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I am a senior lecturer in mathematics in the Department of Physics and Mathematics at Nottingham Trent University.
My main areas of interest are combinatorics and topology, and their applications to neuroscience.
Email:
Google Scholar page
GitHub repositories
ORCID id
CV
Publications:
Heterogeneous and non-random cortical connectivity undergirds efficient, robust and reliable neural codes,
with Daniela Egas Santander, Christoph Pokorny, András Ecker, Jānis Lazovskis, Matteo Santoro, Kathryn Hess, Ran Levi, Michael W. Reimann, bioRxiv.
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Statistical Complexity of Heterogeneous Geometric Networks,
with Keith Malcolm Smith, arXiv.
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Modeling and Simulation of Rat Non-Barrel Somatosensory Cortex. Part I: Modeling Anatomy,
with Michael W. Reimann, Sirio Bolaños Puchet, Daniela Egas Santander, et al., eLife (2024), 13:RP99688, bioRxiv.
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On the Homotopy Type of Multipath Complexes,
with Luigi Caputi, Carlo Collari, and Sabino Di Trani, Mathematika (2023), 70: e12235, arXiv.
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Asymptotic Behaviour of the Containment of Certain Mesh Patterns,
with Dejan Govc, Discrete Mathematics (2022), 345(5):112813, arXiv.
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An Application of Neighbourhoods in Digraphs to the Classification of Binary Dynamics,
with Pedro Conceição, Dejan Govc, Jānis Lazovskis, Ran Levi, and Henri Riihimäki, Network Neuroscience (2022), arXiv.
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Topology of Synaptic Connectivity Constrains Neuronal Stimulus Representation, Predicting Two Complementary Coding Strategies,
with Michael W. Reimann, Henri Riihimäki, Jānis Lazovskis, Christoph Pokorny, and Ran Levi, PLOS ONE (2022), 17(1):e0261702, biorxiv.
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Complexes of Tournaments, Directionality Filtrations and Persistent Homology,
with Dejan Govc and Ran Levi, Journal of Applied and Computational Topology (2021), arXiv.
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Computing Persistent Homology of Directed Flag Complexes,
with Daniel Luetgehetmann, Dejan Govc and Ran Levi, Algorithms (2020), 13(1):19, arXiv.
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The Poset of Mesh Patterns,
with Henning Ulfarsson, Discrete Mathematics (2020), 343(6):111848, arXiv.
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Permutation Graphs and the Abelian Sandpile Model, Tiered Trees and Non-Ambiguous Binary Trees,
with Mark Dukes, Thomas Selig and Einar Steingrímsson, The Electronic Journal of Combinatorics (2019), 26(3):29, arXiv.
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The Poset of Graphs Ordered by Induced Containment,
Journal of Combinatorial Theory, Series A (2019), 168:348-373, arXiv.
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The Abelian Sandpile Model on Ferrers Graphs - A Classification of Recurrent Configurations,
with Mark Dukes, Thomas Selig and Einar Steingrímsson, European Journal of Combinatorics (2019), 81:221-241, arXiv.
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Modular Decomposition of Graphs and the Distance Preserving Property,
with Emad Zahedi, Discrete Applied Mathematics (2019), 265:192-198, arXiv.
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On the Möbius Function and Topology of General Pattern Posets,
The Electronic Journal of Combinatorics (2019), 26(1):49, arXiv.
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EW-Tableaux, Le-Tableaux, Tree-like Tableaux and the Abelian Sandpile Model,
with Thomas Selig and Einar Steingrímsson, The Electronic Journal of Combinatorics (2018), 25(3):14, arXiv.
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On Distance Preserving and Sequentially Distance Preserving Graphs,
with Emad Zahedi, arXiv.
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A Formula for the Möbius Function of the Permutation Poset Based on a Topological Decomposition,
Advances in Applied Mathematics (2017), 91:98-114, arXiv.
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Intervals of Permutations with a Fixed Number of Descents are Shellable,
Discrete Mathematics (2016), 339:118-126, arXiv.
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On the Möbius Function of Permutations With One Descent,
The Electronic Journal of Combinatorics (2014), 21(2):11, arXiv.
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Selected Presentations:
Software:
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Flagser-count: Counts the number of directed cliques in large networks.
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Connectome-analysis: Library of general functions to analyse connectoms.
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Tournser: Computes persistent homology of tournaplexes.
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Deltser: Computes persistent homology of delta complexes.
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Flagser-online An online implementation of Flagser for computing persistent homology of directed flag complexes.
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PermPoset: A program for computing the Möbius function of intervals of the permutation poset.
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Education:
Previous Positions:
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2018-20: | Research fellow. Department of Mathematics. University of Aberdeen.
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Working on the project "Topological Analysis of Neural Systems" with Prof. Ran Levi.
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2015-18: | Research Associate. Department of Computer and Information Science. University of Strathclyde.
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Working on the project "The Möbius Function of the Poset of Permutations" with Prof. Einar Steingrímsson.
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