Search

Abstract Accelerometers, devices that measure body movements, have become valuable tools for studying the fragmentation of rest-activity patterns, a core circadian rhythm dimension, using metrics such as inter-daily stability (IS), intradaily variability (IV), transition probability (TP), and self-similarity parameter (named $$\alpha$$ α ). However, their use remains mainly empirical. Therefore, we investigated the mathematical properties and interpretability of rest-activity fragmentation metrics by providing mathematical proofs for the ranges of IS and IV, proposing maximum likelihood and Bayesian estimators for TP, introducing the activity balance index (ABI) metric, a transformation of $$\alpha$$ α , and describing distributions of these metrics in real-life setting. Analysis of accelerometer data from 2,859 individuals (age=60-83 years, 21.1% women) from the Whitehall II cohort (UK) shows modest correlations between the metrics, except for ABI and $$\alpha$$ α . Sociodemographic (age, sex, education, employment status) and clinical (body mass index (BMI), and number of morbidities) factors were associated with these metrics, with differences observed according to metrics. For example, a difference of 5 units in BMI was associated with all metrics (differences ranging between -0.261 (95% CI -0.302, -0.220) to 0.228 (0.18, 0.268) for standardised TP rest to activity during the awake period and TP activity to rest during the awake period, respectively). These results reinforce the value of these rest-activity fragmentation metrics in epidemiological and clinical studies to examine their role for health. This paper expands on a set of methods that have previously demonstrated empirical value, improves the theoretical foundation for these methods, and evaluates their empirical use in a large dataset.

Understanding the complex dynamics of heart rate variability (HRV) during pregnancy is crucial for monitoring both maternal well-being and fetal health. In this study, we use the Multifractal Detrended Fluctuations Analysis approach to investigate HRV patterns in pregnant individuals during sleep based on RR interval maxima (MM fluctuations). In addition, we study the type of multifractality within MM fluctuations, that is, if it arises from a broad probability density function or from varying long-range correlations. Furthermore, to provide a comprehensive view of HRV changes during sleep in pregnancy, classical temporal and spectral HRV indices were calculated at quarterly intervals during sleep. Our study population consists of 21 recordings from nonpregnant women, 18 from the first trimester (early-pregnancy) and 18 from the second trimester (middle-pregnancy) of pregnancy. Results. There are statistically significant differences (p-value < 0.05) in mean heart rate, rms heart rate, mean MM fluctuations, and standard deviation of MM fluctuations, particularly in the third and fourth quarter of sleep between pregnant and non-pregnant states. In addition, the early-pregnancy group shows significant differences (p-value < 0.05) in spectral indices during the first and fourth quarter of sleep compared to the non-pregnancy group. Furthermore, the results of our research show striking similarities in the average multifractal structure of MM fluctuations between pregnant and non-pregnant states during normal sleep. These results highlight the influence of different long-range correlations within the MM fluctuations, which could be primarily associated with the emergence of sleep cycles on multifractality during sleep. Finally, we performed a separability analysis between groups using temporal and spectral HRV indices as features per sleep quarter. Employing only three features after Principal Component Analysis (PCA) to the original feature set, achieving complete separability among all groups appears feasible. Using multifractal analysis, our study provides a comprehensive understanding of the complex HRV patterns during pregnancy, which holds promise for maternal and fetal health monitoring. The separability analysis also provides valuable insights into the potential for group differentiation using simple measures such as mean heart rate, rms heart rate, and mean MM fluctuations or in the transformed feature space based on PCA.

Ultra-low frequency (ULF) geomagnetic analysis is a robust method for earthquake (EQ) forecasting. We conducted a simultaneous study of EQ precursors around the western part of Java Island in 2020 using wavelet transform (WT) and detrended fluctuation analysis (DFA) methods. ULF geomagnetic data (March to December 2020, 16:00–21:00 UTC or 23.00–04.00 LT) from Lampung Selatan (LPS) geomagnetic station were used to assess the precursors. We analyzed four EQs with an epicenter distance (R) of around 100 km from LPS station and a magnitude (M) greater than 5 Mw. We analyzed changes in the SZ/SG values and α values from the WT and DFA analyses against the threshold (µ±2σ) to identify anomalies related to the EQs. The result showed that SZ/SG anomalies occurred simultaneously with a decrease in α values several weeks prior to probable source EQ when there was a very low geomagnetic activity (Dst ≤ -30 nT). The Mw5.4 (07/07/2020) EQ might be the main source that led to the appearance of the precursor since it had the highest magnitude and KLS values compared to others. The combined WT and DFA results showed anomalies 1.5–13 weeks before the Mw5.4 (07/07/2020) EQ. The results suggest that WT and DFA are suitable methods for detecting EQ precursors but more work is needed to link the precursors to specific EQs.

IntroductionSleep-wake cycle disruption caused by shift work may lead to cardiovascular stress, which is observed as an alteration in the behavior of heart rate variability (HRV). In particular, HRV exhibits complex patterns over different time scales that help to understand the regulatory mechanisms of the autonomic nervous system, and changes in the fractality of HRV may be associated with pathological conditions, including cardiovascular disease, diabetes, or even psychological stress. The main purpose of this study is to evaluate the multifractal-multiscale structure of HRV during sleep in healthy shift and non-shift workers to identify conditions of cardiovascular stress that may be associated with shift work.MethodsThe whole-sleep HRV signal was analyzed from female participants: eleven healthy shift workers and seven non-shift workers. The HRV signal was decomposed into intrinsic mode functions (IMFs) using the empirical mode decomposition method, and then the IMFs were analyzed using the multiscale-multifractal detrended fluctuation analysis (MMF-DFA) method. The MMF-DFA was applied to estimate the self-similarity coefficients, α(q, τ), considering moment orders (q) between –5 and +5 and scales (τ) between 8 and 2,048 s. Additionally, to describe the multifractality at each τ in a simple way, a multifractal index, MFI(τ), was computed.ResultsCompared to non-shift workers, shift workers presented an increase in the scaling exponent, α(q, τ), at short scales (τ < 64 s) with q < 0 in the high-frequency component (IMF1, 0.15–0.4 Hz) and low-frequency components (IMF2–IMF3, 0.04–0.15 Hz), and with q> 0 in the very low frequencies (IMF4, < 0.04 Hz). In addition, at large scales (τ> 1,024 s), a decrease in α(q, τ) was observed in IMF3, suggesting an alteration in the multifractal dynamic. MFI(τ) showed an increase at small scales and a decrease at large scales in IMFs of shift workers.ConclusionThis study helps to recognize the multifractality of HRV during sleep, beyond simply looking at indices based on means and variances. This analysis helps to identify that shift workers show alterations in fractal properties, mainly on short scales. These findings suggest a disturbance in the autonomic nervous system induced by the cardiovascular stress of shift work.

Integrating running gait coordination assessment into athlete monitoring systems could provide unique insight into training tolerance and fatigue-related gait alterations. This study investigated the impact of an overload training intervention and recovery on running gait coordination assessed by field-based self-testing. Fifteen trained distance runners were recruited to perform 1-week of light training (baseline), 2 weeks of heavy training (high intensity, duration, and frequency) designed to overload participants, and a 10-day light taper to allow recovery and adaptation. Field-based running assessments using ankle accelerometry and online short recovery and stress scale (SRSS) surveys were completed daily. Running performance was assessed after each training phase using a maximal effort multi-stage running test-to-exhaustion (RTE). Gait coordination was assessed using detrended fluctuation analysis (DFA) of a stride interval time series. Two participants withdrew during baseline training due to changed personal circumstances. Four participants withdrew during heavy training due to injury. The remaining nine participants completed heavy training and were included in the final analysis. Heavy training reduced DFA values (standardised mean difference (SMD) = −1.44 ± 0.90; p = 0.004), recovery (SMD = −1.83 ± 0.82; p less than 0.001), performance (SMD = −0.36 ± 0.32; p = 0.03), and increased stress (SMD = 1.78 ± 0.94; p = 0.001) compared to baseline. DFA values (p = 0.73), recovery (p = 0.77), and stress (p = 0.73) returned to baseline levels after tapering while performance trended towards improvement from baseline (SMD = 0.28 ± 0.37; p = 0.13). Reduced DFA values were associated with reduced performance (r2 = 0.55) and recovery (r2 = 0.55) and increased stress (r2 = 0.62). Field-based testing of running gait coordination is a promising method of monitoring training tolerance in running athletes during overload training.

Wearable emotion recogniton system is essential in identifying mental health disorders by early detection and continuous monitoring of human emotions to provide proper treatment care. Electrocardiogram (ECG) signals can be used for emotion recognition for its noninvasiveness and easy usability. In this study, Detrended Fluctuation Analysis (DFA) and Extreme Gradient Boost (XG Boost) classifier is used to classify the scary and boring emotion from the ECG signals. For this, ECG signal corresponding to these emotions are obtained from public database. The preprocessing is performed by adding the video IDs to the signal and annotating it. This preprocessed signal is subjected to DFA to understand the power-law correlations and similarity property. Further, from the power law correlations, features namely Hurst exponent and DFA intercept are extracted. These features are subjected to XG Boost classifier to differentiate the two emotions. Results shows that the log-log plot of power law correlation is linear in nature which indicates that ECG signals of both the emotions have long range correlations and self-similarity property. The extracted scaling exponent indicates variations between scary and boring with a mean and standard deviation of 0.81±0.13 and 0.68±0.07 respectively. Similarly, DFA intercept provides mean and standard deviation for scary and boring 0.15±0.06 and 0.17±0.07 respectively, showing less variability in the ECG signal. XG Boost classifier gives accuracy of 80.5% for classifying scary and boring emotion. Thus, the proposed approach can be used for wearable emotion recognition system to differentiate scary and boring emotion.

Riemannian geometry-based classification (RGBC) gained popularity in the field of brain-computer interfaces (BCIs) lately, due to its ability to deal with non-stationarities arising in electroencephalography (EEG) data. Domain adaptation, however, is most often performed on sample covariance matrices (SCMs) obtained from EEG data, and thus might not fully account for components affecting covariance estimation itself, such as regional trends. Detrended cross-correlation analysis (DCCA) can be utilized to estimate the covariance structure of such signals, yet it is computationally expensive in its original form. A recently proposed online implementation of DCCA, however, allows for its fast computation and thus makes it possible to employ DCCA in real-time applications. In this study we propose to replace the SCM with the DCCA matrix as input to RGBC and assess its effect on offline and online BCI performance. First we evaluated the proposed decoding pipeline offline on previously recorded EEG data from 18 individuals performing left and right hand motor imagery (MI), and benchmarked it against vanilla RGBC and popular MI-detection approaches. Subsequently, we recruited eight participants (with previous BCI experience) who operated an MI-based BCI (MI-BCI) online using the DCCA-enhanced Riemannian decoder. Finally, we tested the proposed method on a public, multi-class MI-BCI dataset. During offline evaluations the DCCA-based decoder consistently and significantly outperformed the other approaches. Online evaluation confirmed that the DCCA matrix could be computed in real-time even for 22-channel EEG, as well as subjects could control the MI-BCI with high command delivery (normalized Cohen's κ: 0.7409 ± 0.1515) and sample-wise MI detection (normalized Cohen's κ: 0.5200 ± 0.1610). Post-hoc analysis indicated characteristic connectivity patterns under both MI conditions, with stronger connectivity in the hemisphere contralateral to the MI task. Additionally, fractal scaling exponent of neural activity was found increased in the contralateral compared to the ipsilateral motor cortices (C4 and C3 for left and right MI, respectively) in both classes. Combining DCCA with Riemannian geometry-based decoding yields a robust and effective decoder, that not only improves upon the SCM-based approach but can also provide relevant information on the neurophysiological processes behind MI.

IntroductionMental disorders are a significant concern in contemporary society, with a pressing need to identify biological markers. Long-range temporal correlations (LRTC) of brain rhythms have been widespread in clinical cohort studies, especially in major depressive disorder (MDD). However, research on LRTC in obsessive-compulsive disorder (OCD) is severely limited. Given the high co-occurrence of OCD and MDD, we conducted a comparative LRTC investigation. We assumed that the LRTC patterns will allow us to compare measures of brain cortical balance of excitation and inhibition in OCD and MDD, which will be useful in the area of differential diagnosis.MethodsIn this study, we used the 64-channel resting state EEG of 29 MDD participants, 26 OCD participants, and a control group of 37 volunteers. Detrended fluctuation analyzes was used to assess LRTC.ResultsOur results indicate that all scaling exponents of the three subject groups exhibited persistent LRTC of EEG oscillations. There was a tendency for LRTC to be higher in disorders than in controls, but statistically significant differences were found between the OCD and control groups in the entire frontal and left parietal occipital areas, and between the MDD and OCD groups in the middle and right frontal areas.DiscussionWe believe that these results indicate abnormalities in the inhibitory and excitatory neurotransmitter systems, predominantly affecting areas related to executive functions.

Stroke patients often show postural instability. The patellar tendon reflex is a basic physical examination for stroke patients. This study aimed to explore the correlation between patellar tendon reflex grade and postural stability among stroke patients.

Aerobic and anaerobic thresholds of the three-zone exercise model are often used to evaluate the exercise intensity and optimize the training load. Conventionally, these thresholds are derived from the respiratory gas exchange or blood lactate concentration measurements. Here, we introduce and validate a computational method based on the RR interval (RRI) dynamics of the heart rate (HR) measurement, which enables a simple, yet reasonably accurate estimation of both metabolic thresholds. The method utilizes a newly developed dynamical detrended fluctuation analysis (DDFA) to assess the real-time changes in the dynamical correlations of the RR intervals during exercise. The training intensity is shown to be in direct correspondence with the time- and scale-dependent changes in the DDFA scaling exponent. These changes are further used in the definition of an individual measure to estimate the aerobic and anaerobic threshold. The results for 15 volunteers who participated in a cyclo-ergometer test are compared to the benchmark lactate thresholds, as well as to the ventilatory threshods and alternative HR-based estimates based on the maximal HR and the conventional detrended fluctuation analysis (DFA). Our method provides the best overall agreement with the lactate thresholds and provides a promising, cost-effective alternative to conventional protocols, which could be easily integrated in wearable devices. However, detailed statistical analysis reveals the particular strengths and weaknessess of each method with respect to the agreement and consistency with the thresholds—thus underlining the need for further studies with more data.

Temporal fluctuations in the stride parameters during human walking exhibit long-range correlations, but these long-range correlations in the stride parameters decrease due to aging or neuromuscular diseases. These observations suggest that any quantified index of the long-range correlation can be regarded as an indicator of gait functionality. Considering the effect of task-relevant sensory feedback on augmenting human motor performance, we devised shoes with active insoles that could deliver noisy vibration to the soles of feet and assessed their efficacy in enhancing the long-range correlations in the stride parameters for healthy young adults. The vibration could be wirelessly controlled using a smartphone. The actuators, control unit, and battery in the devised shoes were light and embedded in the shoes. By virtue of this compactness, the shoes could be easily used for daily walking outside a laboratory. We performed walking experiments with 20 healthy adults and evaluated the effects of sub- and supra-threshold vibration on long-range correlations in stride interval and length. We performed detrended fluctuation analysis to quantify the long-range correlation of temporal changes in stride interval and length. We found that supra-threshold vibration, applied to the soles with the amplitude of 130 % of the sensory threshold, significantly increased the long-range correlations in stride interval and length by 10.3 % (p = 0.009) and 10.1 % (p = 0.021), respectively. On the other hand, sub-threshold vibration with the amplitude of 90 % of the sensory threshold had no significant effect. These results demonstrate that additional somatosensory feedback through barely detectable vibrations, which are supplied by compact shoes with active insoles, can enhance the indices of “healthy” complexity of locomotor function.

Background: Breast hypertrophy is a significant health problem with both physiological and psychological impacts on the patients’ lives. Patients with macromastia adopt a corrective posture due to the effect of the breast on the center of gravity and possibly in a subconscious effort to conceal their breasts. Objective: This study aimed to evaluate whether the posture of patients with macromastia changed after the reduction of mammoplasty.Material and Methods: In this prospective study, patients with breast cup sizes C, D, and DD were scheduled for reduction mammoplasty in 3 Shiraz University Hospitals. Age, weight, height, and preoperative cup sizes of the breasts were recorded for every patient, and all patients underwent posture analysis with forceplate before and after reduction mammoplasty. Finally, the preoperative and postoperative data were compared. Results: Mean age at the time of reduction mammaplasty was 43.57±9.1; the mean pre-operation, such as weight, height, and mean the body mass index (BMI) was 76.57±10 kg, 158.28±6 cm and 30.57±4.1, respectively. The average Anterior-posterior (AP) direction velocity before and after the surgery was 0.85±0.12 cm/s and 0.79±0.098, respectively. These values were 0.83±0.09 and 0.81±0.10 for the mediolateral direction. The Detrended Fluctuation Analysis (DFA) value for the AP direction was 1.63±0.3 and 1.60±0.2 for pre-and post-surgery, respectively, which was not statistically different. The DFA value for maximum likelihood (ML) direction was 1.65±0.2 and 1.48±0.2 in pre-op and post-op, respectively, which was statistically significantly different. Conclusion: Reducing the weight of enlarged breasts can correct disturbed sagittal balance and postural sway.

Background: Heart–brain synchronization is the integration of mind, body, and spirit. It occurs when the electrical activity of the heart and brain is synchronized. In recent years, there has been mounting curiosity to investigate the effects of meditation on heart–brain synchronization with respect to mental and emotional health and well-being. The current investigation aims to explore the rhythmic synchronicity between the brain and the heart during heartfulness meditation (HM) practice. Materials and Methods: The study was performed on 45 healthy volunteers who were categorized into three equal groups: long-term meditators (LTMs), short-term meditators (STMs), and nonmeditators (NMs). The electroencephalogram (EEG) signals were recorded to measure the prefrontal activity, and electrocardiogram (ECG) signals were recorded to measure the cardiac activity. The data were recorded in four states: baseline, meditation, transmission, and posttransmission. The detrended fluctuation analysis (DFA) method was used for the analysis of EEG and ECG signals. Results: The result indicates that DFA values of EEG and ECG declined during meditation and transmission states as compared to pre- and postmeditation states. Significant results were obtained for the LTM group in all the states. A positive correlation was also observed between DFA of the heart and brain for the LTM group and no significant correlations were observed for the STM and NM groups. Conclusion: The shreds of evidence suggest that heart–brain synchronization facilitates mental and emotional stability. HM practice has the potential to regulate the fluctuation of the mind. Regular meditation practice may result in physiological synchrony between cardiac and neural behavior, which can be considered a quality index for meditation practice.

Abstract Background Pulmonary vein isolation (PVI) is a cornerstone therapy for paroxysmal atrial fibrillation (PAF). The variations in nonlinear heart rate variability (HRV) between patients with and without recurrences remain unclear. We aimed to characterize the nonlinear HRV before and after PVI in patients with and without recurrence. Methods Twenty‐five drug‐refractory PAF patients (56.0 ± 9.1 years old, 20 males) who received PVI were enrolled. Holter electrocardiography were performed before, 1–3, and 6–12 months after PVI. After 8.2 ± 2.5 months of follow‐ups after PVI, patients were divided into two groups: the recurrence (n = 8) and non‐recurrence (n = 17) groups. Linear and nonlinear HRV variables were analyzed, including the Poincaré Plot analysis and the Detrended Fluctuation Analysis (DFA). Results The non‐recurrence group, but not the recurrence group, had decreased high‐frequency component (HF), the root mean square of successive RR interval differences (RMSSD), and the Poincaré Plot index SD1 1–3 months after PVI and increased DFAslope2 6–12 months after PVI. The non‐recurrence group's LF/HF ratio and DFAslope1 decreased significantly 1–3 and 6–12 months after PVI, respectively, whereas there was no significant change in the recurrence group after PVI. Conclusions Significantly reduced vagal tone 1–3 months after PVI, increased long‐term fractal complexity 6–12 months after PVI, and decreased sympathetic tone as well as short‐term fractal complexity 1–3 and 6–12 months after PVI led to a better AF‐free survival after PVI. These findings suggest that neuromodulation and heart rate dynamics play crucial roles in AF recurrence following PVI.

Introduction: Aging is a physiological process characterized by progressive changes in all organ systems. In the last few decades, the elderly population has been growing, so the scientific community is focusing on the investigation of the aging process, all in order to improve the quality of life in elderly. One of the biggest challenges in studying the impact of the aging on the human body represents the monitoring of the changes that inevitably occur in arterial blood vessels. Therefore, the medical community has invested a great deal of effort in studying and discovering new methods and tools that could be used to monitor the changes in arterial blood vessels caused by the aging process. The goal of our research was to develop a new diagnostic method using a photoplethysmographic sensor and to examine the impact of the aging process on the cardiovascular system in adults. Long-term recorded arterial blood flow waveforms were analyzed using detrended fluctuation analysis.Materials and Methods: The study included 117 respondents, aged 20–70 years. The waveform of the arterial blood flow was recorded for 5 min, with an optical sensor placed above the left common carotid artery, simultaneously with a single-channel ECG. For each cardiac cycle, the blood flow amplitude was determined, and a new time series was formed, which was analyzed non-linearly (DFA method). The values of the scalar coefficients α1 and α2, particularly their ratio (α1/α2) were obtained, which were then monitored in relation to the age of the subjects.Result: The values of the scalar ratio (α1/α2) were significantly different between the subjects older and younger than 50 years. The value of the α1/α2 decreased exponentially with the aging. In the population of middle-aged adults, this ratio had a value around 1, in young adults the value was exclusively higher than 1 and in older adults the value was exclusively lower than 1.Conclusion: The results of this study indicated that the aging led to a decrease in the α1/α2 in the population of healthy subjects. With this non-invasive method, changes in the cardiovascular system due to aging can be detected and monitored.

Abstract Introduction Detrended fluctuation analysis (DFA) is a well‐established method to evaluate scaling indices of time series, which categorize the dynamics of complex systems. In the literature, DFA has been used to study the fluctuations of reaction time Y(n) time series, where n is the trial number. Methods Herein we propose treating each reaction time as a duration time that changes the representation from operational (trial number) time n to event (temporal) time t, or X(t). The DFA algorithm was then applied to the X(t) time series to evaluate scaling indices. The dataset analyzed is based on a Go–NoGo shooting task that was performed by 30 participants under low and high time‐stress conditions in each of six repeated sessions over a 3‐week period. Results This new perspective leads to quantitatively better results in (1) differentiating scaling indices between low versus high time‐stress conditions and (2) predicting task performance outcomes. Conclusion We show that by changing from operational time to event time, the DFA allows discrimination of time‐stress conditions and predicts performance outcomes.

We present an innovative method harnessing multistability within a diode-pumped erbium-doped fiber laser to construct logic gates. Our approach involves manipulating the intensity of external noise to regulate the probability of transitioning among four concurrent attractors. In this manner, we facilitate the realization of OR, AND, NOR, and NAND logic operations, aligning with the coexisting period-1, period-3, period-4, and period-5 orbits. Employing detrended fluctuation analysis, we establish equilibrium in the probability distributions of these states. The obtained results denote a substantial advancement in the field of optical logic gate development, representing a pivotal stride toward the seamless integration of an all-optical logic gate within laser oscillator-based systems.

Continuous adaptations of the movement system to changing environments or task demands rely on superposed fractal processes exhibiting power laws, that is, multifractality. The estimators of the multifractal spectrum potentially reflect the adaptive use of perception, cognition, and action. To observe time-specific behavior in multifractal dynamics, a multiscale multifractal analysis based on DFA (MFMS-DFA) has been recently proposed and applied to cardiovascular dynamics. Here we aimed at evaluating whether MFMS-DFA allows identifying multiscale structures in the dynamics of human movements. Thirty-six (12 females) participants pedaled freely, after a metronomic initiation of the cadence at 60 rpm, against a light workload for 10 min: in reference to cycling (C), cycling while playing “Tetris” on a computer, alone (CT) or collaboratively (CTC) with another pedaling participant. Pedal revolution periods (PRP) series were examined with MFMS-DFA and compared to linearized surrogates, which attested to a presence of multifractality at almost all scales. A marked alteration in multifractality when playing Tetris was evidenced at two scales, τ ≈ 16 and τ ≈ 64 s, yet less marked at τ ≈ 16 s when playing collaboratively. Playing Tetris in collaboration attenuated these alterations, especially in the best Tetris players. This observation suggests the high sensitivity to cognitive demand of MFMS-DFA estimators, extending to the assessment of skill/demand interplay from individual behavior. So, by identifying scale-dependent multifractal structures in movement dynamics, MFMS-DFA has obvious potential for examining brain-movement coordinative structures, likely with sufficient sensitivity to find echo in diagnosing disorders and monitoring the progress of diseases that affect cognition and movement control.

The temporal evolution of the global mean sea level (GMSL) is investigated in the present analysis using the monthly mean values obtained from two sources: a reconstructed dataset and a satellite altimeter dataset. To this end, we use two well-known techniques, detrended fluctuation analysis (DFA) and multifractal DFA (MF-DFA), to study the scaling properties of the time series considered. The main result is that power-law long-range correlations and multifractality apply to both data sets of the global mean sea level. In addition, the analysis revealed nearly identical scaling features for both the 134-year and the last 28-year GMSL-time series, possibly suggesting that the long-range correlations stem more from natural causes. This demonstrates that the relationship between climate change and sea-level anomalies needs more extensive research in the future due to the importance of their indirect processes for ecology and conservation.

Reciprocating compressors and centrifugal pumps are rotating machines used in industry, where fault detection is crucial for avoiding unnecessary and costly downtime. A novel method for fault classification in reciprocating compressors and multi-stage centrifugal pumps is proposed. In the feature extraction stage, raw vibration signals are processed using multi-fractal detrended fluctuation analysis (MFDFA) to extract features indicative of different types of faults. Such MFDFA features enable the training of machine learning models for classifying faults. Several classical machine learning models and a deep learning model corresponding to the convolutional neural network (CNN) are compared with respect to their classification accuracy. The cross-validation results show that all models are highly accurate for classifying the 13 types of faults in the centrifugal pump, the 17 valve faults, and the 13 multi-faults in the reciprocating compressor. The random forest subspace discriminant (RFSD) and the CNN model achieved the best results using MFDFA features calculated with quadratic approximations. The proposed method is a promising approach for fault classification in reciprocating compressors and multi-stage centrifugal pumps.

Profound research on the characteristics of the long-term persistence of wind is greatly significant for understanding the characteristics of wind speed mechanisms as well as for avoiding disasters caused by wind. In the current study, we selected the hourly 10 min wind speed series between 2017 and 2021 from 105 nation-level meteorological stations in Xinjiang and investigated the spatiotemporal variations in the long-term persistence of wind speed in different regions of Xinjiang and in different seasons using detrended fluctuation analysis. The main findings are as follows: (1) The wind speed in Xinjiang shows noticeable annual and seasonal variations, exhibiting satisfactory long-term sustainability. Winter has the best long-term sustainability, followed sequentially by spring, autumn, and summer because of wind speed stability. (2) The long-term persistence of hourly wind speed in Xinjiang exhibits remarkable regionality, with regions with strong wind superior to the remaining regions. (3) The long-term persistence of wind speed within the same season is primarily associated with wind speed magnitude and the dispersion degree between 90% and 100% of the wind speed numerical values. A higher wind speed indicates better long-term persistence. At the same speed, the more discrete the numerical values in the 90–100% distribution range, the better the persistence.

Proprioception is a crucial property for movement stability and balance, but its current assessment, based on clinical testing, lacks precision and adequacy in real contexts. This study proposes assessing proprioception and its sensitivity to training effects through acceleration time series recorded during two slackline experiments. In the first experiment, slackliners of different expertise (highly and poorly trained) had to walk on a slackline for 30 s. In the second, twelve beginners had to balance up on the slackline for at least 11 s before and after a training process. Acceleration time series were recorded in body components (legs and centre of mass) and the slackline. The acceleration fluctuations were analysed through Detrended Fluctuation Analysis. The obtained Hurst (H)-exponents were compared between both groups (first experiment) and before and after training (second experiment) using Whitney and Wilcoxon tests, respectively. The values of H-exponents were lower in the highly trained group (Z = −2.15, p = 0.03) (first experiment), and in the post-training conditions (Z = −2.35, p = 0.02) (second experiment). These results suggest better motor and proprioceptive control with training status. Hence, the time-variability structure of acceleration in real contexts, like slackline tasks, is proposed as an objective measure of proprioception and its training effects.

Detrended fluctuation analysis (DFA) can quantify long-range correlation (LRC) and fractal scaling behavior of signal. We compared the results of variant DFA methods by varying the order of the polynomial and found that the order of 6 was relatively better than the others when both the accuracy and computational cost were taken into account. An alternative DFA method is proposed to quantify the LRC exponent by using best-fit polynomial algorithm in each segment instead of the polynomial of the same order in all of segments. In this study, the best-fit polynomial algorithm with the maximum order of 6 is used to fit the local trend in each segment to detrend the trend of a time series, and then the revised DFA is used to quantify the LRC in the time series. A series of numerical studies demonstrate that the best-fit DFA performs better than regular DFA, especially for the time series with scaling exponent smaller than 0.5. This may be attributed to the improvement of the fitted trend at the end of each segment. The estimation results of variant DFA methods reach stable when the time series length is greater than 1,000.

Abstract The respiratory system reacts instantaneously to intrinsic and extrinsic inputs. This adaptability results in significant fluctuations in breathing parameters, such as respiratory rate, tidal volume, and inspiratory flow profiles. Breathing variability is influenced by several conditions, including sleep, various pulmonary diseases, hypoxia, and anxiety disorders. Recent studies have suggested that weaning failure during mechanical ventilation may be predicted by low respiratory variability. This review describes methods for quantifying breathing variability, summarises the conditions and comorbidities that affect breathing variability, and discusses the potential implications of breathing variability for anaesthesia and intensive care.

Present study is aimed at investigating the solar faculae area from 1990 to 2007 which partially covered the 22nd and 23rd solar cycle. Rescaled Range Analysis (RRA) and Detrended Fluctuation Analysis (DFA) have been adopted to evaluate the behaviour of nonlinear dynamics of solar faculae area. Results show that the value of Hurst exponent for solar faculae area from RRA and DFA is negatively correlated. It means it is non-persistent and long-range correlated. Obtained result is inaccurate so the only solution is to transform the data into stationary data by taking differencing. RRA is applied on residuals and RRA to evaluate the fractal property of the time series. Solar faculae area investigated in this study is fractal in nature and predictable as well. Moreover, the time series of solar faculae area is non-linear as established by the Brock – Dechert – Scheinkman (BDS) test results

Nonlinear analyses of heart rate variability (HRV) can be used to quantify the unpredictability, fractal properties and complexity of heart rate. Fractality and its analysis provides valuable information about cardiovascular health. Multi-Scale Multi-Fractal Detrended Fluctuation Analysis (MSMFDFA) is a complexity-based algorithm that can be used to quantify the multi-fractal dynamics of the HRV time series through investigating characteristic exponents at different time scales. This method is applicable to short time series and it is robust to noise and nonstationarity. We have used MSMFDFA, which enables assessment of HRV in the frequency ranges encompassing the very-low frequency and ultra-low frequency bands, to jointly assess multi-scale and multi-fractal dynamics of HRV signals obtained from telemetric ECG recordings in wildtype mice at baseline and after autonomic nervous system (ANS) blockade, from electrograms recorded from isolated atrial preparations and from spontaneous action potential recordings in isolated sinoatrial node myocytes. Data demonstrate that the fractal profile of the intrinsic heart rate is significantly different from the baseline heart rate in vivo, and it is also altered after ANS blockade at specific scales and fractal order domains. For beating rate in isolated atrial preparations and intrinsic heart rate in vivo, the average fractal structure of the HRV increased and multi-fractality strength decreased. These data demonstrate that fractal properties of the HRV depend on both ANS activity and intrinsic sinoatrial node function and that assessing multi-fractality at different time scales is an effective approach for HRV assessment.

In this paper, we thoroughly analyze the detection of sleep apnea events in the context of Obstructive Sleep Apnea (OSA), which is considered a public health problem because of its high prevalence and serious health implications. We especially evaluate patients who do not always show desaturations during apneic episodes (non-desaturating patients). For this purpose, we use a database (HuGCDN2014-OXI) that includes desaturating and non-desaturating patients, and we use the widely used Physionet Apnea Dataset for a meaningful comparison with prior work. Our system combines features extracted from the Heart-Rate Variability (HRV) and SpO2, and it explores their potential to characterize desaturating and non-desaturating events. The HRV-based features include spectral, cepstral, and nonlinear information (Detrended Fluctuation Analysis (DFA) and Recurrence Quantification Analysis (RQA)). SpO2-based features include temporal (variance) and spectral information. The features feed a Linear Discriminant Analysis (LDA) classifier. The goal is to evaluate the effect of using these features either individually or in combination, especially in non-desaturating patients. The main results for the detection of apneic events are: (a) Physionet success rate of 96.19%, sensitivity of 95.74% and specificity of 95.25% (Area Under Curve (AUC): 0.99); (b) HuGCDN2014-OXI of 87.32%, 83.81% and 88.55% (AUC: 0.934), respectively. The best results for the global diagnosis of OSA patients (HuGCDN2014-OXI) are: success rate of 95.74%, sensitivity of 100%, and specificity of 89.47%. We conclude that combining both features is the most accurate option, especially when there are non-desaturating patterns among the recordings under study.

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 ​

Heart Rate Variability (HRV) can be a useful metric to capture meaningful information about heart function. One of the non-linear indices used to analyze HRV, Detrended Fluctuation Analysis (DFA), finds short and long-term correlations in RR intervals to capture quantitative information about variability. This study focuses on the impact of visual and mental stimulation on HRV as expressed via DFA within healthy adults. Visual stimulation can activate the automatic nervous system to directly impact physiological behavior such as heart rate. In this investigation of HRV, 70 participants (21 males) viewed images on a screen followed by a math and recall task. Each viewing segment lasted 2 min and 18 s. The math and memory recall task segment lasted 4 min total. This process was repeated 9 times during which the participants’ electrocardiogram was recorded. 37 participants (12 males) opted in for an additional 24-h Holter recording after the viewing and task segments of the study were complete. Participants were randomly assigned to either a pure (organized image presentation) or mixed (random image presentation) image regime for the viewing portion of the study to investigate the impact of the external environment on HRV. DFA α1 was extracted from the RR intervals. Our findings suggest that DFA α1 can differentiate between the viewing [DFA α1 range from 0.96 (SD = 0.25) to 1.08 (SD = 0.22)] and the task segments [DFA α1 range from 1.17 (SD = 0.21) to 1.26 (SD = 0.25)], p < 0.0006 for all comparisons. However, DFA α1 was not able to distinguish between the two image regimes. During the 24-hour follow up, participants had an average DFA α1 = 1.09 (SD = 0.14). In conclusion, our findings suggest a graded response in DFA during short term stimulation and a responsiveness in participants to adjust physiologically to their external environment expressed through the DFA exponent.

IntroductionAlthough a few studies suggest that young overweight to obese children and adolescents (YO) may have impaired postural control compared to young normal-weight (YN) peers, little information exists about how these two groups differ in the quality of the underlying balance strategies employed. Hence, the aim of the present study was a first comprehensive examination of the structural complexity of postural sways in these two cohorts during quiet bilateral standing.MethodsNineteen YO secondary school students (13.0 ± 1.4 years; male = 10, female = 9) were carefully matched to YN controls (13.0 ± 1.5 years) for age, sex, height, and school. Mediolateral (ML) and anteriorposterior (AP) acceleration signals were recorded with an inertial measurement unit (IMU) positioned at the trunk while standing barefoot in two conditions: firm and foam support surface. The magnitude of postural fluctuations was obtained using the root mean square (RMS). The temporal structure of the signals was analyzed via sample entropy (SEn), largest Lyapunov exponent (LyE), and detrended fluctuation analysis (α-DFA) algorithm. Reliability was assessed using a test–retest design.ResultsIn both groups, foam standing caused higher postural fluctuations (higher RMS values) and reduced structural complexity (lower SEn values, higher LyE values, higher α-DFA values). In comparison to YN, YO exhibited a higher RMSAP. Especially in ML direction, the acceleration signals of the YO had higher repeatability (smaller SEn values), greater long-range correlations (higher α-DFA values), and lower local stability (higher LyE values). However, these observations were largely independent of the task difficulty. Except for α-DFAAP, the IMU approach proved reliable to characterize posture control.DiscussionOur outcomes confirm postural control deficits in YO compared to their YN peers and indicate impaired regulatory mechanisms reflected as rigidity. Such less complex patterns usually reflect diverse pathologies, are detrimental to compensate for internal or external perturbations, and are attributed to lower adaptability and task performance. Without targeted balance stimuli, YO likely end in a lifelong vicious circle of mutually dependent poor balance regulation and low physical activity.

Long-term memory (LTM) in the climate system has been well recognized and applied in different research fields, but the origins of this property are still not clear. In this work, the authors contribute to this issue by studying model simulations under different scenarios. The global mean temperatures from pre-industrial control runs (piControl), historical (all forcings) simulations, natural forcing only simulations (HistoricalNat), greenhouse gas forcing only simulations (HistoricalGHG), etc., are analyzed using the detrended fluctuation analysis. The authors find that the LTM already exists in the piControl simulations, indicating the important roles of internal natural variability in producing the LTM. By comparing the results among different scenarios, the LTM from the piControl runs is further found to be strengthened by adding natural forcings such as the volcanic forcing and the solar forcing. Accordingly, the observed LTM in the climate system is suggested to be mainly controlled by both the ‘internal’ natural variability and the ‘external’ natural forcings. The anthropogenic forcings, however, may weaken the LTM. In the projections from RCP2.6 to RCP8.5, a weakening trend of the LTM strength is found. In view of the close relations between the climate memory and the climate predictability, a reduced predictability may be expected in a warming climate.

Time-frequency analysis always plays an important role in machine health monitoring owing to its advantage in extracting the fault information contained in non-stationary signal. In this paper, we present a novel technique to detect and diagnose the rolling bearing faults based on high-order synchrosqueezing transform (FSSTH) and detrended fluctuation analysis (DFA). With this method, the high-order synchrosqueezing transform is first utilized to decompose the vibration signal into an ensemble of oscillatory components termed as intrinsic mode functions (IMFs). Meanwhile, an empirical equation, which is based on the DFA, is introduced to adaptively determine the number of IMFs from FSSTH. Then, a time-frequency representation originated from the decomposed modes or corresponding envelopes is exhibited in order to identify the fault characteristic frequencies related to rolling bearing. Experiments are carried out using both simulated signal and real ones from Case Western Reserve University. Results show that the proposed method is more effective for the detection of fault characteristic frequencies compared with the traditional synchrosqueezing transform (SST) based fault diagnosis algorithm, which renders this technique is promising for machine fault diagnosis.

Electrocardiogram (ECG) is a critical biological signal, which usually carries a great deal of essential information about patients. The high quality ECG signals are always required for a proper diagnosis of cardiac disorders. However, the raw ECG signals are highly noisy in nature. In the paper, we propose a hybrid denoising scheme to enhance ECG signals by combining high-order synchrosqueezing transform (FSSTH) with non-local means (NLM). With this method, a noisy ECG signal is first decomposed into an ensemble of intrinsic mode functions (IMFs) by FSSTH. Then, some noise is removed by eliminating a set of noisy IMFs that are determined by a scaling exponent obtained by the detrended fluctuation analysis (DFA); while the remaining IMFs are filtered by NLM. Finally, the denoised ECG signal is obtained by reconstructing the processed IMFs. Experiments are carried out using the simulated ECG signals and real ones from the MIT-BIH database, and the denoising performances are evaluated in terms of signal to noise ratio (SNR), root mean squared error (RMSE) and percent root mean square difference (PRD). Results show that the hybrid denoising scheme involving both FSSTH and NLM is able to suppress complex noise from ECG signals more effectively while preserving the details well.

Assessing power-law cross-correlations between a pair – or among a set – of processes is of great significance in diverse fields of analyses ranging from neuroscience to financial markets. In most cases such analyses are computationally expensive and thus carried out offline once the entire signal is obtained. However, many applications – such as mental state monitoring or financial forecasting – call for fast algorithms capable of estimating scale-free coupling in real time. Detrended cross-correlation analysis (DCCA), a generalization of the detrended fluctuation analysis (DFA) to the bivariate domain, has been introduced as a method designed to quantify power-law cross-correlations between a pair of non-stationary signals. Later, in analogy with the Pearson cross-correlation coefficient, DCCA was adapted to the detrended cross-correlation coefficient (DCCC), however as of now no online algorithms were provided for either of these analysis techniques. Here we introduce a new formula for obtaining the scaling functions in real time for DCCA. Moreover, the formula can be generalized via matrix notation to obtain the scaling relationship between not only a pair of signals, but also all possible pairs among a set of signals at the same time. This includes parallel estimation of the DFA scaling function of each individual process as well, thus allowing also for real-time acquisition of DCCC. The proposed algorithm matches its offline variants in precision, while being substantially more efficient in terms of execution time. We demonstrate that the method can be utilized for mental state monitoring on multi-channel electroencephalographic recordings obtained in eyes-closed and eyes-open resting conditions.

Vehicle driving cycles have complex characteristics, but there are few publicly reported methods for their quantitative characterization. This paper innovatively investigates their multifractal characteristics using the fractal theory to characterize their complex properties, laying the foundation for applications such as vehicle driving cycle feature identification, vehicle energy management strategies (EMS), and so on. To explore the scale-invariance of the vehicle driving cycles, the four vehicle driving cycles were analyzed using the Multifractal Detrended Fluctuation Analysis (MF-DFA) method, three of which are standard vehicle test cycles: the New European Driving Cycle (NEDC), the World-wide harmonized Light-duty Test Cycle (WLTC) and the China Light-duty Vehicle Test Cycle for Passenger Car (CLTC-P), and the other is the Urban Road Real Driving Cycle (URRDC), which was obtained by analyzing and processing vehicle driving data collected in actual urban driving conditions. The fluctuation functions, the generalized Hurst exponents, the mass exponent spectra, the multifractal singularity spectra, and the multifractal characteristic parameters were calculated to verify the multifractal characteristics, and to quantify the fluctuation singularities of different driving cycles as the time series. The results show that the fluctuations of all four driving cycles have long-range anticorrelations and exhibit significant multifractal characteristics. The results can provide a basis for the analysis of the complexity of the vehicle driving cycles.

In this study we investigate possible long-range trends in the cryptocurrency market. We employed the Hurst exponent in a sample covering the period from 1 January 2016 to 26 March 2021. We calculated the Hurst exponent in three non-overlapping consecutive windows and in the whole sample. Using these windows, we assessed the dynamic evolution in the structure and long-range trend behavior of the cryptocurrency market and evaluated possible changes in their behavior towards an efficient market. The innovation of this research is that we employ the Hurst exponent to identify the long-range properties, a tool that is seldomly used in analysis of this market. Furthermore, the use of both the R/S and the DFA analysis and the use of non-overlapping windows enhance our research’s novelty. Finally, we estimated the Hurst exponent for a wide sample of cryptocurrencies that covered more than 80% of the entire market for the last six years. The empirical results reveal that the returns follow a random walk making it difficult to accurately forecast them.

Functional connectivity, quantified by phase synchrony, between brain regions is known to be aberrant in patients with autism spectrum disorder (ASD). Here, we evaluated the long-range temporal correlations of time-varying phase synchrony (TV-PS) of electrocortical oscillations in patients with ASD as well as typically developing people using detrended fluctuation analysis (DFA) after validating the scale-invariance of the TV-PS time series. By comparing the DFA exponents between the two groups, we found that those of the TV-PS time series of high-gamma oscillations were significantly attenuated in patients with ASD. Furthermore, the regions involved in aberrant TV-PS time series were mainly within the social ability and cognition-related cortical networks. These results support the notion that abnormal social functions observed in patients with ASD may be caused by the highly volatile phase synchrony states of electrocortical oscillations.

Study region: Central eastern continental United States. Study focus: Groundwater level prediction is of great significance for the management of global water resources. Recently, machine learning, which can deal with highly nonlinear interactions among complex hydrological factors, has been widely applied to groundwater level prediction. However, previous studies mainly focused on improving the simulation performance in specific regions using different machine learning methods, while this study focused on the impacts of regional characteristics on improving the accuracy of groundwater level prediction using machine learning. New hydrological insights for the region: A gated recurrent unit (GRU) neural network was built for groundwater level simulation in 78 catchments in the study region, and principal component analysis was used to cluster a variety of catchment hydrological variables and determine the input variables for the GRU model. Detrended fluctuation analysis was applied to analyze the autocorrelation of groundwater level in each catchment. This study further explored the influences of the hydrogeological properties of different catchments and the autocorrelation of groundwater levels on machining learning simulations. The results showed that the GRU model performed better in regions where hydrogeological properties could promote more effective responses of groundwater to external changes. Moreover, a negative correlation between the simulation performance of machine learning and the autocorrelation of the groundwater level was found.

Abstract Detrended fluctuation analysis and detrended cross-correlation analysis are used in this study to identify and characterize correlated data. The objective of these two techniques is to separate different fluctuations from the contributions due to external trends by evaluating the autocorrelation and cross-correlation exponents, in order to determine if scale properties persist with the size of the series. Two new methodologies were extended from cross-correlation coefficients for local analysis, which we call the \textit{automatic search procedure

Rangeland ecosystems comprise more than a third of the global land surface, sustaining essential ecosystem services and livelihoods. In Spain, Southeast Spain includes some of the driest regions; accordingly, rangelands from Murcia and Almeria provinces were selected for this study. We used time series metrics and the Hurst Exponent from rescale range and detrended fluctuation analysis to cluster different rangeland dynamics to classify temporally and spatially diverse rangelands. The metrics were only calculated for three time periods that showed significant NDVI changes: March to April, April to July, and September to December. Detrended fluctuation analysis was not previously employed to cluster vegetation. This study used it to improve rangeland classification. K-means and unsupervised random forest were used to cluster the pixels using time series metrics and Hurst exponents. The best clustering results were obtained when unsupervised random forest was used with the Hurst exponent calculated with detrended fluctuation analysis. We used the Silhouette Index to evaluate the clustering results and a spatial comparison with topographical data. Our results show that adding the Hurst exponent, calculated with detrended fluctuation analysis, provided a better classification when clustering NDVI time series, while classifications without the Hurst exponent or with the Hurst exponent calculated with the rescale range method showed lower silhouette values. Overall, this shows the importance of using detrending when calculating the Hurst exponent on vegetation time series, and its usefulness in studying rangeland dynamics for management and research.

Complex systems typically demonstrate a mixture of regularity and flexibility in their behavior, which would make them adaptive. At the same time, adapting to perturbations is a core characteristic of resilience. The first aim of the current research was therefore to test the possible relation between complexity and resilient motor performance (i.e., performance while being perturbed). The second aim was to test whether complexity and resilient performance improve through differential learning. To address our aims, we designed two parallel experiments involving a motor task, in which participants moved a stick with their non-dominant hand along a slider. Participants could score points by moving a cursor as fast and accurately as possible between two boxes, positioned on the right- and left side of the screen in front of them. In a first session, we determined the complexity by analyzing the temporal structure of variation in the box-to-box movement intervals with a Detrended Fluctuation Analysis. Then, we introduced perturbations to the task: We altered the tracking speed of the cursor relative to the stick-movements briefly (i.e., 4 s) at intervals of 1 min (Experiment 1), or we induced a prolonged change of the tracking speed each minute (Experiment 2). Subsequently, participants had three sessions of either classical learning or differential learning. Participants in the classical learning condition were trained to perform the ideal movement pattern, whereas those in the differential learning condition had to perform additional and irrelevant movements. Finally, we conducted a posttest that was the same as the first session. In both experiments, results showed moderate positive correlations between complexity and points scored (i.e., box touches) in the perturbation-period of the first session. Across the two experiments, only differential learning led to a higher complexity index (i.e., more prominent patterns of pink noise) from baseline to post-test. Unexpectedly, the classical learning group improved more in their resilient performance than the differential learning group. Together, this research provides empirical support for the relation between complexity and resilience, and between complexity and differential learning in human motor performance, which should be examined further.

This study aimed to apply different complexity-based methods to surface electromyography (EMG) in order to detect neuromuscular changes after realistic warm-up procedures that included stretching exercises. Sixteen volunteers conducted two experimental sessions. They were tested before, after a standardized warm-up, and after a stretching exercise (static or neuromuscular nerve gliding technique). Tests included measurements of the knee flexion torque and EMG of biceps femoris (BF) and semitendinosus (ST) muscles. EMG was analyzed using the root mean square (RMS), sample entropy (SampEn), percentage of recurrence and determinism following a recurrence quantification analysis (%Rec and %Det) and a scaling parameter from a detrended fluctuation analysis. Torque was significantly greater after warm-up as compared to baseline and after stretching. RMS was not affected by the experimental procedure. In contrast, SampEn was significantly greater after warm-up and stretching as compared to baseline values. %Rec was not modified but %Det for BF muscle was significantly greater after stretching as compared to baseline. The a scaling parameter was significantly lower after warm-up as compared to baseline for ST muscle. From the present results, complexity-based methods applied to the EMG give additional information than linear-based methods. They appeared sensitive to detect EMG complexity increases following warm-up.

Lidar is an active remote sensing technology that has many advantages, but the echo lidar signal is extremely susceptible to noise and complex atmospheric environment, which affects the effective detection range and retrieval accuracy. In this paper, a wavelet transform (WT) and locally weighted scatterplot smoothing (LOWESS) based on ensemble empirical mode decomposition (EEMD) for Rayleigh lidar signal denoising was proposed. The WT method was used to remove the noise in the signal with a signal-to-noise ratio (SNR) higher than 16 dB. The EEMD method was applied to decompose the remaining signal into a series of intrinsic modal functions (IMFs), and then detrended fluctuation analysis (DFA) was conducted to determine the threshold for distinguishing whether noise or signal was the main component of the IMFs. Moreover, the LOWESS method was adopted to remove the noise in the IMFs component containing the signal, and thus, finely extract the signal. The simulation results showed that the denoising effect of the proposed WT-EEMD-LOWESS method was superior to EEMD-WT, EEMD-SVD and VMD-WOA. Finally, the use of WT-EEMD-LOWESS on the measured lidar signal led to significant improvement in retrieval accuracy. The maximum error of density and temperature retrievals was decreased from 1.36% and 125.79 K to 1.1% and 13.84 K, respectively.

Background: Previous studies have associated slowed ventricular conduction with the arrhythmogenesis mediated by the gap junction and sodium channel inhibitor heptanol in mouse hearts. However, they did not study the propagation patterns that might contribute to the arrhythmic substrate. This study used a multi-electrode array mapping technique to further investigate different conduction abnormalities in Langendorff-perfused mouse hearts exposed to 0.1 or 2 mM heptanol. Methods: Recordings were made from the left ventricular epicardium using multi-electrode arrays in spontaneously beating hearts during right ventricular 8 Hz pacing or S1S2 pacing. Results: In spontaneously beating hearts, heptanol at 0.1 and 2 mM significantly reduced the heart rate from 314 ± 25 to 189 ± 24 and 157 ± 7 bpm, respectively (ANOVA, p < 0.05 and p < 0.001). During regular 8 Hz pacing, the mean LATs were increased by 0.1 and 2 mM heptanol from 7.1 ± 2.2 ms to 19.9 ± 5.0 ms (p < 0.05) and 18.4 ± 5.7 ms (p < 0.05). The standard deviation of the mean LATs was increased from 2.5 ± 0.8 ms to 10.3 ± 4.0 ms and 8.0 ± 2.5 ms (p < 0.05), and the median of phase differences was increased from 1.7 ± 1.1 ms to 13.9 ± 7.8 ms and 12.1 ± 5.0 ms by 0.1 and 2 mM heptanol (p < 0.05). P5 took a value of 0.2 ± 0.1 ms and was not significantly altered by heptanol at 0.1 or 2 mM (1.1 ± 0.9 ms and 0.9 ± 0.5 ms, p > 0.05). P50 was increased from 7.3 ± 2.7 ms to 24.0 ± 12.0 ms by 0.1 mM heptanol and then to 22.5 ± 7.5 ms by 2 mM heptanol (p < 0.05). P95 was increased from 1.7 ± 1.1 ms to 13.9 ± 7.8 ms by 0.1 mM heptanol and to 12.1 ± 5.0 ms by 2 mM heptanol (p < 0.05). These changes led to increases in the absolute inhomogeneity in conduction (P5–95) from 7.1 ± 2.6 ms to 31.4 ± 11.3 ms, 2 mM: 21.6 ± 7.2 ms, respectively (p < 0.05). The inhomogeneity index (P5–95/P50) was significantly reduced from 3.7 ± 1.2 to 3.1 ± 0.8 by 0.1 mM and then to 3.3 ± 0.9 by 2 mM heptanol (p < 0.05). Conclusion: Increased activation latencies, reduced CVs, and the increased inhomogeneity index of conduction were associated with both spontaneous and induced ventricular arrhythmias.

In this study, we investigated the performance of nine CMIP5 models for global daily precipitation by comparing with NCEP data from 1960 to 2005 based on the detrended fluctuation analysis (DFA) method. We found that NCEP daily precipitation exhibits long-range correlation (LRC) characteristics in most regions of the world. The LRC of daily precipitation over the central of North American continent is the strongest in summer, while the LRC of precipitation is the weakest for the equatorial central Pacific Ocean. The zonal average scaling exponents of NCEP daily precipitation are smaller in middle and high latitudes than those in the tropics. The scaling exponents are above 0.9 over the tropical middle and east Pacific Ocean for the year and four seasons. Most CMIP5 models can capture the characteristic that zonal mean scaling exponents of daily precipitation reach the peak in the tropics, and then decrease rapidly with the latitude increasing. The zonal mean scaling exponents simulated by CMCC-CMS, GFDL-ESM2G and IPSL-CM5A-MR show consistencies with those of NCEP, while BCC_CSM1.1(m) and FGOALS-g2 cannot capture the seasonal variations of daily precipitation’s LRC. The biases of scaling exponents between CMIP5 models and NCEP are smaller in the high latitudes, and even less than the absolute value of 0.05 in some regions, including Arctic Ocean, Siberian, Southern Ocean and Antarctic. However, for Western Africa, Eastern Africa, Tropical Eastern Pacific and Northern South America, the simulated biases of scaling exponents are greater than the absolute value of 0.05 for the year and all four seasons. In general, the spatial biases of LRC simulated by GFDL-ESM2G, HadGEM2-AO and INM-CM4 are relatively small, which indicating that the LRC characteristics of daily precipitation are well simulated by these models.

By utilizing eight CMIP5 model outputs in historical experiment that simulated daily mean sea surface temperature (SST) and NCEP reanalysis data over 12 ocean basins around the world from 1960 to 2005, this paper evaluates the performance of CMIP5 models based on the detrended fluctuation analysis (DFA) method. The results of National Centers for Environmental Prediction (NCEP) data showed that the SST in most ocean basins of the world had long-range correlation (LRC) characteristics. The DFA values of the SST over ocean basins are large in the tropics and small in high latitudes. In spring and autumn, the zonal average DFA of SST are basically distributed symmetrically in the Northern and Southern Hemispheres. In summer, the zonal average values of DFA in the Northern Hemisphere are larger than those in the southern hemisphere, and vice versa in winter. The performance of HadGEM2-AO, CNRM-CM5, and IPSL-CM5A-MR are all relative well among the eight models in simulating SST over most regions of the global ocean.

Sustained attention is the ability to continually concentrate on task-relevant information, even in the presence of distraction. Understanding the neural mechanisms underlying this ability is critical for comprehending attentional processes as well as neuropsychiatric disorders characterized by attentional deficits, such as attention deficit hyperactivity disorder (ADHD). In this study, we aimed to investigate how trait-like critical oscillations during rest relate to the P300 evoked potential—a biomarker commonly used to assess attentional deficits. We measured long−range temporal correlations (LRTC) in resting-state EEG oscillations as index for criticality of the signal. In addition, the attentional performance of the subjects was assessed as reaction time variability (RTV) in a continuous performance task following an oddball paradigm. P300 amplitude and latencies were obtained from EEG recordings during this task. We found that, after controlling for individual variability in task performance, LRTC were positively associated with P300 amplitudes but not latencies. In line with previous findings, good performance in the sustained attention task was related to higher P300 amplitudes and earlier peak latencies. Unexpectedly, we observed a positive relationship between LRTC in ongoing oscillations during rest and RTV, indicating that greater criticality in brain oscillations during rest relates to worse task performance. In summary, our results show that resting-state neuronal activity, which operates near a critical state, relates to the generation of higher P300 amplitudes. Brain dynamics close to criticality potentially foster a computationally advantageous state which promotes the ability to generate higher event-related potential (ERP) amplitudes.

The daily average land surface air temperature (SAT) simulated by 8 CMIP5 models historical experiments and that from NCEP data during 1960–2005, are used to evaluate the performance of the CMIP5 model based on detrended fluctuation analysis (DFA) method. The DFA results of NCEP data show that SAT in most regions of the world exhibit long-range correlation. The scaling exponents of NCEP SAT show the zonal distribution characteristics of larg in tropics while small in medium and high latitudes. The distribution characteristics of the zonal average scaling exponents of CMCC-CMS, GFDL-ESM2G, IPSL-CM5A-MR are similar to that of NCEP data. From the DFA errors of model-simulated SAT, the performance of IPSL-CM5A-MR is the best among the 8 models throughout the year, the performance of FGOALS-g2 is good in spring and summer, GFDL-ESM2G is the best in autumn, CNRM-CM5 and CMCC-CMS is good in winter. The scaling exponents of model-simulated SAT are closer to that of NCEP data in most areas of the mid-high latitude on the northern hemisphere. However, simulations of SAT in East Asia and Central North American are generally less effective. In spring, most models have better performance in Siberian (SIB), Central Asia (CAS) and Tibetan (TIB). SAT in Northern Europe area are well simulated by most models in summer. In autumn, areas with better performance of most models are Mediterranean, SIB and TIB regions. In winter, SAT in Greenland, SIB and TIB areas are well simulated by most models. Generally speaking, the performance of CMIP5 models for SAT on global continents varies in different seasons and different regions.

Considerable disagreement exists on the linearity of the development of standing balance in children. This study aimed to use different traditional and nonlinear methods to investigate age-related changes in standing balance in preschoolers. A sample of 118 preschoolers took part in this study. A force platform was used to record the center of pressure during standing balance over 15 s in three conditions: eyes open, eyes closed, and/or head extended backward. Detrended fluctuation analysis (DFA), recurrence quantification analysis (RQA), and traditional measures were used to evaluate standing balance. The main results are as follows: (1) Higher range and SD in the anterior-posterior (AP) direction were observed for 5-year-old than for 4-year-old children, while higher DFA coefficient (at shorter time scales) and higher determinism and laminarity in the AP direction were found for 5-year-old children compared to 3- and 4-year-old children; and (2) as sensory conditions became more challenging, all traditional measures increased and DFA coefficients (at shorter and longer time scales) decreased in the AP and mediolateral directions, while determinism and laminarity significantly declined in the AP direction. In conclusion, although increased postural sway, 5-year-old preschool children’s balance performance improved, and their control strategy changed significantly compared with the younger preschoolers. Sensory perturbation (eye closure and/or head extension) changed preschoolers’ balance performance and control strategy. Moreover, both traditional and nonlinear methods provided complementary information on the control of standing balance in preschoolers.

Nausea and emesis resulting from disease or drug treatment may be associated with disrupted gastric myoelectric activity (GMA). Conventional analytical techniques can determine the relative degrees of brady-, normo-, and tachygastric power, but lose information relative to the basic slow wave shape. The aim of the present study was to investigate the application of advanced analytical techniques in the analysis of disrupted GMA recorded after administration of sulprostone, a prostaglandin E3/1 agonist, in ferrets. Ferrets were implanted with radiotelemetry devices to record GMA, blood pressure, heart rate (HR) and core body temperature 1 week before the administration of sulprostone (30 μg/kg) or vehicle (saline, 0.5 mL/kg). GMA was initially analyzed using fast Fourier transformations (FFTs) and a conventional power partitioning. Detrended fluctuation analysis (DFA) was also applied to the GMA recordings to reveal information relative to the fluctuation of signals around local trends. Sample entropy (SampEn) analysis was used for examining the regularity of signals. Conventional signal processing techniques revealed that sulprostone increased the dominant frequency (DF) of slow waves, with an increase in the percentage power of the tachygastric range and a decrease in the percentage power of the normogastric range. DFA revealed that sulprostone decreased the fluctuation function, indicative of a loss of the variability of GMA fluctuations around local trends. Sulprostone increased SampEn values, indicating a loss of regularity in the GMA data. Behaviorally, sulprostone induced emesis and caused defecation. It also increased blood pressure and elevated HR, with an associated decrease in HR variability (HRV). Further analysis of HRV revealed a decrease in both low-frequency (LF) and high-frequency (HF) components, with an overall increase in the LF/HF ratio. Sulprostone did not affect core body temperature. In conclusion, DFA and SampEn permit a detailed analysis of GMA, which is necessary to understand the action of sulprostone to modulate gastric function. The action to decrease HRV and increase the LF/HF ratio may be consistent with a shift toward sympathetic nervous system dominance, commonly seen during nausea.