Persistent Homology on a lattice of multigraphs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916597281587200 |
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| author | Boils, Joaquin Diaz |
| author_facet | Boils, Joaquin Diaz |
| contents | A multicomplex structure is defined from an ordered lattice of multigraphs. This structure will help us to observe the features of Persistent Homology in this context, its interaction with the ordering and the repercussions of the process of merging multigraphs in the calculation of the Betti numbers. For the latter, an extended version of the incremental algorithm is provided. The ideas here developed are mainly oriented to the original example described in [10] and used more extensively in [11] in the context of the formalization of the notion of embodiment in Neuroscience. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02151 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Persistent Homology on a lattice of multigraphs Boils, Joaquin Diaz Algebraic Topology Neurons and Cognition A multicomplex structure is defined from an ordered lattice of multigraphs. This structure will help us to observe the features of Persistent Homology in this context, its interaction with the ordering and the repercussions of the process of merging multigraphs in the calculation of the Betti numbers. For the latter, an extended version of the incremental algorithm is provided. The ideas here developed are mainly oriented to the original example described in [10] and used more extensively in [11] in the context of the formalization of the notion of embodiment in Neuroscience. |
| title | Persistent Homology on a lattice of multigraphs |
| topic | Algebraic Topology Neurons and Cognition |
| url | https://arxiv.org/abs/2502.02151 |