1.6k citations · 2.2k across the 17 of their papers we have counts for
19 papers
Random Recursive Simplicial Complexes
P. L. Krapivsky, M. Lucas
We investigate random recursive simplicial complexes growing by adding, at each step, a vertex together with a simplex formed by joining the new vertex with a randomly chosen exist…
A unified framework for Simplicial Kuramoto models
Marco Nurisso, Alexis Arnaudon, Maxime Lucas +4
Simplicial Kuramoto models have emerged as a diverse and intriguing class of models describing oscillators on simplices rather than nodes. In this paper, we present a unified frame…
Generalized Deep Thermalization for Free Fermions
Maxime Lucas, Lorenzo Piroli, Jacopo De Nardis +1
In non-interacting isolated quantum systems out of equilibrium, local subsystems typically relax to non-thermal stationary states. In the standard framework, information on the res…
Simplicially driven simple contagion
Maxime Lucas, Iacopo Iacopini, Thomas Robiglio +2
Single contagion processes are known to display a continuous transition from an epidemic-free phase at low contagion rates to the epidemic state for rates above a critical threshol…
Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes
Yuanzhao Zhang, Maxime Lucas, Federico Battiston
Higher-order networks have emerged as a powerful framework to model complex systems and their collective behavior. Going beyond pairwise interactions, they encode structured relati…
A Cartesian Bicategory of Polynomial Functors in Homotopy Type Theory
Eric Finster, Samuel Mimram, Maxime Lucas +1
Polynomial functors are a categorical generalization of the usual notion of polynomial, which has found many applications in higher categories and type theory: those are generated…
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…
The folk model category structure on strict -categories is monoidal
Dimitri Ara, Maxime Lucas
We prove that the folk model category structure on the category of strict -categories, introduced by Lafont, Métayer and Worytkiewicz, is monoidal, first, for the Gray tensor pr…
Limitations of the asymptotic approach to dynamics
Julian Newman, Maxime Lucas, Aneta Stefanovska
Standard dynamical systems theory is centred around the coordinate-invariant asymptotic-time properties of autonomous systems. We identify three limitations of this approach. First…
Nonautonomous driving induces stability in network of identical oscillators
Maxime Lucas, Duccio Fanelli, Aneta Stefanovska
Nonautonomous driving of an oscillator has been shown to enlarge the Arnold tongue in parameter space, but little is known about the analogous effect for a network of oscillators.…
Stabilisation of dynamics of oscillatory systems by non-autonomous perturbation
Maxime Lucas, Julian Newman, Aneta Stefanovska
Synchronisation and stability under periodic oscillatory driving are well-understood, but little is known about the effects of aperiodic driving, despite its abundance in nature. H…
Desynchronization induced by time-varying network
Maxime Lucas, Duccio Fanelli, Timoteo Carletti +1
The synchronous dynamics of an array of excitable oscillators, coupled via a generic graph, is studied. Non homogeneous perturbations can grow and destroy synchrony, via a self-con…
A cubical Squier's theorem
Maxime Lucas
Convergent rewriting systems are well-known tools in the study of the word-rewriting problem. In particular, a presentation of a monoid by a finite convergent rewriting system give…
Cubical -categories
Maxime Lucas
In this article we introduce the notion of cubical -categories, for . We show that the equivalence between globular and groupoid -categories p…
A coherence theorem for pseudonatural transformations
Maxime Lucas
We prove coherence theorems for bicategories, pseudofunctors and pseudonatural transformations. These theorems boil down to proving the coherence of some free -categories. I…
Verifying the Steane code with Quantomatic
Ross Duncan, Maxime Lucas
In this paper we give a partially mechanized proof of the correctness of Steane's 7-qubit error correcting code, using the tool Quantomatic. To the best of our knowledge, this repr…