ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


time series

Effect of rare sampling on estimation of directional couplings from time series

The problem of detection and quantitative estimation of directional couplings (mutual influences) between systems from discrete records of their oscillations (time series) arises in different fields of research. This work shows that results of the traditional «Granger causality» approach depend essentially on a sampling interval (a time step). We have revealed the causes and character of the influence of a sampling interval on numerical values of coupling estimates.

Optimization of basis function set for model map reconstruction of short electroencephalogram tracings during epileptic seizure

The problem of compact mathematical model reconstruction of short electroencephalogram tracings during epileptic seizure is solved. This kind of model map can be useful in many applications, for example, in time series segmentation with following clustering of obtained fragments. Optimization methods are proposed as a solution. It is shown that application of optimization methods allows to obtain adequate model at that time decreasing number of modeling map basis functions.

Method for calculation of lyapunov exponents spectrum from data series

The new method for the calculating of the spectrum of the Lyapunov exponents from data series is proposed. The already known methods of the same thematic are investigated. The Roessler system is given as an example for describing the proposed method. The results of numerical modeling are presented.

About the history of econophysics, nonlinear and evolutionary economics

The paper is devoted to the history of physics and evolutionary biology to economics. This influence began with the birth of economics as a separate field of scientific knowledge and changed  with the development of physics and biology. Strengthening the role of statistical methods in the  physics of the twentieth century, the birth of nonlinear physics, biology, evolution is reflected in the  economy and finance, resulting in the appearance of such area as econophysics, nonlinear and  evolutionary economics.

Diagnostics and correction of systematic error while estimating transfer entropy with k-nearest neighbours method

Transfer entropy is widely used to detect the directed coupling in oscillatory systems from their observed time series. The systematic error is detected, while estimating transfer entropy between nonlinear systems with K-nearest neighbours method. The way to minimize this error is suggested: the error is decreasing with increase of the neighbour number. The possibility to detect the systematic error is shown using two sets of measured data. The achieved results make possible to rise the method sensitivity and specificity for weakly coupled nonlinear systems.  

Optimization of Granger causation method parameters for the study of limbic epilepsy

Purpose. The aim is to reveal the dependence of Granger causality results on chosen time scales of constructed empirical models in application to the task of investigation of evolution of coupling between brain areas during limbic seizures. Methods. We use combination of methods for coupling analysis of the experimental time series and approaches to modeling from the first principles, which reproduce the main time and frequency properties of the experimental signals.