Co-occurrence simplicial complexes in mathematics: identifying the holes of knowledge

Résultats de recherche: Contribution à un journal/une revueArticle

18 Downloads (Pure)

Résumé

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.
langue originaleAnglais
journalArXiv pre-print
étatPublié - 11 mars 2018

Empreinte digitale

mathematics
research practice
entropy
knowledge
death
time

mots-clés

    Citer ceci

    @article{baa69821623b4d9caf83f1ad64553536,
    title = "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 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.",
    keywords = "physics.soc-ph, cs.DL, math.HO",
    author = "Vsevolod Salnikov and Daniele Cassese and Renaud Lambiotte and Jones, {Nick S.}",
    note = "24 pages, 12 figures",
    year = "2018",
    month = "3",
    day = "11",
    language = "English",
    journal = "ArXiv pre-print",

    }

    Co-occurrence simplicial complexes in mathematics : identifying the holes of knowledge. / Salnikov, Vsevolod; Cassese, Daniele; Lambiotte, Renaud; Jones, Nick S.

    Dans: ArXiv pre-print, 11.03.2018.

    Résultats de recherche: Contribution à un journal/une revueArticle

    TY - JOUR

    T1 - Co-occurrence simplicial complexes in mathematics

    T2 - identifying the holes of knowledge

    AU - Salnikov, Vsevolod

    AU - Cassese, Daniele

    AU - Lambiotte, Renaud

    AU - Jones, Nick S.

    N1 - 24 pages, 12 figures

    PY - 2018/3/11

    Y1 - 2018/3/11

    N2 - 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.

    AB - 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.

    KW - physics.soc-ph

    KW - cs.DL

    KW - math.HO

    M3 - Article

    JO - ArXiv pre-print

    JF - ArXiv pre-print

    ER -