Louis M. Shekhtman

Debunking in a world of tribes

Social media aggregate people around common interests eliciting collective framing of narratives and worldviews. However, in such a disintermediated environment misinformation is pervasive and attempts to debunk are often undertaken to contrast this trend. In this work, we examine the effectiveness of debunking on Facebook through a quantitative analysis of 54 million users over a time span of five years (Jan 2010, Dec 2014). In particular, we compare how users usually consuming proven (scientific) and unsubstantiated (conspiracy-like) information on Facebook US interact with specific debunking posts. Our findings confirm the existence of echo chambers where users interact primarily with either conspiracy-like or scientific pages. However, both groups interact similarly with the information within their echo chamber. Then, we measure how users from both echo chambers interacted with 50,220 debunking posts accounting for both users consumption patterns and the sentiment expressed in their comments. Sentiment analysis reveals a dominant negativity in the comments to debunking posts. Furthermore, such posts remain mainly confined to the scientific echo chamber. Only few conspiracy users engage with corrections and their liking and commenting rates on conspiracy posts increases after the interaction.

Robustness of a network formed of spatially embedded networks.

We present analytic and numeric results for percolation in a network formed of interdependent spatially embedded networks. We show results for a treelike and a random regular network of networks each with (i) unconstrained dependency links and (ii) dependency links restricted to a maximum Euclidean length r. Analytic results are given for each network of networks with spatially unconstrained dependency links and compared to simulations. For the case of two fully interdependent spatially embedded networks it was found [Li et al., Phys. Rev. Lett. 108, 228702 (2012)] that the system undergoes a first-order phase transition only for r>r(c) ≈ 8. We find here that for treelike networks of networks (composed of n networks) r(c) significantly decreases as n increases and rapidly (n ≥ 11) reaches its limiting value of 1. For cases where the dependencies form loops, such as in random regular networks, we show analytically and confirm through simulations that there is a certain fraction of dependent nodes, q(max), above which the entire network structure collapses even if a single node is removed. The value of q(max) decreases quickly with m, the degree of the random regular network of networks. Our results show the extreme sensitivity of coupled spatial networks and emphasize the susceptibility of these networks to sudden collapse. The theory proposed here requires only numerical knowledge about the percolation behavior of a single network and therefore can be used to find the robustness of any network of networks where the profile of percolation of a singe network is known numerically.

An Introduction to Interdependent Networks

Many real-world phenomena can be modelled using networks. Often, these networks interact with one another in non-trivial ways. Recently, a theory of interdependent networks has been developed which describes dependency between nodes across networks. Interdependent networks have a number of unique properties which are absent in single networks. In particular, systems of interdependent networks often undergo abrupt first-order percolation transitions induced by cascading failures. Here we present an overview of recent developments and significant findings regarding interdependent networks and networks of networks.

The effect of spatiality on multiplex networks

Multilayer infrastructure is often interdependent, with nodes in one layer depending on nearby nodes in another layer to function. The links in each layer are often of limited length, due to the construction cost of longer links. Here, we model such systems as a multiplex network composed of two or more layers, each with links of characteristic geographic length, embedded in 2-dimensional space. This is equivalent to a system of interdependent spatially embedded networks in two dimensions in which the connectivity links are constrained in length but varied while the length of the dependency links is always zero. We find two distinct percolation transition behaviors depending on the characteristic length, ζ, of the links. When ζ is longer than a certain critical value, ζc, abrupt, first-order transitions take place, while for ζ < ζc the transition is continuous. We show that, though in single-layer networks increasing ζ decreases the percolation threshold pc, in multiplex networks it has the opposite effect: increasing pc to a maximum at ζ = ζc. By providing a more realistic topological model for spatially embedded interdependent and multiplex networks and highlighting its similarities to lattice-based models, we provide a new direction for more detailed future studies.Many multiplex networks are embedded in space, with links more likely to exist between nearby nodes than distant nodes. For example, interdependent infrastructure networks can be represented as multiplex networks, where each layer has links among nearby nodes. Here, we model the effect of spatiality on the robustness of a multiplex network embedded in 2-dimensional space, where links in each layer are of variable but constrained length. Based on empirical measurements of real-world networks, we adopt exponentially distributed link lengths with characteristic length ζ. By changing ζ, we modulate the strength of the spatial embedding. When ζ → ∞, all link lengths are equally likely, and the spatiality does not affect the topology. However, when only short links are allowed, and the topology is overwhelmingly determined by the spatial embedding. We find that, though longer links strengthen a single-layer network, they make a multi-layer network more vulnerable. We further find that when ζ is longer than a certain critical value, , abrupt, discontinuous transitions take place, while for the transition is continuous, indicating that the risk of abrupt collapse can be eliminated if the typical link length is shorter than .

Resilience of networks formed of interdependent modular networks

Many infrastructure networks have a modular structure and are also interdependent. While significant research has explored the resilience of interdependent networks, there has been no analysis of the effects of modularity. Here we develop a theoretical framework for attacks on interdependent modular networks and support our results by simulations. We focus on the case where each network has the same number of communities and the dependency links are restricted to be between pairs of communities of different networks. This is very realistic for infrastructure across cities. Each city has its own infrastructures and different infrastructures are dependent within the city. However, each infrastructure is connected within and between cities. For example, a power grid will connect many cities as will a communication network, yet a power station and communication tower that are interdependent will likely be in the same city. It has been shown that single networks are very susceptible to the failure of the interconnected nodes (between communities) Shai et al. and that attacks on these nodes are more crippling than attacks based on betweenness da Cunha et al. In our example of cities these nodes have long range links which are more likely to fail. For both treelike and looplike interdependent modular networks we find distinct regimes depending on the number of modules,

High-Risk Geographic Mobility Patterns among Young Urban and Suburban Persons who Inject Drugs and their Injection Network Members

m

Vulnerability of Interdependent Networks and Networks of Networks

. (i) In the case where there are fewer modules with strong intraconnections, the system first separates into modules in an abrupt first-order transition and then each module undergoes a second percolation transition. (ii) When there are more modules with many interconnections between them, the system undergoes a single transition. Overall, we find that modular structure can influence the type of transitions observed in interdependent networks and should be considered in attempts to make interdependent networks more resilient.

Critical field-exponents for secure message-passing in modular networks

Young people in the USA who inject drugs, particularly those at a risk of residence instability, experience the highest incidence of hepatitis C (HCV) infections. This study examined associations between geographic mobility patterns and sociodemographic, behavioral, and social network characteristics of 164 young (ages 18–30) persons who inject drugs (PWID). We identified a potential bridge sub-population who reported residence in both urban and suburban areas in the past year (crossover transients) and higher-risk behaviors (receptive syringe sharing, multiple sex partners) compared to their residentially localized counterparts. Because they link suburban and urban networks, crossover transients may facilitate transmission of HIV and HCV between higher and lower prevalence areas. Interventions should address risk associated with residential instability, particularly among PWID who travel between urban and suburban areas.

Resilience of networks with community structure behaves as if under an external field

Networks interact with one another in a variety of ways. Even though increased connectivity between networks would tend to make the system more robust, if dependencies exist between networks, these systems are highly vulnerable to random failure or attack. Damage in one network causes damage in another. This leads to cascading failures which amplify the original damage and can rapidly lead to complete system collapse.

Spreading of Failures in Interdependent Networks

We study secure message-passing in the presence of multiple adversaries in modular networks. We assume a dominant fraction of nodes in each module have the same vulnerability, i.e., the same entity spying on them. We find both analytically and via simulations that the links between the modules (interlinks) have effects analogous to a magnetic field in a spin system in that for any amount of interlinks the system no longer undergoes a phase transition. We then define the exponents