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Networks beyond pairwise interactions: structure and dynamics
Federico Battiston, Giulia Cencetti, Iacopo Iacopini +5
The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a great variety of complex…
Strategies for linear rewriting systems: link with parallel rewriting and involutive divisions
Cyrille Chenavier, Maxime Lucas
We study rewriting systems whose underlying set of terms is equipped with a vector space structure over a given field. We introduce parallel rewriting relations, which are rewritin…
Multiorder Laplacian for synchronization in higher-order networks
Maxime Lucas, Giulia Cencetti, Federico Battiston
Traditionally, interaction systems have been described as networks, where links encode information on the pairwise influences among the nodes. Yet, in many systems, interactions ta…
Abstract rewriting internalized
Maxime Lucas
In traditional rewriting theory, one studies a set of terms up to a set of rewriting relations. In algebraic rewriting, one instead studies a vector space of terms, up to a vector…