Universal behavior of cascading failures in interdependent networks

Resilience of weighted networks with dynamical behavior against multi-node removal

In many real-world networks, interactions between nodes are weighted to reflect their strength, such as predator-prey interactions in the ecological network and passenger numbers in airline networks. These weighted networks are prone to cascading effects caused by minor perturbations, which can lead to catastrophic outcomes. This vulnerability highlights the importance of studying weighted network resilience to prevent system collapses. However, due to many variables and weight parameters coupled together, predicting the behavior of such a system governed by a multi-dimensional rate equation is challenging. To address this, we propose a dimension reduction technique that simplifies a multi-dimensional system into a one-dimensional state space. We applied this methodology to explore the impact of weights on the resilience of four dynamics whose weights are assigned by three weight assignment methods. The four dynamical systems are the biochemical dynamical system (B), the epidemic dynamical system (E), the regulatory dynamical system (R), and the birth-death dynamical system (BD). The results show that regardless of the weight distribution, for B, the weights are negatively correlated with the activities of the network, while for E, R, and BD, there is a positive correlation between the weights and the activities of the network. Interestingly, for B, R, and BD, the change in the weights of the system has little impact on the resilience of the system. However, for the E system, the greater the weights the more resilient the system. This study not only simplifies the complexity inherent in weighted networks but also enhances our understanding of their resilience and response to perturbations.

Investigating stronger tolerant network against cascading failures in focusing on changing degree distributions

Many real-world networks with Scale-Free structure are significantly vulnerable against both intentional attacks and catastrophic cascading failures. On the other hand, it has been shown that networks with narrower degree distributions have strong robustness of connectivity by enhancing loops. This paper numerically reveals that such networks are also tolerant against cascading failures. Our findings will be useful in designing stronger tolerant network infrastructures.

Percolation Theories for Quantum Networks

Quantum networks have experienced rapid advancements in both theoretical and experimental domains over the last decade, making it increasingly important to understand their large-scale features from the viewpoint of statistical physics. This review paper discusses a fundamental question: how can entanglement be effectively and indirectly (e.g., through intermediate nodes) distributed between distant nodes in an imperfect quantum network, where the connections are only partially entangled and subject to quantum noise? We survey recent studies addressing this issue by drawing exact or approximate mappings to percolation theory, a branch of statistical physics centered on network connectivity. Notably, we show that the classical percolation frameworks do not uniquely define the network's indirect connectivity. This realization leads to the emergence of an alternative theory called "concurrence percolation", which uncovers a previously unrecognized quantum advantage that emerges at large scales, suggesting that quantum networks are more resilient than initially assumed within classical percolation contexts, offering refreshing insights into future quantum network design.

Fault Root Cause Tracking of the Mechanical Components of CNC Lathes Based on Information Transmission

This study proposes a new method for the immediate fault warning and fault root tracing of CNC lathes. Here, the information acquisition scheme was formulated based on the analysis of the coupling relationship between the mechanical parts of CNC lathes. Once the collected status signals were de-noised and coarse-grained, transfer entropy theory was introduced to calculate the net entropy of information transfer between the mechanical parts, after which the information transfer model was constructed. The sliding window method was used to determine the probability threshold interval of the net information transfer entropy between the lathe mechanical parts under different processing modes. Therefore, the transition critical point was determined according to the information entropy, and the fault development process was clarified. By analyzing the information transfer changes between the parts, fault early warning and fault root tracking on the CNC lathe were realized. The proposed method realizes the digitalization and intelligentization of fault diagnosis and has the advantages of timely and efficient diagnosis. Finally, the effectiveness of the proposed method is verified by a numerical control lathe tool processing experiment.

Coupled disease-vaccination behavior dynamic analysis and its application in COVID-19 pandemic

Predicting the evolutionary dynamics of the COVID-19 pandemic is a complex challenge. The complexity increases when the vaccination process dynamic is also considered. In addition, when applying a voluntary vaccination policy, the simultaneous behavioral evolution of individuals who decide whether and when to vaccinate must be included. In this paper, a coupled disease-vaccination behavior dynamic model is introduced to study the coevolution of individual vaccination strategies and infection spreading. We study disease transmission by a mean-field compartment model and introduce a non-linear infection rate that takes into account the simultaneity of interactions. Besides, the evolutionary game theory is used to investigate the contemporary evolution of vaccination strategies. Our findings suggest that sharing information with the entire population about the negative and positive consequences of infection and vaccination is beneficial as it boosts behaviors that can reduce the final epidemic size. Finally, we validate our transmission mechanism on real data from the COVID-19 pandemic in France.

Increased human risk caused by cascading hazards - A framework

Cascading hazards occur frequently. Unexpected casualties and losses of properties, or even impacts on the society and the environment may ensue from failure to anticipate the amplified risks induced by cascading hazards. Current risk assessment methods pay relatively less attention to quantifying the increased human risk related to "cascading" events. An improved framework for quantifying the human risk caused by cascading hazards is proposed in this paper. The framework considers the interactions among the cascading hazards and among the vulnerabilities of elements to these hazards. Its kernel is to scientifically anticipate and gear up for any new intensified hazards, which may otherwise lead to serious social aftermath. The framework is illustrated with a multi-hazard example close to the epicenter of the Wenchuan earthquake, which involved a chain of hazards including slope failures, a large debris flow, river damming, and flooding.

Percolation transitions in interdependent networks with reinforced dependency links

Dependence can highly increase the vulnerability of interdependent networks under cascading failure. Recent studies have shown that a constant density of reinforced nodes can prevent catastrophic network collapses. However, the effect of reinforcing dependency links in interdependent networks has rarely been addressed. Here, we develop a percolation model for studying interdependent networks by introducing a fraction of reinforced dependency links. We find that there is a minimum fraction of dependency links that need to be reinforced to prevent the network from abrupt transition, and it can serve as the boundary value to distinguish between the first- and second-order phase transitions of the network. We give both analytical and numerical solutions to the minimum fraction of reinforced dependency links for random and scale-free networks. Interestingly, it is found that the upper bound of this fraction is a constant 0.088 01 for two interdependent random networks regardless of the average degree. In particular, we find that the proposed method has higher reinforcement efficiency compared to the node-reinforced method, and its superiority in scale-free networks becomes more obvious as the coupling strength increases. Moreover, the heterogeneity of the network structure profoundly affects the reinforcement efficiency. These findings may provide several useful suggestions for designing more resilient interdependent networks.

Three Decades in Econophysics—From Microscopic Modelling to Macroscopic Complexity and Back

We explore recent contributions to research in Econophysics, switching between Macroscopic complexity and microscopic modelling, showing how each leads to the other and detailing the everyday applicability of both approaches and the tools they help develop. Over the past decades, the world underwent several major crises, leading to significant increase in interdependence and, thus, complexity. We show here that from the perspective of network science, these processes become more understandable and, to some extent, also controllable.

Market impact shapes competitive advantage of investment strategies in financial markets

The formation of an efficient market depends on the competition between different investment strategies, which accelerates all available information into asset prices. By incorporating market impact and two kinds of investment strategies into an agent-based model, we have investigated the coevolutionary mechanism of different investment strategies and the role of market impact in shaping a competitive advantage in financial markets. The coevolution of history-dependent strategies and reference point strategies depends on the levels of market impact and risk tolerance. For low market impact and low risk tolerance, the majority-win effect makes the trend-following strategies become dominant strategies. For high market impact and low risk tolerance, the minority-win effect makes the trend-rejecting strategies coupled with trend-following strategies become dominant strategies. The coupled effects of price fluctuations and strategy distributions have been investigated in depth. A U-shape distribution of history-dependent strategies is beneficial for a stable price, which is destroyed by the existence of reference point strategies with low risk tolerance. A δ-like distribution of history-dependent strategies leads to a large price fluctuation, which is suppressed by the existence of reference point strategies with high risk tolerance. The strategies that earn more in an inefficient market lose more in an efficient market. Such a result gives us another explanation for the principle of risk-profit equilibrium in financial markets: high return in an inefficient market should be coupled with high risk in an efficient market, low return in an inefficient market should be coupled with low risk in an efficient market.

From data to complex network control of airline flight delays

Many critical complex systems and networks are continuously monitored, creating vast volumes of data describing their dynamics. To understand and optimize their performance, we need to discover and formalize their dynamics to enable their control. Here, we introduce a multidisciplinary framework using network science and control theory to accomplish these goals. We demonstrate its use on a meaningful example of a complex network of U.S. domestic passenger airlines aiming to control flight delays. Using the real data on such delays, we build a flight delay network for each airline. Analyzing these networks, we uncover and formalize their dynamics. We use this formalization to design the optimal control for the flight delay networks. The results of applying this control to the ground truth data on flight delays demonstrate the low costs of the optimal control and significant reduction of delay times, while the costs of the delays unabated by control are high. Thus, the introduced here framework benefits the passengers, the airline companies and the airports.

Introducing participatory fairness in emergency communication can support self-organization for survival

Participatory resilience of disaster-struck communities requires reliable communication for self-organized rescue, as conventional communication infrastructure is damaged. Disasters often lead to blackouts preventing citizens from charging their phones, leading to disparity in battery charges and a digital divide in communication opportunities. We propose a value-based emergency communication system based on participatory fairness, ensuring equal communication opportunities for all, regardless of inequality in battery charge. The proposed infrastructure-less emergency communication network automatically and dynamically (i) assigns high-battery phones as hubs, (ii) adapts the topology to changing battery charges, and (iii) self-organizes to remain robust and reliable when links fail or phones leave the network. The novelty of the proposed mobile protocol compared to mesh communication networks is demonstrated by comparative agent-based simulations. An evaluation using the Gini coefficient demonstrates that our network design results in fairer participation of all devices and a longer network lifetime, benefiting the community and its participants.

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.

Recovery patterns and physics of the network

In a progressively interconnected world, the loss of system resilience has consequences for human health, the economy, and the environment. Research has exploited the science of networks to explain the resilience of complex systems against random attacks, malicious attacks, and the localized attacks induced by natural disasters or mass attacks. Little is known about the elucidation of system recovery by the network topology. This study adds to the knowledge of network resilience by examining the nexus of recoverability and network topology. We establish a new paradigm for identifying the recovery behavior of networks and introduce the recoverability measure. Results indicate that the recovery response behavior and the recoverability measure are the function of both size and topology of networks. In small sized networks, the return to recovery exhibits homogeneous recovery behavior over topology, while the return shape is dispersed with an increase in the size of network. A network becomes more recoverable as connectivity measures of the network increase, and less recoverable as accessibility measures of network increase. Overall, the results not only offer guidance on designing recoverable networks, but also depict the recovery nature of networks deliberately following a disruption. Our recovery behavior and recoverability measure has been tested on 16 distinct network topologies. The relevant recovery behavior can be generalized based on our definition for any network topology recovering deliberately.

Resilience of Urban Transport Network-of-Networks under Intense Flood Hazards Exacerbated by Targeted Attacks

Natural hazards including floods can trigger catastrophic failures in interdependent urban transport network-of-networks (NoNs). Population growth has enhanced transportation demand while urbanization and climate change have intensified urban floods. However, despite the clear need to develop actionable insights for improving the resilience of critical urban lifelines, the theory and methods remain underdeveloped. Furthermore, as infrastructure systems become more intelligent, security experts point to the growing threat of targeted cyber-physical attacks during natural hazards. Here we develop a hypothesis-driven resilience framework for urban transport NoNs, which we demonstrate on the London Rail Network (LRN). We find that topological attributes designed for maximizing efficiency rather than robustness render the network more vulnerable to compound natural-targeted disruptions including cascading failures. Our results suggest that an organizing principle for post-disruption recovery may be developed with network science principles. Our findings and frameworks can generalize to urban lifelines and more generally to real-world spatial networks.

Resilience centrality in complex networks

Resilience describes a system's ability to adjust its activity to retain the basic functionality when errors or failures occur in components (nodes) of the network. Due to the complexity of a system's structure, different components in the system exhibit diversity in the ability to affect the resilience of the system, bringing us a great challenge to protect the system from collapse. A fundamental problem is therefore to propose a physically insightful centrality index, with which to quantify the resilience contribution of a node in any systems effectively. However, existing centrality indexes are not suitable for the problem because they only consider the network structure of the system and ignore the impact of underlying dynamic characteristics. To break the limits, we derive a new centrality index: resilience centrality from the 1D dynamic equation of systems, with which we can quantify the ability of nodes to affect the resilience of the system accurately. Resilience centrality unveils the long-sought relations between the ability of nodes in a system's resilience and network structure of the system: the capacity is mainly determined by the degree and weighted nearest-neighbor degree of the node, in which weighted nearest-neighbor degree plays a prominent role. Further, we demonstrate that weighted nearest-neighbor degree has a positive impact on resilience centrality, while the effect of the degree depends on a specific parameter, average weighted degree β_{eff}, in the 1D dynamic equation. To test the performance of our approach, we construct four real networks from data, which corresponds to two complex systems with entirely different dynamic characteristics. The simulation results demonstrate the effectiveness of our resilience centrality, providing us theoretical insights into the protection of complex systems from collapse.