发表机构
Universidad Nacional de Colombia; Virginia Tech（哥伦比亚国立大学; 弗吉尼亚理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出叙事理论，一个抽象框架，用于建模任意数学类型的时变数据，并通过三个片段展示其在信息损失、结构分解及多智能体控制中的应用，强调抽象视角对跨领域研究的指导作用。
AI 中文摘要
现代科学与工程日益依赖时变数据，然而用于建模时间现象的数学工具往往在各自独立的学科中发展，这掩盖了共同原理，并限制了思想跨领域的转移。本章提出叙事理论，这是一个适用于任何数学类型的时变对象的抽象框架，既支持理论研究也支持应用。为阐明这一视角，本章发展出三个片段，每个片段展示一个不同的研究方向。第一个片段探讨一个普遍关切的问题：在不同时变数据表示之间切换时，可能发生何种信息损失？第二个片段关注结构与算法方法：我们如何系统地将时变数据分解为简单部分，并获得描述其结构复杂性的不变量？第三个片段是控制理论中的应用：我们如何对具有切换通信拓扑的多智能体系统进行建模？比任何单个片段更重要的是，这一邀请的核心信息是，一个合适的抽象视角能够组织并引导跨越极其多样的数学与科学领域的研究。
英文摘要
Modern science and engineering increasingly rely on time-varying data, yet the mathematical tools used to model temporal phenomena are often developed within separate disciplines, obscuring common principles and limiting the transfer of ideas across fields. This chapter presents the theory of narratives, an abstract framework for time-varying objects of any mathematical kind that supports both theoretical investigations and applications. To illustrate this perspective, the chapter develops three vignettes, each illustrating a different research direction. The first addresses a general concern: What information loss can occur when switching between different representations of temporal data? The second concerns structural and algorithmic approaches: How can we systematically decompose time-varying data into simple pieces and obtain invariants describing its structural complexity? The third is an application to control theory: How can we model multi-agent systems with switching communication topologies? More important than any individual vignette, the central message of this invitation is that a suitable abstract perspective can organize and guide research across remarkably diverse mathematical and scientific domains.
Comments42 pages, 7 figures. Book chapter
