arXiv subjects

Antoine Allard

Publications and source records attributed to Antoine Allard.

At least 19 recordsLinked to original sources

arXiv2026

Operator-theoretic approach to the partial integration of randomly coupled phase oscillators

In our previous work [arXiv:2504.06248], we adopted Koopman theory to link the existence of different constants of motion to the presence of specific network motifs of Kuramoto oscillators. Yet, it remains to be shown how the partial integration can be carried out using the Koopman generator and its eigenfunctions. In this paper, we construct a random graph from network motifs that admit Koopman eigenfunctions and conserved quantities, and use it to define a partially integrable Kuramoto model. We perform the partial integration of the introduced model when there are monomial eigenfunctions and conserved cross-ratios, while providing an operator-theoretic derivation of the Watanabe-Strogatz transformation based on Magnus expansion and a recent result on closed forms of the Baker-Campbell-Hausdorff formula [arXiv:1502.06589].

math.DS↗

arXiv2026

The impact of behavioral homophily and conformity on epidemic spreading in networks with large groups

Understanding how social behavior influences epidemic dynamics has become a central focus in mathematical epidemiology. In particular, \textit{behavioral homophily} (the tendency of individuals to associate with similar others) and \textit{conformity} (the adjustment of individual behavior to group norms) are key mechanisms in shaping transmission patterns. In this work, we investigate the combined impact of these behavioral processes on the susceptible-infected-susceptible (SIS) dynamics on networks with large, densely connected groups, modeled as cliques. Each individual has an intrinsic behavioral preference, but their expressed behavior within a group is modulated by its composition, reflecting conformity dynamics. Using the approximate master equations (AME) framework, we characterize the interplay between behavioral heterogeneity, group structure, and epidemic localization. Our results reveal that behavioral homophily amplifies the effects of conformity in large groups, enabling minority behaviors to persist as well as substantially shifting epidemic thresholds and spreading regimes.

physics.soc-ph↗

arXiv2026

Simpson's paradox explains the ubiquity of nonlinear, threshold, and complex contagions

Complex contagions describe systems where the probability or rate of contagious transmission is a nonlinear function of the exposure to contagious agents. These models were first studied theoretically but have since been used to capture effects such as nonconformism, social reinforcement or peer pressure in empirical data. However, recent studies have shown that local correlations (e.g., group structure or temporal burstiness) and heterogeneity (e.g., diversity of parameters or covariates) can give the illusion of nonlinear effects even when the dynamics is actually linear. We briefly review these studies to inform a new model and explanation for these effective models of complex contagions. We find global threshold dynamics and superlinear complex contagions even in populations where agents are distributed across social groups described solely by linear or even sublinear contagions. This effect can be understood as a manifestation of Simpson's paradox. Incidence data from heterogeneous groups can look superlinear once averaged over all groups, since the sampling of groups represented at high incidence is biased towards those with stronger local transmission. We then define what we call a Simpson's contagion: a contagion process that looks superlinear when observed over an entire population, but is mechanistically linear or even sublinear in all of its subgroups. By exploring these Simpson's contagions over mathematical case studies, our work contributes to the growing body of literature on the ubiquity of threshold and complex contagions as effective models, and our results stress the pitfall of model selection that ignores correlations and heterogeneity in populations.

physics.soc-ph↗

arXiv2026

Harmonic morphisms and dynamical invariants in network renormalization

Renormalization of complex networks requires principled criteria for assessing whether a coarse-graining preserves dynamical content. We prove that discrete harmonic morphisms -- surjective maps preserving harmonic functions -- provide the minimal condition under which random walks on a fine-grained network project exactly onto random walks on its coarse-grained image, through an appropriate random time change. We formalize this via the harmonic degree, a diagnostic quantifying how closely any network coarse-graining approximates a harmonic morphism. Applying this framework to geometric, Laplacian, and GNN-based renormalization across real-world networks, we find that each method produces a distinct dynamical fingerprint encoding its underlying physical assumptions. Most strikingly, Laplacian renormalization spontaneously yields exact harmonic morphisms in several networks, achieving exact preservation of first-exit random-walk transition structure at specific scales, a property that entropic susceptibility fails to detect. Our results identify a discrete analog of diffusion-preserving conformal maps for irregular network topologies and provide quantitative tools for designing and evaluating multi-scale network descriptions.

cond-mat.stat-mech↗

arXiv2025

Inferring intraciliary dynamics from the gliding motility of Chlamydomonas reinhardtii

The unicellular microalga Chlamydomonas reinhardtii is widely recognized as a premier model living microswimmer for physicists and biophysicists. However, the interest around C. reinhardtii goes beyond its swimming capabilities. In fact, light can drastically alter its behavior: under blue illumination, the cell attaches to a nearby surface and intermittently glides on it. Such a gliding motility is powered by molecular-motor proteins operating on the cell's cilia, and the related machinery has established the cell as a prime reference for the study of intraciliary-transport mechanisms. This is what we focus on in the present work, by combining in-line holographic microscopy -which leads to unprecedented spatial and temporal resolutions on the gliding dynamics -and statistical inference. We show that, while gliding, the cells exhibit anomalous-diffusive features, including Lorentzian-like distributions of displacements, which are reminiscent of enhanced search strategies. The latter may be exploited by the cells to facilitate colony formation, or, more broadly, by organisms possessing an intraciliary-transport machinery for the transport of cargo molecules and signaling. Furthermore, gliding trajectories, by being intermittent, are valid candidates to infer forces at the molecular-motor scale that are necessary for the cells to move, or symetrically, to transport cargo molecules. We report a gliding threshold of about 20 pN, compatible with the activity of single molecular motors.

cond-mat.soft↗

arXiv2025

Tracking phase synchronization between flagella in the time-frequency domain resolves photophobic response

The unicellular microalga Chlamydomonas reinhardtii (CR) is well known for its bi-flagellated swimming in response to light stimuli. This work aims to study the resynchronization of CR flagella after a high light intensity stimulus, known as photoshock. The synchronization is estimated thanks to a quantity defined as the Phase Synchronization Index (PSI). The originality of this approach is to perform a time-frequency computation of a complex PSI based on continuous wavelet transform. Thanks to this analysis, we distinguish three swimming stages involving different frequency bands and phase shifts: synchronized breaststroke swimming, undulatory backward swimming, and resynchronization. This approach also reveals the presence of signal harmonics that set the photoshock response, independently of cell variability. Our results suggest that CR modulates the balance between spectral beating modes, providing a mechanism for robust adaptation to sudden environmental stresses.

physics.bio-ph↗

arXiv2025

Enhanced dispersion of active microswimmers in confined flows

In the presence of a laminar shear flow, the diffusion of passive colloidal particles is enhanced in the direction parallel to the flow. This classical phenomenon is known as Taylor-Aris dispersion. Besides, microorganisms, such as active microswimmers, exhibit an effective diffusive behavior at long times. Combining the two ingredients above, a natural question then emerges on how the effective diffusion of active microswimmers is altered in shear flows -- a widespread situation in natural environments with practical implications, \textit{e.g.} regarding biofilm formation. In this Letter, we investigate the motility and dispersion of \textit{Chlamydomonas reinhardtii} microalgae, within a rectangular microfluidic channel subjected to a sinusoidal Poiseuille flow. Using high-resolution optical microscopy and a particle-tracking algorithm, we reconstruct individual trajectories in various flow conditions and statistically analyze them through moment theory and sliding windowed demodulation. We find that the velocity fluctuations and the dispersion coefficient increase as the flow amplitude is increased, with only weak dependencies on the flow periodicity. Importantly, our results demonstrate that the generalization of Taylor-Aris law to active particles is valid.

cond-mat.stat-mech↗

arXiv2025

One pathogen does not an epidemic make: A review of interacting contagions, diseases, beliefs, and stories

From pathogens and computer viruses to genes and memes, contagion models have found widespread utility across the natural and social sciences. Despite their success and breadth of adoption, the approach and structure of these models remain surprisingly siloed by field. Given the siloed nature of their development and widespread use, one persistent assumption is that a given contagion can be studied in isolation, independently from what else might be spreading in the population. In reality, countless contagions of biological and social nature interact within hosts (interacting with existing beliefs, or the immune system) and across hosts (interacting in the environment, or affecting transmission mechanisms). Additionally, from a modeling perspective, we know that relaxing these assumptions has profound effects on the physics and translational implications of the models. Here, we review mechanisms for interactions in social and biological contagions, as well as the models and frameworks developed to include these interactions in the study of the contagions. We highlight existing problems related to the inference of interactions and to the scalability of mathematical models and identify promising avenues of future inquiries. In doing so, we highlight the need for interdisciplinary efforts under a unified science of contagions and for removing a common dichotomy between social and biological contagions.

physics.soc-ph↗

arXiv2025

Kuramoto meets Koopman: Constants of motion, symmetries, and network motifs

Conserved quantities in phase-oscillator dynamics are well established for identically coupled oscillators, or groups thereof, but the explicit connectivity conditions under which more complex networks admit constants of motion remain difficult to identify. Using Koopman theory, we derive general conditions for the existence of distinct conserved quantities in the Kuramoto model with heterogeneous phase lags on any weighted, directed, and signed graph. To this end, we find Koopman eigenfunctions and continuous Lie symmetries that generate different families of constants of motion. The derived conditions reveal a broad class of network motifs that support conserved quantities and we detect these motifs in hundreds of complex empirical networks. The results thus point to connectivity patterns that can preserve phase relationships over time and motivate further investigations of Koopman spectral properties for dynamics on complex networks.

nlin.AO↗

arXiv2025

The role of hydrodynamics in the synchronisation of {\it Chlamydomonas} flagella

While hydrodynamic coupling has long been considered essential for synchronisation of eukaryotic flagella, recent experiments on the unicellular biflagellate model organism {\it Chlamydomonas} demonstrate that -- at the single cell level -- intracellular mechanical coupling is necessary for coordination. It is therefore unclear what role, if any, hydrodynamic forces actually play in the synchronisation of multiple flagella within individual cells, arguably the building block of large scale coordination. Here we address this question experimentally by transiently blocking hydrodynamic coupling between the two flagella of single {\it Chlamydomonas}. Our results reveal that in wild type cells intracellularly-mediated forces are necessary and sufficient for flagellar synchronisation, with hydrodynamic coupling causing minimal changes in flagellar dynamics. However, fluid-mediated ciliary coupling is responsible for the extended periods of anti-phase synchronisation observed in a mutant with weaker intracellular coupling. At the single-cell level, therefore, flagellar coordination depends on a subtle balance between intracellular and extracellular forces.

physics.bio-ph↗

arXiv2024

On the reconstruction limits of complex networks

Network reconstruction consists in retrieving the hidden interaction structure of a system from observations. Many reconstruction algorithms have been proposed, although less research has been devoted to describe their theoretical limitations. In this work, we take a first-principles approach and build on our earlier definition of reconstructability-the fraction of structural information recoverable from data. We relate this quantity to the true data-generating (TDG) process and delineate an information-theoretic reconstruction limit, i.e., the upper bound of the mutual information between the true underlying graph and any graph reconstructed from observations. These concepts lead us to a principled numerical method to assess the validity of empirically reconstructed networks, based on model selection and a quantity we introduce: the reconstruction index. This index approximates the reconstructability from data, quantifies the variability of the reconstructed network ensemble, and is shown to predict reconstruction error without requiring knowledge of the true underlying network. We characterize this method and test it on empirical time series and networks.

stat.AP↗

arXiv2024

On the Uniform Sampling of the Configuration Model with Centrality Constraints

The Onion Decomposition has recently been shown to provide principled models of complex graphs that better reproduce the sparse networks found in nature, but at the cost of complicated connection rules. We propose a k-edge swapping MCMC algorithm to efficiently obtain a uniform sample from the ensemble of simple graphs with a fixed Onion Decomposition and degree sequence. We prove the non-connectivity of the 2-edge swap algorithm for some small graphs, but then provide numerical experiments to show that this non-connectivity is not a problem for 2-edge swap in many practical cases, and likely irrelevant when using k-edge swaps with k>2. We finish by comparing our null model to other well-known models in the literature, and show that keeping constraints on the meso-scale structures of the Onion Decomposition greatly increases both the structural and functional realism of random graph null model.

cond-mat.stat-mech↗

arXiv2024

Symmetry-driven embedding of networks in hyperbolic space

Hyperbolic models are known to produce networks with properties observed empirically in most network datasets, including heavy-tailed degree distribution, high clustering, and hierarchical structures. As a result, several embeddings algorithms have been proposed to invert these models and assign hyperbolic coordinates to network data. Current algorithms for finding these coordinates, however, do not quantify uncertainty in the inferred coordinates. We present BIGUE, a Markov chain Monte Carlo (MCMC) algorithm that samples the posterior distribution of a Bayesian hyperbolic random graph model. We show that the samples are consistent with current algorithms while providing added credible intervals for the coordinates and all network properties. We also show that some networks admit two or more plausible embeddings, a feature that an optimization algorithm can easily overlook.

stat.CO↗

arXiv2023

Nonlinear bias toward complex contagion in uncertain transmission settings

Current epidemics in the biological and social domains are challenging the standard assumptions of mathematical contagion models. Chief among them are the complex patterns of transmission caused by heterogeneous group sizes and infection risk varying by orders of magnitude in different settings, like indoor versus outdoor gatherings in the COVID-19 pandemic or different moderation practices in social media communities. However, quantifying these heterogeneous levels of risk is difficult and most models typically ignore them. Here, we include these novel features in an epidemic model on weighted hypergraphs to capture group-specific transmission rates. We study analytically the consequences of ignoring the heterogeneous transmissibility and find an induced superlinear infection rate during the emergence of a new outbreak, even though the underlying mechanism is a simple, linear contagion. The dynamics produced at the individual and group levels are therefore more similar to complex, nonlinear contagions, thus blurring the line between simple and complex contagions in realistic settings. We support this claim by introducing a Bayesian inference framework to quantify the nonlinearity of contagion processes. We show that simple contagions on real weighted hypergraphs are systematically biased toward the superlinear regime if the heterogeneity of the weights is ignored, greatly increasing the risk of erroneous classification as complex contagions. Our results provide an important cautionary tale for the challenging task of inferring transmission mechanisms from incidence data. Yet, it also paves the way for effective models that capture complex features of epidemics through nonlinear infection rates.

physics.soc-ph↗

arXiv2023

Exact and rapid linear clustering of networks with dynamic programming

We study the problem of clustering networks whose nodes have imputed or physical positions in a single dimension, for example prestige hierarchies or the similarity dimension of hyperbolic embeddings. Existing algorithms, such as the critical gap method and other greedy strategies, only offer approximate solutions to this problem. Here, we introduce a dynamic programming approach that returns provably optimal solutions in polynomial time -- O(n^2) steps -- for a broad class of clustering objectives. We demonstrate the algorithm through applications to synthetic and empirical networks and show that it outperforms existing heuristics by a significant margin, with a similar execution time.

cs.SI↗

arXiv2023

The D-Mercator method for the multidimensional hyperbolic embedding of real networks

One of the pillars of the geometric approach to networks has been the development of model-based mapping tools that embed real networks in its latent geometry. In particular, the tool Mercator embeds networks into the hyperbolic plane. However, some real networks are better described by the multidimensional formulation of the underlying geometric model. Here, we introduce $D$-Mercator, a model-based embedding method that produces multidimensional maps of real networks into the $(D+1)$-hyperbolic space, where the similarity subspace is represented as a $D$-sphere. We used $D$-Mercator to produce multidimensional hyperbolic maps of real networks and estimated their intrinsic dimensionality in terms of navigability and community structure. Multidimensional representations of real networks are instrumental in the identification of factors that determine connectivity and in elucidating fundamental issues that hinge on dimensionality, such as the presence of universality in critical behavior.

physics.soc-ph↗

arXiv2023

Firing rate distributions in plastic networks of spiking neurons

In recurrent networks of leaky integrate-and-fire (LIF) neurons, mean-field theory has proven successful in describing various statistical properties of neuronal activity at equilibrium, such as firing rate distributions. Mean-field theory has been applied to networks in which either the synaptic weights are homogeneous across synapses and the number of incoming connections of individual neurons is heterogeneous, or vice versa. Here we extend the previous mean-field formalisms to treat networks in which these two sources of structural heterogeneity occur simultaneously, including networks whose synapses are subject to plastic, activity-dependent modulation. The plasticity in our model is mediated by the introduction of one spike trace per neuron: a chemical signal that is released every time the neuron emits a spike and which is degraded over time. The temporal evolution of the trace is controlled by its degradation rate $r_p$ and by the neuron's underlying firing rate $ν$. When the ratio $α=ν/ r_p$ tends to infinity, the trace can be rescaled to be a reliable estimation of the neuron's firing rate. In this regime, the value of any synaptic weight at equilibrium is a function of the pre- and post-synaptic firing rates, and this relation can be used in the mean-field formalism. The solution to the mean-field equations specifies the firing rate and synaptic weight distributions at equilibrium. These equations are exact in the limit of reliable traces but they already provide accurate results when the degradation rate lies within a reasonable range, as we show by comparison with simulations of the full neuronal dynamics in networks composed of excitatory and inhibitory LIF neurons. Overall, this work offers a way to explore and better understand the way in which plasticity shapes both activity and structure in neuronal networks.

q-bio.NC↗

arXiv2023

Modeling critical connectivity constraints in random and empirical networks

Random networks are a powerful tool in the analytical modeling of complex networks as they allow us to write approximate mathematical models for diverse properties and behaviors of networks. One notable shortcoming of these models is that they are often used to study processes in terms of how they affect the giant connected component of the network, yet they fail to properly account for that component. As an example, this approach is often used to answer questions such as how robust is the network to random damage but fails to capture the structure of the network before any inflicted damage. Here, we introduce a simple conceptual step to account for such connectivity constraints in existing models. We distinguish network neighbors into two types of connections that can lead or not to a component of interest, which we call critical and subcritical degrees. In doing so, we capture important structural features of the network in a system of only one or two equations. In particular cases where the component of interest is surprising under classic random network models, such as sparse connected networks, a single equation can approximate state-of-the art models like message passing which require a number of equations linear in system size. We discuss potential applications of this simple framework for the study of infrastructure networks where connectivity constraints are critical to the function of the system.

physics.soc-ph↗