Two’s company, three (or more) is a simplex

By Chad Giusti, Robert Ghrist, D. Bassett. Journal of Computational Neuroscience, 2016

392 citations recorded by the source corpus.

The language of graph theory, or network science, has proven to be an exceptional tool for addressing myriad problems in neuroscience. Yet, the use of networks is predicated on a critical simplifying assumption: that the quintessential unit of interest in a brain is a dyad – two nodes (neurons or brain regions) connected by an edge. While rarely mentioned, this fundamental assumption inherently limits the types of neural structure and function that graphs can be used to model. Here, we describe a generalization of graphs that overcomes these limitations, thereby offering a broad range of new possibilities in terms of modeling and measuring neural phenomena. Specifically, we explore the use of simplicial complexes: a structure developed in the field of mathematics known as algebraic topology, of increasing applicability to real data due to a rapidly growing computational toolset. We review the underlying mathematical formalism as well as the budding literature applying simplicial complexes to neural data, from electrophysiological recordings in animal models to hemodynamic fluctuations in humans. Based on the exceptional flexibility of the tools and recent ground-breaking insights into neural function, we posit that this framework has the potential to eclipse graph theory in unraveling the fundamental mysteries of cognition.

Subfields: Cognitive Neuroscience, Computational Theory and Mathematics, Physiology

View Paper: https://www.semanticscholar.org/paper/0cd7469b7fc4ad90a0552e7124f60f1d216f467f

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Citations in the corpus

Dynamics on higher-order networks: a review (2022, background): “For instance, group interactions take place predominantly in systems arising in neurobiology [10,11], social systems [9,12] and ecology [13,14].”
Higher order interactions in complex networks of phase oscillators promote abrupt synchronization switching (2019, background): “ote that in this Letter we have taken brain dynamics as our primary motivating example due to the existence of direct evidence of higher-order interactions in a system with synchronization properties [11, 12, 14, 17]. However, more general results suggest that higher-order interactions may be import”
Networks beyond pairwise interactions: structure and dynamics (2020, background): “[648] Chad Giusti, Robert Ghrist, and Danielle S Bassett.”