On the topology of random complexes built over stationary point processes.
On the topology of random complexes built over stationary point processes.
复制标题
基于驻点过程构建的随机复形的拓扑。
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
R. Adler
中科院分区：
文献类型：
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作者：
D. Yogeshwaran;R. Adler
切赫和维托里斯-里普斯复合体。特别是，我们得到的结果有关的同源性，通过贝蒂数的增长，当顶点是一个一般的平稳点过程的点。这显着扩展了早期的结果，其中的点是iid观测或点的泊松过程。在处理一般的点过程，其中的点表现出的依赖性，如吸引力，或排斥，我们发现的现象定量不同的iid和泊松的情况下观察到的。从拓扑数据分析的角度来看，我们的结果严重影响考虑模型（非）稳健性的统计推断。
Cech and Vietoris-Rips complexes. In particular, we obtain results about homology, as measured via the growth of Betti numbers, when the vertices are the points of a general stationary point process. This significantly extends earlier results in which the points were either iid observations or the points of a Poisson process. In dealing with general point processes, in which the points exhibit dependence such as attraction, or repulsion, we find phenomena quantitatively different from those observed in the iid and Poisson cases. From the point of view of topological data analysis, our results seriously impact on considerations of model (non) robustness for statistical inference.
随机 2-复合体的拓扑
影响因子：
0.8
作者：
Cohen D
通讯作者：
Cohen D