We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

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.

/pdf/catastrophic-cascade-of-failures-in-interdependent-networks-414vwz21eb.pdf

Catastrophic cascade of failures in interdependent networks

This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

Coverage control for mobile sensing networks

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others We also survey and discuss existing data sets that can be represented as multilayer networks We review attempts to generalize single-layer-network diagnostics to multilayer networks We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks We conclude with a summary and an outlook

Multilayer Networks

[서평]「The Unified Modeling Language User Guide」

We investigate the consequence of failures, occurring on the electrical grid, on a telecommunication network We have focused on the Italian electrical transmission network and the backbone of the internet network for research (GARR) Electrical network has been simulated using the DC power flow method; data traffic on GARR by a model of the TCP/IP basic features The status of GARR nodes has been related to the power level of the (geographically) neighbouring electrical nodes (if the power level of a node is lower than a threshold, all communication nodes depending on it are switched off) The electrical network has been perturbed by lines removal: the consequent re-dispatching reduces the power level in all nodes This reduces the number of active GARR nodes and, thus, its Quality of Service (QoS) Averaging over many configurations of perturbed electrical network, we have correlated the degradation of the electrical network with that of the communication network Results point to a sizeable amplification of the effects of faults on the electrical network on the communication network, also in the case of a moderate coupling between the two networks

Modelling interdependent infrastructures using interacting dynamical models

Critical infrastructure dependency assessment using the input–output inoperability model

Welfare in developed countries strongly relies on many heterogeneous infrastructures generically named as critical infrastructures. These infrastructures, designed as autonomous systems, are actually more and more mutually dependent. This introduces new and extremely dangerous vulnerabilities in the overall system because an accidental or a malicious fault (e.g. terroristic attack) could exploit these 'connections'to unpredictably spread, amplifying its negative consequences and affecting unforeseeable and haphazard sets of users. In this paper, we analyse performance degradation induced on this system of systems by the presence and spreading of failures in order to emphasise the most critical links existing among different phenomena. Due to uncertainties that characterise these systems, we use Fuzzy Numbers (FNs) to represent involved quantities. This allows a modelling approach that can be set up using also qualitative information that are easier to obtain from experts and stakeholders. Moreover, this choice brings to a better characterisation of the level of confidence of our results. Preliminary results on a simple case study illustrate the effectiveness of the proposed approach.

Failures propagation in critical interdependent infrastructures

A major mission area of homeland security is protecting critical infrastructures and key assets. Homeland Security Presidential Directive 7 (HSPD-7) identified seventeen critical infrastructure sectors. This chapter presents two cases. The first case, "Catastrophic Pandemic: Cases in Ethical Decision-Making," provides a worst-case scenario of a worldwide influenza pandemic based on planning documents prepared by the Centers for Disease Control and Prevention (CDC) and the US Department of Health and Human Services (HHS). The second case, "The Impact of Cyber-Security on Critical Infrastructure Protection: The Advanced Persistent Threat," highlights how important the cyber-infrastructure is to critical infrastructure protection across all sectors. The advanced persistent threat highlights a new type of malicious actor that routinely conducts attacks against the cyber-infrastructure using cyber-attack tools. Because of the interconnected nature of the cyber-infrastructure, these attacks can spread quickly and have debilitating effects, as highlighted in the examples in this case.

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Roberto Setola

Papers

Modelling interdependent infrastructures using interacting dynamical models

Critical infrastructure dependency assessment using the input–output inoperability model

Failures propagation in critical interdependent infrastructures

Critical Infrastructure Protection

Agent-based input–output interdependency model