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Simplicial complexes: higher-order spectral dimension and dynamics
Simplicial complexes constitute the underlying topology of interacting complex systems including among the others brain and social interaction networks. They are generalized network structures that allow to go beyond the ...
Explosive higher-order Kuramoto dynamics on simplicial complexes
(American Physical Society, 2020)
The higher-order interactions of complex systems, such as the brain, are captured by their simplicial complex structure and have a significant effect on dynamics. However the existing dynamical models defined on simplicial ...
The higher-order spectrum of simplicial complexes: a renormalization group approach
Network topology is a flourishing interdisciplinary subject that is relevant for different disciplines including quantum gravity and brain research. The discrete topological objects that are investigated in network topology ...