Summary
People in science and engineering often work with data that changes over time, but the math tools they use can be different and hard to compare. This paper by the authors offers a new way to look at such changing data using something called narratives, which helps describe any kind of data that changes over time. They show how this idea works by exploring how information can be lost when changing data formats, how to break down complex time-based data into simpler parts, and how to model systems where groups of agents communicate differently over time. The main point is that by thinking about changing data in this abstract way, many different fields can share ideas and work together better.
time-varying datanarrativesdata representationinformation lossdata decompositionstructural invariantscontrol theorymulti-agent systemscommunication topologyabstract framework
Authors
Wilmer Leal, Benjamin Merlin Bumpus, Jana K. Nickel, Johan García, James Fairbanks, Warren Dixon
Abstract
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.