Co-occurrence simplicial complexes in mathematics: identifying the holes of knowledge
Abstract 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 inev...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-08-01
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| Series: | Applied Network Science |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/s41109-018-0074-3 |
| _version_ | 1818555373700775936 |
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| author | Vsevolod Salnikov Daniele Cassese Renaud Lambiotte Nick S. Jones |
| author_facet | Vsevolod Salnikov Daniele Cassese Renaud Lambiotte Nick S. Jones |
| author_sort | Vsevolod Salnikov |
| collection | DOAJ |
| description | Abstract 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. k-dimensional holes die when every concept in the hole appears in an article together with other k+1 concepts in the hole, 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 size 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 provide further description of the conceptual space by looking for the simplicial analogs of stars and explore the likelihood of edges in a star to be also part of a homological cycle. 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 | 2024-12-12T09:52:32Z |
| format | Article |
| id | doaj.art-f65f350f2d8841c7919b4b9b6bcb0af5 |
| institution | Directory Open Access Journal |
| issn | 2364-8228 |
| language | English |
| last_indexed | 2024-12-12T09:52:32Z |
| publishDate | 2018-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Applied Network Science |
| spelling | doaj.art-f65f350f2d8841c7919b4b9b6bcb0af52022-12-22T00:28:14ZengSpringerOpenApplied Network Science2364-82282018-08-013112310.1007/s41109-018-0074-3Co-occurrence simplicial complexes in mathematics: identifying the holes of knowledgeVsevolod Salnikov0Daniele Cassese1Renaud Lambiotte2Nick S. Jones3University of Namur and NaXysUniversity of Namur and NaXysMathematical Institute, University of OxfordDepartment of Mathematics, Imperial CollegeAbstract 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. k-dimensional holes die when every concept in the hole appears in an article together with other k+1 concepts in the hole, 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 size 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 provide further description of the conceptual space by looking for the simplicial analogs of stars and explore the likelihood of edges in a star to be also part of a homological cycle. 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.http://link.springer.com/article/10.1007/s41109-018-0074-3Co-occurrenceTopological data analysisPersistent homology |
| spellingShingle | Vsevolod Salnikov Daniele Cassese Renaud Lambiotte Nick S. Jones Co-occurrence simplicial complexes in mathematics: identifying the holes of knowledge Applied Network Science Co-occurrence Topological data analysis Persistent homology |
| 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 |
| topic | Co-occurrence Topological data analysis Persistent homology |
| url | http://link.springer.com/article/10.1007/s41109-018-0074-3 |
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