Maxime Lucas
Now: Assistant Professor @ University of Namur
Maxime researches complex systems and their application to the life sciences. Physicist, Belgian, likes a good (or bad) pun.
Papers 18
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Maalouf, A., DelPreto, J., Lucas, M., Poetto, S., Andreas, J., Torralba, A., Gero, S., Petri, G., Rus, D., Gruber, D. F.
We quantitatively document a sperm whale birth event, revealing collective support behaviors across kinship lines. Using high-resolution drone footage, computer vision, and multiscale network analysis, we studied the interactions within a Caribbean sperm whale unit comprising two matrilines. Our results suggest that a female family member led birth assistance and that after delivery, all individuals oriented toward and helped lift the newborn, taking turns in a coordinated, cross-kin effort. Despite historically observed foraging segregation, kinship barriers dissolved as all unit members contributed. These analyses provide evidence of birth attendance, or assistance, in a nonprimate species, a behavior long considered characteristic only of humans and their close relatives.
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Zaffina, L., Monti, C., Poetto, S., Lucas, M., Machado Borges, H. J., Deshpande, R., Tonnesen, P., Gruber, D., Gero, S., Santoro, A., Petri, G.
Predators searching patchy environments must coordinate movements across scales, yet this behavioural hierarchy is not yet technically possible to observe in the deep ocean. Here we show that sperm-whale foraging is organized across two nested levels: directionally persistent search paths and flexible prey-capture tactics. We combine acoustic recordings with reconstructed three-dimensional trajectories from 34 sensor-tag deployments on 20 individual whales in both the eastern Caribbean and the mid-Atlantic. Complete foraging paths exhibit heavy-tailed step lengths and superdiffusive displacement, consistent with Levy-like search. Within these paths, echolocation buzzes resolve into two recurrent acoustic-kinematic tactics, and every sampled whale used both, switching between them within dives. Together, these results reveal a foraging hierarchy in which flexible capture actions unfold within persistent, deliberate large-scale search.
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Aluma, Y., Baron, Z., Barrett, R., Baumgartner, C., Beguš, G., Bhattacharya, S., Bronstein, M. M., Dahan, S., Davis, O., de Haas, S., Defoe, J., DelPreto, J., Dessi, R., Diamant, R., Gatesy, J., George, K., Gero, S., Gibbons, D., Gibbons, D., Gil, S., Goldwasser, S., Gruber, D. F., Harve, O., Hernandez, A., Ishay, M., Jadhav, N., KC, L., Kenny, A., Leitao, A., Lucas, M., Maalouf, A., Malkin, P., Mevorach, Y., Pagani, S., Paradise, O., Petri, G., Poetto, S., Rossi, E., Rus, D., Salino-Hugg, M., Santoro, A., Sharma, P., Tchernov, D., Torralba, A., Tønnesen, P., Vogt, D. M., Wood, R. J.
Wild cetacean birth observations are extremely rare, with observations having been recorded in less than 10% of cetacean species. Here, we describe a detailed accounting of a sperm whale (Physeter macrocephalus) birth off the coast of Dominica within a well-documented social unit and consisted of sperm whales collaboratively lifting the newborn out of the water. We recorded data via multiple concurrent methods: underwater audio, aerial drone video, shipboard photography in addition to behavioral observations spanning before, during and after the whale birth. All 11 members from sperm whale “Unit A” were present and participated in the birth, which lasted 34 min from the time the flukes emerged until the completion of delivery. The sperm whale unit made extensive vocalizations, with statistically significant shifts in coda vocal style corresponding to key events, such as the beginning of the birth and interactions with short-finned pilot whales (Globicephala macrorhynchus) shortly after the birth event. An evolutionary analysis of wild cetacean births suggests that newborns being lifted out of the water dates to before the most recent common ancestor of toothed and baleen whales, >36 million years ago, and that cooperative lifting of the newborn is noted, thus far, only in members of Odontoceti (toothed whales). This study provides the most in-depth observations of a wild cetacean birth.
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Lucas, M., Bisot, C., Petri, G., Declerck, S., Carletti, T.
We develop a computational framework simulating how biological networks like fungal mycelium grow through branching and fusion. Our model shows that these synthetic structures occupy similar regions of performance space as evolved empirical fungal networks, demonstrating that optimal architectural trade-offs emerge from simple local growth mechanics. The findings indicate such networks can simultaneously achieve multiple functional objectives—including transport efficiency, exploration capacity, and structural robustness—without centralized control.
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Nurisso, M., Morandini, M., Lucas, M., Vaccarino, F., Gili, T., Petri, G.
We propose a cross-order Laplacian renormalization group (X-LRG) scheme for arbitrary higher-order networks. The renormalization group is a pillar of the theory of scaling, scale-invariance, and universality in physics. An RG scheme based on diffusion dynamics was recently introduced for complex networks with dyadic interactions. Despite mounting evidence of the importance of polyadic interactions, we still lack a general RG scheme for higher-order networks. Our approach uses a diffusion process to group nodes or simplices, where information can flow between nodes and between simplices (higher-order interactions). This approach allows us (i) to probe higher-order structures, defining scale-invariance at various orders, and (ii) to propose a coarse-graining scheme. We demonstrate our approach on controlled synthetic higher-order systems and then use it to detect the presence of order-specific scale-invariant profiles of real-world complex systems from multiple domains.
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Lucas, M., Aime, N., Callara, A., Fontanelli, L., Sebastiani, L., Santarcangelo, E. L., Petri, G.
This study investigates the neural correlates of hypnosis using network and topological analysis of EEG data, providing evidence relevant to the state-nonstate debate in hypnosis research.
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Robiglio, T., Neri, M., Coppes, D., Agostinelli, C., Battiston, F., Lucas, M., Petri, G.
The interplay between causal mechanisms and emerging collective behaviors is a central aspect of the understanding, control, and prediction of complex networked systems. Here we study this interplay in the context of higher-order mechanisms and behaviors in two representative models: a simplicial Ising model and a simplicial social contagion model. In both systems, we find that group (higher-order) interactions show emergent synergistic (higher-order) behavior. The emergent synergy appears only at the group level and depends in a complex non-linear way on the tradeoff between the strengths of the low- and higher-order mechanisms, and is invisible to low-order behavioral observables. Finally, we present a simple method to detect higher-order mechanisms by using this signature.
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Santoro, A., Battiston, F., Lucas, M., Petri, G., Amico, E.
Traditional models of human brain activity often represent it as a network of pairwise interactions between brain regions. Going beyond this limitation, recent approaches have been proposed to infer higher-order interactions from temporal brain signals involving three or more regions. However, to this day it remains unclear whether methods based on inferred higher-order interactions outperform traditional pairwise ones for the analysis of fMRI data. To address this question, we conducted a comprehensive analysis using fMRI time series of 100 unrelated subjects from the Human Connectome Project. We show that higher-order approaches greatly enhance our ability to decode dynamically between various tasks, to improve the individual identification of unimodal and transmodal functional subsystems, and to strengthen significantly the associations between brain activity and behavior. Overall, our approach sheds new light on the higher-order organization of fMRI time series, improving the characterization of dynamic group dependencies in rest and tasks, and revealing a vast space of unexplored structures within human functional brain data, which may remain hidden when using traditional pairwise approaches.
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Zhang, Y., Skardal, P.S., Battiston, F., Petri, G., Lucas, M.
A key challenge of nonlinear dynamics and network science is to understand how higher-order interactions influence collective dynamics. Although many studies have approached this question through linear stability analysis, less is known about how higher-order interactions shape the global organization of different states. Here, we shed light on this issue by analyzing the rich patterns supported by identical Kuramoto oscillators on hypergraphs. We show that higher-order interactions can have opposite effects on linear stability and basin stability: they stabilize twisted states (including full synchrony) by improving their linear stability, but also make them hard to find by dramatically reducing their basin size. Our results highlight the importance of understanding higher-order interactions from both local and global perspectives.
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Leitao, A., Lucas, M., Poetto, S., Hersh, T. A., Gero, S., Gruber, D., Bronstein, M., Petri, G.
We provide quantitative evidence suggesting social learning in sperm whales across sociocultural boundaries, using acoustic data from the Pacific and Atlantic Oceans. Traditionally, sperm whale populations are categorized into clans based on their vocal repertoire: the rhythmically patterned click sequences (codas) that they use. Among these codas, identity codas function as symbolic markers for each clan, accounting for 35-60% of codas they produce. We introduce a computational method to model whale speech, which encodes rhythmic microvariations within codas, capturing their vocal style. We find that vocal style-clans closely align with repertoire-clans. However, contrary to vocal repertoire, we show that sympatry increases vocal style similarity between clans for non-identity codas, i.e. most codas, suggesting social learning across cultural boundaries. More broadly, this subcoda structure model offers a framework for comparing communication systems in other species, with potential implications for deeper understanding of vocal and cultural transmission within animal societies.
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Zhang, Y., Lucas, M., Battiston, F.
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.
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Lucas, M., Iacopini, I., Robiglio, T., Barrat, A., Petri, G.
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 threshold. This transition can become discontinuous when two simple contagion processes are coupled in a bi-directional symmetric way. However, in many cases, the coupling is not symmetric and the processes can be of a different nature. For example, social behaviors---such as hand-washing or mask-wearing---can affect the spread of a disease, and their adoption dynamics via social reinforcement mechanisms are better described by complex contagion models, rather than by the simple contagion paradigm, which is more appropriate for disease spreading phenomena. Motivated by this example, we consider a simplicial contagion (describing the adoption of a behavior) that uni-directionally drives a simple contagion (describing a disease propagation). We show that, above a critical driving strength, such driven simple contagion can exhibit both discontinuous transitions and bi-stability, which are instead absent in standard simple contagions. We provide a mean-field analytical description of the phase diagram of the system, and complement the results with Markov-chain simulations. Our results provide a novel route for a simple contagion process to display the phenomenology of a higher-order contagion, through a driving mechanism that may be hidden or unobservable in many practical instances.
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Lucas, M., Morris, A., Townsend-Teague, A., Tichit, L., Habermann, B., Barrat, A.
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.
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Nurisso, M., Arnaudon, A., Lucas, M., Peach, R. L., Expert, P., Vaccarino, F., Petri, G.
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 framework to describe different variants of these models, categorized into three main groups: simple models, Hodge-coupled models, and order-coupled (Dirac) models. Our framework is based on topology, discrete differential geometry as well as gradient flows and frustrations, and permits a systematic analysis of their properties. We establish an equivalence between the simple simplicial Kuramoto model and the standard Kuramoto model on pairwise networks under the condition of manifoldness of the simplicial complex. Then, starting from simple models, we describe the notion of simplicial synchronization and derive bounds on the coupling strength necessary or sufficient for achieving it. For some variants, we generalize these results and provide new ones, such as the controllability of equilibrium solutions. Finally, we explore a potential application in the reconstruction of brain functional connectivity from structural connectomes and find that simple edge-based Kuramoto models perform competitively or even outperform complex extensions of node-based models.
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Lucas, M., Townsend-Teague, A., Neri, M., Poetto, S., Morris, A., Habermann, B., Tichit, L.
Phasik is a Python library for analyzing the temporal structure of temporal and partially temporal networks. Temporal networks are used to model complex systems that consist of entities with time-varying interactions. This library provides methods for building temporal networks (including from data), visualizing them, and analyzing their structure. In particular, Phasik focuses on the identification of temporal phases, that is, periods of time during which the system is in a given state. The library supports partially temporal networks for which information about only a subset of the edges’ temporal evolution is available. Phasik is implemented in pure Python and integrates with the rest of the Python scientific stack.
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Landry, N. W., Lucas, M., Iacopini, I., Petri, G., Schwarze, A., Patania, A., Torres, L.
CompleX Group Interactions (XGI) is a library for analyzing higher-order networks. Such networks are used to model interactions of arbitrary size between entities in a complex system. This library provides methods for building hypergraphs and simplicial complexes; algorithms to analyze their structure, visualize them, and simulate dynamical processes on them; and a collection of higher-order datasets. XGI is implemented in pure Python and integrates with the rest of the Python scientific stack. XGI is designed and developed by network scientists with the needs of network scientists in mind.
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Battiston, F., Cencetti, G., Iacopini, I., Latora, V., Lucas, M., Patania, A., Young, J.-G., Petri, G.
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.
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Lucas, M., Cencetti, G., Battiston, F.
The emergence of synchronization in systems of coupled agents is a pivotal phenomenon in physics, biology, computer science, and neuroscience. Traditionally, interaction systems have been described as networks, where links encode information only on the pairwise influences among the nodes. Yet, in many systems, interactions among the units take place in larger groups. Recent work has shown that the presence of higher-order interactions between oscillators can significantly affect the emerging dynamics. However, these early studies have mostly considered interactions up to four oscillators at time, and analytical treatments are limited to the all-to-all setting. Here, we propose a general framework that allows us to effectively study populations of oscillators where higher-order interactions of all possible orders are considered, for any complex topology described by arbitrary hypergraphs, and for general coupling functions. To this end, we introduce a multiorder Laplacian whose spectrum determines the stability of the synchronized solution. Our framework is validated on three structures of interactions of increasing complexity. First, we study a population with all-to-all interactions at all orders, for which we can derive in a full analytical manner the Lyapunov exponents of the system, and for which we investigate the effect of including attractive and repulsive interactions. Second, we apply the multiorder Laplacian framework to synchronization on a synthetic model with heterogeneous higher-order interactions. Finally, we compare the dynamics of coupled oscillators with higher-order and pairwise couplings only, for a real dataset describing the macaque brain connectome, highlighting the importance of faithfully representing the complexity of interactions in real-world systems. Taken together, our multiorder Laplacian allows us to obtain a complete analytical characterization of the stability of synchrony in arbitrary higher-order networks, paving the way toward a general treatment of dynamical processes beyond pairwise interactions.