Burnecki Krzysztof, Sikora Grzegorz, Weron Aleksander
Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Oct;86(4 Pt 1):041912. doi: 10.1103/PhysRevE.86.041912. Epub 2012 Oct 17.
We show how to use a fractional autoregressive integrated moving average (FARIMA) model to a statistical analysis of the subdiffusive dynamics. The discrete time FARIMA(1,d,1) model is applied in this paper to the random motion of an individual fluorescently labeled mRNA molecule inside live E. coli cells in the experiment described in detail by Golding and Cox [Phys. Rev. Lett. 96, 098102 (2006)] as well as to the motion of fluorescently labeled telomeres in the nucleus of live human cells (U2OS cancer) in the experiment performed by Bronstein et al. [Phys. Rev. Lett. 103, 018102 (2009)]. It is found that only the memory parameter d of the FARIMA model completely detects an anomalous dynamics of the experimental data in both cases independently of the observed distribution of random noises.
我们展示了如何使用分数自回归整合移动平均（FARIMA）模型对亚扩散动力学进行统计分析。本文将离散时间FARIMA(1,d,1)模型应用于在戈尔丁和考克斯[《物理评论快报》96, 098102 (2006)]详细描述的实验中单个荧光标记的mRNA分子在活大肠杆菌细胞内的随机运动，以及应用于在布朗斯坦等人[《物理评论快报》103, 018102 (2009)]所进行的实验中荧光标记的端粒在活人细胞（U2OS癌细胞）细胞核内的运动。结果发现，在这两种情况下，FARIMA模型的记忆参数d都能完全检测到实验数据的异常动力学，而与所观察到的随机噪声分布无关。
