Fractional Lévy Stable Motion from a Segmentation Perspective

Abstract

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.

Keywords

• long-term memory
• time series
• segmentation
• confinement
• subdiffusion
• Lévy diffusion