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This paper introduces a new green decomposition model of carbon productivity that aims to further analyze the regional differences in carbon productivity and its interaction with regional industrial performance. We combine desired outputs and undesired outputs orientation, and multiple factor inputs to derive a new green decomposition theorem, establish a new green decomposition model of carbon productivity, and obtain nine effects of regional carbon productivity differences. Empirical analysis is conducted using input-output data from 29 provinces and 15 industries in China, comparing the differences in carbon productivity from both the provincial and industry perspectives and exploring the mechanism of action. This paper provides theoretical basis and empirical evidence for regional carbon productivity enhancement and economic and industrial optimization from the perspective of multi-factor inputs, as well as policy insights for regional low-carbon transition development.

Rehydration is a primary adaptation strategy for alleviating the detrimental effects of drought on crop growth. However, the effects of rehydration on microbial communities in various compartments under drought conditions remain poorly understood. Herein, we explored the response patterns of bacterial and fungal community composition, diversity, ecological network, and assembly process in the bulk soil and rhizosphere of broomcorn millet farmland at 5, 10, 20, and 30 days after rehydration during drought conditions. Compared to drought, rehydration significantly decreased the organic matter (OM), total nitrogen (TN), available potassium (AK), available phosphorus (AP), nitrate nitrogen (NO3--N), and ammonium nitrogen (NH4+-N) contents in rhizosphere, but had no obvious influences on the OM and TN contents in bulk soil on the four sampling days. In the rhizosphere of broomcorn millet field, Firmicutes and Actinobacteria were enriched in drought condition, but Proteobacteria and Bacteroidetes were enriched in rehydration regime. Compared to drought, the relative abundances of Eurotiomycetes, Dothideomycetes, Mortierellomycetes, and Leotiomycetes were enhanced, but Sordariomycetes was reduced on the 5th and 10th days after rehydration. Rehydration increased the bacterial and fungal observed ASVs and Shannon index in the rhizosphere to varying degrees, but had little effect on the bulk soil. Null-model analysis indicated that rehydration deceased the stochastic process of fungal communities in the bulk soil, whereas had no influence on deterministic process of bacterial community in the bulk soil and rhizosphere. More importantly, rhizosphere properties had a greater impact on the bacterial and fungal community composition, diversity, and assembly process than bulk soil. Network analysis revealed that rehydration improved the interconnected taxa in the rhizosphere bacterial network, but reduced microbial interactions in the rhizosphere fungal network compared to drought. This work provides a theoretical foundation for elucidating the role of rehydration regime in governing the ecological services of microbiome of broomcorn millet farmland under drought conditions.

Abstract Rooftop photovoltaics (RPVs) are crucial in achieving energy transition and climate goals, especially in cities with high building density and substantial energy consumption. Estimating RPV carbon mitigation potential at the city level of an entire large country is challenging given difficulties in assessing rooftop area. Here, using multi-source heterogeneous geospatial data and machine learning regression, we identify a total of 65,962 km2 rooftop area in 2020 for 354 Chinese cities, which represents 4 billion tons of carbon mitigation under ideal assumptions. Considering urban land expansion and power mix transformation, the potential remains at 3-4 billion tons in 2030, when China plans to reach its carbon peak. However, most cities have exploited less than 1% of their potential. We provide analysis of geographical endowment to better support future practice. Our study provides critical insights for targeted RPV development in China and can serve as a foundation for similar work in other countries.

This article studies the emission reduction mechanism of high-tiered carbon taxes under green and low-carbon behavior in single and two-stage supply chains. First, based on the Cournot game model, it explores the impact of high-tiered carbon tax policies on supply chain carbon reduction decisions in the green exchange market. By analyzing the effects of implementing a high-tiered carbon tax policy, the basic characteristics of its implementation are identified, and the advantages of a high-tiered carbon tax compared to a unified carbon tax are summarized. Second, it establishes a carbon reduction technology investment cost-sharing model and a carbon tax cost-sharing model under the high-tiered carbon tax policy. It analyzes and studies the impact of high-tiered carbon tax policies on balancing the relationship between members of the two-level supply chain through optimal decision-making of the two-level supply chain under two cost-sharing strategies, revealing the emission reduction mechanism of the two-level supply chain under high-tiered carbon tax policies. The results indicate that there are extreme points in the emission reduction rates of producers in the green exchange market under both the high-tiered carbon tax policy and the unified carbon tax policy. It shows that the two cost-sharing strategies can effectively alleviate the cost burden for producers, increase their marginal profits, and promote further improvement in emission reduction. It explores the emission reduction mechanism of high-tiered carbon taxes and future research should delve into the emission reduction mechanism of high-tiered carbon taxes in different carbon emission departments and regions.

With the change of climate issues and the needs of economic development, the idea of practicing green and low-carbon behaviors sinks deeper and deeper into people's hearts. This paper based on the social cost of carbon (SCC) model, this paper constructs a new carbon social cost model by adding the impact of green low-carbon behavior. Classify climate states, based on Bayesian statistical knowledge, study the posterior probability distribution of climate state transitions, and discuss the optimal carbon policy for different climate states by balancing emission utility costs and utility weighted carbon marginal products. This article also discusses the damage caused by rising temperatures and explores their impact on carbon price policies. then, the paper calculates SCC under four kinds of climate states, which will be visually displayed with graphs. Finally, we compare SCC obtained in this paper with that in other researches. The results show that: (1) Climate status has a significant impact on carbon policy, and carbon price predictions will dynamically change with climate status. (2) Green low-carbon behavior has a positive impact on climate status. (3) There are differences in the impact of the three types of damage caused by rising temperatures on carbon price policies. (4) Green development is conducive to stabilizing the value of SCC. (5) Close monitoring of the climate state helps to update the probability of damage in time so that we can precisely adjust the corresponding policies on SCC. This study provides theoretical and empirical reference for the government to formulate carbon price policies and promote the development of social green behavior.

The potential of periodate (PI) in sludge anaerobic digestion is not tapped, although it has recently attracted great research interest in organic contaminants removal and pathogens inactivation in wastewater treatment. This is the first work to demonstrate significant improvement in methane generation from waste activated sludge (WAS) with PI pretreatment and to provide underlying mechanisms. Biochemical methane potential tests indicated that methane yield enhanced from 100.2 to 146.3 L per kg VS (VS, volatile solids) with PI dosages from 0 to 100 mg per g TS (TS, total solids). Electron spin resonance showed PI could be activated without extra activator addition, which might be attributed to the native transition metals (e.g., Fe2+) in WAS, thereby generating hydroxyl radical (•OH), superoxide radicals (•O2−), and singlet oxygen (1O2). Further scavenging tests demonstrated all of them synergistically promoted WAS disintegration, and their contributions were in the order of •O2− > •OH > 1O2, leading to the release of substantial biodegradable substances (i.e., proteins and polysaccharides) into the liquid phase for subsequent biotransformation. Moreover, fluorescence and ultraviolet spectroscopy analyses indicated the recalcitrant organics (especially lignocellulose and humus) could be degraded by reducing their aromaticity under oxidative stress of PI, thus readily for methanogenesis. Microbial community analysis revealed some microorganisms participating in hydrolysis, acidogenesis, and acetoclastic methanogenesis were enriched after PI pretreatment. The improved key enzyme activities and up-regulated metabolic pathways further provided direct evidence for enhanced methane production. This research was expected to broaden the application scope of PI and provide more diverse pretreatment choices for energy recovery through anaerobic digestion.

Facing the Bicycle Rebalancing Problem (BRP), we established a Rebalancing Incentive System (BRIS). In BRIS, the bicycle operator proposes the method of financial compensation to encourage cylclists to detour some specific stations where the number of bikes is excessive or insufficient and access suitable sations. BRIS mainly includes two objects: the Bike Gym imitating the bicycle environment, and the Spatiotemporal Rebalancing Pricing Algorithm (STRPA) determining the amount of money which is given to the cyclist depending on time. STRPA is a deep reinforcement learning model based on the actor–critic structure, which is the core concept of this paper. In STRPA, the hierarchical principle is introduced to solve the dimensional disaster, and the graph matrix A is introduced to solve the complex node relationship. In addition, the traffic data including the bicycle have strong temporal and spatial characteristics. The gated recurrent unit (GRU), the sub-module of STRPA, can extract the temporal characteristics well, and the graph convolution network (GCN), also a sub-module of STRPA, can extract the spatial characteristic. Finally, our model is superior to the baseline model when verified on the the public bicycle data of Nanjing.

The overuse of nitrogen fertilizers has led to environmental pollution, which has prompted the widespread adoption of biochar as a soil conditioner in agricultural production. To date, there has been a lack of research on the effects of biochar and its combination with nitrogen fertilizer on the quality of broomcorn millet (Panicum miliaceum L.) starch. Thus, this study examined the physicochemical characteristics of starch in two types of broomcorn millet (waxy and non-waxy) under four different conditions, including a control group (N0), nitrogen fertilizer treatment alone (N150), biochar treatment alone (N0+B), and a combination of biochar and nitrogen fertilizer treatments (N150+B). The results showed that, in comparison to the control, all the treatments, particularly N150+B, decreased the content of amylose and gelatinization temperature and enhanced the starch transparency gel consistency and swelling power. In addition, biochar can improve the water solubility of starch and the gelatinization enthalpy. Importantly, the combination of biochar and nitrogen fertilizer increased the proportion of A-granules, final viscosity, starch content, and the average degree of amylopectin in polymerization. Thus, this research indicates that the combinations of biochar and nitrogen fertilizer result in the most significant improvement in the quality of starch produced from broomcorn millet.

In this paper, we are concerned with the nonlinear fractional Schrödinger equation. We extend the result of Guo and Huo and prove that the Cauchy problem of the nonlinear fractional Schrödinger equation is global well-posed in H32−γ(R) with 12≤γ<1. In view of the complexity of the nonlinear fractional Schrödinger equation itself, the local smoothing effect and maximal function estimates are not enough for presenting the global well-posedness for the nonlinear fractional Schrödinger equation. In this paper, we use a suitably iterative scheme and complete the global well-posed result for Equation (R). Moreover, we obtain the orbital stability of standing waves for the above equations via establishing the profile decomposition of bounded sequences in Hs(RN) (0

The cultivation of unique sorghum (resistant to abiotic stresses and re-recognized as healthy food) has attracted interest as an environmentally friendly minor cereal and may be a solution to food and nutritional security. However, information about how the use of selected sorghum grains affects nutritive values and its functional properties from sorghum flours is still lacking. To address this question, we selected six sorghum varieties (i.e., JinZa 34, LiaoZa 19, JinNuo 3, JiZa 127, JiNiang 2, and JiaXian) for the comprehensive analysis of the relationship among nutritional compositions, energy value contributions, and functional properties of sorghum grains. Results showed that Carr’s index (CI) and angle of repose (AR) of all sorghum flours indicated good flow and compressibility properties in terms of micrometric parameters. All sorghums were considered free of tannin. Based on the scatterplot analysis, the proportions of energy contributions due to protein, fat, and carbohydrate (CHO), were highly positively correlated with protein, fat, and CHO, respectively. The significantly different flours of six sorghum varieties resulted in different functional properties. The amylose content showed a highly negative association with light transmittance and water and oil absorption capacities. In addition, amylose had a highly positive relationship with water solubility (WS) and swelling power (SP). JinNuo 3 had the highest nutritional compositions [proximate, mineral, anti-nutritional values, and amino acid (AA) profiles] and functional properties indicating that it could be used as a brewing liquor. Our findings will provide a new opportunity to cultivate sorghum as an environment friendly minor cereal crop in dryland agro-ecosystems of arid and semi-arid regions of northern China for nutritional security, agriculture processing, and non-food industry in the future.

Loss of production due to local water scarcity, i.e., Local Water Scarcity Risk (LWSR), is transferred downstream through international supply chains to distant economies, causing potential economic losses to countries and sectors that do not directly experience actual water scarcity, which is defined as Virtual Water Scarcity Risk (VWSR). Much research has focused on assessing VWSR and characterizing the structure of VWSR transfer networks, without explaining the formation and dynamics of VWSR transfer network patterns. In this study, the global VWSR transfer networks for 2001–2016 are then constructed based on a multi-regional input-output model and complex network theory. The determinants influencing the formation of VWSR transfer networks are further explored using the time-exponential random graph model. The results demonstrate that: (1) The VWSR transfer networks exhibit a distinctly small-world and heterogeneous nature; (2) Asia and Europe are the main targets of VWSR transfers, and Asia is also the main source of risks; (3) China and the USA play a leading role on the import side of VWSR, and India is the largest exporter of VWSR; (4) The evolution of VWSR transfer networks is significantly influenced by transitivity and stability. Countries located on the same continent, sharing geographical borders and having a higher level of economic development, have a facilitating effect on the formation and evolution of VWSR transfer networks. Countries with a higher share of merchandise trade are more inclined to receive VWSR inflows, while the urbanization rate has a restraining effect on VWSR outflows. The study provides a network-based insight that explores the structural evolution of VWSR transfer networks and the determinants of their formation, informing policy makers in developing strategies to mitigate the cascading spread of VWSR.

Unraveling how microbial interactions and assembly process regulate the rhizosphere abundant and rare taxa is crucial for determining how species diversity affects rhizosphere microbiological functions. We assessed the rare and abundant taxa of rhizosphere fungal and bacterial communities in proso millet agroecosystems to explore their biogeographic patterns and co-occurrence patterns based on a regional scale. The taxonomic composition was significantly distinct between the fungal and bacterial abundant and rare taxa. Additionally, the rare taxa of bacteria and fungi exhibited higher diversity and stronger phylogenetic clustering than those of the abundant ones. The phylogenetic turnover rate of abundant taxa of bacteria was smaller than that of rare ones, whereas that of fungi had the opposite trend. Environmental variables, particularly mean annual temperature (MAT) and soil pH, were the crucial factors of community structure in the rare and abundant taxa. Furthermore, a deterministic process was relatively more important in governing the assembly of abundant and rare taxa. Our network analysis suggested that rare taxa of fungi and bacteria were located at the core of maintaining ecosystem functions. Interestingly, MAT and pH were also the important drivers controlling the main modules of abundant and rare taxa. Altogether, these observations revealed that rare and abundant taxa of fungal and bacterial communities showed obvious differences in biogeographic distribution, which were based on the dynamic interactions between assembly processes and co-occurrence networks.

Water consumption has been one of the most important topics in the field of environment and economy. Even though the driving factors of water consumption have been well studied, it is still a daunting task to reveal the influence of the status of provinces in the entire supply chain. By combining the multi-regional input-output (MRIO) model and complex network theory, an inter-provincial virtual water transfer (V WT) network was constructed to analyze the overall structural characteristics of the network model and identify the structural roles of each province. The constructed inter-provincial V WT network exhibited the characteristics of a small-world network, that is, virtual water can be easily transferred from one province to another. Moreover, network analysis revealed that provinces with different positions in the V WT network played discrepant structural roles. Panel regression analysis was further used to quantify the impact of provincial structural roles on their water consumption. The results showed that water consumption in China largely depended on some structural role characteristics in the V WT network. Out-degree and out-strength characterizing the ability of direct exporting virtual water exerted significant positive influences, while in-closeness featuring the indirect virtual water importing rate had a significant negative effect on water usage. This indicated that adjusting the uneven provincial consumption structure, the direct production demand of downstream provinces and the indirect production activities in the supply chain would help reduce water consumption. Therefore, to come true the goal of water conservation in China, it would be necessary to improve the trade structure between direct and indirect exporters and importers in the entire supply chain.

Grain trade in Belt and Road (B&R) countries shows a mismatch between the volume and direction of grain flows and actual demand. With economic and industrial development, the water crisis has intensified, which poses a great challenge to the security of world grain supply and demand. There are few studies on the reconstruction of grain trade relations from the perspective of grain economic value. In this paper, a linear optimization model considering opportunity cost is proposed to fill the gap, and it is compared and analyzed with the optimization model considering only transportation cost. The grain supply and demand structures in both optimization results show characteristics of geographical proximity and long-tail distribution. Furthermore, the economic and water resource benefits resulting from the two optimal configurations are compared and analyzed. It is found that the economic benefits generated by grain trade in B&R countries with the consideration of opportunity cost not only cover transportation costs but also generate an economic value of about 130 trillion US dollars. Therefore, considering opportunity cost in grain trade is of great significance for strengthening cooperation and promoting the economic development of countries under the B&R framework. In terms of resource benefits, the grain trade with consideration of opportunity cost saves nearly 28 billion cubic meters of water, or about 5% of the total virtual water flow. However, about 72 billion cubic meters of water is lost for the grain trade with consideration of transportation cost. This study will help to formulate and adjust policies related to the “Belt and Road Initiative” (B&R Initiative), so as to maximize the economic benefits while optimizing the structure of grain trade and alleviating water scarcity pressures.

Nitrogen is a key factor affecting sorghum growth and grain quality. This experiment was designed to investigate the physicochemical properties of sorghum starch in four sorghum varieties (Liaoza 10, Liaoza 19, Jinza 31, and Jinza 34) under four nitrogen levels: 0 kg/ha urea (N1), 300 kg/ha urea as base fertilizer (N2), 300 kg/ha urea as topdressing at the jointing stage (N3), and 450 kg/ha urea as topdressing at the jointing stage (N4). The results showed that grain size and amylose content increased with increasing nitrogen fertilizer level, peaking at N3. The peak viscosity, final viscosity, gelatinization temperature, initial temperature, final temperature, and enthalpy value increased with the nitrogenous fertilizer level, peaking at N3. The application of nitrogen fertilizer at the jointing period significantly increased the above indicators. However, excess nitrogen at the jointing period (N4) can significantly reduce the above indicators, thus changing the physicochemical properties and structure of sorghum starch. Overall, nitrogen significantly affects the structure and physicochemical properties of sorghum starch.

Inflammatory pain is caused by peripheral tissue injury and inflammation. Inflammation leads to peripheral sensitization, which may further cause central sensitization, resulting in chronic pain and progressive functional disability. Neuroimmune crosstalk plays an essential role in the development and maintenance of inflammatory pain. Studies in recent years have shown that acupuncture can exert anti-inflammatory and analgesic effects by regulating peripheral (i.e., involving local acupoints and inflamed regions) and central neuroimmune interactions. At the local acupoints, acupuncture can activate the TRPV1 and TRPV2 channels of mast cells, thereby promoting degranulation and the release of histamine, adenosine, and other immune mediators, which interact with receptors on nerve endings and initiate neuroimmune regulation. At sites of inflammation, acupuncture enables the recruitment of immune cells, causing the release of opioid peptides, while also exerting direct analgesic effects via nerve endings. Furthermore, acupuncture promotes the balance of immune cells and regulates the release of inflammatory factors, thereby reducing the stimulation of nociceptive receptors in peripheral organs. Acupuncture also alleviates peripheral neurogenic inflammation by inhibiting the release of substance P (SP) and calcitonin gene-related peptide from the dorsal root ganglia. At the central nervous system level, acupuncture inhibits the crosstalk between glial cells and neurons by inhibiting the p38 MAPK, ERK, and JNK signaling pathways and regulating the release of inflammatory mediators. It also reduces the excitability of the pain pathway by reducing the release of excitatory neurotransmitters and promoting the release of inhibitory neurotransmitters from neurons and glial cells. In conclusion, the regulation of neuroimmune crosstalk at the peripheral and central levels mediates the anti-inflammatory and analgesic effects of acupuncture on inflammatory pain in an integrated manner. These findings provide novel insights enabling the clinical application of acupuncture in the treatment of inflammatory diseases.

The scientific judgement of the structural abrupt transition characteristics of the carbon market price is an important means to comprehensively analyze its fluctuation law and effectively prevent carbon market risks. However, the existing methods for identifying structural changes of the carbon market based on carbon price data mostly regard the carbon price series as a deterministic time series and pay less attention to the uncertainty implied by the carbon price series. We propose a framework for identifying abrupt transitions in the carbon market from the perspective of a complex network by considering the influence of random factors on the carbon price series, expressing the carbon price series as a sequence of probability density functions, using the distribution of probability density to reveal the uncertainty information implied by carbon price series and constructing a recurrence network of carbon price probability density. Based on the community structure, the break index and statistical test method are defined. The simulation verifies the effectiveness and superiority of the method compared with traditional methods. An empirical analysis uses the carbon price data of the European Union carbon market and seven pilot carbon markets in China. The results show many abrupt transitions in the carbon price series of the two markets, whose occurrence period is closely related to major events.

Sorghum has good adaptation to drought tolerance and can be successfully cultivated on marginal lands with low input cost. Starch is used in many foods and nonfood industrial applications and as a renewable energy resource. Sorghum starches with different amylose contents affect the different physicochemical properties. In this study, we isolated starches from six sorghum varieties (i.e., Jinza 34, Liaoza 19, Jinnuo 3, Jiza 127, Jiniang 2, and Jiaxian) and investigated them in terms of their chemical compositions and physicochemical properties. All the starch granules had regular polygonal round shapes and showed the characteristic “Maltese cross”. These six sorghum starches showed an A-type diffraction pattern. The highest amylose content of starch in Jinza 127 was 26.90%. Jiaxian had a higher water solubility at 30, 70, and 90 °C. From the flow cytometry analysis based on six sorghum starch granules, Liaoza 19 had a larger and more complex granules (particle percentage (P1) = 66.5%). The Jinza 34 starch had higher peak (4994.00 mPa∙s) and breakdown viscosity (4013.50 mPa∙s) and lower trough viscosity (973.50 mPa∙s). Jinnuo 3 had higher onset temperature, peak temperature, conclusion temperature, gelatinization enthalpy, and gelatinization range. The principal component analysis and hierarchical cluster analysis based on classification of different sorghum starches showed that Jiniang 2 and Jinnuo 3 had similar physicochemical properties and most divergent starches, respectively. Our result provides useful information not only on the use of sorghum starches in food and non-food industries but for the great potential of sorghum-based intercropping systems in maintaining agricultural sustainability.

Natural gas scarcity poses a significant risk to the global economy. The risk of production loss due to natural gas scarcity can be transferred to downstream economies through globalized supply chains. Therefore, it is important to quantify and analyze how natural gas scarcity in some regions affects the Belt and Road (B&R) economies. The embodied natural gas scarcity risks (EGSRs) of B&R economies are assessed and the EGSR transmission network is constructed. The built network shows a small-world nature. This illustrates that any interruption in key countries will quickly spread to neighboring countries, potentially affecting the global economy. The top countries, including Turkey, China, Ukraine, and India are identified in EGSR exports, which also have relatively high values of closeness centrality. The findings illustrate that the shortage of natural gas supply in these countries may have a significant impact on downstream countries or sectors and the resulting economic losses spread rapidly. These countries are critical to the resilience of the B&R economies to natural gas scarcity. The top nations, including Turkmenistan, Macedonia, and Georgia are also identified in EGSR imports, highlighting their vulnerability to natural gas scarcity. Further, the community analysis of the network provides a fresh perspective for formulating fair and reasonable allocation policies of natural gas resources and minimizing the large-scale spread of economic losses caused by natural gas scarcity.

Percolation behavior is of wide applicability and provides insight into functional structure of complex networks. Different from the percolation behaviors of giant component (GC), the finite components make one more clearly explore network percolation behaviors and critical phenomena from a microscopic perspective, especially for large-scale network systems. Here we focus on the percolation behaviors of small component π _s with the size s = 1, 2, 3, … under different failure scenarios such as random attack, localized attack, target attack and intentional attack with limited knowledge. We find theoretically and via simulation that finite components all show the peak shape which is different from GC for random networks including random regular network, Erdős–R $\acute{\mathrm{e}}$ nyi networks and scale-free networks. In particular, we find a new general scaling relationship between $\frac{1}{s}$ and $\frac{1}{{p}_{\mathrm{max}}}$ , p _max represents the value of p (non-failure fraction of initial nodes) corresponding to the peak point of π _s in the network. This finding also provides a potential approach for determining the critical threshold and fill the gap between finite components and GC on the percolation process.

The rapid development of the Belt and Road economics has generated a considerable energy demand. Under the general trend of the global energy transition, natural gas resources are becoming the main driving force. The limited natural gas resources are posing a significant risk to economies, and this risk may also be transferred to other distant regions through economic trade. The aim of this study is to explore the trans-regional (sectoral) transmission pattern of natural gas scarcity risk. The main contribution of this paper is the assessment of the local natural gas scarcity risk (LGSR) and cross-region transfer relationship of embodied natural gas scarcity risk (EGSR), which are evaluated for the BRI economies. In addition, the network amplification effect is considered when evaluating the cross-regional impact of natural gas scarcity risk. The results show that, at the national level, Turkey, Ukraine, and Bulgaria have significant EGSR related to exports activities. The natural gas scarcity risks (GSRs) originating from these countries are mainly transferred to Turkmenistan, Georgia, and Albania, with large EGSR imports. Moreover, by comparing the ranking changes of EGSR imports, EGSR exports, and LGSRs at the national and sectoral levels, countries or sectors with higher LGSRs also have higher EGSR exports. The Top EGSR import and export network consisting of top EGSR flow relationships can well reflect countries’ preferences in choosing EGSR transfer partners. The results suggest that upstream countries and sectors should strengthen cooperation to manage natural gas resources, and provide references for decision makers in highly vulnerable downstream countries and sectors to formulate strategies to avoid the large-scale spread of economic losses caused by natural gas scarcity.

In real systems, some damaged nodes can spontaneously become active again when recovered from themselves or their active neighbours. However, the spontaneous dynamical recovery of complex networks that suffer a local failure has not yet been taken into consideration. To model this recovery process, we develop a framework to study the resilience behaviours of the network under a localised attack (LA). Since the nodes’ state within the network affects the subsequent dynamic evolution, we study the dynamic behaviours of local failure propagation and node recoveries based on this memory characteristic. It can be found that the fraction of active nodes switches back and forth between high network activity and low network activity, which leads to the spontaneous emergence of phase-flipping phenomena. These behaviours can be found in a random regular network, Erdős-Rényi network and Scale-free network, which shows that these three types of networks have the same or different resilience behaviours under an LA and random attack. These results will be helpful for studying the spontaneous recovery real systems under an LA. Our work provides insight into understanding the recovery process and a protection strategy of various complex systems from the perspective of damaged memory.

This article concerns an approximate solution for the Benjamin-Bona-Mahony (BBM) equation with a bilinear control in slowly varying medium. By a sharp estimation of the error term, a suitable approximate solution for this equation is established.