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Higher-Order Description of Brain Function

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Higher-Order Systems

Part of the book series: Understanding Complex Systems ((UCS))

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Abstract

Higher-order interactions have long figured both at the microscopic and macroscopic level in neuronal and whole-brain descriptions, with the aim to capture structural, functional, and ultimately cognitive aspects. They are systematizing the paradigm shift that graph theory introduced by moving from studying neural and brain activation to co-activation patterns. Recently, topology has emerged as a central tool in this context due to its natural capacity to describe relations beyond pairwise interactions, and to recent advances in its computational applications. In this chapter, we summarize fundamental concepts and results of the application of higher-order descriptions to neuroscience. We start from the microscopic scale, describing how higher-order interactions have been introduced and measured in the context of neuronal populations activation patterns and in neural coding theory. We then move to the macroscopic scale, discussing recent applications of topological data analysis to whole-brain data, and finally highlight the challenges related to extracting higher-order signals from low-order ones.

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Authors and Affiliations

  1. University College London, London, WC1E 6BT, UK

    Paul Expert

  2. Imperial College London, Global Digital Health Unit, London, SW72AZ, UK

    Paul Expert

  3. Tokyo Tech World Research Hub Initiative (WRHI), Tokyo Institute of Technology, Yokohama, 226-8503, Japan

    Paul Expert

  4. ISI Foundation, via Chisola 5, 10126, Turin, Italy

    Giovanni Petri

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Editors and Affiliations

  1. Department of Network and Data Science, Central European University, Vienna, Austria

    Federico Battiston

  2. ISI Foundation, Turin, Italy

    Giovanni Petri

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Expert, P., Petri, G. (2022). Higher-Order Description of Brain Function. In: Battiston, F., Petri, G. (eds) Higher-Order Systems. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-91374-8_17

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