arXiv subjects

Albert Díaz-Guilera

Publications and source records attributed to Albert Díaz-Guilera.

At least 19 recordsLinked to original sources

arXiv2026

Equilibrium and dynamics of a three-state opinion model on a network of networks

Opinion formation models typically represent each individual as a single variable. However, in practice each individual holds interconnected beliefs whose internal organization may influence collective outcomes. To explore this dependence, we study a three-state opinion model on a network of networks in which each agent has an internal belief graph and interacts with other agents through an external social graph. Each belief can take two opposite polarized states or a neutral one and a neutrality parameter tunes the relative conviction of the neutral stance. We incorporate temperature into the model to account for external social agitation and for the tolerance of internal cognitive dissonance. We explore the stationary state and dynamics of the model using analytical approaches and Monte Carlo simulations on a fully connected external social graph, with internal belief topologies given by one-dimensional chains, cliques, and star-like structures, where there is a central core belief to which all other beliefs are connected. We find that the critical temperature at which the polarized consensus destabilizes increases with the addition of more beliefs to star-like agents but saturates in the case of ring- and clique-like internal topologies. We also consider binary mixtures of agents with different internal topologies in equal proportions, showing that the interplay between agents is regime-dependent, with the dominant topology depending on the value of the neutrality parameter.

physics.soc-ph↗

arXiv2026

Multilayer network science: theory, methods, and applications

Multilayer network science has emerged as a central framework for analysing interconnected and interdependent complex systems. Its relevance has grown substantially with the increasing availability of rich, heterogeneous data, which makes it possible to uncover and exploit the inherently multilayered organisation of many real-world networks. In this review, we summarise recent developments in the field. On the theoretical and methodological front, we outline core concepts and survey advances in community detection, dynamical processes, temporal networks, higher-order interactions, and machine-learning-based approaches. On the application side, we discuss progress across diverse domains, including interdependent infrastructures, spreading dynamics, computational social science, economic and financial systems, ecological and climate networks, science-of-science studies, network medicine, and network neuroscience. We conclude with a forward-looking perspective, emphasizing the need for standardised datasets and software, deeper integration of temporal and higher-order structures, and a transition toward genuinely predictive models of complex systems.

physics.soc-ph↗

arXiv2024

Exploring the Interplay of Excitatory and Inhibitory Interactions in the Kuramoto Model on Circle Topologies

In the field of collective dynamics, the Kuramoto model serves as a benchmark for the investigation of synchronization phenomena. While mean-field approaches and complex networks have been widely studied, the simple topology of a circle is still relatively unexplored, especially in the context of excitatory and inhibitory interactions. In this work, we focus on the dynamics of the Kuramoto model on a circle with positive and negative connections paying attention to the existence of new attractors different from the synchronized state. Using analytical and computational methods, we find that even for identical oscillators, the introduction of inhibitory interactions significantly modifies the structure of the attractors of the system. Our results extend the current understanding of synchronization in simple topologies and open new avenues for the study of collective dynamics in physical systems.

nlin.AO↗

arXiv2022

Equilibrium and dynamics of a three-state opinion model

We introduce a three-state model to study the effects of a neutral party on opinion spreading, in which the tendency of agents to agree with their neighbors can be tuned to favor either the neutral party or two oppositely polarized parties, and can be disrupted by social agitation mimicked as temperature. We study the equilibrium phase diagram and the non-equilibrium stochastic dynamics of the model with various analytical approaches and with Monte Carlo simulations on different substrates: the fully-connected (FC) graph, the one-dimensional (1D) chain, and Erdös-Rényi (ER) random graphs. We show that, in the mean-field approximation, the phase boundary between the disordered and polarized phases is characterized by a tricritical point. On the FC graph, in the absence of social agitation, kinetic barriers prevent the system from reaching optimal consensus. On the 1D chain, the main result is that the dynamics is governed by the growth of opinion clusters. Finally, for the ER ensemble a phase transition analogous to that of the FC graph takes place, but now the system is able to reach optimal consensus at low temperatures, except when the average connectivity is low, in which case dynamical traps arise from local frozen configurations.

cond-mat.stat-mech↗

arXiv2021

Characterizing Twitter users behaviour during the Spanish Covid-19 first wave

People use Online Social Media to make sense of crisis events. A pandemic crisis like the Covid-19 outbreak is a complex event, involving numerous aspects of the social life on multiple temporal scales. Focusing on the Spanish Twittersphere, we characterized users activity behaviour across the different phases of the Covid-19 first wave. Firstly, we analyzed a sample of timelines of different classes of users from the Spanish Twittersphere in terms of their propensity to produce new information or to amplify information produced by others. Secondly, by performing stepwise segmented regression analysis and Bayesian switchpoint analysis, we looked for a possible behavioral footprint of the crisis in the statistics of users' activity. We observed that generic Spanish Twitter users and journalists experienced an abrupt increment of their tweeting activity between March 9 and March 14, in coincidence with control measures being announced by regional and State level authorities. However, they displayed a stable proportion of retweets before and after the switching point. On the contrary, politicians represented an exception, being the only class of users not experimenting this abrupt change and following a completely endogenous dynamics determined by institutional agenda. On the one hand, they did not increment their overall activity, displaying instead a slight decrease. On the other hand, in times of crisis, politicians tended to strengthen their propensity to amplify information rather than produce it.

cs.SI↗

arXiv2021

Quasi-symmetries in complex networks: a dynamical model approach

The existence of symmetries in complex networks has a significant effect on network dynamic behaviour. Nevertheless, beyond topological symmetry, one should consider the fact that real-world networks are exposed to fluctuations or errors, as well as mistaken insertions or removals. Therefore, the resulting approximate symmetries remain hidden to standard symmetry analysis - fully accomplished by discrete algebra software. There have been a number of attempts to deal with approximate symmetries. In the present work we provide an alternative notion of these weaker symmetries, which we call `quasi-symmetries'. Differently from other definitions, quasi-symmetries remain free to impose any invariance of a particular network property and they are obtained from the phase differences at the steady-state configuration of an oscillatory dynamical model: the Kuramoto-Sakaguchi model. The analysis of quasi-symmetries unveils otherwise hidden real-world networks attributes. On the one hand, we provide a benchmark to determine whether a network has a more complex pattern than that of a random network with regard to quasi-symmetries, namely, if it is structured into separate quasi-symmetric groups of nodes. On the other hand, we define the `dual-network', a weighted network (and its corresponding binnarized counterpart) that effectively encodes all the information of quasi-symmetries in the original network. The latter is a powerful instrument for obtaining worthwhile insights about node centrality (obtaining the nodes that are unique from that act as imitators with respect to the others) and community detection ( quasi-symmetric groups of nodes).

physics.soc-ph↗

arXiv2021

Optimal cost tuning of frustration: Achieving desired states in the Kuramoto-Sakaguchi model

There are numerous examples of studied real-world systems that can be described as dynamical systems characterized by individual phases and coupled in a network like structure. Within the framework of oscillatory models, much attention has been devoted to the Kuramoto model, which considers a collection of oscillators interacting through a sinus function of the phase differences. In this paper, we draw on an extension of the Kuramoto model, called the Kuramoto-Sakaguchi model, which adds a phase lag parameter to each node. We construct a general formalism that allows to compute the set of lag parameters that may lead to any phase configuration within a linear approximation. In particular, we devote special attention to the cases of full synchronization and symmetric configurations. We show that the set of natural frequencies, phase lag parameters and phases at the steady state is coupled by an equation and a continuous spectra of solutions is feasible. In order to quantify the system's strain to achieve that particular configuration, we define a cost function and compute the optimal set of parameters that minimizes it. Despite considering a linear approximation of the model, we show that the obtained tuned parameters for the case of full synchronization enhance frequency synchronization in the nonlinear model as well.

physics.soc-ph↗

arXiv2020

Modeling partial lockdowns in multiplex networks using partition strategies

National stay-at-home orders, or lockdowns, were imposed in several countries to drastically reduce the social interactions mainly responsible for the transmission of the SARS-CoV-2 virus. Despite being essential to slow down the COVID-19 pandemic, these containment measures are associated with an economic burden. In this work, we propose a network approach to model the implementation of a partial lockdown, breaking the society into disconnected components, or partitions. Our model is composed by two main ingredients: a multiplex network representing human contacts within different contexts, formed by a Household layer, a Work layer, and a third Social layer including generic social interactions, and a Susceptible-Infected-Recovered process that mimics the epidemic spreading. We compare different partition strategies, with a twofold aim: reducing the epidemic outbreak and minimizing the economic cost associated to the partial lockdown. We also show that the inclusion of unconstrained social interactions dramatically increases the epidemic spreading, while different kinds of restrictions on social interactions help in keeping the benefices of the network partition.

physics.soc-ph↗

arXiv2018

The Dynamics of Norm Change in the Cultural Evolution of Language

What happens when a new social convention replaces an old one? While the possible forces favoring norm change - such as institutions or committed activists - have been identified since a long time, little is known about how a population adopts a new convention, due to the difficulties of finding representative data. Here we address this issue by looking at changes occurred to 2,541 orthographic and lexical norms in English and Spanish through the analysis of a large corpora of books published between the years 1800 and 2008. We detect three markedly distinct patterns in the data, depending on whether the behavioral change results from the action of a formal institution, an informal authority or a spontaneous process of unregulated evolution. We propose a simple evolutionary model able to capture all the observed behaviors and we show that it reproduces quantitatively the empirical data. This work identifies general mechanisms of norm change and we anticipate that it will be of interest to researchers investigating the cultural evolution of language and, more broadly, human collective behavior.

physics.soc-ph↗

arXiv2018

A complex network framework to model cognition: unveiling correlation structures from connectivity

Several approaches to cognition and intelligence research rely on statistics-based models testing, namely factor analysis. In the present work we exploit the emerging dynamical systems perspective putting the focus on the role of the network topology underlying the relationships between cognitive processes. We go through a couple of models of distinct cognitive phenomena and yet find the conditions for them to be mathematically equivalent. We find a non-trivial attractor of the system that corresponds to the exact definition of a well-known network centrality and hence stress the interplay between the dynamics and the underlying network connectivity, showing that both of the two are relevant. The connectivity structure between cognitive processes is not known but yet it is not any. Regardless of the network considered, it is always possible to recover a positive manifold of correlations. However, we show that different network topologies lead to different plausible statistical models concerning correlations structure, ranging from one to multiple factors models and richer correlation structures.

physics.soc-ph↗

arXiv2018

Collective motion of Active Brownian Particles with polar alignment

We present a comprehensive computational study of the collective behavior emerging from the competition between self-propulsion, excluded volume interactions and velocity-alignment in a two-dimensionnal model of active particles. We consider an extension of the Active Brownian Particles model where the self-propulsion direction of the particles aligns with the one of their neighbors. We analyze the onset of collective motion (flocking) in a low-density regime (10% surface area) and show that it is mainly controlled by the strength of velocity-alignment interactions: the competition between self-propulsion and crowding effects plays a minor role in the emergence of flocking. However, above the flocking threshold, the system presents a richer pattern formation scenario than analogous models without alignment interactions (Active Brownian Particles) or excluded volume effects (Vicsek-like models). Depending on the parameter regime, the structure of the system is characterized by either a broad distribution of finite-sized polar clusters or the presence of an amorphous, highly fluctuating, large-scale traveling structure which can take a lane-like or band-like form (and usually a hybrid structure which is halfway in between both). We establish a phase diagram that summarizes collective behavior of polar Active Brownian Particles and propose a generic mechanism to describe the complexity of the large-scale structures observed in systems of repulsive self-propelled particles.

cond-mat.soft↗

arXiv2017

Interplay between social influence and competitive strategical games in multiplex networks

We present a model that takes into account the coupling between evolutionary game dynamics and social influence. Importantly, social influence and game dynamics take place in different domains, which we model as different layers of a multiplex network. We show that the coupling between these dynamical processes can lead to cooperation in scenarios where the pure game dynamics predicts defection. In addition, we show that the structure of the network layers and the relation between them can further increase cooperation. Remarkably, if the layers are related in a certain way, the system can reach a polarized metastable state.These findings could explain the prevalence of polarization observed in many social dilemmas.

physics.soc-ph↗

arXiv2016

Noise-Induced Polarization Switch in Single and Multiplex Complex Networks

The combination of bistability and noise is ubiquitous in complex systems, from biological to social interactions, and has important implications for their functioning and resilience. We analyze a simple three-state model for bistability in networks under varying unbiased noise. In a fully connected network increasing noise yields a collapse of bistability to an unpolarised state. In contrast, in complex networks noise can abruptly switch the polarization state in an irreversible way. When two networks are combined through increasing multiplex coupling, one is dominant and progressively imposes its state on the other, offsetting or promoting the ability of noise to switch polarization. Our results show that dynamical correlations and asymmetry in dynamical processes in networks are sufficient for allowing unbiased noise to produce abrupt irreversible transitions between extremes, which can be neutralized or enhanced by multiplex coupling.

nlin.AO↗

arXiv2015

Chimera-like states in modular neural networks

Chimera states, namely the coexistence of coherent and incoherent behavior, were previously analyzed in complex networks. However, they have not been extensively studied in modular networks. Here, we consider the neural network of the \textit{C.elegans} soil worm, organized into six interconnected communities, where neurons obey chaotic bursting dynamics. Neurons are assumed to be connected with electrical synapses within their communities and with chemical synapses across them. As our numerical simulations reveal, the coaction of these two types of coupling can shape the dynamics in such a way that chimera-like states can happen. They consist of a fraction of synchronized neurons which belong to the larger communities, and a fraction of desynchronized neurons which are part of smaller communities. In addition to the Kuramoto order parameter $ρ$, we also employ other measures of coherence, such as the chimera-like $χ$ and metastability $λ$ indices, which quantify the degree of synchronization among communities and along time, respectively. We perform the same analysis for networks that share common features with the \textit{C.elegans} neural network. Similar results suggest that under certain assumptions, chimera-like states are prominent phenomena in modular networks, and might provide insight for the behavior of more complex modular networks.

nlin.AO↗

arXiv2015

The role of adjacency matrix degeneration in maximum entropy weighted network models

Complex network null models based on entropy maximization are becoming a powerful tool to characterize and analyze data from real systems. However, it is not easy to extract good and unbiased information from these models: A proper understanding of the nature of the underlying events represented in them is crucial. In this paper we emphasize this fact stressing how an accurate counting of configurations compatible with given constraints is fundamental to build good null models for the case of networks with integer valued adjacency matrices constructed from aggregation of one or multiple layers. We show how different assumptions about the elements from which the networks are built give rise to distinctively different statistics, even when considering the same observables to match those of real data. We illustrate our findings by applying the formalism to three datasets using an open-source software package accompanying the present work and demonstrate how such differences are clearly seen when measuring network observables.

physics.soc-ph↗

arXiv2014

Pattern formation in multiplex networks

The advances in understanding complex networks have generated increasing interest in dynamical processes occurring on them. Pattern formation in activator-inhibitor systems has been studied in networks, revealing differences from the classical continuous media. Here we study pattern formation in a new framework, namely multiplex networks. These are systems where activator and inhibitor species occupy separate nodes in different layers. Species react across layers but diffuse only within their own layer of distinct network topology. This multiplicity generates heterogeneous patterns with significant differences from those observed in single-layer networks. Remarkably, diffusion-induced instability can occur even if the two species have the same mobility rates; condition which can never destabilize single-layer networks. The instability condition is revealed using perturbation theory and expressed by a combination of degrees in the different layers. Our theory demonstrates that the existence of such topology-driven instabilities is generic in multiplex networks, providing a new mechanism of pattern formation.

nlin.AO↗

arXiv2014

The configuration multi-edge model: Assessing the effect of fixing node strengths on weighted network magnitudes

Complex networks grow subject to structural constraints which affect their measurable properties. Assessing the effect that such constraints impose on their observables is thus a crucial aspect to be taken into account in their analysis. To this end,we examine the effect of fixing the strength sequence in multi-edge networks on several network observables such as degrees, disparity, average neighbor properties and weight distribution using an ensemble approach. We provide a general method to calculate any desired weighted network metric and we show that several features detected in real data could be explained solely by structural constraints. We thus justify the need of analytical null models to be used as basis to assess the relevance of features found in real data represented in weighted network form.

physics.soc-ph↗

arXiv2013

Remote synchronization reveals network symmetries and functional modules

We study a Kuramoto model in which the oscillators are associated with the nodes of a complex network and the interactions include a phase frustration, thus preventing full synchronization. The system organizes into a regime of remote synchronization where pairs of nodes with the same network symmetry are fully synchronized, despite their distance on the graph. We provide analytical arguments to explain this result and we show how the frustration parameter affects the distribution of phases. An application to brain networks suggests that anatomical symmetry plays a role in neural synchronization by determining correlated functional modules across distant locations.

nlin.AO↗