Infrastructure network vulnerability

The work presented in this paper aims to propose a methodology of analyzing infrastructure network vulnerability in the field of prevention or reduction of the natural disaster consequences. After a state of the art on vulnerability models in the academic literature, the various vulnerability factors are classified and discussed. Eventually, a general model of vulnerability analysis including societal parameters is presented

Recovery of Interdependent Networks

Recent network research has focused on the cascading failures in a system of interdependent networks and the necessary preconditions for system collapse. An important question that has not been addressed is how to repair a failing system before it suffers total breakdown. Here we introduce a recovery strategy of nodes and develop an analytic and numerical framework for studying the concurrent failure and recovery of a system of interdependent networks based on an efficient and practically reasonable strategy. Our strategy consists of repairing a fraction of failed nodes, with probability of recovery $\gamma$, that are neighbors of the largest connected component of each constituent network. We find that, for a given initial failure of a fraction $1-p$ of nodes, there is a critical probability of recovery above which the cascade is halted and the system fully restores to its initial state and below which the system abruptly collapses. As a consequence we find in the plane $\gamma-p$ of the phase diagram three distinct phases. A phase in which the system never collapses without being restored, another phase in which the recovery strategy avoids the breakdown, and a phase in which even the repairing process cannot avoid the system collapse

Control energy of complex networks towards distinct mixture states

Controlling complex networked systems is a real-world puzzle that remains largely unsolved. Despite recent progress in understanding the structural characteristics of network control energy, target state and system dynamics have not been explored. We examine how varying the final state mixture affects the control energy of canonical and conformity-incorporated dynamical systems. We find that the control energy required to drive a network to an identical final state is lower than that required to arrive a non-identical final state. We also demonstrate that it is easier to achieve full control in a conformity-based dynamical network. Finally we determine the optimal control strategy in terms of the network hierarchical structure. Our work offers a realistic understanding of the control energy within the final state mixture and sheds light on controlling complex systems.This work was funded by The National Natural Science Foundation of China (Grant Nos. 61763013, 61703159, 61403421), The Natural Science Foundation of Jiangxi Province (No. 20171BAB212017), The Measurement and Control of Aircraft at Sea Laboratory (No. FOM2016OF010), and China Scholarship Council (201708360048). The Boston University Center for Polymer Studies is supported by NSF Grants PHY-1505000, CMMI-1125290, and CHE-1213217, and by DTRA Grant HDTRA1-14-1-0017. (61763013 - National Natural Science Foundation of China; 61703159 - National Natural Science Foundation of China; 61403421 - National Natural Science Foundation of China; 20171BAB212017 - Natural Science Foundation of Jiangxi Province; FOM2016OF010 - Measurement and Control of Aircraft at Sea Laboratory; 201708360048 - China Scholarship Council; PHY-1505000 - NSF; CMMI-1125290 - NSF; CHE-1213217 - NSF; HDTRA1-14-1-0017 - DTRA)Published versio

Complexity and robustness of structures against extreme events

Civil structures are designed to support the loads acting on them. At present, the common practitioner considers both ordinary (winds, snow, accidental loads) and extreme events (earthquake, fire), combines the actions in such a way that, once the resistance of the elements is determined, the probability of failure is limited to a prescribed value. The set of events that may interest the structure is known and, therefore, a statistics of the actions is defined a priori. However, other events that are not forecastable may interest the construction. The sources of such events, called “Black Swans” after Taleb, are unknown, as well as their magnitude. For ensuring the integrity of the construction in such situations, which imply large damages, robust measures have to be taken (Chapter 3). Structural engineering is not the only domain in which unexpected events occur. Nature is the realm of contrasts. By means of evolution, living species differentiates, differentiated, in order to survive and reproduce. Various strategies were implemented in order to guarantee a biological robustness. Such mechanisms evoke one fundamental property of systems, the complexity and the connectivity between the components. The interaction between the parts makes the whole system more robust and tolerant to errors and damages (Chapters 1 and 2). Robustness in structures is implemented through classical strategies, which tend to limit the extent of damages through a design based on the consequences (Chapter 4). Being inspired by natural strategies, the idea of complexity in structural engineering is explored. Many issues arise, since a proper definition of this term has not been stated yet (Chapters 5 and 6). The ef- fects of element removal on frame structures, which represent an example of highly connected structural scheme, are investigated. As a result of simple simulations, the trend observed in Nature, which wants the complex systems to be robust to random damages, are spotted in the loaded structural schemes (Chapter 7)

Structural engineering of evolving complex dynamical networks

Networks are ubiquitous in nature and many natural and man-made systems can be modelled as networked systems. Complex networks, systems comprising a number of nodes that are connected through edges, have been frequently used to model large-scale systems from various disciplines such as biology, ecology, and engineering. Dynamical systems interacting through a network may exhibit collective behaviours such as synchronisation, consensus, opinion formation, flocking and unusual phase transitions. Evolution of such collective behaviours is highly dependent on the structure of the interaction network. Optimisation of network topology to improve collective behaviours and network robustness can be achieved by intelligently modifying the network structure. Here, it is referred to as "Engineering of the Network". Although coupled dynamical systems can develop spontaneous synchronous patterns if their coupling strength lies in an appropriate range, in some applications one needs to control a fraction of nodes, known as driver nodes, in order to facilitate the synchrony. This thesis addresses the problem of identifying the set of best drivers, leading to the best pinning control performance. The eigen-ratio of the augmented Laplacian matrix, that is the largest eigenvalue divided by the second smallest one, is chosen as the controllability metric. The approach introduced in this thesis is to obtain the set of optimal drivers based on sensitivity analysis of the eigen-ratio, which requires only a single computation of the eigenvector associated with the largest eigenvalue, and thus is applicable for large-scale networks. This leads to a new "controllability centrality" metric for each subset of nodes. Simulation results reveal the effectiveness of the proposed metric in predicting the most important driver(s) correctly.     Interactions in complex networks might also facilitate the propagation of undesired effects, such as node/edge failure, which may crucially affect the performance of collective behaviours. In order to study the effect of node failure on network synchronisation, an analytical metric is proposed that measures the effect of a node removal on any desired eigenvalue of the Laplacian matrix. Using this metric, which is based on the local multiplicity of each eigenvalue at each node, one can approximate the impact of any node removal on the spectrum of a graph. The metric is computationally efficient as it only needs a single eigen-decomposition of the Laplacian matrix. It also provides a reliable approximation for the "Laplacian energy" of a network. Simulation results verify the accuracy of this metric in networks with different topologies. This thesis also considers formation control as an application of network synchronisation and studies the "rigidity maintenance" problem, which is one of the major challenges in this field. This problem is to preserve the rigidity of the sensing graph in a formation during motion, taking into consideration constraints such as line-of-sight requirements, sensing ranges and power limitations. By introducing a "Lattice of Configurations" for each node, a distributed rigidity maintenance algorithm is proposed to preserve the rigidity of the sensing network when failure in a sensing link would result in loss of rigidity. The proposed algorithm recovers rigidity by activating, almost always, the minimum number of new sensing links and considers real-time constraints of practical formations. A sufficient condition for this problem is proved and tested via numerical simulations. Based on the above results, a number of other areas and applications of network dynamics are studied and expounded upon in this thesis

Multilayer 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.Comment: Working paper; 59 pages, 8 figure

Power system vulnerability and performance: application from complexity scienze and complex network

Power system has been acknowledged as a complex system owing to its complexity resulting from interactions of different layers which include physical layer like generators, transformers, substations and cyber layer like communication units and human decision layer. Complex network theory has been widely used to analyze the power grids from basic topological properties to statistic robustness analysis and dynamic resilience property. However, there are still many problems need to be addressed. This thesis will pay more attention on the application and extension of complexity science and complex network theory in power system analysis from different aspects

Information and Dynamics in Urban Traffic Networks

The study of complex systems has intensified in recent years. Researchers from many different disciplines have realised that the study of systems possessing a large number of degrees of freedom interacting in a non-linear way can offer insights into problems in engineering, biology, economics and many other fields besides. Among the themes in complexity, we focus here the issues of congestion and congestion emergence in the context of urban networks, with particular reference to the effects of dissemination of information about the system’s status. This topic is of great relevance today, due to the increasing availability of real-time information about traffic conditions and the large diffusion of personal devices that allow travellers to access such information. Through the analysis of a few simple models of information propagation in urban environment, we uncover that, contrarily to the naïve expectation, complete information is often detrimental to the global performance of the urban traffic network. Indeed, global or long-range dissemination induces correlations in the systems that become a source for spatial disorder, making the system more prone to the emergence of congested states and pushing it away from its Wardrop equilibrium. The models we study range from simple flow models on network to complete agent-based simulations on real-world networks with interacting agents and dynamical information. We then analyse real data, coming from London’s network of traffic detectors. We confirm that the heterogeneity in the distribution of traffic flow and occupancies across the network reduces its performances, consistently with the results obtained for the information propagation models. In addition, we find a rich phenomenology strikingly similar to the one found in critical self-organised systems. Indeed, we measure power-law correlation functions and 1/f power spectra, hinting to long spatial and temporal effects in the traffic flow, and confirm this result through the community detection analysis of the detectors’ correlation network, which showing that the whole urban area behaves as a single large chunk. We conclude discussing the origin of these features and how they can be used to improve the network performances

On the Impact of Network Topology on Systemic Risk: Network Reconstruction, Stress Testing and Control

In this thesis I undertake four projects that investigate the influence of network topology on financial contagion. In the first project I study the ability of three net- work models to reconstruct the topology and contagion dynamics of a real interbank network. This allows me to identify the main topological properties of networks that affect financial contagion. In the third and fourth projects I develop a framework to reverse stress test interbank networks. Based on this framework I propose a strategy to reduce systemic losses and I test the strategy in interbank networks with different topologies. I develop the methodological background to the reverse stress testing framework in the second project. In this project I study network control theory, to investigate the influence of network topology on the cost of managing the dynamics of networks

Real-time Prediction of Cascading Failures in Power Systems

Blackouts in power systems cause major financial and societal losses, which necessitate devising better prediction techniques that are specifically tailored to detecting and preventing them. Since blackouts begin as a cascading failure (CF), an early detection of these CFs gives the operators ample time to stop the cascade from propagating into a large-scale blackout. In this thesis, a real-time load-based prediction model for CFs using phasor measurement units (PMUs) is proposed. The proposed model provides load-based predictions; therefore, it has the advantages of being applicable as a controller input and providing the operators with better information about the affected regions. In addition, it can aid in visualizing the effects of the CF on the grid. To extend the functionality and robustness of the proposed model, prediction intervals are incorporated based on the convergence width criterion (CWC) to allow the model to account for the uncertainties of the network, which was not available in previous works. Although this model addresses many issues in previous works, it has limitations in both scalability and capturing of transient behaviours. Hence, a second model based on recurrent neural network (RNN) long short-term memory (LSTM) ensemble is proposed. The RNN-LSTM is added to better capture the dynamics of the power system while also giving faster responses. To accommodate for the scalability of the model, a novel selection criterion for inputs is introduced to minimize the inputs while maintaining a high information entropy. The criteria include distance between buses as per graph theory, centrality of the buses with respect to fault location, and the information entropy of the bus. These criteria are merged using higher statistical moments to reflect the importance of each bus and generate indices that describe the grid with a smaller set of inputs. The results indicate that this model has the potential to provide more meaningful and accurate results than what is available in the previous literature and can be used as part of the integrated remedial action scheme (RAS) system either as a warning tool or a controller input as the accuracy of detecting affected regions reached 99.9% with a maximum delay of 400 ms. Finally, a validation loop extension is introduced to allow the model to self-update in real-time using importance sampling and case-based reasoning to extend the practicality of the model by allowing it to learn from historical data as time progresses