Co-occurrence simplicial complexes in mathematics: identifying the holes of knowledge
In the last years complex networks tools contributed to provide insights on the structure of research, through the study of collaboration, citation and co-occurrence networks. The network approach focuses on pairwise relationships, often compressing multidimensional data structures and inevitably lo...
| Main Authors: | , , , |
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| Format: | Journal article |
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Springer Verlag
2018
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| _version_ | 1826292765766451200 |
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| author | Salnikov, V Cassese, D Lambiotte, R Jones, N |
| author_facet | Salnikov, V Cassese, D Lambiotte, R Jones, N |
| author_sort | Salnikov, V |
| collection | OXFORD |
| description | In the last years complex networks tools contributed to provide insights on the structure of research, through the study of collaboration, citation and co-occurrence networks. The network approach focuses on pairwise relationships, often compressing multidimensional data structures and inevitably losing information. In this paper we propose for the first time a simplicial complex approach to word co-occurrences, providing a natural framework for the study of higher-order relations in the space of scientific knowledge. Using topological methods we explore the conceptual landscape of mathematical research, focusing on homological holes, regions with low connectivity in the simplicial structure. We find that homological holes are ubiquitous, which suggests that they capture some essential feature of research practice in mathematics. Holes die when a subset of their concepts appear in the same article, hence their death may be a sign of the creation of new knowledge, as we show with some examples. We find a positive relation between the dimension of a hole and the time it takes to be closed: larger holes may represent potential for important advances in the field because they separate conceptually distant areas. We also show that authors' conceptual entropy is positively related with their contribution to homological holes, suggesting that polymaths tend to be on the frontier of research. |
| first_indexed | 2024-03-07T03:19:45Z |
| format | Journal article |
| id | oxford-uuid:b70646af-08dc-4223-8c1d-c218817ada06 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:19:45Z |
| publishDate | 2018 |
| publisher | Springer Verlag |
| record_format | dspace |
| spelling | oxford-uuid:b70646af-08dc-4223-8c1d-c218817ada062022-03-27T04:45:27ZCo-occurrence simplicial complexes in mathematics: identifying the holes of knowledgeJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b70646af-08dc-4223-8c1d-c218817ada06Symplectic Elements at OxfordSpringer Verlag2018Salnikov, VCassese, DLambiotte, RJones, NIn the last years complex networks tools contributed to provide insights on the structure of research, through the study of collaboration, citation and co-occurrence networks. The network approach focuses on pairwise relationships, often compressing multidimensional data structures and inevitably losing information. In this paper we propose for the first time a simplicial complex approach to word co-occurrences, providing a natural framework for the study of higher-order relations in the space of scientific knowledge. Using topological methods we explore the conceptual landscape of mathematical research, focusing on homological holes, regions with low connectivity in the simplicial structure. We find that homological holes are ubiquitous, which suggests that they capture some essential feature of research practice in mathematics. Holes die when a subset of their concepts appear in the same article, hence their death may be a sign of the creation of new knowledge, as we show with some examples. We find a positive relation between the dimension of a hole and the time it takes to be closed: larger holes may represent potential for important advances in the field because they separate conceptually distant areas. We also show that authors' conceptual entropy is positively related with their contribution to homological holes, suggesting that polymaths tend to be on the frontier of research. |
| spellingShingle | Salnikov, V Cassese, D Lambiotte, R Jones, N Co-occurrence simplicial complexes in mathematics: identifying the holes of knowledge |
| title | Co-occurrence simplicial complexes in mathematics: identifying the holes
of knowledge |
| title_full | Co-occurrence simplicial complexes in mathematics: identifying the holes
of knowledge |
| title_fullStr | Co-occurrence simplicial complexes in mathematics: identifying the holes
of knowledge |
| title_full_unstemmed | Co-occurrence simplicial complexes in mathematics: identifying the holes
of knowledge |
| title_short | Co-occurrence simplicial complexes in mathematics: identifying the holes
of knowledge |
| title_sort | co occurrence simplicial complexes in mathematics identifying the holes of knowledge |
| work_keys_str_mv | AT salnikovv cooccurrencesimplicialcomplexesinmathematicsidentifyingtheholesofknowledge AT cassesed cooccurrencesimplicialcomplexesinmathematicsidentifyingtheholesofknowledge AT lambiotter cooccurrencesimplicialcomplexesinmathematicsidentifyingtheholesofknowledge AT jonesn cooccurrencesimplicialcomplexesinmathematicsidentifyingtheholesofknowledge |