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Non-fungible tokens (NFTs) are a type of digital record of ownership used in a unique way: ensuring authenticity and uniqueness. Due to these characteristics, NFTs have been used in several markets: games, arts, and sports, among others. In 2020, the volume of negotiations of the NFTs was about USD 200 million. Despite the strong interest of economic agents in operating with NFTs, there are still gaps in the literature, regarding their dynamics and price interrelation with other potentially related assets, which deserve to be studied. In this sense, the main purpose in this paper is to analyze the cross-correlation between NFTs and larger cryptocurrencies. To this end, our methodological approach is based on a Detrended Cross-Correlation Analysis correlation coefficient, with a sliding windows approach. Our main finding is that the cross-correlations are not significant, except for a few cryptocurrencies, with weak significance at some moments of time. We also carried out an analysis of the long-term memory of NFTs, which demonstrated the antipersistence of these assets, with results seemingly corroborating the market inefficiency hypothesis. Our results are particularly important for different classes of investors, due to the analysis on different time scales.

The complexity of the center of pressure (COP) provides important information regarding the underlying mechanisms of postural control. The relationships between COP complexity and balance performance are not fully established and might depend on the task constraints and the filtering decomposition of the COP signal. This study assessed COP complexity under different task constraints and it was assessed if emergent dynamics of COP fluctuations differ according to fractional components of COP related to peripheral or central adjustments. One hundred and sixty-two participants performed two sitting balance tasks. Accuracy was required by following a target that moved in the mediolateral (ML) or in the anteroposterior (AP) axis. Complexity dynamics of COP were addressed through detrended fluctuation analysis (DFA) in the axis constrained by accuracy requirements and in the one nonconstrained. Decomposition of COP components was applied by low-pass, band-pass, and high-pass filters. DFA of low-pass and band-pass components of COP in the constrained axis were small-to-moderately related (r = 0.190-0.237) to balance performance. DFA of the high-pass component of the COP exhibited the opposite relationship (r = -0.283 to -0.453) in both axes (constrained and nonconstrained). This study evidences that COP complexity is linked to better performance. This positive relationship complexity/performance is observed in the low- and mid-frequency components of the COP. These components might be related to central mechanisms of postural control. The lack of relationships between the different frequencies analyzed in the study suggests that they are capturing different components of postural control.NEW & NOTEWORTHY The relationship between the complexity of the center of pressure (COP) and balance performance is not fully established. The task constraints and the filtering decomposition of the COP could influence this relationship. COP complexity is related to a better balance performance only in low frequencies and midfrequencies of the COP. The different frequencies measure different postural control components. Filtering decomposition should be explored in future studies to address the underlying mechanisms of postural control.

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.

To record all electrical activity of the human brain, an electroencephalogram (EEG) test using electrodes attached to the scalp is conducted. Analysis of EEG signals plays an important role in the diagnosis and treatment of brain diseases in the biomedical field. One of the brain diseases found in early ages include autism. Autistic behaviours are hard to distinguish, varying from mild impairments, to intensive interruption in daily life. The non-linear EEG signals arising from various lobes of the brain have been studied with the help of a robust technique called Detrended Fluctuation Analysis (DFA). Here, we study the EEG signals of Typically Developing (TD) and children with Autism Spectrum Disorder (ASD) using DFA. The Hurst exponents, which are the outputs of DFA, are used to find out the strength of self-similarity in the signals. Our analysis works towards analysing if DFA can be a helpful analysis for the early detection of ASD.

In this study we investigate possible long-range trends in the cryptocurrency markets. Our sample includes 37 of the most important cryptocurrencies that reflect more than 80% of the relevant market. For the analysis in the empirical part, we employed the Hurst exponent, a statistical tool used to identify long range autocorrelations and memory in time series data. Our sample covers the period from January 1, 2016 to March 26, 2021. We use three non-overlapping windows for the estimation of the Hurst exponent. With these windows, we assess the dynamic evolution in the structure of the cryptocurrencies market and evaluate the move towards an efficient market. The innovation of this research is that we employ the Hurst exponent that is seldomly used in analyzing this market. Furthermore, the use of both the R/S and DFA analysis and the use of non-overlapping windows enhance our research’s novelty. Finally, we estimate the Hurst for a wide sample of cryptocurrencies that covers more than four fifths of the entire market for the last six years.

Evaluation of hydrological variables plays a vital role in watershed management studies. On top of that, Missouri River Basin system is well known as a large water storage capacity in the USA. In this study, multifractality, statistical features, and random behavior of daily flow discharge, suspended sediment discharge, precipitation, and groundwater level were analyzed in the two stations of Missouri River Basin, USA. Detrended fluctuation analysis and multifractal detrended fluctuation analysis were applied in order to evaluate seasonal trends, random behavior, self-affinity features, and the complexity of behavior types [fractional Brownian motion (fBm) and fractional Gaussian noise (fGn)] of time series. Statistical techniques, including the KPSS test, heteroscedasticity test, and autocorrelation function, were utilized to analyze statistical characteristics of repeating patterns of the datasets. Results of fractal and statistical analyses indicated that flow discharge, suspended sediment discharge, and groundwater time series were following self-affinity and fBm characteristics in a non-stationary and heteroscedastic state. Precipitation time series were not self-affine and represented fGn characteristics in a stationary and homoscedastic state. Eventually, this study can be proposed as an applicable method to distinguish the behavior of rivers and anthropogenic impacts in the watershed for effective hydrological planning management.

Purpose: To understand the dynamics of the agricultural commodities market and predict a possible economic crisis, in addition to helping agricultural producers balance their product portfolio, diversifying their goods and reducing risks. Theoretical framework: Prices of agricultural commodities have changed significantly since 2002; although had been an increase in demand, where weather problems negatively affected supply, resulting in price increases. With the global financial crisis of 2008, there was a reduction in international credit and an increase in the US dollar against the Brazilian Real. Design/Methodology/Approach: Detrended Cross-Correlation Analysis and Detrended Fluctuation Analysis methods were used to understand the behavior of the cross correlations of the price of five Brazilian agribusiness commodities (cotton, sugar, coffee, corn and soybeans) for the previous periods, during and after the subprime crisis. Findings: Both methods showed a significant change in the behavior of the series in the period of crisis, when compared to their temporal neighborhoods. Research, Practical & Social Implications: It was found that the crisis changed the structure of the correlation of the returns on the commodities analyzed. This change implies alterations to a possible product portfolio in order to minimize risks. Originality/Value: The long-term nonlinear correlation behavior was calculated and analyzed on the temporal series for the return on the main agricultural commodities in the period of the subprime crisis and its temporal neighborhoods were calculated and analyzed, allowing several changes to be found in the product correlation structure, due to the crisis process. Keywords: Subprime Financial Crisis; Agricultural Commodities; Detrended Fluctuation Analysis; Detrended Cross-Correlation Analysis.

Myocardial infarction (MI), usually termed as heart attack, is one of the main cardiovascular diseases that occur due to the blockage of coronary arteries. This blockage reduces the blood supply to heart muscles, and a prolonged deficiency of blood supply causes the death of heart muscles leading to a heart attack that may cause death. An electrocardiogram (ECG) is used to diagnose MI as it causes variations like ST-T changes in the recorded ECG. Manual inspection of these variations is a tedious task and also requires expertise as the variations produced by MI are often very short in duration with a low amplitude. Hence, these changes may be misinterpreted, leading to delayed diagnosis and appropriate treatment. Therefore, computer-aided analysis of ECG may help to detect MI automatically. In this study, a robust deep learning model is proposed to detect MI based on heart rate variability (HRV) analysis of ECG signals from a single lead. Ultrashort-term HRV analysis is performed to compute HRV analysis features from time-domain and frequency-domain parameters through power spectral density estimations. Nonlinear HRV parameters are also computed using Poincare Plot, Recurrence Analysis, and Detrended Fluctuation Analysis. A finely tuned customized artificial neural network (ANN) algorithm is applied on 23 HRV features for MI detection and classification. The K-fold validation method is used to avoid any biases in results and reported 99.1% accuracy, 100% sensitivity, 98.1% specificity, and 99.0% F1 for MI detection, whereas 98.85% accuracy, 97.40% sensitivity, 99.05% specificity, and 97.70% F1 score is achieved for classification. Furthermore, the ANN algorithm completed its execution in just 59 seconds that indicates the efficiency of the proposed ANN model. The overall performance in terms of computed evaluation matrices and execution time indicates the robustness and cost-effectiveness of the proposed methodology. Thus, the proposed model can be used for high-performance MI detection, even in wearable devices.

New findings What is the topic of this review? Physiological complexity in muscle force and torque fluctuations, specifically the quantification of complexity, how neuromuscular complexityis altered by perturbations and the potential mechanism underlying changes in neuromuscular complexity. What advances does it highlight? The necessity to calculate both magnitude- and complexity-based measures for the thorough evaluation of force/torque fluctuations. Also the need for further research on neuromuscular complexity, particularly how it relates to the performance of functional activities (e.g. manual dexterity, balance, locomotion). Abstract Physiological time series produce inherently complex fluctuations. In the last 30 years, methods have been developed to characterise these fluctuations, and have revealed that they contain information about the function of the system producing them. Two broad classes of metrics are used: (1) those which quantify the regularity of the signal (e.g. entropy metrics); and (2) those which quantify the fractal properties of the signal (e.g. detrended fluctuation analysis). Using these techniques, it has been demonstrated that ageing results in a loss of complexity in the time series of a multitude of signals, including heart rate, respiration, gait and, crucially, muscle force or torque output. This suggests that as the body ages, physiological systems become less adaptable (i.e. the systems' ability to respond rapidly to a changing external environment is diminished). More recently, it has been shown that neuromuscular fatigue causes a substantial loss of muscle torque complexity, a process that can be observed in a few minutes, rather than the decades it requires for the same system to degrade with ageing. The loss of torque complexity with neuromuscular fatigue appears to occur exclusively above the critical torque (at least for tasks lasting up to 30 min). The loss of torque complexity can be exacerbated with previous exercise of the same limb, and reduced by the administration of caffeine, suggesting both peripheral and central mechanisms contribute to this loss. The mechanisms underpinning the loss of complexity are not known but may be related to altered motor unit behaviour as the muscle fatigues.

Present study is aimed at investigating the solar faculae area from 1990 to 2007 which partially covered the22nd and 23rd solar cycle. Rescaled Range Analysis (RRA) and Detrended Fluctuation Analysis (DFA) have beenadopted to evaluate the behaviour of nonlinear dynamics of solar faculae area. Results show that the value of Hurstexponent for solar faculae area from RRA and DFA is negatively correlated. It means it is non-persistent and longrange correlated. Obtained result is inaccurate so the only solution is to transform the data into stationary data by takingdifferencing. RRA is applied on residuals and RRA to evaluate the fractal property of the time series. Solar faculae areainvestigated in this study is fractal in nature and predictable ass well. Moreover, the time series of solar faculae area isnon-linear as established by the Brock – Dechert – Scheinkman (BDS) test results

The detrended fluctuation analysis, a technique for detecting long-range correlations in fractal time series, is used to characterize thermoacoustic oscillations of impending combustion instabiliti...

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.

Saliva has emerged as an efficient screening sample for early stage detection of oral cancer (OC) owing to non-invasiveness coupled with high sensitivity and specificity. Although spectroscopic characterization of saliva in oral potentially malignant disorders OPMDs) and OC is extensively studied, its potential as imaging biomarker is sparsely explored. Further, the literature on crystalline pattern of saliva for other diseases or different physiological conditions is mostly qualitative. This paper proposed multifractal based methodology to quantitatively study alteration of the salivary fern pattern in different OPMDs and OC in relation to normal counterpart. The fern pattern of dried saliva is captured by stereo-zoom microscope in reflective mode and an image dataset is developed. We resort to two dimensional multi-fractal detrended fluctuation analysis (2d MFDFA) to elucidate the complexity and heterogeneity of these micro-structured patterns. Existence of multifractal nature embedded in salivary fern has been validated for the first time. Long range spatial correlation is found to be the origin of multifractality. Variation in multi-scale self-similarity of irregular pattern in different study groups is demonstrated by four features extracted from MFDFA. Statistical analysis shows discriminating nature of these features for combinations of pairwise interclass classification. This study sheds light on acceptability of microscopic images of arborized saliva in fast and cost effective screening of different oral lesions.

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.

The Nagel–Schreckenberg vehicular traffic model is extended to analyse a system of vehicles moving on a scale-free network to study extreme events in them. The dependence of the free-flow and congestion states on the density of vehicles is determined. In particular, a free-flow state at low vehicular density is observed and it gradually transitions to a congested state at higher density. Using detrended fluctuation analysis, it is shown that the flux of vehicles are long range correlated in a regime of low density. At higher densities, the flux becomes uncorrelated. We study the recurrence interval distribution for extreme events and the probability for its occurrence at low and high vehicular density regimes. It is shown that the occurrence probability for extreme events is independent of the degree of the node or the threshold used for defining extreme events

Studies on entomopter’s performance under the influence of gust have received impetus in the past decade. There exists a dire need to ascertain the threshold of the frontal gusty conditions which would destabilize these anthropogenic flyers. This would help to devise methods to mitigate the detrimental effects of gust. In light of this aspect, the present study aims at analyzing the onsets of instability in a flapping wing system subjected to temporal gust by employing recurrence period density entropy (RPDE) and detrended fluctuation analysis (DFA). Simulation of the flapping wing along inclined stroke is carried out for a Reynolds number of 150. This Reynolds number lies in the typical operating regime of fruit flies and entomopters like the Pico aerial vehicle. Numerical simulations are carried out to solve the laminar, unsteady, and incompressible Navier–Stokes equations. The dynamic meshing technique is employed to model flapping kinematics. Nine gusts with a combination of frequency and velocity ratios of 0.1, 0.5, and 1.0 are considered. Instantaneous horizontal and vertical forces are estimated. Time series of these forces are analyzed using RPDE and DFA paradigms. These analyses indicate that gust frequency of an order of magnitude higher than flapping frequency and gust amplitude of the order of magnitude as the wing’s root mean square velocity induces a possible onset of instability.

The paper presents a technique for calculating information-correlation characteristics based on the methods of average mutual information and two-dimensional detrended fluctuation analysis. The experimental samples are structures with an array of self-organized InAs/GaAs quantum dots grown without a cover layer by gas-phase epitaxy from metalorganic compounds. The microstructure of the sample surfaces is studied by scanning electron microscopy. The information-correlation characteristics of InAs/GaAs structures with quantum dots are obtained using two-dimensional detrended fluctuation analysis and average mutual information. The order of the array of quantum dots in the InAs/GaAs structure is estimated depending on the applied technological modes of production. It is found that increasing the growth temperature of the experimental samples from 480 to 520°C increases the ordering of the location of quantum dots on the surface.

Altered movement complexity, indicative of system dysfunction, has been demonstrated with increased running velocity and neuromuscular fatigue. The critical velocity (CV) denotes a metabolic and neuromuscular fatigue threshold. It remains unclear whether changes to complexity during running are coupled with the exercise intensity domain in which it is performed. The purpose of this study was to examine whether movement variability and complexity differ exclusively above the CV intensity during running. Ten endurance-trained participants ran at 95%, 100%, 105% and 115% CV for 20 min or to task failure, whichever occurred first. Movement at the hip, knee, and ankle were sampled throughout using 3D motion analysis. Complexity of kinematics in the first and last 30 s were quantified using sample entropy (SampEn) and detrended fluctuation analysis (DFA-α). Variability was determined using standard deviation (SD). SampEn decreased during all trials in knee flexion/extension and it increased in hip internal/external rotation, whilst DFA-α increased in knee internal/external rotation. SD of ankle plantar/dorsiflexion and inversion/eversion, knee internal/external rotation, and hip flexion/extension and abduction/adduction increased during trials. Hip flexion/extension SampEn values were lowest below CV. DFA-α was lower at higher velocities compared to velocities below CV in ankle plantar/dorsiflexion, hip flexion/extension, hip adduction/abduction, hip internal/external rotation. In hip flexion/extension SD was highest at 115% CV. Changes to kinematic complexity over time are consistent between heavy and severe intensity domains. The findings suggest running above CV results in increased movement complexity and variability, particularly at the hip, during treadmill running.

Every woman spends her life with a cyclic occurrence of the menstrual cycle of approximately 28 days. During a menstrual cycle, there are many physical, psychological and behavioural changes in women that affect the autonomic activities of the heart. However, health management is an important factor to be considered as it influences the entire quality of women life. Thus, Heart Rate Variability (HRV) analysis is an appropriate tool to examine the physiological effects of the menstrual cycle in young healthy women. So, in this paper, Detrended Fluctuation Analysis method (DFA) is used for analyzing the HRV in the phases of the menstrual cycle. In DFA, there is a limitation of abrupt jumps in detrended profile that leads to the inaccurate detection of properties of HRV. In order to overcome the limitations of abrupt jumps in the DFA method, a novel method is proposed in this paper. The trend in proposed method is created by averaging the integrated HRV time series of each window in its respective time scale. Then, cubic interpolation is done for estimating new data points within each averaged segment. Finally, proposed trend is used to estimate scaling exponent function. The proposed method detects the properties of HRV variations accurately among phases of the menstrual cycle when applied on self-recorded dataset.

We aimed to analyse the complexity and fractal nature of heartbeat during constant exercise, at three different intensities, and recovery.Fourteen healthy men underwent 4 separate sessions. The first session was an incremental treadmill test to determine ventilatory thresholds (VT1 and VT2) and maximal aerobic speed (MAS). Each subject ran at VT1 and VT2 speeds and MAS (second, third and fourth day). The duration of VT1 and VT2 loads were selected in such a way that the product intensity-duration (training load) was the same. Sample Entropy (SampEn) and slope of Detrended Fluctuation Analysis (DFA α1) were measured during the whole session.DFA α1 declines with exercise, being less in the VT1 trial than in the other two.SampEn shows no significant change during exercise. The three tests induce the same decline in SampEn, but at the highest intensity (MAS) tends to decline during the exercise itself, whereas at lower intensities (VT1, VT2) the decline is delayed (10 min of recovery). Subsequently, SampEn at VT1 gradually recovers, whereas at VT2 and MAS it remains stable during recovery.In conclusion, exercise produces a loss of heartbeat complexity, but not fractal nature, during recovery and it depends on intensity.

The control of voluntary movements is a dual structure consisting of cognitive and physical controls; cognitive control involves attentional resources, unlike physical control. Various voluntary movements can be performed by combining cognitive and physical controls. Body movements depending on attentional resources are performed using cognitive control; these movements fluctuate with white noise and their fluctuations gradually become the one-over-f fluctuation as the dependence on the attentional resources decreases. The handwriting process of characters is a voluntary movement. This study focused on the relationship between the repetitive handwriting process and the attentional resources allocated to it. The attention resources allocated to the handwriting process depend on the difficulty of the handwriting task. Moreover, the difficulty of a handwriting task is determined by the complexity of the shape of the handwritten characters, and the stroke counts is one indicator of this. Therefore, we focused on five Chinese kanji characters with different stroke counts. We investigated fluctuations in the temporal and spatial handwriting elements (twelve handwriting elements in all) defined within the handwriting process of each Chinese kanji character. The detrended fluctuation analysis was applied to the fluctuation analysis of the handwriting elements. In this paper, we discussed the relationship between the handwriting task difficulties and handwriting elements using local scaling indices based on the detrended fluctuation analysis.

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.

This paper proposes a granular framework for examining the dynamics of stock indexes that exhibit nonparametric and highly volatile behavior, and subsequently carries out the predictive analytics task by integrating detrended fluctuation analysis (DFA), maximal overlap discrete wavelet transformation (MODWT), and machine learning algorithms. DFA test ascertains the key temporal characteristics of the daily closing prices. MODWT decomposes the time series into granular components. Four pattern recognition algorithms—adaptive neuro fuzzy inference system (ANFIS), dynamic evolving neural-fuzzy inference system (DENFIS), bagging and deep belief network (DBN)—are then used on the decomposed components to obtain granular level forecasts. The entire exercise is performed on daily closing prices of Dow Jones Industrial Average (DJIA), National Stock Exchange of India (NIFTY), Karachi Stock Exchange (KSE), Taiwan Stock Exchange (TWSE), Financial Times Stock Exchange (FTSE), and German Stock Exchange (DAX). MODWT-Bagging and MODWT-DBN appear as superior forecasting models.

Objective: Aimless movement or wandering may be a symptom of mild cognitive impairment (MCI) that arises as a consequence of confusion and forgetfulness. This paper presents a support vector machine (SVM) framework based on movement analysis for the prediction of the onset and progression of MCI. Methods: Movement data of 22 subjects with MCI, and 22 other healthy subjects, living independently in smart homes were collected for ten years using motion sensors. Features were extracted from the sensor data using movement metrics, including cyclomatic complexity, detrended fluctuation analysis, fractal index, entropy, and room transitions. Two different SVM classification algorithms were trained using the features, first to predict the progression of MCI in the post-transition period, and second to predict the onset of MCI in the pre-transition phase. Results: The two SVMs were able to detect the onset six months earlier than the clinical diagnosis. The model accuracy in classifying MCI increased monotonically from the onset month and reached maximum (81%) at the 11th post-transition month. The features of cyclomatic complexity contributed significantly to the prediction results. Conclusion: Findings support the use of movement complexity measures and machine learning for monitoring cognitive behavior in an independent living environment.

The influence of ARFIMA model parameters on the accuracy of financial time series forecasting on the example of artificially generated long memory series and daily log returns of RTS index is investigated. The investigated parameters are deviation of the integration order value from its «true» value, as well as the memory «length» considered by the model. Based on the research results, some practical recommendations for modeling using ARFIMA have been formulated.

This study presents a novel approach using adaptive variational mode decomposition with detrended fluctuation analysis to detect the islanding disturbances for photovoltaic based DC micro grid. DC parameters are simple to estimate in comparison to AC profile. Thus DC parameters are recorded under islanding scenario, and processed through proposed adaptive variational mode decomposition which decomposes the signals into intrinsic mode functions. These segregated intrinsic mode functions are further selected optimally by choosing the significant weighted kurtosis index. This optimal selection (maximisation of weighted kurtosis index) is ensured by modified particle swarm optimisation in terms of number of modes (K) and penalty factor (σ). For detection and monitoring (D&M) accurate islanding scenario the significant intrinsic mode functions are subjected to detrended fluctuation analysis, where power exponent (α) values are utilised for correct detection (i.e. distinguishing islanding out of other grid contingencies by two and three dimensional scattering plots). The effectiveness of the proposed D&M for DC micro grid is established in this paper in terms of classification accuracy and relative computational time. The proposed DC side islanding D&M method is less complex (as compared to AC signals) to be implemented. Fastness and accuracy of proposed D&M is established and performed in MATLAB/Simulink platforms.

Purpose1. To improve the causality analysis performance, a novel causality detector based on time-delayed convergent cross mapping (TD-CCM) is proposed in this work. 2. Identify the root cause of plant-wide oscillations in process control system.Design/methodology/approachA novel causality analysis framework is proposed based on denoising and periodicity-removing TD-CCM (time-delayed convergent cross mapping). We first point out that noise and periodicity have adverse effects on causality detection. Then, the empirical mode decomposition (EMD) and detrended fluctuation analysis (FDA) are combined to achieve denoising. The periodicities are effectively removed through singular spectrum analysis (SSA). Following, the TD-CCM can accurately capture the causalities and locate the root cause by analyzing the filtered signals.Findings1. A novel causality detector based on denoising and periodicity-removing time-delayed convergent cross mapping (TD-CCM) is proposed. 2. Simulation studies show that the proposed method is able to improve the causality analysis performance. 3. Industrial case study shows the proposed method can be used to analyze the root cause of plant-wide oscillations in process control system.Originality/value1. A novel causality detector based on denoising and periodicity-removing time-delayed convergent cross mapping (TD-CCM) is proposed. 2. The influences of noise and periodicity on causality analysis are investigated. 3. Simulations and industrial case shows that the proposed method can improve the causality analysis performance and can be used to identify the root cause of plant-wide oscillations in process control system.

Motivation The quantification of long-range correlation of electroencephalogram (EEG) signals is an important research direction for its relevance in helping understanding the brain activity. Epileptic seizures have been studied in the past years where different non-linear statistical approaches have been employed to understand the relationship between the EEG signal and the epileptic discharge. One of the most widely used method for to analyse long memory processes is the detrended fluctuation analysis (DFA). However, no objective and pragmatic methods have been developed to detect crossover points and reference channels in DFA. Results In this article, we propose: (i) two automatic approaches that successfully detect crossover points in DFA related methods on the log–log plot and (ii) a criteria to choose the reference channel for the log-amplitude function. Moreover, the DFA is applied to EEG signals of 10 epileptic patients collected from the CHB-MIT database, being the log-amplitude function used to compare the different brain hemispheres by making use of the methodology proposed in the article. The existence of long-range power-law correlations is demonstrated and indicates that the EEG signals of epileptic patients present three well-defined regions with the first region showing a 1/f noise (pink noise) for seven subjects and a random walk behaviour for three subjects. The second and third regions show anti-persistence behaviour. Moreover, the results of the log-amplitude function were divided in two groups: the first, including seven subjects, where the increase in the scales results in an increase in the fluctuation in the frontal channels and the second, included three subjects, where the fluctuation for large scales are greater for the parietal channels. Availability and implementation The functions used in this article are available in the R package DFA (Mesquita et al., 2020). Supplementary information Supplementary data are available at Bioinformatics online.

The present study is designed to analyse the annual rainfall variability and trend in 30 meteorological stations of the Asir region for the period of 1970–2017 using the Mann-Kendall (MK) test, Modified Mann-Kendall (MMK) test, trend free pre-whitening Mann-Kendall (TFPW MK) test, and the innovative trend analysis (ITA). A comparative study among the trend detection techniques was performed using the correlation coefficient. The future rainfall trend based on the historical rainfall pattern was investigated by using detrended fluctuation analysis (DFA). Results of the MK test showed that 20 stations in the study area observed a negative trend, and out of these, nine stations had significant negative trends at the significance level of 0.01. The findings of the MMK test showed that 23 stations recorded negative trends, and out of these, 18 stations had significant negative trends at the significance level of 0.01. Based on the findings of the TFPW-MK test, 21 stations observed a negative trend, and among these, 10 stations had significant negative trends at the significance of 0.01. ITA detected 25 stations observing a negative trend, and out of these, 18 stations had significant negative trends at the significance level of 0.01. Based on the findings of the tests and their performance, the MMK test appeared as the best performing technique among the MK test family, while ITA appeared as the best trend detection technique among the four techniques because it outperformed (p

This study intends to analyse efficiency, in its weak form, in the financial markets of Indonesia, Malaysia, Philippines, Singapore, Thailand (Asean-5), and China, during the global pandemic (Covid-19). Different approaches have been undertaken to carry out this analysis in order to determine whether: Asean -5 financial markets and China are efficient, in their weak form, during the analysis period? The results indicate that the random walk hypothesis is rejected in all markets. The values of the variance ratios are, in all cases, lower than the unit, which implies that the returns are autocorrelated over time and, there is a reversion to the average, in all indices.In corroboration, the exponents Detrended Fluctuation Analysis (DFA), indicate significant long memories with a larger incidence in the Philippines and Singapore markets, however the Chinese market evidences anti persistence. These results demonstrate that stock prices do not completely reflect the available information and that stock prices movements are not i.i.d. This has implications for investors, as some returns can be expected, creating opportunities for arbitrage and abnormal returns, contrary to the assumptions of random walk and information efficiency. These conclusions also allow market regulators to implement measures to ensure better information in these regional markets.

There is a delayed (lag 1 to 2 days) correlation between acute PM 2.5 (particulate matter 35.4 μg/m3) or low (

Control system performance assessment is significant, especially in practical applications. One of the most important indices for the performance assessment of control systems is minimum variance. Calculating the minimum variance index in multivariate systems requires prior knowledge of system parameters and models, and is therefore an obstacle in practical applications. In this article, an index is proposed for the performance assessment of multivariate control loops, evaluating the system performance with the minimum variance criterion and using only the system’s routine operation data. This index can quantify the performance using neither any prior knowledge of system parameters nor the system’s optimal operation data. The proposed index is based on the Hurst exponent, a parameter for measuring correlations in time series data. In this article, detrended fluctuation analysis and rescaled range analysis are used to estimate the Hurst exponents of system outputs. Using a combination of these Hurst exponents, an index is defined for the performance assessment of multivariate systems. The results of simulation examples illustrate that the proposed index can assess the performance efficiently.

Long-term memory has been studied for decades and it has long been acknowledged that hydrological and hydro-meteorological time series exhibit this property. Physically, long-term memory is explained by saying that the stronger the long-term memory the more likely a series will ‘remember’ its previous value, in other words, the longer a time series is likely to persist in the proximity of a certain value. To increase the benefit of the study of long-term memory, we investigate the extent to which this explanation is accurate and descriptive of long-term memory by developing a ‘persistence measure’ that quantifies the intuitive description of long-term memory. The ‘persistence measure’ is compared to the scaling exponent (α) which quantifies long-term memory using detrended fluctuation analysis. A total of 17,359 series, including hydrological and hydro-meteorological series, downloaded from online sources and 130 synthetic series are analyzed. The main outcome is that two regimes are found. The first is for series with α ≲ 1.05 where the persistence measure is not sensitive to the scaling exponent. Hence, changes in α does not lead to an increase in the memory strength (i.e. the persistence measure). The second regime is for series with α ≳ 1.05 where a statistically significant positive correlation was found. Hence, for a certain range of values of α the physical explanation of long-term memory holds. Nevertheless, it is proposed that adding additional factors may create a more robust ‘persistence measure’ that can be easily understood and incorporated in hydrologists’ work.

This study investigates the hourly prices of the electricity day-ahead market nonstationary characteristics and long-range correlation. Using the detrended fluctuation analysis (DFA) approach, we show evidence of long memory for the Bulgarian day-ahead market between January 20th, 2016 and December 31, 2019. Furthermore, the results from the DFA methodology shows that behavior of the hourly electricity spot prices returns were long term positively correlated. DFA methods can be used as powerful tools for analyzing very volatile series like electricity prices considering the fact that in recent years prices become more volatile due to increased integration of renewables that are intermittent and far more volatile than other commodities normally considered with extreme volatility. Day ahead electricity prices are crucially important for forecasting, derivatives pricing and risk management and therefore in this paper we give a brief introduction on DFA method. This research work was carried out as part of the scientific project “Investigation of the application of new mathematical methods for the analysis of cardiac data” № КP-06-N22/5, date 07.12.2018, funded by the National Science Fund of Bulgaria (BNSF).

A financial time series, such as a stock market index, foreign exchange rate, or a commodity price, fluctuates heavily and shows scaling behaviors. Scaling and multi-scaling behaviors are measured for a nonstationary time series, such as stock market indices, high-frequency stock prices of individual stocks, or the volatility time series of a stock index. We review the fractality, multi-scaling, and multifractality of the financial time series of a stock market. We introduce a detrended fluctuation analysis of the financial time series to extract fluctuation patterns. Multifractality is measured using various methods, such as generalized Hurst exponents, the generalized partition function method, a detrended fluctuation analysis, the detrended moving average method, and a wavelet transformation.

This paper formulates a novel integrated measure for energy market efficiency, by investigating different aspects of the market performance. Different from most existing models focusing on one certain aspect, the novel measure especially takes into consideration the self-similarity (or system memo ability or long-term persistence) via fractality, the attractor properties in phase-space via chaos, and disorder state of data dynamics via entropy. In the proposed method, the most popular data analysis techniques of multi-fractal detrended fluctuation analysis, correlation dimension, and sample entropy are respectively conducted on the market returns to capture the corresponding features, and the entropy weight method is then used to generate the final integrated index. For illustration and verification, the proposed measure is applied to three typical energy markets analyses. The empirical results find that natural gas market and crude oil market are much more efficient than carbon market.

Purpose The new COVID-19 pandemic caused by SARS-CoV-2 initiated in the world a large quarantine, due to the exponential capacity of the virus in spreading from human contact. In the present work, the dynamics of such spreading was evaluated by the analysis of the growth factor of the disease. Method It was applied the space phase of the time series, the detrended fluctuation analysis (DFA) of the series, and the fractal dimension of the space phase. Results It was possible to notice a strange attractor in the space phase of the growth factor indicating that the process is a deterministic chaos. The value of the alpha coefficient by DFA showed to be less than 0.5, characteristic of anti-persistent long-range memory, in which large events alternate with small events, and vice-versa. The fractal dimension of the phase space set was a fractal number, between 1 and 2, another indicator that the growth factor of the disease is not random. Conclusion This global analysis is pointing that the spread of COVID-19 is a deterministic chaos, with long-range memory. Understanding such dynamics may help the control of this disease.

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 article proposes an advanced technique for condition assessment of outdoor insulators based on its surface leakage current through employing detrended fluctuation analysis (DFA). Analysis of surface leakage current of in-service insulator can be useful for assessing its surface condition. In the proposed technique, a tracker signal has been developed based on the fundamental component of surface leakage current to extract the distortions from it which carries significant information about contamination level. DFA has then been applied on the extracted distortions of leakage current to estimate its contamination level. In order to investigate experimentally, surface leakage current of 11-kV disc insulator (contaminated at different level) has been captured at different applied voltage level. The proposed technique has been applied on the captured leakage current to estimate contamination level. Results show that employment of the proposed technique provides satisfactory outcomes regarding assessment of insulator condition, which in turn improves the reliability of power system.

This paper investigates the existence of chaos in concentration dynamics of particulate matter with an aerodynamic diameter less than or equal to $$10\,\upmu \hbox {m}$$ ( $$\hbox {PM}_{10}$$ ) in the greater Athens area (GAA), Greece. It reports findings on three 16-year $$\hbox {PM}_{10}$$ time series recorded by three different air pollution monitoring stations located in GAA and examines if critical fractal epochs with long memory exist. Detrended Fluctuation Analysis (DFA) and Rescaled Range (R/S) Analysis were used via sliding windows of approximately 1-month duration. In all $$\hbox {PM}_{10}$$ time series, several segments were found with critical fractal behaviour and hidden long-memory patterns. All these segments exhibited Hurst exponents above 0.75 and DFA exponents above 1.75. Twelve $$\hbox {PM}_{10}$$ segments with fractality and long memory were commonly identified by both techniques. In one case, long memory was identified concurrently across all three air pollution monitoring stations and in another case, across two stations. The importance of the agreement between two different and independent chaos-analysis techniques is discussed in association with the proper selection of threshold values. This is the second time to address chaos in $$\hbox {PM}_{10}$$ data series in GAA, and the first time to combine two widely accepted techniques, DFA and R/S analysis.

This study analysed long-term rainfall data (1851–2006) over seven climatic zones of India at seasonal and annual scales based on three techniques: (i) linear regression, (ii) multifractal detrende...

The present study examines the influence of a 10 km race of runners with different performance levels on time-domain measures and non-linear dynamics of HRV. Twenty-two male recreational to elite r...

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.

In this study, an attempt has been made to analyze uterine Electromyography (uEMG) signals during Term conditions (pregnancy duration more than 37 weeks of gestational age) using Empirical Mode Decomposition based Detrended Fluctuation Analysis (EMD-DFA). The Term delivery signals are considered from a publicly available database, grouped as T1 (

The robustness of two widespread multifractal analysis methods, one based on detrended fluctuation analysis and one on wavelet leaders, is discussed in the context of time-series containing non-uniform structures with only isolated singularities. Signals generated by simulated and experimentally-realized chaos generators, together with synthetic data addressing particular aspects, are taken into consideration. The results reveal essential limitations affecting the ability of both methods to correctly infer the non-multifractal nature of signals devoid of a cascade-like hierarchy of singularities. Namely, signals harboring only isolated singularities are found to artefactually give rise to broad multifractal spectra, resembling those expected in the presence of a well-developed underlying multifractal structure. Hence, there is a real risk of incorrectly inferring multifractality due to isolated singularities. The careful consideration of local scaling properties and the distribution of H\"older exponent obtained, for example, through wavelet analysis, is indispensable for rigorously assessing the presence or absence of multifractality., Comment: To appear in Nonlinear Dynamics

This paper proposes a strategy for suppressing noise via empirical mode decomposition (EMD)-based hierarchical multiresolution analysis. First, an intrinsic mode function (IMF) index that can differentiate the noise-dominant IMFs and the information-dominant IMFs in the first level of decomposition is determined by the conventional EMD-based denoising method. Next, the EMD is applied to those discarded IMFs in the first level of decomposition to obtain the IMFs in the second level of decomposition. Then, the detrended fluctuation analysis (DFA) is employed to define the IMF index separating the noise-dominant IMFs and the information-dominant IMFs in the second level of decomposition. Information-dominant IMFs in both the first and second levels of decompositions are summed together to obtain the denoised signal. The study is limited to signals that were corrupted by additive white Gaussian noise (AWGN). Extensive computer numerical simulations are conducted on both synthetic signals and practical signals. The results show that our proposed method is promising in some cases, especially at high-input SNR levels. For example, in the case of the CH4 signal with 12-dB input SNR, the processed SNR based on our proposed strategy with the consecutive mean squared error (CMSE) is 23.27 dB, while that based on the conventional CMSE method is only 23.14 dB. Also, our proposed method can extract information from more than one level of decomposition to reconstruct the denoised signal compared to only one level of decomposition in the conventional EMD-based denoising method.

An understanding of the trend in cooling and heating degree-days acts as a driving force for building energy demand under climate change conditions. However, little is known about the spatiotemporal trend patterns in cooling and heating degree-days in recent times and their possible causes in Bangladesh. Therefore, we explored the trend and variability of cooling degree-days (CDD) and heating degree-days (HDD) and their possible reasons for variation for the study period 1980–2017 based on daily temperatures datasets from 27 sites in Bangladesh. The results show that the highest annual mean CDD and HDD were identified in the southwestern and central climatic regions of Bangladesh. The CDD trend has significantly increased in Bangladesh, and the HDD trend has increased but non-significance. The outcomes of detrended fluctuation analysis (DFA) and R/S analysis exhibit that CDD and HDD will continue their contemporary trend direction in the future. Land–Ocean Temperature Index (LOTI) had a significant positive influence on CDD; however, there was no significant correlation between HDD and atmospheric circulation indices. The importance analysis from the random forest (RF) model showed that the LOTI is the highest contributing variable for CDD and East Asian Summer Monsoon Index (EASMI) is the largest influential variable for HDD affecting climate variability in Bangladesh. ECMWF ERA5 reanalysis datasets depict that higher summer geopotential height, an anticyclonic center, enhanced relative humidity, declined total and high cloud covers, decreasing surface solar radiation, and high skin temperature fluxes might have influenced on CDD and HDD variations in Bangladesh.