Pair correlation functions for identifying spatial correlation in discrete domains
Pair correlation functions for identifying spatial correlation in discrete domains
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DOI：
10.1103/physreve.97.062104
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发表时间：
2018-06-04
影响因子：
2.4
通讯作者：
Yates, Christian A.
中科院分区：
文献类型：
--
作者：
Gavagnin, Enrico;Owen, Jennifer P.;Yates, Christian A.
识别和量化空间相关性是研究多智能体系统集体行为的重要方面。配对相关函数(PCF)是一种强大的统计工具，可以提供关于成对代理之间的相关性的定性和定量信息。尽管针对非晶格结构域定义了大量的相变光纤，但最近只有少数研究考虑了离散相变结构域的相变光纤。我们的工作扩展了离散域中空间相关性的研究，定义了一组新的PCF，使用了两种自然和直观的正方形格子距离定义：出租车和均匀度规。我们展示了这些PCF如何比以前的尝试有所改进，并将获得的定量数据进行了比较。我们还将PCF的定义扩展到以前没有研究过的其他类型的规则镶嵌，包括六边形、三角形和长方体。最后，我们为任何镶嵌和度量提供了全面的PCF，允许在识别相关性不那么直观的不规则晶格中进行空间相关性的研究。
Identifying and quantifying spatial correlation are important aspects of studying the collective behavior of multiagent systems. Pair correlation functions (PCFs) are powerful statistical tools that can provide qualitative and quantitative information about correlation between pairs of agents. Despite the numerous PCFs defined for off-lattice domains, only a few recent studies have considered a PCF for discrete domains. Our work extends the study of spatial correlation in discrete domains by defining a new set of PCFs using two natural and intuitive definitions of distance for a square lattice: the taxicab and uniform metric. We show how these PCFs improve upon previous attempts and compare between the quantitative data acquired. We also extend our definitions of the PCF to other types of regular tessellation that have not been studied before, including hexagonal, triangular, and cuboidal. Finally, we provide a comprehensive PCF for any tessellation and metric, allowing investigation of spatial correlation in irregular lattices for which recognizing correlation is less intuitive.