Reading multifractal spectra: Aging by multifractal analysis of heart rate

Makowiec, Danuta; Rynkiewicz, Andrzej; Gałąska, Rafał; Wdowczyk-Szulc, Joanna; Żarczyńska-Buchowiecka, Marta

doi:10.1209/0295-5075/94/68005

Cited by 29 publications

(33 citation statements)

References 44 publications

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“…Following that, Kantelhardt et al (2002) extended DFA into multifractal detrended fluctuation analysis (MFDFA) which enables the multifractal behavior of data to be detected, and by studying their shuffled and surrogate time series and comparing them with the results of the original series, the sources of multifractality can be investigated (Jafari et al 2007; Kimiagar et al 2009;Lim et al 2007;Niu et al 2008;Pedram and Jafari 2008;Telesca et al 2004). MFDFA has been used to study time series in geophysics (Kantelhardt et al 2003;Kavasseri and Nagarajan 2005;Koscielny-Bunde et al 2006), physiology (Dutta 2010;Makowiec et al 2006Makowiec et al , 2011, financial markets (Oswiecimka et al 2005;Yuan et al 2009), and the exchange rates of currencies (Norouzzadeh and Rahmani 2006a, b;Oh et al 2012;Wang et al 2011a, b). Multifractals describe the dynamic characteristics of systems more carefully and comprehensively, and characterize their properties both locally and globally.…”

Section: Introductionmentioning

confidence: 99%

Multifractal analysis of the drought area in seven large regions of China from 1961 to 2012

Hou

Feng

Yan

et al. 2017

Meteorol Atmos Phys

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Based on a monthly drought index, the Standardized Precipitation Index (SPI), we investigate the multifractality of monthly drought areas in seven major regions in China from 1961 to 2012 using multifractal detrended fluctuation analysis. The results show that multifractality is evident in the monthly time series for all seven regions, but its strength varies between areas. From the numerical results, we further examine the stationarity and persistence of the time series in the seven drought areas. The characteristics of the variance of big and small fluctuations are also analyzed. The characteristics of multifractal spectra are used to distinguish the features of the singularity of all the data, as well as the large and small fluctuations and the spread of the changes of fractal patterns, and so on, in the monthly drought area time series for the different regions. Finally, we investigate the possible source(s) of multifractality in the drought series by random shuffling as well as surrogating the original series for each region.

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Section: Introductionmentioning

confidence: 99%

Multifractal analysis of the drought area in seven large regions of China from 1961 to 2012

Hou

Feng

Yan

et al. 2017

Meteorol Atmos Phys

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“…Signals with RR-intervals derived from long-term ECG recordings have been widely used in assessing ANS responses during normal activities in health and disease [16,[18][19][20][21][22][23][24][25][26][27]. The reasons for the observed variations are far from being completely understood [28].…”

Section: Introductionmentioning

confidence: 99%

Entropic Measures of Complexity of Short-Term Dynamics of Nocturnal Heartbeats in an Aging Population

Makowiec

Kaczkowska

Wejer

et al. 2015

Entropy

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Two entropy-based approaches are investigated to study patterns describing differences in time intervals between consecutive heartbeats. The first method explores matrices arising from networks of transitions constructed following events represented by a time series. The second method considers distributions of ordinal patterns of length three, whereby patterns with repeated values are counted as different patterns. Both methods provide estimators of dynamical aspects of short-term heartbeat signals obtained from nocturnal Holter electrocardiogram (ECG) recordings of healthy people of different ages and genders. The deceleration capacity, arising from the adjacency matrix of the network, and the entropy rate, resulting from the transition matrix of the network, are also calculated, and both significantly decay with aging. As people age, the permutation entropy grows, due to the increase in patterns with repeated values. All of these estimators describe in a consistent way changes in the beat-to-beat heart period dynamics caused by aging. An overall slowing Entropy 2015, 17 1254 down of heart period changes is observed, and an increase of permutation entropy results from the progressive increase of patterns with repeated values. This result points to the sympathetic drive becoming dominant in cardiac regulation of nocturnal heart rate with age.

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“…Then, it measures the degree of the series multifractality. If a spectrum has a nonsymmetric shape with one tail larger than the other one, then the larger tail is ignored and the width is estimated as the shorter tail doubled (Makoview and Fuli nski 2010). For q .…”

Section: Discussionmentioning

confidence: 99%

“…For q . 0 the spectrum will have a long left tail when the time series has a multifractal behavior insensitive to local fluctuations with small magnitudes; on the other hand, for q , 0, the spectrum will have a long right tail when the time series has a multifractal behavior insensitive to local fluctuations with large magnitudes (Makoview et al 2011). Generally, the concept of generalized dimension D(a) corresponds to the scaling exponent for the qth moment of the measure.…”

Section: Discussionmentioning

confidence: 99%

Fractal Analysis of Deep Ocean Current Speed Time Series

Cabrera-Brito

Rodrı́guez

García-Weil

et al. 2017

Journal of Atmospheric and Oceanic Technology

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Fractal properties of deep ocean current speed time series, measured at a single-point mooring on the Madeira Abyssal Plain at 1000-and 3000-m depth, are explored over the range between one week and 5 years, by using the detrended fluctuation analysis and multifractal detrended fluctuation analysis methodologies. The detrended fluctuation analysis reveals the existence of two subranges with different scaling behaviors. Long-range temporal correlations following a power law are found in the time-scale range between approximately 50 days and 5 years, while a Brownian motion-type behavior is observed for shorter time scales. The multifractal analysis approach underlines a multifractal structure whose intensity decreases with depth. The analysis of the shuffled and surrogate versions of the original time series shows that multifractality is mainly due to long-range correlations, although there is a weak nonlinear contribution at 1000-m depth, which is confirmed by the detrended fluctuation analysis of volatility time series.

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Reading multifractal spectra: Aging by multifractal analysis of heart rate

Cited by 29 publications

References 44 publications

Multifractal analysis of the drought area in seven large regions of China from 1961 to 2012

Multifractal analysis of the drought area in seven large regions of China from 1961 to 2012

Entropic Measures of Complexity of Short-Term Dynamics of Nocturnal Heartbeats in an Aging Population

Fractal Analysis of Deep Ocean Current Speed Time Series

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