Effect of trends on detrended fluctuation analysis

Prediction of mortality among patients with chronic kidney disease: A systematic review

BACKGROUND

Chronic kidney disease (CKD) is a common medical condition that is increasing in prevalence. Existing published evidence has revealed through regression analyses that several clinical characteristics are associated with mortality in CKD patients. However, the predictive accuracies of these risk factors for mortality have not been clearly demonstrated.

AIM

To demonstrate the accuracy of mortality predictive factors in CKD patients by utilizing the area under the receiver operating characteristic (ROC) curve (AUC) analysis.

METHODS

We searched Ovid MEDLINE, EMBASE, and the Cochrane Library for eligible articles through January 2021. Studies were included based on the following criteria: (1) Study nature was observational or conference abstract; (2) Study populations involved patients with non-transplant CKD at any CKD stage severity; and (3) Predictive factors for mortality were presented with AUC analysis and its associated 95% confidence interval (CI). AUC of 0.70-0.79 is considered acceptable, 0.80-0.89 is considered excellent, and more than 0.90 is considered outstanding.

RESULTS

Of 1759 citations, a total of 18 studies (n = 14579) were included in this systematic review. Eight hundred thirty two patients had non-dialysis CKD, and 13747 patients had dialysis-dependent CKD (2160 patients on hemodialysis, 370 patients on peritoneal dialysis, and 11217 patients on non-differentiated dialysis modality). Of 24 mortality predictive factors, none were deemed outstanding for mortality prediction. A total of seven predictive factors [N-terminal pro-brain natriuretic peptide (NT-proBNP), BNP, soluble urokinase plasminogen activator receptor (suPAR), augmentation index, left atrial reservoir strain, C-reactive protein, and systolic pulmonary artery pressure] were identified as excellent. Seventeen predictive factors were in the acceptable range, which we classified into the following subgroups: predictors for the non-dialysis population, echocardiographic factors, comorbidities, and miscellaneous.

CONCLUSION

Several factors were found to predict mortality in CKD patients. Echocardiography is an important tool for mortality prognostication in CKD patients by evaluating left atrial reservoir strain, systolic pulmonary artery pressure, diastolic function, and left ventricular mass index.

Fractal biomarker of activity in patients with bipolar disorder

BACKGROUND

The output of many healthy physiological systems displays fractal fluctuations with self-similar temporal structures. Altered fractal patterns are associated with pathological conditions. There is evidence that patients with bipolar disorder have altered daily behaviors.

METHODS

To test whether fractal patterns in motor activity are altered in patients with bipolar disorder, we analyzed 2-week actigraphy data collected from 106 patients with bipolar disorder type I in a euthymic state, 73 unaffected siblings of patients, and 76 controls. To examine the link between fractal patterns and symptoms, we analyzed 180-day actigraphy and mood symptom data that were simultaneously collected from 14 patients.

RESULTS

Compared to controls, patients showed excessive regularity in motor activity fluctuations at small time scales (<1.5 h) as quantified by a larger scaling exponent (α1 > 1), indicating a more rigid motor control system. α1 values of siblings were between those of patients and controls. Further examinations revealed that the group differences in α1 were only significant in females. Sex also affected the group differences in fractal patterns at larger time scales (>2 h) as quantified by scaling exponent α2. Specifically, female patients and siblings had a smaller α2 compared to female controls, indicating more random activity fluctuations; while male patients had a larger α2 compared to male controls. Interestingly, a higher weekly depression score was associated with a lower α1 in the subsequent week.

CONCLUSIONS

Our results show sex- and scale-dependent alterations in fractal activity regulation in patients with bipolar disorder. The mechanisms underlying the alterations are yet to be determined.

Fractal motor activity regulation and sex differences in preclinical Alzheimer's disease pathology

INTRODUCTION

Degradation in fractal motor activity regulation (FMAR), a measure of multiscale self-similarity of motor control, occurs in aging and accelerates with clinical progression to Alzheimer's disease (AD). Whether FMAR changes occur during the pre-symptomatic phase of the disease in women and men remains unknown.

METHODS

FMAR was assessed in cognitively normal participants (n = 178) who underwent 7 to 14 days of home actigraphy. Preclinical AD pathology was determined by amyloid imaging-Pittsburgh compound B (PiB) and cerebrospinal fluid (CSF) phosphorylated-tau181 (p-tau) to amyloid beta 42 (Aβ42) ratio.

RESULTS

Degradation in daytime FMAR was overall significantly associated with preclinical amyloid plaque pathology via PiB+ imaging (beta coefficient β = 0.217, standard error [SE] = 0.101, P = .034) and increasing CSF tau181-Aβ42 ratio (β = 0.220, SE = 0.084, P = .009). In subset analysis by sex, the effect sizes were significant in women for PiB+ (β = 0.279, SE = 0.112, P = .015) and CSF (β = 0.245, SE = 0.094, P = .011) but not in men (both Ps > .05). These associations remained after inclusion of daily activity level, apolipoprotein E ε4 carrier status, and rest/activity patterns.

DISCUSSION

Changes in daytime FMAR from actigraphy appear to be present in women early in preclinical AD. This may be a combination of earlier pathology changes in females reflected in daytime FMAR, and a relatively underpowered male group. Further studies are warranted to test FMAR as an early noncognitive physiological biomarker that precedes the onset of cognitive symptoms.

Dynamics of Long-Range Temporal Correlations in Broadband EEG During Different Motor Execution and Imagery Tasks

Brain activity is composed of oscillatory and broadband arrhythmic components; however, there is more focus on oscillatory sensorimotor rhythms to study movement, but temporal dynamics of broadband arrhythmic electroencephalography (EEG) remain unexplored. We have previously demonstrated that broadband arrhythmic EEG contains both short- and long-range temporal correlations that change significantly during movement. In this study, we build upon our previous work to gain a deeper understanding of these changes in the long-range temporal correlation (LRTC) in broadband EEG and contrast them with the well-known LRTC in alpha oscillation amplitude typically found in the literature. We investigate and validate changes in LRTCs during five different types of movements and motor imagery tasks using two independent EEG datasets recorded with two different paradigms-our finger tapping dataset with single self-initiated asynchronous finger taps and publicly available EEG dataset containing cued continuous movement and motor imagery of fists and feet. We quantified instantaneous changes in broadband LRTCs by detrended fluctuation analysis on single trial 2 s EEG sliding windows. The broadband LRTC increased significantly (p < 0.05) during all motor tasks as compared to the resting state. In contrast, the alpha oscillation LRTC, which had to be computed on longer stitched EEG segments, decreased significantly (p < 0.05) consistently with the literature. This suggests the complementarity of underlying fast and slow neuronal scale-free dynamics during movement and motor imagery. The single trial broadband LRTC gave high average binary classification accuracy in the range of 70.54±10.03% to 76.07±6.40% for all motor execution and imagery tasks and hence can be used in brain-computer interface (BCI). Thus, we demonstrate generalizability, robustness, and reproducibility of novel motor neural correlate, the single trial broadband LRTC, during different motor execution and imagery tasks in single asynchronous and cued continuous motor-BCI paradigms and its contrasting behavior with LRTC in alpha oscillation amplitude.

Multifractal Dynamics in Executive Control When Adapting to Concurrent Motor Tasks

There is some evidence that an improved understanding of executive control in the human movement system could be gained from explorations based on scale-free, fractal analysis of cyclic motor time series. Such analyses capture non-linear fractal dynamics in temporal fluctuations of motor instances that are believed to reflect how executive control enlist a coordination of multiple interactions across temporal scales between the brain, the body and the task environment, an essential architecture for adaptation. Here by recruiting elite rugby players with high motor skills and submitting them to the execution of rhythmic motor tasks involving legs and arms concurrently, the main attempt was to build on the multifractal formalism of movement control to show a marginal need of effective adaptation in concurrent tasks, and a preserved adaptability despite complexified motor execution. The present study applied a multifractal analytical approach to experimental time series and added surrogate data testing based on shuffled, ARFIMA, Davies&Harte and phase-randomized surrogates, for assessing scale-free behavior in repeated motor time series obtained while combining cycling with finger tapping and with circling. Single-tasking was analyzed comparatively. A focus-based multifractal-DFA approach provided Hurst exponents (H) of individual time series over a range of statistical moments H(q), q = [−15 15]. H(2) quantified monofractality and H(-15)-H(15) provided an index of multifractality. Despite concurrent tasking, participants showed great capacity to keep the target rhythm. Surrogate data testing showed reasonable reliability in using multifractal formalism to decipher movement control behavior. The global (i.e., monofractal) behavior in single-tasks did not change when adapting to dual-task. Multifractality dominated in cycling and did not change when cycling was challenged by upper limb movements. Likewise, tapping and circling behaviors were preserved despite concurrent cycling. It is concluded that the coordinated executive control when adapting to dual-motor tasking is not modified in people having developed great motor skills through physical training. Executive control likely emerged from multiplicative interactions across temporal scales which puts emphasis on multifractal approaches of the movement system to get critical cues on adaptation. Extending such analyses to less skilled people is appealing in the context of exploring healthy and diseased movement systems.

Network Analysis of Cross-Correlations on Forex Market during Crises. Globalisation on Forex Market

Within the paper, the problem of globalisation during financial crises is analysed. The research is based on the Forex exchange rates. In the analysis, the power law classification scheme (PLCS) is used. The study shows that during crises cross-correlations increase resulting in significant growth of cliques, and also the ranks of nodes on the converging time series network are growing. This suggests that the crises expose the globalisation processes, which can be verified by the proposed analysis.

Characterizing variability and predictability for air pollutants with stochastic models

We investigate the dynamics of particulate matter, nitrogen oxides, and ozone concentrations in Hong Kong. Using fluctuation functions as a measure for their variability, we develop several simple data models and test their predictive power. We discuss two relevant dynamical properties, namely, the scaling of fluctuations, which is associated with long memory, and the deviations from the Gaussian distribution. While the scaling of fluctuations can be shown to be an artifact of a relatively regular seasonal cycle, the process does not follow a normal distribution even when corrected for correlations and non-stationarity due to random (Poissonian) spikes. We compare predictability and other fitted model parameters between stations and pollutants.

Delayed association of acute particulate matter 2.5 air pollution exposure with loss of complexity in cardiac rhythm dynamics: insight from detrended fluctuation analysis

There is a delayed (lag 1 to 2 days) correlation between acute PM 2.5 (particulate matter < 2.5 μm in aerodynamic diameter) exposure and cardiovascular events, but the underlying mechanism remained unclear. We aimed to investigate the delayed impact of acute PM 2.5 exposures on cardiac autonomics through linear and nonlinear heart rate variability (HRV) analyses. Among 6912 patients who had received 24-h Holter ECG between October 1, 2015, to October 31, 2016, 56 patients (31 males, 70.3 ± 12.7 years old) were enrolled. We classified the patients as high (> 35.4 μg/m³) or low (< 35.4 μg/m³) PM 2.5 groups according to their PM 2.5 exposures on the day of Holter recordings (day 0) lag 1 and lag 2 days. Linear and nonlinear HRV parameters〔Detrended fluctuation analysis (DFA) slopes 1 and 2〕were compared. Baseline characteristics were similar between groups. Linear and nonlinear HRV parameters were similar between high- and low-exposure groups on day 0 and lag 1 day, respectively. However, DFA slope 1 was significantly lower in the high-exposure group on lag 2 days (0.784 ± 0.201 vs. 0.964 ± 0.274, p = 0.021). DFA slope 1 of the high-exposure group was significantly lower on daytime periods (9 am to 9 pm, 8 am to 4 pm and 4 pm to 12 pm) but not on nighttime periods. High lag 2 days PM 2.5 exposure is associated with low DFA slope 1 and the relationship is diurnal. This suggests that air pollution might have a delayed impact on the cardiovascular autonomic system.

A non-linear analysis of running in the heavy and severe intensity domains

PURPOSE

Altered movement complexity, indicative of system dysfunction, has been demonstrated with increased running velocity and neuromuscular fatigue. The critical velocity (CV) denotes a metabolic and neuromuscular fatigue threshold. It remains unclear whether changes to complexity during running are coupled with the exercise intensity domain in which it is performed. The purpose of this study was to examine whether movement variability and complexity differ exclusively above the CV intensity during running.

METHODS

Ten endurance-trained participants ran at 95%, 100%, 105% and 115% CV for 20 min or to task failure, whichever occurred first. Movement at the hip, knee, and ankle were sampled throughout using 3D motion analysis. Complexity of kinematics in the first and last 30 s were quantified using sample entropy (SampEn) and detrended fluctuation analysis (DFA-α). Variability was determined using standard deviation (SD).

RESULTS

SampEn decreased during all trials in knee flexion/extension and it increased in hip internal/external rotation, whilst DFA-α increased in knee internal/external rotation. SD of ankle plantar/dorsiflexion and inversion/eversion, knee internal/external rotation, and hip flexion/extension and abduction/adduction increased during trials. Hip flexion/extension SampEn values were lowest below CV. DFA-α was lower at higher velocities compared to velocities below CV in ankle plantar/dorsiflexion, hip flexion/extension, hip adduction/abduction, hip internal/external rotation. In hip flexion/extension SD was highest at 115% CV.

CONCLUSIONS

Changes to kinematic complexity over time are consistent between heavy and severe intensity domains. The findings suggest running above CV results in increased movement complexity and variability, particularly at the hip, during treadmill running.

Multiscale adaptive multifractal analysis and its applications

To precisely analyze the fractal nature of a short-term time series under the multiscale framework, this study introduces multiscale adaptive multifractal analysis (MAMFA) combining the adaptive fractal analysis method with the multiscale multifractal analysis (MMA). MAMFA and MMA are both applied to the two kinds of simulation sequences, and the results show that the MAMFA method achieves better performances than MMA. MAMFA is also applied to the Chinese and American stock indexes and the R-R interval of heart rate data. It is found that the multifractal characteristics of stock sequences are related to the selection of the scale range s. There is a big difference in the Hurst surface's shape of Chinese and American stock indexes and Chinese stock indexes have more obvious multifractal characteristics. For the R-R interval sequence, we find that the subjects with abnormal heart rate have significant shape changes in three areas of Hurst surface compared with healthy subjects, thereby patients can be effectively distinguished from healthy subjects.

Sulprostone-Induced Gastric Dysrhythmia in the Ferret: Conventional and Advanced Analytical Approaches

Nausea and emesis resulting from disease or drug treatment may be associated with disrupted gastric myoelectric activity (GMA). Conventional analytical techniques can determine the relative degrees of brady-, normo-, and tachygastric power, but lose information relative to the basic slow wave shape. The aim of the present study was to investigate the application of advanced analytical techniques in the analysis of disrupted GMA recorded after administration of sulprostone, a prostaglandin E_3/1 agonist, in ferrets. Ferrets were implanted with radiotelemetry devices to record GMA, blood pressure, heart rate (HR) and core body temperature 1 week before the administration of sulprostone (30 μg/kg) or vehicle (saline, 0.5 mL/kg). GMA was initially analyzed using fast Fourier transformations (FFTs) and a conventional power partitioning. Detrended fluctuation analysis (DFA) was also applied to the GMA recordings to reveal information relative to the fluctuation of signals around local trends. Sample entropy (SampEn) analysis was used for examining the regularity of signals. Conventional signal processing techniques revealed that sulprostone increased the dominant frequency (DF) of slow waves, with an increase in the percentage power of the tachygastric range and a decrease in the percentage power of the normogastric range. DFA revealed that sulprostone decreased the fluctuation function, indicative of a loss of the variability of GMA fluctuations around local trends. Sulprostone increased SampEn values, indicating a loss of regularity in the GMA data. Behaviorally, sulprostone induced emesis and caused defecation. It also increased blood pressure and elevated HR, with an associated decrease in HR variability (HRV). Further analysis of HRV revealed a decrease in both low-frequency (LF) and high-frequency (HF) components, with an overall increase in the LF/HF ratio. Sulprostone did not affect core body temperature. In conclusion, DFA and SampEn permit a detailed analysis of GMA, which is necessary to understand the action of sulprostone to modulate gastric function. The action to decrease HRV and increase the LF/HF ratio may be consistent with a shift toward sympathetic nervous system dominance, commonly seen during nausea.

Schizophrenia EEG Signal Classification Based on Swarm Intelligence Computing

One of the serious mental disorders where people interpret reality in an abnormal state is schizophrenia. A combination of extremely disordered thinking, delusion, and hallucination is caused due to schizophrenia, and the daily functions of a person are severely disturbed because of this disorder. A wide range of problems are caused due to schizophrenia such as disturbed thinking and behaviour. In the field of human neuroscience, the analysis of brain activity is quite an important research area. For general cognitive activity analysis, electroencephalography (EEG) signals are widely used as a low-resolution diagnosis tool. The EEG signals are a great boon to understand the abnormality of the brain disorders, especially schizophrenia. In this work, schizophrenia EEG signal classification is performed wherein, initially, features such as Detrend Fluctuation Analysis (DFA), Hurst Exponent, Recurrence Quantification Analysis (RQA), Sample Entropy, Fractal Dimension (FD), Kolmogorov Complexity, Hjorth exponent, Lempel Ziv Complexity (LZC), and Largest Lyapunov Exponent (LLE) are extracted initially. The extracted features are, then, optimized for selecting the best features through four types of optimization algorithms here such as Artificial Flora (AF) optimization, Glowworm Search (GS) optimization, Black Hole (BH) optimization, and Monkey Search (MS) optimization, and finally, it is classified through certain classifiers. The best results show that, for normal cases, a classification accuracy of 87.54% is obtained when BH optimization is utilized with Support Vector Machine-Radial Basis Function (SVM-RBF) kernel, and for schizophrenia cases, a classification accuracy of 92.17% is obtained when BH optimization is utilized with SVM-RBF kernel.

Long-term stability of resting state EEG-based linear and nonlinear measures

This preliminary study is aimed to evaluate the stability of various linear and nonlinear EEG measures over three years on healthy adults. The linear measures, relative powers of EEG frequency bands, interhemispheric (IHAS) and spectral (SASI) asymmetries plus nonlinear Higuchi's fractal dimension (HFD) and detrended fluctuation analyses (DFA), have been calculated from the resting state eyes closed EEG of 17 participants during two sessions separated over three years. Our results indicate that the stability is highest for the nonlinear (HFD and DFA) and the linear (relative powers of EEG frequency bands) EEG measures that use the signal from a single EEG channel and frequency band, followed by the SASI employing signals from a single channel and two frequency bands and lowest for the IHAS employing signals from two channels. The result support the prospect of using EEG-based measures in clinical practice.

Trends and Persistence of Dry–Wet Conditions in Northeast Brazil

We analyze trend and persistence in Standardized Precipitation Index (SPI) time series derived from monthly rainfall data at 133 gauging stations in Pernambuco state, Brazil, using a suite of complementary methods to address the spatially explicit tendencies, and persistence. SPI was calculated for 1-, 3-, 6-, and 12-month time scales from 1950 to 2012. We use Mann–Kendall test and Sen’s slope to determine sign and magnitude of the trend, and detrended fluctuation analysis (DFA) method to quantify long-term correlations. For all time scales significant negative trends are obtained in the Sertão (deep inland) region, while significant positive trends are found in the Agreste (intermediate inland), and Zona da Mata (coastal) regions. The values of DFA exponents show different scaling behavior for different time scales. For short-term conditions described by SPI-1 the DFA exponent is close to 0.5 indicating weak persistency and low predictability, while for medium-term conditions (SPI-3 and SPI-6) DFA exponents are greater than 0.5 and increase with time scale indicating stronger persistency and higher predictability. For SPI-12 that describes long-term precipitation patterns, the values of DFA exponents for inland regions are around 1, indicating strong persistency, while in the shoreline the value of the DFA exponent is between 1.0 and 1.5, indicating anti-persistent fractional Brownian motion. These results should be useful for agricultural planning and water resource management in the region.

Age-Related Distinctions in EEG Signals during Execution of Motor Tasks Characterized in Terms of Long-Range Correlations

The problem of revealing age-related distinctions in multichannel electroencephalograms (EEGs) during the execution of motor tasks in young and elderly adults is addressed herein. Based on the detrended fluctuation analysis (DFA), differences in long-range correlations are considered, emphasizing changes in the scaling exponent α. Stronger responses in elderly subjects are confirmed, including the range and rate of increase in α. Unlike elderly subjects, young adults demonstrated about 2.5 times more pronounced differences between motor task responses with the dominant and non-dominant hand. Knowledge of age-related changes in brain electrical activity is important for understanding consequences of healthy aging and distinguishing them from pathological changes associated with brain diseases. Besides diagnosing age-related effects, the potential of DFA can also be used in the field of brain–computer interfaces.

Significance of trends in gait dynamics

Trends in time series generated by physiological control systems are ubiquitous. Determining whether trends arise from intrinsic system dynamics or originate outside of the system is a fundamental problem of fractal series analysis. In the latter case, it is necessary to filter out the trends before attempting to quantify correlations in the noise (residuals). For over two decades, detrended fluctuation analysis (DFA) has been used to calculate scaling exponents of stride time (ST), stride length (SL), and stride speed (SS) of human gait. Herein, rather than relying on the very specific form of detrending characteristic of DFA, we adopt Multivariate Adaptive Regression Splines (MARS) to explicitly determine trends in spatio-temporal gait parameters during treadmill walking. Then, we use the madogram estimator to calculate the scaling exponent of the corresponding MARS residuals. The durations of ST and SL trends are determined to be independent of treadmill speed and have distributions with exponential tails. At all speeds considered, the trends of ST and SL are strongly correlated and are statistically independent of their corresponding residuals. The averages of scaling exponents of ST and SL MARS residuals are slightly smaller than 0.5. Thus, contrary to the interpretation prevalent in the literature, the statistical properties of ST and SL time series originate from the superposition of large scale trends and small scale fluctuations. We show that trends serve as the control manifolds about which ST and SL fluctuate. Moreover, the trend speed, defined as the ratio of instantaneous values of SL and ST trends, is tightly controlled about the treadmill speed. The strong coupling between the ST and SL trends ensures that the concomitant changes of their values correspond to movement along the constant speed goal equivalent manifold as postulated by Dingwell et al. 10.1371/journal.pcbi.1000856.

More random motor activity fluctuations predict incident frailty, disability, and mortality

Mobile healthcare increasingly relies on analytical tools that can extract meaningful information from ambulatory physiological recordings. We tested whether a nonlinear tool of fractal physiology could predict long-term health consequences in a large, elderly cohort. Fractal physiology is an emerging field that aims to study how fractal temporal structures in physiological fluctuations generated by complex physiological networks can provide important information about system adaptability. We assessed fractal temporal correlations in the spontaneous fluctuations of ambulatory motor activity of 1275 older participants at baseline, with a follow-up period of up to 13 years. We found that people with reduced temporal correlations (more random activity fluctuations) at baseline had increased risk of frailty, disability, and all-cause death during follow-up. Specifically, for 1-SD decrease in the temporal activity correlations of this studied cohort, the risk of frailty increased by 31%, the risk of disability increased by 15 to 25%, and the risk of death increased by 26%. These incidences occurred on average 4.7 years (frailty), 3 to 4.2 years (disability), and 5.8 years (death) after baseline. These observations were independent of age, sex, education, chronic health conditions, depressive symptoms, cognition, motor function, and total daily activity. The temporal structures in daily motor activity fluctuations may contain unique prognostic information regarding wellness and health in the elderly population.

Sleep Network Deterioration as a Function of Dim-Light-At-Night Exposure Duration in a Mouse Model

Artificial light, despite its widespread and valuable use, has been associated with deterioration of health and well-being, including altered circadian timing and sleep disturbances, particularly in nocturnal exposure. Recent findings from our lab reveal significant sleep and sleep electroencephalogram (EEG) changes owing to three months exposure to dim-light-at-night (DLAN). Aiming to further explore the detrimental effects of DLAN exposure, in the present study, we continuously recorded sleep EEG and the electromyogram for baseline 24-h and following 6-h sleep deprivation in a varied DLAN duration scheme. C57BL/6J mice were exposed to a 12:12 h light:DLAN cycle (75lux:5lux) vs. a 12:12 h light:dark cycle (75lux:0lux) for one day, one week, and one month. Our results show that sleep was already affected by a mere day of DLAN exposure with additional complications emerging with increasing DLAN exposure duration, such as the gradual delay of the daily 24-h vigilance state rhythms. We conducted detrended fluctuation analysis (DFA) on the locomotor activity data following 1-month and 3-month DLAN exposure, and a significantly less healthy rest-activity pattern, based on the decreased alpha values, was found in both conditions compared to the control light-dark. Taking into account the behavioral, sleep and the sleep EEG parameters, our data suggest that DLAN exposure, even in the shortest duration, induces deleterious effects; nevertheless, potential compensatory mechanisms render the organism partly adjustable and able to cope. We think that, for this reason, our data do not always depict linear divergence among groups, as compared with control conditions. Chronic DLAN exposure impacts the sleep regulatory system, but also brain integrity, diminishing its adaptability and reactivity, especially apparent in the sleep EEG alterations and particular low alpha values following DFA.

Entropy Analysis of RR-Time Series From Stress Tests

The RR-interval time series or tachograms obtained from electrocardiograms have been widely studied since they reflect the cardiac variability, and this is an indicative of the health status of a person. The tachogram can be seen as a highly non-linear and complex time series, and therefore, should be analyzed with non-linear techniques. In this work, several entropy measures, Sample Entropy (SampEn), Approximate Entropy (ApEn), and Fuzzy Entropy (FuzzyEn) are used as a measure of heart rate variability (HRV). Tachograms belonging to thirty-nine subjects were obtained from a cardiac stress test consisting of a rest period followed by a period of moderate physical activity. Subjects are grouped according to their physical activity using the IPAQ sedentary and active questionnaire, we work with youth and middle-aged adults. The entropy measures for each group show that for the sedentary subjects the values are high at rest and decrease appreciably with moderate physical activity, This happens for both young and middle-aged adults. These results are highly reproducible. In the case of the subjects that exercise regularly, an increase in entropy is observed or they tend to retain the entropy value that they had at rest. It seems that there is a possible correlation between the physical condition of a person with the increase or decrease in entropy during moderate physical activity with respect to the entropy at rest. It was also observed that entropy during longer physical activity tests tends to decrease as fatigue accumulates, but this decrease is small compared to the change that occurs when going from rest to physical activity.

Distinguishing Epileptiform Discharges From Normal Electroencephalograms Using Adaptive Fractal and Network Analysis: A Clinical Perspective

Epilepsy is one of the most common disorders of the brain. Clinically, to corroborate an epileptic seizure-like symptom and to find the seizure localization, electroencephalogram (EEG) data are often visually examined by a clinical doctor to detect the presence of epileptiform discharges. Epileptiform discharges are transient waveforms lasting for several tens to hundreds of milliseconds and are mainly divided into seven types. It is important to develop systematic approaches to accurately distinguish these waveforms from normal control ones. This is a difficult task if one wishes to develop first principle rather than black-box based approaches, since clinically used scalp EEGs usually contain a lot of noise and artifacts. To solve this problem, we analyzed 640 multi-channel EEG segments, each 4s long. Among these segments, 540 are short epileptiform discharges, and 100 are from healthy controls. We have proposed two approaches for distinguishing epileptiform discharges from normal EEGs. The first method is based on Signal Range and EEGs' long range correlation properties characterized by the Hurst parameter H extracted by applying adaptive fractal analysis (AFA), which can also maximally suppress the effects of noise and various kinds of artifacts. Our second method is based on networks constructed from three aspects of the scalp EEG signals, the Signal Range, the energy of the alpha wave component, and EEG's long range correlation properties. The networks are further analyzed using singular value decomposition (SVD). The square of the first singular value from SVD is used to construct features to distinguish epileptiform discharges from normal controls. Using Random Forest Classifier (RF), our approaches can achieve very high accuracy in distinguishing epileptiform discharges from normal control ones, and thus are very promising to be used clinically. The network-based approach is also used to infer the localizations of each type of epileptiform discharges, and it is found that the sub-networks representing the most likely location of each type of epileptiform discharges are different among the seven types of epileptiform discharges.

Transforming Gaussian correlations. Applications to generating long-range power-law correlated time series with arbitrary distribution

The observable outputs of many complex dynamical systems consist of time series exhibiting autocorrelation functions of great diversity of behaviors, including long-range power-law autocorrelation functions, as a signature of interactions operating at many temporal or spatial scales. Often, numerical algorithms able to generate correlated noises reproducing the properties of real time series are used to study and characterize such systems. Typically, many of those algorithms produce a Gaussian time series. However, the real, experimentally observed time series are often non-Gaussian and may follow distributions with a diversity of behaviors concerning the support, the symmetry, or the tail properties. It is always possible to transform a correlated Gaussian time series into a time series with a different marginal distribution, but the question is how this transformation affects the behavior of the autocorrelation function. Here, we study analytically and numerically how the Pearson's correlation of two Gaussian variables changes when the variables are transformed to follow a different destination distribution. Specifically, we consider bounded and unbounded distributions, symmetric and non-symmetric distributions, and distributions with different tail properties from decays faster than exponential to heavy-tail cases including power laws, and we find how these properties affect the correlation of the final variables. We extend these results to a Gaussian time series, which are transformed to have a different marginal distribution, and show how the autocorrelation function of the final non-Gaussian time series depends on the Gaussian correlations and on the final marginal distribution. As an application of our results, we propose how to generalize standard algorithms producing a Gaussian power-law correlated time series in order to create a synthetic time series with an arbitrary distribution and controlled power-law correlations. Finally, we show a practical example of this algorithm by generating time series mimicking the marginal distribution and the power-law tail of the autocorrelation function of real time series: the absolute returns of stock prices.

Extended detrended fluctuation analysis of electroencephalograms signals during sleep and the opening of the blood-brain barrier

Detrended fluctuation analysis (DFA) is widely used to characterize long-range power-law correlations in complex signals. However, it has restrictions when nonstationarity is not limited only to slow variations in the mean value. To improve the characterization of inhomogeneous datasets, we have proposed the extended DFA (EDFA), which is a modification of the conventional method that evaluates an additional scaling exponent to take into account the features of time-varying nonstationary behavior. Based on EDFA, here, we analyze rat electroencephalograms to identify specific changes in the slow-wave dynamics of brain electrical activity associated with two different conditions, such as the opening of the blood-brain barrier and sleep, which are both characterized by the activation of the brain drainage function. We show that these conditions cause a similar reduction in the scaling exponents of EDFA. Such a similarity may represent an informative marker of fluid homeostasis of the central nervous system.

Persistence Analysis and Prediction of Low-Visibility Events at Valladolid Airport, Spain

This work presents an analysis of low-visibility event persistence and prediction at Villanubla Airport (Valladolid, Spain), considering Runway Visual Range (RVR) time series in winter. The analysis covers long- and short-term persistence and prediction of the series, with different approaches. In the case of long-term analysis, a Detrended Fluctuation Analysis (DFA) approach is applied in order to estimate large-scale RVR time series similarities. The short-term persistence analysis of low-visibility events is evaluated by means of a Markov chain analysis of the binary time series associated with low-visibility events. We finally discuss an hourly short-term prediction of low-visibility events, using different approaches, some of them coming from the persistence analysis through Markov chain models, and others based on Machine Learning (ML) techniques. We show that a Mixture of Experts approach involving persistence-based methods and Machine Learning techniques provides the best results in this prediction problem.

Stock markets: A view from soft matter

Different attempts to describe financial markets, and stock prices in particular, with the tools of statistical mechanics can be found in the literature, although a general framework has not been achieved yet. In this paper we use the physics of many-particle systems and the typical concepts of soft matter to study two sets of US and European stocks, comprising the biggest and most stable companies in terms of stock price and trading. Upon correcting for the center-of-mass motion, the structure and dynamics of the systems are studied (in the European set, the structure is studied for the UK subset only). The pair distribution of the stocks, corrected to account for the nonuniform distribution of prices, is close to 1, indicating that there is no direct interaction between stocks, similar to an ideal gas of particles. The dynamics is studied with the mean-squared price displacement (MSPD); the price correlation function, equivalent to the intermediate scattering function; the price fluctuation distribution; and two parameters for collective motions. The MSPD grows linearly and the velocity autocorrelation function is zero, as for isolated Brownian particles. However, the intermediate scattering function follows a stretched exponential decay, the fluctuation distributions deviate from the Gaussian shape, and strong collective motions are identified. These results indicate that the dynamics is much more complex than an ideal gas of Brownian particles, and similar, to some extent, to that of undercooled systems. Finally, two physical systems are discussed to aid in the understanding of these results: a low density colloidal gel, and a dense system of ideal, infinitely thin stars. The former reproduces the dynamical properties of stocks, linear mean-squared displacement (MSD), non-Gaussian fluctuation distribution, and collective motions, but also has strong structural correlations, whereas the latter undergoes a glass transition with the structure of an ideal gas, but the MSD has the typical two-step growth of undercooled systems.

Probabilistic properties of detrended fluctuation analysis for Gaussian processes

Detrended fluctuation analysis (DFA) is one of the most widely used tools for the detection of long-range dependence in time series. Although DFA has found many interesting applications and has been shown to be one of the best performing detrending methods, its probabilistic foundations are still unclear. In this paper, we study probabilistic properties of DFA for Gaussian processes. Our main attention is paid to the distribution of the squared error sum of the detrended process. We use a probabilistic approach to derive general formulas for the expected value and the variance of the squared fluctuation function of DFA for Gaussian processes. We also get analytical results for the expected value of the squared fluctuation function for particular examples of Gaussian processes, such as Gaussian white noise, fractional Gaussian noise, ordinary Brownian motion, and fractional Brownian motion. Our analytical formulas are supported by numerical simulations. The results obtained can serve as a starting point for analyzing the statistical properties of DFA-based estimators for the fluctuation function and long-memory parameter.

Fractal Analysis of Human Gait Variability via Stride Interval Time Series

Fractal analysis of stride interval time series is a useful tool in human gait research which could be used as a marker for gait adaptability, gait disorder, and fall risk among patients with movement disorders. This study is designed to systematically and comprehensively investigate two practical aspects of fractal analysis which significantly affect the outcome: the series length and the parameters used in the algorithm. The Hurst exponent, scaling exponent, and/or fractal dimension are computed from both simulated and experimental data using three fractal methods, namely detrended fluctuation analysis, box-counting dimension, and Higuchi's fractal dimension. The advantages and drawbacks of each method are discussed, in terms of biases and variability. The results demonstrate that a careful selection of fractal analysis methods and their parameters is required, which is dependent on the aim of study (either analyzing differences between experimental groups or estimating an accurate determination of fractal features). A set of guidelines for the selection of the fractal methods and the length of stride interval time series is provided, along with the optimal parameters for a robust implementation for each method.

Dynamic properties of glucose complexity during the course of critical illness: a pilot study

Methods to control the blood glucose (BG) levels of patients in intensive care units (ICU) improve the outcomes. The development of continuous BG levels monitoring devices has also permitted to optimize these processes. Recently it was shown that a complexity loss of the BG signal is linked to poor clinical outcomes. Thus, it becomes essential to decipher this relation to design efficient BG level control methods. In previous studies the BG signal complexity was calculated as a single index for the whole ICU stay. Although, these approaches did not grasp the potential variability of the BG signal complexity. Therefore, we setup this pilot study using a continuous monitoring of central venous BG levels in ten critically ill patients (EIRUS platform, Maquet Critical CARE AB, Solna, Sweden). Data were processed and the complexity was assessed by the detrended fluctuation analysis and multiscale entropy (MSE) methods. Finally, recordings were split into 24 h overlapping intervals and a MSE analysis was applied to each of them. The MSE analysis on time intervals revealed an entropy variation and allowed periodic BG signal complexity assessments. To highlight differences of MSE between each time interval we calculated the MSE complexity index defined as the area under the curve. This new approach could pave the way to future studies exploring new strategies aimed at restoring blood glucose complexity during the ICU stay.

Dynamics of the Global Stock Market Networks Generated by DCCA Methodology

A group of stock markets can be treated as a complex system. We tried to find the financial market crisis by constructing a global 24 stock market network while using detrended cross-correlation analysis. The community structures by the Girvan-Newman method are observed and other network properties, such as the average degree, clustering coefficient, efficiency, and modularity, are quantified. The criterion of correlation between any two markets on the detrended cross-correlation analysis was considered to be 0.7. We used the return (rt) and volatility (|rt|) time series for the periods of 1, 4, 10, and 20-year of composite stock price indices during 1997–2016. Europe (France, Germany, Netherland, UK), USA (USA1, USA2, USA3, USA4) and Oceania (Australia1, Australia2) have been confirmed to make a solid community. This approach also detected the signal of financial crisis, such as Asian liquidity crisis in 1997, world-wide dot-com bubble collapse in 2001, the global financial crisis triggered by the USA in 2008, European sovereign debt crisis in 2010, and the Chinese stock price plunge in 2015 by capturing the local maxima of average degree and efficiency.

Power-law correlations and coupling of active and quiet states underlie a class of complex systems with self-organization at criticality

Physical and biological systems often exhibit intermittent dynamics with bursts or avalanches (active states) characterized by power-law size and duration distributions. These emergent features are typical of systems at the critical point of continuous phase transitions, and have led to the hypothesis that such systems may self-organize at criticality, i.e. without any fine tuning of parameters. Since the introduction of the Bak-Tang-Wiesenfeld (BTW) model, the paradigm of self-organized criticality (SOC) has been very fruitful for the analysis of emergent collective behaviors in a number of systems, including the brain. Although considerable effort has been devoted in identifying and modeling scaling features of burst and avalanche statistics, dynamical aspects related to the temporal organization of bursts remain often poorly understood or controversial. Of crucial importance to understand the mechanisms responsible for emergent behaviors is the relationship between active and quiet periods, and the nature of the correlations. Here we investigate the dynamics of active (θ-bursts) and quiet states (δ-bursts) in brain activity during the sleep-wake cycle. We show the duality of power-law (θ, active phase) and exponential-like (δ, quiescent phase) duration distributions, typical of SOC, jointly emerge with power-law temporal correlations and anti-correlated coupling between active and quiet states. Importantly, we demonstrate that such temporal organization shares important similarities with earthquake dynamics, and propose that specific power-law correlations and coupling between active and quiet states are distinctive characteristics of a class of systems with self-organization at criticality.

Multifractal temporally weighted detrended cross-correlation analysis of multivariate time series

Fractal and multifractal properties of various systems have been studied extensively. In this paper, first, the multivariate multifractal detrend cross-correlation analysis (MMXDFA) is proposed to investigate the multifractal features in multivariate time series. MMXDFA may produce oscillations in the fluctuation function and spurious cross correlations. In order to overcome these problems, we then propose the multivariate multifractal temporally weighted detrended cross-correlation analysis (MMTWXDFA). In relation to the multivariate detrended cross-correlation analysis and multifractal temporally weighted detrended cross-correlation analysis, an innovation of MMTWXDFA is the application of the signed Manhattan distance to calculate the local detrended covariance function. To evaluate the performance of the MMXDFA and MMTWXDFA methods, we apply them on some artificially generated multivariate series. Several numerical tests demonstrate that both methods can identify their fractality, but MMTWXDFA can detect long-range cross correlations and simultaneously quantify the levels of cross correlation between two multivariate series more accurately.

Temporal ordering of input modulates connectivity formation in a developmental neuronal network model of the cortex

Preterm infant brain activity is discontinuous; bursts of activity recorded using EEG (electroencephalography), thought to be driven by subcortical regions, display scale free properties and exhibit a complex temporal ordering known as long-range temporal correlations (LRTCs). During brain development, activity-dependent mechanisms are essential for synaptic connectivity formation, and abolishing burst activity in animal models leads to weak disorganised synaptic connectivity. Moreover, synaptic pruning shares similar mechanisms to spike-timing dependent plasticity (STDP), suggesting that the timing of activity may play a critical role in connectivity formation. We investigated, in a computational model of leaky integrate-and-fire neurones, whether the temporal ordering of burst activity within an external driving input could modulate connectivity formation in the network. Connectivity evolved across the course of simulations using an approach analogous to STDP, from networks with initial random connectivity. Small-world connectivity and hub neurones emerged in the network structure—characteristic properties of mature brain networks. Notably, driving the network with an external input which exhibited LRTCs in the temporal ordering of burst activity facilitated the emergence of these network properties, increasing the speed with which they emerged compared with when the network was driven by the same input with the bursts randomly ordered in time. Moreover, the emergence of small-world properties was dependent on the strength of the LRTCs. These results suggest that the temporal ordering of burst activity could play an important role in synaptic connectivity formation and the emergence of small-world topology in the developing brain.

Complexity Changes in the US and China's Stock Markets: Differences, Causes, and Wider Social Implications

How different are the emerging and the well-developed stock markets in terms of efficiency? To gain insights into this question, we compared an important emerging market, the Chinese stock market, and the largest and the most developed market, the US stock market. Specifically, we computed the Lempel–Ziv complexity (LZ) and the permutation entropy (PE) from two composite stock indices, the Shanghai stock exchange composite index (SSE) and the Dow Jones industrial average (DJIA), for both low-frequency (daily) and high-frequency (minute-to-minute)stock index data. We found that the US market is basically fully random and consistent with efficient market hypothesis (EMH), irrespective of whether low- or high-frequency stock index data are used. The Chinese market is also largely consistent with the EMH when low-frequency data are used. However, a completely different picture emerges when the high-frequency stock index data are used, irrespective of whether the LZ or PE is computed. In particular, the PE decreases substantially in two significant time windows, each encompassing a rapid market rise and then a few gigantic stock crashes. To gain further insights into the causes of the difference in the complexity changes in the two markets, we computed the Hurst parameter H from the high-frequency stock index data of the two markets and examined their temporal variations. We found that in stark contrast with the US market, whose H is always close to 1/2, which indicates fully random behavior, for the Chinese market, H deviates from 1/2 significantly for time scales up to about 10 min within a day, and varies systemically similar to the PE for time scales from about 10 min to a day. This opens the door for large-scale collective behavior to occur in the Chinese market, including herding behavior and large-scale manipulation as a result of inside information.

Examining Human Unipedal Quiet Stance: Characterizing Control through Jerk

We investigated the quality of smoothness during human unipedal quiet stance. Smoothness is quantified by the time rate of change of the accelerations, or jerks, associated with the motion of the foot and can be seen as an indicative of how controlled the balance process is. To become more acquainted with this as a quantity, we wanted to establish whether or not it can be modeled as a (stationary) stochastic process and, if so, explore its temporal scaling behavior. Specifically, our study focused on the jerk concerning the center-of-pressure (COP) for each foot. Data were collected via a force plate for individuals attempting to maintain upright posture using one leg (with eyes open). Positive tests for stochasticity allowed us to treat the time series as a stochastic process and, given this, we took the jerk to be proportional to the increment of the force realizations. Detrended fluctuation analysis was the primary tool used to explore the scaling behavior. Results suggest that both the medial-lateral and anterior-posterior components of the jerk display persistent and antipersistent correlations which can be modeled by fractional Gaussian noise over three different temporal scaling regions. Finally, we discussed certain possible implications of these features such as a jerk-based control over the force on the foot's COP.

Daily Precipitation Threshold for Rainstorm and Flood Disaster in the Mainland of China: An Economic Loss Perspective

Exploring precipitation threshold from an economic loss perspective is critical for rainstorm and flood disaster risk assessment under climate change. Based on the daily gridded precipitation dataset and direct economic losses (DELs) of rainstorm and flood disasters in the mainland of China, this paper first filtered a relatively reasonable disaster-triggering daily precipitation threshold (DDPT) combination according to the relationship between extreme precipitation days and direct economic loss (DEL) rates at province level and then comprehensively analyzed the spatial landscape of DDPT across China. The results show that (1) the daily precipitation determined by the combination of a 10 mm fixed threshold and 99.3th percentile is recognized as the optimal DDPT of rainstorm and flood disasters, and the correlation coefficient between annual extreme precipitation days and DEL rates reached 0.45 (p < 0.01). (2) The optimal DDPT decreases from southeast (up to 87 mm) to northwest (10 mm) across China, and the DDPTs of 7 out of 31 provinces are lower than 25 mm, while 5 provinces are higher than 50 mm on average. These results suggest that DDPTs exist with large spatial heterogeneity across China, and adopting regional differentiated DDPT is helpful for conducting effective disaster risk analysis.

Identifying characteristic time scales in power grid frequency fluctuations with DFA

Frequency measurements indicate the state of a power grid. In fact, deviations from the nominal frequency determine whether the grid is stable or in a critical situation. We aim to understand the fluctuations of the frequency on multiple time scales with a recently proposed method based on detrended fluctuation analysis. It enables us to infer characteristic time scales and generate stochastic models. We capture and quantify known features of the fluctuations like periodicity due to the trading market, response to variations by control systems, and stability of the long time average. We discuss similarities and differences between the British grid and the continental European grid.

Aggressive dominance can decrease behavioral complexity on subordinates through synchronization of locomotor activities

Social environments are known to influence behavior. Moreover, within small social groups, dominant/subordinate relationships frequently emerge. Dominants can display aggressive behaviors towards subordinates and sustain priority access to resources. Herein, Japanese quail (Coturnix japonica) were used, given that they establish hierarchies through frequent aggressive interactions. We apply a combination of different mathematical tools to provide a precise quantification of the effect of social environments and the consequence of dominance at an individual level on the temporal dynamics of behavior. Main results show that subordinates performed locomotion dynamics with stronger long-range positive correlations in comparison to birds that receive few or no aggressions from conspecifics (more random dynamics). Dominant birds and their subordinates also showed a high level of synchronization in the locomotor pattern, likely emerging from the lack of environmental opportunities to engage in independent behavior. Findings suggest that dominance can potentially modulate behavioral dynamics through synchronization of locomotor activities.

Multifractal analysis of financial markets: a review

Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking analogy with hydrodynamic turbulence, from which the idea of multifractality originated, multifractal analysis of financial markets has bloomed, forming one of the main directions of econophysics. We review the multifractal analysis methods and multifractal models adopted in or invented for financial time series and their subtle properties, which are applicable to time series in other disciplines. We survey the cumulating evidence for the presence of multifractality in financial time series in different markets and at different time periods and discuss the sources of multifractality. The usefulness of multifractal analysis in quantifying market inefficiency, in supporting risk management and in developing other applications is presented. We finally discuss open problems and further directions of multifractal analysis.

Scaling behaviour in music and cortical dynamics interplay to mediate music listening pleasure

The pleasure of music listening regulates daily behaviour and promotes rehabilitation in healthcare. Human behaviour emerges from the modulation of spontaneous timely coordinated neuronal networks. Too little is known about the physical properties and neurophysiological underpinnings of music to understand its perception, its health benefit and to deploy personalized or standardized music-therapy. Prior studies revealed how macroscopic neuronal and music patterns scale with frequency according to a 1/f^α relationship, where a is the scaling exponent. Here, we examine how this hallmark in music and neuronal dynamics relate to pleasure. Using electroencephalography, electrocardiography and behavioural data in healthy subjects, we show that music listening decreases the scaling exponent of neuronal activity and-in temporal areas-this change is linked to pleasure. Default-state scaling exponents of the most pleased individuals were higher and approached those found in music loudness fluctuations. Furthermore, the scaling in selective regions and timescales and the average heart rate were largely proportional to the scaling of the melody. The scaling behaviour of heartbeat and neuronal fluctuations were associated during music listening. Our results point to a 1/f resonance between brain and music and a temporal rescaling of neuronal activity in the temporal cortex as mechanisms underlying music appreciation.

Critical Dynamics and Coupling in Bursts of Cortical Rhythms Indicate Non-Homeostatic Mechanism for Sleep-Stage Transitions and Dual Role of VLPO Neurons in Both Sleep and Wake

Origin and functions of intermittent transitions among sleep stages, including brief awakenings and arousals, constitute a challenge to the current homeostatic framework for sleep regulation, focusing on factors modulating sleep over large time scales. Here we propose that the complex micro-architecture characterizing sleep on scales of seconds and minutes results from intrinsic non-equilibrium critical dynamics. We investigate θ- and δ-wave dynamics in control rats and in rats where the sleep-promoting ventrolateral preoptic nucleus (VLPO) is lesioned (male Sprague-Dawley rats). We demonstrate that bursts in θ and δ cortical rhythms exhibit complex temporal organization, with long-range correlations and robust duality of power-law (θ-bursts, active phase) and exponential-like (δ-bursts, quiescent phase) duration distributions, features typical of non-equilibrium systems self-organizing at criticality. We show that such non-equilibrium behavior relates to anti-correlated coupling between θ- and δ-bursts, persists across a range of time scales, and is independent of the dominant physiologic state; indications of a basic principle in sleep regulation. Further, we find that VLPO lesions lead to a modulation of cortical dynamics resulting in altered dynamical parameters of θ- and δ-bursts and significant reduction in θ-δ coupling. Our empirical findings and model simulations demonstrate that θ-δ coupling is essential for the emerging non-equilibrium critical dynamics observed across the sleep-wake cycle, and indicate that VLPO neurons may have dual role for both sleep and arousal/brief wake activation. The uncovered critical behavior in sleep- and wake-related cortical rhythms indicates a mechanism essential for the micro-architecture of spontaneous sleep-stage and arousal transitions within a novel, non-homeostatic paradigm of sleep regulation.SIGNIFICANCE STATEMENT We show that the complex micro-architecture of sleep-stage/arousal transitions arises from intrinsic non-equilibrium critical dynamics, connecting the temporal organization of dominant cortical rhythms with empirical observations across scales. We link such behavior to sleep-promoting neuronal population, and demonstrate that VLPO lesion (model of insomnia) alters dynamical features of θ and δ rhythms, and leads to significant reduction in θ-δ coupling. This indicates that VLPO neurons may have dual role for both sleep and arousal/brief wake control. The reported empirical findings and modeling simulations constitute first evidences of a neurophysiological fingerprint of self-organization and criticality in sleep- and wake-related cortical rhythms; a mechanism essential for spontaneous sleep-stage and arousal transitions that lays the bases for a novel, non-homeostatic paradigm of sleep regulation.

Non-equilibrium critical dynamics of bursts in θ and δ rhythms as fundamental characteristic of sleep and wake micro-architecture

Origin and functions of intermittent transitions among sleep stages, including short awakenings and arousals, constitute a challenge to the current homeostatic framework for sleep regulation, focusing on factors modulating sleep over large time scales. Here we propose that the complex micro-architecture characterizing the sleep-wake cycle results from an underlying non-equilibrium critical dynamics, bridging collective behaviors across spatio-temporal scales. We investigate θ and δ wave dynamics in control rats and in rats with lesions of sleep-promoting neurons in the parafacial zone. We demonstrate that intermittent bursts in θ and δ rhythms exhibit a complex temporal organization, with long-range power-law correlations and a robust duality of power law (θ-bursts, active phase) and exponential-like (δ-bursts, quiescent phase) duration distributions, typical features of non-equilibrium systems self-organizing at criticality. Crucially, such temporal organization relates to anti-correlated coupling between θ- and δ-bursts, and is independent of the dominant physiologic state and lesions, a solid indication of a basic principle in sleep dynamics.

Interaction between the progression of Alzheimer's disease and fractal degradation

Many outputs from healthy neurophysiological systems including motor activity display nonrandom fluctuations with fractal scaling behavior as characterized by similar temporal fluctuation patterns across a range of time scales. Degraded fractal regulation predicts adverse consequences including Alzheimer's dementia. We examined longitudinal changes in the scaling behavior of motor activity fluctuations during the progression of Alzheimer's disease (AD) in 1068 participants in the Rush Memory and Aging Project. Motor activity of up to 10 days was recorded annually for up to 13 years. Cognitive assessments and clinical diagnoses were administered annually in the same participants. We found that fractal regulation gradually degraded over time (p < 0.0001) even during the stage with no cognitive impairment. The degradation rate was more than doubled after the diagnosis of mild cognitive impairment and more than doubled further after the diagnosis of Alzheimer's dementia (p's ≤ 0.0005). Besides, the longitudinal degradation of fractal regulation significantly correlated with the decline in cognitive performance throughout the progression from no cognitive impairment to mild cognitive impairment, and to AD (p < 0.001). All effects remained the same in subsequent sensitivity analyses that included only 255 decedents with autopsy-confirmed Alzheimer's pathology. These results indicate that the progression of AD accelerates fractal degradation and that fractal degradation may be an integral part of the process of AD.

The critical role of respiratory sinus arrhythmia on temporal cardiac dynamics

Temporal cardiac properties provide alternative information in analyzing heart rate variability (HRV), which may be disregarded by the standard HRV analyses. Patients with congestive heart failure (CHF) are known to have distinct temporal features from the healthy individuals. However, the underlying mechanism leading to the variation remains unclear. Whether or not these parameters can finely classify the severity for CHF patients is uncertain as well. In this work, an electrocardiogram was monitored in advanced CHF patients using 24-h Holter in four conditions, including baseline, one and three months after atenolol therapy, and healthy individuals. Slope and area under the curve (AUC) of multiscale entropy (MSE) curve over short (scales 1-5) and long (scales 6-20) scales, and detrended fluctuation analysis (DFA) scaling exponents at short (4-11 beats) and intermediate (>11 beats) window sizes were calculated. The results show that short-time scale MSE-derived parameters (slope: -0.08 ± 0.10, -0.03 ± 0.10, 0.02 ± 0.06, 0.08 ± 0.06; AUC: 4.03 ± 2.11, 4.69 ± 1.28, 4.73 ± 0.94, and 6.17 ± 1.23) and short-time scale DFA exponent (0.79 ± 0.16, 0.95 ± 0.22, 1.11 ± 0.19, and 1.35 ± 0.20) can hierarchically classify all four conditions. More importantly, simulated R-R intervals with different fractions and amplitude of respiratory sinus arrhythmia (RSA) components were examined to validate our hypothesis regarding the essentiality of RSA in the improvement of cardiovascular function, and its tight association with unpredictability and fractal property of HRV, which is in line with our hypothesis that RSA contributes significantly to the generation of the unpredictability and fractal behavior of HR dynamics.NEW & NOTEWORTHY Temporal cardiac properties provide useful diagnostic parameters for patients with congestive heart failure (CHF). Our study hierarchically classified CHF patients with β-blocker treatment by using multiscale entropy and detrended fluctuation analysis. Also, we provided the evidence to validate the critical role of respiratory sinus arrhythmia in the fractal properties of heart rate variability.

Assessment of Fractal Characteristics of Locomotor Activity of Geriatric In-Patients With Alzheimer's Dementia

INTRODUCTION

Many physiological signals yield fractal characteristics, i.e., finer details at higher magnifications resemble details of the whole. Evidence has been accumulating that such fractal scaling is basically a consequence of interaction-dominant feedback mechanisms that cooperatively generate those signals. Neurodegenerative diseases provide a natural framework to evaluate this paradigm when this cooperative function declines. However, methodological issues need to be cautiously taken into account in order to be able to provide reliable as well as valid interpretations of such signal analyses.

METHODS

Two conceptually different fractal analyses, i.e., detrended fluctuation analysis (DFA) and analysis of cumulative distributions of durations (CDDs), are applied to actigraphy data of 36 geriatric in-patients diagnosed with dementia. The impact of the used time resolution for data acquisition on the assessed fractal outcome parameters is particularly investigated. Moreover, associations between these parameters and scores from the Mini-Mental-State-Examination and circadian activity parameters are explored.

RESULTS

Both analyses yield significant deviations from (mono-)fractal scaling over the entire considered time range. DFA provides robust measures for the observed break-down of fractal scaling. In contrast, analysis of CDDs results in measures which highly fluctuate with respect to the time resolution of the assessed data which affects also further derived quantities such as scaling exponents or associations with other (clinically relevant) assessed parameters.

DISCUSSION

To scrutinize actigraphic signal characteristics and especially their (deviations from) fractal scaling may be a useful tool for aiding diagnosis, characterization, and monitoring of dementia. However, results may, besides contextual aspects, also substantially depend on specific methodological choices. In order to arrive at both reliable and valid interpretations, these complications need to be carefully elaborated in future research.

Relationship between muscle metabolic rate and muscle torque complexity during fatiguing intermittent isometric contractions in humans

To test the hypothesis that a system's metabolic rate and the complexity of fluctuations in the output of that system are related, thirteen healthy participants performed intermittent isometric knee extensor contractions at intensities where a rise in metabolic rate would (40% maximal voluntary contraction, MVC) and would not (20% MVC) be expected. The contractions had a 60% duty factor (6 sec contraction, 4 sec rest) and were performed until task failure or for 30 min, whichever occurred sooner. Torque and surface EMG signals were sampled continuously. Complexity and fractal scaling of torque were quantified using approximate entropy (ApEn) and the detrended fluctuation analysis (DFA) α scaling exponent. Muscle metabolic rate was determined using near-infrared spectroscopy. At 40% MVC, task failure occurred after (mean ± SD) 11.5 ± 5.2 min, whereas all participants completed 30 min of contractions at 20% MVC. Muscle metabolic rate increased significantly after 2 min at 40% MVC (2.70 ± 1.48 to 4.04 ± 1.23 %·s-1 , P < 0.001), but not at 20% MVC. Similarly, complexity decreased significantly at 40% MVC (ApEn, 0.53 ± 0.19 to 0.15 ± 0.09; DFA α, 1.37 ± 0.08 to 1.60 ± 0.09; both P < 0.001), but not at 20% MVC. The rates of change of torque complexity and muscle metabolic rate at 40% MVC were significantly correlated (ApEn, ρ = -0.63, P = 0.022; DFA, ρ = 0.58, P = 0.037). This study demonstrated that an inverse relationship exists between muscle torque complexity and metabolic rate during high-intensity contractions.

Refined Multiscale Entropy Using Fuzzy Metrics: Validation and Application to Nociception Assessment

The refined multiscale entropy (RMSE) approach is commonly applied to assess complexity as a function of the time scale. RMSE is normally based on the computation of sample entropy (SampEn) estimating complexity as conditional entropy. However, SampEn is dependent on the length and standard deviation of the data. Recently, fuzzy entropy (FuzEn) has been proposed, including several refinements, as an alternative to counteract these limitations. In this work, FuzEn, translated FuzEn (TFuzEn), translated-reflected FuzEn (TRFuzEn), inherent FuzEn (IFuzEn), and inherent translated FuzEn (ITFuzEn) were exploited as entropy-based measures in the computation of RMSE and their performance was compared to that of SampEn. FuzEn metrics were applied to synthetic time series of different lengths to evaluate the consistency of the different approaches. In addition, electroencephalograms of patients under sedation-analgesia procedure were analyzed based on the patient’s response after the application of painful stimulation, such as nail bed compression or endoscopy tube insertion. Significant differences in FuzEn metrics were observed over simulations and real data as a function of the data length and the pain responses. Findings indicated that FuzEn, when exploited in RMSE applications, showed similar behavior to SampEn in long series, but its consistency was better than that of SampEn in short series both over simulations and real data. Conversely, its variants should be utilized with more caution, especially whether processes exhibit an important deterministic component and/or in nociception prediction at long scales.