Fractal Analysis of Event Related Potential

1993 ◽  
Vol 5 (2) ◽  
pp. 198-201
Author(s):  
Hideto Ide ◽  
◽  
Shinjiro Yagi
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Power Spectrum ◽  
Observational Data ◽  
Fractal Analysis ◽  
Event Related Potential

We have tried to apply fractal analysis to time series which have 1/f power spectrum. Before carrying out any analysis, we expand the idea of fractal to time series. We examine the fractal dimension of time series to simulate the Brawnian function. We apply fractal analysis to observational data of event related potential (ERP) and compare averaging results with those based on fractal analysis.

scholarly journals Solar-Like Oscillations of Procyon A: Stellar Models and Time Series Simulations versus Observations

2000 ◽  
Vol 176 ◽  
pp. 461-462
Author(s):  
C. Barban ◽  
E. Michel ◽  
M. Martic ◽  
J. Schmitt ◽  
J. C. Lebrun ◽  
...  
Keyword(s):  
Time Series ◽  
Power Spectrum ◽  
Numerical Simulations ◽  
Observational Data ◽  
Theoretical Predictions ◽  
Stellar Models ◽  
Excess Power ◽  
New Evidence

AbstractThe aim of this paper (further developed in Barban et al. 1999) is to present new evidence of the possible stellar origin of the observed excess power in the power spectrum of Procyon A presented in Martic et al. (1999) by comparing these observational data with theoretical predictions and numerical simulations.

scholarly journals Fractal analysis of muscle activity patterns during locomotion: pitfalls and how to avoid them

2020 ◽  
Author(s):  
Alessandro Santuz ◽  
Turgay Akay
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Hurst Exponent ◽  
Activity Patterns ◽  
Surrogate Data ◽  
Time Dependent ◽  
Physiological Data ◽  
Adult Mice

AbstractTime-dependent physiological data, such as electromyogram (EMG) recordings from multiple muscles, is often difficult to interpret objectively. Here, we used EMG data gathered during mouse locomotion to investigate the effects of calculation parameters and data quality on two metrics for fractal analysis: the Higuchi’s fractal dimension (HFD) and the Hurst exponent (H). A curve is fractal if it repeats itself at every scale or, in other words, if its shape remains unchanged when zooming in the curve at every zoom level. Many linear and nonlinear analysis methods are available, each of them aiming at the explanation of different data features. In recent years, fractal analysis has become a powerful nonlinear tool to extract information from physiological data not visible to the naked eye. It can present, however, some dangerous pitfalls that can lead to misleading interpretations. To calculate the HFD and the H, we have extracted muscle synergies from normal and mechanically perturbed treadmill locomotion from the hindlimb of adult mice. Then, we used one set per condition (normal and perturbed walking) of the obtained time-dependent coefficients to create surrogate data with different fluctuations over the original mean signal. Our analysis shows that HFD and H are exceptionally sensitive to the presence or absence of perturbations to locomotion. However, both metrics suffer from variations in their value depending on the parameters used for calculations and the presence of quasi-periodic elements in the time series. We discuss those issues giving some simple suggestions to reduce the chance of misinterpreting the outcomes.New & NoteworthyDespite the lack of consensus on how to perform fractal analysis of physiological time series, many studies rely on this technique. Here, we shed light on the potential pitfalls of using the Higuchi’s fractal dimension and the Hurst exponent. We expose and suggest how to solve the drawbacks of such methods when applied to data from normal and perturbed locomotion by combining in vivo recordings and computational approaches.

scholarly journals PM10-PM2.5 time series and fractal analysis

2013 ◽  
Vol 8 (3) ◽  
pp. 234-240 ◽  
Keyword(s):  
Air Pollution ◽  
Time Series ◽  
Fractal Dimension ◽  
Health Effects ◽  
Fractal Analysis ◽  
Series Data ◽  
Data Set ◽  
Factors Affecting ◽  
Power Stations ◽  
Pm10 And Pm2.5

Several epidemiological studies have shown an association between particulate air pollution and health effects. Suspended particulates and more specifically the inhalable PM10 fraction appear to cause respiratory health effects and heart diseases. Furthermore, particulate pollution is of paramount importance in areas with open-pit mines and especially when it is combined with raw lignite transfer and combustion in power stations through the suspension of particles and stack emissions, respectively. The penetration of particles into respiratory track is a function of the size of the particles and thus, it is more likely for the finer PM2.5 fraction to reach the deepest of the lugs. The fast economic growth the last decades has resulted in an increase of the sources of pollution not only in large metropolitan areas but also in medium-sized urban areas like the city of Kozani, Greece. It is the most densely populated city in the area of West Macedonia affected by urban particulate matter originated from local and stationary sources, from regional and long-range transport, and from street dust resuspension. Kozani is located a few kilometers away from lignite power stations that contribute to about 70% of the total electrical energy produced in Greece. Dust emissions seem to be the most serious problem in the area, as the measured ambient concentrations of suspended particles are at high levels and exceed local and international standards. In this study PM10 and PM2.5 concentrations are presented. The measurements have been carried out, from April to December 2002, by the Lab of Atmospheric Pollution and Environmental Physics (LAPEP) of Technological Education Institute of West Macedonia in the commercial centre of the city of Kozani. The temporal variation of PM10 and PM2.5 concentrations was studied and allowed a further insight on the factors affecting the measured ambient particulate levels. PM2.5 – PM10 correlation and PM2.5/PM10 ratios were investigated and compared to those in the literature together with the factors affecting their diurnal variation. The pollution levels were also detected in process of the experimental time series data by fractal dimension. Generally, fractal analysis is able to detect the data set complexity by scaling empirical data using threshold values. These values define the levels of air pollution episodes. The method presented in this study, is the transformation of PM10 and PM2.5 concentrations into a set of points whose dimension was estimated by box counting. This technique has estimated the fractal dimension of both the time series by the relationship between data variance and time scale.

scholarly journals Fractal analysis of the ULF geomagnetic data obtained at Izu Peninsula, Japan in relation to the nearby earthquake swarm of June–August 2000

2003 ◽  
Vol 3 (3/4) ◽  
pp. 229-236 ◽  
Author(s):  
K. Gotoh ◽  
M. Hayakawa ◽  
N. Smirnova
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Active Region ◽  
Fractal Analysis ◽  
Flicker Noise ◽  
Earthquake Swarm ◽  
Fractal Dimensions ◽  
Izu Peninsula ◽  
Geomagnetic Data ◽  
Fractal Characteristics

Abstract. In our recent papers we applied fractal methods to extract the earthquake precursory signatures from scaling characteristics of the ULF geomagnetic data, obtained in a seismic active region of Guam Island during the large earthquake of 8 August 1993. We found specific dynamics of their fractal characteristics (spectral exponents and fractal dimensions) before the earthquake: appearance of the flicker-noise signatures and increase of the time series fractal dimension. Here we analyze ULF geomagnetic data obtained in a seismic active region of Izu Peninsula, Japan during a swarm of the strong nearby earthquakes of June–August 2000 and compare the results obtained in both regions. We apply the same methodology of data processing using the FFT procedure, Higuchi method and Burlaga-Klein approach to calculate the spectral exponents and fractal dimensions of the ULF time series. We found the common features and specific peculiarities in the behavior of fractal characteristics of the ULF time series before Izu and Guam earthquakes. As a common feature, we obtained the same increase of the ULF time series fractal dimension before the earthquakes, and as specific peculiarity – this increase appears to be sharp for Izu earthquake in comparison with gradual increase of the ULF time series fractal dimension for Guam earthquake. The results obtained in both regions are discussed on the basis of the SOC (self-organized criticality) concept taking into account the differences in the depths of the earthquake focuses. On the basis of the peculiarities revealed, we advance methodology for extraction of the earthquake precursory signatures. As an adjacent step, we suggest the combined analysis of the ULF time series in the parametric space polarization ratio – fractal dimension. We reason also upon the advantage of the multifractal approach with respect to the mono-fractal analysis for study of the earthquake preparation dynamics.

scholarly journals ADAPTED BOX-COUNTING METHOD FOR ASSESSMENT OF THE FRACTAL DIMENSION OF FINANCIAL TIME SERIES

2020 ◽  
pp. 185-218
Author(s):  
Robert Garafutdinov ◽  
◽  
Sofya Akhunyanova ◽  
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Computer Image ◽  
Financial Time Series ◽  
Counting Method ◽  
Financial Time ◽  
Box Counting ◽  
Modeling And Prediction ◽  
Box Counting Method

This paper continues research within the framework of the scientific direction in econophysics at the Department of Information Systems and Mathematical Methods in Economics of the faculty of Economics of PSU. Modeling and prediction of financial time series is quite a perspective area of research, because it allows participants of financial processes to reduce risks and make effective decisions. For example, we could research financial processes with the help of fractal analysis. In the article there is studied and worked out in detail one of the methods of fractal analysis of financial time series – the box-counting method for assessment of the fractal dimension. This method is often used in studies conducted by domestic authors, but the authors do not delve into the characteristics and problems of using the box-counting method for analysis of time series, that means that the answers to the interested questions have not yet been given. The main problem is that, as a rule, the analyzed object in the tasks of applying the box-counting method to time series is a computer image of the plot of series. In the article there is proposed the procedure of adaptation of the box-counting method for assessment of the fractal dimension of time series, the procedure does not require the formation of a computer image of the plot. In the article there is considered following difficulties developed from this adaptation: 1) high sensitivity of the resulting estimation of the dimension to the input parameters of the method (the ratio of the sides of the covered by cells plane with the plot; the used range of lengths of the side of the cell; the number of partitions of the plane into cells); 2) the non-obviousness of choosing the optimal values ​​of these parameters. In the article there are analyzed approaches to the selection of these parameters that were proposed by other authors, and there are determined the most suitable approaches for the adapted box-counting method. Also there are developed unique methods for determining the ratio of the sides of the plane with the plot. In the paper there is written the computer program that implements the developed method, and this program is tested on the generated data. The study obtained the following results. The fact of sensitivity of the adapted box-counting method to input parameters is confirmed, that indicates the high importance of the correct choice of these parameters. According to the study, there is found out inability of the proposed methods of automatic determination the ratio of the sides of the plane in relation to artificial time series. There are obtained the most precise (in a statistical sense) estimates of fractal dimension, those found by means of the adapted box-counting method, with the fixed ratio of the sides 1:1. According to comparing the adapted box-counting method and R/S analysis, there are obtained the most precise estimates by the second method (R/S analysis). Finally in the paper there are formulated the possible directions for further research: 1) comparison of the accuracy of various methods for assessment of the fractal dimension on series of different lengths; 2) comparison of the methods of fractal analysis and p-adic analysis for modeling and prediction of financial time series; 3) determination of the conditions of applicability of various methods; 4) approbation of the developed methods for determining of the ratio of the sides of the plane with the plot on real economic data.

scholarly journals Fractal analysis of muscle activity patterns during locomotion: pitfalls and how to avoid them

2020 ◽  
Vol 124 (4) ◽  
pp. 1083-1091 ◽  
Author(s):  
Alessandro Santuz ◽  
Turgay Akay
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Muscle Activity ◽  
Hurst Exponent ◽  
Activity Patterns ◽  
Computational Approaches ◽  
Physiological Time ◽  
Shed Light

Despite the lack of consensus on how to perform fractal analysis of physiological time series, many studies rely on this technique. Here, we shed light on the potential pitfalls of using the Higuchi’s fractal dimension and the Hurst exponent. We expose and suggest how to solve the drawbacks of such methods when applied to data from normal and perturbed locomotion by combining in vivo recordings and computational approaches.

A Characterization of Ultrasonic Power Spectrum by Fractal Analysis–Imaging by Fractal Dimension–

1990 ◽  
Vol 29 (S1) ◽  
pp. 243
Author(s):  
Tsuneo Kikuchi ◽  
Shogo Kiryu ◽  
Sojun Sato ◽  
Hajime Miura
Keyword(s):  
Fractal Dimension ◽  
Power Spectrum ◽  
Fractal Analysis ◽  
Ultrasonic Power

Heterogeneity of Cerebral Blood Flow: a Fractal Approach

2000 ◽  
Vol 39 (02) ◽  
pp. 37-42 ◽  
Author(s):  
P. Hartikainen ◽  
J. T. Kuikka
Keyword(s):  
Blood Flow ◽  
Cerebral Blood Flow ◽  
Fractal Dimension ◽  
Frontal Lobe ◽  
Fractal Analysis ◽  
Relative Dispersion ◽  
Emission Computed Tomography ◽  
Brain Blood Flow ◽  
Healthy Controls ◽  
Fractal Approach

Summary Aim: We demonstrate the heterogeneity of regional cerebral blood flow using a fractal approach and singlephoton emission computed tomography (SPECT). Method: Tc-99m-labelled ethylcysteine dimer was injected intravenously in 10 healthy controls and in 10 patients with dementia of frontal lobe type. The head was imaged with a gamma camera and transaxial, sagittal and coronal slices were reconstructed. Two hundred fifty-six symmetrical regions of interest (ROIs) were drawn onto each hemisphere of functioning brain matter. Fractal analysis was used to examine the spatial heterogeneity of blood flow as a function of the number of ROIs. Results: Relative dispersion (= coefficient of variation of the regional flows) was fractal-like in healthy subjects and could be characterized by a fractal dimension of 1.17 ± 0.05 (mean ± SD) for the left hemisphere and 1.15 ± 0.04 for the right hemisphere, respectively. The fractal dimension of 1.0 reflects completely homogeneous blood flow and 1.5 indicates a random blood flow distribution. Patients with dementia of frontal lobe type had a significantly lower fractal dimension of 1.04 ± 0.03 than in healthy controls. Conclusion: Within the limits of spatial resolution of SPECT, the heterogeneity of brain blood flow is well characterized by a fractal dimension. Fractal analysis may help brain scientists to assess age-, sex- and laterality-related anatomic and physiological changes of brain blood flow and possibly to improve precision of diagnostic information available for patient care.

Optimal Density Determination of Bouguer Anomaly Using Fractal Analysis (Case of study: Charak area,IRAN)

2005 ◽  
Vol 1 (1) ◽  
pp. 21-24
Author(s):  
Hamid Reza Samadi
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Geometry ◽  
Host Rock ◽  
Bouguer Anomaly ◽  
Research Area ◽  
Density Difference ◽  
Optimal Density

In exploration geophysics the main and initial aim is to determine density of under-research goals which have certain density difference with the host rock. Therefore, we state a method in this paper to determine the density of bouguer plate, the so-called variogram method based on fractal geometry. This method is based on minimizing surface roughness of bouguer anomaly. The fractal dimension of surface has been used as surface roughness of bouguer anomaly. Using this method, the optimal density of Charak area insouth of Hormozgan province can be determined which is 2/7 g/cfor the under-research area. This determined density has been used to correct and investigate its results about the isostasy of the studied area and results well-coincided with the geology of the area and dug exploratory holes in the text area

Sign in / Sign up

Export Citation Format

Share Document