Statistical physics approaches to the complex Earth system

Lunar Lithium-7 Sensing (δ7Li): Spectral Patterns and Artificial Intelligence Techniques

Lithium, a critical natural resource integral to modern technology, has influenced diverse industries since its discovery in the 1950s. Of particular interest is lithium-7, the most prevalent lithium isotope on Earth, playing a vital role in applications such as batteries, metal alloys, medicine, and nuclear research. However, its extraction presents significant environmental and logistical challenges. This article explores the potential for lithium exploration on the Moon, driven by its value as a resource and the prospect of cost reduction due to the Moon's lower gravity, which holds promise for future space exploration endeavors. Additionally, the presence of lithium in the solar wind and its implications for material transport across celestial bodies are subjects of intrigue. Drawing from a limited dataset collected during the Apollo missions (Apollo 12, 15, 16, and 17) and leveraging artificial intelligence techniques and sample expansion through bootstrapping, this study develops predictive models for lithium-7 concentration based on spectral patterns. The study areas encompass the Aitken crater, Hadley Rima, and the Taurus-Littrow Valley, where higher lithium concentrations are observed in basaltic lunar regions. This research bridges lunar geology and the formation of the solar system, providing valuable insights into celestial resources and enhancing our understanding of space. The data used in this study were obtained from the imaging sensors (infrared, visible, and ultraviolet) of the Clementine satellite, which significantly contributed to the success of our research. Furthermore, the study addresses various aspects related to statistical analysis, sample quality validation, resampling, and bootstrapping. Supervised machine learning model training and validation, as well as data import and export, were explored. The analysis of data generated by the Clementine probe in the near-infrared (NIR) and ultraviolet-visible (UVVIS) spectra revealed evidence of the presence of lithium-7 (Li-7) on the lunar surface. The distribution of Li-7 on the lunar surface is non-uniform, with varying concentrations in different regions of the Moon identified, supporting the initial hypothesis associating surface Li-7 concentration with exposure to solar wind. While a direct numerical relationship between lunar topography and Li-7 concentration has not been established due to morphological diversity and methodological limitations, preliminary results suggest significant economic and technological potential in lunar lithium exploration and extraction.

Exotic swarming dynamics of high-dimensional swarmalators

Swarmalators are oscillators that can swarm as well as sync via a dynamic balance between their spatial proximity and phase similarity. Swarmalator models employed so far in the literature comprise only one-dimensional phase variables to represent the intrinsic dynamics of the natural collectives. Nevertheless, the latter can indeed be represented more realistically by high-dimensional phase variables. For instance, the alignment of velocity vectors in a school of fish or a flock of birds can be more realistically set up in three-dimensional space, while the alignment of opinion formation in population dynamics could be multidimensional, in general. We present a generalized D-dimensional swarmalator model, which more accurately captures self-organizing behaviors of a plethora of real-world collectives by self-adaptation of high-dimensional spatial and phase variables. For a more sensible visualization and interpretation of the results, we restrict our simulations to three-dimensional spatial and phase variables. Our model provides a framework for modeling complicated processes such as flocking, schooling of fish, cell sorting during embryonic development, residential segregation, and opinion dynamics in social groups. We demonstrate its versatility by capturing the maneuvers of a school of fish, qualitatively and quantitatively, by a suitable extension of the original model to incorporate appropriate features besides a gallery of its intrinsic self-organizations for various interactions. We expect the proposed high-dimensional swarmalator model to be potentially useful in describing swarming systems and programmable and reconfigurable collectives in a wide range of disciplines, including the physics of active matter, developmental biology, sociology, and engineering.

The causality measure of partial mutual information from mixed embedding (PMIME) revisited

The measure of partial mutual information from mixed embedding (PMIME) is an information theory-based measure to accurately identify the direct and directional coupling, termed Granger causality or simply causality, between the observed variables or subsystems of a high-dimensional dynamical and complex system, without any a priori assumptions about the nature of the coupling relationship. In its core, it is a forward selection procedure that aims to iteratively identify the lag-dependence structure of a given observed variable (response) to all the other observed variables (candidate drivers). This model-free approach is capable of detecting nonlinear interactions, abundantly present in real-world complex systems, and it was shown to perform well on multivariate time series of moderately high dimension. However, the PMIME presents some inefficiencies in its performance mainly when applied on strongly stochastic (linear or nonlinear) systems as it may falsely detect non-existent relationships. Moreover, and by construction, the measure cannot extract purely synergetic relationships present in a system. In the current work, the issue of false detections is addressed by introducing an improved resampling significance test and a procedure of rechecking the identified drivers (backward revision). Regarding the inability to detect synergetic relationships, the PMIME is further enhanced by checking pairs as candidate drivers for the response variable after having considered all drivers individually. The effects of these modifications are investigated in a systematic simulation study on properly designed systems involving strong stochasticity, regressor terms with synergetic effects, and a system dimension ranging from 3 to 30. The overall results of the simulations indicate that these modifications indeed improve the performance of PMIME and alleviate to a significant degree the issues of the original algorithm. Guidelines for balancing between accuracy and computational efficiency are also given, particularly relevant for real-world applications. Finally, the measure performance is investigated in the study of futures of various government bonds and stock market indices in the period around COVID-19 pandemic.

Order parameter dynamics in complex systems: From models to data

Collective ordering behaviors are typical macroscopic manifestations embedded in complex systems and can be ubiquitously observed across various physical backgrounds. Elements in complex systems may self-organize via mutual or external couplings to achieve diverse spatiotemporal coordinations. The order parameter, as a powerful quantity in describing the transition to collective states, may emerge spontaneously from large numbers of degrees of freedom through competitions. In this minireview, we extensively discussed the collective dynamics of complex systems from the viewpoint of order-parameter dynamics. A synergetic theory is adopted as the foundation of order-parameter dynamics, and it focuses on the self-organization and collective behaviors of complex systems. At the onset of macroscopic transitions, slow modes are distinguished from fast modes and act as order parameters, whose evolution can be established in terms of the slaving principle. We explore order-parameter dynamics in both model-based and data-based scenarios. For situations where microscopic dynamics modeling is available, as prototype examples, synchronization of coupled phase oscillators, chimera states, and neuron network dynamics are analytically studied, and the order-parameter dynamics is constructed in terms of reduction procedures such as the Ott-Antonsen ansatz, the Lorentz ansatz, and so on. For complicated systems highly challenging to be well modeled, we proposed the eigen-microstate approach (EMP) to reconstruct the macroscopic order-parameter dynamics, where the spatiotemporal evolution brought by big data can be well decomposed into eigenmodes, and the macroscopic collective behavior can be traced by Bose-Einstein condensation-like transitions and the emergence of dominant eigenmodes. The EMP is successfully applied to some typical examples, such as phase transitions in the Ising model, climate dynamics in earth systems, fluctuation patterns in stock markets, and collective motion in living systems.

Complexity and Statistical Physics Approaches to Earthquakes

This Special Issue of Entropy, "Complexity and Statistical Physics Approaches to Earthquakes", sees the successful publication of 11 original scientific articles [...].

Network percolation provides early warnings of abrupt changes in coupled oscillatory systems: An explanatory analysis

Functional networks are powerful tools to study statistical interdependency structures in spatially extended or multivariable systems. They have been used to get insights into the dynamics of complex systems in various areas of science. In particular, percolation properties of correlation networks have been employed to identify early warning signals of critical transitions. In this work, we further investigate the corresponding potential of percolation measures for the anticipation of different types of sudden shifts in the state of coupled irregularly oscillating systems. As a paradigmatic model system, we study the dynamics of a ring of diffusively coupled noisy FitzHugh-Nagumo oscillators and show that, when the oscillators are nearly completely synchronized, the percolation-based precursors successfully provide very early warnings of the rapid switches between the two states of the system. We clarify the mechanisms behind the percolation transition by separating global trends given by the mean-field behavior from the synchronization of individual stochastic fluctuations. We then apply the same methodology to real-world data of sea surface temperature anomalies during different phases of the El Niño-Southern Oscillation. This leads to a better understanding of the factors that make percolation precursors effective as early warning indicators of incipient El Niño and La Niña events.

Arctic weather variability and connectivity

The Arctic's rapid sea ice decline may influence global weather patterns, making the understanding of Arctic weather variability (WV) vital for accurate weather forecasting and analyzing extreme weather events. Quantifying this WV and its impacts under human-induced climate change remains a challenge. Here we develop a complexity-based approach and discover a strong statistical correlation between intraseasonal WV in the Arctic and the Arctic Oscillation. Our findings highlight an increased variability in daily Arctic sea ice, attributed to its decline accelerated by global warming. This weather instability can influence broader regional patterns via atmospheric teleconnections, elevating risks to human activities and weather forecast predictability. Our analyses reveal these teleconnections and a positive feedback loop between Arctic and global weather instabilities, offering insights into how Arctic changes affect global weather. This framework bridges complexity science, Arctic WV, and its widespread implications.

Predicting maximum temperatures over India 10-days ahead using machine learning models

In the months of March-June, India experiences high daytime temperatures (Tmax), which sometimes lead to heatwave-like conditions over India. In this study, 10 different machine learning models are evaluated for their ability to predict the daily Tmax anomalies 10 days ahead in the months of March-June. Several model experiments were carried out to identify an optimal model to predict daily Tmax anomalies over India. The results indicate that the AdaBoost regressor with Multi-layer Perceptron as the base estimator is an optimal model to predict the Tmax anomalies over India in the months of March-June. The optimal model predictions are benchmarked against 10-day persistence predictions and the predictions from the Climate Forecast System (CFS) reforecast. The results indicate that the machine learning model skill is higher than persistence and comparable to CFS reforecast 10-day predictions in April and May. In March and June, the machine learning models have low skill scores and perform no better than persistence. These results indicate that the machine learning models are promising tools to predict the surface air maximum temperature anomalies over India in April and May and can complement predictions from more sophisticated numerical models.

Exploring the intensity, distribution and evolution of teleconnections using climate network analysis

Teleconnections refer to long-range climate system linkages occurring over typically thousands of kilometers. Generally speaking, most teleconnections are attributed to the transmission of energy and propagation of waves although the physical complexity and characteristics behind these waves are not fully understood. To address this knowledge gap, we develop a climate network-based approach to reveal their directions and distribution patterns, evaluate the intensity of teleconnections, and identify sensitive regions using global daily surface air temperature data. Our results reveal a stable average intensity distribution pattern for teleconnections across a substantial spatiotemporal scale from 1948 to 2021, with the extent and intensity of teleconnection impacts increasing more prominently in the Southern Hemisphere over the past 37 years. Furthermore, we pinpoint climate-sensitive regions, such as southeastern Australia, which are likely to face increasing impacts due to global warming. Our proposed method offers new insights into the dynamics of global climate patterns and can inform strategies to address climate change and extreme events.

Interconnected ordinal pattern complex network for characterizing the spatial coupling behavior of gas-liquid two-phase flow

The complex phase interactions of the two-phase flow are a key factor in understanding the flow pattern evolutional mechanisms, yet these complex flow behaviors have not been well understood. In this paper, we employ a series of gas-liquid two-phase flow multivariate fluctuation signals as observations and propose a novel interconnected ordinal pattern network to investigate the spatial coupling behaviors of the gas-liquid two-phase flow patterns. In addition, we use two network indices, which are the global subnetwork mutual information (I) and the global subnetwork clustering coefficient (C), to quantitatively measure the spatial coupling strength of different gas-liquid flow patterns. The gas-liquid two-phase flow pattern evolutionary behaviors are further characterized by calculating the two proposed coupling indices under different flow conditions. The proposed interconnected ordinal pattern network provides a novel tool for a deeper understanding of the evolutional mechanisms of the multi-phase flow system, and it can also be used to investigate the coupling behaviors of other complex systems with multiple observations.

Carrier Transport in Colloidal Quantum Dot Intermediate Band Solar Cell Materials Using Network Science

Colloidal quantum dots (CQDs) have been proposed to obtain intermediate band (IB) materials. The IB solar cell can absorb sub-band-gap photons via an isolated IB within the gap, generating extra electron-hole pairs that increase the current without degrading the voltage, as has been demonstrated experimentally for real cells. In this paper, we model the electron hopping transport (HT) as a network embedded in space and energy so that a node represents the first excited electron state localized in a CQD while a link encodes the Miller-Abrahams (MA) hopping rate for the electron to hop from one node (=state) to another, forming an "electron-HT network". Similarly, we model the hole-HT system as a network so that a node encodes the first hole state localized in a CQD while a link represents the MA hopping rate for the hole to hop between nodes, leading to a "hole-HT network". The associated network Laplacian matrices allow for studying carrier dynamics in both networks. Our simulations suggest that reducing both the carrier effective mass in the ligand and the inter-dot distance increases HT efficiency. We have found a design constraint: It is necessary for the average barrier height to be larger than the energetic disorder to not degrade intra-band absorption.

Universal window size-dependent transition of correlations in complex systems

Correlation analysis serves as an easy-to-implement estimation approach for the quantification of the interaction or connectivity between different units. Often, pairwise correlations estimated by sliding windows are time-varying (on different window segments) and window size-dependent (on different window sizes). Still, how to choose an appropriate window size remains unclear. This paper offers a framework for studying this fundamental question by observing a critical transition from a chaotic-like state to a nonchaotic state. Specifically, given two time series and a fixed window size, we create a correlation-based series based on nonlinear correlation measurement and sliding windows as an approximation of the time-varying correlations between the original time series. We find that the varying correlations yield a state transition from a chaotic-like state to a nonchaotic state with increasing window size. This window size-dependent transition is analyzed as a universal phenomenon in both model and real-world systems (e.g., climate, financial, and neural systems). More importantly, the transition point provides a quantitative rule for the selection of window sizes. That is, the nonchaotic correlation better allows for many regression-based predictions.

A modified extreme event-based synchronicity measure for climate time series

Extreme event-based synchronicity is a specific measure of similarity of extreme event-like time series. It is capable to capture the nonlinear interactions between climatic extreme events. In this study, we proposed a modified extreme event-based synchronicity measure that incorporates two types of extreme events (positive and negative) simultaneously in climate anomalies to characterize the synchronization and time delays. Statistical significance of the modified extreme event synchronization measure is tested by Monte-Carlo simulations. The applications of the modified extreme event-based synchronicity measure on synthetic time series verified that it was superior to the traditional event synchronicity measure. Both synchronous and antisynchronous features between climate time series could be captured by the modified measure. It is potentially applied in investigating the interrelationship between climate extremes and climate index or constructing complex networks of climate variables. In addition, this modified extreme event-based synchronicity measure could be easily applied to other types of time series just by identifying the extreme events properly.

Study of interaction and complete merging of binary cyclones using complex networks

Cyclones are among the most hazardous extreme weather events on Earth. In certain scenarios, two co-rotating cyclones in close proximity to one another can drift closer and completely merge into a single cyclonic system. Identifying the dynamic transitions during such an interaction period of binary cyclones and predicting the complete merger (CM) event are challenging for weather forecasters. In this work, we suggest an innovative approach to understand the evolving vortical interactions between the cyclones during two such CM events (Noru-Kulap and Seroja-Odette) using time-evolving induced velocity-based unweighted directed networks. We find that network-based indicators, namely, in-degree and out-degree, quantify the changes in the interaction between the two cyclones and are excellent candidates to classify the interaction stages before a CM. The network indicators also help to identify the dominant cyclone during the period of interaction and quantify the variation of the strength of the dominating and merged cyclones. Finally, we show that the network measures also provide an early indication of the CM event well before its occurrence.

Organic Disordered Semiconductors as Networks Embedded in Space and Energy

Organic disordered semiconductors have a growing importance because of their low cost, mechanical flexibility, and multiple applications in thermoelectric devices, biosensors, and optoelectronic devices. Carrier transport consists of variable-range hopping between localized quantum states, which are disordered in both space and energy within the Gaussian disorder model. In this paper, we model an organic disordered semiconductor system as a network embedded in both space and energy so that a node represents a localized state while a link encodes the probability (or, equivalently, the Miller-Abrahams hopping rate) for carriers to hop between nodes. The associated network Laplacian matrix allows for the study of carrier dynamics using edge-centric random walks, in which links are activated by the corresponding carrier hopping rates. Our simulation work suggests that at room temperature the network exhibits a strong propensity for small-network nature, a beneficial property that in network science is related to the ease of exchanging information, particles, or energy in many different systems. However, this is not the case at low temperature. Our analysis suggests that there could be a parallelism between the well-known dependence of carrier mobility on temperature and the potential emergence of the small-world property with increasing temperature.

A Digital Template for the Generic Multi-Risk (GenMR) Framework: A Virtual Natural Environment

Extreme disasters, defined as low-probability-high-consequences events, are often due to cascading effects combined to amplifying environmental factors. While such a risk complexity is commonly addressed by the modeling of site-specific multi-risk scenarios, there exists no harmonized approach that considers the full space of possibilities, based on the general relationships between the environment and the perils that populate it. In this article, I define the concept of a digital template for multi-risk R&D and prototyping in the Generic Multi-Risk (GenMR) framework. This digital template consists of a virtual natural environment where different perils may occur. They are geological (earthquakes, landslides, volcanic eruptions), hydrological (river floods, storm surges), meteorological (windstorms, heavy rains), and extraterrestrial (asteroid impacts). Both geological and hydrological perils depend on the characteristics of the natural environment, here defined by two environmental layers: topography and soil. Environmental objects, which alter the layers, are also defined. They are here geomorphic structures linked to some peril source characteristics. Hazard intensity footprints are then generated for primary, secondary, and tertiary perils. The role of the natural environment on intensity footprints and event cascading is emphasized, one example being the generation of a "quake lake". Future developments, à la SimCity, are finally discussed.

Comparative Study on International Research Hotspots and National-Level Policy Keywords of Dynamic Disaster Monitoring and Early Warning in China (2000-2021)

For more than 20 years, disaster dynamic monitoring and early warning have achieved orderly and sustainable development in China, forming a systematic academic research system and top-down policy design, which are inseparable from the research of China's scientific community and the promotion of government departments. In the past, most of the research on dynamic disaster monitoring and early warning focused on specific research in a certain field, scene, and discipline, while a few studies focused on research review or policy analysis, and few studies combined macro and meso research reviews in academia with national policy analysis for comparative analysis. It is necessary and urgent to explore the interaction between scholars' research and policy deployment, which can bring theoretical contributions and policy references to the top-down design, implementation promotion, and academic research of China's dynamic disaster monitoring and early warning. Based on 608 international research articles on dynamic disaster monitoring and early warning published by Chinese scholars from 2000-2021 and 187 national policy documents published during this period, this paper conducts a comparative analysis between the knowledge maps of international research hotspots and the co-occurrence maps of policy keywords on dynamic disaster monitoring and early warning. The research shows that in the stage of initial development (2000-2007), international research articles are few and focused, and research hotspots are somewhat alienated from policy keywords. In the stage of rising development (2008-2015), after the Wenchuan earthquake, research hotspots are closely related to policy keywords, mainly in the fields of geology, engineering disasters, meteorological disasters, natural disasters, etc. Meanwhile, research hotspots also focus on cutting-edge technologies and theories, while national-level policy keywords focus more on overall governance and macro promotion, but the two are gradually closely integrated. In the stage of rapid development (2016-2021), with the continuous attention and policy promotion of the national government, the establishment of the Ministry of Emergency Management, and the gradual establishment and improvement of the disaster early warning and monitoring system, research hotspots and policy keywords are integrated and overlapped with each other, realizing the organic linkage and mutual promotion between academic research and political deployment. The motivation, innovation, integration, and transformation of dynamic disaster monitoring and early warning are promoted by both policy and academic research. The institutions that issue policies at the national level include the State Council and relevant departments, the Ministry of Emergency Management, the Ministry of Water Resources, and other national ministries and commissions. The leading affiliated institutions of scholars' international research include China University of Mining and Technology, Chinese Academy of Sciences, Wuhan University, Shandong University of Science and Technology, and other institutions. The disciplines involved are mainly multidisciplinary geosciences, environmental sciences, electrical and electronic engineering, remote sensing, etc. It is worth noting that in the past two to three years, research and policies focusing on COVID-19, public health, epidemic prevention, environmental governance, and emergency management have gradually increased.

A game theoretical model for the stimulation of public cooperation in environmental collaborative governance

Digital technologies provide a convenient way for the public to participate in environmental governance. Therefore, by means of a two-stage evolutionary model, a new mechanism for promoting public cooperation is proposed to accomplish environmental collaborative governance. Interactive effects of government-enterprise environmental governance are firstly explored, which is the external atmosphere for public behaviour. Second, the evolutionary dynamics of public behaviour is analysed to reveal the internal mechanism of the emergence of public cooperation in environmental collaborative governance projects. Simulations reveal that the interaction of resource elements between government and enterprise is an important basis for environmental governance performance, and that governments can improve this as well as public cooperation by increasing the marginal governance propensity. Similarly, an increase in the government's fixed expenditure item of environmental governance can also significantly improve government-enterprise performance and public cooperation. And finally, the effect of government's marginal incentive propensity on public environmental governance is moderated by enterprises' marginal environmental governance propensity, so that simply increasing the government's marginal incentive propensity cannot improve the evolutionary stable state of public behaviour under the scenario where enterprises' marginal environmental governance propensity is low.

Adaptation of Partial Mutual Information from Mixed Embedding to Discrete-Valued Time Series

A causality analysis aims at estimating the interactions of the observed variables and subsequently the connectivity structure of the observed dynamical system or stochastic process. The partial mutual information from mixed embedding (PMIME) is found appropriate for the causality analysis of continuous-valued time series, even of high dimension, as it applies a dimension reduction by selecting the most relevant lag variables of all the observed variables to the response, using conditional mutual information (CMI). The presence of lag components of the driving variable in this vector implies a direct causal (driving-response) effect. In this study, the PMIME is appropriately adapted to discrete-valued multivariate time series, called the discrete PMIME (DPMIME). An appropriate estimation of the discrete probability distributions and CMI for discrete variables is implemented in the DPMIME. Further, the asymptotic distribution of the estimated CMI is derived, allowing for a parametric significance test for the CMI in the DPMIME, whereas for the PMIME, there is no parametric test for the CMI and the test is performed using resampling. Monte Carlo simulations are performed using different generating systems of discrete-valued time series. The simulation suggests that the parametric significance test for the CMI in the progressive algorithm of the DPMIME is compared favorably to the corresponding resampling significance test, and the accuracy of the DPMIME in the estimation of direct causality converges with the time-series length to the accuracy of the PMIME. Further, the DPMIME is used to investigate whether the global financial crisis has an effect on the causality network of the financial world market.

Detecting Metabolic Thresholds from Nonlinear Analysis of Heart Rate Time Series: A Review

Heart rate time series are widely used to characterize physiological states and athletic performance. Among the main indicators of metabolic and physiological states, the detection of metabolic thresholds is an important tool in establishing training protocols in both sport and clinical fields. This paper reviews the most common methods, applied to heart rate (HR) time series, aiming to detect metabolic thresholds. These methodologies have been largely used to assess energy metabolism and to identify the appropriate intensity of physical exercise which can reduce body weight and improve physical fitness. Specifically, we focused on the main nonlinear signal evaluation methods using HR to identify metabolic thresholds with the purpose of identifying a method which can represent a useful tool for the real-time settings of wearable devices in sport activities. While the advantages and disadvantages of each method, and the possible applications, are presented, this review confirms that the nonlinear analysis of HR time series represents a solid, robust and noninvasive approach to assess metabolic thresholds.

Modeling multi-opinion propagation in complex systems with heterogeneous relationships via Potts model on signed networks

This paper investigates how the heterogenous relationships around us affect the spread of diverse opinions in the population. We apply the Potts model, derived from condensed matter physics on signed networks, to multi-opinion propagation in complex systems with logically contradictory interactions. Signed networks have received increasing attention due to their ability to portray both positive and negative associations simultaneously, while the Potts model depicts the coevolution of multiple states affected by interactions. Analyses and experiments on both synthetic and real signed networks reveal the impact of the topology structure on the emergence of consensus and the evolution of balance in a system. We find that, regardless of the initial opinion distribution, the proportion and location of negative edges in the signed network determine whether a consensus can be formed. The effect of topology on the critical ratio of negative edges reflects two distinct phenomena: consensus and the multiparty situation. Surprisingly, adding a small number of negative edges leads to a sharp breakdown in consensus under certain circumstances. The community structure contributes to the common view within camps and the confrontation (or alliance) between camps. The importance of inter- or intra-community negative relationships varies depending on the diversity of opinions. The results also show that the dynamic process causes an increase in network structural balance and the emergence of dominant high-order structures. Our findings demonstrate the strong effects of logically contradictory interactions on collective behaviors, and could help control multi-opinion propagation and enhance the system balance.

No-exclaves percolation

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

Perspectives on the importance of complex systems in understanding our climate and climate change-The Nobel Prize in Physics 2021

The Nobel Prize in Physics 2021 was awarded to Syukuro Manabe, Klaus Hasselmann, and Giorgio Parisi for their "groundbreaking contributions to our understanding of complex systems," including major advances in the understanding of our climate and climate change. In this Perspective article, we review their key contributions and discuss their relevance in relation to the present understanding of our climate. We conclude by outlining some promising research directions and open questions in climate science.

Heterogeneous Ice Growth in Micron-Sized Water Droplets Due to Spontaneous Freezing

Understanding how ice nucleates and grows into larger crystals is of crucial importance for many research fields. The purpose of this study was to shed light on the phase and structure of ice once a nucleus is formed inside a metastable water droplet. Wide-angle X-ray scattering (WAXS) was performed on micron-sized droplets evaporatively cooled to temperatures where homogeneous nucleation occurs. We found that for our weak hits ice grows more cubic compared to the strong hits that are completely hexagonal. Due to efficient heat removal caused by evaporation, we propose that the cubicity of ice at the vicinity of the droplet’s surface is higher than for ice formed within the bulk of the droplet. Moreover, the Bragg peaks were classified based on their geometrical shapes and positions in reciprocal space, which showed that ice grows heterogeneously with a significant population of peaks indicative of truncation rods and crystal defects. Frequent occurrences of the (100) reflection with extended in-planar structure suggested that large planar ice crystals form at the droplet surface, then fracture into smaller domains to accommodate to the curvature of the droplets. Planar faulting due to misaligned domains would explain the increased cubicity close to the droplet surface.

Percolation analysis of the atmospheric structure

The atmosphere is a thermo-hydrodynamical complex system and provides oxygen to most animal life at the Earth's surface. However, the detection of complexity for the atmosphere remains elusive and debated. Here we develop a percolation-based framework to explore its structure by using the global air temperature field. We find that the percolation threshold is much delayed compared with the prototypical percolation model and the giant cluster eventually emerges explosively. A finite-size-scaling analysis reveals that the observed transition in each atmosphere layer is genuine discontinuous. Furthermore, at the percolation threshold, we uncover that the boundary of the giant cluster is self-affine, with fractal dimension d_{f}, and can be utilized to quantify the atmospheric complexity. Specifically, our results indicate that the complexity of the atmosphere decreases superlinearly with height, i.e., the complexity is higher at the surface than at the top layer and vice versa, due to the atmospheric boundary forcings. The proposed methodology may evaluate and improve our understanding regarding the critical phenomena of the complex Earth system and can be used as a benchmark tool to test the performance of Earth system models.

Cooperative Evolution of China's Excellent Innovative Research Groups from the Perspective of Innovation Ecosystem: Taking an "Environmental Biogeochemistry" Research Innovation Group as a Case Study

Research, understanding, and prediction of complex systems is an important starting point for human beings to tackle major problems and emergencies such as global warming and COVID-19. Research on innovation ecosystem is an important part of research on complex systems. With the rapid development of sophisticated industries, the rise of innovative countries, and the newly developed innovation theory, innovation ecosystem has become a new explanation and new paradigm for adapting to today's global innovation cooperation network and the scientific development of complex systems, which is also in line with China's concept of building an innovative country and promoting comprehensive innovation and international cooperation with scientific and technological innovation as the core. The Innovative Research Group at Peking University is the most representative scientific and technological innovation team in the frontier field of basic research in China. The characteristics of its organization mechanism and dynamic evolution connotation are consistent with the characteristics and evolution of innovation ecosystem. An excellent innovative research group is regarded as a small innovation ecosystem. We selected the "Environmental Biogeochemistry" Innovation Research Group at Peking University as a typical case in order to understand and analyze the evolution of cooperation among scientific and technological innovation teams, improve the healthy development as well as internal and external governance of this special small innovation ecosystem, promote the expansion of an innovation team cooperation network and the improvement of cooperation quality, promote the linkage supports of funding and management departments, and improve their scientific and technological governance abilities. Through scientometrics, visual analysis of knowledge maps, and an exploratory case study, we study the evolution process and development law of team cooperation. It is found that the main node authors of the cooperation network maintain strong cooperation frequency and centrality, and gradually strengthen with the expansion of the cooperation network and the evolution of time. Driven by the internal cooperative governance of the team and the external governance of the funding and management departments, this group has gradually formed a healthy, orderly, open, and cooperative special innovation ecosystem, which is conducive to the stability and sustainable development of the national innovation ecosystem and the global innovation ecosystem.

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.

Inferring the connectivity of coupled chaotic oscillators using Kalman filtering

Inferring the interactions between coupled oscillators is a significant open problem in complexity science, with multiple interdisciplinary applications. While the Kalman filter (KF) technique is a well-known tool, widely used for data assimilation and parameter estimation, to the best of our knowledge, it has not yet been used for inferring the connectivity of coupled chaotic oscillators. Here we demonstrate that KF allows reconstructing the interaction topology and the coupling strength of a network of mutually coupled Rössler-like chaotic oscillators. We show that the connectivity can be inferred by considering only the observed dynamics of a single variable of the three that define the phase space of each oscillator. We also show that both the coupling strength and the network architecture can be inferred even when the oscillators are close to synchronization. Simulation results are provided to show the effectiveness and applicability of the proposed method.

The Impact of Sustainability Goals on Productivity Growth: The Moderating Role of Global Warming

The objective of this paper was to gain novel insights into the complex relationships among Sustainable Development Goals (SDGs) in shaping productivity (GDP/capita) growth. Using dynamic panel regressions on data collected in 138 countries between 2000 and 2017, we found that rising temperatures negatively affect growth and mitigate the impact of other SDGs on growth. We also found that CO₂ emissions have a U-shaped relationship with growth; life expectancy negatively influences growth (positively moderated by rising temperatures), and food security positively impacts growth (negatively moderated by rising temperatures). This study highlights the difficulty of simultaneously implementing SDGs and elucidates novel research perspectives and policies to decrease the negative impacts of climate change on socio-economic and environmental well-being.

Eigen microstates and their evolution of global ozone at different geopotential heights

Studies on stratospheric ozone have attracted much attention due to its serious impacts on climate changes and its important role as a tracer of Earth's global circulation. Tropospheric ozone as a main atmospheric pollutant damages human health as well as the growth of vegetation. Yet, there is still a lack of a theoretical framework to fully describe the variation of ozone. To understand ozone's spatiotemporal variance, we introduce the eigen microstate method to analyze the global ozone mass mixing ratio between January 1, 1979 and June 30, 2020 at 37 pressure layers. We find that eigen microstates at different geopotential heights can capture different climate phenomena and modes. Without deseasonalization, the first eigen microstates capture the seasonal effect and reveal that the phase of the intra-annual cycle moves with the geopotential heights. After deseasonalization, by contrast, the collective patterns from the overall trend, El Niño-Southern Oscillation (ENSO), quasi-biennial oscillation, and tropopause pressure are identified by the first few significant eigen microstates. The theoretical framework proposed here can also be applied to other complex Earth systems.

Identification of multiple influential spreaders on networks by percolation under the SIR model

Identification of multiple influential spreaders on complex networks is of great significance, which can help us speed up information diffusion and prevent disease from spreading to some extent. The traditional top-k strategy to solve an influence maximization problem based on node centrality is unsuitable for selecting several spreaders simultaneously because of influence overlapping. Besides, other heuristic methods have a poor ability to keep the balance between efficiency and computing time. In this paper, an efficient method is proposed to identify the decentralized influential spreaders on networks by edge percolation under the Susceptible-Infected-Recovered (SIR) model. Thanks to the average size of the connected component where one node is located under the edge percolation equivalent to the final spread range of this node under the SIR model approximately, it inspires us to choose suitable spreaders maximize the spread of influence. The experimental results show that our method has high efficiency compared with other benchmark methods on three synthetic networks and six empirical networks, and it also requires less time and cost.