将时变数据分解为简单片段：叙事的结构化分解
Decomposing time-varying data into simple pieces: structured decompositions of narratives
AI总结：
研究如何将时变图分解为更小片段，提出结合结构化分解与持久叙事的范畴论方法，可将静态分解理论提升为时间理论，并应用于时变图，恢复相关时间类似物。
AI中文摘要：
随时间变化的图在各种应用中都会出现，但没有单一标准方法将它们分解成更小的片段。本文提出一种系统的范畴论方法。主要思想是将结构化分解（如推广图分解的树分解）与持久叙事（将时变数据建模为图表）相结合。我们证明，在适当的范畴假设下，任何静态分解理论都可提升为相应的时间理论。作为案例研究，我们将此构造应用于时变图，并恢复普通树宽、补树宽和树独立数的自然时间类似物。
英文摘要：
Graphs that change over time arise throughout applications, but there is no single standard way to decompose them into smaller pieces. In this paper, we propose a systematic categorical method for doing so. The main idea is to combine structured decompositions, which generalize graph decompositions, such as tree-decompositions, with persistent narratives, which model time-varying data as diagrams. We prove that, under suitable categorical hypotheses, any static theory of decompositions can be lifted to a corresponding temporal theory. As case studies, we apply this construction to time-varying graphs and recover natural temporal analogues of ordinary tree-width, complemented tree-width, and the tree-independence number.
