Search Results (18)

Cupping therapy has been demonstrated to improve hemodynamic regulation. Existing studies have reported mean changes of oxyhemoglobin (OxyHb) and deoxyhemoglobin (DeoxyHb), which do not capture the multi-scale regulatory dynamics of the microvasculature. It is therefore unclear whether cupping therapy modulates the complexity and fractal property of hemodynamic signals. The objective of this study was to examine complexity of hemodynamic response to cupping therapy. A 2 by 2 factorial design with repeated measures was used to examine the main effect of pressure (−225 and −300 mmHg) and duration (5 and 10 min) and their interaction. A near infrared spectroscopy (NIRS) was used to measure OxyHb and DeoxyHb concentrations before and after cupping therapy. A total of 18 healthy participants were enrolled in this study. The wavelet analysis, sample entropy and detrended fluctuation analysis (DFA) were used to quantify the oscillatory, complexity, and fractal scaling properties of OxyHb and DeoxyHb signals. A two-way ANOVA with Bonferroni correction was used to examine the main and interaction effects. The results demonstrated that the combined effects of pressure and duration, rather than either factor independently, were the primary determinants of the dynamic hemodynamic response to cupping therapy, with significant Pressure × Duration interactions observed in DeoxyHb myogenic wavelet power (F = 4.636, p = 0.046, η²p = 0.214), OxyHb (F = 5.704, p = 0.029, η²p = 0.251) and DeoxyHb (F = 6.600, p = 0.020, η²p = 0.280) sample entropy, and DeoxyHb DFA scaling exponent (F = 5.598, p = 0.030, η²p = 0.248). In addition, cupping pressure selectively modulated neurogenic DeoxyHb oscillatory power (F = 5.001, p = 0.039, η²p = 0.227), and cupping duration significantly altered the fractal scaling properties of DeoxyHb signals (F = 7.775, p = 0.013, η²p = 0.314). The findings indicate that the interaction of pressure and duration of cupping therapy could effectively modulate hemodynamic responses. To the best of our knowledge, this is the first study investigating the complexity of hemodynamic responses after cupping therapy. Full article

Assessing electricity market efficiency is important for power market reform and the development of sustainable power systems. Efficient prices can improve resource allocation and provide better signals for system operation, system flexibility and low-carbon transition. Against this background, this study examines the efficiency of three representative provincial electricity spot markets in China, Shandong, Shanxi and Guangdong, using day-ahead and real-time price data from January 2022 to August 2024. A multi-method framework including unit root tests, price convergence tests, detrended fluctuation analysis and sample entropy is employed to evaluate market efficiency and compare differences across provinces. The results show that none of the three markets satisfies the weak-form Efficient Market Hypothesis. The fractal analysis and entropy results further suggest that market efficiency remains limited. Cross-provincial differences are nevertheless observed, which may be partly related to intraday load patterns, generation mix, market structure, and market design. This study provides useful evidence for deepening electricity market reform, as well as promoting the efficient and sustainable development of power systems. Full article

Accurate tail risk forecasting in emerging markets is frequently compromised by the nonlinear dynamics and time-varying long memory of high-frequency volatility. In this study, we employ multifractal detrended fluctuation analysis (MF-DFA) to decode the complex market behavior, revealing pronounced multifractality and strong persistence that defy the static assumptions of classical linear models. The multifractal analysis is only used for research motivation and model design, not as input features for the model. To bridge the gap between fractal diagnostics and predictive modeling, we propose an attention-based dynamically reweighted SA-HAR-J-Net framework. This architecture uniquely integrates HAR-style multi-horizon inputs with a bidirectional LSTM (BiLSTM) encoder and a temporal self-attention mechanism. Crucially, the attention module functions as a dynamic reweighting system, allowing the model to adaptively emphasize historical patterns that receive higher attention weights under changing market conditions, thereby mimicking the time-varying correlations inherent in multifractal processes. Furthermore, we incorporate jump proxies and realized higher moments to enhance the capture of extreme tail dynamics. Utilizing a strict expanding-window out-of-sample protocol, the proposed method achieves significantly lower quantile loss and superior calibration relative to established econometric and machine learning benchmarks for Value-at-Risk (VaR) forecasting. This work provides a robust framework for tail risk monitoring by effectively aligning deep learning architectures with the stylized facts of multifractal markets. Full article

Power system blackouts represent typical manifestations of instability in complex systems, whose evolution often exhibits non-stationarity, long-range correlations, and nonlinear scaling behavior. Most reliability assessment methods widely used in engineering practice are built on the core assumptions of event independence and light-tailed distribution, which will inevitably lead to systematic underestimation of extreme tail risks when blackouts actually present long-range memory and power-law heavy-tailed characteristics. Based on long-cycle historical blackout records of China’s power grid spanning 1981–2025, this paper develops an integrated framework combining Self-Organized Criticality (SOC) theory, Hurst exponent analysis, symbolic time-series methods, and Multifractal Detrended Fluctuation Analysis (MFDFA). This study systematically characterizes the evolution law and inherent dependence structure of blackout events from four dimensions: statistical scaling, temporal correlation, nonlinear structure, and multi-scale fractal spectrum. The results show that both the load-loss magnitudes and inter-event intervals of blackouts follow strict power-law distributions, with the system exhibiting scaling behavior consistent with SOC theory. The blackout event sequence presents significant long-range positive correlation and self-similarity, confirming a persistent long-term memory effect in the system evolution. Symbolic analysis further reveals the nonlinear fluctuation patterns and burst clustering behavior of the blackout process, reflecting the intermittency and complexity of blackout risks. MFDFA results verify that the blackout sequence has a broad-spectrum multifractal structure across different temporal scales, and Monte Carlo shuffle tests demonstrate that this multifractality mainly arises from intrinsic long-range temporal correlations, rather than being driven solely by heavy-tailed distribution. This study confirms that blackouts in China’s power grid are not random independent events, but present fractal statistical characteristics consistent with the self-organized critical mechanism. The findings provide a novel fractal perspective and quantitative framework for the statistical characterization, operational security assessment, and multi-scale early-warning modeling of blackout risks in China’s large-scale power systems. Full article

The field of emotion recognition from physiological signals is a growing area of research with significant implications for both mental health monitoring and human–computer interaction. This study introduces a novel approach to detecting emotional states based on fractal analysis of electrodermal activity (EDA) signals. We employed detrended fluctuation analysis (DFA), Hurst exponent estimation, and wavelet entropy calculation to extract fractal features from EDA signals obtained from the CASE dataset, which contains physiological recordings and continuous emotion annotations from 30 participants. The analysis revealed significant differences in fractal features across five emotional states (neutral, amused, bored, relaxed, and scared), particularly those derived from wavelet entropy. A cross-correlation analysis showed robust correlations between fractal features and both the arousal and valence dimensions of emotion, challenging the conventional view of EDA as a predominantly arousal-indicating measure. The application of machine learning for emotion classification using fractal features achieved a leave-one-subject-out accuracy of 84.3% and an F1 score of 0.802, surpassing the performance of previous methods on the same dataset. This study demonstrates the potential of fractal analysis in capturing the intricate, multi-scale dynamics of EDA signals for emotion recognition, opening new avenues for advancing emotion-aware systems and affective computing applications. Full article

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. Full article

The extra-long expressway tunnel has a high socio-economic effect on inter-regional development, with high traffic and strong traffic winds. Nevertheless, the impacts of the tunnel traffic volume on pollutant evolution are rarely considered. This study conducted a field measurement in a real-world extra-long highway tunnel for 578 days. For the first time, the nonlinear dynamics of traffic pollutants (CO, VOCs, NO₂, PM_2.5, PM₁₀) were analyzed using the Multifractal Detrended Fluctuation Analysis approach. Using the Random Forest model, the impacts of traffic and environmental parameters on air quality were quantified. The findings indicated that COVID-19 had a considerable impact on tunnel traffic, although the variance in pollutant concentration was not very noteworthy. The bidirectional effect of traffic was the main reason for this phenomenon. The Canonical Correlation Analysis was unable to quantify the correlation between pollutants and environmental parameters. The pollutant concentration evolution has a steady power-law distribution structure. Further, an inverse Random Forest model was proposed to predict air pollutants. Compared with other prediction models (baseline and machine learning), the proposed model provided higher goodness of fit and lower prediction error, and the prediction accuracy was higher under the semi-enclosed structure of the tunnel. The relative deviations between the predictions and measured data are less than 5%. These findings ascertain the nonlinear evolutionary mechanisms of pollutants inside the expressway tunnel, thus eventually improving tunnel environmental sustainability. The data in this paper can be used to clarify the changes in the traffic environment under the COVID-19 lockdown. Full article

In this paper, a multi-fractal analysis on a diastolic blood pressure signal is conducted. The signal is measured in a time span of circa one day through the multifractal detrended fluctuation analysis framework. The analysis is performed on asymptotic timescales where complex regulating mechanisms play a fundamental role in the blood pressure stability. Given a suitable frequency range and after removing non-stationarities, the blood pressure signal shows interesting scaling properties and a pronounced multifractality imputed to long-range correlations. Finally, a binomial multiplicative model is investigated showing how the analyzed signal can be described by a concise multifractal model with only two parameters. Full article

Exploring the spatial distribution of the multi-fractal scaling behaviours in atmospheric CO₂ concentration time series is useful for understanding the dynamic mechanisms of carbon emission and absorption. In this work, we utilise a well-established multi-fractal detrended fluctuation analysis to examine the multi-fractal scaling behaviour of a column-averaged dry-air mole fraction of carbon dioxide (XCO₂) concentration time series over China, and portray the spatial distribution of the multi-fractal scaling behaviour. As XCO₂ data values from the Greenhouse Gases Observing Satellite (GOSAT) are insufficient, a spatio-temporal thin plate spline interpolation method is applied. The results show that XCO₂ concentration records over almost all of China exhibit a multi-fractal nature. Two types of multi-fractal sources are detected. One is long-range correlations, and the other is both long-range correlations and a broad probability density function; these are mainly distributed in southern and northern China, respectively. The atmospheric temperature and carbon emission/absorption are two possible external factors influencing the multi-fractality of the atmospheric XCO₂ concentration. Highlight: (1) An XCO₂ concentration interpolation is conducted using a spatio-temporal thin plate spline method. (2) The spatial distribution of the multi-fractality of XCO₂ concentration over China is shown. (3) Multi-fractal sources and two external factors affecting multi-fractality are analysed. Full article

To improve the accuracy of centrifugal pump fault diagnosis, a novel fault diagnosis method based on improved multiple fractal detrended fluctuation analysis (MFDFA), the fusion of multi-sensing information derived from the back propagation (BP) neural network and the Dempster–Shafter (D-S) evidence theory, is accordingly proposed. Firstly, the multifractal spectral parameters of four sensor signals under four different operating conditions were extracted as centrifugal pump fault feature vectors using improved MFDFA and input to the BP neural network. Then, the basic trust assignment function was constructed by calculating trustworthiness (both local and global) as priori information, which is based on the output results of the neural networks specific to of each group of sensors. Finally, the basic trust assignment function was fused with decision processing in accordance with the D-S evidence combination rule in order to effectively achieve the multi-sensor information fusion centrifugal pump fault diagnosis. The experimental results show the multiple fractal spectrum feature parameters extracted by the improved MFDFA can accurately reflect the signal essence, and can be used as the fault feature vector. On this basis, this multi-sensor fault diagnosis reduces the uncertainty of fault classification and demonstrates improved accuracy compared to the single-sensor fault diagnosis thanks to being based on a combination of the BP neural networks and D-S evidence theory. Thereby, this method can facilitate accurate diagnosis of the centrifugal pump fault type with high confidence, subsequently providing a novel and alternative method to existing methods of diagnosis. Full article

This paper proposes a new method for epileptic seizure detection in electroencephalography (EEG) signals using nonlinear features based on fractal dimension (FD) and a deep learning (DL) model. Firstly, Bonn and Freiburg datasets were used to perform experiments. The Bonn dataset consists of binary and multi-class classification problems, and the Freiburg dataset consists of two-class EEG classification problems. In the preprocessing step, all datasets were prepossessed using a Butterworth band pass filter with 0.5–60 Hz cut-off frequency. Then, the EEG signals of the datasets were segmented into different time windows. In this section, dual-tree complex wavelet transform (DT-CWT) was used to decompose the EEG signals into the different sub-bands. In the following section, in order to feature extraction, various FD techniques were used, including Higuchi (HFD), Katz (KFD), Petrosian (PFD), Hurst exponent (HE), detrended fluctuation analysis (DFA), Sevcik, box counting (BC), multiresolution box-counting (MBC), Margaos-Sun (MSFD), multifractal DFA (MF-DFA), and recurrence quantification analysis (RQA). In the next step, the minimum redundancy maximum relevance (mRMR) technique was used for feature selection. Finally, the k-nearest neighbors (KNN), support vector machine (SVM), and convolutional autoencoder (CNN-AE) were used for the classification step. In the classification step, the K-fold cross-validation with k = 10 was employed to demonstrate the effectiveness of the classifier methods. The experiment results show that the proposed CNN-AE method achieved an accuracy of 99.736% and 99.176% for the Bonn and Freiburg datasets, respectively. Full article

Recent research has clarified the existence of a networked system involving a cortical and subcortical circuitry regulating both cognition and cardiac autonomic control, which is dynamically organized as a function of cognitive demand. The main interactions span multiple temporal and spatial scales and are extensively governed by nonlinear processes. Hence, entropy and (multi)fractality in heart period time series are suitable to capture emergent behavior of the cognitive-autonomic network coordination. This study investigated how entropy and multifractal-multiscale analyses could depict specific cognitive-autonomic architectures reflected in the heart rate dynamics when students performed selective inhibition tasks. The participants ($N=37$) completed cognitive interference (Stroop color and word task), action cancellation (stop-signal) and action restraint (go/no-go) tasks, compared to watching a neutral movie as baseline. Entropy and fractal markers (respectively, the refined composite multiscale entropy and multifractal-multiscale detrended fluctuation analysis) outperformed other time-domain and frequency-domain markers of the heart rate variability in distinguishing cognitive tasks. Crucially, the entropy increased selectively during cognitive interference and the multifractality increased during action cancellation. An interpretative hypothesis is that cognitive interference elicited a greater richness in interactive processes that form the central autonomic network while action cancellation, which is achieved via biasing a sensorimotor network, could lead to a scale-specific heightening of multifractal behavior. Full article

The mathematical analysis and the assessment of heart rate variability (HRV) based on computer systems can assist the diagnostic process with determining the cardiac status of patients. The new cardio-diagnostic assisting computer system created uses the classic Time-Domain, Frequency-Domain, and Time-Frequency analysis indices, as well as the nonlinear methods (Poincaré plot, Recurrence plot, Hurst R/S method, Detrended Fluctuation Analysis (DFA), Multi-Fractal DFA, Approximate Entropy and Sample Entropy). To test the feasibility of the software developed, 24-hour Holter recordings of four groups of people were analysed: healthy subjects and patients with arrhythmia, heart failure and syncope. Time-Domain (SDNN < 50 ms, SDANN < 100 ms, RMSSD < 17 ms) and Frequency-Domain (the spectrum of HRV in the LF < 550 ms², and HF < 540 ms²) parameter values decreased in the cardiovascular disease groups compared to the control group as a result of lower HRV due to decreased parasympathetic and increased sympathetic activity. The results of the nonlinear analysis showed low values of (SD1 < 56 ms, SD2 < 110 ms) at Poincaré plot (Alpha < 90 ms) at DFA in patients with diseases. Significantly reducing these parameters are markers of cardiac dysfunction. The examined groups of patients showed an increase in the parameters (DET% > 95, REC% > 38, ENTR > 3.2) at the Recurrence plot. This is evidence of a pathological change in the regulation of heart rhythm. The system created can be useful in making the diagnosis by the cardiologist and in bringing greater accuracy and objectivity to the treatment. Full article

Emergent contamination warning systems are critical to ensure drinking water supply security. After detecting the existence of contaminants, identifying the types of contaminants is conducive to taking remediation measures. An online classification method for contaminants, which explored abnormal fluctuation information and the correlation between 12 water quality indicators adequately, is proposed to realize comprehensive and accurate discrimination of contaminants. Firstly, the paper utilized multi-fractal detrended fluctuation analysis (MF-DFA) to select indicators with abnormal fluctuation, used multi-fractal detrended cross-correlation analysis (MF-DCCA) to measure the cross-correlation between indicators. Subsequently, the algorithm fused the abnormal probability of each indicator and constructed the abnormal probability matrix to further judge the abnormal fluctuation of indicators using D–S evidence theory. Finally, the singularity index of the cross-correlation function and the selected indicators were used to classification by cosine distance. Experiments of five chemical contaminants at three concentration levels were implemented, and analysis results show the method can weaken disturbance of water quality background noise and other interfering factors. It effectively improved the classification accuracy at low concentrations compared with another three methods, including methods using triple standard deviation threshold and single indicator fluctuation analysis-only methods without fluctuation analysis. This can be applied to water quality emergency monitoring systems to reduce contaminant misclassification. Full article

This article introduces an integrated photoplethysmographic (PPG) based cardiovascular monitoring system that consists of an individually portable PPG device for recording photoplethysmographic signals and a software system with a serverless architecture for processing, storing, and analyzing the obtained signals. The portable device uses the optical plethysmography technique for measuring blood volume in blood vessels. The device was tested and validated by a comparative analysis of three photoplethysmographic signals and one Electrocardiographic signal registered simultaneously in the target subject. The comparative analysis of these signals shows insignificant deviations in the obtained results, with the mean squared error between the studied signals being less than 21 ms. This deviation cannot affect the results that were obtained from the analysis of the interval series tested. Based on this result, we assume that the detected signals with the proposed device are realistic. The designed software system processes the registered data, performs preprocessing, determines the pulse rate variability, and performs mathematical analysis of PP intervals. Two groups of subjects were studied: 42 patients with arrhythmia and 40 healthy controls. Mathematical methods for data analysis in time and frequency domain and nonlinear methods (Poincaré plots, Rescaled Range Plot, Detrended Fluctuation Analysis, and MultiFractal Detrended Fluctuation Analysis) are applied. The obtained results are presented in tabular form and some of them in graphical form. The parameters studied in the time and frequency domain, as well as with the nonlinear methods, have statistical significance (p < 0.05) and they can distinguish between the two studied groups. Visual analysis of PP intervals, based on Poincare’s nonlinear method, provides important information on the physiological status of patients, allowing for one to see at a glance the entire PP interval series and quickly detect cardiovascular disorders, if any. The photoplethysmographic data of healthy individuals and patients diagnosed with arrhythmia were recorded, processed, and examined through the system under the guidance of a cardiologist. The results were analyzed and it was concluded that this system could serve to monitor patients with cardiovascular diseases and, when the condition worsens, a signal could be generated and sent to the hospital for undertaking immediate measures to stabilize patient’s health. Full article