论文标题
持续形态引起的加性部分匹配
Additive Partial Matchings Induced by Persistence Morphisms
论文作者
论文摘要
鉴于持久模块的形态（又称持久性形态）$ f \ colon v \ rightarrow u $，我们介绍了一个新颖的操作员，该新颖操作员确定了$ v $和$ f $引起的条形图之间的部分匹配。我们表明，所提出的操作员相对于持续形态的直接总和是加性的，并且包含的信息比图像持久模块$ f v $和等级不变。我们还说明了在Bauer-LeSnick的部分匹配$χ_f$上使用我们的诱导部分匹配的一些优势。最后，我们提供了一个持续的态度系列，其中包含由摩尔斯过滤构建的模块，其中$χ_f$，$ f v $，等级不变和我们拟议的诱导部分匹配是等效的。
Given a morphism of persistence modules (a.k.a. persistence morphism) $f\colon V \rightarrow U$, we introduce a novel operator that determines a partial matching between the barcodes of $V$ and $U$ induced by $f$. We show that the proposed operator is additive with respect to the direct sum of persistence morphisms and contains more information than the image persistence module $f V$ and the rank invariant. We also illustrate some advantages of using our induced partial matching over the Bauer-Lesnick partial matching $χ_f$. Lastly, we provide a family of persistence morphisms that contain modules built from Morse filtrations, for which $χ_f$, $f V$, the rank invariant and our proposed induced partial matching are equivalent.
