arXiv subjects

Romualdo Pastor-Satorras

Publications and source records attributed to Romualdo Pastor-Satorras.

At least 37 records · Page 2Linked to original sources

arXiv2022

The advantage of self-protecting interventions in mitigating epidemic circulation at the community level

Protecting interventions of many types (both pharmaceutical and non-pharmaceutical) can be deployed against the spreading of a communicable disease, as the worldwide COVID-19 pandemic has dramatically shown. Here we investigate in detail the effects at the population level of interventions that provide an asymmetric protection between the people involved in a single interaction. Masks of different filtration types, either protecting mainly the wearer or the contacts of the wearer, are a prominent example of these interventions. By means of analytical calculations and extensive simulations of simple epidemic models on networks, we show that interventions protecting more efficiently the adopter (e.g the mask wearer) are more effective than interventions protecting primarily the contacts of the adopter in reducing the prevalence of the disease and the number of concurrently infected individuals ("flattening the curve"). This observation is backed up by the study of a more realistic epidemic model on an empirical network representing the patterns of contacts in the city of Portland. Our results point out that promoting wearer-protecting face masks and other self-protecting interventions, though deemed selfish and inefficient, can actually be a better strategy to efficiently curtail pandemic spreading.

physics.soc-ph↗

arXiv2022

Flocking dynamics mediated by weighted social networks

We study the effects of animal social networks with a weighted pattern of interactions on the flocking transition exhibited by models of self-organized collective motion. Considering a model representing dynamics on a one-dimensional substrate, application of a heterogeneous mean-field theory provides a phase diagram as function of the heterogeneity of the network connections and the correlations between weights and degree. In this diagram we observe two phases, one corresponding to the presence of a transition and other to a transition suppressed in an always ordered system, already observed in the non-weighted case. Interestingly, a third phase, with no transition in an always disordered state, is also obtained. These predictions, numerically recovered in computer simulations, are also fulfilled for the more realistic Vicsek model, with movement in a two-dimensional space. Additionally, we observe at finite network sizes the presence of a maximum threshold for particular weight configurations, indicating that it is possible to tune weights to achieve a maximum resilience to noise effects. Simulations in real weighted animal social networks show that, in general, the presence of weights diminishes the value of the flocking threshold, thus increasing the fragility of the flocking state. The shift in the threshold is observed to depend on the heterogeneity of the weight pattern.

physics.soc-ph↗

arXiv2021

Influence of individual nodes for continuous-time Susceptible-Infected-Susceptible dynamics on synthetic and real-world networks

In the study of epidemic dynamics a fundamental question is whether a pathogen initially affecting only one individual will give rise to a limited outbreak or to a widespread pandemic. The answer to this question crucially depends not only on the parameters describing the infection and recovery processes but also on where, in the network of interactions, the infection starts from. We study the dependence on the location of the initial seed for the Susceptible-Infected-Susceptible epidemic dynamics in continuous time on networks. We first derive analytical predictions for the dependence on the initial node of three indicators of spreading influence (probability to originate an infinite outbreak, average duration and size of finite outbreaks) and compare them with numerical simulations on random uncorrelated networks, finding a very good agreement. We then show that the same theoretical approach works fairly well also on a set of real-world topologies of diverse nature. We conclude by briefly investigating which topological network features determine deviations from the theoretical predictions.

physics.soc-ph↗

arXiv2021

Phase transitions on a class of generalized Vicsek-like models of collective motion

Systems composed of interacting self-propelled particles (SPPs) display different forms of order-disorder phase transitions relevant to collective motion. In this paper we propose a generalization of the Vicsek model characterized by an angular noise term following an arbitrary probability density function, which might depend on the state of the system and thus have a multiplicative character. We show that the well established vectorial Vicsek model can be expressed in this general formalism by deriving the corresponding angular probability density function, as well as we propose two new multiplicative models consisting on a bivariate Gaussian and a wrapped Gaussian distributions. With the proposed formalism, the mean-field system can be solved using the mean resultant length of the angular stochastic term. Accordingly, when the SPPs interact globally, the character of the phase transition depends on the choice of the noise distribution, being first-order with an hybrid scaling for the vectorial and wrapped Gaussian distributions, and second order for the bivariate Gaussian distribution. Numerical simulations reveal that this scenario also holds when the interactions among SPPs are given by a static complex network. On the other hand, using spatial short-range interactions displays, in all the considered instances, a discontinuous transition with a coexistence region, consistent with the original formulation of the Vicsek model.

nlin.AO↗

arXiv2021

The localization of non-backtracking centrality in networks and its physical consequences

The spectrum of the non-backtracking matrix plays a crucial role in determining various structural and dynamical properties of networked systems, ranging from the threshold in bond percolation and non-recurrent epidemic processes, to community structure, to node importance. Here we calculate the largest eigenvalue of the non-backtracking matrix and the associated non-backtracking centrality for uncorrelated random networks, finding expressions in excellent agreement with numerical results. We show however that the same formulas do not work well for many real-world networks. We identify the mechanism responsible for this violation in the localization of the non-backtracking centrality on network subgraphs whose formation is highly unlikely in uncorrelated networks, but rather common in real-world structures. Exploiting this knowledge we present an heuristic generalized formula for the largest eigenvalue, which is remarkably accurate for all networks of a large empirical dataset. We show that this newly uncovered localization phenomenon allows to understand the failure of the message-passing prediction for the percolation threshold in many real-world structures.

physics.soc-ph↗

arXiv2020

Amplitude death and restoration in networks of oscillators with random-walk diffusion

We study the death and restoration of collective oscillations in networks of oscillators coupled through random-walk diffusion. Differently than the usual diffusion coupling used to model chemical reactions, here the equilibria of the uncoupled unit is not a solution of the coupled ensemble. Instead, the connectivity modifies both, the original unstable fixed point and the stable limit-cycle, making them node-dependent. Using numerical simulations in random networks we show that, in some cases, this diffusion induced heterogeneity stabilizes the initially unstable fixed point via a Hopf bifurcation. Further increasing the coupling strength the oscillations can be restored as well. Upon numerical analysis of the stability properties we conclude that this is a novel case of amplitude death. Finally we use a heterogeneous mean-field reduction of the system in order to proof the robustness of this phenomena upon increasing the system size.

nlin.AO↗

arXiv2020

Influential spreaders for recurrent epidemics on networks

The identification of which nodes are optimal seeds for spreading processes on a network is a non-trivial problem that has attracted much interest recently. While activity has mostly focused on non-recurrent type of dynamics, here we consider the problem for the Susceptible-Infected-Susceptible (SIS) spreading model, where an outbreak seeded in one node can originate an infinite activity avalanche. We apply the theoretical framework for avalanches on networks proposed by Larremore et al. [Phys. Rev. E 85, 066131 (2012)], to obtain detailed quantitative predictions for the spreading influence of individual nodes (in terms of avalanche duration and avalanche size) both above and below the epidemic threshold. When the approach is complemented with an annealed network approximation, we obtain fully analytical expressions for the observables of interest close to the transition, highlighting the role of degree centrality. Comparison of these results with numerical simulations performed on synthetic networks with power-law degree distribution reveals in general a good agreement in the subcritical regime, leaving thus some questions open for further investigation relative to the supercritical region.

physics.soc-ph↗

arXiv2020

Cumulative Merging Percolation and the epidemic transition of the Susceptible-Infected-Susceptible model in networks

We consider cumulative merging percolation (CMP), a long-range percolation process describing the iterative merging of clusters in networks, depending on their mass and mutual distance. For a specific class of CMP processes, which represents a generalization of degree-ordered percolation, we derive a scaling solution on uncorrelated complex networks, unveiling the existence of diverse mechanisms leading to the formation of a percolating cluster. The scaling solution accurately reproduces universal properties of the transition. This finding is used to infer the critical properties of the Susceptible-Infected-Susceptible (SIS) model for epidemics in infinite and finite power-law distributed networks. Here discrepancies between analytical approaches and numerical results regarding the finite size scaling of the epidemic threshold are a crucial open issue in the literature. We find that the scaling exponent assumes a nontrivial value during a long preasymptotic regime. We calculate this value, finding good agreement with numerical evidence. We also show that the crossover to the true asymptotic regime occurs for sizes much beyond currently feasible simulations. Our findings allow us to rationalize and reconcile all previously published results (both analytical and numerical), thus ending a long-standing debate.

cond-mat.stat-mech↗

arXiv2019

Scalar model of flocking dynamics on complex social networks

We investigate the effects of long-range social interactions in flocking dynamics by studying the dynamics of a scalar model of collective motion embedded in a complex network representing a pattern of social interactions, as observed in several social species. In this scalar model we find a phenomenology analogous to that observed in the classic Vicsek model: In networks with low heterogeneity, a phase transition separates an ordered from a disordered phase. At high levels of heterogeneity, instead, the transition is suppressed and the system is always ordered. This observation is backed up analytically by the solution of a modified scalar model within an heterogeneous mean-field approximation. Our work extends the understanding of the effects of social interactions in flocking dynamics and opens the path to the analytical study of more complex topologies of social ties.

physics.soc-ph↗

arXiv2019

Quantifying echo chamber effects in information spreading over political communication networks

Echo chambers in online social networks, in which users prefer to interact only with ideologically-aligned peers, are believed to facilitate misinformation spreading and contribute to radicalize political discourse. In this paper, we gauge the effects of echo chambers in information spreading phenomena over political communication networks. Mining 12 million Twitter messages, we reconstruct a network in which users interchange opinions related to the impeachment of the former Brazilian President Dilma Rousseff. We define a continuous {political position} parameter, independent of the network's structure, that allows to quantify the presence of echo chambers in the strongly connected component of the network, reflected in two well-separated communities of similar sizes with opposite views of the impeachment process. By means of simple spreading models, we show that the capability of users in propagating the content they produce, measured by the associated spreadability, strongly depends on their attitude. Users expressing pro-impeachment sentiments are capable to transmit information, on average, to a larger audience than users expressing anti-impeachment sentiments. Furthermore, the users' spreadability is correlated to the diversity, in terms of political position, of the audience reached. Our method can be exploited to identify the presence of echo chambers and their effects across different contexts and shed light upon the mechanisms allowing to break echo chambers.

physics.soc-ph↗

arXiv2019

Spectral properties and the accuracy of mean-field approaches for epidemics on correlated networks

We present a comparison between stochastic simulations and mean-field theories for the epidemic threshold of the susceptible-infected-susceptible (SIS) model on correlated networks (both assortative and disassortative) with power-law degree distribution $P(k)\sim k^{-γ}$. We confirm the vanishing of the threshold regardless of the correlation pattern and the degree exponent $γ$. Thresholds determined numerically are compared with quenched mean-field (QMF) and pair quenched mean-field (PQMF) theories. Correlations do not change the overall picture: QMF and PQMF provide estimates that are asymptotically correct for large size for $γ<5/2$, while they only capture the vanishing of the threshold for $γ>5/2$, failing to reproduce quantitatively how this occurs. For a given size, PQMF is more accurate. We relate the variations in the accuracy of QMF and PQMF predictions with changes in the spectral properties (spectral gap and localization) of standard and modified adjacency matrices, which rule the epidemic prevalence near the transition point, depending on the theoretical framework. We also show that, for $γ<5/2$, while QMF provides an estimate of the epidemic threshold that is asymptotically exact, it fails to reproduce the singularity of the prevalence around the transition.

physics.soc-ph↗

arXiv2019

Random walks in non-Poissoinan activity driven temporal networks

The interest in non-Markovian dynamics within the complex systems community has recently blossomed, due to a new wealth of time-resolved data pointing out the bursty dynamics of many natural and human interactions, manifested in an inter-event time between consecutive interactions showing a heavy-tailed distribution. In particular, empirical data has shown that the bursty dynamics of temporal networks can have deep consequences on the behavior of the dynamical processes running on top of them. Here, we study the case of random walks, as a paradigm of diffusive processes, unfolding on temporal networks generated by a non-Poissonian activity driven dynamics. We derive analytic expressions for the steady state occupation probability and first passage time distribution in the infinite network size and strong aging limits, showing that the random walk dynamics on non-Markovian networks are fundamentally different from what is observed in Markovian networks. We found a particularly surprising behavior in the limit of diverging average inter-event time, in which the random walker feels the network as homogeneous, even though the activation probability of nodes is heterogeneously distributed. Our results are supported by extensive numerical simulations. We anticipate that our findings may be of interest among the researchers studying non-Markovian dynamics of time-evolving complex topologies.

cond-mat.stat-mech↗

arXiv2018

Relevance of backtracking paths in epidemic spreading on networks

The understanding of epidemics on networks has greatly benefited from the recent application of message-passing approaches, which allow to derive exact results for irreversible spreading (i.e. diseases with permanent acquired immunity) in locally-tree like topologies. This success has suggested the application of the same approach to reversible epidemics, for which an individual can contract the epidemic and recover repeatedly. The underlying assumption is that backtracking paths (i.e. an individual is reinfected by a neighbor he/she previously infected) do not play a relevant role. In this paper we show that this is not the case for reversible epidemics, since the neglect of backtracking paths leads to a formula for the epidemic threshold that is qualitatively incorrect in the large size limit. Moreover we define a modified reversible dynamics which explicitly forbids direct backtracking events and show that this modification completely upsets the phenomenology.

cond-mat.stat-mech↗

arXiv2018

Eigenvector localization in real networks and its implications for epidemic spreading

The spectral properties of the adjacency matrix, in particular its largest eigenvalue and the associated principal eigenvector, dominate many structural and dynamical properties of complex networks. Here we focus on the localization properties of the principal eigenvector in real networks. We show that in most cases it is either localized on the star defined by the node with largest degree (hub) and its nearest neighbors, or on the densely connected subgraph defined by the maximum $K$-core in a $K$-core decomposition. The localization of the principal eigenvector is often strongly correlated with the value of the largest eigenvalue, which is given by the local eigenvalue of the corresponding localization subgraph, but different scenarios sometimes occur. We additionally show that simple targeted immunization strategies for epidemic spreading are extremely sensitive to the actual localization set.

physics.soc-ph↗

arXiv2018

Effects of heterogeneous social interactions on flocking dynamics

Social relationships characterize the interactions that occur within social species and may have an important impact on collective animal motion. Here, we consider a variation of the standard Vicsek model for collective motion in which interactions are mediated by an empirically motivated scale-free topology that represents a heterogeneous pattern of social contacts. We observe that the degree of order of the model is strongly affected by network heterogeneity: more heterogeneous networks show a more resilient ordered state; while less heterogeneity leads to a more fragile ordered state that can be destroyed by sufficient external noise. Our results challenge the previously accepted equivalence between the {\em static} Vicsek model and the equilibrium XY model on the network of connections, and point towards a possible equivalence with models exhibiting a different symmetry.

physics.soc-ph↗

arXiv2017

Evolutionary dynamics of the cryptocurrency market

The cryptocurrency market surpassed the barrier of \$100 billion market capitalization in June 2017, after months of steady growth. Despite its increasing relevance in the financial world, however, a comprehensive analysis of the whole system is still lacking, as most studies have focused exclusively on the behaviour of one (Bitcoin) or few cryptocurrencies. Here, we consider the history of the entire market and analyse the behaviour of 1,469 cryptocurrencies introduced between April 2013 and June 2017. We reveal that, while new cryptocurrencies appear and disappear continuously and their market capitalization is increasing (super-)exponentially, several statistical properties of the market have been stable for years. These include the number of active cryptocurrencies, the market share distribution and the turnover of cryptocurrencies. Adopting an ecological perspective, we show that the so-called neutral model of evolution is able to reproduce a number of key empirical observations, despite its simplicity and the assumption of no selective advantage of one cryptocurrency over another. Our results shed light on the properties of the cryptocurrency market and establish a first formal link between ecological modelling and the study of this growing system. We anticipate they will spark further research in this direction.

physics.soc-ph↗

arXiv2017

Relating Topological Determinants of Complex Networks to Their Spectral Properties: Structural and Dynamical Effects

The largest eigenvalue of a network's adjacency matrix and its associated principal eigenvector are key elements for determining the topological structure and the properties of dynamical processes mediated by it. We present a physically grounded expression relating the value of the largest eigenvalue of a given network to the largest eigenvalue of two network subgraphs, considered as isolated: The hub with its immediate neighbors and the densely connected set of nodes with maximum $K$-core index. We validate this formula showing that it predicts with good accuracy the largest eigenvalue of a large set of synthetic and real-world topologies. We also present evidence of the consequences of these findings for broad classes of dynamics taking place on the networks. As a byproduct, we reveal that the spectral properties of heterogeneous networks built according to the linear preferential attachment model are qualitatively different from those of their static counterparts.

physics.soc-ph↗

arXiv2017

Effects of temporal correlations in social multiplex networks

Multi-layered networks represent a major advance in the description of natural complex systems, and their study has shed light on new physical phenomena. Despite its importance, however, the role of the temporal dimension in their structure and function has not been investigated in much detail so far. Here we study the temporal correlations between layers exhibited by real social multiplex networks. At a basic level, the presence of such correlations implies a certain degree of predictability in the contact pattern, as we quantify by an extension of the entropy and mutual information analyses proposed for the single-layer case. At a different level, we demonstrate that temporal correlations are a signature of a 'multitasking' behavior of network agents, characterized by a higher level of switching between different social activities than expected in a uncorrelated pattern. Moreover, temporal correlations significantly affect the dynamics of coupled epidemic processes unfolding on the network. Our work opens the way for the systematic study of temporal multiplex networks and we anticipate it will be of interest to researchers in a broad array of fields.

physics.soc-ph↗