Department of Mathematics, Brigham Young University, Provo, Utah, United States of America.
PLoS One. 2021 Dec 20;16(12):e0261021. doi: 10.1371/journal.pone.0261021. eCollection 2021.
The mean square displacement (MSD) is an important statistical measure on a stochastic process or a trajectory. In this paper we find an approximation to the mean square displacement for a model of cell motion. The model is a discrete-time jump process which approximates a force-based model for cell motion. In cell motion, the mean square displacement not only gives a measure of overall drift, but it is also an indicator of mode of transport. The key to finding the approximation is to find the mean square displacement for a subset of the state space and use it as an approximation for the entire state space. We give some intuition as to why this is an unexpectedly good approximation. A lower bound and upper bound for the mean square displacement are also given. We show that, although the upper bound is far from the computed mean square displacement, in rare cases the large displacements are approached.
均方位移（Mean Square Displacement，MSD）是一种用于描述随机过程或轨迹的重要统计量。在本文中，我们找到了一种用于细胞运动模型的均方位移近似方法。该模型是一种离散时间跳跃过程，它近似于基于力的细胞运动模型。在细胞运动中，均方位移不仅可以衡量整体漂移，还可以指示运输方式。找到近似方法的关键是找到状态空间的一个子集的均方位移，并将其用作整个状态空间的近似值。我们给出了一些为什么这是一种出乎意料的好近似的直观解释。我们还给出了均方位移的下界和上界。我们表明，尽管上界与计算出的均方位移相差甚远，但在极少数情况下，仍可以接近大位移。
