Tipping elements are components of the Earth system that may shift abruptly and irreversibly from one state to another at specific thresholds. It is not well understood to what degree tipping of one system can influence other regions or tipping elements. Here, we propose a climate network approach to analyse the global impacts of a prominent tipping element, the Amazon Rainforest Area (ARA). We find that the ARA exhibits strong correlations with regions such as the Tibetan Plateau (TP) and West Antarctic ice sheet. Models show that the identified teleconnection propagation path between the ARA and the TP is robust under climate change. In addition, we detect that TP snow cover extent has been losing stability since 2008. We further uncover that various climate extremes between the ARA and the TP are synchronized under climate change. Our framework highlights that tipping elements can be linked and also the potential predictability of cascading tipping dynamics.

Air pollution fluctuations have been found to strongly depend on the weather dynamics. Here we identify the significant atmospheric processes that affect the local daily variability of air pollution. We develop a multilayered network analysis to detect the interlinks between the 500‐hPa geopotential height and surface air pollution in both China and the United States. We find that Rossby waves significantly affect air pollution fluctuations through the development of cyclone and anticyclone systems and further affect the local stability of the air and the winds. Some of these systems are remote (∼3,000 km) and lead to air pollution 1–2 days later. Thus, the impact of Rossby waves on human life is greater than previously believed. The rapid warming of the Arctic could slow down Rossby waves, thus increasing human health risks. Our method can help to determine the risk assessment of such extreme events and can improve potential predictability.

Emergence refers to the existence or formation of collective behaviors in complex systems. Here, we develop a theoretical framework based on the eigen microstate theory to analyze the emerging phenomena and dynamic evolution of complex system. In this framework, the statistical ensemble composed of M microstates of a complex system with N agents is defined by the normalized N × M matrix A , whose columns represent microstates and order of row is consist with the time. The ensemble matrix A can be decomposed as A = ∑ I = 1 r σ I U I ⨂ V I , where r = min ( N , M ) , eigenvalue σ _I behaves as the probability amplitude of the eigen microstate U _I so that ∑ I = 1 r σ I 2 = 1 and U _I evolves following V _I . In a disorder complex system, there is no dominant eigenvalue and eigen microstate. When a probability amplitude σ _I becomes finite in the thermodynamic limit, there is a condensation of the eigen microstate U _I in analogy to the Bose–Einstein condensation of Bose gases. This indicates the emergence of U _I and a phase transition in complex system. Our framework has been applied successfully to equilibrium three-dimensional Ising model, climate system and stock markets. We anticipate that our eigen microstate method can be used to study non-equilibrium complex systems with unknown order-parameters, such as phase transitions of collective motion and tipping points in climate systems and ecosystems.

Using finite-size scaling, we have investigated the percolation phase transitions of evolving random networks under a generalized Achlioptas process (GAP). During this GAP, the edge with a minimum product of two connecting cluster sizes is taken with a probability p from two randomly chosen edges. This model becomes the Erd\"os-R\'enyi network at p=0.5 and the random network under the Achlioptas process at p=1. Using both the fixed point of the size ratio s2/s1 and the straight line of lns1, where s1 and s2 are the reduced sizes of the largest and the second-largest cluster, we demonstrate that the phase transitions of this model are continuous for 0.5$\leqslant${}p$\leqslant${}1. From the slopes of lns1 and ln(s2/s1)$'${} at the critical point, we get critical exponents $\beta${} and $\nu${} of the phase transitions. At 0.5$\leqslant${}p$\leqslant${}0.8, it is found that $\beta${}, $\nu${}, and s2/s1 at critical point are unchanged and the phase transitions belong to the same universality class. When p$\geqslant${}0.9, $\beta${}, $\nu${}, and s2/s1 at critical point vary with p and the universality class of phase transitions depends on p.

Cell migration plays important roles in many biological processes, but how migrating cells orchestrate intracellular molecules and subcellular structures to regulate their speed and direction is still not clear. Here, by characterizing the intracellular diffusion and the three-dimensional lamellipodium structures of fish keratocyte cells, we observe a strong positive correlation between the intracellular diffusion and cell migration speed and, more importantly, discover a switching of cell migration modes with reversible intracellular diffusion variation and lamellipodium structure deformation. Distinct from the normal fast mode, cells migrating in the newly-found slow mode have a deformed lamellipodium with swollen-up front and thinned-down rear, reduced intracellular diffusion and compartmentalized macromolecule distribution in the lamellipodium. Furthermore, in turning cells, both lamellipodium structure and intracellular diffusion dynamics are also changed, with left-right symmetry breaking. We propose a mechanism involving the front-localized actin polymerization and increased molecular crowding in the lamellipodium to explain how cells spatiotemporally coordinate the intracellular diffusion dynamics and the lamellipodium structure in regulating their migrations.