Detrended Fluctuation Analysis of Arrhythmia: Scaling Exponent as an Index of Heart Wellness

2011 ◽  
Author(s):  
Toru Yazawa ◽  
Albert M. Hutapea ◽  
Tomoo Katsuyama ◽  
Yukio Shimoda
Keyword(s):  
Time Series ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
A Value ◽  
Healthy State ◽  
Interval Time Series ◽  
Detrended Fluctuation ◽  
Analytical Technology ◽  
Heart Condition

Well-established technologies to analyze biological signals including rhythmic heartbeat are available and accessible to scholars. However, stronger empirical evidence is required to justify the use of these technologies as practical tools in the field of biomedicine. Here we conducted analyses of heartbeat interval time series using an analytical technology developed across three decades—detrended fluctuation analysis (DFA)—to verify the power-law/scaling characteristics of signals that fluctuate in a regular, irregular, or erratic manner. We believe that DFA is a useful tool because it can quantify the heart condition by a scaling exponent, with a value of one (1) set as the default for a healthy state. This baseline value can be compared to a clinical thermometer, where the baseline is 37 °C for a physiologically healthy condition. Our study aimed to ascertain and confirm the utility of DFA in evaluating heart wellness, specifically in the context of studying arrhythmic heartbeat. We present case studies to confirm that DFA is a beneficial tool that quantifies the scaling exponent of a heart’s condition as “nonstationarily” beating and dynamically controlled. From an engineering perspective, we show that the heart condition can be classified into two typical categories: a healthy rhythm with a scaling exponent of one (1.0), and arrhythmia with a lower scaling exponent (0.7 or less).

scholarly journals DETRENDED FLUCTUATION ANALYSIS OF THE TCP-RED ALGORITHM

2009 ◽  
Vol 19 (12) ◽  
pp. 4237-4245 ◽  
Author(s):  
XI CHEN ◽  
SIU-CHUNG WONG ◽  
CHI K. TSE ◽  
LJILJANA TRAJKOVIĆ
Keyword(s):  
Time Series ◽  
Long Range ◽  
Power Law ◽  
Detrended Fluctuation Analysis ◽  
Time Series Data ◽  
Analytical Models ◽  
Series Data ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Detrended Fluctuation

It has been observed that Internet gateways employing Transport Control Protocol (TCP) and the Random Early Detection (RED) control algorithm may exhibit instability and oscillatory behavior. Most control methods proposed in the past have been based on analytical models that rely on statistical measurements of network parameters. In this paper, we apply the detrended fluctuation analysis (DFA) method to analyze stability of the TCP-RED system. The DFA is used to analyze time-series data and generate power-law scaling exponents, which indicate the long-range correlations of the time series. We quantify the stability of the TCP-RED system by examining the variation of the DFA power-law scaling exponent when the system parameters are varied. We also study the long-range power-law correlations of TCP window periods.

SCALING ANALYSIS OF THE A-PHASE DYNAMICS DURING SLEEP

Fractals ◽  
2020 ◽  
Vol 28 (02) ◽  
pp. 2050050
Author(s):  
V. E. ARCE-GUEVARA ◽  
M. O. MENDEZ ◽  
J. S. MURGUÍA ◽  
A. ALBA ◽  
H. GONZÁLEZ-AGUILAR ◽  
...  
Keyword(s):  
Binary Sequence ◽  
Fluctuation Analysis ◽  
Scaling Analysis ◽  
Scaling Exponent ◽  
Sleep State ◽  
Phase Dynamics ◽  
A Value ◽  
Sleep Condition ◽  
Detrended Fluctuation

In this work, the scaling behavior of the sleep process is evaluated by using detrended fluctuation analysis based on wavelets. The analysis is carried out from arrivals of short and recurrent cortical events called A-phases, which in turn build up the Cyclic Alternating Pattern phenomenon, and are classified in three types: A1, A2 and A3. In this study, 61 sleep recordings corresponding to healthy, nocturnal frontal lobe epilepsy patients and sleep-state misperception subjects, were analyzed. From the A-phase annotations, the onsets were extracted and a binary sequence with one second resolution was generated. An item in the sequence has a value of one if an A-phase onset occurs in the corresponding window, and a value of zero otherwise. In addition, we consider other different temporal resolutions from 2[Formula: see text]s to 256[Formula: see text]s. Furthermore, the same analysis was carried out for sequences obtained from the different types of A-phases and their combinations. The results of the numerical analysis showed a relationship between the time resolutions and the scaling exponents; specifically, for higher time resolutions a white noise behavior is observed, whereas for lower time resolutions a behavior towards to [Formula: see text]-noise is exhibited. Statistical differences among groups were observed by applying various wavelet functions from the Daubechies family and choosing the appropriate sequence of A-phase onsets. This scaling analysis allows the characterization of the free-scale dynamic of the sleep process that is specific for each sleep condition. The scaling exponent could be useful as a diagnosis parameter in clinics when sleep macrostructure does not offer enough information.

scholarly journals AUTOMATICALLY DETECTING "SIGNIFICANT EVENTS" ON SenseCam

2013 ◽  
Vol 11 (06) ◽  
pp. 1350050 ◽  
Author(s):  
NA LI ◽  
MARTIN CRANE ◽  
HEATHER J. RUSKIN
Keyword(s):  
Time Series ◽  
Detrended Fluctuation Analysis ◽  
Time Windows ◽  
Fluctuation Analysis ◽  
Discrete Wavelet ◽  
Dominant Eigenvalue ◽  
Multiple Time ◽  
Correlation Relationship ◽  
Significant Events ◽  
Detrended Fluctuation

SenseCam is an effective memory-aid device that can automatically record images and other data from the wearer's whole day. The main issue is that, while SenseCam produces a sizeable collection of images over the time period, the vast quantity of captured data contains a large percentage of routine events, which are of little interest to review. In this article, the aim is to detect "Significant Events" for the wearers. We use several time series analysis methods such as Detrended Fluctuation Analysis (DFA), Eigenvalue dynamics and Wavelet Correlations to analyse the multiple time series generated by the SenseCam. We show that Detrended Fluctuation Analysis exposes a strong long-range correlation relationship in SenseCam collections. Maximum Overlap Discrete Wavelet Transform (MODWT) was used to calculate equal-time Correlation Matrices over different time scales and then explore the granularity of the largest eigenvalue and changes of the ratio of the sub-dominant eigenvalue spectrum dynamics over sliding time windows. By examination of the eigenspectrum, we show that these approaches enable detection of major events in the time SenseCam recording, with MODWT also providing useful insight on details of major events. We suggest that some wavelet scales (e.g., 8 minutes–16 minutes) have the potential to identify distinct events or activities.

scholarly journals Investigating Long-Range Dependence of Emerging Asian Stock Markets Using Multifractal Detrended Fluctuation Analysis

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1157
Author(s):  
Faheem Aslam ◽  
Saima Latif ◽  
Paulo Ferreira
Keyword(s):  
Time Series ◽  
Long Range ◽  
Stock Markets ◽  
Detrended Fluctuation Analysis ◽  
Financial Time Series ◽  
Long Range Dependence ◽  
Fluctuation Analysis ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Financial Time ◽  
Detrended Fluctuation

The use of multifractal approaches has been growing because of the capacity of these tools to analyze complex properties and possible nonlinear structures such as those in financial time series. This paper analyzes the presence of long-range dependence and multifractal parameters in the stock indices of nine MSCI emerging Asian economies. Multifractal Detrended Fluctuation Analysis (MFDFA) is used, with prior application of the Seasonal and Trend Decomposition using the Loess (STL) method for more reliable results, as STL separates different components of the time series and removes seasonal oscillations. We find a varying degree of multifractality in all the markets considered, implying that they exhibit long-range correlations, which could be related to verification of the fractal market hypothesis. The evidence of multifractality reveals symmetry in the variation trends of the multifractal spectrum parameters of financial time series, which could be useful to develop portfolio management. Based on the degree of multifractality, the Chinese and South Korean markets exhibit the least long-range dependence, followed by Pakistan, Indonesia, and Thailand. On the contrary, the Indian and Malaysian stock markets are found to have the highest level of dependence. This evidence could be related to possible market inefficiencies, implying the possibility of institutional investors using active trading strategies in order to make their portfolios more profitable.

(MULTI)FRACTALITY OF PHYSIOLOGICAL TIME-SERIES

2006 ◽  
Vol 16 (07) ◽  
pp. 2103-2110 ◽  
Author(s):  
ANDREA KNEŽEVIĆ ◽  
MLADEN MARTINIS
Keyword(s):  
Physical Activity ◽  
Time Series ◽  
Angina Pectoris ◽  
Stable Angina ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Stable Angina Pectoris ◽  
Nonlinear Methods ◽  
Rr Interval ◽  
Detrended Fluctuation

This paper contains the application of fractal concept in analyzing heartbeat (RR interval) fluctuations measured under controlled physical activity for subjects with stable angina pectoris (SAP). Results that illustrate the separation ability of the nonlinear methods, such as the Hurst R/S method, the detrended fluctuation analysis, DFA, and the method of G-moments, in distinguishing healthy from SAP subjects in scaling parameter space are presented.

The scaling of time series size towards detrended fluctuation analysis

2016 ◽  
Vol 27 (11) ◽  
pp. 1650138
Author(s):  
Xiaolei Gao ◽  
Liwei Ren ◽  
Pengjian Shang ◽  
Guochen Feng
Keyword(s):  
Time Series ◽  
Stock Returns ◽  
Detrended Fluctuation Analysis ◽  
Finite Size ◽  
Finite Size Effect ◽  
Fluctuation Analysis ◽  
Exponential Relationship ◽  
Significant Information ◽  
Sequence Segmentation ◽  
Detrended Fluctuation

In this paper, we introduce a modification of detrended fluctuation analysis (DFA), called multivariate DFA (MNDFA) method, based on the scaling of time series size [Formula: see text]. In traditional DFA method, we obtained the influence of the sequence segmentation interval [Formula: see text], and it inspires us to propose a new model MNDFA to discuss the scaling of time series size towards DFA. The effectiveness of the procedure is verified by numerical experiments with both artificial and stock returns series. Results show that the proposed MNDFA method contains more significant information of series compared to traditional DFA method. The scaling of time series size has an influence on the auto-correlation (AC) in time series. For certain series, we obtain an exponential relationship, and also calculate the slope through the fitting function. Our analysis and finite-size effect test demonstrate that an appropriate choice of the time series size can avoid unnecessary influences, and also make the testing results more accurate.

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