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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.06286 |
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| _version_ | 1866909894274187264 |
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| author | Gao, Jing-Wen He, Yunan Liu, Jian |
| author_facet | Gao, Jing-Wen He, Yunan Liu, Jian |
| contents | Topological data analysis (TDA), as a relatively recent approach, has demonstrated great potential in capturing the intrinsic and robust structural features of complex data. While persistent homology, as a core tool of TDA, focuses on characterizing geometric shapes and topological structures, the automorphism groups of Vietoris-Rips complexes can capture the structured symmetry features of data. In this work, we propose a multi-scale symmetry analysis approach that leverages persistent automorphism modules to quantify variations in symmetries across scales. By modifying the category of graphs and constructing a suitable functor from the graph category to the category of modules, we ensure that the persistent automorphism module forms a genuine persistence module. Furthermore, we apply this framework to the structural analysis of fullerenes, predicting the stability of 12 fullerene molecules with a competitive correlation coefficient of 0.979. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06286 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multi-scale symmetry analysis in molecular structures Gao, Jing-Wen He, Yunan Liu, Jian Combinatorics Topological data analysis (TDA), as a relatively recent approach, has demonstrated great potential in capturing the intrinsic and robust structural features of complex data. While persistent homology, as a core tool of TDA, focuses on characterizing geometric shapes and topological structures, the automorphism groups of Vietoris-Rips complexes can capture the structured symmetry features of data. In this work, we propose a multi-scale symmetry analysis approach that leverages persistent automorphism modules to quantify variations in symmetries across scales. By modifying the category of graphs and constructing a suitable functor from the graph category to the category of modules, we ensure that the persistent automorphism module forms a genuine persistence module. Furthermore, we apply this framework to the structural analysis of fullerenes, predicting the stability of 12 fullerene molecules with a competitive correlation coefficient of 0.979. |
| title | Multi-scale symmetry analysis in molecular structures |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.06286 |