Topological Sequence Analysis of Genomes: Delta Complex approaches
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912471758929920 |
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| author | Liu, Jian Shen, Li Chen, Dong Wei, Guo-Wei |
| author_facet | Liu, Jian Shen, Li Chen, Dong Wei, Guo-Wei |
| contents | Algebraic topology has been widely applied to point cloud data to capture geometric shapes and topological structures. However, its application to genome sequence analysis remains rare. In this work, we propose topological sequence analysis (TSA) techniques by constructing $Δ$-complexes and classifying spaces, leading to persistent homology, and persistent path homology on genome sequences. We also develop $Δ$-complex-based persistent Laplacians to facilitate the topological spectral analysis of genome sequences. Finally, we demonstrate the utility of the proposed TSA approaches in phylogenetic analysis using Ebola virus sequences and whole bacterial genomes. The present TSA methods are more efficient than earlier TSA model, k-mer topology, and thus have a potential to be applied to other time-consuming sequential data analyses, such as those in linguistics, literature, music, media, and social contexts. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_05452 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological Sequence Analysis of Genomes: Delta Complex approaches Liu, Jian Shen, Li Chen, Dong Wei, Guo-Wei Algebraic Topology Quantitative Methods Primary 55N31, Secondary 62R40, 68Q07 Algebraic topology has been widely applied to point cloud data to capture geometric shapes and topological structures. However, its application to genome sequence analysis remains rare. In this work, we propose topological sequence analysis (TSA) techniques by constructing $Δ$-complexes and classifying spaces, leading to persistent homology, and persistent path homology on genome sequences. We also develop $Δ$-complex-based persistent Laplacians to facilitate the topological spectral analysis of genome sequences. Finally, we demonstrate the utility of the proposed TSA approaches in phylogenetic analysis using Ebola virus sequences and whole bacterial genomes. The present TSA methods are more efficient than earlier TSA model, k-mer topology, and thus have a potential to be applied to other time-consuming sequential data analyses, such as those in linguistics, literature, music, media, and social contexts. |
| title | Topological Sequence Analysis of Genomes: Delta Complex approaches |
| topic | Algebraic Topology Quantitative Methods Primary 55N31, Secondary 62R40, 68Q07 |
| url | https://arxiv.org/abs/2507.05452 |