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Spatial-temporal structures in noise processes: Microscopic and Macroscopic dynamics

机译:噪声过程中的空间时间结构:微观和宏观动力学

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Noise processes are often modelled as stochastic processes. We have used a multivariate method based on the application of Principal Component Analysis (PCA) in order to classify different spatial-temporal structures taken as noise. When the structures have a correlation in time, a parameter distinguishing between fast and slow dynamics appears naturally. We have found this parameter in previous contributions with a different meaning depending on the context. Especially interesting is the application to the characterization of 1/f noise. In this paper we have extended the method in order to apply it to different kind of systems exhibiting, for example, self-organizing properties or brownian motion. One goal is trying to define a criterion to distinguish between fast and slow dynamics parameters. Finally, a statistical analysis is made in order to find the conditions for the application of the method to a wide range of different systems.
机译:噪声过程通常是随机过程的建模。我们使用了基于主成分分析(PCA)的应用的多变量方法,以便将不同的空间 - 时间结构分类为噪声。当结构在时间上具有相关性时,区分快速和慢动动力学之间的参数自然。我们在以前的贡献中找到了此参数,其含义不同,具体而言。特别有趣的是应用于1 / f噪声的表征。在本文中,我们已经扩展了该方法,以便将其应用于表现出的不同类型的系统,例如,自组织属性或布朗运动。一个目标正在尝试定义一个标准,以区分快速和慢速动态参数。最后,进行统计分析,以便在广泛的不同系统中找到应用方法的条件。

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