Complex networks have been studied intensively for a decade, but research still focuses on the limited case of a single, non-interacting network. Modern systems are coupled together and therefore should be modelled as interdependent networks. A fundamental property of interdependent networks is that failure of nodes in one network may lead to failure of dependent nodes in other networks. This may happen recursively and can lead to a cascade of failures. In fact, a failure of a very small fraction of nodes in one network may lead to the complete fragmentation of a system of several interdependent networks. A dramatic real-world example of a cascade of failures ('concurrent malfunction') is the electrical blackout that affected much of Italy on 28 September 2003: the shutdown of power stations directly led to the failure of nodes in the Internet communication network, which in turn caused further breakdown of power stations. Here we develop a framework for understanding the robustness of interacting networks subject to such cascading failures. We present exact analytical solutions for the critical fraction of nodes that, on removal, will lead to a failure cascade and to a complete fragmentation of two interdependent networks. Surprisingly, a broader degree distribution increases the vulnerability of interdependent networks to random failure, which is opposite to how a single network behaves. Our findings highlight the need to consider interdependent network properties in designing robust networks.

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Catastrophic cascade of failures in interdependent networks

This document provides guidance on how to secure Industrial Control Systems (ICS), including Supervisory Control and Data Acquisition (SCADA) systems, Distributed Control Systems (DCS), and other control system configurations such as Programmable Logic Controllers (PLC), while addressing their unique performance, reliability, and safety requirements The document provides an overview of ICS and typical system topologies, identifies typical threats and vulnerabilities to these systems, and provides recommended security countermeasures to mitigate the associated risks

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Guide to Industrial Control Systems (ICS) Security

This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal polynomial bases, analytical formulae for calculating the global sensitivity indices in terms of the expansion coefficients, and dimension-reduction integration for estimating the expansion coefficients. Due to identical dimensional structures of PDD and analysis-of-variance decomposition, the proposed method facilitates simple and direct calculation of the global sensitivity indices. Numerical results of the global sensitivity indices computed for smooth systems reveal significantly higher convergence rates of the PDD approximation than those from existing methods, including polynomial chaos expansion, random balance design, state-dependent parameter, improved Sobol’s method, and sampling-based methods. However, for non-smooth functions, the convergence properties of the PDD solution deteriorate to a great extent, warranting further improvements. The computational complexity of the PDD method is polynomial, as opposed to exponential, thereby alleviating the curse of dimensionality to some extent. Mathematical modeling of complex systems often requires sensitivity analysis to determine how an output variable of interest is influenced by individual or subsets of input variables. A traditional local sensitivity analysis entails gradients or derivatives, often invoked in design optimization, describing changes in the model response due to the local variation of input. Depending on the model output, obtaining gradients or derivatives, if they exist, can be simple or difficult. In contrast, a global sensitivity analysis (GSA), increasingly becoming mainstream, characterizes how the global variation of input, due to its uncertainty, impacts the overall uncertain behavior of the model. In other words, GSA constitutes the study of how the output uncertainty from a mathematical model is divvied up, qualitatively or quantitatively, to distinct sources of input variation in the model [1].

Reliability Engineering and System Safety

The National Academy of Sciences founded The National Academies Press (NAP) with the goal of publishing reports of all four national academies. Annually, NAP publishes more than 200 books from the fields of science, engineering and medicine and offers more than 4000 titles in PDF on its website (http://www.nap.edu/) free of charge.

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The National Academies Press

Aspects concerning the structure and behaviours of individual networks have been studied intensely in the past decade, but the exploration of interdependent systems in the context of complex networks has started only recently. This article reviews a general framework for modelling the percolation properties of interacting networks and the first results drawn from its study.

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Networks formed from interdependent networks

The notion that our nation's critical infrastructures are highly interconnected and mutually dependent in complex ways, both physically and through a host of information and communications technologies (so-called "cyberbased systems"), is more than an abstract, theoretical concept. As shown by the 1998 failure of the Galaxy 4 telecommunications satellite, the prolonged power crisis in California, and many other recent infrastructure disruptions, what happens to one infrastructure can directly and indirectly affect other infrastructures, impact large geographic regions and send ripples throughout the national a global economy. This article presents a conceptual framework for addressing infrastructure interdependencies that could serve as the basis for further understanding and scholarship in this important area. We use this framework to explore the challenges and complexities of interdependency. We set the stage for this discussion by explicitly defining the terms infrastructure, infrastructure dependencies, and infrastructure interdependencies and introducing the fundamental concept of infrastructures as complex adaptive systems. We then focus on the interrelated factors and system conditions that collectively define the six dimensions. Finally, we discuss some of the research challenges involved in developing, applying, and validating modeling and simulation methodologies and tools for infrastructure interdependency analysis.

T.K. Kelly

Papers

Identifying, understanding, and analyzing critical infrastructure interdependencies

Knowing the Enemy