Nonlinear and multifractal detrended fluctuation analysis of radon time series in a volcanic touristic cave.

Radioactive radon gas poses significant threats to human health. Understanding the complexities of radon distribution and the dynamic relationship with atmospheric parameters will help in mitigating its impact. In this study, Multifractal Detrended Fluctuation Analysis (MF-DFA) and chaos analysis were used to examine the fractal structure in radon gas at La Cueva del Viento, Tenerife, between January 2021 and December 2022. The results showed that radon has multifractal properties in 2021, 2022, and 2021-2022, with values of the spectrum with of about 0.43, 0.49 and 0.44 respectively. The multifractality in radon gas was found to be driven by both long-range correlations and fat-tail distribution. Radon gas concentration at La Cueva del Viento was found to be chaotic in nature, hence, long-term prediction is impossible. Meteorological parameters such as relative humidity, air temperature and pressure were found to contribute to the variation in radon gas concentration within the cave. Relative humidity was observed to have the strongest cross-correlation with radon gas in 2021, 2022, and 2021-2022. The results from this study will help in dosimetric control for both workers and visitors to the cave.

Evaluating and Comparing Measures of Aperiodic Neural Activity.

Neuro-electrophysiological recordings contain prominent aperiodic activity - meaning irregular activity, with no characteristic frequency - which has variously been referred to as 1/f (or 1/f-like activity), fractal, or 'scale-free' activity. Previous work has established that aperiodic features of neural activity is dynamic and variable, relating (between subjects) to healthy aging and to clinical diagnoses, and also (within subjects) tracking conscious states and behavioral performance. There are, however, a wide variety of conceptual frameworks and associated methods for the analyses and interpretation of aperiodic activity - for example, time domain measures such as the autocorrelation, fractal measures, and/or various complexity and entropy measures, as well as measures of the aperiodic exponent in the frequency domain. There is a lack of clear understanding of how these different measures relate to each other and to what extent they reflect the same or different properties of the data, which makes it difficult to synthesize results across approaches and complicates our overall understanding of the properties, biological significance, and demographic, clinical, and behavioral correlates of aperiodic neural activity. To address this problem, in this project we systematically survey the different approaches for measuring aperiodic neural activity, starting with an automated literature analysis to curate a collection of the most common methods. We then evaluate and compare these methods, using statistically representative time series simulations. In doing so, we establish consistent relationships between the measures, showing that much of what they capture reflects shared variance - though with some notable idiosyncrasies. Broadly, frequency domain methods are more specific to aperiodic features of the data, whereas time domain measures are more impacted by oscillatory activity. We extend this analysis by applying the measures to a series of empirical EEG and iEEG datasets, replicating the simulation results. We conclude by summarizing the relationships between the multiple methods, emphasizing opportunities for reexamining previous findings and for future work.

Quantifying exercise intensity with fractal correlation properties of heart rate variability: a study on incremental and constant-speed running.

The short-term scaling exponent of detrended fluctuation analysis (DFAα1) applied to interbeat intervals may provide a method to identify ventilatory thresholds and indicate systemic perturbation during prolonged exercise. The purposes of this study were to (i) identify the gas exchange threshold (GET) and respiratory compensation point (RCP) using DFAα1 values of 0.75 and 0.5 from incremental exercise, (ii) compare DFAα1 thresholds with DFAα1 measures during constant-speed running near the maximal lactate steady state (MLSS), and (iii) assess the repeatability of DFAα1 between MLSS trials. Twelve runners performed an incremental running test and constant-speed running 5% below, at, and 5% above the MLSS, plus a repeat trial at MLSS. During 30-min running trials near MLSS, DFAα1 responses were variable (i.e., 0.27-1.24) and affected by intensity (p = 0.031) and duration (p = 0.003). No difference in DFAα1 was detected between MLSS trials (p = 0.597). In the early phase (~ 8 min), DFAα1 measures at MLSS (0.71 [0.13]) remained higher than the DFAα1 identified at RCP from the incremental test (0.57 [0.13]; p = 0.024). In addition, following ~ 18 min of constant speed running at MLSS, DFAα1 measures (0.64 [0.14]) remained higher than 0.5 (p = 0.011)-the value thought to demarcate the boundaries between heavy and severe exercise intensities. Accordingly, using fixed DFAα1 values associated with the RCP from incremental exercise to guide constant-speed exercise training may produce a greater than expected exercise intensity, however; the dependency of DFAα1 on intensity and duration suggest its potential utility to quantify systemic perturbations imposed by continuous exercise.

The Cumulative Impacts of Fatigue during Overload Training Can Be Tracked Using Field-Based Monitoring of Running Stride Interval Correlations.

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

Temporal assessment of Gross alpha emissions from the petroleum industry in Tenerife, Canary Islands (2001-2022).

A ca. 76% decrease in gross alpha activity levels, measured in surface aerosols collected in the city of Santa Cruz de Tenerife (Spain), has been explained in the present study in connection with the reduction of activities, and eventual closure, of an oil refinery in the city. Gross Alpha in surface aerosols, collected at weekly intervals over a period of 22 years (2001-2022), was used for the analysis. The dynamic behaviour of the gross alpha time series was studied using statistical wavelet, multifractal analysis, empirical decomposition method, multivariate analysis, principal component, and cluster analyses approaches. This was performed to separate the impact of other sources of alpha emitting radionuclides influencing the gross alpha levels at this site. These in-depth analyses revealed a noteworthy shift in the dynamic behaviour of the gross alpha levels following the refinery's closure in 2013. This analysis also attributed fluctuations and trends in the gross alpha levels to factors such as the 2008 global economic crisis and the refinery's gradual reduction of activity leading up to its closure. The mixed-model approach, incorporating multivariate regression and autoregressive integrated moving average methods, explained approximately 84% of the variance of the gross alpha levels. Finally, this work underscored the marked reduction in alpha activity levels following the refinery's closure, alongside the decline of other pollutants (CO, SO2, NO, NO2, Benzene, Toluene and Xylene) linked to the primary industrial activity in the municipality of Santa Cruz de Tenerife.

Combining features on vertical ground reaction force signal analysis for multiclass diagnosing neurodegenerative diseases.

Neurodegenerative diseases (NDDs), which are caused by the degeneration of neurons and their functions, affect a significant part of the world's population. Although gait disorders are one of the critical and common markers to determine the presence of NDDs, diagnosing which NDD the patients have among a group of NDDs using gait data is still a significant challenge to be addressed. In this study, we addressed the multi-class classification of NDDs and aim to diagnose Parkinson's disease (PD), Amyotrophic lateral sclerosis disease (AD), and Huntington's disease (HD) from a group containing NDDs and healthy control subjects. We also examined the impact of disease-specific identified features derived from VGRF signals. Detrended Fluctuation Analysis (DFA), Dynamic Time Warping (DTW) and Autocorrelation (AC) were used for feature extraction on Vertical Ground Reaction Force (VGRF) signals. To compare the performance of the features, we employed Support Vector Machines, K-Nearest Neighbors, and Neural Networks as classifiers. In three-class problem addressing the classification of AD, PD and HD 93.3% accuracy rate was achieved, while in the four classes case, in which NDDs and HC groups were considered together, 93.5% accuracy rate was yielded. Considering the disease-specific impact of features, it is revealed that while DFA based features diagnose patients with AD with the highest accuracy, DTW has been shown to be more successful in diagnosing PD. AC based features provided the highest accuracy in diagnosing HD. Although gait disorder is common for NDDs, each disease may have its own distinctive gait rhythms; therefore, it is important to identify disease-specific patterns and parameters for the diagnosis of each disease. To increase the diagnostic accuracy, it is necessary to use a combination of features, which were effective for each disease diagnosis. Determining a limited number of disease-specific features would provide NDD diagnostic systems suitable to be deployed in edge-computing environments.

Multifractal analysis of heart rate variability in pregnancy during sleep.

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

Benefits From Different Modes of Slow and Deep Breathing on Vagal Modulation.

Slow and deep breathing (SDB) is a relaxation technique that can increase vagal activity. Respiratory sinus arrhythmia (RSA) serves as an index of vagal function usually quantified by the high-frequency power of heart rate variability (HRV). However, the low breathing rate during SDB results in deviations when estimating RSA by HRV. Besides, the impact of the inspiration-expiration (I: E) ratio and guidelines ways (fixed breathing rate or intelligent guidance) on SDB is not yet clear. In our study, 30 healthy people (mean age = 26.5 years, 17 females) participated in three SDB modes, including 6 breaths per minute (bpm) with an I:E ratio of 1:1/ 1:2, and intelligent guidance mode (I:E ratio of 1:2 with guiding to gradually lower breathing rate to 6 bpm). Parameters derived from HRV, multimodal coupling analysis (MMCA), Poincaré plot, and detrended fluctuation analysis were introduced to examine the effects of SDB exercises. Besides, multiple machine learning methods were applied to classify breathing patterns (spontaneous breathing vs. SDB) after feature selection by max-relevance and min-redundancy. All vagal-activity markers, especially MMCA-derived RSA, statistically increased during SDB. Among all SDB modes, breathing at 6 bpm with a 1:1 I:E ratio activated the vagal function the most statistically, while the intelligent guidance mode had more indicators that still significantly increased after training, including SDRR and MMCA-derived RSA, etc. About the classification of breathing patterns, the Naive Bayes classifier has the highest accuracy (92.2%) with input features including LFn, CPercent, pNN50, [Formula: see text], SDRatio, [Formula: see text], and LF. Our study proposed a system that can be applied to medical devices for automatic SDB identification and real-time feedback on the training effect. We demonstrated that breathing at 6 bpm with an I:E ratio of 1:1 performed best during the training phase, while intelligent guidance mode had a more long-lasting effect.

Measures of fragmentation of rest activity patterns: mathematical properties and interpretability based on accelerometer real life data.

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

Prediction of Sudden Cardiac Death With Ultra-Short-Term Heart Rate Fluctuations.

BACKGROUND: Conventional measures of heart rate variability (HRV) have shown only modest associations with sudden cardiac death (SCD). Detrended fluctuation analysis (DFA), with novel methodological developments to evaluate the short-term scaling exponent, is a potentially superior method compared to conventional HRV tools. OBJECTIVES: In this study, the authors studied the analysis of the association between DFA and SCD. METHODS: The investigators studied the predictive value of ultra-short-term heart rate fluctuations (1-minute electrocardiogram samples) with DFA at rest and during different stages of physical exertion for incident SCD among 2,794 participants undergoing clinical exercise testing in the prospective FINCAVAS (Finnish Cardiovascular Study). The novel key DFA measure, the short-scale scaling exponent computed with second-order detrending (DFA2 α1), was the main exposure variable. SCDs were defined by American Heart Association/European Society of Cardiology criteria using death certificates with written accounts of the events. RESULTS: During a median follow-up of 8.3 years (Q1-Q3: 6.4-10.5), 83 SCDs occurred. DFA2 α1 measured at rest (but not in exercise) associated highly significantly with the risk of SCD, with 1-SD lower values associating with a 2.4-fold (Q1-Q3: 2.0-3.0) risk (P < 0.001). The results persisted when adjusting for other major risk factors for SCD, including age, cardiovascular morbidities, cardiorespiratory fitness, heart rate reduction, and left ventricular ejection fraction. Associations between conventional HRV parameters (measured at any stage of exercise or at rest) and SCD were substantially weaker and statistically nonsignificant after adjusting for other risk factors. CONCLUSIONS: Ultra-short-term DFA2 α1, when measured at rest, is a powerful and independent predictor of SCD. The association between DFA2 α1 and SCD is modified by physical exertion.

Time series analysis of a 22-year record of 7Be, 210Pb and gross alpha activities in the Canary Islands (Spain) using Principal Component and Multifractal Detrended Fluctuation Analyses.

The long-term variability of a 22-year dataset of 7Be, 210Pb and gross alpha concentrations in surface aerosols collected in the Canary Islands has been analysed in this study. These "time series" were collected on a weekly basis. Various analytical techniques, including Principal Component Analysis (PCA), K-means clustering, correlation analyses, and back-trajectory were used to determine the variability of the data and assess the statistical importance of the source of the air masses reaching the study area. Monthly and annual variations for the time series were also studied. As expected, 7Be, 210Pb time series showed common variability, while gross alpha concentrations were strongly correlated with average PM10 concentration in air. The fractal properties of the time series were studied to gain a deeper understanding of the underlying structure and dynamics of the data. Multifractal Detrended Fluctuation Analysis (MF-DFA) and Multifractal Detrended Cross-Correlation Analysis (MF-DCCA) techniques were also used to detect and analyse the multifractal characteristics of the 7Be, 210Pb, and gross alpha time series. Multifractality was observed, with values of 0.28, 0.67, and 0.61 for 7Be, 210Pb, and gross alpha, respectively. Long-range correlation was found to be the source of the observed multifractality in the three parameters. Multifractal detrended cross-correlation analysis supports the correlation between 7Be - Alpha, 210Pb - Alpha, and 7Be - 210Pb pairs. The results from this study will help model the transport and destiny of natural radionuclides in the atmosphere at this site. The evolution and interactions between 7Be, 210Pb, and gross alpha, reported herein occurred not just locally but also across extensive temporal domains, leading to the emergence of multifractal behaviour in their concentrations. These long-range behaviours/correlations might result from various factors such as atmospheric circulation patterns, global transport mechanisms, or large-scale environmental processes.

Assessing cardiovascular stress based on heart rate variability in female shift workers: a multiscale-multifractal analysis approach.

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

Long-range temporal correlations in resting state alpha oscillations in major depressive disorder and obsessive-compulsive disorder.

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

Fractals in Neuroimaging.

Several natural phenomena can be described by studying their statistical scaling patterns, hence leading to simple geometrical interpretation. In this regard, fractal geometry is a powerful tool to describe the irregular or fragmented shape of natural features, using spatial or time-domain statistical scaling laws (power-law behavior) to characterize real-world physical systems. This chapter presents some works on the usefulness of fractal features, mainly the fractal dimension and the related Hurst exponent, in the characterization and identification of pathologies and radiological features in neuroimaging, mainly, magnetic resonance imaging.

Combining detrended cross-correlation analysis with Riemannian geometry-based classification for improved brain-computer interface performance.

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

Fractal Time Series: Background, Estimation Methods, and Performances.

Over the past 40 years, from its classical application in the characterization of geometrical objects, fractal analysis has been progressively applied to study time series in several different disciplines. In neuroscience, starting from identifying the fractal properties of neuronal and brain architecture, attention has shifted to evaluating brain signals in the time domain. Classical linear methods applied to analyzing neurophysiological signals can lead to classifying irregular components as noise, with a potential loss of information. Thus, characterizing fractal properties, namely, self-similarity, scale invariance, and fractal dimension (FD), can provide relevant information on these signals in physiological and pathological conditions. Several methods have been proposed to estimate the fractal properties of these neurophysiological signals. However, the effects of signal characteristics (e.g., its stationarity) and other signal parameters, such as sampling frequency, amplitude, and noise level, have partially been tested. In this chapter, we first outline the main properties of fractals in the domain of space (fractal geometry) and time (fractal time series). Then, after providing an overview of the available methods to estimate the FD, we test them on synthetic time series (STS) with different sampling frequencies, signal amplitudes, and noise levels. Finally, we describe and discuss the performances of each method and the effect of signal parameters on the accuracy of FD estimation.

Multifractal Multiscale Analysis of Human Movements during Cognitive Tasks.

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

The Complexity of Center of Pressure Positions During Quiet Stance and Its Relationship to Cognition, Aging, and Falls.

BACKGROUND: In a secondary analysis of data taken from a publicly available database, we examined cognitive performance, postural sway, and relations between them for 4 groups: younger and older individuals with versus without a recent history of falls. Our objective was to compare linear versus nonlinear measures of postural activity as post hoc predictors of cognitive performance and falling. METHODS: We evaluated standing body sway in 147 participants (18-85-years old) over 60 seconds, separately with eyes-open and with eyes-closed. We evaluated cognitive performance using portions of the Trail Making Test. We evaluated postural activity in terms of standard deviation, velocity, and amplitude of the Center of Pressure (CoP). Separately, we used detrended fluctuation analysis (DFA) to examine the complexity of CoP displacements. Using analysis of variance, we conducted separate analyses of cognitive performance and postural activity comparing Younger and Older Adults and Non-fallers and Fallers, taking into account Vision (eyes-closed vs open) and the direction of postural movements (Anteroposterior vs Mediolateral) while also controlling for participants' characteristics. We used moderation analyses to evaluate whether relationships between Trail Making Test scores and the linear and nonlinear outcomes were moderated by Age group or Fall status. RESULTS: For postural activity, only DFA differed between Non-fallers and Fallers. Older adults exhibited increased complexity associated with better processing speed function, while fallers show an opposite association, relying on processing speed to increase postural rigidity instead of facilitating adaptive control of balance. CONCLUSIONS: We conclude that DFA can provide information regarding postural activity and cognitive performance that cannot be obtained from more traditional, linear measures of postural activity and that DFA may be a valuable tool for assessing fall risk.

Scale-Fractal Detrended Fluctuation Analysis for Fault Diagnosis of a Centrifugal Pump and a Reciprocating Compressor.

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.

Stride-to-stride variability is altered when running to isochronous visual cueing but remains unaltered with fractal cueing.

Running synchronised to external cueing is often implemented in both clinical and training settings, and isochronous cueing has been shown to improve running economy. However, such cueing disregards the natural stride-to-stride fluctuations present in human locomotion which is thought to reflect higher levels of adaptability. The present study aimed to investigate how alterations in the temporal structure of cueing affect stride-to-stride variability during running. We hypothesised that running using cueing with a fractal-like structure would preserve the natural stride-to-stride variability of young adults. Thirteen runners performed four 8-min trials: one uncued (UNC) trial and three cued trials presenting an isochronous (ISO), a fractal (FRC) and a random (RND) structure. Repeated measures ANOVAs were used to identify changes in the dependent variables. We have found no main effect on the cardiorespiratory parameters, whereas a significant main effect was observed in the temporal structure of stride-to-stride variability. During FRC, the participants were able to retain the fractal patterns of their natural locomotor variability observed during the UNC condition, while during the ISO and RND they exhibited more random of fluctuations (i.e., lower values of fractal scaling). Our results demonstrate that cueing based on the natural stride-to-stride fluctuations opens new avenues for training and rehabilitation.