L. A. Braunstein

Competing for Attention in Social Media under Information Overload Conditions.

Modern social media are becoming overloaded with information because of the rapidly-expanding number of information feeds. We analyze the user-generated content in Sina Weibo, and find evidence that the spread of popular messages often follow a mechanism that differs from the spread of disease, in contrast to common belief. In this mechanism, an individual with more friends needs more repeated exposures to spread further the information. Moreover, our data suggest that for certain messages the chance of an individual to share the message is proportional to the fraction of its neighbours who shared it with him/her, which is a result of competition for attention. We model this process using a fractional susceptible infected recovered (FSIR) model, where the infection probability of a node is proportional to its fraction of infected neighbors. Our findings have dramatic implications for information contagion. For example, using the FSIR model we find that real-world social networks have a finite epidemic threshold in contrast to the zero threshold in disease epidemic models. This means that when individuals are overloaded with excess information feeds, the information either reaches out the population if it is above the critical epidemic threshold, or it would never be well received.

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 for 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 γ, that are neighbors of the largest connected component of each constituent network. We find that, for a given initial failure of a fraction 1u2009−u2009p 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 γu2009−u2009p 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 prevent system collapse.

Cascading failures in interdependent networks with finite functional components

We present a cascading failure model of two interdependent networks in which functional nodes belong to components of size greater than or equal to s. We find theoretically and via simulation that in complex networks with random dependency links the transition is first order for s≥3 and continuous for s=2. We also study interdependent lattices with a distance constraint r in the dependency links and find that increasing r moves the system from a regime without a phase transition to one with a second-order transition. As r continues to increase, the system collapses in a first-order transition. Each regime is associated with a different structure of domain formation of functional nodes.

Conservative model for synchronization problems in complex networks.

In this paper we study the scaling behavior of the interface fluctuations (roughness) for a discrete model with conservative noise on complex networks. Conservative noise is a noise which has no external flux of deposition on the surface and the whole process is due to the diffusion. It was found that in Euclidean lattices the roughness of the steady state W(s) does not depend on the system size. Here, we find that for scale-free networks of N nodes, characterized by a degree distribution P(k) approximately k(-lambda), W(s) is independent of N for any lambda. This behavior is very different than the one found by Pastore y Piontti [Phys. Rev. E 76, 046117 (2007)] for a discrete model with nonconservative noise, which implies an external flux, where W(s) approximately ln N for lambda<3 , and was explained by nonlinear terms in the analytical evolution equation for the interface [La Rocca, Phys. Rev. E 77, 046120 (2008)]. In this work we show that in these processes with conservative noise the nonlinear terms are not relevant to describe the scaling behavior of W(s).

Publisher's Note: Cascading failures in interdependent networks with finite functional components [Phys. Rev. E 94, 042304 (2016)]

This corrects the article DOI: 10.1103/PhysRevE.94.042304.

Interacting Social Processes on Interconnected Networks

We propose and study a model for the interplay between two different dynamical processes –one for opinion formation and the other for decision making– on two interconnected networks A and B. The opinion dynamics on network A corresponds to that of the M-model, where the state of each agent can take one of four possible values (S = −2,−1, 1, 2), describing its level of agreement on a given issue. The likelihood to become an extremist (S = ±2) or a moderate (S = ±1) is controlled by a reinforcement parameter r ≥ 0. The decision making dynamics on network B is akin to that of the Abrams-Strogatz model, where agents can be either in favor (S = +1) or against (S = −1) the issue. The probability that an agent changes its state is proportional to the fraction of neighbors that hold the opposite state raised to a power β. Starting from a polarized case scenario in which all agents of network A hold positive orientations while all agents of network B have a negative orientation, we explore the conditions under which one of the dynamics prevails over the other, imposing its initial orientation. We find that, for a given value of β, the two-network system reaches a consensus in the positive state (initial state of network A) when the reinforcement overcomes a crossover value r*(β), while a negative consensus happens for r < r*(β). In the r − β phase space, the system displays a transition at a critical threshold βc, from a coexistence of both orientations for β < βc to a dominance of one orientation for β > βc. We develop an analytical mean-field approach that gives an insight into these regimes and shows that both dynamics are equivalent along the crossover line (r*, β*).

Structural crossover of polymers in disordered media

We present a unified scaling theory for the structural behavior of polymers embedded in a disordered energy substrate. An optimal polymer configuration is defined as the polymer configuration that minimizes the sum of interacting energies between the monomers and the substrate. The fractal dimension of the optimal polymer in the limit of strong disorder (SD) was found earlier to be larger than the fractal dimension in weak disorder (WD). We introduce a scaling theory for the crossover between the WD and SD limits. For polymers of various sizes in the same disordered substrate we show that polymers with a small number of monomers N<<N* will behave as in SD, while large polymers with length N>>N* will behave as in WD. This implies that small polymers will be relatively more compact compared to large polymers even in the same substrate. The crossover length N* is a function of nu and a , where nu is the percolation correlation length exponent and a is the parameter which controls the broadness of the disorder. Furthermore, our results show that the crossover between the strong and weak disorder limits can be seen even within the same polymer configuration. If one focuses on a segment of size n<<N* within a long polymer (N>>N*) that segment will have a higher fractal dimension compared to a segment of size n>>N*.

Multiple outbreaks in epidemic spreading with local vaccination and limited vaccines

How to prevent the spread of human diseases is a great challenge for the scientific community and so far there are many studies in which immunization strategies have been developed. However, these kind of strategies usually do not consider that medical institutes may have limited vaccine resources available. In this manuscript, we explore the Susceptible-Infected-Recovered (SIR) model with local dynamic vaccination, and considering limited vaccines. In this model, susceptibles in contact with an infected individual, are vaccinated -with probability

Erratum: Corrigendum: Recovery of Interdependent Networks

omega

Competing dynamical processes on two interacting networks

- and then get infected -with probability