Abstract framework organizes analysis of changing time data
Time-Varying Data as Sheaves: an Invitation to Narratives
Artificial IntelligenceMultiagent Systems
Summary
Handling data that changes over time is tricky because different fields use different math tools, making it hard to share ideas. The authors introduce an abstract idea called narratives that can describe any kind of data as it changes over time. They show examples about how changing data can lose information, how to break down complicated time data into simple parts, and how to model systems where groups of agents communicate differently over time. Their main point is that this new way of thinking can help connect different scientific areas that study time-varying data.
What this means in practice
- •For systems engineers: Model multi-agent systems where communication links change dynamically using a unified abstract framework for time-varying data.
- •For data analysts: Detect and quantify information loss when converting temporal data between different mathematical representations.
A theory result. No direct application yet.
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.