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Disentangling high-order mechanisms and high-order behaviours in complex systems

Nature Physics volume 18, pages 476–477 (2022)Cite this article

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To the Editor — Battiston et al1. provide a comprehensive overview of how investigations of complex systems should take into account interactions between more than two elements, which can be modelled by hypergraphs and studied via topological data analysis. Following a separate line of enquiry, a broad literature has developed information-theoretic tools to characterize high-order interdependencies from observed data. While these could seem to be competing approaches aiming to address the same question, in this correspondence we clarify that this is not the case, and that a complete account of higher-order phenomena needs to embrace both.

The investigation of high-order behaviour in data has a long history, stemming from foundational work in information theory2 and its early applications in biophysics3,4. These early efforts led to the formalization of high-order behaviour into the framework of partial information decomposition and its subsequent developments5,6,7. This literature has established formal bases for the analysis of high-order interdependencies exhibited by groups of three or more variables, and a description of their (synergistic or redundant) nature. While our primary focus here is on information-theoretic techniques, a number of other frameworks exist for probing the dynamics of complex systems beyond pairwise interactions — for a comprehensive review, see ref. 8.

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Fig. 1: Contrasting high-order mechanisms and behaviours in complex systems.

References

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Acknowledgements

F.R. was supported by the Ad Astra Chandaria Foundation. P.M. was funded by the Wellcome Trust (grant no. 210920/Z/18/Z). A.L. was supported by a Gates Cambridge Scholarship (OPP1144). T.V. is supported by the NSF-NRT grant 1735095, Interdisciplinary Training in Complex Networks and Systems at Indiana University Bloomington. S.S. was supported by the Italian MIUR PRIN 2017 (2017WZFTZP). A.L. and T.V. gratefully acknowledge the support of a Young Researchers’ Bridge Grant from the Complex Systems Society.

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Author notes

  1. These authors contributed equally: Fernando E. Rosas, Pedro A. M. Mediano, Andrea I. Luppi.

Authors and Affiliations

  1. Data Science Institute, Imperial College London, London, UK

    Fernando E. Rosas

  2. Centre for Psychedelic Research, Imperial College London, London, UK

    Fernando E. Rosas

  3. Centre for Complexity Science, Imperial College London, London, UK

    Fernando E. Rosas & Henrik J. Jensen

  4. Department of Informatics, University of Sussex, Brighton, UK

    Fernando E. Rosas

  5. Department of Psychology, University of Cambridge, Cambridge, UK

    Pedro A. M. Mediano

  6. Department of Psychology, Queen Mary University of London, London, UK

    Pedro A. M. Mediano

  7. University Division of Anaesthesia, University of Cambridge, Cambridge, UK

    Andrea I. Luppi

  8. Department of Clinical Neurosciences, University of Cambridge, Cambridge, UK

    Andrea I. Luppi

  9. Leverhulme Centre for the Future of Intelligence, University of Cambridge, Cambridge, UK

    Andrea I. Luppi

  10. The Alan Turing Institute, London, UK

    Andrea I. Luppi

  11. Department of Psychological & Brain Sciences, Indiana University, Bloomington, IN, USA

    Thomas F. Varley

  12. School of Informatics, Computing, and Engineering, Indiana University, Bloomington, IN, USA

    Thomas F. Varley

  13. Centre for Complex Systems and Faculty of Engineering, The University of Sydney, Sydney, New South Wales, Australia

    Joseph T. Lizier

  14. Dipartimento Interateneo di Fisica, Università degli Studi di Bari Aldo Moro, Bari, Italy

    Sebastiano Stramaglia

  15. INFN, Sezione di Bari, Bari, Italy

    Sebastiano Stramaglia

  16. Department of Mathematics, Imperial College London, London, UK

    Henrik J. Jensen

  17. Institute of Innovative Research, Tokyo Institute of Technology, Tokyo, Japan

    Henrik J. Jensen

  18. Department of Data Analysis, Ghent University, Ghent, Belgium

    Daniele Marinazzo

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Correspondence to Fernando E. Rosas, Pedro A. M. Mediano or Andrea I. Luppi.

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Rosas, F.E., Mediano, P.A.M., Luppi, A.I. et al. Disentangling high-order mechanisms and high-order behaviours in complex systems. Nat. Phys. 18, 476–477 (2022). https://doi.org/10.1038/s41567-022-01548-5

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