Automatic filters for the detection of coherent structure in spatiotemporal systems.
Automatic filters for the detection of coherent structure in spatiotemporal systems.
复制标题
用于检测时空系统中相干结构的自动滤波器。
DOI：
10.1103/physreve.73.036104
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
Moore,Cristopher
中科院分区：
文献类型：
--
作者：
Shalizi,CosmaRohilla;Haslinger,Robert;Rouquier,Jean-Baptiste;Klinkner,KristinaLisa;Moore,Cristopher
目前用于识别空间扩展系统中连贯结构的大多数方法依赖于这些结构所采取的形式的先验信息。本文提出了两种自动过滤空间动力系统变化构型和提取相干结构的方法。其一，局部灵敏度滤波，是局部Lyapunov指数方法的一种改进，适用于元胞自动机和其他离散空间系统。另一种是局部统计复杂性过滤，计算在给定点附近对系统行为进行最佳预测所需的信息量。通过研究这些量的时空分布变化，我们可以在各种形成模式的元胞自动机中找到连贯的结构，而无需猜测或假设该结构的形式。我们将这两种滤波器应用于基本元胞自动机和周期元胞自动机（ECA和CCA），发现它们很容易识别粒子、结构域和其他更复杂的结构。我们将ECA的结果与早期基于形式语言理论的结果和基于序参数和自由能的更传统方法的结果进行了比较。虽然灵敏度和统计复杂性同样擅长揭示结构，但它们基于不同的系统属性（分别是动态的和概率的），并提供互补的信息。
Most current methods for identifying coherent structures in spatially extended systems rely on prior information about the form which those structures take. Here we present two approaches toautomaticallyfilter the changing configurations of spatial dynamical systems and extract coherent structures. One,local sensitivityfiltering, is a modification of the local Lyapunov exponent approach suitable to cellular automata and other discrete spatial systems. The other,local statistical complexityfiltering, calculates the amount of information needed for optimal prediction of the system’s behavior in the vicinity of a given point. By examining the changing spatiotemporal distributions of these quantities, we can find the coherent structures in a variety of pattern-forming cellular automata, without needing to guess or postulate the form of that structure. We apply both filters to elementary and cyclical cellular automata (ECA and CCA) and find that they readily identify particles, domains, and other more complicated structures. We compare the results from ECA with earlier ones based upon the theory of formal languages and the results from CCA with a more traditional approach based on an order parameter and free energy. While sensitivity and statistical complexity are equally adept at uncovering structure, they are based on different system properties (dynamical and probabilistic, respectively) and provide complementary information.