Impactful scientists have higher tendency to involve collaborators in new topics.

In scientific research, collaboration is one of the most effective ways to take advantage of new ideas, skills, and 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 a controlled surrogate. In particular, we find that highly productive scientists tend to have a higher fraction of single-topic collaborators, while highly cited-i.e., impactful-scientists have a higher fraction of multitopic collaborators. We also suggest a plausible mechanism for this distinction. Moreover, we investigate the cases where scientists involve existing collaborators in 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.

Microscopic Intervention Yields Abrupt Transition in Interdependent Ferromagnetic Networks.

The study of interdependent networks has recently experienced a boost with the development of experimentally testable materials that physically realize their novel critical behaviors, calling for systematic studies that go beyond the percolation paradigm. Here we study the critical kinetics and phase transitions of a model of interdependent spatial ferromagnetic networks 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 influences the microscopic kinetics of the model. Furthermore, we show the existence of a new phase where localized microscopic interventions by heating or magnetic fields yield a macroscopic phase transition. Our results unveil rich phenomena and realistic protocols for controlling the macroscopic phases of interdependent materials by means of microscopic interventions.

Optimal resilience of modular interacting networks.

Coupling between networks is widely prevalent in real systems and has dramatic effects on their resilience and functional properties. However, current theoretical models tend to assume homogeneous coupling where all the various subcomponents interact with one another, whereas real-world systems tend to have various different coupling patterns. We develop two frameworks to explore the resilience of such modular networks, including specific deterministic coupling patterns and coupling patterns where specific subnetworks are connected randomly. We find both analytically and numerically that the location of the percolation phase transition varies nonmonotonically with the fraction of interconnected nodes when the total number of interconnecting links remains fixed. Furthermore, there exists an optimal fraction [Formula: see text] of interconnected nodes where the system becomes optimally resilient and is able to withstand more damage. Our results suggest that, although the exact location of the optimal [Formula: see text] varies based on the coupling patterns, for all coupling patterns, there exists such an optimal point. Our findings provide a deeper understanding of network resilience and show how networks can be optimized based on their specific coupling patterns.

Network-based forecasting of climate phenomena.

Network theory, as emerging from complex systems science, can provide critical predictive power for mitigating the global warming crisis and other societal challenges. Here we discuss the main differences of this approach to classical numerical modeling and highlight several cases where the network approach substantially improved the prediction of high-impact phenomena: 1) El Niño events, 2) droughts in the central Amazon, 3) extreme rainfall in the eastern Central Andes, 4) the Indian summer monsoon, and 5) extreme stratospheric polar vortex states that influence the occurrence of wintertime cold spells in northern Eurasia. In this perspective, we argue that network-based approaches can gainfully complement numerical modeling.

Multiple metastable network states in urban traffic.

While abrupt regime shifts between different metastable states have occurred in natural systems from many areas including ecology, biology, and climate, evidence for this phenomenon in transportation systems has been rarely observed so far. This limitation might be rooted in the fact that we lack methods to identify and analyze possible multiple states that could emerge at scales of the entire traffic network. Here, using percolation approaches, we observe such a metastable regime in traffic systems. In particular, we find multiple metastable network states, corresponding to varying levels of traffic performance, which recur over different days. Based on high-resolution global positioning system (GPS) datasets of urban traffic in the megacities of Beijing and Shanghai (each with over 50,000 road segments), we find evidence supporting the existence of tipping points separating three regimes: a global functional regime and a metastable hysteresis-like regime, followed by a global collapsed regime. We can determine the intrinsic critical points where the metastable hysteresis-like regime begins and ends and show that these critical points are very similar across different days. Our findings provide a better understanding of traffic resilience patterns and could be useful for designing early warning signals for traffic resilience management and, potentially, other complex systems.

Dynamics of cascades in spatial interdependent networks.

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

Percolation Theories for Quantum Networks.

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

Fractal Fluctuations at Mixed-Order Transitions in Interdependent Networks.

We study the critical features of the order parameter's fluctuations near the threshold of mixed-order phase transitions in randomly interdependent spatial networks. Remarkably, we find that although the structure of the order parameter is not scale invariant, its fluctuations are fractal up to a well-defined correlation length ξ^{'} that diverges when approaching the mixed-order transition threshold. We characterize the self-similar nature of these critical fluctuations through their effective fractal dimension d_{f}^{'}=3d/4, and correlation length exponent ν^{'}=2/d, where d is the dimension of the system. By analyzing percolation and magnetization, we demonstrate that d_{f}^{'} and ν^{'} are the same for both, i.e., independent of the symmetry of the process for any d of the underlying networks.

Propinquity drives the emergence of network structure and density.

The lack of large-scale, continuously evolving empirical data usually limits the study of networks to the analysis of snapshots in time. This approach has been used for verification of network evolution mechanisms, such as preferential attachment. However, these studies are mostly restricted to the analysis of the first links established by a new node in the network and typically ignore connections made after each node's initial introduction. Here, we show that the subsequent actions of individuals, such as their second network link, are not random and can be decoupled from the mechanism behind the first network link. We show that this feature has strong influence on the network topology. Moreover, snapshots in time can now provide information on the mechanism used to establish the second connection. We interpret these empirical results by introducing the "propinquity model," in which we control and vary the distance of the second link established by a new node and find that this can lead to networks with tunable density scaling, as found in real networks. Our work shows that sociologically meaningful mechanisms are influencing network evolution and provides indications of the importance of measuring the distance between successive connections.

Scale-free resilience of real traffic jams.

The concept of resilience can be realized in natural and engineering systems, representing the ability of a system to adapt and recover from various disturbances. Although resilience is a critical property needed for understanding and managing the risks and collapses of transportation systems, an accepted and useful definition of resilience for urban traffic as well as its statistical property under perturbations are still missing. Here, we define city traffic resilience based on the spatiotemporal clusters of congestion in real traffic and find that the resilience follows a scale-free distribution in 2D city road networks and 1D highways with different exponents but similar exponents on different days and in different cities. The traffic resilience is also revealed to have a scaling relation between the cluster size of the spatiotemporal jam and its recovery duration independent of microscopic details. Our findings of universal traffic resilience can provide an indication toward better understanding and designing of these complex engineering systems under internal and external disturbances.

Switch between critical percolation modes in city traffic dynamics.

Percolation transition is widely observed in networks ranging from biology to engineering. While much attention has been paid to network topologies, studies rarely focus on critical percolation phenomena driven by network dynamics. Using extensive real data, we study the critical percolation properties in city traffic dynamics. Our results suggest that two modes of different critical percolation behaviors are switching in the same network topology under different traffic dynamics. One mode of city traffic (during nonrush hours or days off) has similar critical percolation characteristics as small world networks, while the other mode (during rush hours on working days) tends to behave as a 2D lattice. This switching behavior can be understood by the fact that the high-speed urban roads during nonrush hours or days off (that are congested during rush hours) represent effective long-range connections, like in small world networks. Our results might be useful for understanding and improving traffic resilience.

Universal behavior of cascading failures in interdependent networks.

Catastrophic and major disasters in real-world systems, such as blackouts in power grids or global failures in critical infrastructures, are often triggered by minor events which originate a cascading failure in interdependent graphs. We present here a self-consistent theory enabling the systematic analysis of cascading failures in such networks and encompassing a broad range of dynamical systems, from epidemic spreading, to birth-death processes, to biochemical and regulatory dynamics. We offer testable predictions on breakdown scenarios, and, in particular, we unveil the conditions under which the percolation transition is of the first-order or the second-order type, as well as prove that accounting for dynamics in the nodes always accelerates the cascading process. Besides applying directly to relevant real-world situations, our results give practical hints on how to engineer more robust networked systems.

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

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

Statistical physics approaches to the complex Earth system.

Global warming, extreme climate events, earthquakes and their accompanying socioeconomic disasters pose significant risks to humanity. Yet due to the nonlinear feedbacks, multiple interactions and complex structures of the Earth system, the understanding and, in particular, the prediction of such disruptive events represent formidable challenges to 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 of the Earth system, including climate extreme events, earthquakes and geological 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, and entropy can be applied to complex Earth systems. 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 concepts and theories can be useful in the field of Earth system science.

Concurrence Percolation in Quantum Networks.

Establishing long-distance quantum entanglement, i.e., entanglement transmission, in quantum networks (QN) is a key and timely challenge for developing efficient quantum communication. Traditional comprehension based on classical percolation assumes a necessary condition for successful entanglement transmission between any two infinitely distant nodes: they must be connected by at least a path of perfectly entangled states (singlets). Here, we relax this condition by explicitly showing that one can focus not on optimally converting singlets but on establishing concurrence-a key measure of bipartite entanglement. We thereby introduce a new statistical theory, concurrence percolation theory (ConPT), remotely analogous to classical percolation but fundamentally different, built by generalizing bond percolation in terms of "sponge-crossing" paths instead of clusters. Inspired by resistance network analysis, we determine the path connectivity by series and parallel rules and approximate higher-order rules via star-mesh transforms. Interestingly, we find that the entanglement transmission threshold predicted by ConPT is lower than the known classical-percolation-based results and is readily achievable on any series-parallel networks such as the Bethe lattice. ConPT promotes our understanding of how well quantum communication can be further systematically improved versus classical statistical predictions under the limitation of QN locality-a "quantum advantage" that is more general and efficient than expected. ConPT also shows a percolationlike universal critical behavior derived by finite-size analysis on the Bethe lattice and regular two-dimensional lattices, offering new perspectives for a theory of criticality in entanglement statistics.

Climate network percolation reveals the expansion and weakening of the tropical component under global warming.

Global climate warming poses a significant challenge to humanity; it is associated with, e.g., rising sea level and declining Arctic sea ice. Increasing extreme events are also considered to be a result of climate warming, and they may have widespread and diverse effects on health, agriculture, economics, and political conflicts. Still, the detection and quantification of climate change, both in observations and climate models, constitute a main focus of the scientific community. Here, we develop an approach based on network and percolation frameworks to study the impacts of climate changes in the past decades using historical models and reanalysis records, and we analyze the expected upcoming impacts using various future global warming scenarios. We find an abrupt transition during the evolution of the climate network, indicating a consistent poleward expansion of the largest cluster that corresponds to the tropical area, as well as the weakening of the strength of links in the tropic. This is found both in the reanalysis data and in the Coupled Model Intercomparison Project Phase 5 (CMIP5) 21st century climate change simulations. The analysis is based on high-resolution surface (2 m) air temperature field records. We discuss the underlying mechanism for the observed expansion of the tropical cluster and associate it with changes in atmospheric circulation represented by the weakening and expansion of the Hadley cell. Our framework can also be useful for forecasting the extent of the tropical cluster to detect its influence on different areas in response to global warming.

Local structure can identify and quantify influential global spreaders in large scale social networks.

Measuring and optimizing the influence of nodes in big-data online social networks are important for many practical applications, such as the viral marketing and the adoption of new products. As the viral spreading on a social network is a global process, it is commonly believed that measuring the influence of nodes inevitably requires the knowledge of the entire network. Using percolation theory, we show that the spreading process displays a nucleation behavior: Once a piece of information spreads from the seeds to more than a small characteristic number of nodes, it reaches a point of no return and will quickly reach the percolation cluster, regardless of the entire network structure; otherwise the spreading will be contained locally. Thus, we find that, without the knowledge of the entire network, any node's global influence can be accurately measured using this characteristic number, which is independent of the network size. This motivates an efficient algorithm with constant time complexity on the long-standing problem of best seed spreaders selection, with performance remarkably close to the true optimum.

Flexibility of thought in high creative individuals represented by percolation analysis.

Flexibility of thought is theorized to play a critical role in the ability of high creative individuals to generate novel and innovative ideas. However, this has been examined only through indirect behavioral measures. Here we use network percolation analysis (removal of links in a network whose strength is below an increasing threshold) to computationally examine the robustness of the semantic memory networks of low and high creative individuals. Robustness of a network indicates its flexibility and thus can be used to quantify flexibility of thought as related to creativity. This is based on the assumption that the higher the robustness of the semantic network, the higher its flexibility. Our analysis reveals that the semantic network of high creative individuals is more robust to network percolation compared with the network of low creative individuals and that this higher robustness is related to differences in the structure of the networks. Specifically, we find that this higher robustness is related to stronger links connecting between different components of similar semantic words in the network, which may also help to facilitate spread of activation over their network. Thus, we directly and quantitatively examine the relation between flexibility of thought and creative ability. Our findings support the associative theory of creativity, which posits that high creative ability is related to a flexible structure of semantic memory. Finally, this approach may have further implications, by enabling a quantitative examination of flexibility of thought, in both healthy and clinical populations.

Punishment diminishes the benefits of network reciprocity in social dilemma experiments.

Network reciprocity has been widely advertised in theoretical studies as one of the basic cooperation-promoting mechanisms, but experimental evidence favoring this type of reciprocity was published only recently. When organized in an unchanging network of social contacts, human subjects cooperate provided the following strict condition is satisfied: The benefit of cooperation must outweigh the total cost of cooperating with all neighbors. In an attempt to relax this condition, we perform social dilemma experiments wherein network reciprocity is aided with another theoretically hypothesized cooperation-promoting mechanism-costly punishment. The results reveal how networks promote and stabilize cooperation. This stabilizing effect is stronger in a smaller-size neighborhood, as expected from theory and experiments. Contrary to expectations, punishment diminishes the benefits of network reciprocity by lowering assortment, payoff per round, and award for cooperative behavior. This diminishing effect is stronger in a larger-size neighborhood. An immediate implication is that the psychological effects of enduring punishment override the rational response anticipated in quantitative models of cooperation in networks.

Resilience of networks with community structure behaves as if under an external field.

Although detecting and characterizing community structure is key in the study of networked systems, we still do not understand how community structure affects systemic resilience and stability. We use percolation theory to develop a framework for studying the resilience of networks with a community structure. We find both analytically and numerically that interlinks (the connections among communities) affect the percolation phase transition in a way similar to an external field in a ferromagnetic- paramagnetic spin system. We also study universality class by defining the analogous critical exponents δ and γ, and we find that their values in various models and in real-world coauthor networks follow the fundamental scaling relations found in physical phase transitions. The methodology and results presented here facilitate the study of network resilience and also provide a way to understand phase transitions under external fields.