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Scale-invariant behaviors have been found in the patterns of written text in phonetic languages, such as in word-length series and word-frequency series. In this study, we examined whether the scale-invariant behaviors exist in the sequential characters of Four Great Chinese Novels. In particular, one Chinese character is featured by its length (the number of its strokes), its frequency (the number of its appearance in a novel) and the number of its interpretations in a dictionary. Then, we obtained character-length series, character-frequency series and interpretation-number series for each novel. For each series of each novel, based on the method of Detrended Fluctuation Analysis, we observed that the scale-invariant behavior, which is characterized by a scaling exponent larger than 0.5, exists at scales larger than a crossover, which is equal to the average paragraph-length, i.e. around 300 characters. Moreover, these scaling exponents are positively correlated between different types of series. Typically, the correlation of scaling exponents is largest between the character-length series and the interpretation-number series. Our findings shed light on the temporal organization of Chinese written texts, and the correlation among the character lengths, the character frequencies and the interpretation numbers. [ABSTRACT FROM AUTHOR]

Obstructive sleep apnea (OSA) is a common disorder which can cause periodic fluctuations in heart rate. To diagnose sleep apnea, some studies analyze electrocardiogram (ECG) signals by adopting chaos-based analysis. This research is going to specifically focus on whether it is possible to use chaos-based analysis of heart rate variability (HRV) signals rather than using chaotic analysis of ECG signals to diagnose OSA. While conventional studies mostly use chaos-based analysis of ECG signals to detect OSA, here, we apply correlation dimension (CD) as a chaotic index to analyze HRV data in OSA patients. For this purpose, 17 patients with OSA and 9 healthy individuals referred to a sleep clinic in Isfahan/Iran are studied, and their HRV time series were extracted from 1-h ECG signals recorded overnight. The preliminary step to calculate CD is phase-space reconstruction of the system based on HRV time series. Corresponding parameters, including embedding dimension and lag time, are estimated optimally using enhanced related methods, and then CD is calculated using Grassberger–Procaccia algorithm. Moreover, to evaluate our results, detrended fluctuation analysis (DFA), one of the well-known nonlinear methods in HRV analysis to detect OSA, is also applied to our data and the result is compared with those obtained from CD analysis of HRV. CD index with P < 0.005 indicates a significant difference in nonlinear dynamics of HRV signals detected from OSA patients and healthy individuals. [ABSTRACT FROM AUTHOR]

We discuss the use of fractal analysis of geophysical big data as a precursory method for the estimation of current seismic hazard. We begin by analyzing GPS time series of land surface displacements recorded in various regions of the planet exhibiting different degrees of seismic activity. We show how the quantitative measure of chaoticity based on a modified detrended fluctuation analysis (DFA) method can be used to distinguish critical and noncritical regimes of evolution of the Earth's crust. Having established the reference values for the measure of chaoticity, we then choose California as the case study region and apply modified DFA to over 1200 time series for determining local areas currently exposed to higher seismic hazard. We comprehensively analyze the results obtained and compare them with those produced by conventional risk assessment methods. We demonstrate consistency of our results and yet discover that the suggested approach allows us to quantify two qualitatively different mechanisms involved in the growth of seismic hazards. We propose a hypothesis which relates these mechanisms to the known mechanisms of earthquake generation that evince a growth of collective behavior in the Earth's crust on the eve of an earthquake. In order to verify the hypothesis, we analyze the same GPS data by an independent statistical method, canonical coherence analysis (CCA), which permits us to quantify the degree of synchronized behavior of constituents of the Earth's crust. The CCA method confirms our previously obtained estimates, thus supporting fractal analysis of GPS time series as a suitable precursory method for current seismic hazard assessment. [ABSTRACT FROM AUTHOR]

The purpose of this study is to understand the characteristics of the spatial distribution of forest fire occurrences with the local indicators of temporal burstiness in Korea. Forest fire damage data were produced in the form of areas by combining the forest fire damage ledger information with VIIRS-based forest fire occurrence data. Then, detrended fluctuation analysis and the local indicator of temporal burstiness were applied. In the results, the forest fire occurrence follows a self-organized criticality mechanism, and the temporal irregularities of fire occurrences exist. When the forest fire occurrence time series in Gyeonggi-do Province, which had the highest value of the local indicator of temporal burstiness, was checked, it was found that the frequency of forest fires was increasing at intervals of about 10 years. In addition, when the frequencies of forest fires and the spatial distribution of the local indicators of forest fire occurrences were compared, it was found that there were spatial differences in the occurrence of forest fires. This study is meaningful in that it analyzed the time series characteristics of the distribution of forest fires in Korea to understand that forest fire occurrences have long-term temporal correlations and identified areas where the temporal irregularities of forest fire occurrences are remarkable with the local indicators of temporal burstiness.

Detrended Fluctuation Analysis (DFA) has become a standard method to quantify the correlations and scaling properties of real-world complex time series. For a given scale ℓ of observation, DFA provides the function F(ℓ), which quantifies the fluctuations of the time series around the local trend, which is substracted (detrended). If the time series exhibits scaling properties, then F(ℓ)∼ℓα asymptotically, and the scaling exponent α is typically estimated as the slope of a linear fitting in the logF(ℓ) vs. log(ℓ) plot. In this way, α measures the strength of the correlations and characterizes the underlying dynamical system. However, in many cases, and especially in a physiological time series, the scaling behavior is different at short and long scales, resulting in logF(ℓ) vs. log(ℓ) plots with two different slopes, α1 at short scales and α2 at large scales of observation. These two exponents are usually associated with the existence of different mechanisms that work at distinct time scales acting on the underlying dynamical system. Here, however, and since the power-law behavior of F(ℓ) is asymptotic, we question the use of α1 to characterize the correlations at short scales. To this end, we show first that, even for artificial time series with perfect scaling, i.e., with a single exponent α valid for all scales, DFA provides an α1 value that systematically overestimates the true exponent α. In addition, second, when artificial time series with two different scaling exponents at short and large scales are considered, the α1 value provided by DFA not only can severely underestimate or overestimate the true short-scale exponent, but also depends on the value of the large scale exponent. This behavior should prevent the use of α1 to describe the scaling properties at short scales: if DFA is used in two time series with the same scaling behavior at short scales but very different scaling properties at large scales, very different values of α1 will be obtained, although the short scale properties are identical. These artifacts may lead to wrong interpretations when analyzing real-world time series: on the one hand, for time series with truly perfect scaling, the spurious value of α1 could lead to wrongly thinking that there exists some specific mechanism acting only at short time scales in the dynamical system. On the other hand, for time series with true different scaling at short and large scales, the incorrect α1 value would not characterize properly the short scale behavior of the dynamical system.

The lymphatic system of the brain meninges and head plays a crucial role in the clearance of amyloid-β protein (Aβ), a peptide thought to be pathogenic in Alzheimer’s disease (AD), from the brain. The development of methods to modulate lymphatic clearance of Aβ from the brain coild be a revolutionary step in the therapy of AD. The opening of the blood–brain barrier (OBBB) by focused ultrasound is considered as a possible tool for stimulation of clearance of Aβ from the brain of humans and animals. Here, we propose an alternative method of noninvasive music-induced OBBB that is accompanied by the activation of clearance of fluorescent Aβ (Fαβ) from the mouse brain. Using confocal imaging, fluorescence microscopy, and magnetic resonance tomography, we clearly demonstrate that OBBB by music stimulates the movement of Fαβ and Omniscan in the cerebrospinal fluid and lymphatic clearance of Fαβ from the brain. We propose the extended detrended fluctuation analysis (EDFA) as a promising method for the identification of OBBB markers in the electroencephalographic (EEG) patterns. These pilot results suggest that music-induced OBBB and the EDFA analysis of EEG can be a noninvasive, low-cost, labeling-free, clinical perspective and completely new approach for the treatment and monitoring of AD.

Brain electrical activity recorded as electroencephalogram data provides relevant information that can contribute to a better understanding of pathologies and human behaviour. This study explores extant electroencephalogram (EEG) signals in search of patterns that could differentiate subjects undertaking mental tasks and reveals insights on said data. We estimated the power spectral density of the signals and found that the subjects showed stronger gamma brain waves during activity while presenting alpha waves at rest. We also found that subjects who performed better in those tasks seemed to present less power density in high-frequency ranges, which could imply decreased brain activity during tasks. In a time-domain analysis, we used Hall–Wood and Robust–Genton estimators along with the Hurst exponent by means of a detrented fluctuation analysis and found that the first two fractal measures are capable of better differentiating signals between the rest and activity datasets. The statistical results indicated that the brain region corresponding to Fp channels might be more suitable for analysing EEG data from patients conducting arithmetic tasks. In summary, both frequency- and time-based methods employed in the study provided useful insights and should be preferably used together in EEG analysis.

In this paper, we have modified the Detrended Fluctuation Analysis (DFA) using the ternary Cantor set. We propose a modification of the DFA algorithm, Cantor DFA (CDFA), which uses the Cantor set theory of base 3 as a scale for segment sizes in the DFA algorithm. An investigation of the phenomena generated from the proof using real-world time series based on the theory of the Cantor set is also conducted. This new approach helps reduce the overestimation problem of the Hurst exponent of DFA by comparing it with its inverse relationship with α of the Truncated Lévy Flight (TLF). CDFA is also able to correctly predict the memory behavior of time series.

MODIS-NDVI data from 2002 to 2014 were analysed to evaluate the effect of fire on vegetation in a test site located in Daxing'anling region (Inner Mongolia and Heilongjiang Province). Fire-affected and fire-unaffected areas were processed using two statistical approaches: detrended fluctuation analysis (DFA) and Fisher–Shannon (FS) method. The DFA allows the detection of scaling behaviour in nonstationary signals, whereas the FS method permits to identify the organization/order structure in complex signals. Our findings show that the results obtained by jointly using the two methods are consistent, enabling the characterization and discrimination between the fire-affected and fire-unaffected areas. In particular, among the investigated indices, the mean value of Fisher information measure (FIM) represents the most significant in discriminating between burned and unburned sites; its mean value for burned sites is about 2.5 that is significantly larger than that obtained for unburned sites (∼1.3). FIM is also characterized by the larger effectiveness in discriminating the two classes of sites on the base of its receiver operating characteristic based performance. The scaling exponents estimated by means of the DFA of the fire-affected pixels are averagely higher than those of the fire-unaffected ones, which, furthermore, are characterized by lower organization and higher disorder degree. Both of the two methods would contribute to identify the impact of fires on vegetation.

Non-linear analysis of electrograms (EGM) has been proposed as a tool to detect critical conduction sites (e.g., rotors vortex, multiple wavefronts) in atrial fibrillation (AF). Likewise, studies have shown that multifractal analysis is useful to detect critical activity in EGM signals. However, the multifractal spectrum does not consider the temporal information. There is a new mathematical formalism to overcome this limitation: the timesingularity multifractal spectrum distribution (TS-MFSD), which involves the time variation of the spectrum. In this manuscript, we describe the methodology to compute the TS-MFSD from EGM signals. Moreover, we propose a methodology to extract features from time-singularity spectrum and from singularity energy spectrum (SES). We tested the features in an EGM database labeled by experts as: non-fragmented, discrete fragmented potentials, disorganized activity, and continuous activity. We tested the area under the receiver operating characteristic (ROC) curve. The proposed features achieve an area under the ROC curve of 95.17% when detecting signals with continuous activity. These results outperform those reported using multifractal analysis. To our knowledge, this is the first work that report the use of TS-MFSD in biomedical signals and our findings suggest that time-singularity has the potential to be used in the study of non-stationary behavior of EGM signals in AF.

IntroductionMany physiological signals yield fractal characteristics, i.e., finer details at higher magnifications resemble details of the whole. Evidence has been accumulating that such fractal scaling is basically a consequence of interaction-dominant feedback mechanisms that cooperatively generate those signals. Neurodegenerative diseases provide a natural framework to evaluate this paradigm when this cooperative function declines. However, methodological issues need to be cautiously taken into account in order to be able to provide reliable as well as valid interpretations of such signal analyses.MethodsTwo conceptually different fractal analyses, i.e., detrended fluctuation analysis (DFA) and analysis of cumulative distributions of durations (CDDs), are applied to actigraphy data of 36 geriatric in-patients diagnosed with dementia. The impact of the used time resolution for data acquisition on the assessed fractal outcome parameters is particularly investigated. Moreover, associations between these parameters and scores from the Mini-Mental-State-Examination and circadian activity parameters are explored.ResultsBoth analyses yield significant deviations from (mono-)fractal scaling over the entire considered time range. DFA provides robust measures for the observed break-down of fractal scaling. In contrast, analysis of CDDs results in measures which highly fluctuate with respect to the time resolution of the assessed data which affects also further derived quantities such as scaling exponents or associations with other (clinically relevant) assessed parameters.DiscussionTo scrutinize actigraphic signal characteristics and especially their (deviations from) fractal scaling may be a useful tool for aiding diagnosis, characterization, and monitoring of dementia. However, results may, besides contextual aspects, also substantially depend on specific methodological choices. In order to arrive at both reliable and valid interpretations, these complications need to be carefully elaborated in future research.

In the study of human cognitive activity using electroencephalogram (EEG), the brain dynamics parameters and characteristics play a crucial role. They allow to investigate the changes in functionality depending on the environment and task performance process, and also to access the intensity of the brain activity in various locations of the cortex and its dependencies. Usually, the dynamics of activation of different brain areas during the cognitive tasks are being studied by spectral analysis based on power spectral density (PSD) estimation, and coherence analysis, which are de facto standard tools in quantitative characterization of brain activity. PSD and coherence reflect the strength of oscillations and similarity of the emergence of these oscillations in the brain, respectively, while the concept of stability of brain activity over time is not well defined and less formalized. We propose to employ the detrended fluctuation analysis (DFA) as a measure of the EEG persistence over time, and use the DFA scaling exponent as its quantitative characteristics. We applied DFA to the study of the changes in activation in brain dynamics during mental calculations and united it with PSD and coherence estimation. In the experiment, EEGs during resting state and mental serial subtraction from 36 subjects were recorded and analyzed in four frequency ranges: θ1 (4.1–5.8 Hz), θ2 (5.9–7.4 Hz), β1 (13–19.9 Hz), and β2 (20–25 Hz). PSD maps to access the intensity of cortex activation and coherence to quantify the connections between different brain areas were calculated, the distribution of DFA scaling exponent over the head surface was exploited to measure the time characteristics of the dynamics of brain activity. Obtained arrangements of DFA scaling exponent suggest that normal functioning of the brain is characterized by long-term temporal correlations in the cortex. Topographical distribution of the DFA scaling exponent was comparable for θ and β frequency bands, demonstrating the largest values of DFA scaling exponent during cognitive activation. The study shows that the long-term temporal correlations evaluated by DFA can be of great interest for diagnosis of the variety of brain dysfunctions of different etiology in the future.

AimMeasurements of Non-linear dynamics of heart rate variability (HRV) provide new possibilities to monitor cardiac autonomic activity during exercise under different environmental conditions. Using detrended fluctuation analysis (DFA) technique to assess correlation properties of heart rate (HR) dynamics, the present study examines the influence of normobaric hypoxic conditions (HC) in comparison to normoxic conditions (NC) during a constant workload exercise.Materials and MethodsNine well trained cyclists performed a continuous workload exercise on a cycle ergometer with an intensity corresponding to the individual anaerobic threshold until voluntary exhaustion under both NC and HC (15% O2). The individual exercise duration was normalized to 10% sections (10–100%). During exercise HR and RR-intervals were continuously-recorded. Besides HRV time-domain measurements (meanRR, SDNN), fractal correlation properties using short-term scaling exponent alpha1 of DFA were calculated. Additionally, blood lactate (La), oxygen saturation of the blood (SpO2), and rating of perceived exertion (RPE) were recorded in regular time intervals.ResultsWe observed significant changes under NC and HC for all parameters from the beginning to the end of the exercise (10% vs. 100%) except for SpO2 and SDNN during NC: increases for HR, La, and RPE in both conditions; decreases for SpO2 and SDNN during HC, meanRR and DFA-alpha1 during both conditions. Under HC HR (40–70%), La (10–90%), and RPE (50–90%) were significantly-higher, SpO2 (10–100%), meanRR (40–70%), and DFA-alpha1 (20–60%) were significantly-lower than under NC.ConclusionUnder both conditions, prolonged exercise until voluntary exhaustion provokes a lower total variability combined with a reduction in the amplitude and correlation properties of RR fluctuations which may be attributed to increased organismic demands. Additionally, HC provoked higher demands and loss of correlation properties at an earlier stage during the exercise regime, implying an accelerated alteration of cardiac autonomic regulation.

Heart failure (HF) is one of the most frequent heart diseases. It is usually characterized with structural and functional cardiac abnormalities followed by dysfunction of autonomic cardiac control. Current methods of heartbeat interval analysis are not capable to differentiate HF patients and some new differentiation of HF patients could be useful in the determination of the direction of their treatment. In this study, we examined potential of the ratio of the short-term and long-term scaling exponents (α1 and α2) to separate HF patients with similar level of reduced cardiac autonomic nervous system control and with no significant difference in age, left ventricular ejection fraction (LVEF) and NYHA class. Thirty-five healthy control subjects and 46 HF patients underwent 20 min of continuous supine resting ECG recording. The interbeat interval time series were analyzed using standardized power spectrum analysis, detrended fluctuation analysis method and standard Poincaré plot (PP) analysis with measures of asymmetry of the PP. Compared with healthy control group, in HF patients linear measures of autonomic cardiac control were statistically significantly reduced (p < 0.05), heart rate asymmetry was preserved (Cup > Cdown, p < 0.01), and long-term scaling exponent α2 was significantly higher. Cluster analysis of the ratio of short- and long-term scaling exponents showed capability of this parameter to separate four clusters of HF patients. Clusters were determined by interplay of presence of short-term and long-term correlations in interbeat intervals. Complementary measure, commonly accepted ratio of the PP descriptors, SD2/SD1, showed tendency toward statistical significance to separate HF patients in obtained clusters. Also, heart rate asymmetry was preserved only in two clusters. Finally, a multiple regression analysis showed that the ratio α1/α2 could be used as an integrated measure of cardiac dynamic with complex physiological background which, besides spectral components as measures of autonomic cardiac control, also involves breathing frequency and mechanical cardiac parameter, left ventricular ejection fraction.

The correlational structure of stride-to-stride fluctuations differs between healthy and pathological gait. Uncorrelated and anti-persistent stride-to-stride fluctuations are believed to indicate pathology whereas persistence represents healthy functioning. However, this reading can be questioned because the correlational structure changes with task constraints, like acoustic pacing, signifying the tightness of control over particular gait parameters. We tested this “tightness-of-control interpretation” by varying the maneuverability range during treadmill walking (small, intermediate, and large walking areas), with and without acoustic pacing. Stride-speed fluctuations exhibited anti-persistence, suggesting that stride speeds were tightly controlled, with a stronger degree of anti-persistence for smaller walking areas. Constant-speed goal-equivalent-manifold decompositions revealed simultaneous control of stride times and stride lengths, especially for smaller walking areas to limit stride-speed fluctuations. With acoustic pacing, participants followed both constant-speed and constant-stride-time task goals. This was reflected by a strong degree of anti-persistence around the stride-time by stride-length point that uniquely satisfied both goals. Our results strongly support the notion that anti-persistence in stride-to-stride fluctuations reflect the tightness of control over the associated gait parameter, while not tightly regulated gait parameters exhibit statistical persistence. We extend the existing body of knowledge by showing quantitative changes in anti-persistence of already tightly regulated stride-speed fluctuations.

This paper presents an exploratory analysis of the mitochondrial DNA (mtDNA) of 32 species in the subphylum Vertebrata, divided in 7 taxonomic classes. Multiple stochastic parameters, such as the Hurst and detrended fluctuation analysis (DFA) exponents, Shannon entropy, and Chargaff ratio are computed for each DNA sequence. The biological interpretation of these parameters leads to defining a triplet of novel indices. These new functions incorporate the long-range correlations, the probability of occurrence of nucleic bases, and the ratio of pyrimidines-to-purines. Results suggest that relevant regions in mtDNA can be located using the proposed indices. Furthermore, early results from clustering algorithms indicate that the indices introduced might be useful in phylogenetic studies.

Pulmonary hypertension (PH) is a fatal disease—even with state-of-the-art medical treatment. Non-invasive clinical tools for risk stratification are still lacking. The aim of this study was to investigate the clinical utility of heart rhythm complexity in risk stratification for PH patients. We prospectively enrolled 54 PH patients, including 20 high-risk patients (group A; defined as WHO functional class IV or class III with severely compromised hemodynamics), and 34 low-risk patients (group B). Both linear and non-linear heart rate variability (HRV) variables, including detrended fluctuation analysis (DFA) and multiscale entropy (MSE), were analyzed. In linear and non-linear HRV analysis, low frequency and high frequency ratio, DFAα1, MSE slope 5, scale 5, and area 6–20 were significantly lower in group A. Among all HRV variables, MSE scale 5 (AUC: 0.758) had the best predictive power to discriminate the two groups. In multivariable analysis, MSE scale 5 (p = 0.010) was the only significantly predictor of severe PH in all HRV variables. In conclusion, the patients with severe PH had worse heart rhythm complexity. MSE parameters, especially scale 5, can help to identify high-risk PH patients.

Estimates suggest that more than 70% of the world’s rangelands are degraded. The Normalized Difference Vegetation Index (NDVI) is commonly used by ecologists and agriculturalists to monitor vegetation and contribute to more sustainable rangeland management. This paper aims to explore the scaling character of NDVI and NDVI anomaly (NDVIa) time series by applying three fractal analyses: generalized structure function (GSF), multifractal detrended fluctuation analysis (MF-DFA), and Hurst index (HI). The study was conducted in four study areas in Southeastern Spain. Results suggest a multifractal character influenced by different land uses and spatial diversity. MF-DFA indicated an antipersistent character in study areas, while GSF and HI results indicated a persistent character. Different behaviors of generalized Hurst and scaling exponents were found between herbaceous and tree dominated areas. MF-DFA and surrogate and shuffle series allow us to study multifractal sources, reflecting the importance of long-range correlations in these areas. Two types of long-range correlation appear to be in place due to short-term memory reflecting seasonality and longer-term memory based on a time scale of a year or longer. The comparison of these series also provides us with a differentiating profile to distinguish among our four study areas that can improve land use and risk management in arid rangelands.

In rotary machinery, bearings are susceptible to different types of mechanical faults, including ball, inner race, and outer race faults. In condition-based monitoring (CBM), several techniques have been proposed in fault diagnostics based on the vibration measurements. For this paper, we studied the fractal characteristics of non-stationary vibration signals collected from bearings under different health conditions. Using the detrended fluctuation analysis (DFA), we proposed a novel method to diagnose the bearing faults based on the scaling exponent (α1) of vibration signal at the short-time scale. In vibration data with high sampling rate, our results showed that the proposed measure, scaling exponent, provides an accurate identification of the health state of the bearing. At the end, we evaluated the performance of the proposed method under different data quality issues, data loss and induced noise.

Moroccan family business companies are becoming an attractive investment in Casablanca stock exchange. In this study, presence of fractal and chaos in Moroccan family business stock returns is examined. In particular, return series are analyzed by stationary wavelet transform to decompose original series into long- and short-term variations. Then, detrended fluctuation analysis and artificial neural networks are used to estimate, respectively Hurst exponent and largest Lyapunov exponent. Results from fractal analysis show that short variations in returns are anti-persistent, whilst long variations are persistent. Besides, results from chaos tests reveal that both short and long variations in returns are chaotic. Such conclusions should be taken into account in active portfolio optimization and management. [ABSTRACT FROM AUTHOR]

Temporal cardiac properties provide alternative information in analyzing heart rate variability (HRV), which may be disregarded by the standard HRV analyses. Patients with congestive heart failure (CHF) are known to have distinct temporal features from the healthy individuals. However, the underlying mechanism leading to the variation remains unclear. Whether or not these parameters can finely classify the severity for CHF patients is uncertain as well. In this work, an electrocardiogram was monitored in advanced CHF patients using 24-h Holter in four conditions, including baseline, one and three months after atenolol therapy, and healthy individuals. Slope and area under the curve (AUC) of multiscale entropy (MSE) curve over short (scales 1-5) and long (scales 6-20) scales, and detrended fluctuation analysis (DFA) scaling exponents at short (4-11 beats) and intermediate (>11 beats) window sizes were calculated. The results show that short-time scale MSE-derived parameters (slope: -0.08 ± 0.10, -0.03 ± 0.10, 0.02 ± 0.06, 0.08 ± 0.06; AUC: 4.03 ± 2.11, 4.69 ± 1.28, 4.73 ± 0.94, and 6.17 ± 1.23) and short-time scale DFA exponent (0.79 ± 0.16, 0.95 ± 0.22, 1.11 ± 0.19, and 1.35 ± 0.20) can hierarchically classify all four conditions. More importantly, simulated R-R intervals with different fractions and amplitude of respiratory sinus arrhythmia (RSA) components were examined to validate our hypothesis regarding the essentiality of RSA in the improvement of cardiovascular function, and its tight association with unpredictability and fractal property of HRV, which is in line with our hypothesis that RSA contributes significantly to the generation of the unpredictability and fractal behavior of HR dynamics. [ABSTRACT FROM AUTHOR]

A comprehensive understanding of the changing behaviors of precipitation concentration and intensity plays a pivotal role in water resource management. Hence, we investigated the spatiotemporal changing behaviors of frequency and intensity of 13 precipitation indices and their probable causes of changes in precipitation systems. This study used daily precipitation datasets from 23 sites in Bangladesh and six atmospheric circulation indices during 1975–2017. The results showed that the precipitation concentration index (LCI) varies between 0.57 and 0.63, and the highest value was found in the southeastern region. The precipitation days frequency indices such as AD, LPD, MPD, HPD, and WPD have significantly increased in Bangladesh while precipitation intensity indices such as AII, LPI, MPI, HPI, and WPI have significantly declined; all types of indices have clear rapid changes. The results of detrended fluctuation analysis (DFA) exhibit long-term correlations among all precipitation indices, suggesting that these indices will sustain their present trend line in the upcoming period. The Sunspot (SS) and East Asian Summer Monsoon Index (EASMI) had a negative influence on ACI and South Asian Summer Monsoon index (SASMI) had a strong positive influence on precipitation days frequency indices. The significance analysis using the random forest (RF) algorithm showed that SS is the largest contributing factor affecting the precipitation systems in Bangladesh. ECMWF ERA5 reanalysis datasets revealed that elevating summer geopotential height, higher anticyclonic anomaly, increasing low and decreasing high cloud covers and lower solar radiation with adequate moisture divergence fluxes contributed to variations in precipitation extremes in Bangladesh. Linear trend of Arid days, AD (a), Sequential Mann-kendall test to detect rapid change (b), DFA long term forecasting of ACI (c) and Cross wavelet between SASMI and ACI (d). Unlabelled Image • Concentration index (LCI) vary between 0.57 and 0.63. The highest value was in southeastern part and the lowest LCI value was in eastern part. • Precipitation days frequency indices significantly increased, whereas precipitation intensity indices significantly decreased. • Sunspot is the most important factor influencing the precipitation systems using the RF model. • SS and EASMI had negative (or positive) impacts, while SASMI had positive (or negative) effect on most precipitation indices. [ABSTRACT FROM AUTHOR]

Previous research indicates the correlation structure of gait parameters (i.e., fractal dynamics) decreases with age. This decrease is suggested to reflect a reduced capacity for locomotor adaptation in older adults. The purpose of this study was to investigate potential differences between physical activity-matched young and older adults’ fractal dynamics and gait adaptability during unperturbed and asymmetric walking, and to determine if fractal dynamics predict adaptive capacity. Fifteen young (28.9 ± 5.6 years, nine women) and 15 older (64.7 ± 2.7, nine women) adults with similar habitual physical activity levels walked at preferred speed, half of preferred speed, and asymmetrically whereby their dominant and non-dominant legs moved at preferred and half-preferred speed, respectively. Fractal correlations (scaling exponent α) of stride times were assessed through detrended fluctuation analysis, and gait adaptation to asymmetric walking on the basis of lower limb relative phase. Both cohorts displayed similar fractal dynamics at preferred speed and asymmetric walking, while older adults exhibited greater α during slow walking. Both groups exhibited comparable gait adaptation to split-belt walking based on analysis of lower limb relative phase. Fractal dynamics during preferred speed and asymmetric walking was moderately associated with gait adaptation in the young and older adult cohorts, respectively. In these activity-matched groups, there were no age-based reductions in fractal dynamics or gait adaptation, and fractal scaling α was moderately associated with gait adaptation. These findings suggest that stride time fractal dynamics and gait adaptation may be preserved in older adults who habitually perform moderate intensity physical activity. [ABSTRACT FROM AUTHOR]

Introduction: Many physiological signals yield fractal characteristics, i.e., finer details at higher magnifications resemble details of the whole. Evidence has been accumulating that such fractal scaling is basically a consequence of interaction-dominant feedback mechanisms that cooperatively generate those signals. Neurodegenerative diseases provide a natural framework to evaluate this paradigm when this cooperative function declines. However, methodological issues need to be cautiously taken into account in order to be able to provide reliable as well as valid interpretations of such signal analyses. Methods: Two conceptually different fractal analyses, i.e., detrended fluctuation analysis (DFA) and analysis of cumulative distributions of durations (CDDs), are applied to actigraphy data of 36 geriatric in-patients diagnosed with dementia. The impact of the used time resolution for data acquisition on the assessed fractal outcome parameters is particularly investigated. Moreover, associations between these parameters and scores from the Mini-Mental-State-Examination and circadian activity parameters are explored. Results: Both analyses yield significant deviations from (mono-)fractal scaling over the entire considered time range. DFA provides robust measures for the observed break-down of fractal scaling. In contrast, analysis of CDDs results in measures which highly fluctuate with respect to the time resolution of the assessed data which affects also further derived quantities such as scaling exponents or associations with other (clinically relevant) assessed parameters. Discussion: To scrutinize actigraphic signal characteristics and especially their (deviations from) fractal scaling may be a useful tool for aiding diagnosis, characterization, and monitoring of dementia. However, results may, besides contextual aspects, also substantially depend on specific methodological choices. In order to arrive at both reliable and valid interpretations, these complications need to be carefully elaborated in future research. [ABSTRACT FROM AUTHOR]

Background: Accelerometers are included in a wide range of devices that monitor and track physical activity for health-related applications. However, the clinical utility of the information embedded in their rich time-series data has been greatly understudied and has yet to be fully realized. Here, we examine the potential for fractal complexity of actigraphy data to serve as a clinical biomarker for mortality risk.Methods: We use detrended fluctuation analysis (DFA) to analyze actigraphy data from the National Health and Nutrition Examination Survey (NHANES; n = 11,694). The DFA method measures fractal complexity (signal self-affinity across time-scales) as correlations between the amplitude of signal fluctuations in time-series data across a range of time-scales. The slope, α, relating the fluctuation amplitudes to the time-scales over which they were measured describes the complexity of the signal.Results: Fractal complexity of physical activity (α) decreased significantly with age (p = 1.29E-6) and was lower in women compared with men (p = 1.79E-4). Higher levels of moderate-to-vigorous physical activity in older adults and in women were associated with greater fractal complexity. In adults aged 50-79 years, lower fractal complexity of activity (α) was associated with greater mortality (hazard ratio = 0.64; 95% confidence interval = 0.49-0.82) after adjusting for age, exercise engagement, chronic diseases, and other covariates associated with mortality.Conclusions: Wearable accelerometers can provide a noninvasive biomarker of physiological aging and mortality risk after adjusting for other factors strongly associated with mortality. Thus, this fractal analysis of accelerometer signals provides a novel clinical application for wearable accelerometers, advancing efforts for remote monitoring of physiological health by clinicians. [ABSTRACT FROM AUTHOR]

This study tests weak form efficiency in frontier markets. Mutual information and detrended fluctuation analyses are performed to assess global correlation and long range dependence in the stock markets of twenty three countries. The results indicate that Slovenia is the only case where there is evidence compatible with weak form efficiency. The relatively less inefficient markets are mainly located in Europe and America, and the relatively more inefficient mainly in the Middle East. This information is useful for investors, but also for the assessed countries' regulators as they indicate that relevant impediments are preventing the exploitation of potential profitable opportunities. [ABSTRACT FROM AUTHOR]

In the study of human cognitive activity using electroencephalogram (EEG), the brain dynamics parameters and characteristics play a crucial role. They allow to investigate the changes in functionality depending on the environment and task performance process, and also to access the intensity of the brain activity in various locations of the cortex and its dependencies. Usually, the dynamics of activation of different brain areas during the cognitive tasks are being studied by spectral analysis based on power spectral density (PSD) estimation, and coherence analysis, which are de facto standard tools in quantitative characterization of brain activity. PSD and coherence reflect the strength of oscillations and similarity of the emergence of these oscillations in the brain, respectively, while the concept of stability of brain activity over time is not well defined and less formalized. We propose to employ the detrended fluctuation analysis (DFA) as a measure of the EEG persistence over time, and use the DFA scaling exponent as its quantitative characteristics. We applied DFA to the study of the changes in activation in brain dynamics during mental calculations and united it with PSD and coherence estimation. In the experiment, EEGs during resting state and mental serial subtraction from 36 subjects were recorded and analyzed in four frequency ranges: θ1 (4.1–5.8 Hz), θ2 (5.9–7.4 Hz), β1 (13–19.9 Hz), and β2 (20–25 Hz). PSD maps to access the intensity of cortex activation and coherence to quantify the connections between different brain areas were calculated, the distribution of DFA scaling exponent over the head surface was exploited to measure the time characteristics of the dynamics of brain activity. Obtained arrangements of DFA scaling exponent suggest that normal functioning of the brain is characterized by long-term temporal correlations in the cortex. Topographical distribution of the DFA scaling exponent was comparable for θ and β frequency bands, demonstrating the largest values of DFA scaling exponent during cognitive activation. The study shows that the long-term temporal correlations evaluated by DFA can be of great interest for diagnosis of the variety of brain dysfunctions of different etiology in the future. [ABSTRACT FROM AUTHOR]