2018
DOI: 10.1088/1361-6404/aae790
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Simplicial complexes and complex systems

Abstract: We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis 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 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 s… Show more

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Cited by 144 publications
(114 citation statements)
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“…(iii) Case γ ∈ (3,4) In this case we consider the asymptotic expansion of Q (T n ) and H(T n ) for ∆p < 0 and ∆T n < 0 with |∆T n | 1 and |∆p| 1 given by…”
Section: Case With Power-law Distribution Qm With Power-law Exponent γmentioning
confidence: 99%
“…(iii) Case γ ∈ (3,4) In this case we consider the asymptotic expansion of Q (T n ) and H(T n ) for ∆p < 0 and ∆T n < 0 with |∆T n | 1 and |∆p| 1 given by…”
Section: Case With Power-law Distribution Qm With Power-law Exponent γmentioning
confidence: 99%
“…However, with few exceptions (including [6][7][8]), little attention has been paid to the synchronization dynamics of coupled oscillator systems where interactions are not pair-wise, but rather n-way, with n ≥ 3. Such interactions are called "simplicial", where an n-simplex represents an interaction between n + 1 units, so 2-simplices describe three-way interactions, etc [9]. Recent advances suggest that simplicial interactions may be vital in general oscillator systems [10][11][12] and may play an important role in brain dynamics [13][14][15] and other complex systems phenomena such as, the dynamics of collaborations [16] or social contagion [17].…”
mentioning
confidence: 99%
“…In particular, our understanding of both natural and man-made systems has significantly improved by studying how network structures and dynamical processes combined shape the overall systems' behavior. Recently, the network science community has turned its attention to network geometry [6][7][8][9] to better represent the kinds of interactions that one can find beyond typical pairwise interactions.…”
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confidence: 99%