In order to develop a new diagnostic method for partial epilepsy using fractaldimension measurement of theory of nonlinear dynamics, two kinds of EEG fractaldimensions (correlation dimension Dc and wave form dimension...In order to develop a new diagnostic method for partial epilepsy using fractaldimension measurement of theory of nonlinear dynamics, two kinds of EEG fractaldimensions (correlation dimension Dc and wave form dimension Dw) were calculatedand compared. It was observed that most of the EEG fractal dimension values of Dcand Dw at the epileptic electrodes were smaller than those at the non-epilepticelectrodes. The results showed that the fractal dimension could be a special parameterto diagnose epilepsy diseases and are worthy to study further.展开更多
The article presents the results of recent investigations into Holter monitoring of ECG, using non-linear analysis methods. This paper discusses one of the modern methods of time series analysis--a method of determini...The article presents the results of recent investigations into Holter monitoring of ECG, using non-linear analysis methods. This paper discusses one of the modern methods of time series analysis--a method of deterministic chaos theory. It involves the transition from study of the characteristics of the signal to the investigation of metric (and probabilistic) properties of the reconstructed attractor of the signal. It is shown that one of the most precise characteristics of the functional state of biological systems is the dynamical trend of correlation dimension and entropy of the reconstructed attractor. On the basis of this it is suggested that a complex programming apparatus be created for calculating these characteristics on line. A similar programming product is being created now with the support of RFBR. The first results of the working program, its adjustment, and further development, are also considered in the article.展开更多
Properties of fractional Brownian motions (fBms) have been investigated by researchers in different fields, e.g. statistics, hydrology, biology, finance, and public transportation, which has helped us better underst...Properties of fractional Brownian motions (fBms) have been investigated by researchers in different fields, e.g. statistics, hydrology, biology, finance, and public transportation, which has helped us better understand many complex time series observed in nature [1-4]. The Hurst exponent H (0 〈 H 〈 1) is the most important parameter characterizing any given time series F(t), where t represents the time steps, and the fractal dimension D is determined via the relation D = 2 - H.展开更多
The significance of the fluctuation and randomness of the time series of each pollutant in environmental quality assessment is described for the first time in this paper. A comparative study was made of three differen...The significance of the fluctuation and randomness of the time series of each pollutant in environmental quality assessment is described for the first time in this paper. A comparative study was made of three different computing methods: the same starting point method, the striding averaging method, and the stagger phase averaging method. All of them can be used to calculate the Hurst index, which quantifies fluctuation and randomness. This study used real water quality data from Shazhu monitoring station on Taihu Lake in Wuxi, Jiangsu Province. The results show that, of the three methods, the stagger phase averaging method is best for calculating the Hurst index of a pollutant time series from the perspective of statistical regularity.展开更多
文摘In order to develop a new diagnostic method for partial epilepsy using fractaldimension measurement of theory of nonlinear dynamics, two kinds of EEG fractaldimensions (correlation dimension Dc and wave form dimension Dw) were calculatedand compared. It was observed that most of the EEG fractal dimension values of Dcand Dw at the epileptic electrodes were smaller than those at the non-epilepticelectrodes. The results showed that the fractal dimension could be a special parameterto diagnose epilepsy diseases and are worthy to study further.
文摘The article presents the results of recent investigations into Holter monitoring of ECG, using non-linear analysis methods. This paper discusses one of the modern methods of time series analysis--a method of deterministic chaos theory. It involves the transition from study of the characteristics of the signal to the investigation of metric (and probabilistic) properties of the reconstructed attractor of the signal. It is shown that one of the most precise characteristics of the functional state of biological systems is the dynamical trend of correlation dimension and entropy of the reconstructed attractor. On the basis of this it is suggested that a complex programming apparatus be created for calculating these characteristics on line. A similar programming product is being created now with the support of RFBR. The first results of the working program, its adjustment, and further development, are also considered in the article.
基金partially supported by the National Natural Science Foundation of China(Grant Nos.11173064,11233001,11233008,and U1531131)the Strategic Priority Research Program,the Emergence of Cosmological Structures of the Chinese Academy of Sciences(Grant No.XDB09000000)
文摘Properties of fractional Brownian motions (fBms) have been investigated by researchers in different fields, e.g. statistics, hydrology, biology, finance, and public transportation, which has helped us better understand many complex time series observed in nature [1-4]. The Hurst exponent H (0 〈 H 〈 1) is the most important parameter characterizing any given time series F(t), where t represents the time steps, and the fractal dimension D is determined via the relation D = 2 - H.
基金supported by the Eleventh Five-Year Key Technology R and D Program,China(Grant No.2006BAC02A15)the Colleges and Universities in Jiangsu Province Natural Science-Based Research Projects(Grant No.2006BAC02A15)+1 种基金the Jiangsu Province Post-Doctoral Fund Projects(Grant No.0801006C)the China Post-Doctoral Science Foundation(Grant No.20080441032)
文摘The significance of the fluctuation and randomness of the time series of each pollutant in environmental quality assessment is described for the first time in this paper. A comparative study was made of three different computing methods: the same starting point method, the striding averaging method, and the stagger phase averaging method. All of them can be used to calculate the Hurst index, which quantifies fluctuation and randomness. This study used real water quality data from Shazhu monitoring station on Taihu Lake in Wuxi, Jiangsu Province. The results show that, of the three methods, the stagger phase averaging method is best for calculating the Hurst index of a pollutant time series from the perspective of statistical regularity.