Failure-recovery model with competition between failures in complex networks: a dynamical approach

Real systems are usually composed by units or nodes whose activity can be interrupted and restored intermittently due to complex interactions not only with the environment, but also with the same system. Majdand\v{z}i\'c $et\;al.$ [Nature Physics 10, 34 (2014)] proposed a model to study systems in which active nodes fail and recover spontaneously in a complex network and found that in the steady state the density of active nodes can exhibit an abrupt transition and hysteresis depending on the values of the parameters. Here we investigate a model of recovery-failure from a dynamical point of view. Using an effective degree approach we find that the systems can exhibit a temporal sharp decrease in the fraction of active nodes. Moreover we show that, depending on the values of the parameters, the fraction of active nodes has an oscillatory regime which we explain as a competition between different failure processes. We also find that in the non-oscillatory regime, the critical fraction of active nodes presents a discontinuous drop which can be related to a "targeted" k-core percolation process. Finally, using mean field equations we analyze the space of parameters at which hysteresis and oscillatory regimes can be found

Synchronization in interacting Scale Free Networks

We study the fluctuations of the interface, in the steady state, of the Surface Relaxation Model (SRM) in two scale free interacting networks where a fraction $q$ of nodes in both networks interact one to one through external connections. We find that as $q$ increases the fluctuations on both networks decrease and thus the synchronization reaches an improvement of nearly $40\%$ when $q=1$. The decrease of the fluctuations on both networks is due mainly to the diffusion through external connections which allows to reducing the load in nodes by sending their excess mostly to low-degree nodes, which we report have the lowest heights. This effect enhances the matching of the heights of low-and high-degree nodes as $q$ increases reducing the fluctuations. This effect is almost independent of the degree distribution of the networks which means that the interconnection governs the behavior of the process over its topology.Comment: 13 pages, 7 figures. Added a relevant reference.Typos fixe

Recovery of Interdependent Networks

Recent network research has focused on the cascading failures in a system of interdependent networks and the necessary preconditions for system collapse. An important question that has not been addressed is how to repair a failing system before it suffers total breakdown. Here we introduce a recovery strategy of nodes and develop an analytic and numerical framework for studying the concurrent failure and recovery of a system of interdependent networks based on an efficient and practically reasonable strategy. Our strategy consists of repairing a fraction of failed nodes, with probability of recovery $\gamma$, that are neighbors of the largest connected component of each constituent network. We find that, for a given initial failure of a fraction $1-p$ of nodes, there is a critical probability of recovery above which the cascade is halted and the system fully restores to its initial state and below which the system abruptly collapses. As a consequence we find in the plane $\gamma-p$ of the phase diagram three distinct phases. A phase in which the system never collapses without being restored, another phase in which the recovery strategy avoids the breakdown, and a phase in which even the repairing process cannot avoid the system collapse

Reversible bootstrap percolation: Fake news and fact checking

Bootstrap percolation has been used to describe opinion formation in society and other social and natural phenomena. The formal equation of the bootstrap percolation may have more than one solution, corresponding to several stable fixed points of the corresponding iteration process. We construct a reversible bootstrap percolation process, which converges to these extra solutions displaying a hysteresis typical of discontinuous phase transitions. This process provides a reasonable model for fake news spreading and the effectiveness of fact checking. We show that sometimes it is not sufficient to discard all the sources of fake news in order to reverse the belief of a population that formed under the influence of these sources

Synchronization in Scale Free networks: The role of finite size effects

Synchronization problems in complex networks are very often studied by researchers due to its many applications to various fields such as neurobiology, e-commerce and completion of tasks. In particular, Scale Free networks with degree distribution $P(k)\sim k^{-\lambda}$, are widely used in research since they are ubiquitous in nature and other real systems. In this paper we focus on the surface relaxation growth model in Scale Free networks with $2.5< \lambda <3$, and study the scaling behavior of the fluctuations, in the steady state, with the system size $N$. We find a novel behavior of the fluctuations characterized by a crossover between two regimes at a value of $N=N^*$ that depends on $\lambda$: a logarithmic regime, found in previous research, and a constant regime. We propose a function that describes this crossover, which is in very good agreement with the simulations. We also find that, for a system size above $N^{*}$, the fluctuations decrease with $\lambda$, which means that the synchronization of the system improves as $\lambda$ increases. We explain this crossover analyzing the role of the network's heterogeneity produced by the system size $N$ and the exponent of the degree distribution.Comment: 9 pages and 5 figures. Accepted in Europhysics Letter

Small-scale spatial variability of soil CO2 flux: Implication for monitoring strategy

In recent decades, soil CO2 flux measurements have been often used in both volcanic and seismically active areas to investigate the interconnections between temporal and spatial anomalies in degassing and telluric activities. In this study, we focus on a narrow degassing area of the Piton de la Fournaise volcano, that has been chosen for its proximity and link with the frequently active volcanic area. Our aim is to constrain the degassing in this narrow area and identify the potential processes involved in both spatial and temporal soil CO2 variations in order to provide an enhanced monitoring strategy for soil CO2 flux. We performed a geophysical survey (self-potential measurements: SP; electrical resistivity tomography: ERT) to provide a high-resolution description of the subsurface. We identified one main SP negative anomaly dividing the area in two zones. Based on these results, we set ten control points, from the site of the main SP negative anomaly up to 230 m away, where soil CO2 fluxes were weekly measured during one year of intense eruptive activity at Piton de la Fournaise. Our findings show that lateral and vertical soil heterogeneities and structures exert a strong control on the degassing pattern. We find that temporal soil CO2 flux series at control points close to the main SP negative anomaly better record variations linked to the volcanic activity. We also show that the synchronicity between the increase of soil CO2 flux and deep seismicity can be best explained by a pulsed process pushing out the CO2 already stored and fractionated in the system. Importantly, our findings show that low soil CO2 fluxes and low carbon isotopic signature are able to track variations of volcanic activity in the same way as high fluxes and high carbon isotopic signature do. This result gives important insights in terms of monitoring strategy of volcanic and seismotectonic areas in geodynamics contexts characterized by difficult environmental operational conditions as commonly met in tropical areaPublished13-264A. Oceanografia e climaJCR Journa

Structural and functional heterogeneity of hemocyanin: intra- and inter-specific comparison in four species of portunid crabs (Crustacea: Portunidae)

This work is focused on hemocyanin (Hc) heterogeneity at population level and on the biochemical characterization of the different subunit patterns. Two different approaches have been used: we have characterized Hc subunit composition to describe the subunit polymorphism. Then, we have measured the Hc oxygen-binding affinity to disclose the physiological implications of such heterogeneity. In order to evaluate the intra- and inter-specific variability, different populations of Liocarcinus depurator, Liocarcinus marmoreus, Liocarcinus holsatus, Necora puber (Crustacea: Portunidae), from British Isles and Adriatic Sea, have been sampled. Results indicate that Hc polymorphism normally occurs at both intra- and interspecific levels and involves the protein subunit type. These evidences extend to the portunid Hc the concept of molecular heterogeneity within species that have been previously reported for other decapod and amphipod crustaceans. Besides, the results support the view that subunit composition of crustacean Hcs is almost species-specific, but also that closely related species share a common pattern. Furthermore, this heterogeneity corresponds to different stability of the native oligomers quaternary structure and different oxygen affinity. The results are discussed in relation with the environmental regimes that characterize the different sampling areas. In addition to Hc, the hemolymph collected in specimens from different sampling areas contained also a non-respiratory pseudo-Hc. This paper reports for the first time the occurrence of pseudo-Hc at the level of population

Disease spreading with social distancing: A prevention strategy in disordered multiplex networks

The frequent emergence of diseases with the potential to become threats at local and global scales, such as influenza A(H1N1), SARS, MERS, and recently COVID-19 disease, makes it crucial to keep designing models of disease propagation and strategies to prevent or mitigate their effects in populations. Since isolated systems are exceptionally rare to find in any context, especially in human contact networks, here we examine the susceptible-infected-recovered model of disease spreading in a multiplex network formed by two distinct networks or layers, interconnected through a fraction q of shared individuals (overlap). We model the interactions through weighted networks, because person-to-person interactions are diverse (or disordered); weights represent the contact times of the interactions. Using branching theory supported by simulations, we analyze a social distancing strategy that reduces the average contact time in both layers, where the intensity of the distancing is related to the topology of the layers. We find that the critical values of the distancing intensities, above which an epidemic can be prevented, increase with the overlap q. Also we study the effect of the social distancing on the mutual giant component of susceptible individuals, which is crucial to keep the functionality of the system. In addition, we find that for relatively small values of the overlap q, social distancing policies might not be needed at all to maintain the functionality of the system.Fil: Pérez, Ignacio Augusto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; ArgentinaFil: Di Muro, Matias Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; ArgentinaFil: la Rocca, Cristian Ernesto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; ArgentinaFil: Braunstein, Lidia Adriana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentin