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Military personnel in combat roles often perform gait tasks with additional load, which can affect the contributions of joint mechanical work (positive and negative). Furthermore, different locomotion patterns can also affect joint specific work contributions. While mean behavior of joint work is important to understanding gait, changes in joint kinetic modulation, or the regulation/control of stride-to-stride joint work variability is necessary to elucidate locomotor system function. Suboptimal modulation exhibited as a stochastic time-series (large fluctuation followed by an opposite smaller fluctuation) could potentially affect locomotion efficiency and portend injury risk. It remains unclear how the locomotor system responds to a combination of load perturbations and varying locomotion patterns.What are the interactive effects of load magnitude and locomotion pattern on joint positive/negative work and joint work modulation in healthy, active, recruit-aged women?Eleven healthy, active, recruit-aged (18-33 years) women ran and forced-marched (walking at a velocity an individual would typically jog) in bodyweight (BW), an additional 25 % of BW (+25 %BW) and an additional 45 % of BW (+45 %BW) conditions at a velocity above their gait transition velocity. Joint work was calculated as the time integral of joint power. Joint work modulation was assessed with detrended fluctuation analysis (DFA) on consecutive joint work time-series.Joint work contributions shifted proximally for forced-marching demonstrated by lesser (p .001) positive/negative ankle work but greater (p = .001) positive hip work contributions compared to running. Running exhibited optimal positive ankle work modulation compared to forced-marching (p = .040). Knee and ankle negative joint work modulation was adversely impacted compared to the hip during forced-marching (p .001).Employing forced-marching gait while under loads of 25 and 45 % of BW reduces the ability of the plantar-flexors and knee extensors to optimally contribute to energy absorption and propulsion in recruit-aged women, potentially reducing metabolic efficiency and increasing injury risk.

The impairment of short-term heart rate regulation in patients with heart failure with preserved ejection fraction (HFpEF) can cause acute hemodynamic collapse. Detrended fluctuation analysis (DFA) is a useful tool for the diagnosis of heart diseases and the prediction of mortality. In DFA, the short-term scaling exponent α is decreased in heart failure. However, its change in HFpEF patients remains unclear.Twenty patients diagnosed with HFpEF [defined as brain natriuretic peptide (BNP)100 pg/mL, ejection fraction (EF) ≥50%, and without significant valvular disease], 20 diagnosed with non-HFpEF (BNP 100 pg/mL and EF 50%), and 20 control subjects generally matched for age and gender were enrolled. Holter electrocardiography was performed, and heart rate variability was calculated. In the DFA, the scaling exponents in 1000 beats were calculated for each 15-min segment and the average of all segments was used. We compared both the short-term (11 beats, α1) and long-term (≥11 beats, α2) scaling exponents among the three groups.In the HFpEF, non-HFpEF, and control groups, α1 was 0.73 ± 0.27, 0.66 ± 0.29, and 1.01 ± 0.20 (p 0.01), and α2 was 0.95 ± 0.08, 0.88 ± 0.11, and 0.96 ± 0.07 (p 0.01), respectively. The α1 exponent was significantly decreased in the HFpEF group (p 0.01 vs. control) and the non-HFpEF group (p 0.01 vs. control), while the α2 exponent was significantly decreased in the non-HFpEF group only (p 0.05 vs. HFpEF and control).Short-term heart rate regulation is impaired in patients with HFpEF, while patients with non-HFpEF have both short-term and long-term impairment.

Background Persons with lower limb amputation often experience decreased physical capacity, difficulty walking, and increased fall risk. To either prevent or recover from a loss of balance, one must effectively regulate their stepping movements. It is therefore critical to identify how well persons with amputation regulate stepping. Here, we used a multi-objective control framework based on Goal Equivalent Manifolds to identify how persons with transtibial amputation (TTA) regulate lateral stepping while walking without and with lateral perturbations. Research question When walking in destabilizing environments, do otherwise healthy persons with TTA exhibit greater difficulty regulating lateral stepping due to impaired control? Or do they instead continue to use similar strategies to regulate lateral stepping despite their amputation? Methods Eight persons with unilateral TTA and thirteen able-bodied (AB) controls walked in a virtual environment under three conditions: no perturbations, laterally oscillating visual field, and laterally oscillating treadmill platform. We analyzed step-to-step time series of step widths and absolute lateral body positions. We computed means, standard deviations and Detrended Fluctuation Analysis scaling exponents for each time series and computed how much participants directly corrected step width and position deviations at each step. We compared our results to computational predictions to identify the underlying causes of our experimental findings. Results All participants exhibited significantly increased variability, decreased scaling exponents, and tighter direct control when perturbed. Simulations from our stepping regulation models revealed that people responded to the increased variability produced by the imposed perturbations by tightening their control of both step width and lateral position. Participants with TTA exhibited only a few minor differences from AB in lateral stepping regulation, even when subjected to substantially destabilizing lateral perturbations. Significance Since control of stepping is intrinsically multi-objective, developing effective interventions to reduce fall risk in persons with amputation will likely require strategies that adopt multi-objective approaches.

Background Time-domain and non-linear methods can be used to quantify beat-to-beat repolarization variability but whether measures of repolarization variability can predict ventricular arrhythmogenesis in mice have never been explored. Methods Left ventricular monophasic action potentials (MAPs) were recorded during constant right ventricular 8 ​Hz pacing in Langendorff-perfused mouse hearts, in the presence or absence of the gap junction and sodium channel inhibitor heptanol (0.1, 0.5, 1 or 2 ​mM). Results Under control conditions, mean action potential duration (APD) was 39.4 ​± ​8.1 ​ms. Standard deviation (SD) of APDs was 0.3 ​± ​0.2 ​ms, coefficient of variation was 0.9 ​± ​0.8% and the root mean square (RMS) of successive differences in APDs was 0.15 ​± ​0.14 ​ms. Poincaré plots of APDn+1 against APDn revealed ellipsoid morphologies with a SD along the line-of-identity (SD2) to SD perpendicular to the line-of-identity (SD1) ratio of 4.6 ​± ​2.1. Approximate and sample entropy were 0.61 ​± ​0.12 and 0.76 ​± ​0.26, respectively. Detrended fluctuation analysis revealed short- and long-term fluctuation slopes of 1.49 ​± ​0.27 and 0.81 ​± ​0.36, respectively. Heptanol at 2 ​mM induced ventricular tachycardia in five out of six hearts. None of the above parameters were altered by heptanol during which reproducible electrical activity was observed (KW-ANOVA, P ​> ​0.05). Contrastingly, SD2/SD1 decreased to 2.03 ​± ​0.41, approximate and sample entropy increased to 0.82 ​± ​0.12 and 1.45 ​± ​0.34, and short-term fluctuation slope decreased to 0.82 ​± ​0.19 during the 20-s period preceding spontaneous ventricular tachy-arrhythmias (n ​= ​6, KW-ANOVA, P ​, Graphical abstract Image 1, Highlights • None of the parameters on variability determined using time-domain or non-linear analyses was altered by heptanol. • In the immediate periods preceding the onset of spontaneous ventricular tachycardia, the following changes were observed. • SD2/SD1 was decreased, approximate and sample entropy were increased, and short-term fluctuation slope was decreased. • These measures of repolarization variability could be used to predict impending ventricular arrhythmias in mouse hearts.

Ambulating while carrying a mission specific load is one of the most frequently executed occupational tasks for the military, especially for individuals in combat roles. Prolonged ambulation is a naturally dynamic and complex process, characterized by highly multi-dimensional interactions within the gait mechanics of the lower extremity. Recent wearable sensors studies, like inertial measurement unit (IMU)-related gait studies have demonstrated that machine learning (MLN) algorithms and fractal analysis can successfully discriminate between classes, such as movement patterns, injury, age and sex. This study attempts to classify fractal gait patterns of women and men using IMU-based signal data obtained from accelerometer, gyroscope and magnetometer during a 2 km loaded (20 kg) march. Random Forest (RF) MLN algorithm was used to generate a model that can measure the accuracy and identify the importance of IMU-based signal-related fractal variables. A total of 18 variables were calculated using 2 fractal methods, detrended fluctuation analysis (DFA) and wavelet transform-based power spectral density (PSD), from 3 IMU-based signals in their 3 axes (medial-lateral, vertical and anterior-posterior). A total of 33 healthy adults (17 men [26.7±5.9 years] and 16 women [25.2±4.5 years]) volunteered for this study. A 9-axis IMU sensor was attached to each participant at each of the following locations: feet, shanks, thighs and lumbar spine. An independent training-testing approach, called one-vs-one (i.e., variables from one IMU-based signal were trained and tested using another IMU-based signal) was applied to determine the classification accuracy (i.e., similarities between IMUs) and variable importance (score ranges: 0.0-1.0) measures. These values were then used to select the variables that best independently describe the rank in classification margin. The results from each IMU sensor placement based on the fractal values showed ‘moderate’ accuracy (50-75%), with the exception of two cases: the left shank yielded ‘good’ accuracy (80.1%) compared with the right shank, and the right thigh generated ‘poor’ accuracy (48.9%) compared with the left foot. No IMU location showed excellent accuracy (>90%). The results indicate that each IMU placement location has their own fractal patterns that are not similar to another IMU location in terms of sex classification. The analysis of the variable importance in the classification margin showed that most of the PSD resulted variables were classified as ‘most important’ compared with the DFA resulted variables. IMU sensors, and the associated analyses, could be used during military load carriage to evaluate changes in gait resulting from injury, fatigue or overtraining.

Background Healthy gait dynamics are characterized by the presence of fractal, persistent stride-to-stride variations, which become more random with Parkinson’s disease (PD). Rhythmic auditory stimulation with fractal beat-to-beat variations can change gait dynamics in people with PD toward more persistence. Research question How does gait in people with PD change when synchronizing steps with fractal melodic metronomes with different step-to-beat ratios, and which stimulus do they prefer? Methods In this cross-sectional study, 15 people with PD and 15 healthy older adults walked over-ground in three conditions: self-paced, paced by a fractal auditory stimulus with a 1:1 step-to-beat ratio (‘metronome’), and fractal auditory stimulus with a 1:2 step-to-beat ratio (‘music’). Gait dynamics were recorded with instrumented insoles, and detrended fluctuation analysis (DFA) was applied to the series of stride time intervals. Stimuli preference was assessed using Likert-like scales and open-ended questions. ANOVAs were used to compare mean, coefficient of variation, α-DFA, and the responses from the continuous Likert scales. Pearson correlations were used to assess the relationship between ‘music’ and ‘metronome’ enjoyment or difficulty with gait outcomes, and to determine the association between baseline α-DFA and changes due to the stimuli. Results Our major findings are that (i) stride-to-stride variations were more persistent with the ‘metronome’ compared to baseline for both groups, (ii) the effect was greater for people with lower α-DFA at baseline (i.e., more random stride-to-stride variations), and (iii) both groups found the ‘metronome’ less difficult to synchronize with. Significance This study showed that people with PD and healthy older adults walk with higher statistical persistence in their stride-to-stride variations when instructed to synchronize their steps with a fractal stimulus. Participants with lower persistence at baseline benefited the most from the fractal ‘metronome’, highlighting the importance to develop patient-centered tests and interventions.

This paper presents sound innovations in the processes for geographical data collection and data evaluation for multiscale analysis of terrain altitude. Data sets were collected along several transects, as well as different geographical directions, in three dissimilar zones of Spain, for the sake of Detrended Fluctuation Analysis (DFA) proper trade off. Used terrain data base consists of a 1003 × 1003-pixel matrix, with 1-m pixel resolution, provided by Official Spanish GIS. For multiscale terrain altitude analysis, generalized Hurst dimensions (H(q)) and multifractality index (ΔH(q)) were calculated on several transects crossing the areas under study. The results show, for all cases, a self-affine characteristic within most of the scale range, as well as a persistent character and a variable value of ΔH(q). Directionality analysis results, for both parameters, when represented by means of a rose plot, clearly demonstrate the differences in the scaling behavior along and across mountains, natural vegetation and crop lands and it could define a new metric for the landscape. Each of the three geographical areas covered by current statement of work clearly shows its particular anisotropy, this situation will be verified using a wider geographical data base in forthcoming works.

Electroencephalogram (EEG) is one of the most important signals for diagnosis of Autism Spectrum Disorder (ASD). There are different challenges such as feature selection and the existence of artifacts in EEG signals. This article aims to present a robust method for early diagnosis of ASD from EEG signal. The study population consists of 34 children with ASD between 3–12 years and 11 healthy children in the same ranges of age. The proposed approach uses linear and nonlinear features such as Power Spectrum, Wavelet Transform, Fast Fourier Transform (FFT), Fractal Dimension, Correlation Dimension, Lyapunov Exponent, Entropy, Detrended Fluctuation Analysis and Synchronization Likelihood for describing the EEG signal. In addition Density Based Clustering is utilized for artifact removal and robustness. Besides, features selection is applied based on different criterions such as Mutual Information (MI), Information Gain (IG), Minimum-Redundancy Maximum-Relevancy (mRmR) and Genetic Algorithm (GA). Finally, the K-Nearest-Neighbor (KNN) and Support Vector Machines (SVM) classifiers are used for final decision. As a result, the investigation indicates that the classification accuracy of the approach using SVM is 90.57% while for KNN it is 72.77%. Moreover, the sensitivity of the proposed method is 99.91% for SVM and 91.96% for KNN. Also, experiments show that DFA, LE, Entropy and SL features have considerable influence in promoting the classification accuracy.

The influence of reduction in emissions on the inherent temporal characteristics of PM2.5 and NO2 concentration time series in six urban cities of India is assessed by computing the Hurst exponent using Detrended Fluctuation Analysis (DFA) during the lockdown period (March 24–April 20, 2020) and the corresponding period during the previous two years (i.e., 2018 and 2019). The analysis suggests the anticipated impact of confinement on the PM2.5 and NO2 concentration in urban cities, causing low concentrations. It is observed that the original PM2.5 and NO2 concentration time series is persistent but filtering the time series by fitting the autoregressive process of order 1 on the actual time series and subtracting it changes the persistence property significantly. It indicates the presence of linear correlations in the PM2.5 and NO2 concentrations. Hurst exponent of the PM2.5 and NO2 concentration during the lockdown period and previous two years shows that the inherent temporal characteristics of the short-term air pollutant concentrations (APCs) time series do not change even after withholding the emissions. The meteorological variations also do not change over the three time periods. The finding helps in developing the prediction models for future policy decisions to improve urban air quality across cities.

The process of reading a specific text is considered complex and little known in neuroscience, since it involves the vision, memory, motor control, learning, among others. In this sense, an excellent possibility to study the brain activity in the reading task can be achieved by the analysis of the multi-channel Electroencephalogram (EEG) and also with new statistical methods, like the detrended fluctuation analysis method (DFA). In this paper it will be proposed a model to analyze the brain activity in the reading task, performed by two subjects using a 22-channels EEG (NEUROMAP® model E Q S A 260 ). In order to test our model, two adults subjects (graduates) were tested here. These subjects were arranged in a chair facing a panel with the specific text, excluding involuntary movements that activated regions of the brain that were not being stimulated by reading. For the first subject, chosen at random, the text was presented before the task for understanding and some memorization. For the other subject the text was presented at the time of task. For the signal processing we chose 11 bio-electrodes located at the frontal, parietal, temporal and occipital regions of the brain. Therefore, to treat these non-stationary bio-signals we must apply robust and modern statistical techniques. With this objective, DFA method was applied in order to analyze the F D F A ( n ) fluctuation function in multi-channel EEG bio-sensors, more specifically the difference of its logarithm, i.e., Δ l o g F D F A . The results show that the use of this new function can be useful for brain activities. This paper, as we shall see here, is an initial contribution for EEG data analyze, that would be of medical interest, mainly in neuroscience area.

We studied the whole and aftershock-depleted shallow (depth ≤ 30 km) Taiwanese seismicity from 1990 to 2017 by using several independent methods. The coefficient of variations and the Allan Factor have revealed that time-clustering characterizes not only the time distribution of the whole seismic catalogue, but also that of the aftershock-depleted one, although this displays time-clustering at larger timescales. In particular the Allan Factor shows that at small timescales the seismic process of the whole as well as the aftershock-depleted one can be well described by a Poisson process. The detrended fluctuation analysis clearly evidence persistence in the interevent times and weak persistence or randomness in the magnitudes. The singular spectrum analysis of the daily counts in the aftershock-depleted catalogue reveals the existence of quasi-monthly and bi-weekly periodicities. Furthermore, quasi-annual and quasi-semestral periodicities have been identified that strengthen the link between seismic activity in Taiwan and Earth’s tides.

Within the perimeter of patent collaboration networks, the average distance of collaborations and the number of countries involved per each collaboration have been shown to have increased steadily in time. Less attention, though, has been devoted to assessing whether this growth of cross-country collaborations is stable in time. To address this scientific question we focus on the identification of long-term correlations (i.e. temporal persistence). Our data set consists of time series of yearly average collaboration radii and of cross-border links in the Euro-American subsystem of the global collaboration network for the period 1978–2014. To investigate the fundamental persistence properties of these time series, we use Detrended Fluctuation Analysis, a method that allows us to measure long-term correlations in detrended signals. Also, we devise a general and original procedure to assess the statistical significance of results for short time series. Our results, showing that long-term correlations do exist in the majority of our signals, reinforce the hypothesis of a diminishing role of geographical distance in technological collaborations. Results at national level show that a significant degree of heterogeneity in persistence parameters can be detected within Europe, irrespectively of the efforts towards the set-up of an integrated European Research Area.

Research question The current study investigated stride-to-stride fluctuations of step rate and contact time in response to enforced step frequency perturbations as well as adaptation and de-adaptation behavior. Methods Forty distance runners ran at a self-selected speed and were asked to match five different enforced step frequencies (150, 160, 170, 180, and 190 beats per min). The influence of experience was explored, because running is a skill that presumably gets better with practice, and increased years of running experience is protective against injury. Detrended fluctuation analysis was used to determine the strength of long-range correlations in gait fluctuations at baseline, during the perturbation, and post-perturbation. Adaptive response was measured by the ability to match, rate of matching, and aftereffect of step frequency perturbations. Results The structure of stride-to-stride fluctuations for step rate and contact time did not change during the perturbation or post-perturbation compared to baseline. However, fluctuations in step rate were affected by the level of perturbation. Runners with the most experience had a less persistent structural gait pattern for both step rate and contact time at baseline. Highly experienced runners also demonstrated the best adaptive response. They better matched the enforced step frequency, reached the enforced step frequency sooner, and returned to preferred step frequency more quickly following removal of the perturbation. Significance These findings indicate baseline locomotor flexibility may be beneficial to achieve task demands and return to a stable state once the task is complete. Increased locomotor flexibility may also be a contributing factor for reduced injury risk in experienced runners.

The knowledge of geological strata sequences and their exact boundaries depths is of a great importance in the characterization of oil and gas reservoirs. The aim of automated well-to-well correlation approaches is to facilitate and accelerate the procedure of geological boundary detection. In this study, we implement an automatic well-to-well correlation approach based on pattern extraction from well-logs. The well-log patterns are recognized by calculating several statistical and fractal parameters. As a fractal parameter, we select the wavelet standard deviation exponent, calculated by the discrete wavelet transform. Furthermore, to select the proper wavelet function, as the heart of wavelet transform, the energy to Shannon entropy ratio criterion is implemented. The statistical pattern recognition parameters of this study include average value, maximum to minimum ratio, coefficient of variation, and the trend angle of well-log data (i.e., Gamma ray log) in a window around the geological boundary. Moreover, the analysis of variance (ANOVA) tool and the Tukey multiple comparison method are implemented to evaluate the effectiveness of each parameter (i.e., fractal or statistical parameters) during the determination of boundary depths. The gamma ray logs from three wells of an oil field are used as a dataset for the evaluation of our algorithm. The outputs of our methodology are also compared with the new detrended fluctuation analysis (DFA) method, which show promising outcomes over it. The results show that the average value of the signal, among the analyzed parameters, is the most effective parameter; however, implementing the combination of all fractal and statistical parameters can improve the accuracy of the geological boundary detection.

Among the sports fans beliefs about "hot hands" and "winning streaks" are widely spread, while the scientific debate about these effects is still ongoing. Recently in a paper by P. Ferreira [Physica A 500: 92-96] detrended fluctuation analysis was applied to the NBA teams' win records. It was shown that 28 considered NBA teams exhibit persistence in the win record time series. In this paper we take the same data set and compare the obtained results against various random models. We find that the empirical results are consistent with the results obtained from various simple random models., Comment: 10 pages, 4 figures, 3 tables

By employing Detrended Fluctuation Analysis (DFA), which has been established as a standard method to investigate long range correlations in nonstationary time series, we study the temporal correlations between the magnitudes of the earthquakes that occurred before the recent deadly Mexico M8.2 earthquake on 7 September 2017 in Chiapas region. Our aim here is to shed light on the origin of the following precursory phenomenon found in our previous publication (Sarlis et al., 2018): Upon considering the analysis of seismicity in the new time domain termed natural time, it was shown that the entropy change of seismicity under time reversal exhibited an important minimum almost 3 months before this major earthquake. Here the application of DFA to earthquake magnitude time series reveals that this minimum of the entropy change of seismicity is preceded as well as followed by characteristic changes of temporal correlations between earthquake magnitudes, which are quantified by the DFA exponent α . In particular, before this minimum the long range correlations breakdown to an almost random behavior possibly turning to anticorrelation ( α ≤ 0 . 5 ) while after the minimum (and before the major M8.2 earthquake) long range correlations develop with an exponent α between 0.6 and 0.7.

Based on multi-fractal detrended fluctuation analysis (MF-DFA) method, the extended self-similarity (ESS) is incorporated to develop a novel method to quantify multi-fractal characteristics. Detailed results show that compared with MF-DFA this new extended self-similarity based MF-DFA (ESS-MF-DFA) method can significantly extend scaling range and reduce uncertainties in estimating the exponents. Moreover, although ESS-MF-DFA method is developed from the DFA method with a fundamental assumption of a definite scaling range between fluctuation function and scale, ESS-MF-DFA can still work well even when DFA fails due to no scaling range between fluctuation function and scale. Furthermore, a criterion without estimating the generalized Hurst exponents is developed based on ESS-MF-DFA to distinguish multi-fractal from mono-fractal behavior and to quantify multi-fractal strength. All these results indicate that ESS-MF-DFA outperforms MF-DFA in reliably handling multi-fractal quantifications for much wider fields.

This paper adopts multifractal methods to analyze the multifractal characteristics of polluted time series in Beijing, Zhengzhou, and Jinan. The results of the multifractal detrended fluctuation analysis (MF-DFA) show that each of three air quality index (AQI) time series has multifractal characteristics, which provides evidence that the multifractal method but the traditional linear or monofractal method is feasible. The sources of multifractality in three AQI time series are all from long-range correlations and fat tail distributions, although the highlighted sources are different in three cities. The results of the coupling detrended fluctuation analysis (CDFA) show that SO2 has a vital impact on air quality in each of three cities. O 3 has an important impact on air quality in Beijing and Jinan city and NO2 has an important impact on air quality in Zhengzhou city. It is noted that PM 2.5 has not as large an impact as we imagine in three cities. It has a relatively large impact on air quality of Zhengzhou city, while it has a small impact on air quality of Beijing and Jinan city. The chi square χ 2 test further confirms the above results.

The aim of the present study was to investigate how age and sensory deprivation affect the temporal organization of CoP sway variability and the postural corrective commands during standing balance in typically developing preschoolers. A sample of 57 children aged 3–5 years participated in the study. Structural stabilometric descriptors of sample entropy (SEn), detrended fluctuation analysis (DFA), and sway density curve (SDC) analysis were employed to assess features of center of pressure sway. A force platform was used to collect center of pressure data during standing balance over 40 s in four conditions: standing on rigid and foam surfaces with eyes open and closed. The main results are as follows: (1) sample entropy decreased and DFA_coefficient increased with age, while the SDC variables remained unaltered among the 3-, 4-, and 5-year-old children; (2) as sensory conditions became more challenging, sample entropy decreased and DFA_coefficient increased, while MT and MD decreased and MD increased; age did not influence the responses to sensorial deprivation. In conclusion, 5-year-old children showed decreased variability of CoP sway during standing balance compared with the younger children, but all children used the same corrective torques to control for perturbations. More challenging sensory deprivation conditions resulted in decreased variability of postural sway, higher amplitudes and more frequent correcting torques for stabilization, but age did not influence these behaviors.

The purpose of the study was to compare the effects of a feedback-controlled treadmill (FeedbackTM) to a traditional fixed-speed treadmill (FixedTM) on spatiotemporal gait means, variability, and dynamics. The study also examined inter-session reliability when using the FeedbackTM. Ten young adults walked on the FeedbackTM for a 5-minute familiarization followed by a 16-minute experimental trial. They returned within one week and completed a 5-minute familiarization followed by a 16-minute experimental trial each for FeedbackTM and FixedTM conditions. Mean walking speed and step time, length, width, and speed means and coefficient of variation were calculated from all experimental conditions. Step time, length, width, and speed gait dynamics were analyzed using detrended fluctuation analysis. Mean differences between experimental trials were determined using ANOVAs and reliability between FeedbackTM sessions was determined by intraclass correlation coefficient. No difference was found in mean walking speed nor spatiotemporal variables, with the exception of step width, between the experimental trials. All mean spatiotemporal variables demonstrated good to excellent reliability between sessions, while coefficient of variation was not reliable. Gait dynamics of step time, length, width, and speed were significantly more persistent during the FeedbackTM condition compared to FixedTM, especially step speed. However, gait dynamics demonstrated fair to poor reliability between FeedbackTM sessions. When walking on the FeedbackTM, users maintain a consistent set point, yet the gait dynamics around the mean are different when compared to walking on a FixedTM. In addition, spatiotemporal gait dynamics and variability may not be consistent across separate days when using the FeedbackTM.

Experimental time series often contain bad segments that arise from artifacts, changes in experimental conditions, or failures in recording equipment. Such segments are usually removed from the time series during the preprocessing stage that can alter the correlation or other properties of the signals. Aiming to reveal how the effects of data loss depend on the amount of missing data, we consider here different regimes of regular and chaotic dynamics with excluded segments. Using several data processing techniques, namely, the wavelet-transform modulus maxima (WTMM) approach, the detrended fluctuation analysis (DFA) and the multiresolution analysis based on the discrete wavelet-transform (DWT), we demonstrate essentially different effects of the missing data for positively correlated time series and anti-correlated signals. All the techniques show that positively correlated time series are significantly less sensitive to excluded segments and enable the characterization of the object’s properties even under the condition of an extreme data loss. We verify the ability of characterizing physiological systems using an example of the cerebrovascular dynamics based on time series with missing data. A weak sensitivity of the cerebral blood flow to data loss is an important issue for diagnostic-related studies.

The time evolutions of transient current data for As2Te3(In) thin films were measured at different electric fields for the dc voltages of 0.001 V, 0.002 V, 0.005 V, 0.01 V, 0.1 V, 0.5 V and 1 V at room temperature (296 K). Transient current was analyzed by means of time series analysis in order to identify different conduction regimes. The maximal Lyapunov exponents for the transient currents were calculated. Positive maximal Lyapunov exponents reflected electric field dependence with positive Lyapunov exponents. Existence of a positive Lyapunov exponent means sensitive dependence on initial conditions and As2Te3(In) is known to have memory effects hence different initial conditions for each dc current measurement. Detrended Fluctuation Analysis was utilized to characterize the behavior of dc current time series which is invariant to initial conditions. Detrended Fluctuation Analysis identified three different conduction regimes with multiple conduction mechanisms. © 2018 Elsevier B.V.

An experimental investigation on the self-excited spiky oscillations in a glow discharge plasma device is presented. The system showed a continuous transition from chaotic bursting to chaotic spiking states with the increase in the applied discharge voltage at a particular pressure. Below a threshold discharge voltage, the system exhibits a fixed point dynamical behaviour and with the increase in the discharge voltage bursting type oscillations appear which are identified as “fold/fold circle” type. The occurrence of the relaxation type spiky oscillations is attributed to the formation and disruption of anode double layer. The burst phases occurred intermittently and the frequency of their occurrence increased with increase in the discharge voltage and finally the oscillation turned into spiking behaviour. The intermittent oscillations manifested the scaling law of the average laminar phase with respect to the change in the discharge voltage. The scaling law of the intermittent oscillations was similar to type III intermittency. During the transition, the system changes its behaviour from long range correlation to long range anti correlation. Detrended fluctuation analysis technique has been used to identify the nature of long range correlations. We found that bursting oscillations show scale invariant, long-range correlation behaviour whereas spiking oscillations show scale invariant, long range anti correlation behaviour.

Covid-19 is a dangerous communicable virus which lets down the world economy. Severe respiratory syndrome SARS-COV-2 leads to Corona Virus Disease (COVID-19) and has the capability of transmission through human-to-human and surface-to-human transmission leads the world to catastrophic phase. Computational system based biological signal analysis helps medical officers in handling COVID-19 tasks like ECG monitoring at Intensive care, fatal ventricular fibrillation, etc., This paper is on diagnosing heart dysfunctions such as tachycardia, bradycardia, ventricular fibrillation, cardiac arrhythmia using fuzzy relations and artificial intelligence algorithm. In this study, the heart pulse base signal and features like spectral entropy, largest lyapunov exponent, Poincare plot and detrended fluctuation analysis are extracted and presented for classification purpose. The RR intervals of Poincare plot summarize RR time series obtained from an ECG in one picture, and a time interval quantities derives information duration of HRV. This analysis eases the prediction of heart rate fluctuation due to Covid or other heart disorders. The better accuracy level in diagnosing heart pulse irregularity using Artificial Neural network(ANN) is an integer value (0 to 4)but for Fuzzy Classifier, it is 0.8 to 0.9.The processing time for analyzing heart dysfunctionalties is 0.05 s using ANN which is far better than Fuzzy classifier.

Music therapy is a frequently used tool to treat cardiac and neurological diseases. It has been proven that music impacts human body as well as mind. The reason behind such impact of music on humans is because of the release of a chemical agent inside the brain known as dopamine also known as the happy hormone. Autonomic Nervous System (ANS) is reactive to the chemical stimuli which comprises of sympathetic and parasympathetic nerves. In this paper, we present the effect of Bengali folk music on ANS. The signals were taken while the subject is listening to music and also during normal resting condition. In time series analysis, multifractal detrended fluctuation analysis (MF-DFA) is used for determining the statistical self-affinity and highly chaotic behavior of a signal. Multifractal detrended fluctuation analysis is used as a quantifying parameter to detect the effect of Bengali folk music on ANS. Our experimental result shows a satisfactory result in this context.

The objective of this work is to analyze the scaling behavior of wind speed in the region of the state of Bahia, northeastern Brazil, in search of long-range correlations and other information about the crossover phenomena. Thus, data from 41 automatic surface stations were used for a period of five years—between 2015 and 2020—for onshore reading. For offshore readings, data from a surface station located in the Abrolhos Archipelago were used. To achieve this goal, the DFA (detrended fluctuation analysis) technique was used in the analysis of measured data at the stations, along with numerical simulations using the WRF (weather research and forecasting) mesoscale model. The results of the analysis of hourly average wind speed from the measured and simulated data show the existence of scale behavior with the appearance, in most cases, of a double crossover—onshore and offshore. This suggests the phenomenon's dependence on the time period of the analyzed data, and also on the geographic location, showing a strong correlation with the Atlantic and Pacific oscillations (La Nina and El Nino), indicating the influence of local, mesoscale, and macroscale effects in the region of study. For the offshore case, the measured data and simulations presented a subdiffusive behavior ( α ≥ 1 ) before the first crossover, and persistence ( 0.5 α 1 ) for the other two scales. For the onshore case, the results showed different behaviors, with some stations and simulations showing subdiffusive behavior and others showing persistence before and after the first and second crossovers, but most showed persistence between the first and second crossovers. The results of the analysis of daily averages of station data and simulations confirm the existence of only one crossover as a reflection of global effects (macroscale), since local effects have a daily cycle (mesoscale). The DFA method does not detect fluctuations in the measured and simulated data at all locations—especially in regions with extreme slopes, or in lowland plains—as double crossover, and in a few cases even simple crossovers are not recorded. From a practical point of view, unlike other methods to detect wind persistence, the methodology considered in this study reveal the multifractality in the wind speed data, showing that fluctuations in wind speed can be dominated by atmospheric phenomena governed by a local or regional meteorological system, while fluctuations on long-range time scales in some locations can be influenced by global weather patterns, providing new perspectives about the best locations for wind energy.

Numerous previous studies have proved the enormous potential of high frequency EEG in emotion recognition, however, the current existing EEG analytic methods are not so effective when dealing with high frequency oscillations. Therefore, a novel refined-detrended fluctuation analysis method multi-order detrended fluctuation analysis (MODFA) was proposed. The best fitting order is selected according to the inflection point in the dependence degree curve of high frequency EEG and multi-order polynomial. MODFA measures the power-law long-range correlation of high frequency nonlinear signals. Prefrontal EEG signals were recorded during six emotion-inducing tasks (neutral, fear, sad, happy, anger, and disgust). To confirm the susceptibility and efficiency of MODFA indices, including hurst-exponent MODFA-h1 and intercept MODFA-a1, on emotion recognition, we compared MODFA with original detrended fluctuation analysis, as well as the conventionally used fuzzy entropy (FE) and power spectral density (PSD) on high frequency EEG oscillations (62.50–93.75 Hz). The results showed that MODFA achieved the best performance in binary emotion classification (positive and negative, accuracy = 96.81%), ternary classification (neutral, positive, and negative, accuracy = 76.39%), and six-classification (accuracy = 42.17%). Moreover, along with inducing time, the cumulative effects of the four negative emotions (fear, sad, anger, and disgust) were observed by MODFA-a1, FE, and PSD, which demonstrated that the accumulation of negative emotions are associated with the prefrontal lobe and could be measured via high frequency gamma rhythms. These findings indicated the nonlinear dynamics of high frequency brain activity during emotion induction, and the prefrontal EEG-based emotion recognition might have great application prospect in real-life practice.

This work innovates by proposing the combination of DFA with the SVM and RBFK methods, two supervised algorithms that use the kernel-method, for the imbalance level classification in a scaled-down wind turbine. The results obtained were compared with other techniques proposed in previous works. The vibration signals analyzed were acquired under certain work conditions, and it is possible grouping them into 3 or 7 categories. It is worth mentioning that the dataset examined here is composed of the same signals used by previous works aiming at comparing results. The aforecited kernel-methods (Support Vector Machine and Radial Basis Function Kernel) classified, with a high success rate, the output of detrended fluctuation analysis (DFA) of vibration signals according to their respective working conditions. In the classification of three major classes, the performance achieved by both classifiers reduces with the increase in the rotation speed. The best average success rates reached at 900 rpm, 1200 rpm and 1500 rpm were, respectively, 99.96% by RBFK, 99.24% by RBFK and 98.73% by SVM. For seven imbalance levels, both classifiers showed the best performance at 900 rpm again. In this case, the best rates reached 98.83% by RBFK. At 1200 and 1500 rpm, the rates are slightly different.

The possibility of distinguishing between different types of complex oscillations using datasets contaminated with measurement noise is studied based on multiresolution wavelet analysis (MWA). Unlike the conventional approach, which characterizes the differences in terms of standard deviations of detail wavelet coefficients at independent resolution levels, we consider ways to improve the separation between complex motions by applying several measures for the decomposition coefficients. We show that MWA’s capabilities in diagnosing dynamics can be expanded by applying detrended fluctuation analysis (DFA) to sets of detail wavelet coefficients or by computing the excess of the probability density function of these sets.

Based on the detrended fluctuation analysis (DFA), we address the problem of recognizing the electrical activity of the brain associated with movements of the right arm and the imagination of this procedure. In experiments with untrained volunteers, we show the possibility to distinguish between the related EEG patterns. We also demonstrate significant distinctions in the scaling features between background records and EEG signals associated with mental intentions that can be transformed to control commands for brain–computer interfaces. This effect is observed in many EEG channels, although individual features of subjects provided various distributions of brain areas with the most prominent differences.

Broadband power line communications (PLC) is considered to be one of the most promising technologies to fulfill data transmission in smart grids. To understand PLC signal characteristics and overcome the shortcomings of traditional statistical properties, the mono-fractal and multi-fractal theories are introduced to understand the self-similarity characteristics of the PLC signals. Four common methods, namely, rescaled range analysis, variance-time plot method, periodic diagram analysis and wavelet-based method are used to study the nonlinear properties. Fractal analysis at different frequencies and times are also performed to verify further. The results reveal self-similarity of the PLC signals. Besides the mono-fractal properties, the paper tests the multi-fractal properties of PLC signals by the means of multi-fractal detrended fluctuation analysis (MFDFA). We estimated the multi-fractal spectrum of power low exponents from the measured PLC signals. We also proposed a new algorithm to improve the traditional MFDFA, where wavelet theory is integrated.

We study the scaling features in the evolutionary dynamics of two coupled chaotic systems based on the sequences of return times into a Poincare section, contaminated with additive (measuring) noise. Using three models of chaotic systems: the Rossler oscillator, the Lorenz system, and the nephron model, and the detrended fluctuation analysis (DFA) as an approach for data processing, we demonstrate that the anti-correlated sequences of return times of synchronous motions show a higher sensitivity to measuring noise than the positively correlated series of return times of asynchronous oscillations. This conclusion is confirmed by the results for various oscillatory regimes in all models considered.

Investigating the dynamics of long-term memory in online rating behaviors is significant for understanding the evolution mechanism of collective behaviors and trust formation for online social networks. Since users are allowed to deliver ratings in many online systems, ratings can well reflect the user’s opinions. In this paper, we empirically investigate the long-term memory, measured by the Detrended Fluctuation Analysis, in collective rating behaviors before and after the trust formation. The results for the Epinions data set show that, comparing with the null model generated by the reshuffle process, the Hurst exponent of trustors (trustees) decreases 7.12% (9.05%) before and increases 7.36% (9.20%) after trust formation, which stably remains close to 0.5 in null model I and 0.6 in null model II, suggesting that the collective rating behavior plays an important role for the trust formation. Furthermore, we divide users into 8 groups according to the user degree and find that the correlation of the user degree and the variation of Hurst exponent, measured by the Pearson Correlation Coefficient, is 0.8629 and 0.8620 before and after trust formation respectively, reflecting a significant correlation between user degrees and collective rating behavior patterns. Finally, we select the users without creating other trust relations around the trust formation time and the result suggests that the collective rating behaviors indeed change for the trust formation. This work helps deeply understand the intrinsic feedback effects between collective behaviors and trust relationship.

Detrended fluctuation analysis (DFA) is a standard method to evaluate long-range correlations embedded in non-stationary time series. To obtain a reliable estimation of scaling behavior, it requires the length of a time series is long enough (at least ∼ 10 , 000 ), which is not always the case in reality. How to evaluate long-range correlation behavior in a very short time series is still an open problem. In the present paper, we propose an improvement of DFA by correcting the bias in estimation of variance, called Unbiased Detrended Fluctuation Analysis (UDFA). Extensive calculations show its high-performance. For instance, from a fractional Brownian motion (fBm) series with length 500 the estimated long-range correlation exponent has negligible bias and acceptable confidence region (standard deviation less than 0.05). As a typical example, the proposed method is used to monitor evolution of fractal gait rhythm of a volunteer. Rich patterns are found in the evolutionary process.

In the recent past, coronal mass ejection (CME) has received much research attention for its geo-effectiveness. In this paper, an investigation has been made to identify the scaling pattern of the CME linear speed time series data (February 1999 to December 2007 of solar cycle 23) collected from the Solar and Heliospheric Observatory (SOHO) using Multi-Fractal Detrended Fluctuation Analysis (MFDFA) and Multi-Fractal Detrended Moving Average (MFDMA) method. The scaling exponent, generalized Hurst exponent, singularity strength and also the singularity spectrum have been computed to quantify the multifractality and to identify the singularities of the time series data. An effort has also been made to find out the possible sources which are responsible for the multifractality in the signal by studying the scaling patterns of the shuffled and surrogate version of the original data. It has been revealed in this paper that CME linear speed signal exhibit multifractal behaviour with long-term persistence. Both the long-range temporal correlation and the broad probability density function (pdf) are found to be the primary source of multifractality in the signal. The singularities or abruptness present in the signal are found to vary with time, and this fluctuation follows an AR (2) model.

This study empirically compares the development of China’s interest rate market in the past decade. The yield of Shibor market from 2006 to 2016 showed anti-persistence, and the later five-year trend was stronger than that in the previous half period, indicating a significantly growing trend of China’s interest rate market. We perform a comparative analysis of detrended fluctuation analysis (DFA), detrending moving average (DMA) algorithm, and the maximum overlap wavelet transform (DFA-MODWT) using grey and original sequences. The autoregressive integrated moving average model is adopted to generate set-point H sequences. Results illustrated that 1) for original sequences, both the DFA-MODWT and DMA ( θ = 0 . 5 ) shows outstanding performances when the set Hurst exponents are 0.6 and 0.7 and 0.8 and 0.9, respectively. 2) For grey sequences, G-DFA performs best among the three methods, followed by G-DMA and G-DFA-MODWT. 3) The long-range correlation of the original sequences is slightly lower than the set values. On the contrary, the long-range correlation of grey sequences is much higher than the set values. Thus, the grey sequence exerts a strong aggregation effect as it can accumulate the trend of the sequence. Our results show that the grey sequence can determine the regular pattern from the messy sequence. However, grey sequences tend to be overly analyzed and misleading when large volumes of data are involved. Empirical studies confirm that China’s interest rate market remains an inefficient market.

In this article, we explore the dynamics of memory and the correlation structure in investor attention. Information on whether a time series is a pure noise or has a short or long range memory is important for predictive modelling of the series and analyzing its relationship with other variables. Existing studies on time series memory of stock variables are limited to price, volume, returns and conditional variance of returns. We carry out an in depth analysis to understand the dependence structure of stock’s investor attention time series (IATS) for energy market. In this process, we first investigate the existence of correlated dependence in IATS and analyze its dynamics using detrended fluctuation analysis. Further, we check how this dependence changes a) with frequency of sampled data b) during volatility clustering periods of price and volume of underlying stocks. Finally, we perfom detrended cross correlation analysis on local and global IATS to find any cross correlation dependence between the two. We use relative search query volume in Google to quantify IATS for a particular stock and analyze top 20 energy companies based on their market capitalization. The obtained detrended fluctuation coefficients for stock’s IATS differ significantly from 0.5 indicating the existence of memory in the series. The dynamics of this memory exhibits persistent and mean reverting behavior. We also observed a reasonably high positive cross correlation dependence between local and global IATS. Finally we find that volatility clustering has little effect on dependence structure of investor attention time series. We also include a few examples to illustrate practical implications of these results.

The relationship between ozone and its main precursors exhibits complex non-linear feature in the atmospheric photochemical system. Therefore, sophisticated mathematical and nonlinear methods are very important for studying the O3 sensitivity to its precursors and improving the O3 prediction model. In this study, the coupling detrended fluctuation analysis (CDFA) method has been used to investigate the multi-temporal scaling pattern of coupling correlations between O3 and its precursors. Hourly concentrations of ozone (O3), nitrogen oxide (NOx) and non-methane hydrocarbons (NMHCs) from 1 March 2016 to 28 February 2017 of two traffic monitoring sites in Taiwan are analyzed. Coupling multifractality features are confirmed in the temporal distribution of coupling correlations between O3 and its precursors. And the sources of coupling multifractal features are investigated by the phase randomized surrogates and the shuffling procedures. Moreover, in order to confirm the ozone sensitivity to its precursors at different time scales, a novel dynamical index, namely the coupling sensitivity degree (CSD), is introduced based on CDFA method. High temporal scale resolution of the O3-NMHCs-NOx sensitivity is presented based on the concept of sliding window. And the O3-NMHCs-NOx sensitivity regime can be shown visually by the temporal evolutions of the CSD on the whole year. Furthermore, statistics of seasonal CSD values are obtained by averaging the hourly sliding values. Result shows that the CSD values for both NMHCs and NOx are greatest in summer due to the more active photochemical reaction, compared to the other seasons. Meanwhile, the photochemical system is more sensitive to NMHCs for the two sites, which is consistent with the characteristics of pollutant emissions in the urban traffic area. At last, the diurnal pattern of the CSD for NMHCs and NOx are investigated. It is found that the greatest CSD for both NMHCs and NOx series are synchronized to the maximum O3 generation. This study provides a feasible and effective dynamical index to describe O3-NOx-NMHCs sensitivity, and suggests a new approach to improve the ozone prediction models in the photochemical system.

Structure health monitoring of composite structures is essential for safety assurance and attracted more attention in recent years. In this paper, a low velocity impact (LVI) monitoring system based on detrended fluctuation analysis (DFA) and centroid localization algorithm is proposed. First, the distance from the LVI to neighboring FBG sensors can be estimated by analyzing the Hurst exponents calculated from response signal of LVI with different distance to monitoring FBG sensors by DFA. Then, the LVI location can be determined by region identification algorithm and centroid localization algorithm. To verify the performance of the proposed LVI monitoring system, a LVI localization system using optical fiber Bragg grating (FBG) sensor was constructed and validated on a CFRP plate with 240 mm*240 mm*3 mm experiment area. The experiment results showed that the average error of localization was 31.5 mm. The proposed localization method based on DFA and centroid localization algorithm demonstrates an effective means of LVI localization.

International audience; Gastrointestinal nematodes are known to be one of the most economically important parasites in livestock production. In order to test whether fractal analysis of behaviour can be used as a diagnostic tool for detection of infected animals, we investigated fractal patterns in the behavioural activity of domestic sheep (Ovis aries) in relation to strongylid infection. Temporal dynamics in activity patterns of 20 sheep were recorded at high resolutions using tri-axial accelerometer loggers attached to the neck of naturally infected subjects. We measured fractal dynamics in the resultant acceleration time series, divided into periods of activity and inactivity, using several fractal methods and tested the prediction that temporal complexity in the activity patterns of infected control sheep and experimentally dewormed sheep should differ. Detrended fluctuation analysis (DFA) revealed that sheep behaviour sequences were characterized by long-range correlations, meaning that acceleration fluctuations are not random but depend on long-term activity events. Generalized linear mixed models built to test for the effect of deworming on fractal estimates showed that the temporal organization of sheep activity varies with the status of strongylid infection. Our results indicate that sheep treated with anthelmintics exhibited a higher complexity in their activity sequences than parasitized sheep, suggesting that organizational patterns of their behaviour change with gastrointestinal parasite infection. Thus, we provide evidence for the potential utility of fractal methods in behavioural welfare monitoring.

In recent years, complex models of cardiac regulation have integrated heart rate variability (HRV) as a measure of the cardiac autonomic activity during exercise. Using detrended fluctuation analysis (DFA) technique, the present study examines the influence of cycling cadence and exercise duration on non-linear dynamics of HRV. Sixteen trained cyclists performed a 60-minute exercise bout at 90% of the individual anaerobic threshold on a bicycle ergometer. Cadence was changed every 10 min (90–120–60–120–60–90 rpm). Heart rate (HR) and RR-intervals were recorded continuously during exercise. HRV time domain measures (meanRR, SDNN) and correlation properties were analyzed using short-term scaling exponent alpha1 of DFA. Moreover, blood lactate (La) and rating of perceived exertion (RPE) were recorded at regular intervals at the end of condition. HR, La and RPE increased significantly at 120 rpm compared to 60 rpm. In contrast, all analyzed HRV parameters (meanRR, SDNN, DFA-alpha1) showed a significant decrease during cycling at 120 rpm compared to 60 rpm. The comparison of the first and last 10 min with the same cadence indicates a significant increase in HR and RPE, but also a significant decrease in all analyzed HRV measures. The decrease of HRV values over time and in relation to the increase in cadence indicates a decrease in the overall variability as well as a reduction in complexity of the RR-interval-fluctuations due to the increased organismic demands. Therefore, the decrease of DFA-alpha1 might be associated with a withdrawal of the organismic system aiming at the maintenance of the homeostasis under the control of the central nervous system. In this context, non-linear HRV analyses provide a more systemic view of cardiac regulation during exercise.

Autoregressive models are commonly used for modeling time-series from nature, economics and finance. This work explored simple autoregressive AR ( p ) models to remove long-term trends in detrended fluctuation analysis (DFA). Crude oil prices and bitcoin exchange rate were considered, with the former corresponding to a mature market and the latter to an emergent market. Results showed that AR ( p ) -based DFA performs similar to traditional DFA. However, the former DFA provides information on stability of long-term trends, which is valuable for understanding and quantifying the dynamics of complex time series from financial systems.

The wind speed persistence is an important factor in the assessment of wind energy potential. In this paper, we explore the persistence of Mean Wind Speed (MWS) with many years of record using Detrended Fluctuation Analysis (DFA) over China. The results illustrate that there exist irregular high-frequency fluctuations for daily MWS anomaly records. Long-term persistence of MWS is found for all meteorological observed sites. We also make some numerical tests in order to verify the significance of long-term persistence by shuffling the data records many times. These facts prove that the MWS anomaly records have long-term persistence over all the stations in China. The mean value 0.64 in DFA-exponents for all stations over China is also obviously higher than the value 0.53 according to interval threshold of 95% confidence level after shuffling the MWS records many times. In addition, the values of scaling exponent vary from station to station over China. Long-term persistence of MWS in spatial distributions seems to be downward trends from east to west China. Many factors may affect long-term persistence of MWS such as southwest monsoon, Tibetan Plateau landform and atmosphere–ocean–land interaction and so on. Possible physical mechanism need further analysis in the future.

Basketball is one of the favourite sports in the United States and NBA the most popular basketball league in the world, followed not only by Americans but by fans everywhere. At present, people are increasingly interested in betting on sports in general and on basketball in particular. So analysis of trends in the results could be important for gamblers. In this paper, detrended fluctuation analysis is applied to 28 NBA teams, in order to understand if their results have (or not) any kind of memory. Our results show that all the teams are persistent in their results. Nevertheless, some teams have higher persistence than others, which could be important for gamblers in deciding how to bet.

Human locomotion is an inherently complex activity that requires the coordination and control of neurophysiological and biomechanical degrees of freedom across various spatiotemporal scales. Locomotor patterns must constantly be altered in the face of changing environmental or task demands, such as heterogeneous terrains or obstacles. Variability in stride times occurring at short time scales (e.g., 5–10 strides) is statistically correlated to larger fluctuations occurring over longer time scales (e.g., 50–100 strides). This relationship, known as fractal dynamics, is thought to represent the adaptive capacity of the locomotor system. However, this has not been tested empirically. Thus, the purpose of this study was to determine if stride time fractality during steady state walking associated with the ability of individuals to adapt their gait patterns when locomotor speed and symmetry are altered. Fifteen healthy adults walked on a split-belt treadmill at preferred speed, half of preferred speed, and with one leg at preferred speed and the other at half speed (2:1 ratio asymmetric walking). The asymmetric belt speed condition induced gait asymmetries that required adaptation of locomotor patterns. The slow speed manipulation was chosen in order to determine the impact of gait speed on stride time fractal dynamics. Detrended fluctuation analysis was used to quantify the correlation structure, i.e., fractality, of stride times. Cross-correlation analysis was used to measure the deviation from intended anti-phasing between legs as a measure of gait adaptation. Results revealed no association between unperturbed walking fractal dynamics and gait adaptability performance. However, there was a quadratic relationship between perturbed, asymmetric walking fractal dynamics and adaptive performance during split-belt walking, whereby individuals who exhibited fractal scaling exponents that deviated from 1/f performed the poorest. Compared to steady state preferred walking speed, fractal dynamics increased closer to 1/f when participants were exposed to asymmetric walking. These findings suggest there may not be a relationship between unperturbed preferred or slow speed walking fractal dynamics and gait adaptability. However, the emergent relationship between asymmetric walking fractal dynamics and limb phase adaptation may represent a functional reorganization of the locomotor system (i.e., improved interactivity between degrees of freedom within the system) to be better suited to attenuate externally generated perturbations at various spatiotemporal scales.

In this paper we investigate the evolution of the energy emitted by CO2 and NO from the Earth's thermosphere on a global scale using both observational and empirically derived data. In the beginning, we analyze the daily power observations of CO2 and NO received from the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) equipment on the NASA Thermosphere-Ionosphere-Mesosphere Energetics and Dynamics (TIMED) satellite for the entire period 2002–2016. We then perform the same analysis on the empirical daily power emitted by CO2 and NO that were derived recently from the infrared energy budget of the thermosphere during 1947–2016. The tool used for the analysis of the observational and empirical datasets is the detrended fluctuation analysis, in order to investigate whether the power emitted by CO2 and by NO from the thermosphere exhibits power-law behavior. The results obtained from both observational and empirical data do not support the establishment of the power-law behavior. This conclusion reveals that the empirically derived data are characterized by the same intrinsic properties as those of the observational ones, thus enhancing the validity of their reliability.

Background and Objective Depressive disorder is one of the leading causes of burden of disease today and it is presumed to take the first place in the world in 2030. Early detection of depression requires a patient-friendly inexpensive method based on easily measurable objective indicators. This study aims to compare various single-channel electroencephalographic (EEG) measures in application for detection of depression. Methods The EEG recordings were performed on a group of 13 medication-free depressive outpatients and 13 gender and age matched controls. The recorded 30-channel EEG signal was analysed using linear methods spectral asymmetry index, alpha power variability and relative gamma power and nonlinear methods Higuchi's fractal dimension, detrended fluctuation analysis and Lempel-Ziv complexity. Classification accuracy between depressive and control subjects was calculated using logistic regression analysis with leave-one-out cross-validation. Calculations were performed separately for each EEG channel. Results All calculated measures indicated increase with depression. Maximal testing accuracy using a single measure was 81% for linear and 77% for nonlinear measures. Combination of two linear measures provides the accuracy of 88% and two nonlinear measures of 85%. Maximal classification accuracy of 92% was indicated using mixed combination of three linear and three nonlinear measures. Conclusions The results of this preliminary study confirm that single-channel EEG analysis, employing the combination of measures, can provide discrimination of depression at the level of multichannel EEG analysis. The performed study shows that there is no single superior measure for detection of depression.

Prolonged walking could alter postural control leading to an increased risk of falls in older adults. The aim of this study was to determine the effect of level and uphill prolonged walking on the postural control of older adults. Sixteen participants (64 ± 5 years) attended 3 visits. Postural control was assessed during quiet standing and the limits of stability immediately pre, post and post 15 min rest a period of 30 min walking on level and uphill (5.25%) gradients on separate visits. Each 30 min walk was divided into 3 10 min blocks, the limits of stability were measured between each block. Postural sway elliptical area (PRE: 1.38 ± 0.22 cm2, POST: 2.35 ± 0.50 cm2, p = .01), medio-lateral (PRE: 1.33 ± 0.03, POST: 1.40 ± 0.03, p = .01) and anterio-posterior detrended fluctuation analysis alpha exponent (PRE: 1.43 ± 0.02, POST: 1.46 ± 0.02, p = .04) increased following walking. Medio-lateral alpha exponent decreased between post and post 15 min’ rest (POST: 1.40 ± 0.03, POST15: 1.36 ± 0.03, p = .03). Forward limits of stability decreased between the second walking interval and post 15 min’ rest (Interval 2: 28.1 ± 1.6%, POST15: 25.6 ± 1.6%, p = .01) and left limits of stability increased from pre-post 15 min’ rest (PRE: 27.7 ± 1.2%, POST15: 29.4 ± 1.1%, p = .01). The neuromuscular alterations caused by prolonged walking decreased the anti-persistence of postural sway and altered the limits of stability in older adults. However, 15 min’ rest was insufficient to return postural control to pre-exercise levels.

Detrended fluctuation analysis (DFA) is an effective method to accurately quantify long-term correlations embedded in a nonstationary time series. In this paper, we study the effect of signal filtering of a signal on the DFA method. The theoretical and simulated results show that the signal filtering will affect the range of scale in DFA. Moreover, this effect is different for fractal Gaussian noise series and fractal Brown movement series. Our study is meaningful for improving accuracy and efficiency of DFA method in theory and practice.

This study investigates the nonlinear dynamics of the stratospheric ozone layer at Pakistan atmospheric region. Ozone considered now the most important issue in the world because of its diverse effects on earth biosphere, including human health, ecosystem, marine life, agriculture yield and climate change. Therefore, this paper deals with total monthly time series data of stratospheric ozone over the Pakistan atmospheric region from 1970 to 2013. Two approaches, basic statistical analysis and Fractal dimension (D) have adapted to study the nature of nonlinear dynamics of stratospheric ozone level. Results obtained from this research have shown that the Hurst exponent values of both methods of fractal dimension revealed an anti-persistent behavior (negatively correlated), i.e. decreasing trend for all lags and Rescaled range analysis is more appropriate as compared to Detrended fluctuation analysis. For seasonal time series all month follows an anti-persistent behavior except in the month of November which shown persistence behavior i.e. time series is an independent and increasing trend. The normality test statistics also confirmed the nonlinear behavior of ozone and the rejection of hypothesis indicates the strong evidence of the complexity of data. This study will be useful to the researchers working in the same field in the future to verify the complex nature of stratospheric ozone.