arXiv subjects

Renaud Lambiotte

Publications and source records attributed to Renaud Lambiotte.

At least 37 records · Page 2Linked to original sources

arXiv2025

Nonequilibrium physics of brain dynamics

Information processing in the brain is coordinated by the dynamic activity of neurons and neural populations at a range of spatiotemporal scales. These dynamics, captured in the form of electrophysiological recordings and neuroimaging, show evidence of time-irreversibility and broken detailed balance suggesting that the brain operates in a nonequilibrium stationary state. Furthermore, the level of nonequilibrium, measured by entropy production or irreversibility appears to be a crucial signature of cognitive complexity and consciousness. The subsequent study of neural dynamics from the perspective of nonequilibrium statistical physics is an emergent field that challenges the assumptions of symmetry and maximum-entropy that are common in traditional models. In this review, we discuss the plethora of exciting results emerging at the interface of nonequilibrium dynamics and neuroscience. We begin with an introduction to the mathematical paradigms necessary to understand nonequilibrium dynamics in both continuous and discrete state-spaces. Next, we review both model-free and model-based approaches to analysing nonequilibrium dynamics in both continuous-state recordings and neural spike-trains, as well as the results of such analyses. We briefly consider the topic of nonequilibrium computation in neural systems, before concluding with a discussion and outlook on the field.

q-bio.NC↗

arXiv2025

From reductionism to realism: Holistic mathematical modelling for complex biological systems

At its core, the physics paradigm adopts a reductionist approach, aiming to understand fundamental phenomena by decomposing them into simpler, elementary processes. While this strategy has been tremendously successful in physics, it has often fallen short in addressing fundamental questions in the biological sciences. This arises from the inherent complexity of biological systems, characterised by heterogeneity, polyfunctionality and interactions across spatiotemporal scales. Nevertheless, the traditional framework of complex systems modelling falls short, as its emphasis on broad theoretical principles has often failed to produce predictive, empirically-grounded insights. To advance towards actionable mathematical models in biology, we argue, using neuroscience as a case study, that it is necessary to move beyond reductionist approaches and instead embrace the complexity of biological systems - leveraging the growing availability of high-resolution data and advances in high-performance computing. We advocate for a holistic mathematical modelling paradigm that harnesses rich representational structures such as annotated and multilayer networks, employs agent-based models and simulation-based approaches, and focuses on the inverse problem of inferring system dynamics from observations. We emphasise that this approach is fully compatible with the search for fundamental biophysical principles, and highlight the potential it holds to drive progress in mathematical biology over the next two decades.

physics.bio-ph↗

arXiv2025

Gremban Expansion for Signed Networks: Algebraic and Combinatorial Foundations for Community-Faction Detection

This article deals with the characterization and detection of community and faction structures in signed networks. We approach the study of these mesoscale structures through the lens of the Gremban expansion. This graph operation lifts a signed graph to a larger unsigned graph, and allows the extension of standard techniques from unsigned to signed graphs. We develop the combinatorial and algebraic properties of the Gremban expansion, with a focus on its inherent involutive symmetry. The main technical result is a bijective correspondence between symmetry-respecting cut-sets in the Gremban expansion, and regular cut-sets and frustration sets in the signed graph (i.e., the combinatorial structures that underlie communities and factions respectively). This result forms the basis for our new approach to community-faction detection in signed networks, which makes use of spectral clustering techniques that naturally respect the required symmetries. We demonstrate how this approach distinguishes the two mesoscale structures, how to generalize the approach to multi-way clustering and discuss connections to network dynamical systems.

cs.DM↗

arXiv2025

Dynamic models of gentrification

The phenomenon of gentrification of an urban area is characterized by the displacement of lower-income residents due to rising living costs and an influx of wealthier individuals. This study presents an agent-based model that simulates urban gentrification through the relocation of three income groups -- low, middle, and high -- driven by living costs. The model incorporates economic and sociological theories to generate realistic neighborhood transition patterns. We introduce a temporal network-based measure to track the outflow of low-income residents and the inflow of middle- and high-income residents over time. Our experiments reveal that high-income residents trigger gentrification and that our network-based measure consistently detects gentrification patterns earlier than traditional count-based methods, potentially serving as an early detection tool in real-world scenarios. Moreover, the analysis also highlights how city density promotes gentrification. This framework offers valuable insights for understanding gentrification dynamics and informing urban planning and policy decisions.

physics.soc-ph↗

arXiv2025

Entropy-based models to randomize real-world hypergraphs

Network theory has often disregarded many-body relationships, solely focusing on pairwise interactions: neglecting them, however, can lead to misleading representations of complex systems. Hypergraphs represent a suitable framework for describing polyadic interactions. Here, we leverage the representation of hypergraphs based on the incidence matrix for extending the entropy-based approach to higher-order structures: in analogy with the Exponential Random Graphs, we introduce the Exponential Random Hypergraphs (ERHs). After exploring the asymptotic behaviour of thresholds generalising the percolation one, we apply ERHs to study real-world data. First, we generalise key network metrics to hypergraphs; then, we compute their expected value and compare it with the empirical one, in order to detect deviations from random behaviours. Our method is analytically tractable, scalable and capable of revealing structural patterns of real-world hypergraphs that differ significantly from those emerging as a consequence of simpler constraints.

cs.SI↗

arXiv2025

Exploring the Non-uniqueness of Node Co-occurrence Matrices of Hypergraphs

Hypergraphs extend traditional networks by capturing multi-way or group interactions. Given the complexity of hypergraph data and the wide range of methodology available for pairwise network analysis, hypergraph data is often projected onto a weighted and undirected network. The simplest of these projections, often referred to as a node co-occurrence matrix, is known to be non-unique, as distinct non-isomorphic hypergraphs can produce the same weighted adjacency matrix. This non-uniqueness raises important questions about the structural information lost during the projection and how to efficiently quantify the complexity of the original hypergraph. Here we develop a search algorithm to identify all hypergraphs corresponding to a given projection, analyze its runtime, and explore its parallelisability. Applying this algorithm to projections derived from a random hypergraph model, we characterize conditions under which projections are non-unique. Our findings provide a new framework and set of computational tools to investigate projections of hypergraphs.

cs.SI↗

arXiv2025

Modeling Urban Air Quality Using Taxis as Sensors

Monitoring urban air quality with high spatiotemporal resolution continues to pose significant challenges. We investigate the use of taxi fleets as mobile sensing platforms, analyzing over 100 million PM2.5 readings from more than 3,000 vehicles across six major U.S. cities during one year. Our findings show that taxis provide fine-grained, street-level air quality insights while ensuring city-wide coverage. We further explore urban air quality modeling using traffic congestion, built environment, and human mobility data to predict pollution variability. Our results highlight geography-specific seasonal patterns and demonstrate that models based solely on traffic and wind speeds effectively capture a city's pollution dynamics. This study establishes taxi fleets as a scalable, near-real-time air quality monitoring tool, offering new opportunities for environmental research and data-driven policymaking.

physics.soc-ph↗

arXiv2025

RankMerging: A supervised learning-to-rank framework to predict links in large social network

Uncovering unknown or missing links in social networks is a difficult task because of their sparsity and because links may represent different types of relationships, characterized by different structural patterns. In this paper, we define a simple yet efficient supervised learning-to-rank framework, called RankMerging, which aims at combining information provided by various unsupervised rankings. We illustrate our method on three different kinds of social networks and show that it substantially improves the performances of unsupervised metrics of ranking. We also compare it to other combination strategies based on standard methods. Finally, we explore various aspects of RankMerging, such as feature selection and parameter estimation and discuss its area of relevance: the prediction of an adjustable number of links on large networks.

cs.SI↗

arXiv2025

Unveiling the Importance of Nonshortest Paths in Quantum Networks

Quantum networks (QNs) exhibit stronger connectivity than predicted by classical percolation, yet the origin of this phenomenon remains unexplored. We apply a statistical physics model -- concurrence percolation -- to uncover the origin of stronger connectivity on hierarchical scale-free networks, the ($U,V$) flowers. These networks allow full analytical control over path connectivity through two adjustable path-length parameters, $U \leq V$. This precise control enables us to determine critical exponents well beyond current simulation limits, revealing that classical and concurrence percolations, while both satisfying the hyperscaling relation, fall into distinct universality classes. This distinction arises from how they "superpose" parallel, non-shortest path contributions into overall connectivity. Concurrence percolation, unlike its classical counterpart, is sensitive to non-shortest paths and shows higher resilience to detours as these paths lengthen. This enhanced resilience is also observed in real-world hierarchical, scale-free Internet networks. Our findings highlight a crucial principle for QN design: when non-shortest paths are abundant, they notably enhance QN connectivity beyond what is achievable with classical percolation.

quant-ph↗

arXiv2025

Coarse-graining Directed Networks with Ergodic Sets Preserving Diffusive Dynamics

In this paper, we introduce ergodic sets, subsets of nodes of the networks that are dynamically disjoint from the rest of the network (i.e. that can never be reached or left following to the network dynamics). We connect their definition to purely structural considerations of the network and study some of their basic properties. We study numerically the presence of such structures in a number of synthetic network models and in classes of networks from a variety of real-world applications, and we use them to present a compression algorithm that preserve the random walk diffusive dynamics of the original network.

cs.SI↗

arXiv2025

Concise network models of memory dynamics reveal explainable patterns in path data

Networks are a powerful tool to model the structure and dynamics of complex systems across scales. Direct connections between system components are often represented as edges, while paths and walks capture indirect interactions. This approach assumes that flows in the system are sequences of independent transitions. Path data from real-world systems often have higher-order dependencies, which require more sophisticated models. In this work, we propose a method to construct concise networks from path data that interpolate between first and second-order models. We prioritise simplicity and interpretability by creating state nodes that capture latent modes of second-order effects and introducing an interpretable measure to balance model size and accuracy. In both synthetic and real-world applications, our method reveals large-scale memory patterns and constructs concise networks that provide insights beyond the first-order model at the fraction of the size of a second-order model.

physics.soc-ph↗

arXiv2025

Garbage in Garbage out: Impacts of data quality on criminal network intervention

Criminal networks such as human trafficking rings are threats to the rule of law, democracy and public safety in our global society. Network science provides invaluable tools to identify key players and design interventions for Law Enforcement Agencies (LEAs), e.g., to dismantle their organisation. However, poor data quality and the adaptiveness of criminal networks through self-organization make effective disruption extremely challenging. Although there exists a large body of work building and applying network scientific tools to attack criminal networks, these work often implicitly assume that the network measurements are accurate and complete. Moreover, there is thus far no comprehensive understanding of the impacts of data quality on the downstream effectiveness of interventions. This work investigates the relationship between data quality and intervention effectiveness based on classical graph theoretic and machine learning-based approaches. Decentralization emerges as a major factor in network robustness, particularly under conditions of incomplete data, which renders attack strategies largely ineffective. Moreover, the robustness of centralized networks can be boosted using simple heuristics, making targeted attack more infeasible. Consequently, we advocate for a more cautious application of network science in disrupting criminal networks, the continuous development of an interoperable intelligence ecosystem, and the creation of novel network inference techniques to address data quality challenges.

physics.soc-ph↗

arXiv2024

Broken detailed balance and entropy production in directed networks

The structure of a complex network plays a crucial role in determining its dynamical properties. In this work, we show that the the degree to which a network is directed and hierarchically organised is closely associated with the degree to which its dynamics break detailed balance and produce entropy. We consider a range of dynamical processes and show how different directed network features affect their entropy production rate. We begin with an analytical treatment of a 2-node network followed by numerical simulations of synthetic networks using the preferential attachment and Erdös-Renyi algorithms. Next, we analyse a collection of 97 empirical networks to determine the effect of complex real-world topologies. Finally, we present a simple method for inferring broken detailed balance and directed network structure from multivariate time-series and apply our method to identify non-equilibrium dynamics and hierarchical organisation in both human neuroimaging and financial time-series. Overall, our results shed light on the consequences of directed network structure on non-equilibrium dynamics and highlight the importance and ubiquity of hierarchical organisation and non-equilibrium dynamics in real-world systems.

physics.soc-ph↗

arXiv2024

Network shell structure based on hub and non-hub nodes

The shell structure holds significant importance in various domains such as information dissemination, supply chain management, and transportation. This study focuses on investigating the shell structure of hub and non-hub nodes, which play important roles in these domains. Our framework explores the topology of Erdös-Rényi (ER) and Scale-Free (SF) networks, considering source node selection strategies dependent on the nodes' degrees. We define the shell $l$ in a network as the set of nodes at a distance $l$ from a given node and represent $r_l$ as the fraction of nodes outside shell $l$. Statistical properties of the shells are examined for a selected node, taking into account the node's degree. For a network with a given degree distribution, we analytically derive the degree distribution and average degree of nodes outside shell $l$ as functions of $r_l$. Moreover, we discover that $r_l$ follows an iterative functional form $r_l = ϕ(r_{l-1})$, where $ϕ$ is expressed in terms of the generating function of the original degree distribution of the network.

physics.soc-ph↗

arXiv2024

Modularity, Hierarchical Flows and Symmetry of the Drosophila Connectome

This report investigates the modular organisation of the Central region in the Drosophila connectome. We identify groups of neurones amongst which information circulates rapidly before spreading to the rest of the network using Infomap. We find that information flows along pathways linking distant neurones, forming modules that span across the brain. Remarkably, these modules, derived solely from neuronal connectivity patterns, exhibit a striking left-right symmetry in their spatial distribution as well as in their connections. We also identify a hierarchical structure at the coarse-grained scale of these modules, demonstrating the directional nature of information flow in the system.

q-bio.NC↗

arXiv2024

Decomposing force fields as flows on graphs reconstructed from stochastic trajectories

Disentangling irreversible and reversible forces from random fluctuations is a challenging problem in the analysis of stochastic trajectories measured from real-world dynamical systems. We present an approach to approximate the dynamics of a stationary Langevin process as a discrete-state Markov process evolving over a graph-representation of phase-space, reconstructed from stochastic trajectories. Next, we utilise the analogy of the Helmholtz-Hodge decomposition of an edge-flow on a contractible simplicial complex with the associated decomposition of a stochastic process into its irreversible and reversible parts. This allows us to decompose our reconstructed flow and to differentiate between the irreversible currents and reversible gradient flows underlying the stochastic trajectories. We validate our approach on a range of solvable and nonlinear systems and apply it to derive insight into the dynamics of flickering red-blood cells and healthy and arrhythmic heartbeats. In particular, we capture the difference in irreversible circulating currents between healthy and passive cells and healthy and arrhythmic heartbeats. Our method breaks new ground at the interface of data-driven approaches to stochastic dynamics and graph signal processing, with the potential for further applications in the analysis of biological experiments and physiological recordings. Finally, it prompts future analysis of the convergence of the Helmholtz-Hodge decomposition in discrete and continuous spaces.

cond-mat.stat-mech↗

arXiv2024

Community detection on directed networks with missing edges

Identifying significant community structures in networks with incomplete data is a challenging task, as the reliability of solutions diminishes with increasing levels of missing information. However, in many empirical contexts, some information about the uncertainty in the network measurements can be estimated. In this work, we extend the recently developed Flow Stability framework, originally designed for detecting communities in time-varying networks, to address the problem of community detection in weighted, directed networks with missing links. Our approach leverages known uncertainty levels in nodes' out-degrees to enhance the robustness of community detection. Through comparisons on synthetic networks and a real-world network of messaging channels on the Telegram platform, we demonstrate that our method delivers more reliable community structures, even when a significant portion of data is missing.

cs.SI↗

arXiv2024

Matrix-weighted networks for modeling multidimensional dynamics

Networks are powerful tools for modeling interactions in complex systems. While traditional networks use scalar edge weights, many real-world systems involve multidimensional interactions. For example, in social networks, individuals often have multiple interconnected opinions that can affect different opinions of other individuals, which can be better characterized by matrices. We propose a novel, general framework for modeling such multidimensional interacting dynamics: matrix-weighted networks (MWNs). We present the mathematical foundations of MWNs and examine consensus dynamics and random walks within this context. Our results reveal that the coherence of MWNs gives rise to non-trivial steady states that generalize the notions of communities and structural balance in traditional networks.

cs.SI↗