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

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

Air pollution causes widespread environmental and health problems and severely hinders the life quality of urban residents. Traffic is a critical for human life and its emissions are a major source of pollution, aggravating urban air pollution. However, the complex interaction between the traffic emissions and the air pollution in the cities has not yet been revealed. In particular, the spread of the COVID-19 has caused various cities to implement different traffic restriction policies according to the local epidemic situation, which provides the possibility to explore the relationship between urban traffic and air pollution. Here we explore the influence of traffic to air pollution by reconstructing a multi-layer complex network base on traffic index and air quality index. We uncover that air quality in Beijing-Tianjin-Hebei (BTH), Chengdu-Chongqing Economic Circle (CCS) and Central China (CC) regions are significantly influenced by the surrounding traffic conditions after the outbreak. Under different fights against the epidemic stages, the influence of traffic in other cities on the air pollution reached the maximum in stage 2 (also called Initial Progress in Containing the Virus). For BTH and CC regions, the impact of traffic on air quality becomes larger in the first two stages and then decreases, while for CC, the significant impact occurs in Phase 3 among regions. For other regions, however, the changes are not evident. Our presented network-based framework provides a new perspective in the field of transportation and environment, and maybe helpful to guide the government to formulate air pollution mitigation and traffic restriction policies.

Beyond its obvious macro-economic relevance, fiat money has important micro-economic implications. They matter for addressing No. 8 in Smale's "Mathematical Problems for the Next Century": extend the mathematical model of general equilibrium theory to include price adjustments. In the canonical Arrow-Debreu framework, equilibrium prices are set by a fictitious auctioneer. Removing that fiction raises the question of how prices are set and adjusted by decentralised actors with incomplete information. We investigate this question through a very basic model where a unique factor of production, labour, produces a single consumption good, called jelly for brevity. The point of the model is to study a price dynamics based on the firm's expectations about jelly demand and labour supply. The system tends towards economic equilibrium, however, depending on the initial conditions it might not get there. In different model versions, different kinds of money are introduced. Compared to the case of no money, the introduction of money as a store of value facilitates the system reaching economic equilibrium. If money is introduced as a third commodity, i.e. there is also a demand for money, the system dynamics in general becomes more complex.