NIMRAD in action: Fluctuation spectroscopy based on the scaling properties of beta-distribution. How to extract stable parameters from non-stationary long-time series?

R. Nigmatullin教授

俄罗斯喀山联邦大学 Kazan (Volga region) Federal University

王春雷 教授

2014-04-21 15:40

知新楼C座7楼报告厅

A new method for analysis of long-time series ("large" data) is suggested. The method generalizes the well-known detrended fluctuation analysis (DFA) approach [1] and uses the scaling properties of the beta-distribution function. This new method allows finding the stable parameters and reducing the series containing 105 and more data points to analysis of 10-20 stable parameters, only. The new procedure of clusterization with the usage of the generalized Pearson correlation function allows taking into account the influence of different factors and combine/separate different parameters into a statistical cluster with respect to the qualitative external parameters considered. The most interesting feature of the proposed approach is that it admits the secondary fit of the reduced parameters that were calculated in the results of the first fitting procedure. The proposed method is rather flexible and general and can be applied to a wide set of large data. As an example the membrane currents containing 250000 data points characterizing the current of “control” series belonging to different biologic cells are considered. In the results of application of the method it becomes possible to realize the essential reduction of the initial long-time series and obtain 20 stable parameters that admit the further clusterization in accordance with influence of some qualitative factor. In our case this factor coincides with currents recorded from living cells and empty electrodes, when the presence of biological material was absent. The definite separation of these long-time series in terms of the reduced parameters from the background noise, i.e. current referring to disconnected equipment was obtained. The method opens new possibilities in creation of a reduced database (specific fingerprints) of different long-time series for their comparison and subsequent analysis. We think that the fluctuation spectroscopy based on beta-distribution (FSBD) function is applicable to a wide set of "large data", where the clearly expressed trend is absent and the urgent necessity of reduction of these data for their further comparison exists.

[1] Hausdorff JM, Peng C-K, Ladin Z, Wei JY, Goldberger AL. Is walking a random walk? Evidence for long-range correlations in the stride interval of human gait. J Appl Physiol 1995; 78: 349–58.

尼格马图林教授，科学博士, 俄罗斯喀山联邦大学物理研究所 理论物理系。

尼格马图林教授出生于1947年俄罗斯联邦鞑靼斯坦共和国的首府喀山。于1973年在喀山州立大学获得博士学位，然后于1993年在同一所大学获得物理和数学博士学位。 现在是喀山联邦大学（伏尔加区）的物理数学全职教授。1982-1983年期间，在英国Jonscher教授的实验室从事电介质物理研究。从1990年起，成为国际电介质协会的成员。1998年他和法国同事A. Le Mehaute 博士和L. Nivanen博士一起出版了关于分形几何和分数阶微积分的专著。目前的研究兴趣是电介质物理，发展S/N处理分析的新方法以及分数阶微积分和分形几何在不同物理领域的应用。他已经发表了220余篇论文，SCI引用超过1800次，H-因子17。是2012年南京召开第五届分数阶微积分及其应用国际会议的plenary speaker之一，http://em.hhu.edu.cn/fda12/Committees.html