论文标题
序列，条形码和同源性
Sequents, barcodes, and homology
论文作者
论文摘要
我们考虑了基于逻辑思想从数据中产生假设的问题。我们介绍了一个条形码的概念，我们称之为序列条形码，在拓扑数据分析中反映了持续的同源性理论中的条形码。我们证明了这些条形码在类比中的稳定性的理论结果，其持续同源理论的结果相似。此外，我们表明，我们的新的条形码概念可以用数据引起的拓扑空间的特定过滤来解释。最后，我们讨论了序列条形码在癌症基因组学区域引起的发现问题中的具体应用。
We consider the problem of generating hypothesis from data based on ideas from logic. We introduce a notion of barcodes, which we call sequent barcodes, that mirrors the barcodes in persistent homology theory in topological data analysis. We prove a theoretical result on the stability of these barcodes in analogy with similar results in persistent homology theory. Additionally we show that our new notion of barcodes can be interpreted in terms of a persistent homology of a particular filtration of topological spaces induced by the data. Finally, we discuss a concrete application of the sequent barcodes in a discovery problem arising from the area of cancer genomics.
