Dr Vitaliy Kurlin: mathematics & computer science

I'm 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 the group in Data Science.

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.
• Project : A continuous visualisation of crystal datasets.
  The aim is to design and implement new algorithms for visualising periodic crystals in a continuous way. An infinite periodic crystal in 3-space is obtained from a finite motif of molecules, atoms or ions (modeled as zero-size points or balls of different radii) in a unit cell (a non-rectangular box) that is periodically translated along the 3 edges of the unit cell. Traditionally crystals were classified by discrete invariants, such as symmetry groups, that are unstable under atomic vibrations. This project will use the recent isometry invariants of crystals introduced in the paper on Average Minimum Distances. A new software will compute stronger stable-under-noise invariants to visualise crystal datasets in a hierarchical way by varying a continuous threshold of similarity. Here is my 30-min video introduction.
• 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 parameters that makes an output unstable under perturbations of original data. he project will combine the rigorous approaches HoPeS and TMap 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.
• Project : An algorithmic classification of periodic textiles.
  The aim is to implement a software tool to automatically classify textile structures and knotted strands in materials. Formally, a textile or a 2-periodic link is a set of lines and closed curves in a thickened plane that are preserved by translations along two linearly independent vectors. Textiles are considered equivalent (or periodically isotopic) if they can be continuously deformed to each other through intermediate textiles. Other students working on this project in the past have implemented a combinatorial encoding of textiles, automatic generation of textile codes and some invariants that distinguish textiles. The latest reference is CaG 2020.
• Project : Automated alarms saving lives in a medical environment.
  The aim is to implement alarms to automatically analyse data in real-time and alert doctors in time to carry life-saving treatment. One example is for invasive devices that should be taken from patients before they become too integrated with a human body, hence hard to extract. Another example is to monitor an evolution of cancer data and issue just-in-time alerts before a cancer becomes incurable. One more possible direction is to predict by machine learning tools how much money will be spent by the NHS on an individual patient, on a specific disease or on a whole population within a certain area in the next 20 years.
• 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.
• 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

• 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

• 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 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 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 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. Information-geometry based space group optimization algorithm.
• 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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