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Neuro-Topology

In this section
Neuro-Topology

Neuro-Topology is a new and exciting branch of applied algebraic topology which aims to investigate questions and data arising in neuroscience by topological means.

The Aberdeen Neuro-Topology Research Group is a part of the Institute of Mathematics at the 51cg. The group was established by Ran Levi in 2017 and is funded by an EPSRC grant – Topological Analysis of Neural Systems, and a collaboration agreement with the Blue Brain Project in EPFL, Switzerland.

In our research we aim to use any applicable tool in the arsenal of algebraic topology, geometry, algebra and combinatorics to gain information about natural and artificial neural networks, as well as analyse data that arises in neuroscience by topological means.

People

Ran Levi
Head of group

ntp-ran-leviInterests and specialisation: Algebraic Topology, Homotopy Theory of classifying spaces of finite groups, Applications of topology and geometry to neuroscience and other networks, Classical Homotopy Theory, Representation Theory of finite groups and interactions with homotopy theory.


Research Associates

Matthew Burfitt

Interests and Specialisation: Background in algebraic topology and unstable homotopy theory. Currently interested in applications of topology to data analysis and machine learning. In particular topological data analysis and applications to the geometry and topology to artificial neural networks, neuroscience and brain data. A major part of my current work is collaborating on the PUFFINS study to develop method for analysing data coming from fast field cycling MRI.


Luigi Caputi

Interest and specialisation: background in Algebraic Topology and Coarse Geometry. In particular, coarse and cyclic homology theories, stable homology, algebraic K-theory and trace maps. Currently interested in applications of (persistent) homology, homotopy and category theory to graphs and complex systems, more specifically to neuroscience and brain dynamics.


Henri Riihimäki

ntp-henriInterests and specialisation: Background in applied topology. Particularly persistent homology, machine learning and data analysis on topological and combinatorial data. Currently looking into topology and algebra of combinatorial structures and discrete curvature on networks with a focus on functional brain networks.

Honorary Research Associates

Dejan Govc

Dejan GovcInterests and specialisation: Algebraic and Combinatorial Topology, Persistent Homology and Topological Data Analysis (with Applications to Neuroscience), Unimodal Category, Covering Type, Sheaf Theory.  Enumerative and Algebraic Combinatorics.


Jason Smith

ntp-jason-smithInterests and specialisation: Combinatorics and Applied Topology. In particular, poset topology, graph theory, persistent homology, permutation patterns, and the Abelian Sandpile model.


Jānis Lazovskis

ntp-janisInterests and specialisation: Topological data analysis, Sheaf theory, Stratified spaces of simplicial complexes, Visualization of topological data.

Postgraduate Students

Pedro Rodrigues

ntp-pedroInterests and specialisation: Pedro is a PhD student interested on Algebraic Topology, Topological Combinatorics, Geometric Group Theory and applications. He is currently working on the preservation of algebraic structures of (co)homology groups under Morse-type reductions.

Papers and Talks
Theoretical papers and preprints
  1. Daisuke Kishimoto, Ran Levi,  To appear in Kyoto Journal of Mathematics.
     
  2. Wojciech Chacholski, Ran Levi, Roy Meshulam,  . 
     
  3. Kouyemon Iriye, Daisuke Kishimoto, Ran Levi,  
Applied papers and preprints
  1. Daniel Luetgehetmann, Dejan Govc, Jason P Smith, Ran Levi ,.
     
  2. Reimann MW, Nolte M, Scolamiero M, Turner K, Perin K, Chindemi G, Dlotko P, Levi R, Hess K, Markram H, .
     
  3. Lida Kanari, Pawel Dlotko, Martina Scolamiero, Ran Levi, Julian Shillcock, Kathryn Hess and Henry Markram, .
     
  4. Janis Lazovskis, .
     
  5. Henri Riihimäki and José Licón-Saláiz, .
     
  6. Wojciech Chachólski and Henri Riihimäki, .
     
  7. Dejan Govc, Richard Hepworth, .
     
  8. Dejan Govc, Waclaw Marzantowicz, Petar Pavesic,
     
  9. Dejan Govc, Ran Levi, Jason P Smith, .
     
  10. Dejan Govc,
     
  11. M. J. Catanzaro, Justin M. Curry, B. T. Fasy, Janis Lazovskis, G. Malen, H. Riess, B. Wang, M. Zabka,
     
  12. Henri Riihimäki, Wojciech Chachólski, Jakob Theorell, Jan Hillert, Ryan Ramanujam; .
     
  13. Dejan Govc, Jason P. Smith;  
     
  14. Luigi Caputi, Anna Pidnebesna, Jaroslav Hlinka;  (2021)
     
  15. Luigi Caputi, Carlo Collari, Sabino Di Trani;  (2021)
     
  16. Luigi Caputi, Carlo Collari, Sabino Di Trani; ; (2021)
     
  17. Pedro Conceição, Dejan Govc, Jānis Lazovskis, Ran Levi, Henri Riihimäki, Jason P. Smith; ; (2021) To appear in Network Neuroscience. 
     
  18. Michael W. Reimann, Henri Riihimäki, Jason P. Smith, Jānis Lazovskis, Christoph Pokorny, Ran Levi; ; (2021) To appear in Plos One.
     
  19. Luigi Caputi, Daniele Celoria, Carlo Collari; ; (2021)
     
  20. Luigi Caputi, Daniele Celoria, Carlo Collari; ; (2022)
     
  21. Henri Riihimäki, ; (2022)
     
  22. Pedro Conceição, Juliano Morimoto, ; (2022)
Selected Talks and Presentations
  1. Poster: s in digraphs to the classification of binary dynamics; Topological Data Analysis Workshop; Institute for Mathematical and Statistical Innovation, 27/4/2021
     
  2. Janis Lazovskis, EPSRC Hub Seminar,.
     
  3. Ran Levi, .
     
  4. Ran Levi,  (Video)
Software

Software created in the group

flagser: Computing the homology of directed flag complexes.

  • Created by: Daniel Lütgehetmann, Jason P Smith
  • and
  • : An online implementation of Flagser (by Jason Smith)

flagser count: A program for counting directed cliques in directed graphs, adapted from Flagser

  • Created by: Jason P Smith

tournser: Computing the persistent homology of tournaplexes

  • Created by: Jason P Smith

deltser: Computing the homology of delta complexes (semi-simplicial sets)

  • Created by: Jason P Smith

easy-mapper: A user-focused Python implementation of the mapper algorithm.

  • Created by: Jānis Lazovskis
Links
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