论文标题
针对差异功能的定向持续同源理论
A directed persistent homology theory for dissimilarity functions
论文作者
论文摘要
我们开发了针对定向的简单复合物的持久同源性理论，该理论在奇数维度中检测到持续的定向循环。我们将持续的同源性与经典的持久同源性相关联，证明了一些稳定性结果，并讨论了我们方法的计算挑战。我们定向的持续同源理论是由具有半级系数的同源性的动机：通过明确删除添加剂倒置，我们能够以定向循环为代数。
We develop a theory of persistent homology for directed simplicial complexes which detects persistent directed cycles in odd dimensions. We relate directed persistent homology to classical persistent homology, prove some stability results, and discuss the computational challenges of our approach. Our directed persistent homology theory is motivated by homology with semiring coefficients: by explicitly removing additive inverses, we are able to detect directed cycles algebraically.
