Showing 1–50 of 221 results for author: Havlin, S

Criticality and reduced dynamical resilience in PM2.5 pollution systems

Authors: Yuan Chen, Yongwen Zhang, Xu Li, Dean Chen, Jingfang Fan, Yosef Ashkenazy, Deliang Chen, Shlomo Havlin

Abstract: Concentration-based metrics underpin air-quality assessment, while dynamical persistence and recovery describe how rapidly high-PM2.5 episodes dissipate and how strongly they retain memory. Here we introduce a finite-memory multiplicative reversion (FMMR) process that links the lognormal concentration backbone of PM2.5 variability with event recurrence, temporal memory, variance amplification and… ▽ More Concentration-based metrics underpin air-quality assessment, while dynamical persistence and recovery describe how rapidly high-PM2.5 episodes dissipate and how strongly they retain memory. Here we introduce a finite-memory multiplicative reversion (FMMR) process that links the lognormal concentration backbone of PM2.5 variability with event recurrence, temporal memory, variance amplification and local dynamical resilience. Across station observations and reanalysis data, elevated PM2.5 regimes show a coherent set of critical signatures: stronger memory, rising autocorrelation, broader upper tails, amplified variance, reduced resilience and more clustered exceedance events. Together, these co-occurring signals reveal dynamical criticality in PM2.5 pollution systems, with critical slowing down expressed as a loss of restoring capacity under high-pollution conditions. A gridded comparison across populated and emission-influenced regions further shows that areas with similar PM2.5 burden can differ in recovery capacity, while eastern China has shifted toward higher resilience during recent air-quality improvements and India and West Africa occupy lower-resilience states. By identifying where pollution burden and recovery capacity diverge, these findings establish dynamical persistence and resilience as complementary dimensions of PM2.5 risk and provide a quantitative basis for resilience-oriented air-quality assessment. △ Less

Submitted 16 July, 2026; originally announced July 2026.

Comments: 33 pages, 4 figures

Planetary climate interactions of the Qinghai-Tibetan Plateau

Authors: Ziyan Wang, Teng Liu, Shang Wang, Sheng Fang, Jun Meng, Xiaosong Chen, Jürgen Kurths, Shlomo Havlin, Fahu Chen, Johan Rockström, Deliang Chen, Hans Joachim Schellnhuber, Jingfang Fan

Abstract: The Qinghai-Tibetan Plateau (QTP), Earth's "Third Pole", profoundly shapes the Asian monsoon and regional climate and exerts far-reaching influence on the global climate system. Yet its role in organizing planetary-scale climate interactions remains poorly quantified. Here we develop a climate network framework to explicitly resolve the planetary teleconnection architecture associated with the QTP… ▽ More The Qinghai-Tibetan Plateau (QTP), Earth's "Third Pole", profoundly shapes the Asian monsoon and regional climate and exerts far-reaching influence on the global climate system. Yet its role in organizing planetary-scale climate interactions remains poorly quantified. Here we develop a climate network framework to explicitly resolve the planetary teleconnection architecture associated with the QTP across historical observations and future climate projections, with physical consistency assessed using Lagrangian trajectory diagnostics and targeted numerical experiments. We uncover a persistent and directional interaction structure linking the QTP with multiple major climate tipping elements. In particular, we identify a robust tripolar interaction mode coupling the QTP with both the Arctic and Antarctica through coherent atmospheric-oceanic pathways. Our findings establish the QTP as a critical planetary climate integrator, revealing a significant blind spot in current climate models and risk frameworks regarding cascading tipping dynamics in a warming world. △ Less

Submitted 18 April, 2026; originally announced April 2026.

Comments: 40 pages, 4 figures, 4 extended data figures, 1 extended data table

Two phase transitions in modular multiplex networks

Authors: Yael Kfir-Cohen, Dana Ben Porath, Bnaya Gross, Sergey Buldyrev, Shlomo Havlin

Abstract: Modular networks, such as critical infrastructures, are often built from distinct, densely connected modules (e.g., cities) that are sparsely interconnected. When such networks are gradually and randomly disrupted under a percolation process, they undergo two critical phase transitions. The first transition occurs when modules become isolated from one another, while the second corresponds to the c… ▽ More Modular networks, such as critical infrastructures, are often built from distinct, densely connected modules (e.g., cities) that are sparsely interconnected. When such networks are gradually and randomly disrupted under a percolation process, they undergo two critical phase transitions. The first transition occurs when modules become isolated from one another, while the second corresponds to the collapse of the entire network, including the internal connectivity of the modules. Here, we study these phase transitions in modular multiplex networks and compare them with those observed in single-layer modular networks. We focus on models in which the modules are arranged and connected either as a Random Regular network or as a two-dimensional square lattice. We show here that these systems exhibit diverse transition behaviors, with some transitions occurring continuously and others abruptly; notably, one realistic model could display two distinct first-order transitions in the same system. For the modular Random Regular multiplex, we further characterize the spatial transition through its scaling behavior, revealing signatures of a mixed-order phase transitions. In addition, we analytically determine the critical threshold at which modules become disconnected. Our results highlight the crucial role of modular organization and the critical role of interdependence in shaping network vulnerabilities under failures. △ Less

Submitted 10 February, 2026; originally announced February 2026.

Comments: 6 pages, 6 figures

The mechanistic origin of branching-driven nucleation in abrupt phase transitions

Authors: Leyang Xue, Shengling Gao, Bnaya Gross, Orr Levy, Daqing Li, Zengru Di, Lazaros K. Gallos, Shlomo Havlin

Abstract: Phase transitions are the macroscopic manifestation of microscopic processes that drive a system towards a new state. The detailed evolution of these processes, particularly in abrupt phase transitions, are currently not fully understood. Here, we introduce a theoretical framework based on internal node dependencies within a single-layer lattice. Crucially, we demonstrate that the fundamental mech… ▽ More Phase transitions are the macroscopic manifestation of microscopic processes that drive a system towards a new state. The detailed evolution of these processes, particularly in abrupt phase transitions, are currently not fully understood. Here, we introduce a theoretical framework based on internal node dependencies within a single-layer lattice. Crucially, we demonstrate that the fundamental mechanism underlying abrupt transitions is nucleation propagation preceded by a slow cascading process which scales with the range of dependencies. Our findings show that the synergy between these two distinct stages is essential for the occurrence of an abrupt transition. The first stage of a slow cascading mechanism was recently observed experimentally in superconducting layered materials, where heat acts as the dependency links, for the limit of infinite dependency range. Our model thus generalizes the framework to include finite dependency ranges, revealing previously unobserved mechanisms that could be experimentally verified through controlling the range of thermal diffusion in the material. As a universal mechanism, our model provides a robust method to test nucleation-controlled phase transitions in multiple systems, providing a path to discover and understand microscopic mechanisms in phase transitions. △ Less

Submitted 20 January, 2026; originally announced January 2026.

Long-term prediction of ENSO with physics-guided Deep Echo State Networks

Authors: Zejing Zhang, Jun Meng, Zhongpu Qiu, Wansuo Duan, Jian Gao, Zixiang Yan, Jinghua Xiao, Xiaosong Chen, Wenju Cai, Jürgen Kurths, Shlomo Havlin, Jingfang Fan

Abstract: The El Niño-Southern Oscillation (ENSO) is a dominant mode of interannual climate variability, yet the mechanisms limiting its long-lead predictability remain unclear. Here we develop a physics-guided Deep Echo State Network (DESN) that operates on physically interpretable climate modes selected from the extended recharge oscillator (XRO) framework. DESN achieves skillful Niño3.4 predictions up to… ▽ More The El Niño-Southern Oscillation (ENSO) is a dominant mode of interannual climate variability, yet the mechanisms limiting its long-lead predictability remain unclear. Here we develop a physics-guided Deep Echo State Network (DESN) that operates on physically interpretable climate modes selected from the extended recharge oscillator (XRO) framework. DESN achieves skillful Niño3.4 predictions up to 16-20 months ahead with minimal computational cost. Mechanistic experiments show that extended predictability arises from nonlinear coupling between warm water volume and inter-basin climate modes. Error-growth analysis further indicates a finite ENSO predictability horizon of approximately 30 months. These results demonstrate that physics-guided reservoir computing provides an efficient and interpretable framework for diagnosing and predicting ENSO at long lead times. △ Less

Submitted 17 January, 2026; originally announced January 2026.

The origin of long-range links of air pollution in China

Authors: Qiuyue Li, Daqing Li, Yossi Ashkenazy, Shlomo Havlin

Abstract: Weather conditions significantly influence the formation and dispersion of pollution variations. Here we study networks of pollution as well as climate networks and find that pollutants may not only have an impact close to their source but also show a significant correlation with pollutant concentrations thousands of kilometers away. We develop a pollution network model based on cross-correlation… ▽ More Weather conditions significantly influence the formation and dispersion of pollution variations. Here we study networks of pollution as well as climate networks and find that pollutants may not only have an impact close to their source but also show a significant correlation with pollutant concentrations thousands of kilometers away. We develop a pollution network model based on cross-correlation between PM2.5 concentration time series in different sites in China to detect stable long-range links during the last ten years. A multi-network analysis of the 500 hPa geopotential height and PM2.5 concentration suggests that long-range correlations in PM2.5 levels are also influenced by synoptic activity. △ Less

Submitted 7 September, 2025; originally announced September 2025.

Comments: 7 pages, 4 figures

The Spontaneous Cascading Mechanism Behind Critical Phenomena in Self-Coupled Lasers

Authors: Jiaoqing Wang, Yael Kfir-Cohen, Chenni Xu, Bnaya Gross, Aswathy Sundaresan, Shlomo Havlin, Patrick Sebbah

Abstract: The basic physics of lasers is characterized by a second-order continuous phase transition at the critical lasing threshold. Nevertheless, laser bistability with abrupt transitions has been reported in some laser systems, but its underlying mechanism has never been explored. Here we study experimentally and theoretically a novel nonlinearly self-coupled laser system. We show both experimentally an… ▽ More The basic physics of lasers is characterized by a second-order continuous phase transition at the critical lasing threshold. Nevertheless, laser bistability with abrupt transitions has been reported in some laser systems, but its underlying mechanism has never been explored. Here we study experimentally and theoretically a novel nonlinearly self-coupled laser system. We show both experimentally and theoretically that this system experiences spontaneous cascading that yields an abrupt mixed-order transition. At the critical point, a long-lived cascading plateau is observed, characterized by a critical branching factor equal to one. When deviating from criticality, the branching factor departs monotonically from one. The critical scaling close to and at the critical point resembles similar phenomena observed recently in other interdependent systems, suggesting a common universal cascading origin for abrupt transitions. Our results shed light on the cascading mechanism of abrupt transitions in laser systems, which can be utilized for future research and applications. △ Less

Submitted 29 August, 2025; originally announced August 2025.

Dynamics of critical cascades in interdependent networks

Authors: Dolev Dilmoney, Bnaya Gross, Shlomo Havlin, Nadav M. Shnerb

Abstract: The collapse of interdependent networks, as well as similar avalanche phenomena, is driven by cascading failures. At the critical point, the cascade begins as a critical branching process, where each failing node (element) triggers, on average, the failure of one other node. As nodes continue to fail, the network becomes increasingly fragile and the branching factor grows. If the failure process d… ▽ More The collapse of interdependent networks, as well as similar avalanche phenomena, is driven by cascading failures. At the critical point, the cascade begins as a critical branching process, where each failing node (element) triggers, on average, the failure of one other node. As nodes continue to fail, the network becomes increasingly fragile and the branching factor grows. If the failure process does not reach extinction during its critical phase, the network undergoes an abrupt collapse. Here, we implement the analogy between this dynamic and birth-death processes to derive new analytical results and significantly optimize numerical calculations. Using this approach, we analyze three key aspects of the dynamics: the probability of collapse, the duration of avalanches, and the length of the cascading plateau phase preceding a collapse. This analysis quantifies how system size and the intensity of the initial triggering event influence these characteristics. △ Less

Submitted 9 April, 2025; originally announced April 2025.

The microscopic origin of abrupt transitions in interdependent systems

Authors: Bnaya Gross, Irina Volotsenko, Yuval Sallem, Nahala Yadid, Ivan Bonamassa, Shlomo Havlin, Aviad Frydman

Abstract: Phase transitions are fundamental features of statistical physics. While the well-studied continuous phase transitions are known to be controlled by external \textit{macroscopic} changes in the order parameter, the origin of abrupt transitions is not yet clear. Here we show that abrupt phase transitions may occur due to a unique internal \textit{microscopic} cascading mechanism, resulting from dep… ▽ More Phase transitions are fundamental features of statistical physics. While the well-studied continuous phase transitions are known to be controlled by external \textit{macroscopic} changes in the order parameter, the origin of abrupt transitions is not yet clear. Here we show that abrupt phase transitions may occur due to a unique internal \textit{microscopic} cascading mechanism, resulting from dependency interactions. We experimentally unveil the underlying mechanism of the abrupt transition in interdependent superconducting networks to be governed by a unique metastable state of a long-living resistance cascading plateau. This plateau is characterized by spontaneous \textit{microscopic} changes that last for \textit{thousands} of seconds, followed by a \textit{macroscopic} phase shift of the system. Similar microscopic mechanisms are expected to be found in a variety of systems showing abrupt transitions. △ Less

Submitted 23 October, 2024; v1 submitted 5 March, 2024; originally announced March 2024.

Time persistence of climate and carbon flux networks

Authors: Ting Qing, Fan Wang, Qiuyue Li, Gaogao Dong, Lixin Tian, Shlomo Havlin

Abstract: The persistence of the global climate system is critical for assuring the sustainability of the natural ecosystem and the further development of the prosperity of socio-economics. In this paper, we develop a framework and analyze the time persistence of the yearly networks of climate and carbon flux, based on cross-correlations between sites, using daily data from China, the contiguous United Stat… ▽ More The persistence of the global climate system is critical for assuring the sustainability of the natural ecosystem and the further development of the prosperity of socio-economics. In this paper, we develop a framework and analyze the time persistence of the yearly networks of climate and carbon flux, based on cross-correlations between sites, using daily data from China, the contiguous United States, and the Europe land region during 2000-2019. There are many studies on time persistence of single nodes, e.g., climate variables at a given location, however persistence at a network level has been rarely discussed. Here we develop a framework to study time persistence of network and we apply it to climate and carbon flux. Our framework for determining the persistence is based on analyzing the similarity between the network structures, i.e., the links of climate and carbon flux in different years of systems using the Jaccard index. Our Jaccard results reveal that the similarity of climate and carbon flux networks in different years are within the range of 0.51$\pm$ 0.09 (p-value<0.05), implying that the climate and carbon flux networks studied in the Earth's climate system are generally persistent and in a steady state. Our results suggest that close to 50% of the links appear regularly in different years. We find a very small decay in similarity when the gap between the years increases. However, we observe unique behavior of less similarity to other years in the carbon flux network of the Chinese region during the years 2004-2005 and 2015-2016. This seems to reflect China's carbon reduction policies in these specific years. Analyzing the persistence and evolution of the climate and carbon flux networks, enhance our understanding of the spatial and temporal evolution of the global climate system. △ Less

Submitted 24 February, 2024; originally announced February 2024.

Comments: 46 pages, 44 figures

Regional Greening as a `Positive' Tipping Phenomenon

Authors: Yu Sun, Teng Liu, Shang Wang, Jun Meng, Yongwen Zhang, Saini Yang, Xiaosong Chen, Deliang Chen, Jürgen Kurths, Shlomo Havlin, Hans Joachim Schellnhuber, Jingfang Fan

Abstract: Earth system tipping elements have been predominantly investigated for their potential to trigger \textit{negative} ecological, climatic, and societal shifts. Yet, an overlooked but seminal avenue exists in the form of \textit{positive} tipping phenomena, whose underlying mechanisms and benefits remain largely underexplored. To bridge this gap, our research introduces a fundamental percolation-bas… ▽ More Earth system tipping elements have been predominantly investigated for their potential to trigger \textit{negative} ecological, climatic, and societal shifts. Yet, an overlooked but seminal avenue exists in the form of \textit{positive} tipping phenomena, whose underlying mechanisms and benefits remain largely underexplored. To bridge this gap, our research introduces a fundamental percolation-based framework to assess the criticality and resilience of planetary terrestrial vegetation systems. Leveraging high-resolution satellite data, we focus on greening-induced positive tipping dynamics driven by global warming. We feature the Qinghai-Tibetan Plateau (QTP) and the Sahel region as contrasting yet analogous case studies. Our analysis uncovers an intriguing phenomenon where vegetation fragmentation aligns with a percolation threshold, exhibiting a scale-invariant pattern characterized by nearly perfect power laws with three critical exponents. Remarkably, contrary to conventional destructive tipping elements, these regions act as favorable tipping elements, transitioning from fragmented to cohesive vegetation patterns due to anthropogenic climate change and afforestation efforts. Furthermore, we propose an \textit{optimal resilience enhancement model} to reinforce vegetation robustness while minimizing socio-economic costs. This study provides valuable insights into the favorable aspects of tipping elements under climate change and offers effective strategies for enhancing ecological resilience against environmental threats. △ Less

Submitted 6 December, 2023; originally announced December 2023.

A complexity perspective on the geographical location of companies: How distance reduce trade between firms

Authors: Eduardo Viegas, Orr Levy, Shlomo Havlin, Hideki Takayasu, Misako Takayasu

Abstract: Geometrical distance is an important constraining factor underpinning the emergence of social and economic interactions of complex systems. Yet, agent-based studies supported by granular analysis of distances are limited. Here, we develop a complexity method that places the real physical world, represented by the actual geographical location of individual firms in Japan, at the epicentre of our re… ▽ More Geometrical distance is an important constraining factor underpinning the emergence of social and economic interactions of complex systems. Yet, agent-based studies supported by granular analysis of distances are limited. Here, we develop a complexity method that places the real physical world, represented by the actual geographical location of individual firms in Japan, at the epicentre of our research. By combining methods derived from network science (to evaluate the emerging properties of the agents) together with information theory measures (to capture the strength of interaction among these agents), we can systematically analyse a comprehensive dataset of Japanese inter-firm business transactions network and evaluate the effects of spatial features on the structural patterns of the economy. We find that the normalised probability distributions of distances between interacting firms show a power law like decay concomitant to the sizes of firms and regions, with slower decays in major cities. Furthermore, small firms would reach large distances to become a customer of large firms while trading between either only small firms, or only large firms, tends to be at smaller distances. However, a time evolution analysis suggests that a level of market optimisation occurs over time as a reduction in the overall average trading distances in last 20 years can be observed. Lastly, our analysis concerning the trading dynamics among prefectures indicate that the preference to trade with neighbouring prefectures tends to be more pronounced at rural regions as opposed to the larger central conurbations, leading to the formation of three distinct types of regional geographical clusters. △ Less

Submitted 27 November, 2023; originally announced November 2023.

Nucleation phenomena and extreme vulnerability of spatial k-core systems

Authors: Leyang Xue, Shengling Gao, Lazaros K. Gallos, Orr Levy, Bnaya Gross, Zengru Di, Shlomo Havlin

Abstract: K-core percolation is a fundamental dynamical process in complex networks with applications that span numerous real-world systems. Earlier studies focus primarily on random networks without spatial constraints and reveal intriguing mixed-order transitions. However, real-world systems, ranging from transportation and communication networks to complex brain networks, are not random but are spatially… ▽ More K-core percolation is a fundamental dynamical process in complex networks with applications that span numerous real-world systems. Earlier studies focus primarily on random networks without spatial constraints and reveal intriguing mixed-order transitions. However, real-world systems, ranging from transportation and communication networks to complex brain networks, are not random but are spatially embedded. Here, we study k-core percolation on two-dimensional spatially embedded networks and show that, in contrast to regular percolation, the length of connections can control the transition type, leading to four different types of phase transitions associated with novel phenomena and a rich phase diagram. A key finding is the existence of a metastable phase in which microscopic localized damage, independent of system size, can cause a macroscopic phase transition, a result which cannot be achieved in traditional percolation. In this case, local failures can spontaneously propagate the damage radially until the system entirely collapses, a phenomenon analogous to the nucleation process. These findings suggest novel features and extreme vulnerabilities of spatially embedded k-core network systems, and highlight the necessity to take into account the characteristic length of links when designing robust spatial networks. Furthermore, our insight about the microscopic processes and their origin during the mixed order and first order abrupt transitions in k-core networks could shed light on the mechanisms of many systems where such transitions occur. △ Less

Submitted 10 July, 2024; v1 submitted 22 November, 2023; originally announced November 2023.

Comments: 17 pages, 13 figures

Percolation Theories for Quantum Networks

Authors: Xiangyi Meng, Xinqi Hu, Yu Tian, Gaogao Dong, Renaud Lambiotte, Jianxi Gao, Shlomo Havlin

Abstract: 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 dista… ▽ More 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. △ Less

Submitted 19 November, 2023; v1 submitted 27 October, 2023; originally announced October 2023.

Reduced seismic activity after mega earthquakes

Authors: Yongwen Zhang, Maor Elbaz, Shlomo Havlin, Yosef Ashkenazy

Abstract: Mainshocks are often followed by increased earthquake activity (aftershocks). According to the Omori-Utsu law, the rate of aftershocks decays as a power law over time. While aftershocks typically occur in the vicinity of the mainshock, previous studies have suggested that mainshocks can also trigger earthquakes in remote locations. Here we examine the earthquake rate in the days following mega-ear… ▽ More Mainshocks are often followed by increased earthquake activity (aftershocks). According to the Omori-Utsu law, the rate of aftershocks decays as a power law over time. While aftershocks typically occur in the vicinity of the mainshock, previous studies have suggested that mainshocks can also trigger earthquakes in remote locations. Here we examine the earthquake rate in the days following mega-earthquakes (magnitude >= 7.5) and find that the rate is significantly lower beyond a certain distance from the epicenter compared to surrogate data. However, the remote earthquake rate after the strongest earthquakes (magnitude >= 8) can also be significantly higher than that of the rate based on surrogate data. Comparing our findings to the global ETAS model, we find that the model does not capture the earthquake rate found in the data, hinting at a potential missing mechanism. We suggest that the diminished earthquake rate is due the release of global energy/tension subsequent to substantial mainshock events. This conjecture holds the potential to enhance our comprehension of the intricacies governing post-seismic activity. △ Less

Submitted 3 October, 2023; originally announced October 2023.

Critical behavior of cascading failures in overloaded networks

Authors: Ignacio A. Perez, Dana Ben Porath, Cristian E. La Rocca, Lidia A. Braunstein, Shlomo Havlin

Abstract: While network abrupt breakdowns due to overloads and cascading failures have been studied extensively, the critical exponents and the universality class of such phase transitions have not been discussed. Here, we study breakdowns triggered by failures of links and overloads in networks with a spatial characteristic link length $ζ$. Our results indicate that this abrupt transition has features and… ▽ More While network abrupt breakdowns due to overloads and cascading failures have been studied extensively, the critical exponents and the universality class of such phase transitions have not been discussed. Here, we study breakdowns triggered by failures of links and overloads in networks with a spatial characteristic link length $ζ$. Our results indicate that this abrupt transition has features and critical exponents similar to those of interdependent networks, suggesting that both systems are in the same universality class. For weakly embedded systems (i.e., $ζ$ of the order of the system size $L$) we observe a mixed-order transition, where the order parameter collapses following a long critical plateau. On the other hand, strongly embedded systems (i.e., $ζ\ll L$) exhibit a pure first-order transition, involving nucleation and the growth of damage. The system's critical behavior in both limits is similar to that observed in interdependent networks. △ Less

Submitted 6 March, 2024; v1 submitted 10 July, 2023; originally announced July 2023.

Comments: 6 pages, 6 figures

Dynamics of cascades in spatial interdependent networks

Authors: Bnaya Gross, Ivan Bonamassa, Shlomo Havlin

Abstract: The dynamics of cascading failures in spatial interdependent networks significantly depend on the interaction range of dependency couplings between layers. In particular, for 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… ▽ More The dynamics of cascading failures in spatial interdependent networks significantly depend on the interaction range of dependency couplings between layers. In particular, for 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 layout 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. △ Less

Submitted 6 July, 2023; v1 submitted 1 July, 2023; originally announced July 2023.

Enhancing Traffic Flow Efficiency through an Innovative Decentralized Traffic Control Based on Traffic Bottlenecks

Authors: Nimrod Serok, Shlomo Havlin, Efrat Blumenfeld Lieberthal

Abstract: To address the challenge of conflicting traffic flows that complete on opposing cycle times in a specific phase of the traffic light, we proposed a novel decentralized traffic light control methodology based on the identification of the congestion's bottleneck and its influence. By computing the cost of each congested tree, this methodology, called the Tree Method, prioritizes bottlenecks based on… ▽ More To address the challenge of conflicting traffic flows that complete on opposing cycle times in a specific phase of the traffic light, we proposed a novel decentralized traffic light control methodology based on the identification of the congestion's bottleneck and its influence. By computing the cost of each congested tree, this methodology, called the Tree Method, prioritizes bottlenecks based on global influence, i.e., their impact on the entire road network. To test this methodology, we used SUMO (Simulation of Urban Mobility) as a traffic simulator to run various simulations with both realistic and abstract Origin-Destination (OD) matrices under different traffic loads. By prioritizing traffic flows based on their global cost, rather than merely local ones, the Tree Method accurately identified the root cause of traffic-tree congestion and its effect along the traffic upstream. It exhibited major improvements in both the throughput and the average travel time measurements. Further in-depth analyses of individual simulation runs and time-based performance demonstrated that the Tree Method is superior compared to other methods, not only in terms of average performance but also for the majority of drivers and throughout most of the time. Another significant advantage of this method is its simplicity of analysis, facilitating real-time adjustments in each cycle and aligning with the inherent feedback dynamics of traffic flows. This feature makes the Tree Method highly suitable for integration into actual traffic control systems. △ Less

Submitted 24 June, 2023; originally announced June 2023.

Microscopic intervention yields abrupt transition in interdependent magnetic networks

Authors: Bnaya Gross, Ivan Bonamassa, Shlomo Havlin

Abstract: The study of interdependent networks has recently experienced a boost with the development of experimentally testable materials that physically realize their critical behaviors, calling for systematic studies that go beyond the percolation paradigm. Here we study the critical phase transition of interdependent spatial magnetic networks model where dependency couplings between networks are realized… ▽ More The study of interdependent networks has recently experienced a boost with the development of experimentally testable materials that physically realize their critical behaviors, calling for systematic studies that go beyond the percolation paradigm. Here we study the critical phase transition of interdependent spatial magnetic networks model where dependency couplings between networks are realized by a thermal interaction having a tunable spatial range. We show how the critical phenomena and the phase diagram of this realistic model are highly affected by the range of thermal dissipation and how the latter changes the transition from continuous to abrupt. Furthermore, we show that microscopic interventions of localized heating and localized magnetic field yield a macroscopic phase transition and novel phase diagrams. Our results provide novel and realistic insights about controlling the macroscopic phases of interdependent materials by means of localized microscopic interventions. △ Less

Submitted 8 June, 2023; originally announced June 2023.

Possible origin for the similar phase transitions in k-core and interdependent networks

Authors: Shengling Gao, Leyang Xue, Bnaya Gross, Zhikun She, Daqing Li, Shlomo Havlin

Abstract: The models of $k$-core percolation and interdependent networks (IN) have been extensively studied in their respective fields. A recent study has revealed that they share several common critical exponents. However, several newly discovered exponents in IN have not been explored in $k$-core percolation, and the origin of the similarity still remains unclear. Here, we investigate k-core percolation i… ▽ More The models of $k$-core percolation and interdependent networks (IN) have been extensively studied in their respective fields. A recent study has revealed that they share several common critical exponents. However, several newly discovered exponents in IN have not been explored in $k$-core percolation, and the origin of the similarity still remains unclear. Here, we investigate k-core percolation in random networks. We find that for k-core percolation,the fractality of the giant component fluctuations is manifested by a fractal fluctuation dimension, $\widetilde d_f = 3/4$, within a correlation \emph{size} $N'$ that scales as $N' \propto (p-p_c)^{-\widetildeν}$, with $\widetildeν= 2$, same as found in IN. Indeed, here, $\widetildeν\equiv d\cdot ν'$ and $\widetilde{d}_f \equiv d'_f/d$, where $ν'$ and $d'_f$ are respectively the same as the correlation \emph{length} exponent and the fractal fluctuation dimension observed in $d$-dimensional IN spatial networks. These two new exponents found here for $k$-core percolation demonstrate the same scaling behaviors as found for IN with the same critical exponents, reinforcing the similarity between the two models. Furthermore, we suggest that these two models are similar since both have two types of interactions: short-range (SR) connectivity and long-range (LR) influences. In IN the LR are the influences of dependency links while in k-core we find here that for $k=1$ and $k=2$ the influences are short range while for $k\geq3$ the influence is long range. In addition, analytical arguments for a universal hyper-scaling relation for the fractal fluctuation dimension of the $k$-core giant component and for IN as well as for any mixed-order transition are established.Our analysis enhances the comprehension of k-core percolation and supports the generalization of the concept of fractal fluctuations in mixed-order phase transitions. △ Less

Submitted 5 August, 2023; v1 submitted 10 May, 2023; originally announced May 2023.

Disruptive papers in science are losing impact

Authors: An Zeng, Ying Fan, Zengru Di, Yougui Wang, Shlomo Havlin

Abstract: The impact and originality are two critical dimensions for evaluating scientific publications, measured by citation and disruption metrics respectively. Despite the extensive effort made to understand the statistical properties and evolution of each of these metrics, the relations between the two remain unclear. In this paper, we study the evolution during last 70 years of the correlation between… ▽ More The impact and originality are two critical dimensions for evaluating scientific publications, measured by citation and disruption metrics respectively. Despite the extensive effort made to understand the statistical properties and evolution of each of these metrics, the relations between the two remain unclear. In this paper, we study the evolution during last 70 years of the correlation between scientific papers' citation and disruption, finding surprisingly a decreasing trend from positive to negative correlations over the years. Consequently, during the years, there are fewer and fewer disruptive works among the highly cited papers. These results suggest that highly disruptive studies nowadays attract less attention from the scientific community. The analysis on papers' references supports this trend, showing that papers citing older references, less popular references and diverse references become to have less citations. Possible explanations for the less attention phenomenon could be due to the increasing information overload in science, and citations become more and more prominent for impact. This is supported by the evidence that research fields with more papers have a more negative correlation between citation and disruption. Finally, we show the generality of our findings by analyzing and comparing six disciplines. △ Less

Submitted 5 May, 2023; originally announced May 2023.

Comments: 35 pages, 6+13 figures

Dense network motifs enhance dynamical stability

Authors: Bnaya Gross, Shlomo Havlin, Baruch Barzel

Abstract: Network motifs are the building blocks of complex networks and are significantly involved in the network dynamics such as information processing and local operations in the brain, biological marks for drug targets, identifying and predicting protein complexes in PPI networks, as well as echo chambers in social networks. Here we show that dense motifs such as cliques have different stable states th… ▽ More Network motifs are the building blocks of complex networks and are significantly involved in the network dynamics such as information processing and local operations in the brain, biological marks for drug targets, identifying and predicting protein complexes in PPI networks, as well as echo chambers in social networks. Here we show that dense motifs such as cliques have different stable states than the network itself. These stable states enhance the dynamical stability of the network and can even turn local stable states into global ones. Moreover, we show how cliques create polarization phenomena and global opinion changes. △ Less

Submitted 24 April, 2023; originally announced April 2023.

Increased earthquake rate prior to mainshocks

Authors: Eitan E. Asher, Shlomo Havlin, Shay Moshel, Yosef Ashkenazy

Abstract: According to the Omori-Utsu law, the rate of aftershocks after a mainshock decays as a power law with an exponent close to 1. This well-established law was intensively used in the past to study and model the statistical properties of earthquakes. Moreover, according to the so-called inverse Omori law, the rate of earthquakes should also increase prior to a mainshock -- this law has received much l… ▽ More According to the Omori-Utsu law, the rate of aftershocks after a mainshock decays as a power law with an exponent close to 1. This well-established law was intensively used in the past to study and model the statistical properties of earthquakes. Moreover, according to the so-called inverse Omori law, the rate of earthquakes should also increase prior to a mainshock -- this law has received much less attention due to its large uncertainty. Here, we mainly study the inverse Omori law based on a highly detailed Southern California earthquake catalog, which is complete for magnitudes larger than M>0.3. First, we develop a technique to identify mainshocks, foreshocks, and aftershocks. We then find, based on a statistical procedure we developed, that the rate of earthquakes is higher a few days prior to a mainshock. We find that this increase is much smaller for a catalog with a magnitude threshold of m over 2.5 and for the Epidemic-Type Aftershocks Sequence (ETAS) model catalogs, even when used with a small magnitude threshold. We also analyze the rate of aftershocks after mainshocks and find that the Omori-Utsu law does not hold for many individual mainshocks and that it may be valid only statistically when considering many mainshocks together. Yet, the analysis of the ETAS model based on the Omori-Utsu law exhibits similar behavior as that of the real catalogs, indicating the validity of this law. △ Less

Submitted 25 August, 2023; v1 submitted 8 February, 2023; originally announced February 2023.

Comments: 19 pages, 7 figures

The effect of cities and distance on COVID-19 spreading in the United States

Authors: Troy McMahon, Shlomo Havlin, Lazaros K. Gallos

Abstract: The COVID-19 pandemic has evolved over time through multiple spatial and temporal dynamics. The varying extent of interactions among different geographical areas can result to a complex pattern of spreading so that influences between these areas can be hard to discern. Here, we use cross-correlation analysis to detect synchronous evolution and potential inter-influences in the time evolution of ne… ▽ More The COVID-19 pandemic has evolved over time through multiple spatial and temporal dynamics. The varying extent of interactions among different geographical areas can result to a complex pattern of spreading so that influences between these areas can be hard to discern. Here, we use cross-correlation analysis to detect synchronous evolution and potential inter-influences in the time evolution of new COVID-19 cases at the county level in the USA. Our analysis identified two main time periods with distinguishable features in the behavior of correlations. In the first phase, there were few strong correlations which only emerged between urban areas. In the second phase of the epidemic, strong correlations became widespread and there was a clear directionality of influence from urban to rural areas. In general, the effect of distance between two counties was much weaker than that of the counties population. Such analysis can provide possible clues on the evolution of the disease and may identify parts of the country where intervention may be more efficient in limiting the disease spread. △ Less

Submitted 14 November, 2022; originally announced November 2022.

Comments: 18 pages, 7 figures

Teleconnections among Tipping Elements in the Earth System

Authors: Teng Liu, Dean Chen, Lan Yang, Jun Meng, Zanchenling Wang, Josef Ludescher, Jingfang Fan, Saini Yang, Deliang Chen, Jürgen Kurths, Xiaosong Chen, Shlomo Havlin, Hans Joachim Schellnhuber

Abstract: Tipping elements of the Earth system may shift abruptly and irreversibly from one state to another at tipping points, resulting in a growing threat to our society. Yet, it is not fully clear how to assess and quantify the influence of a tipping element and how to explore the teleconnections between different tipping elements. To fill this knowledge gap, we propose a climate network approach to qua… ▽ More Tipping elements of the Earth system may shift abruptly and irreversibly from one state to another at tipping points, resulting in a growing threat to our society. Yet, it is not fully clear how to assess and quantify the influence of a tipping element and how to explore the teleconnections between different tipping elements. To fill this knowledge gap, we propose a climate network approach to quantitatively analyze the global impacts of a prominent tipping element, the Amazon Rainforest Area (ARA). We find that regions, such as, the Tibetan Plateau (TP) and West Antarctic ice sheet, are characterized by higher network weighted links and exhibit strong correlations with the ARA. We then identify a teleconnection propagation path between the ARA and the TP. This path is robust under climate change as simulated by various climate models of CMIP5 and CMIP6. In addition, we detect early warning signals for critical transition in the snow cover extent on the Tibetan Plateau by applying critical slowing down indicators, lag-1 autocorrelation and detrended fluctuation analysis. We find that the snow cover of the TP has been losing stability since 2008, revealing that the TP is operating like a tipping element and approaching a potential tipping point. We further uncover that various climate extremes between the ARA and the TP are significantly synchronized under climate change. Our framework provides new insights into how tipping elements are linked to each other and into the potential predictability of cascading tipping dynamics. △ Less

Submitted 9 September, 2022; originally announced September 2022.

Impactful scientists have higher tendency to involve collaborators in new topics

Authors: An Zeng, Ying Fan, Zengru Di, Yougui Wang, Shlomo Havlin

Abstract: In scientific research, collaboration is one of the most effective ways to take advantage of new ideas, skills, resources, and for performing interdisciplinary research. Although collaboration networks have been intensively studied, the question of how individual scientists choose collaborators to study a new research topic remains almost unexplored. Here, we investigate the statistics and mechani… ▽ More In scientific research, collaboration is one of the most effective ways to take advantage of new ideas, skills, resources, and for performing interdisciplinary research. Although collaboration networks have been intensively studied, the question of how individual scientists choose collaborators to study a new research topic remains almost unexplored. Here, we investigate the statistics and mechanisms of collaborations of individual scientists along their careers, revealing that, in general, collaborators are involved in significantly fewer topics than expected from controlled surrogate. In particular, we find that highly productive scientists tend to have higher fraction of single-topic collaborators, while highly cited, i.e., impactful, scientists have higher fraction of multi-topic collaborators. We also suggest a plausible mechanism for this distinction. Moreover, we investigate the cases where scientists involve existing collaborators into a new topic. We find that compared to productive scientists, impactful scientists show strong preference of collaboration with high impact scientists on a new topic. Finally, we validate our findings by investigating active scientists in different years and across different disciplines. △ Less

Submitted 13 August, 2022; originally announced August 2022.

Comments: 26+23 pages, 6+18 figures

External field and critical exponents in controlling dynamics on complex networks

Authors: Hillel Sanhedrai, Shlomo Havlin

Abstract: Dynamical processes on complex networks, ranging from biological, technological and social systems, show phase transitions between distinct global states of the system. Often, such transitions rely upon the interplay between the structure and dynamics that takes place on it, such that weak connectivity, either sparse network or frail interactions, might lead to global activity collapse, while stro… ▽ More Dynamical processes on complex networks, ranging from biological, technological and social systems, show phase transitions between distinct global states of the system. Often, such transitions rely upon the interplay between the structure and dynamics that takes place on it, such that weak connectivity, either sparse network or frail interactions, might lead to global activity collapse, while strong connectivity leads to high activity. Here, we show that controlling dynamics of a fraction of the nodes in such systems acts as an external field in a continuous phase transition. As such, it defines corresponding critical exponents, both at equilibrium and of the transient time. We find the critical exponents for a general class of dynamics using the leading orders of the dynamic functions. By applying this framework to three examples, we reveal distinct universality classes. △ Less

Submitted 5 August, 2022; originally announced August 2022.

Improving robustness of spatial networks via reinforced nodes

Authors: Nir Vaturi, Bnaya Gross, Shlomo Havlin

Abstract: Many real-world networks are embedded in space, and their resilience in the presence of reinforced nodes has not been studied. Here we model such networks using a spatial network model that have an exponential distribution of link length $r$ having a characteristic length $ζ$. We find that reinforced nodes can significantly increase the resilience of the networks which varies with strength of spat… ▽ More Many real-world networks are embedded in space, and their resilience in the presence of reinforced nodes has not been studied. Here we model such networks using a spatial network model that have an exponential distribution of link length $r$ having a characteristic length $ζ$. We find that reinforced nodes can significantly increase the resilience of the networks which varies with strength of spatial embedding. We also study different reinforced node distribution strategies for improving the network resilience. Interestingly, we find that the best strategy is highly dependent on the stage of the percolation process, i.e., the expected fraction of failures. Finally, we show that the reinforced nodes are analogous to an external field in percolation phase transition i.e., having the same critical exponents and that the critical exponents satisfy Widom's relation. △ Less

Submitted 19 July, 2022; originally announced July 2022.

Comments: 7 pages, 10 figures

Delayed Impact of Interdisciplinary Research

Authors: Yang Zhang, Yang Wang, Haifeng Du, Shlomo Havlin

Abstract: Interdisciplinary research increasingly fuels innovation, and is considered to be a key to tomorrow breakthrough. Yet little is known about whether interdisciplinary research manifests delayed impact. Here, we use the time to reach the citation peak to quantify the highest impact time and citation dynamics, and examine its relationship with interdisciplinarity. Using large scale publication datase… ▽ More Interdisciplinary research increasingly fuels innovation, and is considered to be a key to tomorrow breakthrough. Yet little is known about whether interdisciplinary research manifests delayed impact. Here, we use the time to reach the citation peak to quantify the highest impact time and citation dynamics, and examine its relationship with interdisciplinarity. Using large scale publication datasets, our results suggest that interdisciplinary papers show significant delayed impact both microscopically per paper and macroscopically collectively, as it takes longer time for interdisciplinary papers to reach their citation peak. Furthermore, we study the underlying forces of such delayed impact, finding that the effect goes beyond the Matthew effect (i.e., the rich-get-richer effect). Finally, we find that team size and content conventionality only partly account for this effect. Overall, our results suggest that governments, research administrators, funding agencies should be aware of this general feature of interdisciplinary science, which may have broad policy implications. △ Less

Submitted 9 July, 2022; originally announced July 2022.

Comments: 21 pages, 4 figures

Sustaining a network by controlling a fraction of nodes

Authors: Hillel Sanhedrai, Shlomo Havlin

Abstract: Multi-stability is a widely observed phenomenon in real complex networked systems, such as technological infrastructures, ecological systems, gene regulation, transportation and more. When a system functions normally but there exists also a potential state with abnormal low activity, although the system is at equilibrium it might make a transition into the low activity undesired state due to exter… ▽ More Multi-stability is a widely observed phenomenon in real complex networked systems, such as technological infrastructures, ecological systems, gene regulation, transportation and more. When a system functions normally but there exists also a potential state with abnormal low activity, although the system is at equilibrium it might make a transition into the low activity undesired state due to external disturbances and perturbations. Thus, such a system can be regarded as unsustainable, due to the danger of falling into the potential inactive state. Here we explore, analytically and by simulations, how supporting the activity of a fraction $ρ$ of nodes can turn an unsustainable system to be sustainable by eliminating the inactive potential stable state. We thus unveil a new sustainability phase diagram in the presence of a fraction of controlled nodes $ρ$. This phase diagram could provide guidelines to sustain a network by external intervention and/or by strengthening the connectivity of the network. △ Less

Submitted 26 May, 2022; originally announced May 2022.

Epidemics on evolving networks with varying degrees

Authors: Hillel Sanhedrai, Shlomo Havlin

Abstract: Epidemics on complex networks is a widely investigated topic in the last few years, mainly due to the last pandemic events. Usually, real contact networks are dynamic, hence much effort has been invested in studying epidemics on evolving networks. Here we propose and study a model for evolving networks based on varying degrees, where at each time step a node might get, with probability $r$, a new… ▽ More Epidemics on complex networks is a widely investigated topic in the last few years, mainly due to the last pandemic events. Usually, real contact networks are dynamic, hence much effort has been invested in studying epidemics on evolving networks. Here we propose and study a model for evolving networks based on varying degrees, where at each time step a node might get, with probability $r$, a new degree and new neighbors according to a given degree distribution, instead of its former neighbors. We find analytically, using the generating functions framework, the epidemic threshold and the probability for a macroscopic spread of disease depending on the rewiring rate $r$. Our analytical results are supported by numerical simulations. We find surprisingly that the impact of the rewiring rate $r$ has qualitative different trends for networks having different degree distributions. That is, in some structures, such as random regular networks the dynamics enhances the epidemic spreading while in others such as scale free the dynamics reduces the spreading. In addition, for scale-free networks, we reveal that fast dynamics of the network, $r=1$, changes the epidemic threshold to nonzero rather than zero found for $r<1$, which is similar to the known case of $r=0$, i.e., a static network. Finally, we find the epidemic threshold also for a general distribution of the recovery time. △ Less

Submitted 10 January, 2022; v1 submitted 6 January, 2022; originally announced January 2022.

Percolation on spatial anisotropic networks

Authors: Ouriel Gotesdyner, Bnaya Gross, Dana Vaknin Ben Porath, Shlomo Havlin

Abstract: Many realistic systems such as infrastructures are characterized by spatial structure and anisotropic alignment. Here we propose and study a model for dealing with such characteristics by introducing a parameter that controls the strength of the anisotropy in the spatial network. This parameter is added to an existing isotropic model used to describe networks under spatial constraints, thus genera… ▽ More Many realistic systems such as infrastructures are characterized by spatial structure and anisotropic alignment. Here we propose and study a model for dealing with such characteristics by introducing a parameter that controls the strength of the anisotropy in the spatial network. This parameter is added to an existing isotropic model used to describe networks under spatial constraints, thus generalizing the spatial model to take into account both spatial and anisotropic features. We study the resilience of such networks by using a percolation process and find that anisotropy has a negative impact on a network's robustness. In addition, our results suggest that the anisotropy in this model does not affect the critical exponent of the correlation length, $ν$, which remains the same as the known $ν$ in 2D isotropic lattices. △ Less

Submitted 2 January, 2022; originally announced January 2022.

Comments: 9 pages, 5 figures

Cascading failures in isotropic and anisotropic spatial networks induced by localized attacks and overloads

Authors: I. A. Perez, D. Vaknin Ben Porath, C. E. La Rocca, S. V. Buldyrev, L. A. Braunstein, S. Havlin

Abstract: In this paper we study the Motter-Lai model of cascading failures induced by overloads in both isotropic and anisotropic spatial networks, generated by placing nodes in a square lattice and using various distributions of link lengths and angles. Anisotropy has not been earlier considered in the Motter-Lai model and is a real feature that may affect the cascading failures. This could reflect the ex… ▽ More In this paper we study the Motter-Lai model of cascading failures induced by overloads in both isotropic and anisotropic spatial networks, generated by placing nodes in a square lattice and using various distributions of link lengths and angles. Anisotropy has not been earlier considered in the Motter-Lai model and is a real feature that may affect the cascading failures. This could reflect the existence of a preferred direction in which a given attribute of the system manifests, such as power lines that follow a city built parallel to the coast. We show that the anisotropy causes a greater spread of damage along the preferential direction of links. We also identify the critical linear size, $l_c$, for a square shaped localized attack, which satisfies with high probability that above $l_c$ the cascading disrupts the giant component of functional nodes, while below $l_c$ the damage does not spread. We find that, for networks with any characteristic link length, their robustness decreases with the strength of the anisotropy. We show that the value of $l_c$ is finite and independent of the system size (for large systems), both for isotropic and anisotropic networks. Thus, in contrast to random attacks, where the critical fraction of nodes that survive the initial attack, $p_c$, is usually below 1, here $p_c = 1$. Note that the analogy to $p_c = 1$ is also found for localized attacks in interdependent spatial networks. Finally, we measure the final distribution of functional cluster sizes and find a power-law behavior, with exponents similar to regular percolation. This indicates that, after the cascade which destroys the giant component, the system is at a percolation critical point. Additionally, we observe a crossover in the value of the distribution exponent, from critical percolation in a two-dimensional lattice for strong spatial embedding, to mean-field percolation for weak embedding. △ Less

Submitted 16 March, 2022; v1 submitted 21 December, 2021; originally announced December 2021.

Comments: 22 pages, 11 figures

Topological-temporal properties of evolving networks

Authors: Alberto Ceria, Shlomo Havlin, Alan Hanjalic, Huijuan Wang

Abstract: Many real-world complex systems including human interactions can be represented by temporal (or evolving) networks, where links activate or deactivate over time. Characterizing temporal networks is crucial to compare such systems and to study the dynamical processes unfolding on them. A systematic method to characterize simultaneously the temporal and topological relations of active links (also ca… ▽ More Many real-world complex systems including human interactions can be represented by temporal (or evolving) networks, where links activate or deactivate over time. Characterizing temporal networks is crucial to compare such systems and to study the dynamical processes unfolding on them. A systematic method to characterize simultaneously the temporal and topological relations of active links (also called contacts or events), in order to compare different real-world networks and to detect their common patterns or differences is still missing. In this paper, we propose a method to characterize to what extent contacts that happen close in time occur also close in topology. Specifically, we study the interrelation between temporal and topological properties of contacts from three perspectives: (1) the autocorrelation of the time series recording the total number of contacts happened at each time step in a network; (2) the interplay between the topological distance and interevent time of two contacts; (3) the temporal correlation of contacts within local neighborhoods beyond a node pair. By applying our method on 13 real-world temporal networks, we found that temporal-topological correlation of contacts is more evident in virtual contact networks than in physical contact ones. This could be due to the lower cost and easier access of online communications than physical interactions, allowing and possibly facilitating social contagion, i.e., interactions of one individual may influence the activity of its neighbors. We also identify different patterns between virtual and physical networks and among physical contact networks at, e.g., school and workplace, in the formation of correlation in local neighborhoods. Detected patterns and differences may further inspire the development of more realistic temporal network models, that could reproduce jointly temporal and topological properties of contacts. △ Less

Submitted 29 August, 2022; v1 submitted 2 November, 2021; originally announced November 2021.

Comments: Manuscript accepted by Journal of Complex Networks

Identification and prioritization of urban traffic bottlenecks

Authors: Nimrod Serok, Shlomo Havlin, Efrat Blumenfeld Lieberthal

Abstract: The increasing urbanization process we have been witnessing in the last decades is accompanied by a significant increase in traffic congestion in cities around the world. The effect of the congestion is represented in the enormous time people spent on roads leading to significant money waste and air pollution. Here, we present a new methodology for identification, cost evaluation, and thus, priori… ▽ More The increasing urbanization process we have been witnessing in the last decades is accompanied by a significant increase in traffic congestion in cities around the world. The effect of the congestion is represented in the enormous time people spent on roads leading to significant money waste and air pollution. Here, we present a new methodology for identification, cost evaluation, and thus, prioritization of congestion sources, the jam bottlenecks. It extends existing methods as it is based on network analysis of the entire road network and can be applied to different traffic models. Our results show that the macro-stability, presented by scaling characteristics of the traffic bottlenecks, overshadows the existence of meso-dynamics, where the bottlenecks change their location in time and space. This means that to plan and manage traffic jams in different locations and at different times, it is required to implement a framework, as developed here, that tracks traffic and evaluates the relative effect of each evolving bottleneck on the entire road network. △ Less

Submitted 29 October, 2021; originally announced October 2021.

Realizing interdependent couplings as thermal or higher-order interactions

Authors: Ivan Bonamassa, Bnaya Gross, Shlomo Havlin

Abstract: Interdependence is a fundamental ingredient to analyze the stability of many real-world complex systems featuring functional liasons. Yet, physical realizations of this coupling are still unknown, due to the lack of a theoretical framework for their study. To address this gap, we develop an interdependent magnetization framework and show that dependency links between $K-1$ pairwise networks of Isi… ▽ More Interdependence is a fundamental ingredient to analyze the stability of many real-world complex systems featuring functional liasons. Yet, physical realizations of this coupling are still unknown, due to the lack of a theoretical framework for their study. To address this gap, we develop an interdependent magnetization framework and show that dependency links between $K-1$ pairwise networks of Ising spins can be rigorously mapped to directed $K$-spin interactions or to adaptive thermal couplings. We adopt the thermal portrait to determine analytically the phase diagram of the model under different structural configurations and we corroborate our results by extensive simulations. We find that interdependence acts like an entropic force that amplifies site-to-site thermal fluctuations, yielding unusual forms of vulnerability and making the system's functioning often unrecoverable. Finally, we discover an isomorphism between the ground state of random multi-spin models and interdependent percolation on randomly coupled networks. This connection raises new perspectives of cross-fertilization, providing unfamiliar methods with relevant implications in the study of constraint satisfaction as well as to the functional robustness of interdependent systems. △ Less

Submitted 2 December, 2024; v1 submitted 17 October, 2021; originally announced October 2021.

Comments: 24 pages, 10 figures

Scaling of variations in traveling distances and times of taxi routes

Authors: Xiaoyan Feng, Huijun Sun, Bnaya Gross, Jianjun Wu, Daqing Li, Xin Yang, Dong Zhou, Ziyou Gao, Shlomo Havlin

Abstract: The importance of understanding human mobility patterns has led many studies to examine their spatial-temporal scaling laws. These studies mainly reveal that human travel can be highly non-homogeneous with power-law scaling distributions of distances and times. However, investigating and quantifying the extent of variability in time and space when traveling the same air distance has not been addre… ▽ More The importance of understanding human mobility patterns has led many studies to examine their spatial-temporal scaling laws. These studies mainly reveal that human travel can be highly non-homogeneous with power-law scaling distributions of distances and times. However, investigating and quantifying the extent of variability in time and space when traveling the same air distance has not been addressed so far. Using taxi data from five large cities, we focus on several novel measures of distance and time to explore the spatio-temporal variations of taxi travel routes relative to their typical routes during peak and nonpeak periods. To compare all trips using a single measure, we calculate the distributions of the ratios between actual travel distances and the average travel distance as well as between actual travel times and the average travel time for all origin destinations (OD) during peak and nonpeak periods. In this way, we measure the scaling of the distribution of all single trip paths with respect to their mean trip path. Our results surprisingly demonstrate very broad distributions for both the distance ratio and time ratio, characterized by a long-tail power-law distribution. Moreover, all analyzed cities have larger exponents in peak hours than in nonpeak hours. We suggest that the interesting results of shorter trip lengths and times, characterized by larger exponents during rush hours, are due to the higher availability of travelers in rush hours compared to non-rush hours... △ Less

Submitted 13 October, 2021; originally announced October 2021.

Local Field Potential Journey into the Basal Ganglia

Authors: Eitan E. Asher, Maya Slovik, Rae Mitelman, Hagai Bergman, Shlomo Havlin, Shay Moshel

Abstract: Local Field potential (LFP) in the basal ganglia (BG) nuclei in the brain have attracted much research and clinical interest. However, the origin of this signal is still under debate throughout the last decades. The question is whether it is a local subthreshold phenomenon, synaptic input to neurons or it is a flow of electrical signals merged as volume conduction which are generated from simultan… ▽ More Local Field potential (LFP) in the basal ganglia (BG) nuclei in the brain have attracted much research and clinical interest. However, the origin of this signal is still under debate throughout the last decades. The question is whether it is a local subthreshold phenomenon, synaptic input to neurons or it is a flow of electrical signals merged as volume conduction which are generated from simultaneous firing neurons in the cerebral cortex and obeys the Maxwell equations. In this study, we recorded in a monkey brain simultaneously LFP's from the cerebral cortex, in the frontal lobe and primary motor cortex (M1) and in sites in all BG nuclei: the striatum, globus pallidus, and subthalamic nucleus. All the records were taken from human primate model (vervet monkey), during spontaneous activity. Developing and applying a novel method to identify significant cross-correlations (potential links) while removing "spurious" correlations, we found a tool that may discriminate between the two major phenomena of synaptic inputs (as we define as information flow) and volume conduction. We find mainly two major paths flows of field potential, that propagates with two different time delays, from the primary motor cortex, and from the frontal cortex. Our results indicate that the two path flows may represent the two mechanisms of volume conduction and information flow. △ Less

Submitted 19 October, 2022; v1 submitted 10 October, 2021; originally announced October 2021.

Asymmetry in earthquake interevent time intervals

Authors: Yongwen Zhang, Yosef Ashkenazy, Shlomo Havlin

Abstract: Here we focus on a basic statistical measure of earthquake catalogs that has not been studied before, the asymmetry of interevent time series (e.g., reflecting the tendency to have more aftershocks than spontaneous earthquakes). We define the asymmetry metric as the ratio between the number of positive interevent time increments minus negative increments and the total (positive plus negative) numb… ▽ More Here we focus on a basic statistical measure of earthquake catalogs that has not been studied before, the asymmetry of interevent time series (e.g., reflecting the tendency to have more aftershocks than spontaneous earthquakes). We define the asymmetry metric as the ratio between the number of positive interevent time increments minus negative increments and the total (positive plus negative) number of increments. Such asymmetry commonly exists in time series data for non-linear geophysical systems like river flow which decays slowly and increases rapidly. We find that earthquake interevent time series are significantly asymmetric, where the asymmetry function exhibits a significant crossover to weak asymmetry at large lag-index. We suggest that the Omori law can be associated with the large asymmetry at short time intervals below the crossover whereas overlapping aftershock sequences and the spontaneous events can be associated with a fast decay of asymmetry above the crossover. We show that the asymmetry is better reproduced by a recently modified ETAS model with two triggering processes in comparison to the standard ETAS model which only has one. △ Less

Submitted 13 August, 2021; originally announced August 2021.

Effects of mobility restrictions during COVID19 in Italy

Authors: Alex Smolyak, Giovanni Bonaccorsi, Andrea Flori, Fabio Pammolli, Shlomo Havlin

Abstract: To reduce the spread and the effect of the COVID-19 global pandemic, non-pharmaceutical interventions (NPIs) have been adopted on multiple occasions by governments. In particular lockdown policies, i.e., generalized mobility restrictions, have been employed to fight the first wave of the pandemic. We analyze data reflecting mobility levels over time in Italy before, during and after the national l… ▽ More To reduce the spread and the effect of the COVID-19 global pandemic, non-pharmaceutical interventions (NPIs) have been adopted on multiple occasions by governments. In particular lockdown policies, i.e., generalized mobility restrictions, have been employed to fight the first wave of the pandemic. We analyze data reflecting mobility levels over time in Italy before, during and after the national lockdown, in order to assess some direct and indirect effects. By applying methodologies based on percolation and network science approaches, we find that the typical network characteristics, while very revealing, do not tell the whole story. In particular, the Italian mobility network during lockdown has been damaged much more than node- and edge-level metrics indicate. Additionally, many of the main Provinces of Italy are affected by the lockdown in a surprisingly similar fashion, despite their geographical and economic dissimilarity. Based on our findings we offer an approach to estimate unavailable high-resolution economic dimensions, such as real time Province-level GDP, based on easily measurable mobility information. △ Less

Submitted 4 August, 2021; originally announced August 2021.

Comments: 15 pages, 8 figures

Optimization of robustness based on reinforced nodes in a modular network

Authors: Yael Kfir-Cohen, Dana Vaknin, Shlomo Havlin

Abstract: Many systems such as critical infrastructure exhibit a modular structure with many links within the modules and few links between them. One approach to increase the robustness of these systems is to reinforce a fraction of the nodes in each module, so that the reinforced nodes provide additional needed sources for themselves as well as for their nearby neighborhood. Since reinforcing a node can be… ▽ More Many systems such as critical infrastructure exhibit a modular structure with many links within the modules and few links between them. One approach to increase the robustness of these systems is to reinforce a fraction of the nodes in each module, so that the reinforced nodes provide additional needed sources for themselves as well as for their nearby neighborhood. Since reinforcing a node can be an expensive task, the efficiency of the decentralization process by reinforced nodes is vital. In our study we analyze a new model which combines both above mentioned features of real complex systems - modularity and reinforced nodes. Using tools from percolation theory, we derived an analytical solution for any partition of reinforced nodes; between nodes which have links that connect them to other modules ("inter-nodes") and nodes which have connections only within their modules ("intra-nodes"). Among our results, we find that near the critical percolation point ($p\approx p_c$) the robustness is greatly affected by the distribution. In particular, we find a partition of reinforced nodes which yields an optimal robustness and we show that the optimal partition remains constant for high average degrees. △ Less

Submitted 25 July, 2021; originally announced July 2021.

Cascading failures in anisotropic interdependent networks of spatial modular structures

Authors: Dana Vaknin, Amir Bashan, Lidia A. Braunstein, Sergey V. Buldyrev, Shlomo Havlin

Abstract: The structure of real-world multilayer infrastructure systems usually exhibits anisotropy due to constraints of the embedding space. For example, geographical features like mountains, rivers and shores influence the architecture of critical infrastructure networks. Moreover, such spatial networks are often non-homogeneous but rather have a modular structure with dense connections within communitie… ▽ More The structure of real-world multilayer infrastructure systems usually exhibits anisotropy due to constraints of the embedding space. For example, geographical features like mountains, rivers and shores influence the architecture of critical infrastructure networks. Moreover, such spatial networks are often non-homogeneous but rather have a modular structure with dense connections within communities and sparse connections between neighboring communities. When the networks of the different layers are interdependent, local failures and attacks may propagate throughout the system. Here we study the robustness of spatial interdependent networks which are both anisotropic and heterogeneous. We also evaluate the effect of localized attacks having different geometrical shapes. We find that anisotropic networks are more robust against localized attacks and that anisotropic attacks, surprisingly, even on isotropic structures, are more effective than isotropic attacks. △ Less

Submitted 26 June, 2021; originally announced June 2021.

Spatial correlations in geographical spreading of COVID-19 in USA

Authors: Troy McMahon, Adrian Chan, Shlomo Havlin, Lazaros K. Gallos

Abstract: The global spread of the COVID-19 pandemic has followed complex pathways, largely attributed to the high virus infectivity, human travel patterns, and the implementation of multiple mitigation measures. The resulting geographic patterns describe the evolution of the epidemic and can indicate areas which are at risk of an outbreak. Here, we analyze the spatial correlations of new active cases in US… ▽ More The global spread of the COVID-19 pandemic has followed complex pathways, largely attributed to the high virus infectivity, human travel patterns, and the implementation of multiple mitigation measures. The resulting geographic patterns describe the evolution of the epidemic and can indicate areas which are at risk of an outbreak. Here, we analyze the spatial correlations of new active cases in USA at the county level and characterize the extent of these correlations at different times. We show that the epidemic did not progress uniformly and we identify various stages which are distinguished by significant differences in the correlation length. Our results indicate that the correlation length may be large even during periods when the number of cases declines. We find that correlations between urban centers were much more significant than between rural areas and this finding indicates that long-range spreading was mainly facilitated by travel between cities, especially at the first months of the epidemic. We also show the existence of a percolation transition in November 2020, when the largest part of the country was connected to a spanning cluster, and a smaller-scale transition in January 2021, with both times corresponding to the peak of the epidemic in the country. △ Less

Submitted 26 June, 2021; originally announced June 2021.

Comments: 16 pages, 5 figures

Comment on "Inverse Square Lévy Walks are not Optimal Search Strategies for d $\geq$ 2" [Phys. Rev. Lett. 124, 080601 (2020)]

Authors: S. V. Buldyrev, E. P. Raposo, F. Bartumeus, S. Havlin, F. R. Rusch, M. G. E. da Luz, G. M. Viswanathan

Abstract: It is widely accepted that inverse square Lévy walks are optimal search strategies because they maximize the encounter rate with sparse, randomly distributed, replenishable targets when the search restarts in the vicinity of the previously visited target, which becomes revisitable again with high probability, i.e., non-destructive foraging [Nature 401, 911 (1999)]. The precise conditions for the v… ▽ More It is widely accepted that inverse square Lévy walks are optimal search strategies because they maximize the encounter rate with sparse, randomly distributed, replenishable targets when the search restarts in the vicinity of the previously visited target, which becomes revisitable again with high probability, i.e., non-destructive foraging [Nature 401, 911 (1999)]. The precise conditions for the validity of this Lévy flight foraging hypothesis (LFH) have been widely described in the literature [Phys. Life Rev. 14, 94 (2015)]. Nevertheless, three objecting claims to the LFH have been raised recently for $d \geq 2$: (i) the capture rate $η$ has linear dependence on the target density $ρ$ for all values of the Lévy index $α$; (ii) "the gain $η_{max}/η$ achieved by varying $α$ is bounded even in the limit $ρ\to 0 $" so that "tuning $α$ can only yield a marginal gain"; (iii) depending on the values of the radius of detection $a$, the restarting distance $l_c$ and the scale parameter $s$, the optimum is realized for a range of $α$ [Phys. Rev. Lett. 124, 080601 (2020)]. Here we answer each of these three criticisms in detail and show that claims (i)-(iii) do not actually invalidate the LFH. Our results and analyses restore the original result of the LFH for non-destructive foraging. △ Less

Submitted 22 March, 2021; v1 submitted 19 March, 2021; originally announced March 2021.

Journal ref: Physical Review Letters 126, 048901 (2021)

Reviving a failed network through microscopic interventions

Authors: Hillel Sanhedrai, Jianxi Gao, Amir Bashan, Moshe Schwartz, Shlomo Havlin, Baruch Barzel

Abstract: From mass extinction to cell death, complex networked systems often exhibit abrupt dynamic transitions between desirable and undesirable states. Such transitions are often caused by topological perturbations, such as node or link removal, or decreasing link strengths. The problem is that reversing the topological damage, namely retrieving the lost nodes or links, or reinforcing the weakened intera… ▽ More From mass extinction to cell death, complex networked systems often exhibit abrupt dynamic transitions between desirable and undesirable states. Such transitions are often caused by topological perturbations, such as node or link removal, or decreasing link strengths. The problem is that reversing the topological damage, namely retrieving the lost nodes or links, or reinforcing the weakened interactions, does not guarantee the spontaneous recovery to the desired functional state. Indeed, many of the relevant systems exhibit a hysteresis phenomenon, remaining in the dysfunctional state, despite reconstructing their damaged topology. To address this challenge, we develop a two-step recovery scheme: first - topological reconstruction to the point where the system can be revived, then dynamic interventions, to reignite the system's lost functionality. Applying this method to a range of nonlinear network dynamics, we identify the recoverable phase of a complex system, a state in which the system can be reignited by microscopic interventions, for instance, controlling just a single node. Mapping the boundaries of this dynamical phase, we obtain guidelines for our two-step recovery. △ Less

Submitted 21 July, 2022; v1 submitted 26 November, 2020; originally announced November 2020.

Journal ref: Nature Physics. 2022 Mar;18(3):338-49

Globalization emergence in the European Patent Office (EPO) patent network

Authors: Maria Tsouchnika, Alex Smolyak, Panos Argyrakis, Shlomo Havlin

Abstract: We studied the evolution of the European Patent Office (EPO) patents applicants' collaborations network, within a 35 years span of data (1978-2013). Focusing on the Giant Component (GC) formation process over many time-windows, distributed throughout the data timeline, we found that the features governing this phenomenon are indicative of emerging globalization in the applicants' collaborations. T… ▽ More We studied the evolution of the European Patent Office (EPO) patents applicants' collaborations network, within a 35 years span of data (1978-2013). Focusing on the Giant Component (GC) formation process over many time-windows, distributed throughout the data timeline, we found that the features governing this phenomenon are indicative of emerging globalization in the applicants' collaborations. The timeline appears to be divided into three regimes, corresponding to three states of the network's evolution. In the early years state, the GC takes long to form and the instant of its creation is easily pinpointed, while it features geographically segregated groups of applicants with technologically similar activities. In contrast, in the late years state, the GC forms quickly, the exact point of its creation is harder to spot, the applicants' activities are more disparate technologically, while their inter-regional collaborations are significantly increased. The middle years are an intermediate state between the two extreme of early and late years. Moreover, we concluded that the critical patents, which induce the GC's formation, are typically introduced by large-sized applicants and also that top patent-producing applicants are likely to submit critical patents, albeit at a lower rate than their overall patent submission. Lastly, we uncovered the crucial role that Japan plays in the network's coherence, through its prominent participation in the GC and the critical patents. △ Less

Submitted 21 September, 2020; originally announced September 2020.

Comments: 20 pages, 19 figures

Statistical physics approaches to the complex Earth system

Authors: Jingfang Fan, Jun Meng, Josef Ludescher, Xiaosong Chen, Yosef Ashkenazy, Jurgen Kurths, Shlomo Havlin, Hans Joachim Schellnhuber

Abstract: Global climate change, extreme climate events, earthquakes and their accompanying natural disasters pose significant risks to humanity. Yet due to the nonlinear feedbacks, strategic interactions and complex structure of the Earth system, the understanding and in particular the predicting of such disruptive events represent formidable challenges for both scientific and policy communities. During th… ▽ More Global climate change, extreme climate events, earthquakes and their accompanying natural disasters pose significant risks to humanity. Yet due to the nonlinear feedbacks, strategic interactions and complex structure of the Earth system, the understanding and in particular the predicting of such disruptive events represent formidable challenges for both scientific and policy communities. During the past years, the emergence and evolution of Earth system science has attracted much attention and produced new concepts and frameworks. Especially, novel statistical physics and complex networks-based techniques have been developed and implemented to substantially advance our knowledge for a better understanding of the Earth system, including climate extreme events, earthquakes and Earth geometric relief features, leading to substantially improved predictive performances. We present here a comprehensive review on the recent scientific progress in the development and application of how combined statistical physics and complex systems science approaches such as, critical phenomena, network theory, percolation, tipping points analysis, as well as entropy can be applied to complex Earth systems (climate, earthquakes, etc.). Notably, these integrating tools and approaches provide new insights and perspectives for understanding the dynamics of the Earth systems. The overall aim of this review is to offer readers the knowledge on how statistical physics approaches can be useful in the field of Earth system science. △ Less

Submitted 5 September, 2020; originally announced September 2020.

Epidemic spreading and control strategies in spatial modular network

Authors: Bnaya Gross, Shlomo Havlin

Abstract: 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 SIR model and study analytically and numerically the epidemic spread on a recently devel… ▽ More 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 SIR 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. △ Less

Submitted 6 September, 2020; originally announced September 2020.

Comments: 8 pages, 7 figures

Interdependent transport via percolation backbones in spatial networks

Authors: Bnaya Gross, Ivan Bonamassa, Shlomo Havlin

Abstract: The functionality of nodes in a network is often described by the structural feature of belonging to the giant component. However, when dealing with problems like transport, a more appropriate functionality criterion is for a node to belong to the network's backbone, where the flow of information and of other physical quantities (such as current) occurs. Here we study percolation in a model of int… ▽ More The functionality of nodes in a network is often described by the structural feature of belonging to the giant component. However, when dealing with problems like transport, a more appropriate functionality criterion is for a node to belong to the network's backbone, where the flow of information and of other physical quantities (such as current) occurs. Here we study percolation in a model of interdependent resistor networks and show the effect of spatiality on their coupled functioning. We do this on a realistic model of spatial networks, featuring a Poisson distribution of link-lengths. We find that interdependent resistor networks are significantly more vulnerable than their percolation-based counterparts, featuring first-order phase transitions at link-lengths where the mutual giant component still emerges continuously. We explain this apparent contradiction by tracing the origin of the increased vulnerability of interdependent transport to the crucial role played by the dandling ends. Moreover, we interpret these differences by considering an heterogeneous $k$-core percolation process which enables to define a one-parameter family of functionality criteria whose constraints become more and more stringent. Our results highlight the importance that different definitions of nodes functionality have on the collective properties of coupled processes, and provide better understanding of the problem of interdependent transport in many real-world networks. △ Less

Submitted 4 September, 2020; originally announced September 2020.

Comments: 7 pages, 6 figures

Cascading Failures in Complex Networks

Authors: Lucas D. Valdez, Louis Shekhtman, Cristian E. La Rocca, Xin Zhang, Sergey V. Buldyrev, Paul A. Trunfio, Lidia A. Braunstein, Shlomo Havlin

Abstract: Cascading failure is a potentially devastating process that spreads on real-world complex networks and can impact the integrity of wide-ranging infrastructures, natural systems, and societal cohesiveness. One of the essential features that create complex network vulnerability to failure propagation is the dependency among their components, exposing entire systems to significant risks from destabil… ▽ More Cascading failure is a potentially devastating process that spreads on real-world complex networks and can impact the integrity of wide-ranging infrastructures, natural systems, and societal cohesiveness. One of the essential features that create complex network vulnerability to failure propagation is the dependency among their components, exposing entire systems to significant risks from destabilizing hazards such as human attacks, natural disasters or internal breakdowns. Developing realistic models for cascading failures as well as strategies to halt and mitigate the failure propagation can point to new approaches to restoring and strengthening real-world networks. In this review, we summarize recent progress on models developed based on physics and complex network science to understand the mechanisms, dynamics and overall impact of cascading failures. We present models for cascading failures in single networks and interdependent networks and explain how different dynamic propagation mechanisms can lead to an abrupt collapse and a rich dynamic behavior. Finally, we close the review with novel emerging strategies for containing cascades of failures and discuss open questions that remain to be addressed. △ Less

Submitted 21 July, 2020; originally announced July 2020.

Comments: This review has been accepted for publication in the Journal of Complex Networks Published by Oxford University Press