Many real world complex systems such as critical infrastructure networks are embedded in space and their components may depend on one another to function. They are also susceptible to geographically localized damage caused by malicious attacks or natural disasters. Here, we study a general model of spatially embedded networks with dependencies under localized attacks. We develop a theoretical and numerical approach to describe and predict the effects of localized attacks on spatially embedded systems with dependencies. Surprisingly, we find that a localized attack can cause substantially more damage than an equivalent random attack. Furthermore, we find that for a broad range of parameters, systems which appear stable are in fact metastable. Though robust to random failures—even of finite fraction—if subjected to a localized attack larger than a critical size which is independent of the system size (i.e., a zero fraction), a cascading failure emerges which leads to complete system collapse. Our results demonstrate the potential high risk of localized attacks on spatially embedded network systems with dependencies and may be useful for designing more resilient systems.

Rifamycin antibiotics (Rifs) target bacterial RNA polymerases (RNAPs) and are widely used to treat infections including tuberculosis. The utility of these compounds is threatened by the increasing incidence of resistance (RifR). As resistance mechanisms found in clinical settings may also occur in natural environments, here we postulated that bacteria could have evolved to produce rifamycin congeners active against clinically relevant resistance phenotypes. We survey soil metagenomes and identify a tailoring enzyme-rich family of gene clusters encoding biosynthesis of rifamycin congeners (kanglemycins, Kangs) with potent in vivo and in vitro activity against the most common clinically relevant RifR mutations. Our structural and mechanistic analyses reveal the basis for Kang inhibition of RifR RNAP. Unlike Rifs, Kangs function through a mechanism that includes interfering with 5′-initiating substrate binding. Our results suggest that examining soil microbiomes for new analogues of clinically used antibiotics may uncover metabolites capable of circumventing clinically important resistance mechanisms.

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.

From critical infrastructure, to physiology and the human brain, complex systems rarely occur in isolation. Instead, the functioning of nodes in one system often promotes or suppresses the functioning of nodes in another. Despite advances in structural interdependence, modeling interdependence and other interactions between dynamic systems has proven elusive. Here we define a broadly applicable dynamic dependency link and develop a general framework for interdependent and competitive interactions between general dynamic systems. We apply our framework to studying interdependent and competitive synchronization in multi-layer oscillator networks and cooperative/competitive contagions in an epidemic model. Using a mean-field theory which we verify numerically, we find explosive transitions and rich behavior which is absent in percolation models including hysteresis, multi-stability and chaos. The framework presented here provides a powerful new way to model and understand many of the interacting complex systems which surround us. * Electronic address: michael.danziger@biu.ac.il † Electronic address: ivan.bms.2011@gmail.com but without a general framework or ability to uncover universal patterns between systems [26-28].arXiv:1705.00241v1 [cond-mat.stat-mech]