Maxime Lucas

selected publications

1. Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes

   Y. Zhang*,  M. Lucas*, and  F. Battiston

   Nat. Commun., 2023

   Abs Preprint DOI Code Bib Slides Video

   Higher-order interactions, through which three or more entities interact simultaneously, are important to the faithful modeling of many real-world complex systems. Recent efforts have focused on elucidating the effects of these nonpairwise interactions on the collective behaviors of coupled systems. Interestingly, several examples of higher-order interactions promoting synchronization have been found, raising speculations that this might be a general phenomenon. Here, we demonstrate that even for simple systems such as Kuramoto oscillators, the effects of higher-order interactions are highly nuanced. In particular, we show numerically and analytically that hyperedges typically enhance synchronization in random hypergraphs, but have the opposite effect in simplicial complexes. As an explanation, we identify higher-order degree heterogeneity as the key structural determinant of synchronization stability in systems with a fixed coupling budget. Typical to nonlinear systems, we also capture regimes where pairwise and nonpairwise interactions synergize to optimize synchronization. Our work contributes to a better understanding of dynamical systems with structured higher-order interactions.

   @article{zhang2023higher,
     title = {Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes},
     author = {Zhang*, Y. and Lucas*, M. and Battiston, F.},
     year = {2023},
     journal = {Nat. Commun.},
     volume = {14},
     number = {1},
     pages = {1605},
     doi = {10.1038/s41467-023-37190-9},
   }

2. Inferring cell cycle phases from a partially temporal network of protein interactions

   M. Lucas,  A. Morris,  A. Townsend-Teague,  L. Tichit,  B. H. Habermann, and  A. Barrat

   Cell Rep. Methods, 2023

   Abs Preprint DOI Code Bib Slides

   The temporal organization of biological systems is key for understanding them, but current methods for identifying this organization are often ad hoc and require prior knowledge. We present Phasik, a method that automatically identifies this multiscale organization by combining time series data (protein or gene expression) and interaction data (protein-protein interaction network). Phasik builds a (partially) temporal network and uses clustering to infer temporal phases. We demonstrate the method’s effectiveness by recovering well-known phases and sub-phases of the cell cycle of budding yeast and phase arrests of mutants. We also show its general applicability using temporal gene expression data from circadian rhythms in wild-type and mutant mouse models. We systematically test Phasik’s robustness and investigate the effect of having only partial temporal information. As time-resolved, multiomics datasets become more common, this method will allow the study of temporal regulation in lesser-known biological contexts, such as development, metabolism, and disease.

   @article{lucas2023inferring,
     title = {Inferring cell cycle phases from a partially temporal network of protein interactions},
     author = {Lucas, M. and Morris, A. and Townsend-Teague, A. and Tichit, L. and Habermann, B. H. and Barrat, A.},
     year = {2023},
     journal = {Cell Rep. Methods},
     pages = {100397},
     biorxiv = {10.1101/2021.03.26.437187v1},
     doi = {https://doi.org/10.1016/j.crmeth.2023.100397},
   }

3. Networks beyond pairwise interactions: structure and dynamics

   F. Battiston,  G. Cencetti,  I. Iacopini,  V. Latora,  M. Lucas,  A. Patania,  J.-G. Young, and  G. Petri

   Phys. Rep., 2020

   Abs Preprint DOI Bib

   The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a variety of complex systems has been successfully described as networks whose interacting pairs of nodes are connected by links. Yet, from human communications to chemical reactions and ecological systems, interactions can often occur in groups of three or more nodes and cannot be described simply in terms of dyads. Until recently little attention has been devoted to the higher-order architecture of real complex systems. However, a mounting body of evidence is showing that taking the higher-order structure of these systems into account can enhance our modeling capacities and help us understand and predict their dynamical behavior. Here we present a complete overview of the emerging field of networks beyond pairwise interactions. We discuss how to represent higher-order interactions and introduce the different frameworks used to describe higher-order systems, highlighting the links between the existing concepts and representations. We review the measures designed to characterize the structure of these systems and the models proposed to generate synthetic structures, such as random and growing bipartite graphs, hypergraphs and simplicial complexes. We introduce the rapidly growing research on higher-order dynamical systems and dynamical topology, discussing the relations between higher-order interactions and collective behavior. We focus in particular on new emergent phenomena characterizing dynamical processes, such as diffusion, synchronization, spreading, social dynamics and games, when extended beyond pairwise interactions. We conclude with a summary of empirical applications, and an outlook on current modeling and conceptual frontiers.

   @article{battiston2020networks,
     title = {Networks beyond pairwise interactions: structure and dynamics},
     author = {Battiston, F. and Cencetti, G. and Iacopini, I. and Latora, V. and Lucas, M. and Patania, A. and Young, J.-G. and Petri, G.},
     journal = {Phys. Rep.},
     year = {2020},
     volume = {874},
     pages = {1--92},
     publisher = {Elsevier},
     doi = {10.1016/j.physrep.2020.05.004},
   }