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.

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.

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.

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.

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.

Long-term memory in Staphylococcus aureus α-hemolysin ion channel kinetics.

The kinetics of an ion channel are classically understood as a random process. However, studies have shown that in complex ion channels, formed by multiple subunits, this process can be deterministic, presenting long-term memory. Staphylococcus aureus α-hemolysin (α-HL) is a toxin that acts as the major factor in Staphylococcus aureus virulence. α-HL is a water-soluble protein capable of forming ion channels into lipid bilayers, by insertion of an amphipathic  ß-barrel. Here, the α-HL was used as an experimental model to study memory in ion channel kinetics. We applied the approximate entropy (ApEn) approach to analyze randomness and the Detrended Fluctuation Analysis (DFA) to investigate the existence of long memory in α-HL channel kinetics. Single-channel currents were measured through experiments with α-HL channels incorporated in planar lipid bilayers. All experiments were carried out under the following conditions: 1 M NaCl solution, pH 4.5; transmembrane potential of + 40 mV and temperature 25 ± 1 °C. Single-channel currents were recorded in real-time in the memory of a microcomputer coupled to an A/D converter and a patch-clamp amplifier. The conductance value of the α-HL channels was 0.82 ± 0.0025 nS (n = 128). The DFA analysis showed that the kinetics of α-HL channels presents long-term memory ([Formula: see text] = 0.63 ± 0.04). The ApEn outcomes showed low complexity to dwell times when open (ApEno = 0.5514 ± 0.28) and closed (ApEnc = 0.1145 ± 0.08), corroborating the results of the DFA method.

Scale-Free Dynamics in Instantaneous Alpha Frequency Fluctuations: Validation, Test-Retest Reliability and Its Relationship with Task Manipulations.

Previous studies showed that scale-free structures and long-range temporal correlations are ubiquitous in physiological signals (e.g., electroencephalography). This is supposed to be associated with optimized information processing in human brain. The instantaneous alpha frequency (IAF) (i.e., the instantaneous frequency of alpha band of human EEG signals) may dictate the resolution at which information is sampled and/or processed by cortical neurons. To the best of our knowledge, no research has examined the scale-free dynamics and potential functional significance of IAF. Here, through three studies (Study 1: 25 participants; Study 2: 82 participants; Study 3: 26 participants), we investigated the possibility that time series of IAF exhibit scale-free property through maximum likelihood based detrended fluctuation analysis (ML-DFA). This technique could provide the scaling exponent (i.e., DFA exponent) on the basis of presence of scale-freeness being validated. Then the test-retest reliability (Study 1) and potential influencing factors (Study 2 and Study 3) of DFA exponent of IAF fluctuations were investigated. Firstly, the scale-free property was found to be inherent in IAF fluctuations with fairly high test-retest reliability over the parietal-occipital region. Moreover, the task manipulations could potentially modulate the DFA exponent of IAF fluctuations. Specifically, in Study 2, we found that the DFA exponent of IAF fluctuations in eye-closed resting-state condition was significantly larger than that in eye-open resting-state condition. In Study 3, we found that the DFA exponent of IAF fluctuations in eye-open resting-state condition was significantly larger than that in visual n-back tasks. The DFA exponent of IAF fluctuations in the 0-back task was significantly larger than in the 2-back and 3-back tasks. The results in studies 2 and 3 indicated that: (1) a smaller DFA exponent of IAF fluctuations should signify more efficient online visual information processing; (2) the scaling property of IAF fluctuations could reflect the physiological arousal level of participants.

Fractal complexity alternations in paroxysmal atrial fibrillation patients with and without recurrence after pulmonary vein isolation.

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

Validation of a non-linear index of heart rate variability to determine aerobic and anaerobic thresholds during incremental cycling exercise in women.

Studies highlight the usage of non-linear time series analysis of heart rate variability (HRV) using the short-term scaling exponent alpha1 of Detrended Fluctuation Analysis (DFA-alpha1) during exercise to determine aerobic and anaerobic thresholds. The present study aims to further verify this approach in women. Gas exchange and HRV data were collected from 26 female participants with different activity levels. Oxygen uptake (VO2) and heart rate (HR) at first (VT1) and second ventilatory thresholds (VT2) were compared with DFA-alpha1-based thresholds 0.75 (HRVT1) and 0.50 (HRVT2). Results: VO2 at VT1 and VT2 were 25.2 ml/kg/min (± 2.8) and 31.5 ml/kg/min (± 3.6) compared with 26.5 ml/kg/min (± 4.0) and 31.9 ml/kg/min (± 4.5) for HRVT1 and HRVT2, respectively (ICC3,1 = 0.77, 0.84; r = 0.81, 0.86, p < 0.001). The mean HR at VT1 was 147 bpm (± 15.6) and 167 bpm (± 12.7) for VT2, compared with 152 bpm (± 15.5) and 166 bpm (± 13.2) for HRVT1 and HRVT2, respectively (ICC3,1 = 0.87, 0.90; r = 0.87, 0.90, p < 0.001). Bland-Altman analysis for VT1 vs. HRVT1 showed a mean difference of - 1.3 ml/kg/min (± 2.4; LoA: 3.3, - 6.0 ml/kg/min) for VO2 and of - 4.7 bpm (± 7.8; LoA: 10.6, - 20.0 bpm) for HR. VT2 vs. HRVT2 showed a mean difference of - 0.4 ml/kg/min (± 2.3; LoA: 4.1, - 4.9 ml/kg/min) for VO2 and 0.5 bpm (± 5.7; LoA: 11.8, - 10.8 bpm) for HR. DFA-alpha1-based thresholds showed good agreement with traditionally used thresholds and could be used as an alternative approach for marking organismic transition zones for intensity distribution in women.

Correlation properties of heart rate variability to assess the first ventilatory threshold and fatigue in runners.

PURPOSE: The short-term scaling exponent alpha1 of detrended fluctuation analysis (DFA-a1) of heart rate variability (HRV) has shown potential to delineate the first ventilatory threshold (VT1). The aims of this study were to investigate the accuracy of this method for VT1 determination in runners using a consumer grade chest belt and to explore the effects of acute fatigue. METHODS: We compared oxygen uptake (V̇O2) and heart rate (HR) at gas exchange VT1 to V̇O2 and HR at a DFA-a1 value of 0.75. Gas exchange and HRV data were obtained from 14 individuals during a treadmill run involving two incremental ramps. Agreement was assessed using Bland-Altman analysis and linear regression. RESULTS: Bland-Altman analysis between gas exchange and HRV V̇O2 and HR at VT1 during the first ramp showed a mean (95% limits of agreement) bias of -0.5 (-6.8 to 5.8) ml∙kg-1∙min-1, and -0.9 (-12.2 to 10.5) beats∙min-1, with R2 of 0.83 and 0.56, respectively. During the second ramp, the differences were -7.3 (-18.1 to 3.5) ml∙kg-1∙min-1 and -12.3 (-30.4 to 5.9) beats∙min-1, with R2 of 0.62 and 0.43, respectively. CONCLUSION: A chest-belt derived DFA-a1 of 0.75 is closely related to gas exchange VT1, with the variability in accuracy at an individual level being similar to gas exchange methods. This suggests this to be a useful method for exercise intensity demarcation. The altered relationship during the second ramp indicates that DFA-a1 is only able to accurately demarcate exercise intensity thresholds in a non-fatigued state, but also opens opportunities for fatigue-based training prescription.

The first ventilatory threshold determined with a nonlinear method (DFA-a1) to analyse heart rate variability derived from a chest-belt shows close agreement to the gas exchange first ventilatory threshold, with the variability in accuracy at an individual level being similar to gas exchange methods. This suggests this to be a useful method for exercise intensity demarcation.The altered relationship during fatigue indicates that DFA-a1 is only able to accurately demarcate exercise intensity thresholds in a non-fatigued state, but this also opens opportunities for fatigue-based training prescription.

Combining Heart Rate Variability and Oximetry to Improve Apneic Event Screening in Non-Desaturating Patients.

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 Between-Day Reliability of Correlation Properties of Heart Rate Variability During Running.

The short-term scaling exponent of detrended fluctuation analysis (DFA-a1) of heart rate variability may be a helpful tool to assess autonomic balance as a prelude to daily, individualized training. For this concept to be useful, between-session reliability should be acceptable. The aim of this study was to explore the reliability of DFA-a1 during a low-intensity exercise session in both a non-fatigued and a fatigued condition in healthy males and females. Ten participants completed two sessions with each containing an exhaustive treadmill ramp protocol. Before and after the fatiguing ramp, a standardized submaximal low-intensity exercise bout was performed during which DFA-a1, heart rate, and oxygen consumption (VO2) were measured. We compared between-session reliability of all metrics prior to the ramps (i.e., non-fatigued status) and after the first ramp (i.e., fatigued status). Intraclass correlation coefficients (ICC) with 95% confidence intervals (CI), the standard error of measurement, and the smallest worthwhile change (SWC) were determined. The ICC and SWC pre fatiguing ramp were 0.85 (95% CI 0.39-0.96) and 5.5% for DFA-a1, 0.85 (0.38-0.96) and 2.2% for heart rate, and 0.84 (0.31-0.96) and 3.1% for VO2. Post fatiguing ramp, the ICC and SWC were 0.55 (0.00-0.89) and 7.9% for DFA-a1, 0.91 (0.62-0.98) and 1.6% for heart rate, and 0.80 (0.17-0.95) and 3.0% for VO2. DFA-a1 shows generally acceptable to good between-session reliability with a SWC of 0.06 and 0.07 (5.5-7.9%) during non-fatigued and fatigued conditions. This suggests that this metric may be useful to inform on training readiness.

Postural control strategies are revealed by the complexity of fractional components of COP.

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.

ECG and Heart Rate Variability in Sleep-Related Breathing Disorders.

Here we discuss the current perspectives of comprehensive heart rate variability (HRV) analysis in electrocardiogram (ECG) signals as a non-invasive and reliable measure to assess autonomic function in sleep-related breathing disorders (SDB). It is a tool of increasing interest as different facets of HRV can be implemented to screen and diagnose SDB, monitor treatment efficacy, and prognose adverse cardiovascular outcomes in patients with sleep apnea. In this context, the technical aspects, pathophysiological features, and clinical applications of HRV are discussed to explore its usefulness in better understanding SDB.

Heart Rate Variability from Wearable Photoplethysmography Systems: Implications in Sleep Studies at High Altitude.

The interest in photoplethysmography (PPG) for sleep monitoring is increasing because PPG may allow assessing heart rate variability (HRV), which is particularly important in breathing disorders. Thus, we aimed to evaluate how PPG wearable systems measure HRV during sleep at high altitudes, where hypobaric hypoxia induces respiratory disturbances. We considered PPG and electrocardiographic recordings in 21 volunteers sleeping at 4554 m a.s.l. (as a model of sleep breathing disorder), and five alpine guides sleeping at sea level, 6000 m and 6800 m a.s.l. Power spectra, multiscale entropy, and self-similarity were calculated for PPG tachograms and electrocardiography R-R intervals (RRI). Results demonstrated that wearable PPG devices provide HRV measures even at extremely high altitudes. However, the comparison between PPG tachograms and RRI showed discrepancies in the faster spectral components and at the shorter scales of self-similarity and entropy. Furthermore, the changes in sleep HRV from sea level to extremely high altitudes quantified by RRI and PPG tachograms in the five alpine guides tended to be different at the faster frequencies and shorter scales. Discrepancies may be explained by modulations of pulse wave velocity and should be considered to interpret correctly autonomic alterations during sleep from HRV analysis.

Fractal Properties of Heart Rate Dynamics: A New Biomarker for Anesthesia-Biphasic Changes in General Anesthesia and Decrease in Spinal Anesthesia.

Processed electroencephalogram (EEG) has been considered a useful tool for measuring the depth of anesthesia (DOA). However, because of its inability to detect the activities of the brain stem and spinal cord responsible for most of the vital signs, a new biomarker for measuring the multidimensional activities of the central nervous system under anesthesia is required. Detrended fluctuation analysis (DFA) is a new technique for detecting the scaling properties of nonstationary heart rate (HR) behavior. This study investigated the changes in fractal properties of heart rate variability (HRV), a nonlinear analysis, under intravenous propofol, inhalational desflurane, and spinal anesthesia. We compared the DFA method with traditional spectral analysis to evaluate its potential as an alternative biomarker under different levels of anesthesia. Eighty patients receiving elective procedures were randomly allocated different anesthesia. HRV was measured with spectral analysis and DFA short-term (4-11 beats) scaling exponent (DFAα1). An increase in DFAα1 followed by a decrease at higher concentrations during propofol or desflurane anesthesia is observed. Spinal anesthesia decreased the DFAα1 and low-/high-frequency ratio (LF/HF ratio). DFAα1 of HRV is a sensitive and specific method for distinguishing changes from baseline to anesthesia state. The DFAα1 provides a potential real-time biomarker to measure HRV as one of the multiple dimensions of the DOA.

A New Look at Calendar Anomalies: Multifractality and Day-of-the-Week Effect.

Stock markets can become inefficient due to calendar anomalies known as the day-of-the-week effect. Calendar anomalies are well known in the financial literature, but the phenomena remain to be explored in econophysics. This paper uses multifractal analysis to evaluate if the temporal dynamics of market returns also exhibit calendar anomalies such as day-of-the-week effects. We apply multifractal detrended fluctuation analysis (MF-DFA) to the daily returns of market indices worldwide for each day of the week. Our results indicate that distinct multifractal properties characterize individual days of the week. Monday returns tend to exhibit more persistent behavior and richer multifractal structures than other day-resolved returns. Shuffling the series reveals that multifractality arises from a broad probability density function and long-term correlations. The time-dependent multifractal analysis shows that the Monday returns' multifractal spectra are much wider than those of other days. This behavior is especially persistent during financial crises. The presence of day-of-the-week effects in multifractal dynamics of market returns motivates further research on calendar anomalies for distinct market regimes.

Nonlinear Statistical Features of the Seismicity in the Subduction Zone of Tehuantepec Isthmus, Southern México.

After the M8.2 main-shock occurred on 7 September 2017 at the Isthmus of Tehuantepec, Mexico, the spatial distribution of seismicity has showed a clear clusterization of earthquakes along the collision region of the Tehuantepec Transform/Ridge with the Middle America Trench off Chiapas. Furthermore, nowadays, the temporal rate of occurrence in the number of earthquakes has also showed a pronounced increase. On the basis of this behavior, we studied the sequence of magnitudes of the earthquakes which occurred within the Isthmus of Tehuantepec in southern Mexico from 2010 to 2020. Since big earthquakes are considered as a phase transition, after the M8.2 main-shock, one must expect changes in the Tehuantepec ridge dynamics, which can be observed considering that the b-value in the Gutenberg-Richter law, has also showed changes in time. The goal of this paper is to characterize the behavior of the seismic activity by using the Gutenberg-Richter law, multifractal detrended fluctuation analysis, visibility graph and nowcasting method. Those methods have showed important parameters in order to assess risk, the multifractality and connectivity. Our findings indicate, first that b-value shows a dependency on time, which is clearly described by our analyses based on nowcasting method, multifractality and visibility graph.

Spatial Distribution of Multi-Fractal Scaling Behaviours of Atmospheric XCO2 Concentration Time Series during 2010-2018 over China.

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.

Breathing variability-implications for anaesthesiology and intensive care.

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