Cascading failures in spatially-embedded random networks

Cascading failures constitute an important vulnerability of interconnected systems. Here we focus on the study of such failures on networks in which the connectivity of nodes is constrained by geographical distance. Specifically, we use random geometric graphs as representative examples of such spatial networks, and study the properties of cascading failures on them in the presence of distributed flow. The key finding of this study is that the process of cascading failures is non-self-averaging on spatial networks, and thus, aggregate inferences made from analyzing an ensemble of such networks lead to incorrect conclusions when applied to a single network, no matter how large the network is. We demonstrate that this lack of self-averaging disappears with the introduction of a small fraction of long-range links into the network. We simulate the well studied preemptive node removal strategy for cascade mitigation and show that it is largely ineffective in the case of spatial networks. We introduce an altruistic strategy designed to limit the loss of network nodes in the event of a cascade triggering failure and show that it performs better than the preemptive strategy. Finally, we consider a real-world spatial network viz. a European power transmission network and validate that our findings from the study of random geometric graphs are also borne out by simulations of cascading failures on the empirical network.Comment: 13 pages, 15 figure

Evolution of Threats in the Global Risk Network

With a steadily growing population and rapid advancements in technology, the global economy is increasing in size and complexity. This growth exacerbates global vulnerabilities and may lead to unforeseen consequences such as global pandemics fueled by air travel, cyberspace attacks, and cascading failures caused by the weakest link in a supply chain. Hence, a quantitative understanding of the mechanisms driving global network vulnerabilities is urgently needed. Developing methods for efficiently monitoring evolution of the global economy is essential to such understanding. Each year the World Economic Forum publishes an authoritative report on the state of the global economy and identifies risks that are likely to be active, impactful or contagious. Using a Cascading Alternating Renewal Process approach to model the dynamics of the global risk network, we are able to answer critical questions regarding the evolution of this network. To fully trace the evolution of the network we analyze the asymptotic state of risks (risk levels which would be reached in the long term if the risks were left unabated) given a snapshot in time, this elucidates the various challenges faced by the world community at each point in time. We also investigate the influence exerted by each risk on others. Results presented here are obtained through either quantitative analysis or computational simulations.Comment: 27 pages, 15 figure

Evolution of the Global Risk Network Mean-Field Stability Point

With a steadily growing human population and rapid advancements in technology, the global human network is increasing in size and connection density. This growth exacerbates networked global threats and can lead to unexpected consequences such as global epidemics mediated by air travel, threats in cyberspace, global governance, etc. A quantitative understanding of the mechanisms guiding this global network is necessary for proper operation and maintenance of the global infrastructure. Each year the World Economic Forum publishes an authoritative report on global risks, and applying this data to a CARP model, we answer critical questions such as how the network evolves over time. In the evolution, we compare not the current states of the global risk network at different time points, but its steady state at those points, which would be reached if the risk were left unabated. Looking at the steady states show more drastically the differences in the challenges to the global economy and stability the world community had faced at each point of the time. Finally, we investigate the influence between risks in the global network, using a method successful in distinguishing between correlation and causation. All results presented in the paper were obtained using detailed mathematical analysis with simulations to support our findings.Comment: 11 pages, 5 figures, the 6th International Conference on Complex Networks and Their Application

Divide-and-rule policy in the Naming Game

The Naming Game is a classic model for studying the emergence and evolution of language in a population. In this paper, we consider the Naming Game with multiple committed opinions and investigate the dynamics of the game on a complete graph with an arbitrary large population. The homogeneous mixing condition enables us to use mean-field theory to analyze the opinion evolution of the system. However, when the number of opinions increases, the number of variables describing the system grows exponentially. We focus on a special scenario where the largest group of committed agents competes with a motley of committed groups, each of which is significantly smaller than the largest one, while the majority of uncommitted agents initially hold one unique opinion. We choose this scenario for two reasons. The first is that it arose many times in different societies, while the second is that its complexity can be reduced by merging all agents of small committed groups into a single committed group. We show that the phase transition occurs when the group of the largest committed fraction dominates the system, and the threshold for the size of the dominant group at which this transition occurs depends on the size of the committed group of the unified category. Further, we derive the general formula for the multi-opinion evolution using a recursive approach. Finally, we use agent-based simulations to reveal the opinion evolution in the random graphs. Our results provide insights into the conditions under which the dominant opinion emerges in a population and the factors that influence this process.Comment: 13 pages, 12 figure