论文标题
一颗统治所有这些的钻石：关于锯齿形，级别和延伸持久性的旧主题和新主题
One Diamond to Rule Them All: Old and new topics about zigzag, levelsets and extended persistence
论文作者
论文摘要
十多年前引入了扩展和曲折的持久性，作为普通持久性的概括。在克服普通持久性的某些局限性的同时，它们俩都享有不错的计算属性，这使它们成为普通和多参数持久性之间的中间，并具有已经存在的有效软件实现。然而，他们的代数理论更加复杂，在扩展持久性的情况下，才开始出现。在这种情况下，本文介绍了该主题基础方面的丰富自言自语介绍，并着眼于它们所涉及的最新应用，例如计算合理理论和多参数持久性。
Extended and zigzag persistence were introduced more than ten years ago, as generalizations of ordinary persistence. While overcoming certain limitations of ordinary persistence, they both enjoy nice computational properties, which make them an intermediate between ordinary and multi-parameter persistence, with already existing efficient software implementations. Nevertheless, their algebraic theory is more intricate, and in the case of extended persistence, was formulated only very recently. In this context, this paper presents a richly illustrated self-contained introduction to the foundational aspects of the topic, with an eye towards recent applications in which they are involved, such as computational sheaf theory and multi-parameter persistence.
