Abstract

We provide a short introduction to the field of topological data analysis (TDA) and discuss its possible relevance for the study of complex systems. TDA provides a set of tools to characterise the shape of data, in terms of the presence of holes or cavities between the points. The methods, based on the notion of simplicial complexes, generalise standard network tools by naturally allowing for many-body interactions and providing results robust under continuous deformations of the data. We present strengths and weaknesses of current methods, as well as a range of empirical studies relevant to the field of complex systems, before identifying future methodological challenges to help understand the emergence of collective phenomena.

Original languageEnglish
Article number014001
JournalEuropean Journal of Physics
Volume40
Issue number1
DOIs
Publication statusPublished - 1 Jan 2019

Fingerprint

complex systems
cavities
interactions

Keywords

  • network science
  • persistence homology
  • simplicial complexes
  • topological data analysis

Cite this

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title = "Simplicial complexes and complex systems",
abstract = "We provide a short introduction to the field of topological data analysis (TDA) and discuss its possible relevance for the study of complex systems. TDA provides a set of tools to characterise the shape of data, in terms of the presence of holes or cavities between the points. The methods, based on the notion of simplicial complexes, generalise standard network tools by naturally allowing for many-body interactions and providing results robust under continuous deformations of the data. We present strengths and weaknesses of current methods, as well as a range of empirical studies relevant to the field of complex systems, before identifying future methodological challenges to help understand the emergence of collective phenomena.",
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author = "Vsevolod Salnikov and Daniele Cassese and Renaud Lambiotte",
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Simplicial complexes and complex systems. / Salnikov, Vsevolod; Cassese, Daniele; Lambiotte, Renaud.

In: European Journal of Physics, Vol. 40, No. 1, 014001, 01.01.2019.

Research output: Contribution to journalArticle

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