arXiv subjects

Thomas Peron

Publications and source records attributed to Thomas Peron.

17 recordsLinked to original sources

arXiv2026

SVD Incidence Centrality: A Unified Spectral Framework for Node and Edge Analysis in Directed Networks and Hypergraphs

Identifying influential nodes and edges in directed networks remains a fundamental challenge across domains from social influence to biological regulation. Most existing centrality measures face a critical limitation: they either discard directional information through symmetrization or produce sparse, implementation-dependent rankings that obscure structural importance. We introduce a unified spectral framework for centrality analysis in directed networks grounded in the Singular value decomposition of the incidence matrix. The proposed approach derives both vertex and edge centralities via the pseudoinverse of Hodge Laplacians, yielding dense and well-resolved rankings that overcome the sparsity limitations commonly observed in betweenness centrality for directed graphs. Unlike traditional measures that require graph symmetrization, our framework naturally preserves directional information, enabling principled hub/authority analysis while maintaining mathematical consistency through spectral graph theory. The method extends naturally to hypergraphs through the same mathematical foundation. Experimental validation on real-world networks demonstrates the framework's effectiveness across diverse domains where traditional centrality measures encounter limitations due to implementation dependencies and sparse outputs.

cs.SI↗

arXiv2025

Comprehensive indicators and fine granularity refine density scaling laws in rural-urban systems

Density scaling laws complement traditional population scaling laws by enabling the analysis of the full range of human settlements and revealing rural-to-urban transitions with breakpoints at consistent population densities. However, previous studies have been constrained by the granularity of rural and urban units, as well as limitations in the quantity and diversity of indicators. This study addresses these gaps by examining Middle Layer Super Output Areas (MSOAs) in England and Wales, incorporating an extensive set of 117 indicators for the year 2021, spanning age, ethnicity, educational attainment, religion, disability, economic activity, mortality, crime, property transactions, and road accidents. Results indicate that the relationship between indicator density and population density is best described by a segmented power-law model with a consistent breakpoint (33 +- 5 persons per hectare) for 92 of the 117 indicators. Additionally, increasing granularity reveals further rural-to-urban transitions not observed at coarser spatial resolutions. Our findings also highlight the influence of population characteristics on scaling exponents, where stratifying dementia and ischaemic heart disease by older age groups (aged 70 and above) significantly affects these exponents, illustrating a protective urban effect.

physics.soc-ph↗

arXiv2024

Predicting soccer matches with complex networks and machine learning

Soccer attracts the attention of many researchers and professionals in the sports industry. Therefore, the incorporation of science into the sport is constantly growing, with increasing investments in performance analysis and sports prediction industries. This study aims to (i) highlight the use of complex networks as an alternative tool for predicting soccer match outcomes, and (ii) show how the combination of structural analysis of passing networks with match statistical data can provide deeper insights into the game patterns and strategies used by teams. In order to do so, complex network metrics and match statistics were used to build machine learning models that predict the wins and losses of soccer teams in different leagues. The results showed that models based on passing networks were as effective as ``traditional'' models, which use general match statistics. Another finding was that by combining both approaches, more accurate models were obtained than when they were used separately, demonstrating that the fusion of such approaches can offer a deeper understanding of game patterns, allowing the comprehension of tactics employed by teams relationships between players, their positions, and interactions during matches. It is worth mentioning that both network metrics and match statistics were important and impactful for the mixed model. Furthermore, the use of networks with a lower granularity of temporal evolution (such as creating a network for each half of the match) performed better than a single network for the entire game.

cs.SI↗

arXiv2024

Effects of clustering heterogeneity on the spectral density of sparse networks

We derive exact equations for the spectral density of sparse networks with an arbitrary distribution of the number of single edges and triangles per node. These equations enable a systematic investigation of the effect of clustering on the spectral properties of the network adjacency matrix. In the case of heterogeneous networks, we demonstrate that the spectral density becomes more symmetric as the fluctuations in the triangle-degree sequence increase. This phenomenon is explained by the small clustering coefficient of networks with a large variance of the triangle-degree distribution. In the homogeneous case of regular clustered networks, we find that both perturbative and non-perturbative approximations fail to predict the spectral density in the high-connectivity limit. This suggests that traditional large-degree approximations may be ineffective in studying the spectral properties of networks with more complex motifs. Our theoretical results are fully confirmed by numerical diagonalizations of finite adjacency matrices.

cond-mat.dis-nn↗

arXiv2021

Mean-field theory of vector spin models on networks with arbitrary degree distributions

Understanding the relationship between the heterogeneous structure of complex networks and cooperative phenomena occurring on them remains a key problem in network science. Mean-field theories of spin models on networks constitute a fundamental tool to tackle this problem and a cornerstone of statistical physics, with an impressive number of applications in condensed matter, biology, and computer science. In this work we derive the mean-field equations for the equilibrium behavior of vector spin models on high-connectivity random networks with an arbitrary degree distribution and with randomly weighted links. We demonstrate that the high-connectivity limit of spin models on networks is not universal in that it depends on the full degree distribution. Such nonuniversal behavior is akin to a remarkable mechanism that leads to the breakdown of the central limit theorem when applied to the distribution of effective local fields. Traditional mean-field theories on fully-connected models, such as the Curie-Weiss, the Kuramoto, and the Sherrington-Kirkpatrick model, are only valid if the network degree distribution is highly concentrated around its mean degree. We obtain a series of results that highlight the importance of degree fluctuations to the phase diagram of mean-field spin models by focusing on the Kuramoto model of synchronization and on the Sherrington-Kirkpatrick model of spin-glasses. Numerical simulations corroborate our theoretical findings and provide compelling evidence that the present mean-field theory describes an intermediate regime of connectivity, in which the average degree $c$ scales as a power $c \propto N^{b}$ ($b < 1$) of the total number $N \gg 1$ of spins. Our findings put forward a novel class of spin models that incorporate the effects of degree fluctuations and, at the same time, are amenable to exact analytic solutions.

cond-mat.dis-nn↗

arXiv2021

Network processes on clique-networks with high average degree: the limited effect of higher-order structure

In this paper, we investigate the effect of local structures on network processes. We investigate a random graph model that incorporates local clique structures to deviate from the locally tree-like behavior of most standard random graph models. For the process of bond percolation, we derive analytical approximations for large outbreaks and the critical percolation value. Interestingly, these derivations show that when the average degree of a vertex is large, the influence of the deviations from the locally tree-like structure is small. Our simulations show that this insensitivity to local clique structures often already kicks in for networks with average degrees as low as 6. Furthermore, we show that the different behavior of bond percolation on clustered networks compared to tree-like networks that was found in previous works can be almost completely attributed to differences in degree sequences rather than differences in clustering structures. We finally show that these results also extend to completely different types of dynamics, by deriving similar conclusions and simulations for the Kuramoto model on the same types of clustered and non-clustered networks.

physics.soc-ph↗

arXiv2021

Statistical properties of mutualistic-competitive random networks

Mutualistic networks are used to study the structure and processes inherent to mutualistic relationships. In this paper, we introduce a random matrix ensemble (RME) representing the adjacency matrices of mutualistic networks composed by two vertex sets of sizes $n$ and $m-n$. Our RME depends on three parameters: the network size $n$, the size of the smaller set $m$, and the connectivity between the two sets $\alpha$, where $\alpha$ is the ratio of current adjacent pairs over the total number of possible adjacent pairs between the sets. We focus on the the spectral, eigenvector and topological properties of the RME by computing, respectively, the ratio of consecutive eigenvalue spacings $r$, the Shannon entropy of the eigenvectors $S$, and the Randi\'c index $R$. First, within a random matrix theory approach (i.e., a statistical approach), we identify a parameter $\xi\equiv\xi(n,m,\alpha)$ that scales the average normalized measures $\left< \overline{X} \right>$ (with $X$ representing $r$, $S$ and $R$). Specifically, we show that (i) $\xi\propto \alpha n$ with a weak dependence on $m$, and (ii) for $\xi<1/10$ most vertices in the mutualistic network are isolated, while for $\xi>10$ the network acquires the properties of a complete network, i.e., the transition from isolated vertices to a complete-like behavior occurs in the interval $1/10<\xi<10$. Then, we demonstrate that our statistical approach predicts reasonably well the properties of real-world mutualistic networks; that is, the universal curves $\left< \overline{X} \right>$ vs. $\xi$ show good correspondence with the properties of real-world networks.

cond-mat.dis-nn↗

arXiv2021

Interspecific competition shapes the structural stability of mutualistic networks

Mutualistic networks have attracted increasing attention in the ecological literature in the last decades as they play a key role in the maintenance of biodiversity. Here, we develop an analytical framework to study the structural stability of these networks including both mutualistic and competitive interactions. Analytical and numerical analyses show that the structure of the competitive network fundamentally alters the necessary conditions for species coexistence in communities. Using 50 real mutualistic networks, we show that when the relative importance of shared partners is incorporated via weighted competition, the feasibility area in the parameter space is highly correlated with May's stability criteria and can be predicted by a functional relationship between the number of species, the network connectance and the average interaction strength in the community. Our work reopens a decade-long debate about the complexity-stability relationship in ecological communities, and highlights the role of the relative structures of different interaction types.

physics.soc-ph↗

arXiv2021

Discordant synchronization patterns on directed networks of identical phase oscillators with attractive and repulsive couplings

We study the collective dynamics of identical phase oscillators on globally coupled networks whose interactions are asymmetric and mediated by positive and negative couplings. We split the set of oscillators into two interconnected subpopulations. In this setup, oscillators belonging to the same group interact via symmetric couplings while the interaction between subpopulations occurs in an asymmetric fashion. By employing the dimensional reduction scheme of the Ott-Antonsen (OA) theory, we verify the existence of traveling-wave and $\pi$-states, in addition to the classical fully synchronized and incoherent states. Bistability between all collective states is reported. Analytical results are generally in excellent agreement with simulations; for some parameters and initial conditions, however, we numerically detect chimera-like states which are not captured by the OA theory.

nlin.AO↗

arXiv2020

Spacing ratio characterization of the spectra of directed random networks

Previous literature on random matrix and network science has traditionally employed measures derived from nearest-neighbor level spacing distributions to characterize the eigenvalue statistics of random matrices. This approach, however, depends crucially on eigenvalue unfolding procedures, which in many situations represent a major hindrance due to constraints in the calculation, specially in the case of complex spectra. Here we study the spectra of directed networks using the recently introduced ratios between nearest- and next-to-nearest eigenvalue spacing, thus circumventing the shortcomings imposed by spectral unfolding. Specifically, we characterize the eigenvalue statistics of directed Erd\H{o}s-R\'enyi (ER) random networks by means of two adjacency matrix representations; namely (i) weighted non-Hermitian random matrices and (ii) a transformation on non-Hermitian adjacency matrices which produces weighted Hermitian matrices. For both representations, we find that the distribution of spacing ratios becomes universal for a fixed average degree, in accordance with undirected random networks. Furthermore, by calculating the average spacing ratio as a function of the average degree, we show that the spectral statistics of directed ER random networks undergoes a transition from Poisson to Ginibre statistics for model (i) and from Poisson to Gaussian Unitary Ensemble statistics for model (ii). Eigenvector delocalization effects of directed networks are also discussed.

cond-mat.dis-nn↗

arXiv2020

Comparison of different spike train synchrony measures regarding their robustness to erroneous data from bicuculline induced epileptiform activity

As synchronized activity is associated with basic brain functions and pathological states, spike train synchrony has become an important measure to analyze experimental neuronal data. Many different measures of spike train synchrony have been proposed, but there is no gold standard allowing for comparison of results between different experiments. This work aims to provide guidance on which synchrony measure is best suitable to quantify the effect of epileptiform inducing substances (e.g. bicuculline (BIC)) in in vitro neuronal spike train data. Spike train data from recordings are likely to suffer from erroneous spike detection, such as missed spikes (false negative) or noise (false positive). Therefore, different time-scale dependent (cross-correlation, mutual information, spike time tiling coefficient) and time-scale independent (Spike-contrast, phase synchronization, A-SPIKE-synchronization, A-ISI-distance, ARI-SPIKE-distance) synchrony measures were compared in terms of their robustness to erroneous spike trains. As a result of the in silico manipulated data, Spike-contrast was the only measure being robust to false negative as well as false-positive spikes. Analyzing the experimental data set revealed that all measures were able to capture the effect of BIC in a statistically significant way, with Spike-contrast showing the highest statistical significance even at low spike detection thresholds. In summary, we suggest the usage of Spike-contrast to complement established synchrony measures, as it is time scale independent and robust to erroneous spike trains.

q-bio.QM↗

arXiv2019

A machine learning approach to predicting dynamical observables from network structure

Estimating the outcome of a given dynamical process from structural features is a key unsolved challenge in network science. The goal is hindered by difficulties associated to nonlinearities, correlations and feedbacks between the structure and dynamics of complex systems. In this work, we develop an approach based on machine learning algorithms that is shown to provide an answer to the previous challenge. Specifically, we show that it is possible to estimate the outbreak size of a disease starting from a single node as well as the degree of synchronicity of a system made up of Kuramoto oscillators. In doing so, we show which topological features of the network are key for this estimation, and provide a rank of the importance of network metrics with higher accuracy than previously done. Our approach is general and can be applied to any dynamical process running on top of complex networks. Likewise, our work constitutes an important step towards the application of machine learning methods to unravel dynamical patterns emerging in complex networked systems.

physics.soc-ph↗

arXiv2019

Collective dynamics of random Janus oscillator networks

Janus oscillators have been recently introduced as a remarkably simple phase oscillator model that exhibits non-trivial dynamical patterns -- such as chimeras, explosive transitions, and asymmetry-induced synchronization -- that once were only observed in specifically tailored models. Here we study ensembles of Janus oscillators coupled on large homogeneous and heterogeneous networks. By virtue of the Ott-Antonsen reduction scheme, we find that the rich dynamics of Janus oscillators persists in the thermodynamic limit of random regular, Erd\H{o}s-R\'enyi and scale-free random networks. We uncover for all these networks the coexistence between partially synchronized state and a multitude of states displaying global oscillations. Furthermore, abrupt transitions of the global and local order parameters are observed for all topologies considered. Interestingly, only for scale-free networks, it is found that states displaying global oscillations vanish in the thermodynamic limit.

nlin.AO↗

arXiv2019

On the onset of synchronization of Kuramoto oscillators in scale-free networks

Despite the great attention devoted to the study of phase oscillators on complex networks in the last two decades, it remains unclear whether scale-free networks exhibit a nonzero critical coupling strength for the onset of synchronization in the thermodynamic limit. Here, we systematically compare predictions from the heterogeneous degree mean-field (HMF) and the quenched mean-field (QMF) approaches to extensive numerical simulations on large networks. We provide compelling evidence that the critical coupling vanishes as the number of oscillators increases for scale-free networks characterized by a power-law degree distribution with an exponent $2 < \gamma \leq 3$, in line with what has been observed for other dynamical processes in such networks. For $\gamma > 3$, we show that the critical coupling remains finite, in agreement with HMF calculations and highlight phenomenological differences between critical properties of phase oscillators and epidemic models on scale-free networks. Finally, we also discuss at length a key choice when studying synchronization phenomena in complex networks, namely, how to normalize the coupling between oscillators.

cond-mat.stat-mech↗

arXiv2018

Pattern Recognition Approach to Violin Shapes of MIMO database

Since the landmarks established by the Cremonese school in the 16th century, the history of violin design has been marked by experimentation. While great effort has been invested since the early 19th century by the scientific community on researching violin acoustics, substantially less attention has been given to the statistical characterization of how the violin shape evolved over time. In this paper we study the morphology of violins retrieved from the Musical Instrument Museums Online (MIMO) database -- the largest freely accessible platform providing information about instruments held in public museums. From the violin images, we derive a set of measurements that reflect relevant geometrical features of the instruments. The application of Principal Component Analysis (PCA) uncovered similarities between violin makers and their respective copyists, as well as among luthiers belonging to the same family lineage, in the context of historical narrative. Combined with a time-windowed approach, thin plate splines visualizations revealed that the average violin outline has remained mostly stable over time, not adhering to any particular trends of design across different periods in music history.

stat.AP↗

arXiv2017

Global teleconnectivity structures of the El Ni\~no-Southern Oscillation and large volcanic eruptions -- An evolving network perspective

Recent work has provided ample evidence that global climate dynamics at time-scales between multiple weeks and several years can be severely affected by the episodic occurrence of both, internal (climatic) and external (non-climatic) perturbations. Here, we aim to improve our understanding on how regional to local disruptions of the "normal" state of the global surface air temperature field affect the corresponding global teleconnectivity structure. Specifically, we present an approach to quantify teleconnectivity based on different characteristics of functional climate network analysis. Subsequently, we apply this framework to study the impacts of different phases of the El Ni\~no-Southern Oscillation (ENSO) as well as the three largest volcanic eruptions since the mid 20th century on the dominating spatiotemporal co-variability patterns of daily surface air temperatures. Our results confirm the existence of global effects of ENSO which result in episodic breakdowns of the hierarchical organization of the global temperature field. This is associated with the emergence of strong teleconnections. At more regional scales, similar effects are found after major volcanic eruptions. Taken together, the resulting time-dependent patterns of network connectivity allow a tracing of the spatial extents of the dominating effects of both types of climate disruptions. We discuss possible links between these observations and general aspects of atmospheric circulation.

physics.ao-ph↗

arXiv2016

Tweaking Synchronisation by Link Addition

Natural and man-made networks often possess locally tree-like sub-structures. Taking such tree networks as our starting point, we show how the addition of links changes the synchronization properties of the network. We focus on two different methods of link addition. The first method adds single links that create cycles of a well-defined length. Following a topological approach we introduce cycles of varying length and analyze how this feature, as well as the position in the network, alters the synchronous behaviour. We show that in particular short cycles can lead to a maximum change of the Laplacian's eigenvalue spectrum, dictating the synchronization properties of such networks. The second method connects a certain proportion of the initially unconnected nodes. We simulate dynamical systems on these network topologies, with the nodes' local dynamics being either a discrete or continuous. Here our main result is that a certain amount of additional links, with the relative position in the network being crucial, can be beneficial to ensure stable synchronization.

nlin.CD↗