt Bright. The Metric Quotient Graph - A Graph Invariant for Periodic Point Clouds.
• 19 February 2021. Fraser Holloway. The Development of Novel Pulse Shape Analysis Algorithms for AGATA.
• 12 February 2021 (joint with the Oxford seminar). Phil Smith. Density functions of periodic point sets.
• 5 February 2021. Viktor Zamaraev. On forbidden induced subgraphs for unit disk graphs.
• 29 January 2021. Marjan Safi-Samghabadi. How to automate systems [in industry].
• 22 January 2021. Milo Torda. Densest plane group packings of regular polygons.
• 15 January 2021. Grzegorz Muszynski. PhD viva practice 2: Pattern Recognition for Weather Phenomena in Climate Data.
• 8 January 2021. Grzegorz Muszynski. PhD viva practice 1: Pattern Recognition for Weather Phenomena in Climate Data.
• 11 December 2020. Dan Widdowson. Asymptotic behaviour of the Average Minimum Distances.
• 4 December 2020. Aidan Watmuff. Using k-modes clustering to identify different types of cyclists.
• 20 November 2020. Matt Bright. The invariant-based formula for the linking number of line segments.
• 13 November 2020. Muizdeen Raji. Machine learning for mass cytometry data of chronic lymphocytic leukemia.
• 11 November 2020 (joint with the ACTO group). 15-min introductions to Periodic Geometry by Vitaliy, Marco, Phil.
• 30 October 2020. Matt Bright. SOAP (Smooth Overlap of Atomic Positions) and other local descriptors of crystals.
• 23 October 2020. Informal discussions of potential final year projects in five subgroups led by senior PhD students.
• 16 October 2020. Vitaliy Kurlin. An introduction to research problems on crystals for new final year project students.
• 9 October 2020. Katerina Vriza. One class classification as a practical approach for accelerating co-crystal discovery.
  (plus two more short practice talks by the new PhD students Daniel Widdowson and Jonathan McManus).
• 2 October 2020. Cameron Hargreaves. Computation of the Wasserstein metric (Earth Mover's Distance).
• 29 September 2020. Yury Elkin. The mergegram of a clustering dendrogram for point clouds.
• 18 September 2020. Marco Mosca. A discussion of distance-based invariants of crystals.

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Group seminars in the academic year 2019-2020 (37 talks)

• 17 July 2020. Milo Torda. Space group optimization algorithm based on information geometry.
• 16 July 2020. Yury Elkin. The mergegram of a clustering dendrogram and its stability.
• 10 July 2020. Marco Mosca. Average Minimum Distances are stable isometry invariants of crystals.
• 3 July 2020. Katerina Vriza. Machine Learning in Materials Science. Case study: molecular co-crystals.
• 19 June 2020. Marco Mosca. Voronoi-based similarity distances between arbitrary crystal lattices.
• 12 June 2020. Grzegorz Muszynski. Topological Data Analysis for recognizing Atmospheric River patterns.
• 5 June 2020. Grzegorz Muszynski. Atmospheric Blocking Pattern Recognition in Global Climate Simulation Data.
• 29 May 2020. Vitaliy Kurlin. An introduction to research problems on crystals for new and future students.
• 22 May 2020. Thomas Welsch. Synthesis through Unification Genetic Programming.
• 15 May 2020. Matt Bright. Encoding and topological computation on textile structures.
• 30 April 2020. Phil Smith. Stability of density functions of periodic crystals.
• 24 April 2020. Phil Smith. Stability of Voronoi diagrams under perturbations.
• 27 March 2020. Vitaliy Kurlin. A continuous approach to a crystal classification.
• 20 March 2020. Vitaliy Kurlin and Marco Mosca. Reduced cells of crystals.
• 6 March 2020. Three talks at different times: 10-12, 13-14 and 14-15.
  Yury Elkin (10-12). Machine learning techniques in Topological Data Analysis.
  Muizdeen Raji (13-14). Statistical analysis of microRNA and messenger RNA profiling.
  Cristian Badoi (14-15). Samply: predicting formulae of chemical compounds.
• 28 February 2020. Thomas Welsch. Evolutionary computation for program synthesis.
• 21 February 2020. Phil Smith. Voronoi domains and Brillouin zones of periodic point sets.
• 14 February 2020. Matt Bright. Classifying fabric structures: an application of knot theory.
• 7 February 2020. Marco Mosca. Voronoi-based similarity distances between crystal lattices.
• 31 January 2020. Cameron Hargreaves. The dimensionality reduction by UMAP and applications to solid state discovery.
• 17 January 2020. Muizdeen Raji. Machine learning for cell clustering and predictions from mass cytometry data.
• 10 January 2020. Phil Smith. Packing functions are new isometry invariants of periodic crystals.
• 13 December 2019. Fraser Holloway. Machine Learning and Topological Data Analysis for Pulse Shape Analysis.
• 6 December 2019. Katerina Vriza. Machine learning methods for predicting co-crystals.
• 29 November 2019. Cristian Badoi, Aaron Butterworth, Daniel Gardam. Sampling a space of chemicals.
• 22 November 2019. Thomas Welsch. An introduction to program synthesis.
• 15 November 2019. Yury Elkin. Stability of hierarchical clustering algorithms.
• 8 November 2019. Cameron Hargreaves. The Minimal Cost Flow atomic similarity.
• 1 November 2019. Matt Bright. Realisability of Gauss paragraphs for 2-periodic links.
• 25 October 2019. Georg Osang (IST Austria). Periodic Delaunay triangulations.
• 18 October 2019. Marco Mosca. Delaunay triangulations and Voronoi diagrams.
• 11 October 2019. Thomas Welsch. Identification of organic compounds by a liquid crystal sensor.
• 4 October 2019. Vitaliy Kurlin. Isometric invariants of periodic point clouds.
• 27 September 2019. Phil Smith. Resolution-independent meshes of superpixels.
• 20 September 2019. Milo Torda. Dense periodic packings in the light of crystal structure prediction.

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Group seminars in the academic year 2018-2019 (30 talks)

• 19 July 2019. Milo Torda. Crystallographic point groups and space groups from a group theoretic perspective.
• 10 July 2019. Phil Smith. An introduction to persistent homology (DMML seminar at 10 in Ashton 208).
• 5 July 2019. Milo Torda. Periodic packings in the light of crystal structure prediction.
• 28 June 2019. Cameron Hargreaves. Topological techniques for structural similarities in ionic compounds.
• 21 June 2019. Marco Mosca. Geometric invariants for clustering datasets of crystal structures.
• 14 June 2019. Krasen Samardzhiev. A change of a basis for linear maps in a matrix form.
• 7 June 2019. Katerina Vriza. Data-driven discovery of functional molecular co-crystals.
• 31 May 2019. Vitaliy Kurlin. Mathematical problems for infinite periodic structures.
• 24 May 2019. Yury Elkin. Links between persistence modules and hierarchical clustering.
• 3 May 2019. Cameron Hargreaves. Persistent homology for the filtration of alpha-complexes.
• 29 March 2019. Linear algebra exercises by Katerina, Marco, Thomas, Cameron, Krasen, Phil.
• 8 March 2019. Milo Torda. Algorithmic computation of homology groups for 2-dimensional complexes.
• 1 March 2019. Algorithmic computation of 1D homology by Katerina, Marco, Cameron, Thomas, Milo.
• 22 February 2019. Algorithmic computation of 0D homology by Katerina, Marco, Cameron, Thomas, Milo.
• 15 February 2019. Phil Smith. An introduction to homology groups with examples for graphs.
• 8 February 2019. Cameron Hargreaves. Persistent homology and its applications with the Ripser.
• 1 February 2019. Marco Mosca. Reduced cell theory and the instability of Niggli's reduced cell.
• 18 January 2019. Grzegorz Muszynski. Support Vector Machine and t-Distributed Stochastic Neighbor Embedding.
• 11 January 2019. Grzegorz Muszynski. Topological & Machine Learning Pattern Detection Methods in Climate Data.
• 14 December 2018. Phil Smith. Skeletonisation algorithms for unstructured point clouds with theoretical guarantees.
• 7 December 2018. Yury Elkin. Dual-tree algorithms and applications to data skeletonization.
• 30 November 2018. Fraser Holloway. A classification of pulse shapes from AGATA.
• 23 November 2018. Miloslav Torda. Optimal lattice packings in Euclidean spaces.
• 9 November 2018. Katerina Vriza. Symmetry groups of crystals in dimensions 2 and 3.
• 2 November 2018. Arshad Siddiqui. Polygonal vortex meshes in microscopic images.
• 26 October 2018. Cameron Hargreaves. Crystal lattices and notations for space groups.
• 19 October 2018. Thomas Welsch. Helping a robot to see a correctly placed piece of cloth.
• 12 October 2018. Krasen Samardzhiev. A Python-based tutorial on alpha-complexes.
• 5 October 2018. Krasen Samardzhiev. A Python-based tutorial on Delaunay triangulations.
• 28 September 2018. Marco Mosca. Voronoi diagrams and Delaunay triangulations.

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Group seminars in the academic year 2017-2018 (25 talks)

The photo below was taken in February 2018. Members from left to right: Naohiko Ban, Asim Munshi, Eris Tricker, Krasen Samardzhiev, Vitaliy Kurlin, Grzegorz Muszynski, Philip Smith.

• 14 June 2018. Krasen Samardzhiev. A Python-based tutorial on Topological Data Analysis.
• 31 May 2018. Grzegorz Muszynski. Diffusion maps for dimensionality reduction with examples.
• 24 May 2018. Grzegorz Muszynski. Periodic behaviour in low-dimensional representations of climate data.
• 10 May 2018. Krasen Samardzhiev. 1D persistent homology of census data in the US.
• 3 May 2018. Phil Smith. Reeb graphs and alpha-Reeb graphs for data skeletonisation.
• 26 April 2018. Phil Smith. Duality between persistent homology in dimensions 0 and 1 for 2D clouds.
• 12 April 2018. Krasen Samardzhiev. Persistent homology of alpha-complexes for 2D clouds.
• 22 March 2018. Krasen Samardzhiev. Homology groups: matrix computations.
• 15 March 2018. Krasen Samardzhiev. Homology groups: manual computations.
• 8 March 2018. Yury Elkin. Data skeletonisation algorithms for unorganised point clouds.
• 22 February 2018. Naohiko Ban. Reconstruction of a vortex structure from 2D sequential images.
• 15 February 2018. Eris Tricker. Converting pixel-based skeletons into planar graphs.
• 8 February 2018. Asim Munshi. Thinning algorithms for black-and-white images.
• 25 January 2018. Grzegorz Muszynski. A topological detection of Atmospheric Rivers.
• 18 January 2018. Krasen Samardzhiev. Kuratowski's criterion for planar graphs.
• 11 January 2018. Yury Elkin. Straightening algorithms for polygonal curves.
• 20 December 2017. Yury Elkin. Skeletons of 3D clouds from micelles.
• 14 December 2017. Fraser Holloway. Pulse shapes from AGATA.
• 7 December 2017. Graham Briggs. Periodic crystal structures.
• 30 November 2017. Phil Smith. Simplest polygonal surfaces.
• 23 November 2017. Yury Elkin. The Euler characteristic.
• 16 November 2017. Krasen Samardzhiev. The union-find algorithm.
• 9 November 2017. Krasen Samardzhiev. Clustering algorithms for point clouds.
• 2 November 2017. Phil Smith. Topological equivalences of graphs.
• 17 October 2017. Phil Smith. Combinatorial graphs.

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Links to useful resources for completing projects

• LaTeX Wikibook, LaTeX tutorials by Andrew Roberts.
• Graphics program: Inkscape available for free.
• Free tutorials on HTML by W3Schools.
• Free tutorials on Java by Oracle.

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