论文标题
短暂的持久性特征和过滤链复合物的稳定性
Ephemeral persistence features and the stability of filtered chain complexes
论文作者
论文摘要
我们通过在过滤后的链复合物的背景下，在usher和Zhang的构造上构建构造，加强了有限度量空间的越定稳定性定理（VR）持续的同源性。过滤链络合物级别上存在的信息包括持续零的点，这些点为同源级别提供的其他信息提供了其他信息。事实证明，所产生的不变式，称为详细的条形码，具有比常规条形码更强的歧视功率，在某些对这些短暂点敏感的指标下被证明是稳定的。在某些情况下，我们提供了计算详细条形码之间此类指标的方法。我们还展示了具有相同（标准的）VR条形码的有限度量空间的几个示例，但具有不同的详细VR条形码，因此证实了这些短暂点可以增强标准VR条形码。
We strengthen the usual stability theorem for Vietoris-Rips (VR) persistent homology of finite metric spaces by building upon constructions due to Usher and Zhang in the context of filtered chain complexes. The information present at the level of filtered chain complexes includes points with zero persistence which provide additional information to that present at homology level. The resulting invariant, called verbose barcode, which has a stronger discriminating power than the usual barcode, is proved to be stable under certain metrics that are sensitive to these ephemeral points. In some situations, we provide ways to compute such metrics between verbose barcodes. We also exhibit several examples of finite metric spaces with identical (standard) VR barcodes yet with different verbose VR barcodes thus confirming that these ephemeral points strengthen the standard VR barcode.
