@misc{10481/70631,
year = {2021},
month = {5},
url = {http://hdl.handle.net/10481/70631},
abstract = {Simplicial synchronization reveals the role that topology and geometry
have in determining the dynamical properties of simplicial complexes. Simplicial
network geometry and topology are naturally encoded in the spectral properties of the
graph Laplacian and of the higher-order Laplacians of simplicial complexes. Here
we show how the geometry of simplicial complexes induces spectral dimensions
of the simplicial complex Laplacians that are responsible for changing the phase
diagram of the Kuramoto model. In particular, simplicial complexes displaying a
non-trivial simplicial network geometry cannot sustain a synchronized state in the
infinite network limit if their spectral dimension is smaller or equal to four. This
theoretical result is here verified on the Network Geometry with Flavor simplicial
complex generative model displaying emergent hyperbolic geometry. On its turn
simplicial topology is shown to determine the dynamical properties of the higher-
order Kuramoto model. The higher-order Kuramoto model describes synchronization
of topological signals, i.e. phases not only associated to the nodes of a simplicial
complexes but associated also to higher-order simplices, including links, triangles
and so on.},
title = {Geometry, Topology and Simplicial Synchronization},
author = {Torres Agudo, Joaquín and Millán Vidal, Ana Paula and Restrepo, Juan G. and Bianconi, Ginestra},
}