The SLH framework for modeling quantum input-output networks

Many emerging quantum technologies demand precise engineering and control over networks consisting of quantum mechanical degrees of freedom connected by propagating electromagnetic fields, or quantum input-output networks. Here we review recent progress in theory and experiment related to such quantum input-output networks, with a focus on the SLH framework, a powerful modeling framework for networked quantum systems that is naturally endowed with properties such as modularity and hierarchy. We begin by explaining the physical approximations required to represent any individual node of a network, eg. atoms in cavity or a mechanical oscillator, and its coupling to quantum fields by an operator triple $(S,L,H)$. Then we explain how these nodes can be composed into a network with arbitrary connectivity, including coherent feedback channels, using algebraic rules, and how to derive the dynamics of network components and output fields. The second part of the review discusses several extensions to the basic SLH framework that expand its modeling capabilities, and the prospects for modeling integrated implementations of quantum input-output networks. In addition to summarizing major results and recent literature, we discuss the potential applications and limitations of the SLH framework and quantum input-output networks, with the intention of providing context to a reader unfamiliar with the field.Comment: 60 pages, 14 figures. We are still interested in receiving correction

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

Networking - A Statistical Physics Perspective

Efficient networking has a substantial economic and societal impact in a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption require new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with non-linear large scale systems. This paper aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications.Comment: (Review article) 71 pages, 14 figure

Stochastic Dynamics of Cascading Failures in Electric-Cyber Infrastructures

Emerging smart grids consist of tightly-coupled systems, namely a power grid and a communication system. While today\u27s power grids are highly reliable and modern control and communication systems have been deployed to further enhance their reliability, historical data suggest that they are yet vulnerable to large failures. A small set of initial disturbances in power grids in conjunction with lack of effective, corrective actions in a timely manner can trigger a sequence of dependent component failures, called cascading failures. The main thrust of this dissertation is to build a probabilistic framework for modeling cascading failures in power grids while capturing their interactions with the coupled communication systems so that the risk of cascading failures in the composite complex electric-cyber infrastructures can be examined, analyzed and predicted. A scalable and analytically tractable continuous-time Markov chain model for stochastic dynamics of cascading failures in power grids is constructed while retaining key physical attributes and operating characteristics of the power grid. The key idea of the proposed framework is to simplify the state space of the complex power system while capturing the effects of the omitted variables through the transition probabilities and their parametric dependence on physical attributes and operating characteristics of the system. In particular, the effects of the interdependencies between the power grid and the communication system have been captured by a parametric formulation of the transition probabilities using Monte-Carlo simulations of cascading failures. The cascading failures are simulated with a coupled power-system simulation framework, which is also developed in this dissertation. Specifically, the probabilistic model enables the prediction of the evolution of the blackout probability in time. Furthermore, the asymptotic analysis of the blackout probability as time tends to infinity enables the calculation of the probability mass function of the blackout size, which has been shown to have a heavy tail, e.g., power-law distribution, specifically when the grid is operating under stress scenarios. A key benefit of the model is that it enables the characterization of the severity of cascading failures in terms of a set of operating characteristics of the power grid. As a generalization to the Markov chain model, a regeneration-based model for cascading failures is also developed. The regeneration-based framework is capable of modeling cascading failures in a more general setting where the probability distribution of events in the system follows an arbitrarily specified distribution with non-Markovian characteristics. Further, a novel interdependent Markov chain model is developed, which provides a general probabilistic framework for capturing the effects of interactions among interdependent infrastructures on cascading failures. A key insight obtained from this model is that interdependencies between two systems can make two individually reliable systems behave unreliably. In particular, we show that due to the interdependencies two chains with non-heavy tail asymptotic failure distribution can result in a heavy tail distribution when coupled. Lastly, another aspect of future smart grids is studied by characterizing the fundamental bounds on the information rate in the sensor network that monitors the power grid. Specifically, a distributed source coding framework is presented that enables an improved estimate of the lower bound for the minimum required communication capacity to accurately describe the state of components in the information-centric power grid. The models developed in this dissertation provide critical understanding of cascading failures in electric-cyber infrastructures and facilitate reliable and quick detection of the risk of blackouts and precursors to cascading failures. These capabilities can guide the design of efficient communication systems and cascade aware control policies for future smart grids

Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

Social Reinforcement: Cascades, Entrapment and Tipping

There are many social situations in which the actions of different agents reinforce each other. These include network effects and the threshold models used by sociologists (Granovetter, Watts) as well as Leibenstein's "bandwagon effects." We model such situations as a game with increasing differences, and show that tipping of equilibria as discussed by Schelling, cascading and Dixit's results on clubs with entrapment are natural consequences of this mutual reinforcement. If there are several equilibria, one of which Pareto dominates, then we show that the inefficient equilibria can be tipped to the efficient one, a result of interest in the context of coordination problems.