We report Warm Spitzer full-orbit phase observations of WASP-12b at 3.6 and 4.5 µm. This extremely inflated hot Jupiter is thought to be overflowing its Roche lobe, undergoing mass loss, accretion onto its host star, and has been claimed to have a C/O ratio in excess of unity. We are able to measure the transit depths, eclipse depths, thermal and ellipsoidal phase variations at both wavelengths. The large amplitude phase variations, combined with the planet's previously-measured day-side spectral energy distribution, is indicative of non-zero Bond albedo and very poor day-night heat redistribution. The transit depths in the mid-infrared -(R p /R * ) 2 = 0.0123(3) and 0.0111(3) at 3.6 and 4.5 µm, respectively-indicate that the atmospheric opacity is greater at 3.6 than at 4.5 µm, in disagreement with model predictions, irrespective of C/O ratio. The secondary eclipse depths are consistent with previous studies: F day /F * = 0.0038(4) and 0.0039(3) at 3.6 and 4.5 µm, respectively. We do not detect ellipsoidal variations at 3.6 µm, but our parameter uncertainties -estimated via prayer-bead Monte Carlo-keep this non-detection consistent with model predictions. At 4.5 µm, on the other hand, we detect ellipsoidal variations that are much stronger than predicted. If interpreted as a geometric effect due to the planet's elongated shape, these variations imply a 3:2 ratio for the planet's longest:shortest axes and a relatively bright day-night terminator. If we instead presume that the 4.5 µm ellipsoidal variations are due to uncorrected systematic noise and we fix the amplitude of the variations to zero, the best fit 4.5 µm transit depth becomes commensurate with the 3.6 µm depth, within the uncertainties. The relative transit depths are then consistent with a Solar composition and short scale height at the terminator. Assuming zero ellipsoidal variations also yields a much deeper 4.5 µm eclipse depth, consistent with a Solar composition and modest temperature inversion. We suggest future observations that could distinguish between these two scenarios. 11 We follow Agol et al. (2010), who compared many centroiding algorithms and found this one to be optimal. Using fluxweighted centroiding instead of PSF-fitting results in slightly worse χ 2 , commensurate correlated noise as measured using β (see first Section 4.1), and consistent astrophysical parameters.

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.

Although detecting and characterizing community structure is key in the study of networked systems, we still do not understand how community structure affects systemic resilience and stability. We use percolation theory to develop a framework for studying the resilience of networks with a community structure. We find both analytically and numerically that interlinks (the connections among communities) affect the percolation phase transition in a way similar to an external field in a ferromagnetic- paramagnetic spin system. We also study universality class by defining the analogous critical exponents and, and we find that their values in various models and in real-world coauthor networks follow the fundamental scaling relations found in physical phase transitions. The methodology and results presented here facilitate the study of network resilience and also provide a way to understand phase transitions under external fields.

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 ζ → 0 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, ζc, abrupt, discontinuous transitions take place, while for ζ < ζc the transition is continuous, indicating that the risk of abrupt collapse can be eliminated if the typical link length is shorter than ζc.

Many infrastructure networks have a modular structure and are also interdependent with other infrastructures. 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 through simulations. We focus, for simplicity, 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 particularly realistic for modeling infrastructure across cities. Each city has its own infrastructures and different infrastructures are dependent only 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 previously been shown that single networks are very susceptible to the failure of the interconnected nodes (between communities) (Shai et al 2014 arXiv:1404.4748) and that attacks on these nodes are even more crippling than attacks based on betweenness (da Cunha et al 2015 arXiv:1502.00353). 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, m. (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 significantly influence the type of transitions observed in interdependent networks and should be considered in attempts to make interdependent networks more resilient.