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Natural and technological interdependent systems have been shown to be highly vulnerable due to cascading failures and an abrupt collapse of global connectivity under initial failure. Mitigating the risk by partial disconnection endangers their functionality. Here we propose a systematic strategy of selecting a minimum number of autonomous nodes that(More)
—Blackouts in power grids typically result from cascading failures. The key importance of the electric power grid to society encourages further research into sustaining power system reliability and developing new methods to manage the risks of cascading blackouts. Adequate software tools are required to better analyse, understand, and assess the(More)
We show that considering only the largest cluster suffices to obtain a first-order percolation transition. As opposed to previous realizations of explosive percolation, our models obtain Gaussian cluster distributions and compact clusters as one would expect at first-order transitions. We also discover that the cluster perimeters are fractal at the(More)
The random sequential adsorption (RSA) model has served as a paradigm for diverse phenomena in physical chemistry, as well as in other areas such as biology, ecology, and sociology. In the present work, we survey aspects of the RSA model with emphasis on the approach to and properties of jammed states obtained for large times in continuum deposition versus(More)
Resilience of most critical infrastructures against failure of elements that appear insignificant is usually taken for granted. The World Airline Network (WAN) is an infrastructure that reduces the geographical gap between societies, both small and large, and brings forth economic gains. With the extensive use of a publicly maintained data set that contains(More)
The optimal path crack model on uncorrelated surfaces, recently introduced by Andrade et al. [Phys. Rev. Lett. 103, 225503 (2009).], is studied in detail and its main percolation exponents computed. In addition to β/ν=0.46±0.03, we report γ/ν=1.3±0.2 and τ=2.3±0.2. The analysis is extended to surfaces with spatial long-range power-law correlations, where(More)
The suitable interpolation between classical percolation and a special variant of explosive percolation enables the explicit realization of a tricritical percolation point. With high-precision simulations of the order parameter and the second moment of the cluster size distribution a fully consistent tricritical scaling scenario emerges yielding the(More)
Examples of synchronization can be found in a wide range of phenomena such as neurons firing, lasers cascades, chemical reactions, and opinion formation. However, in many situations the formation of a coherent state is not pleasant and should be mitigated. For example, the onset of synchronization can be the root of epileptic seizures, traffic congestion in(More)
Interconnected networks have been shown to be much more vulnerable to random and targeted failures than isolated ones, raising several interesting questions regarding the identification and mitigation of their risk. The paradigm to address these questions is the percolation model, where the resilience of the system is quantified by the dependence of the(More)
Global synchronization in a complex network of oscillators emerges from the interplay between its topology and the dynamics of the pairwise interactions among its numerous components. When oscillators are spatially separated, however, a time delay appears in the interaction which might obstruct synchronization. Here we study the synchronization properties(More)