Dechant, P.-P. orcid.org/0000-0002-4694-4010, He, Y.-H., Heyes, E. et al. (1 more author) (2022) Cluster Algebras: Network Science and Machine Learning. [Preprint]
Abstract
Cluster algebras have recently become an important player in mathematics and physics. In this work, we investigate them through the lens of modern data science, specifically with techniques from network science and machine-learning. Network analysis methods are applied to the exchange graphs for cluster algebras of varying mutation types. The analysis indicates that when the graphs are represented without identifying by permutation equivalence between clusters an elegant symmetry emerges in the quiver exchange graph embedding. The ratio between number of seeds and number of quivers associated to this symmetry is computed for finite Dynkin type algebras up to rank 5, and conjectured for higher ranks. Simple machine learning techniques successfully learn to differentiate cluster algebras from their seeds. The learning performance exceeds 0.9 accuracies between algebras of the same mutation type and between types, as well as relative to artificially generated data.
Metadata
Item Type: | Preprint |
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Authors/Creators: |
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Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > PRIME |
Depositing User: | Symplectic Publications |
Date Deposited: | 20 Oct 2023 15:20 |
Last Modified: | 20 Oct 2023 15:21 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:203749 |