AI 中文总结
本文提出融合高阶信息论与拓扑数据分析的框架，通过O-information和持续同调识别环境网络中的稳健高阶结构，并将不确定性解释为信息拓扑的不稳定性。
AI 中文摘要
环境系统以复杂的空间交互为特征，这些交互无法通过成对关系或局部不确定性度量来完全描述。我们提出了一个统一框架，结合高阶信息论与拓扑数据分析，以刻画环境网络的组织与不确定性。空间实体（以监测站或市政当局为代表）被嵌入到Delaunay单纯复形中，并使用O-information来量化相邻三元组之间的冗余性与协同性。由此产生的高阶交互场通过持续同调进行分析，从而能够识别在交互尺度上保持稳定的拓扑结构。该方法被应用于基于每周NO2和O3观测的空气质量监测网络以及多灾害区域评估。我们表明，表现出强O-information和持续拓扑结构的区域对应于稳健的环境模式，而以异质机制和快速变化交互为特征的区域则表现出更高的不确定性。基于这些结果，我们引入了一个拓扑不确定性框架，该框架整合了单纯形散度、高阶交互和拓扑不确定性。我们的结果表明，不确定性不仅可被解释为统计变异性，还可被解释为底层信息拓扑的不稳定性。通过将O-information和持续同调整合到一个共同的空间框架中，所提出的方法为在环境和多灾害系统中检测稳健的高阶结构和拓扑不确定区域提供了一种新方法论。
英文摘要
Environmental systems are characterized by complex spatial interactions that cannot be fully described through pairwise relationships or local uncertainty measures. We propose a unified framework combining higher-order information theory and topological data analysis to characterize the organization and uncertainty of environmental networks. Spatial entities, represented by monitoring stations or municipalities, are embedded into a Delaunay simplicial complex, and O-information is used to quantify redundancy and synergy among neighboring triplets. The resulting field of higher-order interactions is analyzed through persistent homology, enabling the identification of topological structures that remain stable across interaction scales. The methodology is applied to both an air-quality monitoring network based on weekly \(\mathrm{NO_2}\) and \(\mathrm{O_3}\) observations and a multi-hazard territorial assessment. We show that regions exhibiting strong O-information and persistent topological structures correspond to robust environmental patterns, whereas areas characterized by heterogeneous regimes and rapidly varying interactions display increased uncertainty. Building on these results, we introduce a topological uncertainty framework that integrates simplex divergence, higher-order interactions, and topological uncertainty. Our results demonstrate that uncertainty can be interpreted not only as statistical variability but also as the instability of the underlying information topology. By integrating O-information and persistent homology within a common spatial framework, the proposed approach provides a new methodology for detecting robust higher-order structures and topologically uncertain regions in environmental and multi-hazard systems.
