Complexity, Coordination, and Health: Avoiding Pitfalls and Erroneous Interpretations in Fractal Analyses

Medicina ◽  
2011 ◽  
Vol 47 (7) ◽  
pp. 393 ◽  
Author(s):  
Vivien Marmelat ◽  
Didier Delignières
Keyword(s):  
Long Range ◽  
Fluctuation Analysis ◽  
Short Term ◽  
Long Range Correlations ◽  
Optimal Functioning ◽  
Fractal Analyses ◽  
Serial Correlations ◽  
Walking Velocity ◽  
Fractal Fluctuation ◽  
Detrended Fluctuation

Background and Objective. The analysis of fractal fluctuation has become very popular because of the close relationships between health, adaptability, and long-range correlations. 1/f noise is considered a “magical” threshold, characterizing optimal functioning, and a decrease or conversely and increase of serial correlations, with respect to 1/f noise, is supposed to sign a kind of disadaptation of the system. Empirical results, however, should be interpreted with caution. In experimental series, serial correlations often present a complex pattern, resulting from the combination of long-range and short-term correlated processes. We show, in the present paper, that an increase in serial correlations cannot be directly interpreted as an increase in long-range correlations. Material and Methods. Eleven participants performed four walking bouts following 4 individually determined velocities (slow, comfortable, high, and critical). Series of 512 stride intervals were collected under each condition. The strength of serial correlation was measured by the detrended fluctuation analysis. The effective presence of 1/f fluctuation was tested through ARFIMA modeling. Results. The strength of serial correlations tended to increase with walking velocity. However, the ARFIMA modeling showed that long-range correlations were significantly present only at slow and comfortable velocities. Conclusions. The strength of correlations, as measured by classical methods, cannot be considered as predictive of the genuine presence of long-range correlations. Sometimes systems can present the moderate levels of effective long-range correlations, whereas in others cases, series can present high correlation levels without being long-range correlated.

scholarly journals Scaling behaviour of the global tropopause

2009 ◽  
Vol 9 (2) ◽  
pp. 677-683 ◽  
Author(s):  
C. Varotsos ◽  
M. Efstathiou ◽  
C. Tzanis
Keyword(s):  
Long Range ◽  
Detrended Fluctuation Analysis ◽  
Sea Surface ◽  
Fluctuation Analysis ◽  
Tropopause Height ◽  
Time Intervals ◽  
Long Range Correlations ◽  
Scaling Behaviour ◽  
Detrended Fluctuation ◽  
Global Mean

Abstract. Detrended fluctuation analysis is applied to the time series of the global tropopause height derived from the 1980–2004 daily radiosonde data, in order to detect long-range correlations in its time evolution. Global tropopause height fluctuations in small time-intervals are found to be positively correlated to those in larger time intervals in a power-law fashion. The exponent of this dependence is larger in the tropics than in the middle and high latitudes in both hemispheres. Greater persistence is observed in the tropopause of the Northern than in the Southern Hemisphere. A plausible physical explanation of the fact that long-range correlations in tropopause variability decreases with increasing latitude is that the column ozone fluctuations (that are closely related with the tropopause ones) exhibit long range correlations, which are larger in tropics than in the middle and high latitudes at long time scales. This finding for the tropopause height variability should reduce the existing uncertainties in assessing the climatic characteristics. More specifically the reliably modelled values of a climatic variable (i.e. past and future simulations) must exhibit the same scaling behaviour with that possibly existing in the real observations of the variable under consideration. An effort has been made to this end by applying the detrended fluctuation analysis to the global mean monthly land and sea surface temperature anomalies during the period January 1850–August 2008. The result obtained supports the findings presented above, notably: the correlations between the fluctuations in the global mean monthly land and sea surface temperature display scaling behaviour which must characterizes any projection.

scholarly journals DETRENDED FLUCTUATION ANALYSIS OF AUTOREGRESSIVE PROCESSES

2007 ◽  
Vol 07 (03) ◽  
pp. L249-L255 ◽  
Author(s):  
VASILE V. MORARIU ◽  
LUIZA BUIMAGA-IARINCA ◽  
CĂLIN VAMOŞ ◽  
ŞTEFAN M. ŞOLTUZ
Keyword(s):  
Long Range ◽  
Detrended Fluctuation Analysis ◽  
Short Range ◽  
Interaction Constant ◽  
Fluctuation Analysis ◽  
Autoregressive Processes ◽  
Long Range Correlations ◽  
Correlation Exponent ◽  
The Relationship ◽  
Detrended Fluctuation

Autoregressive processes (AR) have typical short-range memory. Detrended Fluctuation Analysis (DFA) was basically designed to reveal long-range correlations in non stationary processes. However DFA can also be regarded as a suitable method to investigate both long-range and short-range correlations in non stationary and stationary systems. Applying DFA to AR processes can help understanding the non-uniform correlation structure of such processes. We systematically investigated a first order autoregressive model AR(1) by DFA and established the relationship between the interaction constant of AR(1) and the DFA correlation exponent. The higher the interaction constant the higher is the short-range correlation exponent. They are exponentially related. The investigation was extended to AR(2) processes. The presence of an interaction between distant terms with characteristic time constant in the series, in addition to a near by interaction will increase the correlation exponent and the range of correlation while the effect of a distant negative interaction will significantly decrease the range of interaction, only. This analysis demonstrate the possibility to identify an AR(1) model in an unknown DFA plot or to distinguish between AR(1) and AR(2) models.

scholarly journals IMPACT OF TANDEM REPEATS ON THE SCALING OF NUCLEOTIDE SEQUENCES

2006 ◽  
Vol 16 (10) ◽  
pp. 3103-3108
Author(s):  
RADHAKRISHNAN NAGARAJAN ◽  
MEENAKSHI UPRETI
Keyword(s):  
Long Range ◽  
Detrended Fluctuation Analysis ◽  
Tandem Repeats ◽  
Nucleotide Sequences ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Long Range Correlations ◽  
Reliable Estimation ◽  
Detrended Fluctuation

Techniques such as detrended fluctuation analysis (DFA) and its extensions have been widely used to determine the nature of scaling in nucleotide sequences. In this brief communication we show that tandem repeats which are ubiquitous in nucleotide sequences can prevent reliable estimation of possible long-range correlations. Therefore, it is important to investigate the presence of tandem repeats prior to scaling exponent estimation.

scholarly journals Fractal Analysis of Deep Ocean Current Speed Time Series

2017 ◽  
Vol 34 (4) ◽  
pp. 817-827 ◽  
Author(s):  
Laura Cabrera-Brito ◽  
German Rodriguez ◽  
Luis García-Weil ◽  
Mercedes Pacheco ◽  
Esther Perez ◽  
...  
Keyword(s):  
Time Series ◽  
Long Range ◽  
Detrended Fluctuation Analysis ◽  
Single Point ◽  
Deep Ocean ◽  
Current Speed ◽  
Ocean Current ◽  
Fluctuation Analysis ◽  
Long Range Correlations ◽  
Detrended Fluctuation

AbstractFractal 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.

scholarly journals MINIMIZING THE EFFECT OF SINUSOIDAL TRENDS IN DETRENDED FLUCTUATION ANALYSIS

2005 ◽  
Vol 15 (05) ◽  
pp. 1767-1773 ◽  
Author(s):  
RADHAKRISHNAN NAGARAJAN ◽  
RAJESH G. KAVASSERI
Keyword(s):  
Long Range ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Long Range Correlations ◽  
Smoothing Filter ◽  
Detrended Fluctuation

The detrended fluctuation analysis (DFA) [Peng et al., 1994] and its extensions (MF-DFA) [Kantelhardt et al., 2002] have been used extensively to determine possible long-range correlations in self-affine signals. While the DFA has been claimed to be a superior technique, recent reports have indicated its susceptibility to trends in the data. In this report, a smoothing filter is proposed to minimize the effect of sinusoidal trends and distortion in the log–log plots obtained by DFA and MF-DFA techniques.

THE ORTHOGONAL V-SYSTEM DETRENDED FLUCTUATION ANALYSIS

2011 ◽  
Vol 10 (02) ◽  
pp. 189-206 ◽  
Author(s):  
AIJING LIN ◽  
PENGJIAN SHANG ◽  
HUI MA
Keyword(s):  
Long Range ◽  
Power Law ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Smoothing Algorithm ◽  
Scaling Exponents ◽  
Long Range Correlations ◽  
Piecewise Function ◽  
Robust Techniques ◽  
Detrended Fluctuation

The Detrended Fluctuation Analysis (DFA) and its extensions (MF-DFA) have been proposed as robust techniques to determine possible long-range correlations in self-affine signals. However, many studies have reported the susceptibility of DFA to trends which give rise to spurious crossovers and prevent reliable estimations of the scaling exponents. Lately, several modifications of the DFA method have been reported with many different techniques for eliminating the monotonous and periodic trends. In this study, a smoothing algorithm based on the Orthogonal V-system (OVS) is proposed to minimize the effect of power-law trends, periodic trends, assembled trends and piecewise function trends. The effectiveness of the new method is demonstrated on monofractal data and multifractal data corrupted with different trends.

Tracking Performance Changes With Running-Stride Variability When Athletes Are Functionally Overreached

2017 ◽  
Vol 12 (3) ◽  
pp. 357-363 ◽  
Author(s):  
Joel T. Fuller ◽  
Clint R. Bellenger ◽  
Dominic Thewlis ◽  
John Arnold ◽  
Rebecca L. Thomson ◽  
...  
Keyword(s):  
Long Range ◽  
Prolonged Exposure ◽  
Time Trial ◽  
Training Load ◽  
Fluctuation Analysis ◽  
Long Range Correlations ◽  
Stride Interval ◽  
Fixed Order ◽  
Detrended Fluctuation ◽  
Heavy Training

Purpose:Stride-to-stride fluctuations in running-stride interval display long-range correlations that break down in the presence of fatigue accumulated during an exhaustive run. The purpose of the study was to investigate whether long-range correlations in running-stride interval were reduced by fatigue accumulated during prolonged exposure to a high training load (functional overreaching) and were associated with decrements in performance caused by functional overreaching.Methods:Ten trained male runners completed 7 d of light training (LT7), 14 d of heavy training (HT14) designed to induce a state of functional overreaching, and 10 d of light training (LT10) in a fixed order. Running-stride intervals and 5-km time-trial (5TT) performance were assessed after each training phase. The strength of long-range correlations in running-stride interval was assessed at 3 speeds (8, 10.5, and 13 km/h) using detrended fluctuation analysis.Results:Relative to performance post-LT7, time to complete the 5TT was increased after HT14 (+18 s; P < .05) and decreased after LT10 (–20 s; P = .03), but stride-interval long-range correlations remained unchanged at HT14 and LT10 (P > .50). Changes in stride-interval long-range correlations measured at a 10.5-km/h running speed were negatively associated with changes in 5TT performance (r –.46; P = .03).Conclusions:Runners who were most affected by the prolonged exposure to high training load (as evidenced by greater reductions in 5TT performance) experienced the greatest reductions in stride-interval long-range correlations. Measurement of stride-interval long-range correlations may be useful for monitoring the effect of high training loads on athlete performance.

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