# The paper on "Limits of Predictability of Cascading Overload Failures in Spatially-Embedded Networks with Disttibuted Flows," by A. Moussawi, N. Derzsy, X. Lin, B.K. Szymanski & G. Korniss appeared in Scientific Reports, vol. 7.

The paper entitled "Limits of Predictability of Cascading Overload Failures in Spatially-Embedded Networks with Distributed Flows," by Alaa Moussawi, Noemi Derzsy, Xin Lin, Boleslaw K. Szymanski & G. Korniss was published in Scientific Reports, vol. 7:11729 on September 15, 2017. Since cascading failures are a critical vulnerability of complex information or infrastructure networks this paper investigates the properties of load-based cascading failures in real and synthetic spatially-embedded network structures. It also proposes mitigation strategies to reduce the severity of damages caused by such failures. We introduce a stochastic method for optimal heterogeneous distribution of resources (node capacities) subject to a fixed total cost. Additionally, we design and compare the performance of networks with N-stable and (N-1)-stable network-capacity allocations by triggering cascades using various real-world node-attack and node-failure scenarios. We show that failure mitigation through increased node protection can be effectively achieved against single-node failures. However, mitigating against multiple node failures is much more difficult due to the combinatorial increase in possible sets of initially failing nodes. We analyze the robustness of the system with increasing protection, and find that a critical tolerance exists at which the system undergoes a phase transition, and above which the network almost completely survives an attack. Moreover, we show that cascade-size distributions measured in this region exhibit a power-law decay. Finally, we find a strong correlation between cascade sizes induced by individual nodes and sets of nodes. We also show that network topology alone is a weak predictor in determining the progression of cascading failures. The paper is available at the link below.