Jason P. Smith

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.

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Publications:
Statistical Complexity of Heterogeneous Geometric Networks,
with Keith Malcolm Smith, arXiv.
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., bioRxiv.
On the Homotopy Type of Multipath Complexes,
with Luigi Caputi, Carlo Collari, and Sabino Di Trani, Mathematika (2023), 70: e12235, arXiv.
Asymptotic Behaviour of the Containment of Certain Mesh Patterns,
with Dejan Govc, Discrete Mathematics (2022), 345(5):112813, arXiv.
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.
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.
Complexes of Tournaments, Directionality Filtrations and Persistent Homology,
with Dejan Govc and Ran Levi, Journal of Applied and Computational Topology (2021), arXiv.
Computing Persistent Homology of Directed Flag Complexes,
with Daniel Luetgehetmann, Dejan Govc and Ran Levi, Algorithms (2020), 13(1):19, arXiv.
The Poset of Mesh Patterns,
with Henning Ulfarsson, Discrete Mathematics (2020), 343(6):111848, arXiv.
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.
The Poset of Graphs Ordered by Induced Containment,
Journal of Combinatorial Theory, Series A (2019), 168:348-373, arXiv.
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.
Modular Decomposition of Graphs and the Distance Preserving Property,
with Emad Zahedi, Discrete Applied Mathematics (2019), 265:192-198, arXiv.
On the Möbius Function and Topology of General Pattern Posets,
The Electronic Journal of Combinatorics (2019), 26(1):49, arXiv.
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.
On Distance Preserving and Sequentially Distance Preserving Graphs,
with Emad Zahedi, arXiv.
A Formula for the Möbius Function of the Permutation Poset Based on a Topological Decomposition,
Advances in Applied Mathematics (2017), 91:98-114, arXiv.
Intervals of Permutations with a Fixed Number of Descents are Shellable,
Discrete Mathematics (2016), 339:118-126, arXiv.
On the Möbius Function of Permutations With One Descent,
The Electronic Journal of Combinatorics (2014), 21(2):11, arXiv.

Selected Presentations:
Intervals of Permutations with a Fixed Number of Descents are Shellable.
Combinatorial Algebraic Topology and its Applications to Permutation Patterns.
A Formula for the Möbius Function of the Permutation Poset.
Poset of Graphs.
Tournaplexes and their Applications to Neuroscience.
Using Neighbourhoods to Classify Functional Brain Data.

Software:
Flagser-count: Counts the number of directed cliques in large networks.
Connectome-analysis: Library of general functions to analyse connectoms.
Tournser: Computes persistent homology of tournaplexes.
Deltser: Computes persistent homology of delta complexes.
Flagser-online An online implementation of Flagser for computing persistent homology of directed flag complexes.
PermPoset: A program for computing the Möbius function of intervals of the permutation poset.

Education:
Ph.D in Computer and Information Science. University of Strathclyde. 2012-2015. Advisor: Einar Steingrímsson.
Thesis: On the Möbius Function and Topology of the Permutation Poset
MMath. University of Bath. 2008-2012.

Previous Positions:
2018-20: Research fellow. Department of Mathematics. University of Aberdeen.
Working on the project "Topological Analysis of Neural Systems" with Prof. Ran Levi.
2015-18: Research Associate. Department of Computer and Information Science. University of Strathclyde.
Working on the project "The Möbius Function of the Poset of Permutations" with Prof. Einar Steingrímsson.