Hurricane Ida's blackout-heatwave compound risk in a changing climate

The emerging tropical cyclone (TC)-blackout-heatwave compound risk under climate change is not well understood. In this study, we employ projections of TCs, sea level rise, and heatwaves, in conjunction with power system resilience modeling, to evaluate historical and future TC-blackout-heatwave compound risk in Louisiana, US. We find that the return period for a compound event comparable to Hurricane Ida (2021), with approximately 35 million customer hours of simultaneous power outage and heatwave exposure in Louisiana, is around 278 years in the historical climate of 1980-2005. Under the SSP5-8.5 emissions scenario, this return period is projected to decrease to 16.2 years by 2070-2100, a ~17 times reduction. Under the SSP2-4.5 scenario, it decreases to 23.1 years, representing a ~12 times reduction. Heatwave intensification is the primary driver of this increased risk, reducing the return period by approximately 5 times under SSP5-8.5 and 3 times under SSP2-4.5. Increased TC activity is the second driver, reducing the return period by 40% and 34% under the respective scenarios. These findings enhance our understanding of compound climate hazards and inform climate adaptation strategies.

Network analysis with quantum dynamics clarifies why photosystem II exploits both chlorophyll a and b

In green plants, chlorophyll a and chlorophyll b are the predominant pigments bound to light-harvesting proteins. While the individual characteristics of these chlorophylls are well understood, the advantages of their coexistence remain unclear. In this study, we establish a method to simulate excitation energy transfer within the entire photosystem II supercomplex by using network analysis integrated with quantum dynamic calculations. We then investigate the effects of the coexistence of chlorophyll a and chlorophyll b by comparing various chlorophyll compositions. Our results reveal that the natural chlorophyll composition allows the excited energy to preferentially flow through specific domains that act as safety valves, preventing downstream overflow. Our findings suggest that the light-harvesting proteins in a photosystem II supercomplex achieve evolutionary advantages with the natural chlorophyll a/b ratio, capturing light energy efficiently and safely across various light intensities. Using our framework, one can better understand how green plants harvest light energy and adapt to changing environmental conditions.

A New Approach to Electrical Fault Detection in Urban Structures Using Dynamic Programming and Optimized Support Vector Machines

Electrical power systems are crucial, yet vulnerable, due to their complex and interconnected nature, necessitating effective fault detection and diagnostics to ensure stability and prevent disruptions. Advances in artificial intelligence (AI) and the Internet of Things (IoT) have transformed the ability to identify and resolve electrical system problems efficiently. Electrical systems operate at various scales, ranging from individual households to large-scale regional grids. In this study, we focus on medium-scale urban infrastructures. These environments present unique electrical challenges, such as phase imbalances and transient voltage fluctuations, which require robust fault detection mechanisms. This work investigates the use of AI with dynamic programming and a support vector machine (SVM) to improve fault detection. The data collected from voltage measurements in urban office buildings with smart meters over a period of six weeks was used to develop an AI model, demonstrating its applicability to similar urban infrastructures. This model achieved high accuracy in detecting system failures, identifying them with a performance greater than 99%, highlighting the potential of smart sensing technologies combined with AI to improve urban infrastructure management. The integration of smart sensors and advanced data analytics significantly increases the reliability and efficiency of energy systems, promoting sustainable and resilient urban environments.

Quantifying cascading power outages during climate extremes considering renewable energy integration

Climate extremes, such as hurricanes, combined with large-scale integration of environment-sensitive renewables, could exacerbate the risk of widespread power outages. We introduce a coupled climate-energy model for cascading power outages, which comprehensively captures the impacts of climate extremes on renewable generation, and transmission and distribution networks. The model is validated with the 2022 Puerto Rico catastrophic blackout during Hurricane Fiona - a unique system-wide blackout event with complete records of weather-induced outages. The model reveals a resilience pattern that was not captured by the previous models: early failure of certain critical components enhances overall system resilience. Sensitivity analysis on various scenarios of behind-the-meter solar integration demonstrates that lower integration levels (below 45%, including the current level) exhibit minimal impact on system resilience in this event. However, surpassing this critical level without pairing it with energy storage can exacerbate the probability of catastrophic blackouts.

Hybrid universality classes of systemic cascades

Cascades are self-reinforcing processes underlying the systemic risk of many complex systems. Understanding the universal aspects of these phenomena is of fundamental interest, yet typically bound to numerical observations in ad-hoc models and limited insights. Here, we develop a unifying approach that reveals two distinct universality classes of cascades determined by the global symmetry of the cascading process. We provide hyperscaling arguments predicting hybrid critical phenomena characterized by a combination of both mean-field spinodal exponents and d-dimensional corrections, and show how parity invariance influences the geometry and lifetime of critical avalanches. Our theory applies to a wide range of networked systems in arbitrary dimensions, as we demonstrate by simulations encompassing classic and novel cascade models, revealing universal principles of cascade critical phenomena amenable to experimental validation.

Cascades Towards Noise-Induced Transitions on Networks Revealed Using Information Flows

Complex networks, from neuronal assemblies to social systems, can exhibit abrupt, system-wide transitions without external forcing. These endogenously generated "noise-induced transitions" emerge from the intricate interplay between network structure and local dynamics, yet their underlying mechanisms remain elusive. Our study unveils two critical roles that nodes play in catalyzing these transitions within dynamical networks governed by the Boltzmann-Gibbs distribution. We introduce the concept of "initiator nodes", which absorb and propagate short-lived fluctuations, temporarily destabilizing their neighbors. This process initiates a domino effect, where the stability of a node inversely correlates with the number of destabilized neighbors required to tip it. As the system approaches a tipping point, we identify "stabilizer nodes" that encode the system's long-term memory, ultimately reversing the domino effect and settling the network into a new stable attractor. Through targeted interventions, we demonstrate how these roles can be manipulated to either promote or inhibit systemic transitions. Our findings provide a novel framework for understanding and potentially controlling endogenously generated metastable behavior in complex networks. This approach opens new avenues for predicting and managing critical transitions in diverse fields, from neuroscience to social dynamics and beyond.

Cascading Failure in Cyber-Physical Systems: A Review on Failure Modeling and Vulnerability Analysis

Cascading failures pose a significant security threat to networked systems, with recent global incidents underscoring their destructive potential. The security threat of cascading failures has always existed, but the evolution of cyber-physical systems (CPSs) has introduced novel dimensions to cascading failures, intensifying their threats owing to the intricate fusion of cyber and physical domains. Addressing these threats requires a nuanced understanding achieved through failure modeling and vulnerability analysis. By analyzing the historical failures in different CPSs, the cascading failure in CPSs is comprehensively defined as a complicated propagation process in coupled cyber and physical systems, initialized by natural accidents or human interference, which exhibits a progressive evolution within the networked structure and ultimately results in unexpected large-scale systemic failures. Subsequently, this study advances the development of instructions for modeling cascading failures and conducting vulnerability analyses within CPSs. The examination also delves into the core challenges inherent in these methodologies. Moreover, a comprehensive survey and classification of extant research methodologies and solutions are undertaken, accompanied by a concise evaluation of their advancements and limitations. To validate the performance of these methodologies, numerical experiments are conducted to ascertain their distinct features. In conclusion, this article advocates for future research initiatives, particularly emphasizing the exploration of uncertainty analysis, defense strategies, and verification platforms. By addressing these areas, the resilience of CPSs against cascading failures can be significantly enhanced.

Focus on the disruption of networks and system dynamics

Networks are designed to ensure proper functioning and sustained operability of the underlying systems. However, disruptions are generally unavoidable. Internal interactions and external environmental effects can lead to the removal of nodes or edges, resulting in unexpected collective behavior. For instance, a single failing node or removed edge may trigger a cascading failure in an electric power grid. This Focus Issue delves into recent advances in understanding the impacts of disruptions on networks and their system dynamics. The central theme is the disruption of networks and their dynamics from the perspectives of both data-driven analysis as well as modeling. Topics covered include disruptions in the dynamics of empirical systems such as nuclear reaction networks, infrastructure networks, social networks, epidemics, brain dynamics, and physiology. Emphasis is placed on various phenomena in collective behavior, including critical phase transitions, irregular collective dynamics, complex patterns of synchrony and asynchrony, chimera states, and anomalous oscillations. The tools used for these studies include control theory, diffusion processes, stochastic processes, and network theory. This collection offers an exciting addition to the evolving landscape of network disruption research.

Scalable synchronization cluster in networked chaotic oscillators

Cluster synchronization in synthetic networks of coupled chaotic oscillators is investigated. It is found that despite the asymmetric nature of the network structure, a subset of the oscillators can be synchronized as a cluster while the other oscillators remain desynchronized. Interestingly, with the increase in the coupling strength, the cluster is expanding gradually by recruiting the desynchronized oscillators one by one. This new synchronization phenomenon, which is named "scalable synchronization cluster," is explored theoretically by the method of eigenvector-based analysis, and it is revealed that the scalability of the cluster is attributed to the unique feature of the eigenvectors of the network coupling matrix. The transient dynamics of the cluster in response to random perturbations are also studied, and it is shown that in restoring to the synchronization state, oscillators inside the cluster are stabilized in sequence, illustrating again the hierarchy of the oscillators. The findings shed new light on the collective behaviors of networked chaotic oscillators and are helpful for the design of real-world networks where scalable synchronization clusters are concerned.

Predicting dynamic stability from static features in power grid models using machine learning

A reliable supply with electric power is vital for our society. Transmission line failures are among the biggest threats for power grid stability as they may lead to a splitting of the grid into mutual asynchronous fragments. New conceptual methods are needed to assess system stability that complement existing simulation models. In this article, we propose a combination of network science metrics and machine learning models to predict the risk of desynchronization events. Network science provides metrics for essential properties of transmission lines such as their redundancy or centrality. Machine learning models perform inherent feature selection and, thus, reveal key factors that determine network robustness and vulnerability. As a case study, we train and test such models on simulated data from several synthetic test grids. We find that the integrated models are capable of predicting desynchronization events after line failures with an average precision greater than 0.996 when averaging over all datasets. Learning transfer between different datasets is generally possible, at a slight loss of prediction performance. Our results suggest that power grid desynchronization is essentially governed by only a few network metrics that quantify the networks' ability to reroute the flow without creating exceedingly high static line loadings.

Dynamics of cascades in spatial interdependent networks

The dynamics of cascading failures in spatial interdependent networks significantly depends on the interaction range of dependency couplings between layers. In particular, for an increasing range of dependency couplings, different types of phase transition accompanied by various cascade kinetics can be observed, including mixed-order transition characterized by critical branching phenomena, first-order transition with nucleation cascades, and continuous second-order transition with weak cascades. We also describe the dynamics of cascades at the mutual mixed-order resistive transition in interdependent superconductors and show its similarity to that of percolation of interdependent abstract networks. Finally, we lay out our perspectives for the experimental observation of these phenomena, their phase diagrams, and the underlying kinetics, in the context of physical interdependent networks. Our studies of interdependent networks shed light on the possible mechanisms of three known types of phase transitions, second order, first order, and mixed order as well as predicting a novel fourth type where a microscopic intervention will yield a macroscopic phase transition.

Connectome-based modelling of neurodegenerative diseases: towards precision medicine and mechanistic insight

Neurodegenerative diseases are the most common cause of dementia. Although their underlying molecular pathologies have been identified, there is substantial heterogeneity in the patterns of progressive brain alterations across and within these diseases. Recent advances in neuroimaging methods have revealed that pathological proteins accumulate along specific macroscale brain networks, implicating the network architecture of the brain in the system-level pathophysiology of neurodegenerative diseases. However, the extent to which 'network-based neurodegeneration' applies across the wide range of neurodegenerative disorders remains unclear. Here, we discuss the state-of-the-art of neuroimaging-based connectomics for the mapping and prediction of neurodegenerative processes. We review findings supporting brain networks as passive conduits through which pathological proteins spread. As an alternative view, we also discuss complementary work suggesting that network alterations actively modulate the spreading of pathological proteins between connected brain regions. We conclude this Perspective by proposing an integrative framework in which connectome-based models can be advanced along three dimensions of innovation: incorporating parameters that modulate propagation behaviour on the basis of measurable biological features; building patient-tailored models that use individual-level information and allowing model parameters to interact dynamically over time. We discuss promises and pitfalls of these strategies for improving disease insights and moving towards precision medicine.

Synchronization stability of power-grid-tied converters

Synchronization stability is one of central problems in power systems, and it is becoming much more complicated with the high penetration of renewable energy and power electronics devices. In this paper, we review recent work by several nonlinear models for renewable-dominated power systems in terms of multiple timescales, in particular, grid-tied converters within the DC voltage timescale. For the simplest model, a second-order differential equations called the generalized swing equation by considering only the phase-locked loop (PLL) is obtained, which shows a similar form with the well-known swing equation for a synchronous generator in the traditional power systems. With more outer controllers included, fourth-order and fifth-order models can be obtained. The fourth-order model is called the extended generalized swing equation, exhibiting the combined function of grid synchronization and active power balance on the DC capacitor. In addition, a nonlinear model for a two coupled converter system is given. Based on these studies, we find that the PLL plays a key role in synchronization stability. In summary, the value of this paper is to clarify the key concept of the synchronization stability in renewable-dominated power systems based on different nonlinear models, which still lacks systematic studies and is controversial in the field of electrical power engineering. Meanwhile, it clearly uncovers that the synchronization stability of converters has its root in the phase synchronization concept in nonlinear sciences.

Predicting the cascading dynamics in complex networks via the bimodal failure size distribution

Cascading failure as a systematic risk occurs in a wide range of real-world networks. Cascade size distribution is a basic and crucial characteristic of systemic cascade behaviors. Recent research works have revealed that the distribution of cascade sizes is a bimodal form indicating the existence of either very small cascades or large ones. In this paper, we aim to understand the properties and formation characteristics of such bimodal distribution in complex networks and further predict the final cascade size. We first find that the bimodal distribution is ubiquitous under certain conditions in both synthetic and real networks. Moreover, the large cascades distributed in the right peak of bimodal distribution are resulted from either the failure of nodes with high load at the first step of the cascade or multiple rounds of cascades triggered by the initial failure. Accordingly, we propose a hybrid load metric (HLM), which combines the load of the initial broken node and the load of failed nodes triggered by the initial failure, to predict the final size of cascading failures. We validate the effectiveness of HLM by computing the accuracy of identifying the cascades belonging to the right and left peaks of the bimodal distribution. The results show that HLM is a better predictor than commonly used network centrality metrics in both synthetic and real-world networks. Finally, the influence of network structure on the optimal HLM is discussed.

Fragmentation of outage clusters during the recovery of power distribution grids

The understanding of recovery processes in power distribution grids is limited by the lack of realistic outage data, especially large-scale blackout datasets. By analyzing data from three electrical companies across the United States, we find that the recovery duration of an outage is connected with the downtime of its nearby outages and blackout intensity (defined as the peak number of outages during a blackout), but is independent of the number of customers affected. We present a cluster-based recovery framework to analytically characterize the dependence between outages, and interpret the dominant role blackout intensity plays in recovery. The recovery of blackouts is not random and has a universal pattern that is independent of the disruption cause, the post-disaster network structure, and the detailed repair strategy. Our study reveals that suppressing blackout intensity is a promising way to speed up restoration.

Understanding Braess’ Paradox in power grids

The ongoing energy transition requires power grid extensions to connect renewable generators to consumers and to transfer power among distant areas. The process of grid extension requires a large investment of resources and is supposed to make grid operation more robust. Yet, counter-intuitively, increasing the capacity of existing lines or adding new lines may also reduce the overall system performance and even promote blackouts due to Braess’ paradox. Braess’ paradox was theoretically modeled but not yet proven in realistically scaled power grids. Here, we present an experimental setup demonstrating Braess’ paradox in an AC power grid and show how it constrains ongoing large-scale grid extension projects. We present a topological theory that reveals the key mechanism and predicts Braessian grid extensions from the network structure. These results offer a theoretical method to understand and practical guidelines in support of preventing unsuitable infrastructures and the systemic planning of grid extensions.

Edge-Based Decentralized Adaptive Pinning Synchronization of Complex Networks Under Link Attacks

This article studies the pinning synchronization problem with edge-based decentralized adaptive schemes under link attacks. The link attacks considered here are a class of malicious attacks to break links between neighboring nodes in complex networks. In such an insecure network environment, two kinds of edge-based decentralized adaptive update strategies (synchronous and asynchronous) on coupling strengths and gains are designed to realize the security synchronization of complex networks. Moreover, by virtue of the edge pinning technique, the corresponding secure synchronization problem is considered under the case where only a small fraction of coupling strengths and gains is updated. These designed adaptive strategies do not require any global information, and therefore, the obtained results in this article are developed in a fully decentralized framework. Finally, a numerical example is provided to verify the availability of the achieved theoretical outcomes.

Cascading traffic jamming in a two-dimensional Motter and Lai model

We study the cascading traffic jamming on a two-dimensional random geometric graph using the Motter and Lai model. The traffic jam is caused by a localized attack incapacitating a circular region or a line of a certain size, as well as a dispersed attack on an equal number of randomly selected nodes. We investigate if there is a critical size of the attack above which the network becomes completely jammed due to cascading jamming, and how this critical size depends on the average degree 〈k〉 of the graph, on the number of nodes N in the system, and the tolerance parameter α of the Motter and Lai model.

Tropical cyclone-blackout-heatwave compound hazard resilience in a changing climate

Tropical cyclones (TCs) have caused extensive power outages. The impacts of TC-caused blackouts may worsen in the future as TCs and heatwaves intensify. Here we couple TC and heatwave projections and power outage and recovery process analysis to investigate how TC-blackout-heatwave compound hazard risk may vary in a changing climate, with Harris County, Texas as an example. We find that, under the high-emissions scenario RCP8.5, long-duration heatwaves following strong TCs may increase sharply. The expected percentage of Harris residents experiencing at least one longer-than-5-day TC-blackout-heatwave compound hazard in a 20-year period could increase dramatically by a factor of 23 (from 0.8% to 18.2%) over the 21^st century. We also reveal that a moderate enhancement of the power distribution network can significantly mitigate the compound hazard risk. Thus, climate adaptation actions, such as strategically undergrounding distribution network and developing distributed energy sources, are urgently needed to improve coastal power system resilience.

The study found that long-duration heatwaves are much more likely to follow power-damaging tropical cyclones in the future RCP8.5 climate, with the impact of longer-than-5-day tropical cyclone-blackout-heatwave compound hazard increasing by a factor of 23 over the 21st century.

No-exclaves percolation

Network robustness has been a pivotal issue in the study of system failure in network science since its inception. To shed light on this subject, we introduce and study a new percolation process based on a new cluster called an 'exclave' cluster. The entities comprising exclave clusters in a network are the sets of connected unfailed nodes that are completely surrounded by the failed (i.e., nonfunctional) nodes. The exclave clusters are thus detached from other unfailed parts of the network, thereby becoming effectively nonfunctional. This process defines a new class of clusters of nonfunctional nodes. We call it the no-exclave percolation cluster (NExP cluster), formed by the connected union of failed clusters and the exclave clusters they enclose. Here we showcase the effect of NExP cluster, suggesting a wide and disruptive collapse in two empirical infrastructure networks. We also study on two-dimensional Euclidean lattice to analyze the phase transition behavior using finite-size scaling. The NExP model considering the collective failure clusters uncovers new aspects of network collapse as a percolation process, such as quantitative change of transition point and qualitative change of transition type. Our study discloses hidden indirect damage added to the damage directly from attacks, and thus suggests a new useful way for finding nonfunctioning areas in complex systems under external perturbations as well as internal partial closures.

Influential Spreader Identification in Complex Networks Based on Network Connectivity and Efficiency

Influential spreader identification is a vital research area in complex network theory, which has important influence on application and popularization. Each of the existing methods has its own advantages and disadvantages, and there are still various methods proposed to solve this issue. In this paper, we come up with a new centrality of influential spreader identification based on network connectivity and efficiency (CEC). The consequences of spreader deletion can be generally divided into two parts, one is that the connectivity of network topology is destroyed, and the other is that network’s performance is degraded, which makes the network unable to meet the functional requirement. Therefore, the relative changes of connectivity and efficiency of network before and after removing spreaders are used to present the influence of spreaders. We adopt susceptible-infected (SI) model, a well-known infectious disease model, to verify the effectiveness of CEC through the spreading ability simulation of spreaders in actual networks. And the simulation results demonstrate the superiority of CEC.

Absence of pure voltage instabilities in the third-order model of power grid dynamics

Secure operation of electric power grids fundamentally relies on their dynamical stability properties. For the third-order model, a paradigmatic model that captures voltage dynamics, three routes to instability are established in the literature: a pure rotor angle instability, a pure voltage instability, and one instability induced by the interplay of both. Here, we demonstrate that one of these routes, the pure voltage instability, requires infinite voltage amplitudes and is, thus, nonphysical. We show that voltage collapse dynamics nevertheless exist in the absence of any voltage instabilities.

Non-Markovian random walks characterize network robustness to nonlocal cascades

Localized perturbations in a real-world network have the potential to trigger cascade failures at the whole system level, hindering its operations and functions. Standard approaches analytically tackling this problem are mostly based either on static descriptions, such as percolation, or on models where the failure evolves through first-neighbor connections, crucially failing to capture the nonlocal behavior typical of real cascades. We introduce a dynamical model that maps the failure propagation across the network to a self-avoiding random walk that, at each step, has a probability to perform nonlocal jumps toward operational systems' units. Despite the inherent non-Markovian nature of the process, we are able to characterize the critical behavior of the system out of equilibrium, as well as the stopping time distribution of the cascades. Our numerical experiments on synthetic and empirical biological and transportation networks are in excellent agreement with theoretical expectation, demonstrating the ability of our framework to quantify the vulnerability to nonlocal cascade failures of complex systems with interconnected structure.

The Fractal Tapestry of Life: II Entailment of Fractional Oncology by Physiology Networks

This is an essay advocating the efficacy of using the (noninteger) fractional calculus (FC) for the modeling of complex dynamical systems, specifically those pertaining to biomedical phenomena in general and oncological phenomena in particular. Herein we describe how the integer calculus (IC) is often incapable of describing what were historically thought to be simple linear phenomena such as Newton's law of cooling and Brownian motion. We demonstrate that even linear dynamical systems may be more accurately described by fractional rate equations (FREs) when the experimental datasets are inconsistent with models based on the IC. The Network Effect is introduced to explain how the collective dynamics of a complex network can transform a many-body noninear dynamical system modeled using the IC into a set of independent single-body fractional stochastic rate equations (FSREs). Note that this is not a mathematics paper, but rather a discussion focusing on the kinds of phenomena that have historically been approximately and improperly modeled using the IC and how a FC replacement of the model better explains the experimental results. This may be due to hidden effects that were not anticapated in the IC model, or to an effect that was acknowledged as possibly significant, but beyond the mathematical skills of the investigator to Incorporate into the original model. Whatever the reason we introduce the FRE used to describe mathematical oncology (MO) and review the quality of fit of such models to tumor growth data. The analytic results entailed in MO using ordinary diffusion as well as fractional diffusion are also briefly discussed. A connection is made between a time-dependent fractional-order derivative, technically called a distributed-order parameter, and the multifractality of time series, such that an observed multifractal time series can be modeled using a FRE with a distributed fractional-order derivative. This equivalence between multifractality and distributed fractional derivatives has not received the recognition in the applications literature we believe it warrants.

The effect of renewable energy incorporation on power grid stability and resilience

Contemporary proliferation of renewable power generation is causing an overhaul in the topology, composition, and dynamics of electrical grids. These low-output, intermittent generators are widely distributed throughout the grid, including at the household level. It is critical for the function of modern power infrastructure to understand how this increasingly distributed layout affects network stability and resilience. This paper uses dynamical models, household power consumption, and photovoltaic generation data to show how these characteristics vary with the level of distribution. It is shown that resilience exhibits daily oscillations as the grid's effective structure and the power demand fluctuate. This can lead to a substantial decrease in grid resilience, explained by periods of highly clustered generator output. Moreover, the addition of batteries, while enabling consumer self-sufficiency, fails to ameliorate these problems. The methodology identifies a grid's susceptibility to disruption resulting from its network structure and modes of operation.

Autonomous inference of complex network dynamics from incomplete and noisy data

The availability of empirical data that capture the structure and behaviour of complex networked systems has been greatly increased in recent years; however, a versatile computational toolbox for unveiling a complex system's nodal and interaction dynamics from data remains elusive. Here we develop a two-phase approach for the autonomous inference of complex network dynamics, and its effectiveness is demonstrated by the tests of inferring neuronal, genetic, social and coupled oscillator dynamics on various synthetic and real networks. Importantly, the approach is robust to incompleteness and noises, including low resolution, observational and dynamical noises, missing and spurious links, and dynamical heterogeneity. We apply the two-phase approach to infer the early spreading dynamics of influenza A flu on the worldwide airline network, and the inferred dynamical equation can also capture the spread of severe acute respiratory syndrome and coronavirus disease 2019. These findings together offer an avenue to discover the hidden microscopic mechanisms of a broad array of real networked systems.

Recovery coupling in multilayer networks

The increased complexity of infrastructure systems has resulted in critical interdependencies between multiple networks-communication systems require electricity, while the normal functioning of the power grid relies on communication systems. These interdependencies have inspired an extensive literature on coupled multilayer networks, assuming a hard interdependence, where a component failure in one network causes failures in the other network, resulting in a cascade of failures across multiple systems. While empirical evidence of such hard failures is limited, the repair and recovery of a network requires resources typically supplied by other networks, resulting in documented interdependencies induced by the recovery process. In this work, we explore recovery coupling, capturing the dependence of the recovery of one system on the instantaneous functional state of another system. If the support networks are not functional, recovery will be slowed. Here we collected data on the recovery time of millions of power grid failures, finding evidence of universal nonlinear behavior in recovery following large perturbations. We develop a theoretical framework to address recovery coupling, predicting quantitative signatures different from the multilayer cascading failures. We then rely on controlled natural experiments to separate the role of recovery coupling from other effects like resource limitations, offering direct evidence of how recovery coupling affects a system's functionality.

Functional observability and target state estimation in large-scale networks

Observing the states of a network is fundamental to our ability to explore and control the dynamics of complex natural, social, and technological systems. The problem of determining whether the system is observable has been addressed by network control researchers over the past decade. Progress on the further problem of actually designing and implementing efficient algorithms to infer the states from limited measurements has been hampered by the high dimensionality of large-scale networks. Noting that often only a small number of state variables in a network are essential for control, intervention, and monitoring purposes, this work develops a graph-based theory and highly scalable methods that achieve accurate estimation of target variables of network systems with minimal sensing and computational resources.

The quantitative understanding and precise control of complex dynamical systems can only be achieved by observing their internal states via measurement and/or estimation. In large-scale dynamical networks, it is often difficult or physically impossible to have enough sensor nodes to make the system fully observable. Even if the system is in principle observable, high dimensionality poses fundamental limits on the computational tractability and performance of a full-state observer. To overcome the curse of dimensionality, we instead require the system to be functionally observable, meaning that a targeted subset of state variables can be reconstructed from the available measurements. Here, we develop a graph-based theory of functional observability, which leads to highly scalable algorithms to 1) determine the minimal set of required sensors and 2) design the corresponding state observer of minimum order. Compared with the full-state observer, the proposed functional observer achieves the same estimation quality with substantially less sensing and fewer computational resources, making it suitable for large-scale networks. We apply the proposed methods to the detection of cyberattacks in power grids from limited phase measurement data and the inference of the prevalence rate of infection during an epidemic under limited testing conditions. The applications demonstrate that the functional observer can significantly scale up our ability to explore otherwise inaccessible dynamical processes on complex networks.

The transition to synchronization on branching hierarchical lattices

We study the transition to synchronization on hierarchical lattices using the evolution of Chaté-Manneville maps placed on a triangular lattice. Connections are generated between the levels of the triangular lattice, assuming that each site is connected to its neighbors on the level below with probability half. The maps are diffusively coupled, and the map parameters increase hierarchically, depending on the map parameters at the sites they are coupled to in the previous level. The system shows a transition to synchronization, which is second order in nature, with associated critical exponents. However, the V-lattice, which is a special realization of this lattice, shows a transition to synchronization that is discontinuous with accompanying hysteretic behavior. This transition can thus be said to belong to the class of explosive synchronization with the explosive nature depending on the nature of the substrate. We carry out finite-size-finite-time scaling for the continuous transition and analyze the scaling of the jump size for the discontinuous case. We discuss the implications of our results and draw parallels with avalanche statistics on branching hierarchical lattices.

Power-grid stability predictions using transferable machine learning

Complex network analyses have provided clues to improve power-grid stability with the help of numerical models. The high computational cost of numerical simulations, however, has inhibited the approach, especially when it deals with the dynamic properties of power grids such as frequency synchronization. In this study, we investigate machine learning techniques to estimate the stability of power-grid synchronization. We test three different machine learning algorithms-random forest, support vector machine, and artificial neural network-training them with two different types of synthetic power grids consisting of homogeneous and heterogeneous input-power distribution, respectively. We find that the three machine learning models better predict the synchronization stability of power-grid nodes when they are trained with the heterogeneous input-power distribution rather than the homogeneous one. With the real-world power grids of Great Britain, Spain, France, and Germany, we also demonstrate that the machine learning algorithms trained on synthetic power grids are transferable to the stability prediction of the real-world power grids, which implies the prospective applicability of machine learning techniques on power-grid studies.

Machine learning dismantling and early-warning signals of disintegration in complex systems

From physics to engineering, biology and social science, natural and artificial systems are characterized by interconnected topologies whose features - e.g., heterogeneous connectivity, mesoscale organization, hierarchy - affect their robustness to external perturbations, such as targeted attacks to their units. Identifying the minimal set of units to attack to disintegrate a complex network, i.e. network dismantling, is a computationally challenging (NP-hard) problem which is usually attacked with heuristics. Here, we show that a machine trained to dismantle relatively small systems is able to identify higher-order topological patterns, allowing to disintegrate large-scale social, infrastructural and technological networks more efficiently than human-based heuristics. Remarkably, the machine assesses the probability that next attacks will disintegrate the system, providing a quantitative method to quantify systemic risk and detect early-warning signals of system's collapse. This demonstrates that machine-assisted analysis can be effectively used for policy and decision-making to better quantify the fragility of complex systems and their response to shocks.

Mesoscopic model reduction for the collective dynamics of sparse coupled oscillator networks

The behavior at bifurcation from global synchronization to partial synchronization in finite networks of coupled oscillators is a complex phenomenon, involving the intricate dynamics of one or more oscillators with the remaining synchronized oscillators. This is not captured well by standard macroscopic model reduction techniques that capture only the collective behavior of synchronized oscillators in the thermodynamic limit. We introduce two mesoscopic model reductions for finite sparse networks of coupled oscillators to quantitatively capture the dynamics close to bifurcation from global to partial synchronization. Our model reduction builds upon the method of collective coordinates. We first show that standard collective coordinate reduction has difficulties capturing this bifurcation. We identify a particular topological structure at bifurcation consisting of a main synchronized cluster, the oscillator that desynchronizes at bifurcation, and an intermediary node connecting them. Utilizing this structure and ensemble averages, we derive an analytic expression for the mismatch between the true bifurcation from global to partial synchronization and its estimate calculated via the collective coordinate approach. This allows to calibrate the standard collective coordinate approach without prior knowledge of which node will desynchronize. We introduce a second mesoscopic reduction, utilizing the same particular topological structure, which allows for a quantitative dynamical description of the phases near bifurcation. The mesoscopic reductions significantly reduce the computational complexity of the collective coordinate approach, reducing from O(N²) to O(1). We perform numerical simulations for Erdős-Rényi networks and for modified Barabási-Albert networks demonstrating remarkable quantitative agreement at and close to bifurcation.

Network isolators inhibit failure spreading in complex networks

In our daily lives, we rely on the proper functioning of supply networks, from power grids to water transmission systems. A single failure in these critical infrastructures can lead to a complete collapse through a cascading failure mechanism. Counteracting strategies are thus heavily sought after. In this article, we introduce a general framework to analyse the spreading of failures in complex networks and demostrate that not only decreasing but also increasing the connectivity of the network can be an effective method to contain damages. We rigorously prove the existence of certain subgraphs, called network isolators, that can completely inhibit any failure spreading, and we show how to create such isolators in synthetic and real-world networks. The addition of selected links can thus prevent large scale outages as demonstrated for power transmission grids.

Percolation of attack with tunable limited knowledge

Percolation models shed a light on network integrity and functionality and have numerous applications in network theory. This paper studies a targeted percolation (α model) with incomplete knowledge where the highest degree node in a randomly selected set of n nodes is removed at each step, and the model features a tunable probability that the removed node is instead a random one. A "mirror image" process (β model) in which the target is the lowest degree node is also investigated. We analytically calculate the giant component size, the critical occupation probability, and the scaling law for the percolation threshold with respect to the knowledge level n under both models. We also derive self-consistency equations to analyze the k-core organization including the size of the k core and its corona in the context of attacks under tunable limited knowledge. These percolation models are characterized by some interesting critical phenomena and reveal profound quantitative structure discrepancies between Erdős-Rényi networks and power-law networks.

Distribution of blackouts in the power grid and the Motter and Lai model

Carreras, Dobson, and colleagues have studied empirical data on the sizes of the blackouts in real grids and modeled them with computer simulations using the direct current approximation. They have found that the resulting blackout sizes are distributed as a power law and suggested that this is because the grids are driven to the self-organized critical state. In contrast, more recent studies found that the distribution of cascades is bimodal resulting in either a very small blackout or a very large blackout, engulfing a finite fraction of the system. Here we reconcile the two approaches and investigate how the distribution of the blackouts changes with model parameters, including the tolerance criteria and the dynamic rules of failure of the overloaded lines during the cascade. In addition, we study the same problem for the Motter and Lai model and find similar results, suggesting that the physical laws of flow on the network are not as important as network topology, overload conditions, and dynamic rules of failure.

Percolation of heterogeneous flows uncovers the bottlenecks of infrastructure networks

Whether it be the passengers’ mobility demand in transportation systems, or the consumers’ energy demand in power grids, the primary purpose of many infrastructure networks is to best serve this flow demand. In reality, the volume of flow demand fluctuates unevenly across complex networks while simultaneously being hindered by some form of congestion or overload. Nevertheless, there is little known about how the heterogeneity of flow demand influences the network flow dynamics under congestion. To explore this, we introduce a percolation-based network analysis framework underpinned by flow heterogeneity. Thereby, we theoretically identify bottleneck links with guaranteed decisive impact on how flows are passed through the network. The effectiveness of the framework is demonstrated on large-scale real transportation networks, where mitigating the congestion on a small fraction of the links identified as bottlenecks results in a significant network improvement.

Infrastructure networks are characterized by fluctuations of flow demand between different points and temporal congestion or overload on flow pathways. Hamedmoghadam et al. identify congestion bottlenecks in networks relevant to communication, transportation, water supply, and power distribution.

Modelling cascading failures in networks with the harmonic closeness

Many studies on cascading failures adopt the degree or the betweenness of a node to define its load. From a novel perspective, we propose an approach to obtain initial loads considering the harmonic closeness and the impact of neighboring nodes. Based on simulation results for different adjustable parameter θ, local parameter δ and proportion of attacked nodes f, it is found that in scale-free networks (SF networks), small-world networks (SW networks) and Erdos-Renyi networks (ER networks), there exists a negative correlation between optimal θ and δ. By the removal of the low load node, cascading failures are more likely to occur in some cases. In addition, we find a valuable result that our method yields better performance compared with other methods in SF networks with an arbitrary f, SW and ER networks with large f. Moreover, the method concerning the harmonic closeness makes these three model networks more robust for different average degrees. Finally, we perform the simulations on twenty real networks, whose results verify that our method is also effective to distribute the initial load in different real networks.

Small-Signal Stability of Multi-Converter Infeed Power Grids with Symmetry

Traditional power systems have been gradually shifting to power-electronic-based ones, with more power electronic devices (including converters) incorporated recently. Faced with much more complicated dynamics, it is a great challenge to uncover its physical mechanisms for system stability and/or instability (oscillation). In this paper, we first establish a nonlinear model of a multi-converter power system within the DC-link voltage timescale, from the first principle. Then, we obtain a linearized model with the associated characteristic matrix, whose eigenvalues determine the system stability, and finally get independent subsystems by using symmetry approximation conditions under the assumptions that all converters’ parameters and their susceptance to the infinite bus (Bg) are identical. Based on these mathematical analyses, we find that the whole system can be decomposed into several equivalent single-converter systems and its small-signal stability is solely determined by a simple converter system connected to an infinite bus under the same susceptance Bg. These results of large-scale multi-converter analysis help to understand the power-electronic-based power system dynamics, such as renewable energy integration. As well, they are expected to stimulate broad interests among researchers in the fields of network dynamics theory and applications.

Modeling epidemic spreading through public transit using time-varying encounter network

Passenger contact in public transit (PT) networks can be a key mediate in the spreading of infectious diseases. This paper proposes a time-varying weighted PT encounter network to model the spreading of infectious diseases through the PT systems. Social activity contacts at both local and global levels are also considered. We select the epidemiological characteristics of coronavirus disease 2019 (COVID-19) as a case study along with smart card data from Singapore to illustrate the model at the metropolitan level. A scalable and lightweight theoretical framework is derived to capture the time-varying and heterogeneous network structures, which enables to solve the problem at the whole population level with low computational costs. Different control policies from both the public health side and the transportation side are evaluated. We find that people's preventative behavior is one of the most effective measures to control the spreading of epidemics. From the transportation side, partial closure of bus routes helps to slow down but cannot fully contain the spreading of epidemics. Identifying "influential passengers" using the smart card data and isolating them at an early stage can also effectively reduce the epidemic spreading.

Open database analysis of scaling and spatio-temporal properties of power grid frequencies

The electrical energy system has attracted much attention from an increasingly diverse research community. Many theoretical predictions have been made, from scaling laws of fluctuations to propagation velocities of disturbances. However, to validate any theory, empirical data from large-scale power systems are necessary but are rarely shared openly. Here, we analyse an open database of measurements of electric power grid frequencies across 17 locations in 12 synchronous areas on three continents. The power grid frequency is of particular interest, as it indicates the balance of supply and demand and carries information on deterministic, stochastic, and control influences. We perform a broad analysis of the recorded data, compare different synchronous areas and validate a previously conjectured scaling law. Furthermore, we show how fluctuations change from local independent oscillations to a homogeneous bulk behaviour. Overall, the presented open database and analyses constitute a step towards more shared, collaborative energy research.

Power grid frequencies mirror the state of the grid. Here, Rydin Gorjão et al. analyse measurements of power grid frequencies across areas and continents and uncover scaling laws of their fluctuations and spatio-temporal dynamics, which could aid the design, operation and control of power systems.

Epidemic spreading and control strategies in spatial modular network

Epidemic spread on networks is one of the most studied dynamics in network science and has important implications in real epidemic scenarios. Nonetheless, the dynamics of real epidemics and how it is affected by the underline structure of the infection channels are still not fully understood. Here we apply the susceptible-infected-recovered model and study analytically and numerically the epidemic spread on a recently developed spatial modular model imitating the structure of cities in a country. The model assumes that inside a city the infection channels connect many different locations, while the infection channels between cities are less and usually directly connect only a few nearest neighbor cities in a two-dimensional plane. We find that the model experience two epidemic transitions. The first lower threshold represents a local epidemic spread within a city but not to the entire country and the second higher threshold represents a global epidemic in the entire country. Based on our analytical solution we proposed several control strategies and how to optimize them. We also show that while control strategies can successfully control the disease, early actions are essentials to prevent the disease global spread.

Nonlinear model of cascade failure in weighted complex networks considering overloaded edges

Considering the elasticity of the real networks, the components in the network have a redundant capacity against the load, such as power grids, traffic networks and so on. Moreover, the interaction strength between nodes is often different. This paper proposes a novel nonlinear model of cascade failure in weighted complex networks considering overloaded edges to describe the redundant capacity for edges and capture the interaction strength of nodes. We fill this gap by studying a nonlinear weighted model of cascade failure with overloaded edges over synthetic and real weighted networks. The cascading failure model is constructed for the first time according to the overload coefficient, capacity parameter, weight coefficient, and distribution coefficient. Then through theoretical analysis, the conditions for stopping failure cascades are obtained, and the analysis shows the superiority of the constructed model. Finally, the cascading invulnerability is simulated in several typical network models and the US power grid. The results show that the model is a feasible and reasonable change of weight parameters, capacity coefficient, distribution coefficient, and overload coefficient can significantly improve the destructiveness of complex networks against cascade failure. Our methodology provides an efficacious reference for the control and prevention of cascading failures in many real networks.

Emergence of Scale-Free Blackout Sizes in Power Grids

We model power grids as graphs with heavy-tailed sinks, which represent demand from cities, and study cascading failures on such graphs. Our analysis links the scale-free nature of blackout sizes to the scale-free nature of city sizes, contrasting previous studies suggesting that this nature is governed by self-organized criticality. Our results are based on a new mathematical framework combining the physics of power flow with rare event analysis for heavy-tailed distributions, and are validated using various synthetic networks and the German transmission grid.

Vulnerability Assessment for Power Transmission Lines under Typhoon Weather Based on a Cascading Failure State Transition Diagram

The analysis of the fault propagation path of transmission lines and the method of identification of vulnerable lines during typhoon weather conditions is of great significance. In this context, this paper introduces the failure probability model of transmission lines under such conditions by considering both wind speed and the load of the lines. The Monte Carlo simulation (MCS) and the DC model based on OPA are applied to simulate the failure of transmission lines. The cascading failure state transition diagram (CFSTD) is proposed based on the failure chains and the criticality ranking of nodes in CFSTD by the average weight coefficient (AWC) for identifying vulnerable lines of the power grid under such conditions. A new weight in CFSTD is proposed to describe the vulnerability of each line and a new resilience index is used to assess the impacts of a typhoon on the system. The proposed method is demonstrated by using the modified IEEE 118-bus test system. Results show that the method proposed in this paper can simulate the fault propagation path, and identify the critical components of power grid under a typhoon.

Dynamic Network Characteristics of Power-electronics-based Power Systems

Power flow studies in traditional power systems aim to uncover the stationary relationship between voltage amplitude and phase and active and reactive powers; they are important for both stationary and dynamic power system analysis. With the increasing penetration of large-scale power electronics devices including renewable generations interfaced with converters, the power systems become gradually power-electronics-dominant and correspondingly their dynamical behavior changes substantially. Due to the fast dynamics of converters, such as AC current controller, the quasi-stationary state approximation, which has been widely used in power systems, is no longer appropriate and should be reexamined. In this paper, for a better description of network characteristics, we develop a novel concept of dynamic power flow and uncover an explicit dynamic relation between the instantaneous powers and the voltage vectors. This mathematical relation has been well verified by simulations on transient analysis of a small power-electronics-based power system, and a small-signal frequency-domain stability analysis of a voltage source converter connected to an infinitely strong bus. These results demonstrate the applicability of the proposed method and shed an improved light on our understanding of power-electronics-dominant power systems, whose dynamical nature remains obscure.

Dynamics of tipping cascades on complex networks

Tipping points occur in diverse systems in various disciplines such as ecology, climate science, economy, and engineering. Tipping points are critical thresholds in system parameters or state variables at which a tiny perturbation can lead to a qualitative change of the system. Many systems with tipping points can be modeled as networks of coupled multistable subsystems, e.g., coupled patches of vegetation, connected lakes, interacting climate tipping elements, and multiscale infrastructure systems. In such networks, tipping events in one subsystem are able to induce tipping cascades via domino effects. Here, we investigate the effects of network topology on the occurrence of such cascades. Numerical cascade simulations with a conceptual dynamical model for tipping points are conducted on Erdős-Rényi, Watts-Strogatz, and Barabási-Albert networks. Additionally, we generate more realistic networks using data from moisture-recycling simulations of the Amazon rainforest and compare the results to those obtained for the model networks. We furthermore use a directed configuration model and a stochastic block model which preserve certain topological properties of the Amazon network to understand which of these properties are responsible for its increased vulnerability. We find that clustering and spatial organization increase the vulnerability of networks and can lead to tipping of the whole network. These results could be useful to evaluate which systems are vulnerable or robust due to their network topology and might help us to design or manage systems accordingly.

Resistance and robustness of the global coral-symbiont network

Increasing ocean temperatures have widespread consequences for coral reefs, one of which is coral bleaching. We analyzed a global network of associations between coral species and Symbiodiniaceae for resistance to temperature stress and robustness to perturbations. Null networks were created by changing either the physiological parameters of the nodes or the structures of the networks. We developed a bleaching model in which each link, association, is given a weight based on temperature thresholds for specific host-symbiont pairs and links are removed as temperature increases. Resistance to temperature stress was determined from the response of the networks to the bleaching model. Ecological robustness, defined by how much perturbation is needed to decrease the number of nodes by 50%, was determined for multiple removal models that considered traits of the hosts, symbionts, and their associations. Network resistance to bleaching and robustness to perturbations differed from the null networks and varied across spatial scales, supporting that thermal tolerances, local association patterns, and environment play an important role in network persistence. Networks were more robust to attacks on associations than to attacks on species. Although the global network was fairly robust to random link removals, when links are removed according to the bleaching model, robustness decreases by about 20%. Specific environmental attacks, in the form of increasing temperatures, destabilize the global network of coral species and Symbiodiniaceae. On a global scale, the network was more robust to removals of links with susceptible Symbiodiniaceae than it was to removals of links with susceptible hosts. Thus, the symbionts convey more stability to the symbiosis than the hosts when the system is under an environmental attack. However, our results also provide evidence that the environment of the networks affects robustness to link perturbations. Our work shows that ecological resistance and robustness can be assessed through network analysis that considers specific biological traits and functional weaknesses. The global network of associations between corals and Symbiodiniaceae and its distribution of thermal tolerances are non-random, and the evolution of this architecture has led to higher sensitivity to environmental perturbations.

Influencer identification in dynamical complex systems

The integrity and functionality of many real-world complex systems hinge on a small set of pivotal nodes, or influencers. In different contexts, these influencers are defined as either structurally important nodes that maintain the connectivity of networks, or dynamically crucial units that can disproportionately impact certain dynamical processes. In practice, identification of the optimal set of influencers in a given system has profound implications in a variety of disciplines. In this review, we survey recent advances in the study of influencer identification developed from different perspectives, and present state-of-the-art solutions designed for different objectives. In particular, we first discuss the problem of finding the minimal number of nodes whose removal would breakdown the network (i.e. the optimal percolation or network dismantle problem), and then survey methods to locate the essential nodes that are capable of shaping global dynamics with either continuous (e.g. independent cascading models) or discontinuous phase transitions (e.g. threshold models). We conclude the review with a summary and an outlook.

A comparative analysis of link removal strategies in real complex weighted networks

In this report we offer the widest comparison of links removal (attack) strategies efficacy in impairing the robustness of six real-world complex weighted networks. We test eleven different link removal strategies by computing their impact on network robustness by means of using three different measures, i.e. the largest connected cluster (LCC), the efficiency (Eff) and the total flow (TF). We find that, in most of cases, the removal strategy based on the binary betweenness centrality of the links is the most efficient to disrupt the LCC. The link removal strategies based on binary-topological network features are less efficient in decreasing the weighted measures of the network robustness (e.g. Eff and TF). Removing highest weight links first is the best strategy to decrease the efficiency (Eff) in most of the networks. Last, we found that the removal of a very small fraction of links connecting higher strength nodes or of highest weight does not affect the LCC but it determines a rapid collapse of the network efficiency Eff and the total flow TF. This last outcome raises the importance of both to adopt weighted measures of network robustness and to focus the analyses on network response to few link removals.