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math-ph2021
Connecting Hodge and Sakaguchi-Kuramoto: a mathematical framework for coupled oscillators on simplicial complexes
Alexis Arnaudon, Robert L. Peach, Giovanni Petri +1
We formulate a general Kuramoto model on weighted simplicial complexes where phases oscillators are supported on simplices of any order . Crucially, we introduce linear and non-…
physics.soc-ph2021★ 16 cited
Relative, local and global dimension in complex networks
Robert L. Peach, Alexis Arnaudon, Mauricio Barahona
Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical…