短期流量守恒：带符号最优传输
Conservation of Short-term Flows: Signed Optimal Transport
AI总结：
本文构建带符号最优传输的理论框架，证明变分问题中最优耦合的存在性与唯一性，提供双边际约束下无损信息传输的算法方案，设计适配时间序列与面板结构分析的经验分析框架，衔接理论与实践。
AI中文摘要：
本文构建了带符号最优传输的理论框架，由连续介质传输方程诱导的全局平坦度测度作为正则项。我们从调和分析视角研究传输网络，证明变分问题中最优耦合的存在性与唯一性，并提供双边际约束下保证无损信息传输的算法方案。为衔接理论与实践，我们为所得最优估计量设计了经验分析框架，该框架具有足够通用性，可适配网络的时间序列与面板结构分析，源于局部紧阿贝尔群的固有不变性。
英文摘要：
This paper develops a theoretical framework for signed optimal transport. A global flatness measure induced by the continuum transport equation serves as the regularizer. We examine transport networks from a harmonic analysis perspective, prove the existence and uniqueness of the optimal coupling in the variational problem, and provide an algorithmic scheme that guarantees lossless information transport under bi-marginal constraints. To bridge theory with practice, we design an empirical analysis framework for the resulting optimal estimators, which is sufficiently general to accommodate both time-series and panel-structural analyses of the network, owing to the intrinsic invariance properties of locally compact abelian groups.
