Background: With rapid urbanization, mental health challenges such as depression and emotional distress are becoming increasingly common. Contact with natural environments has been shown to improve mental health, yet most studies focus on direct associations between environmental exposure and mental health. The behavioral mechanisms underlying these benefits remain underexplored. This study aims to investigate whether outdoor activity frequency mediates the relationship between individuals’ intention to engage in outdoor activities and depressive mood. Methods: We used data from the 2021 Chinese General Social Survey (CGSS). Drawing on the Theory of Planned Behavior (TPB) and supported by Stress Recovery Theory (SRT) and Attention Restoration Theory (ART), we constructed a mediation model. Ordinary Least Squares regression, ordered logistic regression, and mediation analysis were applied to assess the relationships among outdoor activity intention, activity frequency, and depressive mood. Results: The analyses revealed three main findings. First, outdoor activity intention alone did not directly reduce depressive mood. Second, outdoor activity frequency significantly alleviated depressive mood, suggesting that actual behavioral engagement with nature is critical. Third, the effect of outdoor activity intention on depressive mood was fully mediated by activity frequency. Conclusions: The results demonstrate that the mental health benefits of natural environments are not automatically derived from intention or preference but require active and frequent engagement. These findings provide empirical support for behavior-based interventions in urban mental health strategies and establish a theoretical foundation for future research on the pathways linking nature and mental health.

With a comprehensive review of relevant literature, data, and theories, this study collects post-pandemic data from the Shanghai Stock Exchange 50 Index. Utilizing the Sparse Inverse Covariance Estimation method (GraphicalLassoCV), the research computes the conditional correlation among stocks. Additionally, an unsupervised learning method, the Affinity Propagation algorithm from machine learning, is employed to further analyze and explore the market structure of the Shanghai Stock Exchange 50 Index in the post-pandemic period. The results reveal that the constituent stocks of SSE 50 are divided into 11 clusters, and specific clusters exhibit industry cohesion, reflecting similar intraday volatility patterns within sectors. Clusters 5 and 6 encompass various industries, implying shared price fluctuations across different sectors. Clusters 8 and 9, predominantly composed of financial listed companies, emerge as the largest clusters with the highest total market capitalization, signifying significant influence in the market. Furthermore, Cluster 5 exhibits noteworthy market capitalization, representing diverse manufacturing stocks. This underscores the potential risk of common fluctuations among stocks from the cluser.

An injective edge-coloring of a graph G is an edge-coloring $$\phi $$ ϕ of G , not necessarily proper, such that $$\phi (e_1) \ne \phi (e_2)$$ ϕ ( e 1 ) ≠ ϕ ( e 2 ) whenever there exists an edge $$e_3$$ e 3 adjacent to both $$e_1$$ e 1 and $$e_2$$ e 2 . In particular, edges in a triangle must receive distinct colors. The minimum number of colors needed in an injective edge-coloring of G , denoted by $$\chi _{inj}^{\prime }(G)$$ χ inj ′ ( G ) , is called the injective chromatic index of G . In this paper, we study $$K_4$$ K 4 -minor free graphs, or equivalently, graphs with treewidth at most 2. Axenovich et al. [1] studied the injective chromatic index of graphs with treewidth at most k , and their result implies that every $$K_4$$ K 4 -minor free graph has injective chromatic index at most 9. This improves a linear bound established by Lv et al. [6] to a constant. For subcubic graphs, Kostochka et al. [5] showed that every subcubic planar graph has injective chromatic index at most 6, which implies that every subcubic $$K_4$$ K 4 -minor free graph has injective chromatic index at most 6. In the paper, we study $$K_4$$ K 4 -minor free graphs with maximum degree at most 4 and prove that every such graph has injective chromatic index at most 7.