现代科学和工程越来越依赖于时变数据,，但用于模拟时间现象的数学工具通常是在不同学科内开发的,，模糊了共同原理并限制了跨领域的思想转移。本章介绍了叙事理论,，这是一个针对任何数学类型的时变对象的抽象框架，支持理论研究和应用。 To illustrate this perspective, the chapter develops three vignettes, each illustrating a different research direction.第一个解决了普遍关心的问题: 在时态数据的不同表示之间切换时会发生什么信息丢失? 第二个涉及结构和算法方法: 我们如何系统地将时变数据分解为简单的片段并获得描述其结构复杂性的不变量? 第三个是控制理论的应用: 我们如何通过切换通信拓扑来建模多智能体系统? 比任何单独的小插图更重要, 此邀请的中心信息是合适的抽象视角可以组织和 guide research across remarkably diverse mathematical and scientific domains.
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.
科目: 人工智能 (cs.AI); 多智能体系统 (cs.MA); 系统与控制 (eess.SY); 类别理论 (math.CT)
Subjects: Artificial Intelligence (cs.AI); Multiagent Systems (cs.MA); Systems and Control (eess.SY); Category Theory (math.CT)