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Robust control theory has been successfully applied to numerous real-world problems using a small set of devices called controllers. However, the real systems represented by networks contain unreliable components and modern robust control engineering has not addressed the problem of structural changes on complex networks including scale-free topologies. Here, we introduce the concept of structurally robust control of complex networks and provide a concrete example using an algorithmic framework that is widely applied in engineering. The developed analytical tools, computer simulations, and real network analyses lead herein to the discovery that robust control can be achieved in scale-free networks with exactly the same order of controllers required in a standard nonrobust configuration by adjusting only the minimum degree. The presented methodology also addresses the probabilistic failure of links in real systems, such as neural synaptic unreliability in Caenorhabditis elegans, and suggests a new direction to pursue in studies of complex networks in which control theory has a role. [ABSTRACT FROM AUTHOR]

Increasingly accessible financial data allow researchers to infer market-dynamics-based laws and to propose models that are able to reproduce them. In recent years, several stylized facts have been uncovered. Here we perform an extensive analysis of foreign exchange data that leads to the unveiling of a statistical financial law. First, our findings show that, on average, volatility increases more when the price exceeds the highest (or lowest) value, i.e., breaks the resistance line. We call this the breaking-acceleration effect. Second, our results show that the probability P(T) to break the resistance line in the past time T follows power law in both real data and theoretically simulated data. However, the probability calculated using real data is rather lower than the one obtained using a traditional Black-Scholes (BS) model. Taken together, the present analysis characterizes a different stylized fact of financial markets and shows that the market exceeds a past (historical) extreme price fewer times than expected by the BS model (the resistance effect). However, when the market does, we predict that the average volatility at that time point will be much higher. These findings indicate that any Markovian model does not faithfully capture the market dynamics. [ABSTRACT FROM AUTHOR]