从分割角度看分数莱维稳定运动

Aleksander A. Stanislavsky, Aleksander Weron
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引用次数: 0

摘要

通过对 Golding-Cox mRNA 数据集的分割分析,可以将这些轨迹描述为分数李维稳定运动(FLSM)。FLSM 方法有几个重要的优点。只需使用几个参数,它就能检测出具有非高斯约束部分的分段轨迹中的跳跃。每个参数的值都表明了封闭区段的贡献。mRNA 轨迹中的非高斯特征归因于轨迹分段。每个片段可以处于以下一种扩散模式:自由扩散、封闭运动和不动。当自由扩散片段与封闭或不动片段交替出现时,分段轨迹的均方位移类似于亚扩散。受限段既有高斯(正态)统计,也有非高斯统计。如果将随机轨迹估算为 FLSM,它们可以表现为亚扩散或列维扩散。这种方法可用于分析具有非高斯行为的经验数据,对扩散轨迹进行统计分类有助于揭示异常动态。
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Fractional Lévy Stable Motion from a Segmentation Perspective
The segmentation analysis of the Golding–Cox mRNA dataset clarifies the description of these trajectories as a Fractional Lévy Stable Motion (FLSM). The FLSM method has several important advantages. Using only a few parameters, it allows for the detection of jumps in segmented trajectories with non-Gaussian confined parts. The value of each parameter indicates the contribution of confined segments. Non-Gaussian features in mRNA trajectories are attributed to trajectory segmentation. Each segment can be in one of the following diffusion modes: free diffusion, confined motion, and immobility. When free diffusion segments alternate with confined or immobile segments, the mean square displacement of the segmented trajectory resembles subdiffusion. Confined segments have both Gaussian (normal) and non-Gaussian statistics. If random trajectories are estimated as FLSM, they can exhibit either subdiffusion or Lévy diffusion. This approach can be useful for analyzing empirical data with non-Gaussian behavior, and statistical classification of diffusion trajectories helps reveal anomalous dynamics.
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