@misc{10481/69280,
year = {2021},
month = {6},
url = {http://hdl.handle.net/10481/69280},
abstract = {Simplicial complexes capture the underlying network topology and geometry of complex
systems ranging from the brain to social networks. Here we show that algebraic topology is a
fundamental tool to capture the higher-order dynamics of simplicial complexes. In particular
we consider topological signals, i.e., dynamical signals defined on simplices of different
dimension, here taken to be nodes and links for simplicity. We show that coupling between
signals defined on nodes and links leads to explosive topological synchronization in which
phases defined on nodes synchronize simultaneously to phases defined on links at a discontinuous
phase transition. We study the model on real connectomes and on simplicial
complexes and network models. Finally, we provide a comprehensive theoretical approach
that captures this transition on fully connected networks and on random networks treated
within the annealed approximation, establishing the conditions for observing a closed
hysteresis loop in the large network limit.},
organization = {Agencia Española de Investigación
	FIS2017-84256-P},
organization = {Consejería de Conocimiento, Investigación y Universidad, Junta de Andalucía},
organization = {Royal Society

IEC\NSFC \191147},
organization = {Ministerio de Ciencia y Tecnología

	MICYT},
organization = {European Regional Development Fund

A-FQM-175-UGR18	ERDF},
publisher = {Springer Nature},
title = {Higher-order simplicial synchronization of coupled topological signals},
doi = {10.1038/s42005-021-00605-4},
author = {Ghorbanchian, Reza and Restrepo, Juan G. and Torres Agudo, Joaquín and Bianconi, Ginestra},
}