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Title: Simplicial cascades are orchestrated by the multidimensional geometry of neuronal complexes
Abstract Cascades over networks (e.g., neuronal avalanches, social contagions, and system failures) often involve higher-order dependencies, yet theory development has largely focused on pairwise-interaction models. Here, we develop a ‘simplicial threshold model’ (STM) for cascades over simplicial complexes that encode dyadic, triadic and higher-order interactions. Focusing on small-world models containing both short- and long-range k -simplices, we explore spatio-temporal patterns that manifest as a frustration between local and nonlocal propagations. We show that higher-order interactions and nonlinear thresholding coordinate to robustly guide cascades along a k -dimensional generalization of paths that we call ‘geometrical channels’. We also find this coordination to enhance the diversity and efficiency of cascades over a simplicial-complex model for a neuronal network, or ‘neuronal complex’. We support these findings with bifurcation theory and data-driven approaches based on latent geometry. Our findings provide fruitful directions for uncovering the multiscale, multidimensional mechanisms that orchestrate the spatio-temporal patterns of nonlinear cascades.  more » « less
Award ID(s):
2052720
NSF-PAR ID:
10397882
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Communications Physics
Volume:
5
Issue:
1
ISSN:
2399-3650
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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