Junlong Zhang

Shuai Pang, Junlong Zhang, Yu Liu et al.

Urban space is highly heterogeneous, with economic and population activities concentrating in localized centers. However, the global organization of such intra-urban centers remains poorly understood due to the lack of consistent, comparable data. Here we develop a scalable geospatial framework using nighttime light observations to identify over 15,000 intra-urban centers worldwide. We uncover a robust regularity: despite differences in city size, geography, and development context, total urban area scales linearly with the number of centers, implying a roughly constant spatial footprint per center. This macroscopic regularity is underpinned by two independent sublinear scaling laws -- center number and urban area both scale with population at closely matched rates -- whose ratio cancels to produce the observed linear relationship. At the within-city level, this constancy manifests as a characteristic Voronoi coverage area per center that is consistent across regions, and centers are more regularly spaced than spatial null models predict. As a consequence, polycentric cities maintain stable accessibility as they expand. These findings provide a new empirical foundation for understanding the spatial organization of urban growth.

Jiawei Li, Xinyue Liang, Junlong Zhang et al.

Process supervision enhances the performance of large language models in reasoning tasks by providing feedback at each step of chain-of-thought reasoning. However, due to the lack of effective process supervision methods, even advanced large language models are prone to logical errors and redundant reasoning. We claim that the effectiveness of process supervision significantly depends on both the accuracy and the length of reasoning chains. Moreover, we identify that these factors exhibit a nonlinear relationship with the overall reward score of the reasoning process. Inspired by these insights, we propose a novel process supervision paradigm, PSPO*, which systematically outlines the workflow from reward model training to policy optimization, and highlights the importance of nonlinear rewards in process supervision. Based on PSPO*, we develop the PSPO-WRS, which considers the number of reasoning steps in determining reward scores and utilizes an adjusted Weibull distribution for nonlinear reward shaping. Experimental results on six mathematical reasoning datasets demonstrate that PSPO-WRS consistently outperforms current mainstream models.