Investigating Early Warning Signals in Climate Simulations using Complex Networks

The climate system is prone to various tipping mechanisms at the global scale, such as the abrupt changes induced by the potential shutdown of the Atlantic meridional overturning circulation. Thus, it is essential to develop robust Early Warning Signals (EWSs) to assess the risk of crossing tipping points. Classically, EWSs are statistical measures based on time series of climate state variables, and their spatial distribution is not exploited. However, spatial information is crucial to identifying the starting location and development of a transition process. Methods that use spatial information become particularly relevant in the current era, when satellite observations with high spatiotemporal coverage produce huge amounts of data. We use complex networks constructed from several climate variables (like surface air temperature, specific humidity and cloud cover) on the numerical grid of climate simulations. Using the pyUnicorn Python package [1], we construct networks based on linear and nonlinear spatial correlations of time series at each grid point. We seek for network properties that can serve as EWS when approaching a state transition at the planetary scale, as obtained by the MIT general circulation model in a coupled-aquaplanet configuration for CO2 concentration-driven simulations. We show that network indicators such as the normalized degree, the average length distance and the betweenness centrality are capable of detecting tipping points at the global scale [2]. We assess and compare the applicability as EWS of these indicators to traditional methods. Moreover, we analyse climate networks’ ability to identify nonlinear dynamical patterns. Finally, we discuss the generalisation to network indicators that include causal relationships.

In recent years, various early warning signals of critical transition have been presented, such as autocorrelation at lag 1 [AR(1)], variance, the propagator based on detrended fluctuation analysis (DFA-propagator), and so on. Many studies have shown that the climate system has the characteristics of long-term memory (LTM). Will the LTM characteristics of the climate system change as it approaches possible critical transition points? In view of this, the present paper first studies whether the LTM of several folding (folded bifurcation) models changes consistently as they approach their critical points slowly by the rescaled range (R/S) analysis. The results of numerical experiments show that when the control parameters of the folding model are close to its critical threshold, the Hurst exponent H exhibits an almost monotonic increase (significance level α = 0.05). We compare the performance of R/S with the existing indicators, including AR(1), variance, and DFA-propagator, and find that R/S is a perfectly valid alternative. When there is no extra false noise, AR(1) and variance have good early warning effects. After the addition of extra Gaussian white noise of different intensities, the values of AR(1) and variance change significantly. As a result, the DFA-propagator based on AR(1) calibration also changed significantly. Compared with the other three indicators, the early warning effect of H has stronger ability to resist the interference of external false signals. To further verify the validity of increasing H, paleoclimate reconstruction of Cariaco Basin sediment core grayscale record with long trends filtered out is studied by R/S analysis. The other three early warning signals are calculated in the same way. The data contain a well-known abrupt climate change: the transition between the Younger Dryas (YD) and the Holocene. We find that approximately 300 years before this abrupt climate change occurred, before 11.7 kyr BP, the LTM exponents for Cariaco Basin deglacial grayscale data present an obvious increasing trend at a significant level of α = 0.05. Meanwhile, the variation trend of H and DFA-propagator is basically similar. This shows that increasing H by R/S analysis is an effective early warning signal, which indicates that a dynamic system is approaching its possible critical transition points; H is a completely valid alternative signal for AR(1) and DFA-propagator. The main conclusion of this paper is based on numerical experiments. The precise relationship between H and the stability of the underlying state approaching the transition needs to be further studied. Significance Statement Dynamic systems have critical transition points, and these systems will suddenly change from a stable state to another alternative one beyond these points. Using several simple theoretical models and paleoclimate data, we study whether the characteristics of long-term memory, which are ubiquitous in complex systems in nature and society, change as a system approaches its critical transition point. The results show that the long-term memory of a dynamic system increases significantly with the approach of the critical point, whether in theoretical models or in paleoclimate data.

Analysis of Turkey’s airport network structure and centrality in the opening-out period after the first wave of COVID-19: A complex network approach

We apply the idea of dynamical network markers (Chen et al 2012 Sci. Rep. 2 342) to foreign exchange markets so that early warning signals can be provided for any abrupt changes. The dynamical network marker constructed achieves a high odds ratio for forecasting these sudden changes. In addition, we also extend the notion of the dynamical network marker by using recurrence plots so that the notion can be applied to delay coordinates and point processes. Thus, the dynamical network marker is useful in a variety of contexts in science, technology, and society.

Since the middle of the 20th century, multinational companies have experienced great development on the quantity and the trade scale under the dual influence of globalization and informationization. As the main body of international business, multinational companies' foreign direct investment led to large flow of the final products, intermediate products, technology and services on a global scale and the flow takes its internal trade as medium. Internal trade of the multinational company lead to international trade transfer and international industry restructuring, which played a very important role in accelerating economic globalization.

Abrupt shifts in vegetation productivity induced by environmental change profoundly affect ecosystem functions and services, such as carbon sequestration, biodiversity maintenance and climate regulation, yet their long-term global patterns and underlying drivers remain insufficiently understood. In this study, abrupt shifts in vegetation productivity were identified using two independent long-term satellite datasets, and early warning signals were assessed through ecosystem resilience. The main drivers of resilience decline were further examined across land-cover, climate and human-activity dimensions. The results showed that negative abrupt shifts were predominantly concentrated in high northern latitudes and equatorial regions, and that both negative and positive abrupt shifts displayed distinct increasing trends after 2002. A sharp decline in ecosystem resilience was also detected during the 4 years preceding abrupt shifts. Changes in water availability were identified as the primary factor contributing to the reduced resilience of global ecosystems, as evidenced by the driver trajectory, generalized additive models and convergent cross-mapping methods. This study provides insight into the pervasive occurrence of abrupt shifts in vegetation productivity and the discernible impact of climate change. When projecting vegetation dynamics under future climate change, it is essential to consider the significant uncertainties associated with abrupt shifts.

Many complex networks exist to facilitate the transport of material or information. In this capacity, the authors are often concerned with the continued flow of material or information when a fraction of the links in the complex network is disrupted. In other words, the authors are interested in the robustness of the complex network. In this paper, the authors survey measures of robustness like the average path length, the average clustering coefficient, the global efficiency, the size of largest cluster and use these to analyze the robustness of the bus network in Hanoi, Vietnam. The authors find that the bus network is robust against random failure but sensitive to targeted attack, in agreement with its scale-free character. By examining sharp drops in the average path length within the largest cluster of the Hanoi bus network under successive targeted attack, the authors identify five nodes whose loss lead to the fragmentation of the network into five or six disconnected clusters. These isolated clusters represent geographically the Central, Western, Southern, and Northwestern districts of Hanoi. Special considerations must therefore be given to these five nodes when planners wish to expand the bus network, or make it more robust.

In order to closely fit the characteristics of continuing education, the development of continuing education teaching activities under the network background should not only be combined with the characteristics of professional adult education but also make reasonable use of modern teaching models in the actual teaching process. Based on the community detection algorithm in complex networks, this article makes thorough research and analysis on the complexity of Chinese continuing education by using complex network technology. By establishing the characteristics of vertex degree distribution, average path length, and clustering coefficient of complex networks, it is confirmed that Chinese continuing education has scale-free network characteristics and small-world network characteristics. The three aspects of relationship strength comprehensively analyze the information dissemination speed, scope, interpretation, and application; through the combination of the ant colony algorithm and complex network technology, multiple information dissemination paths are abstracted in Chinese continuing education. The research shows that the application of complex network algorithms can effectively improve the speed and quality of continuing education in China. It is found that the government should increase the number of adult education projects and improve the level of project categories, form key adult education research basis to promote the diversification of research subjects, expand the space for adult education projects to balance regional and provincial differences and attach importance to basic research on adult education, and integrate applied research.

Inferring the dependence structure of complex networks from the observation of the non-linear dynamics of its components is among the common, yet far from resolved challenges faced when studying real-world complex systems. While a range of methods using the ordinal patterns framework has been proposed to particularly tackle the problem of dependence inference in the presence of non-linearity, they come with important restrictions in the scope of their application. Hereby, we introduce the sign patterns as an extension of the ordinal patterns, arising from a more flexible symbolization which is able to encode longer sequences with lower number of symbols. After transforming time series into sequences of sign patterns, we derive improved estimates for statistical quantities by considering necessary constraints on the probabilities of occurrence of combinations of symbols in a symbolic process with prohibited transitions. We utilize these to design an asymptotic chi-squared test to evaluate dependence between two time series and then apply it to the construction of climate networks, illustrating that the developed method can capture both linear and non-linear dependences, while avoiding bias present in the naive application of the often used Pearson correlation coefficient or mutual information.

Large-scale software systems usually consist of a huge number of modules, and have a series of releases along with these modules. This can be seen as software evolution. In recent years, researchers have put forward several models of software evolution by employing the theory of complex networks. In this paper, we put forward a refined model of software evolution based on the BA model: module-based evolution. We theoretically prove that the power-law degree distribution can be held in our model. We also build a tool to construct and analyze the class diagrams of JDK (Java Development Kits) evolved from version 1.2 to 1.6. The class diagrams can be seen as complex networks under evolution. We apply the module-based evolution model to these complex networks and simulate the evolution of key network features such as average clustering coefficient and average path length. Compared with real networks, our model can precisely describe the evolution of these features, and be used to help developers understand the characteristics of large-scale software evolution.

A novel Durer-pentagon-based complex network was constructed by adding a centre node. The properties of the complex network including the average degree, clustering coefficient, average path length, and fractal dimension were determined. The proposed complex network is small-world and fractal.

The properties found in complex networks (e.g., small-world, scale-free) have been used to characterize the behaviour of several processes such as epidemics or oscillators. We analyze the impact of such properties on the quality of a routing process. Using a Mixed Integer/Linear Program, the routing minimizes the number of ports installed in a previously designed network. Ports are network components which we use as a simplification of the capital cost in communication networks. Using data mining techniques, we are able to predict the minimal number of ports of a network with small error rate given the network's properties and under the assumption of a realistic traffic distribution. We find that the average betweenness and the average path length are good indicators of the number of ports. We then present exploratory work on the dynamic aspects by considering that nodes join the network, which corresponds to the deployment of communication equipment. We consider several approaches to deploy the equipment, and report on the number of ports for each approach. By comparing approaches, having less edges can still yield better performances which motivates investigations on the design. Furthermore, this dynamic case confirms the static one since a tradeoff between the average betweenness and the average path length seems to be a key element in efficient designs.

Retracted.

People-to-people interactions in the real world and in virtual environments (e.g., Facebook) can be represented through complex networks. Changes of the structural properties of these complex networks are caused through a variety of dynamic processes. While accepting the fact that variability in individual patterns of behavior (i.e., establishment of random or FOAF-type potential links) in social environments might lead to an increase or decrease in the structural properties of a complex network, in this paper, we focus on another factor that may contribute to such changes, namely the size of personal networks. Any personal network comes with the cost of maintaining individual connections. Despite the fact that technology has shrunk our world, there is also a limit to how many close friends one can keep and count on. It is a relatively small number. In this paper, we develop a multi-agent based model to capture, compare, and explain the structural changes within a growing social network (e.g., expanding the social relations beyond one's social circles). We aim to show that, in addition to various dynamic processes of human interactions, limitations on the size of personal networks can also lead to changes in the structural properties of networks (i.e., the average shortest-path length). Our simulation result shows that the famous small world theory of interconnectivity holds true or even can be shrunk, if people manage to utilize all their existing connections to reach other parties. In addition to this, it can clearly be observed that the network's average path length has a significantly smaller value, if the size of personal networks is set to larger values in our network growth model. Therefore, limitations on the size of personal networks in network growth models lead to an increase in the network's average path length.

Flexible behaviors are organized by complex neural networks in the prefrontal cortex. Recent studies have suggested that such networks exhibit multiple dynamical states, and can switch rapidly from one state to another. In many complex systems such as the brain, the early-warning signals that may predict whether a critical threshold for state transitions is approaching are extremely difficult to detect. We hypothesized that increases in firing irregularity are a crucial measure for predicting state transitions in the underlying neuronal circuits of the prefrontal cortex. We used both experimental and theoretical approaches to test this hypothesis. Experimentally, we analyzed activities of neurons in the prefrontal cortex while monkeys performed a maze task that required them to perform actions to reach a goal. We observed increased firing irregularity before the activity changed to encode goal-to-action information. Theoretically, we constructed theoretical generic neural networks and demonstrated that changes in neuronal gain on functional connectivity resulted in a loss of stability and an altered state of the networks, accompanied by increased firing irregularity. These results suggest that assessing the temporal pattern of neuronal fluctuations provides important clues regarding the state stability of the prefrontal network. We also introduce a novel scheme that the prefrontal cortex functions in a metastable state near the critical point of bifurcation. According to this scheme, firing irregularity in the prefrontal cortex indicates that the system is about to change its state and the flow of information in a flexible manner, which is essential for executive functions. This metastable and/or critical dynamical state of the prefrontal cortex may account for distractibility and loss of flexibility in the prefrontal cortex in major mental illnesses such as schizophrenia.