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 transition point, yielding a fractal dimension of 1.23 ± 0.03, close to that of watersheds.

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 that on lattice substrates, and on pre-patterned surfaces. The latter model has been of recent interest in the context of efforts to use pre-patterning as a tool to improve selfassembly in micro-and nanoscale surface structure engineering.

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 guarantee a smooth transition in robustness. Our method which is based on betweenness is tested on various examples including the famous 2003 electrical blackout of Italy. We show that, with this strategy, the necessary number of autonomous nodes can be reduced by a factor of five compared to a random choice. We also find that the transition to abrupt collapse follows tricritical scaling characterized by a set of exponents which is independent on the protection strategy.

Percolation is the paradigm for random connectivity and has been one of the most applied statistical models. With simple geometrical rules a transition is obtained which is related to magnetic models. This transition is, in all dimensions, one of the most robust continuous transitions known. We present a very brief overview of more than 60 years of work in this area and discuss several open questions for a variety of models, including classical, explosive, invasion, bootstrap, and correlated

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 information about airports and alternative connections between these airports, we empirically reveal that the WAN is a redundant and resilient network for long distance air travel, but otherwise breaks down completely due to removal of short and apparently insignificant connections. These short range connections with moderate number of passengers and alternate flights are the connections that keep remote parts of the world accessible. It is surprising, insofar as there exists a highly resilient and strongly connected core consisting of a small fraction of airports (around 2.3%) together with an extremely fragile star-like periphery. Yet, in spite of their relevance, more than 90% of the world airports are still interconnected upon removal of this core. With standard and unconventional removal measures we compare both empirical and topological perceptions for the fragmentation of the world. We identify how the WAN is organized into different classes of clusters based on the physical proximity of airports and analyze the consequence of this fragmentation.