Although most of wealth and innovation have been the result of human interaction and cooperation, we are not yet able to quantitatively predict the spatial distributions of three main elements of cities: population, roads, and socioeconomic interactions. By a simple model mainly based on spatial attraction and matching growth mechanisms, we reveal that the spatial scaling rules of these three elements are in a consistent framework, which allows us to use any single observation to infer the others. All numerical and theoretical results are consistent with empirical data from ten representative cities. In addition, our model can also provide a general explanation of the origins of the universal super- and sub-linear aggregate scaling laws and accurately predict kilometre-level socioeconomic activity. Our work opens a new avenue for uncovering the evolution of cities in terms of the interplay among urban elements, and it has a broad range of applications.

This work proposes a data-driven model which could predict the viscosity of diverse DESs accurately and rapidly, and the model interpretation given by SHAP deepens the understanding of the viscosity of DESs.

Deep eutectic solvents (DESs) have been widely applied to recover spent lithium-ion batteries (LIBs); however, developing effective and efficient systems for cathode leaching via the traditional trial-and-error method requires substantial efforts. This work aims to accelerate the discovery of novel promising DESs by leveraging the conditional Generative Adversarial Network (CGAN). Three databases were constructed: (i) DESs leaching cathodes, (ii) DESs leaching metal oxides, and (iii) DES properties. The absolute Spearman's rank correlation and agglomerative hierarchical clustering analysis ensured the selection of an optimal feature set for building predictive models. An XGBoost model was developed, achieving remarkable performance (R² = 0.9702, MSE = 0.0007) in predicting cathode solubility in DESs. We employed the Shapley additive explanation (SHAP) method to quantify the importance of acidity, coordination, and reducibility of DESs and provide insights into further research. To accelerate time-consuming investigational procedures, a CGAN model was established, rapidly identifying promising DESs like ChCl : Glycolic acid, with excellent agreement between predictions and experimental results. This study offers a general data analysis framework for other metal oxides (e.g., Cu_xO, Fe_xO_y, ZnO) leaching using DESs, enabling accurate solubility prediction and deepening the understanding of cathode leaching mechanisms. The CGAN model significantly accelerates the development of a DES-based process for lithium-ion cathode recycling, saving development time and effort. Overall, this work facilitates the efficient discovery and development of effective DESs for the recovery of valuable metals from spent LIB cathodes.

Clusters or communities can provide a coarse-grained description of complex systems at multiple scales, but their detection remains challenging in practice. Community detection methods often define communities as dense subgraphs, or subgraphs with few connections in-between, via concepts such as the cut, conductance, or modularity. Here we consider another perspective built on the notion of local dominance, where low-degree nodes are assigned to the basin of influence of high-degree nodes, and design an efficient algorithm based on local information. Local dominance gives rises to community centers, and uncovers local hierarchies in the network. Community centers have a larger degree than their neighbors and are sufficiently distant from other centers. The strength of our framework is demonstrated on synthesized and empirical networks with ground-truth community labels. The notion of local dominance and the associated asymmetric relations between nodes are not restricted to community detection, and can be utilised in clustering problems, as we illustrate on networks derived from vector data.