arXiv subjects

Antoine Allard

Publications and source records attributed to Antoine Allard.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2023

Dimension matters when modeling network communities in hyperbolic spaces

Over the last decade, random hyperbolic graphs have proved successful in providing geometric explanations for many key properties of real-world networks, including strong clustering, high navigability, and heterogeneous degree distributions. These properties are ubiquitous in systems as varied as the internet, transportation, brain or epidemic networks, which are thus unified under the hyperbolic network interpretation on a surface of constant negative curvature. Although a few studies have shown that hyperbolic models can generate community structures, another salient feature observed in real networks, we argue that the current models are overlooking the choice of the latent space dimensionality that is required to adequately represent clustered networked data. We show that there is an important qualitative difference between the lowest-dimensional model and its higher-dimensional counterparts with respect to how similarity between nodes restricts connection probabilities. Since more dimensions also increase the number of nearest neighbors for angular clusters representing communities, considering only one more dimension allows us to generate more realistic and diverse community structures.

physics.soc-ph↗

arXiv2023

Duality between predictability and reconstructability in complex systems

Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here, we find an intricate relationship between predictability and reconstructability using an information-theoretical point of view. We use the mutual information between a random graph and a stochastic process evolving on this random graph to quantify their codependence. Then, we show how the uncertainty coefficients, which are intimately related to that mutual information, quantify our ability to reconstruct a graph from an observed time series, and our ability to predict the evolution of a process from the structure of its interactions. Interestingly, we find that predictability and reconstructability, even though closely connected by the mutual information, can behave differently, even in a dual manner. We prove how such duality universally emerges when changing the number of steps in the process, and provide numerical evidence of other dualities occurring near the criticality of multiple different processes evolving on different types of structures.

cond-mat.stat-mech↗

arXiv2023

Geometric description of clustering in directed networks

First principle network models are crucial to make sense of the intricate topology of real complex networks. While modeling efforts have been quite successful in undirected networks, generative models for networks with asymmetric interactions are still not well developed and are unable to reproduce several basic topological properties. This is particularly disconcerting considering that real directed networks are the norm rather than the exception in many natural and human-made complex systems. In this paper, we fill this gap and show how the network geometry paradigm can be elegantly extended to the case of directed networks. We define a maximum entropy ensemble of geometric (directed) random graphs with a given sequence of in- and out-degrees. Beyond these local properties, the ensemble requires only two additional parameters to fix the level of reciprocity and the seven possible types of 3-node cycles in directed networks. A systematic comparison with several representative empirical datasets shows that fixing the level of reciprocity alongside the coupling with an underlying geometry is able to reproduce the wide diversity of clustering patterns observed in real complex directed networks.

physics.soc-ph↗

arXiv2022

Hypergraph reconstruction from noisy pairwise observations

The network reconstruction task aims to estimate a complex system's structure from various data sources such as time series, snapshots, or interaction counts. Recent work has examined this problem in networks whose relationships involve precisely two entities-the pairwise case. Here we investigate the general problem of reconstructing a network in which higher-order interactions are also present. We study a minimal example of this problem, focusing on the case of hypergraphs with interactions between pairs and triplets of vertices, measured imperfectly and indirectly. We derive a Metropolis-Hastings-within-Gibbs algorithm for this model and use the algorithms to highlight the unique challenges that come with estimating higher-order models. We show that this approach tends to reconstruct empirical and synthetic networks more accurately than an equivalent graph model without higher-order interactions.

cs.SI↗

arXiv2022

Dimension reduction of dynamics on modular and heterogeneous directed networks

Dimension reduction is a common strategy to study non-linear dynamical systems composed by a large number of variables. The goal is to find a smaller version of the system whose time evolution is easier to predict while preserving some of the key dynamical features of the original system. Finding such a reduced representation for complex systems is, however, a difficult task. We address this problem for dynamics on weighted directed networks, with special emphasis on modular and heterogeneous networks. We propose a two-step dimension-reduction method that takes into account the properties of the adjacency matrix. First, units are partitioned into groups of similar connectivity profiles. Each group is associated to an observable that is a weighted average of the nodes' activities within the group. Second, we derive a set of conditions that must be fulfilled for these observables to properly represent the original system's behavior, together with a method for approximately solving them. The result is a reduced adjacency matrix and an approximate system of ODEs for the observables' evolution. We show that the reduced system can be used to predict some characteristic features of the complete dynamics for different types of connectivity structures, both synthetic and derived from real data, including neuronal, ecological, and social networks. Our formalism opens a way to a systematic comparison of the effect of various structural properties on the overall network dynamics. It can thus help to identify the main structural driving forces guiding the evolution of dynamical processes on networks.

math.DS↗

arXiv2022

Limits of Individual Consent and Models of Distributed Consent in Online Social Networks

Personal data are not discrete in socially-networked digital environments. A user who consents to allow access to their profile can expose the personal data of their network connections to non-consented access. Therefore, the traditional consent model (informed and individual) is not appropriate in social networks where informed consent may not be possible for all users affected by data processing and where information is distributed across users. Here, we outline the adequacy of consent for data transactions. Informed by the shortcomings of individual consent, we introduce both a platform-specific model of "distributed consent" and a cross-platform model of a "consent passport." In both models, individuals and groups can coordinate by giving consent conditional on that of their network connections. We simulate the impact of these distributed consent models on the observability of social networks and find that low adoption would allow macroscopic subsets of networks to preserve their connectivity and privacy.

physics.soc-ph↗

arXiv2022

Hierarchical team structure and multidimensional localization (or siloing) on networks

Knowledge silos emerge when structural properties of organizational interaction networks limit the diffusion of information. These structural barriers are known to take many forms at different scales - hubs in otherwise sparse organisations, large dense teams, or global core-periphery structure - but we lack an understanding of how these different structures interact. Here we bridge the gap between the mathematical literature on localization of spreading dynamics and the more applied literature on knowledge silos in organizational interaction networks. To do so, we introduce a new model that considers a layered structure of teams to unveil a new form of hierarchical localization (i.e., the localization of information at the top or center of an organization) and study its interplay with known phenomena of mesoscopic localization (i.e., the localization of information in large groups), $k$-core localization (i.e., around denser $k$-cores) and hub localization (i.e., around high degree stars). We also include a complex contagion mechanism by considering a general infection kernel which can depend on hierarchical level (influence), degree (popularity), infectious neighbors (social reinforcement) or team size (importance). This general model allows us to study the multifaceted phenomenon of information siloing in complex organizational interaction networks and opens the door to new optimization problems to promote or hinder the emergence of different localization regimes.

physics.soc-ph↗

arXiv2022

Predicting the diversity of early epidemic spread on networks

The interplay of biological, social, structural and random factors makes disease forecasting extraordinarily complex. The course of an epidemic exhibits average growth dynamics determined by features of the pathogen and the population, yet also features significant variability reflecting the stochastic nature of disease spread. In this work, we reframe a stochastic branching process analysis in terms of probability generating functions and compare it to continuous time epidemic simulations on networks. In doing so, we predict the diversity of emerging epidemic courses on both homogeneous and heterogeneous networks. We show how the challenge of inferring the early course of an epidemic falls on the randomness of disease spread more so than on the heterogeneity of contact patterns. We provide an analysis which helps quantify, in real time, the probability that an epidemic goes supercritical or conversely, dies stochastically. These probabilities are often assumed to be one and zero, respectively, if the basic reproduction number, or R0, is greater than 1, ignoring the heterogeneity and randomness inherent to disease spread. This framework can give more insight into early epidemic spread by weighting standard deterministic models with likelihood to inform pandemic preparedness with probabilistic forecasts.

q-bio.PE↗

arXiv2022

The role of directionality, heterogeneity and correlations in epidemic risk and spread

Most models of epidemic spread, including many designed specifically for COVID-19, implicitly assume mass-action contact patterns and undirected contact networks, meaning that the individuals most likely to spread the disease are also the most at risk to receive it from others. Here, we review results from the theory of random directed graphs which show that many important quantities, including the reproduction number and the epidemic size, depend sensitively on the joint distribution of in- and out-degrees ("risk" and "spread"), including their heterogeneity and the correlation between them. By considering joint distributions of various kinds, we elucidate why some types of heterogeneity cause a deviation from the standard Kermack-McKendrick analysis of SIR models, i.e., so-called mass-action models where contacts are homogeneous and random, and some do not. We also show that some structured SIR models informed by realistic complex contact patterns among types of individuals (age or activity) are simply mixtures of Poisson processes and tend not to deviate significantly from the simplest mass-action model. Finally, we point out some possible policy implications of this directed structure, both for contact tracing strategy and for interventions designed to prevent superspreading events. In particular, directed graphs have a forward and backward version of the classic "friendship paradox" -- forward edges tend to lead to individuals with high risk, while backward edges lead to individuals with high spread -- such that a combination of both forward and backward contact tracing is necessary to find superspreading events and prevent future cascades of infection.

physics.soc-ph↗

arXiv2021

The network epidemiology of an Ebola epidemic

Connecting the different scales of epidemic dynamics, from individuals to communities to nations, remains one of the main challenges of disease modeling. Here, we revisit one of the largest public health efforts deployed against a localized epidemic: the 2014-2016 Ebola Virus Disease (EVD) epidemic in Sierra Leone. We leverage the data collected by the surveillance and contact tracing protocols of the Sierra Leone Ministry of Health and Sanitation, the US Centers for Disease Control and Prevention, and other responding partners to validate a network epidemiology framework connecting the population (incidence), community (local forecasts), and individual (secondary infections) scales of disease transmission. In doing so, we gain a better understanding of what brought the EVD epidemic to an end: Reduction of introduction in new clusters (primary cases), and not reduction in local transmission patterns (secondary infections). We also find that the first 90 days of the epidemic contained enough information to produce probabilistic forecasts of EVD cases; forecasts which we show are confirmed independently by both disease surveillance and contact tracing. Altogether, using data available two months before the start of the international support to the local response, network epidemiology could have inferred heterogeneity in local transmissions, the risk for superspreading events, and probabilistic forecasts of eventual cases per community. We expect that our framework will help connect large data collection efforts with individual behavior, and help reduce uncertainty during health emergencies and emerging epidemics.

q-bio.PE↗

arXiv2021

Influential groups for seeding and sustaining nonlinear contagion in heterogeneous hypergraphs

Several biological and social contagion phenomena, such as superspreading events or social reinforcement, are the results of multi-body interactions, for which hypergraphs offer a natural mathematical description. In this paper, we develop a novel mathematical framework based on approximate master equations to study contagions on random hypergraphs with a heterogeneous structure, both in terms of group size (hyperedge cardinality) and of membership of nodes to groups (hyperdegree). The characterization of the inner dynamics of groups provides an accurate description of the contagion process, without losing the analytical tractability. Using a contagion model where multi-body interactions are mapped onto a nonlinear infection rate, our two main results show how large groups are influential, in the sense that they drive both the early spread of a contagion and its endemic state (i.e., its stationary state). First, we provide a detailed characterization of the phase transition, which can be continuous or discontinuous with a bistable regime, and derive analytical expressions for the critical and tricritical points. We find that large values of the third moment of the membership distribution suppress the emergence of a discontinuous phase transition. Furthermore, the combination of heterogeneous group sizes and nonlinear contagion facilitates the onset of a mesoscopic localization phase, where contagion is sustained only by the largest groups, thereby inhibiting bistability as well. Second, we formulate the problem of optimal seeding for hypergraph contagion, and we compare two strategies: tuning the allocation of seeds according to either individual node or group properties. We find that, when the contagion is sufficiently nonlinear, groups are more effective seeds of contagion than individual nodes.

physics.soc-ph↗

arXiv2021

Microbial narrow-escape is facilitated by wall interactions

Cells have evolved efficient strategies to probe their surroundings and navigate through complex environments. From metastatic spread in the body to swimming cells in porous materials, escape through narrow constrictions - a key component of any structured environment connecting isolated micro-domains - is one ubiquitous and crucial aspect of cell exploration. Here, using the model microalgae Chlamydomonas reinhardtii, we combine experiments and simulations to achieve a tractable realization of the classical Brownian narrow escape problem in the context of active confined matter. Our results differ from those expected for Brownian particles or leaking chaotic billiards and demonstrate that cell-wall interactions substantially modify escape rates and, under generic conditions, expedite spread dynamics.

physics.bio-ph↗

arXiv2021

Universal nonlinear infection kernel from heterogeneous exposure on higher-order networks

The colocation of individuals in different environments is an important prerequisite for exposure to infectious diseases on a social network. Standard epidemic models fail to capture the potential complexity of this scenario by (1) neglecting the higher-order structure of contacts which typically occur through environments like workplaces, restaurants, and households; and by (2) assuming a linear relationship between the exposure to infected contacts and the risk of infection. Here, we leverage a hypergraph model to embrace the heterogeneity of environments and the heterogeneity of individual participation in these environments. We find that combining heterogeneous exposure with the concept of minimal infective dose induces a universal nonlinear relationship between infected contacts and infection risk. Under nonlinear infection kernels, conventional epidemic wisdom breaks down with the emergence of discontinuous transitions, super-exponential spread, and hysteresis.

physics.soc-ph↗

arXiv2021

Deep learning of contagion dynamics on complex networks

Forecasting the evolution of contagion dynamics is still an open problem to which mechanistic models only offer a partial answer. To remain mathematically or computationally tractable, these models must rely on simplifying assumptions, thereby limiting the quantitative accuracy of their predictions and the complexity of the dynamics they can model. Here, we propose a complementary approach based on deep learning where the effective local mechanisms governing a dynamic on a network are learned from time series data. Our graph neural network architecture makes very few assumptions about the dynamics, and we demonstrate its accuracy using different contagion dynamics of increasing complexity. By allowing simulations on arbitrary network structures, our approach makes it possible to explore the properties of the learned dynamics beyond the training data. Finally, we illustrate the applicability of our approach using real data of the COVID-19 outbreak in Spain. Our results demonstrate how deep learning offers a new and complementary perspective to build effective models of contagion dynamics on networks.

physics.soc-ph↗

arXiv2021

Social confinement and mesoscopic localization of epidemics on networks

Recommendations around epidemics tend to focus on individual behaviors, with much less efforts attempting to guide event cancellations and other collective behaviors since most models lack the higher-order structure necessary to describe large gatherings. Through a higher-order description of contagions on networks, we model the impact of a blanket cancellation of events larger than a critical size and find that epidemics can suddenly collapse when interventions operate over groups of individuals rather than at the level of individuals. We relate this phenomenon to the onset of mesoscopic localization, where contagions concentrate around dominant groups.

physics.soc-ph↗