Time-Varying Data as Sheaves: an Invitation to Narratives
[Sztuczna inteligencja] Autorzy: Wilmer Leal, Benjamin Merlin Bumpus, Jana K. Nickel i 3 więcej
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 thi…
- Kategoria arxiv
- cs.AI
- Kategoria
- Sztuczna inteligencja