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

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

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.

/pdf/networks-formed-from-interdependent-networks-56ypv3825y.pdf

Networks formed from interdependent networks

Today's strongly connected, global networks have produced highly interdependent systems that we do not understand and cannot control well. These systems are vulnerable to failure at all scales, posing serious threats to society, even when external shocks are absent. As the complexity and interaction strengths in our networked world increase, man-made systems can become unstable, creating uncontrollable situations even when decision-makers are well-skilled, have all data and technology at their disposal, and do their best. To make these systems manageable, a fundamental redesign is needed. A 'Global Systems Science' might create the required knowledge and paradigm shift in thinking.

Globally networked risks and how to respond

Review on modeling and simulation of interdependent critical infrastructure systems

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

Tissue engineering of blood vessels is a promising strategy in regenerative medicine with a broad spectrum of potential applications. However, many hurdles for tissue-engineered vascular grafts, such as poor mechanical properties, thrombogenicity and cell over-growth inside the construct, need to be overcome prior to the clinical application. To surmount these shortcomings, we developed a poly-L-lactide (PLLA)/poly-epsilon-caprolactone (PCL) scaffold releasing heparin by a combination of electrospinning and fused deposition modeling technique. PLLA/heparin scaffolds were produced by electrospinning in tubular shape and then fused deposition modeling was used to armor the tube with a single coil of PCL on the outer layer to improve mechanical properties. Scaffolds were then seeded with human mesenchymal stem cells (hMSCs) and assayed in terms of morphology, mechanical tensile strength, cell viability and differentiation. This particular scaffold design allowed the generation of both a drug delivery system amenable to surmount thrombogenic issues and a microenvironment able to induce endothelial differentiation. At the same time, the PCL external coiling improved mechanical resistance of the microfibrous scaffold. By the combination of two notable techniques in biofabrication--electrospinning and FDM--and exploiting the biological effects of heparin, we developed an ad hoc differentiating device for hMSCs seeding, able to induce differentiation into vascular endothelium.

https://iopscience.iop.org/article/10.1088/1758-5082/2/1/014102/pdf

Combining electrospinning and fused deposition modeling for the fabrication of a hybrid vascular graft.

In this paper, a simulation tool specifically designed for the analysis of heterogeneous and (inter)dependent infrastructures is proposed. The simulator, named Critical Infrastructure Simulation by Interdependent Agents (CISIA), adopts a modular and sufficiently abstract representation of the different infrastructures' components to allow consistent descriptions, starting from the incomplete and generic data acquirable from stakeholders. An important part of the modelling effort was reserved for the representation of the dependencies and interdependencies, these being the cause of the complex behaviours we are interested in. Each component interacts with the others via a multitude of mechanisms that codify different concepts of proximity. The simulator has been used to analyse, in a simplified scenario, crisis evolution in the urban area of Rome, in the presence of a failure in the electric power system.

Simulation of heterogeneous and interdependent critical infrastructures

Model Critical Infrastructure via a Mixed Holistic-Reductionistic Approach

Politzer manoeuvre causes retrograde inflation of the middle ear by forcing air through the Eustachian tube. It has been proposed as nonsurgical treatment of middle ear with effusion, Eustachian tube dysfunction and negative middle ear pressure from elevation changes. Even if Politzer manoeuvre can be considered a classical technique, it is generally performed without any feedback about its correctness neither about qualitative evidence about its efficacy. In this paper we describe an innovative device, named OtoFree, specifically designed to support medical doctors during Politzer manoeuvre. OtoFree provides information about the correctness of the manoeuvre and also useful hints about the treatments results.

S. De Porcellinis

Papers

Modelling interdependent infrastructures using interacting dynamical models

Combining electrospinning and fused deposition modeling for the fabrication of a hybrid vascular graft.

Simulation of heterogeneous and interdependent critical infrastructures

Model Critical Infrastructure via a Mixed Holistic-Reductionistic Approach

An innovative device to support Politzer manoeuvre