Sikora Grzegorz, Burnecki Krzysztof, Wyłomańska Agnieszka
Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wyb. Wyspianskiego 27, 50-370 Wroclaw, Poland.
Phys Rev E. 2017 Mar;95(3-1):032110. doi: 10.1103/PhysRevE.95.032110. Epub 2017 Mar 7.
Anomalous diffusion in crowded fluids, e.g., in cytoplasm of living cells, is a frequent phenomenon. A common tool by which the anomalous diffusion of a single particle can be classified is the time-averaged mean square displacement (TAMSD). A classical mechanism leading to the anomalous diffusion is the fractional Brownian motion (FBM). A validation of such process for single-particle tracking data is of great interest for experimentalists. In this paper we propose a rigorous statistical test for FBM based on TAMSD. To this end we analyze the distribution of the TAMSD statistic, which is given by the generalized chi-squared distribution. Next, we study the power of the test by means of Monte Carlo simulations. We show that the test is very sensitive for changes of the Hurst parameter. Moreover, it can easily distinguish between two models of subdiffusion: FBM and continuous-time random walk.
在拥挤流体中，例如活细胞的细胞质中，反常扩散是一种常见现象。一种可用于对单个粒子的反常扩散进行分类的常用工具是时间平均均方位移（TAMSD）。导致反常扩散的一个经典机制是分数布朗运动（FBM）。对单粒子追踪数据的此类过程进行验证对实验人员来说非常有意义。在本文中，我们基于TAMSD提出了一种针对FBM的严格统计检验。为此，我们分析了TAMSD统计量的分布，它由广义卡方分布给出。接下来，我们通过蒙特卡罗模拟研究检验的功效。我们表明该检验对赫斯特参数的变化非常敏感。此外，它可以很容易地区分两种亚扩散模型：FBM和连续时间随机游走。
