Physiological time series: distinguishing fractal noises from motions

Reduced temporal variability of cortical excitation/inhibition ratio in schizophrenia

Altered neural excitation/inhibition (E/I) balance has long been suspected as a potential underlying cause for clinical symptoms in schizophrenia (SZ). Recent methodological advancements linking the spectral slope (β) of neurophysiological recordings - such as them electroencephalogram (EEG) - to E/I ratio provided much-needed tools to better understand this plausible relationship. Importantly, most approaches treat E/I ratio as a stationary feature in a single scaling range. On the other hand, previous research indicates that this property might change over time, as well as it can express different characteristics in low- and high-frequency regimes. In line, in this study we analyzed resting-state EEG recordings from 30 patients with SZ and 31 healthy controls (HC) and characterized E/I ratio via β separately for low- (1-4 Hz) and high- (20-45 Hz) frequency regimes in a time-resolved manner. Results from this analysis confirmed the bimodal nature of power spectra in both HC and SZ, with steeper spectral slopes in the high- compared to low-frequency ranges. We did not observe any between-group differences in stationary (i.e., time-averaged) neural signatures, however, the temporal variance of β in the 20-45 Hz regime was significantly reduced in SZ patients when compared to HC, predominantly over regions corresponding to the dorsal attention network. Furthermore, this alteration was found correlated to positive clinical symptom scores. Our study indicates that altered E/I ratio dynamics are a characteristic trait of SZ that reflect pathophysiological processes involving the parietal and occipital cortices, potentially responsible for some of the clinical features of the disorder.

Detection of respiratory frequency rhythm in human alpha phase shifts: topographic distributions in wake and drowsy states

Introduction

The relationship between brain activity and respiration is recently attracting increasing attention, despite being studied for a long time. Respiratory modulation was evidenced in both single-cell activity and field potentials. Among EEG and intracranial measurements, the effect of respiration was prevailingly studied on amplitude/power in all frequency bands.

Methods

Since phases of EEG oscillations received less attention, we applied our previously published carrier frequency (CF) mathematical model of human alpha oscillations on a group of 10 young healthy participants in wake and drowsy states, using a 14-channel average reference montage. Since our approach allows for a more precise calculation of CF phase shifts (CFPS) than any individual Fourier component, by using a 2-s moving Fourier window, we validated the new method and studied, for the first time, temporal waveforms CFPS(t) and their oscillatory content through FFT (CFPS(t)).

Results

Although not appearing equally in all channel pairs and every subject, a clear peak in the respiratory frequency region, 0.21-0.26 Hz, was observed (max at 0.22 Hz). When five channel pairs with the most prominent group averaged amplitudes at 0.22 Hz were plotted in both states, topographic distributions changed significantly-from longitudinal, connecting frontal and posterior channels in the wake state to topographically split two separate regions-frontal and posterior in the drowsy state. In addition, in the drowsy state, 0.22-Hz amplitudes decreased for all pairs, while statistically significant reduction was obtained for 20/91 (22%) pairs.

Discussion

These results potentially evidence, for the first time, the respiratory frequency modulation of alpha phase shifts, as well as the significant impact of wakeful consciousness on the observed oscillations.

Fractal Analysis of Electrodermal Activity for Emotion Recognition: A Novel Approach Using Detrended Fluctuation Analysis and Wavelet Entropy

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

Pattern analysis using lower body human walking data to identify the gaitprint

All people have a fingerprint that is unique to them and persistent throughout life. Similarly, we propose that people have a gaitprint, a persistent walking pattern that contains unique information about an individual. To provide evidence of a unique gaitprint, we aimed to identify individuals based on basic spatiotemporal variables. 81 adults were recruited to walk overground on an indoor track at their own pace for four minutes wearing inertial measurement units. A total of 18 trials per participant were completed between two days, one week apart. Four methods of pattern analysis, a) Euclidean distance, b) cosine similarity, c) random forest, and d) support vector machine, were applied to our basic spatiotemporal variables such as step and stride lengths to accurately identify people. Our best accuracy (98.63%) was achieved by random forest, followed by support vector machine (98.40%), and the top 10 most similar trials from cosine similarity (98.40%). Our results clearly demonstrate a persistent walking pattern with sufficient information about the individual to make them identifiable, suggesting the existence of a gaitprint.

Temporal complexity of the BOLD-signal in preterm versus term infants

Preterm birth causes alterations in structural and functional cerebral development that are not fully understood. Here, we investigate whether basic characteristics of BOLD signal itself might differ across preterm, term equivalent, and term infants. Anatomical, fMRI, and diffusion weighted imaging data from 716 neonates born at 23-43 weeks gestational age were obtained from the Developing Human Connectome Project. Hurst exponent (H; a measure of temporal complexity of a time-series) was computed from the power spectral density of the BOLD signal within 13 resting state networks. Using linear mixed effects models to account for scan age and birth age, we found that H increased with age, that earlier birth age contributed to lower H values, and that H increased most in motor and sensory networks. We then tested for a relationship between temporal complexity and structural development using H and DTI-based estimates of myelination and found moderate but significant correlations. These findings suggest that the temporal complexity of BOLD signal in neonates relates to age and tracks with known developmental trajectories in the brain. Elucidating how these signal-based differences might relate to maturing hemodynamics in the preterm brain could yield new information about neurophysiological vulnerabilities during this crucial developmental period.

Aperiodic and Hurst EEG exponents across early human brain development: A systematic review

In electroencephalographic (EEG) data, power-frequency slope exponents (1/f_β) can provide non-invasive markers of in vivo neural activity excitation-inhibition (E:I) balance. E:I balance may be altered in neurodevelopmental conditions; hence, understanding how 1/fβ evolves across infancy/childhood has implications for developing early assessments/interventions. This systematic review (PROSPERO-ID: CRD42023363294) explored the early maturation (0-26 yrs) of resting-state EEG 1/f measures (aperiodic [AE], power law [PLE] and Hurst [HE] exponents), including studies containing ≥1 1/f measures and ≥10 typically developing participants. Five databases (including Embase and Scopus) were searched during March 2023. Forty-two studies were identified (Nparticipants=3478). Risk of bias was assessed using the Quality Assessment with Diverse Studies tool. Narrative synthesis of HE data suggests non-stationary EEG activity occurs throughout development. Age-related trends were complex, with rapid decreases in AEs during infancy and heterogenous changes thereafter. Regionally, AE maxima shifted developmentally, potentially reflecting spatial trends in maturing brain connectivity. This work highlights the importance of further characterising the development of 1/f measures to better understand how E:I balance shapes brain and cognitive development.

Resting-state fractal brain connectivity is associated with impaired cognitive performance in healthy aging

Aging affects cognitive functions even in the absence of ongoing pathologies. The neurophysiological basis of age-related cognitive decline (CD), however, is not completely understood. Alterations in both functional brain connectivity and in the fractal scaling of neuronal dynamics have been linked to aging and cognitive performance. Recently, fractal connectivity (FrC) has been proposed - combining the two concepts - for capturing long-term interactions among brain regions. FrC was shown to be influenced by increased mental workload; however, no prior studies investigated how resting-state FrC relates to cognitive performance and plausible CD in healthy aging. We recruited 19 healthy elderly (HE) and 24 young control (YC) participants, who underwent resting-state electroencephalography (EEG) measurements and comprehensive cognitive evaluation using 7 tests of the Cambridge Neurophysiological Test Automated Battery. FrC networks were reconstructed from EEG data using the recently introduced multiple-resampling cross-spectral analysis (MRCSA). Elderly individuals could be characterized with increased response latency and reduced performance in 4-4 tasks, respectively, with both reaction time and accuracy being affected in two tasks. Auto- and cross-spectral exponents - characterizing regional fractal dynamics and FrC, respectively, - were found reduced in HE when compared to YC over most of the cortex. Additionally, fractal scaling of frontoparietal connections expressed an inverse relationship with task performance in visual memory and sustained attention domains in elderly, but not in young individuals. Our results confirm that the fractal nature of brain connectivity - as captured by MRCSA - is affected in healthy aging. Furthermore, FrC appears as a sensitive neurophysiological marker of age-related CD.

Fingerprints of decreased cognitive performance on fractal connectivity dynamics in healthy aging

Analysis of brain functional connectivity (FC) could provide insight in how and why cognitive functions decline even in healthy aging (HA). Despite FC being established as fluctuating over time even in the resting state (RS), dynamic functional connectivity (DFC) studies involving healthy elderly individuals and assessing how these patterns relate to cognitive performance are yet scarce. In our recent study we showed that fractal temporal scaling of functional connections in RS is not only reduced in HA, but also predicts increased response latency and reduced task solving accuracy. However, in that work we did not address changes in the dynamics of fractal connectivity (FrC) strength itself and its plausible relationship with mental capabilities. Therefore, here we analyzed RS electroencephalography recordings of the same subject cohort as previously, consisting of 24 young and 19 healthy elderly individuals, who also completed 7 different cognitive tasks after data collection. Dynamic fractal connectivity (dFrC) analysis was carried out via sliding-window detrended cross-correlation analysis (DCCA). A machine learning method based on recursive feature elimination was employed to select the subset of connections most discriminative between the two age groups, identifying 56 connections that allowed for classifying participants with an accuracy surpassing 92%. Mean of DCCA was found generally increased, while temporal variability of FrC decreased in the elderly when compared to the young group. Finally, dFrC indices expressed an elaborate pattern of associations-assessed via Spearman correlation-with cognitive performance scores in both groups, linking fractal connectivity strength and variance to increased response latency and reduced accuracy in the elderly population. Our results provide further support for the relevance of FrC dynamics in understanding age-related cognitive decline and might help to identify potential targets for future intervention strategies.

RespirAnalyzer: an R package for analyzing data from continuous monitoring of respiratory signals

Motivation

The analysis of data obtained from continuous monitoring of respiratory signals (CMRS) holds significant importance in improving patient care, optimizing sports performance, and advancing scientific understanding in the field of respiratory health.

Results

The R package RespirAnalyzer provides an analytic tool specifically for feature extraction, fractal and complexity analysis for CMRS data. The package covers a wide and comprehensive range of data analysis methods including obtaining inter-breath intervals (IBI) series, plotting time series, obtaining summary statistics of IBI series, conducting power spectral density, multifractal detrended fluctuation analysis (MFDFA) and multiscale sample entropy analysis, fitting the MFDFA results with the extended binomial multifractal model, displaying results using various plots, etc. This package has been developed from our work in directly analyzing CMRS data and is anticipated to assist fellow researchers in computing the related features of their CMRS data, enabling them to delve into the clinical significance inherent in these features.

Availability and implementation

The package for Windows is available from both Comprehensive R Archive Network (CRAN): https://cran.r-project.org/web/packages/RespirAnalyzer/index.html and GitHub: https://github.com/dongxinzheng/RespirAnalyzer.

Tenets and Methods of Fractal Analysis (1/f Noise)

This chapter deals with the methodical challenges confronting researchers of the fractal phenomenon known as pink or 1/f noise. This chapter introduces concepts and statistical techniques for identifying fractal patterns in empirical time series. It defines some basic statistical terms, describes two essential characteristics of pink noise (self-similarity and long memory), and outlines four parameters representing the theoretical properties of fractal processes: the Hurst coefficient (H), the scaling exponent (α), the power exponent (β), and the fractional differencing parameter (d) of the ARFIMA (autoregressive fractionally integrated moving average) method. Then, it compares and evaluates different approaches to estimating fractal parameters from observed data and outlines the advantages, disadvantages, and constraints of some popular estimators. The final section of this chapter answers the questions: Which strategy is appropriate for the identification of fractal noise in empirical settings and how can it be applied to the data?

Fractal Analysis of the Cerebrovascular System Pathophysiology

The cerebrovascular system is characterized by parameters such as arterial blood pressure (ABP), cerebral perfusion pressure (CPP), and cerebral blood flow velocity (CBFV). These are regulated by interconnected feedback loops resulting in a fluctuating and complex time course. They exhibit fractal characteristics such as (statistical) self-similarity and scale invariance which could be quantified by fractal measures. These include the coefficient of variation, the Hurst coefficient H, or the spectral exponent α in the time domain, as well as the spectral index ß in the frequency domain. Prior to quantification, the time series has to be classified as either stationary or nonstationary, which determines the appropriate fractal analysis and measure for a given signal class. CBFV was characterized as a nonstationary (fractal Brownian motion) signal with spectral index ß between 2.0 and 2.3. In the high-frequency range (>0.15 Hz), CBFV variability is mainly determined by the periodic ABP variability induced by heartbeat and respiration. However, most of the spectral power of CBFV is contained in the low-frequency range (<0.15 Hz), where cerebral autoregulation acts as a low-pass filter and where the fractal properties are found. Cerebral vasospasm, which is a complication of subarachnoid hemorrhage (SAH), is associated with an increase in ß denoting a less complex time course. A reduced fractal dimension of the retinal microvasculature has been observed in neurodegenerative disease and in stroke. According to the decomplexification theory of illness, such a diminished complexity could be explained by a restriction or even dropout of feedback loops caused by disease.

Persistent post-COVID headache is associated with suppression of scale-free functional brain dynamics in non-hospitalized individuals

INTRODUCTION

Post-acute coronavirus disease 2019 (COVID-19) syndrome (PACS) is a growing concern, with headache being a particularly debilitating symptom with high prevalence. The long-term effects of COVID-19 and post-COVID headache on brain function remain poorly understood, particularly among non-hospitalized individuals. This study focused on the power-law scaling behavior of functional brain dynamics, indexed by the Hurst exponent (H). This measure is suppressed during physiological and psychological distress and was thus hypothesized to be reduced in individuals with post-COVID syndrome, with greatest reductions among those with persistent headache.

METHODS

Resting-state blood oxygenation level-dependent (BOLD) functional magnetic resonance imaging data were collected for 57 individuals who had COVID-19 (32 with no headache, 14 with ongoing headache, 11 recovered) and 17 controls who had cold and flu-like symptoms but  tested negative for COVID-19. Individuals were assessed an average of 4-5 months after COVID testing, in a cross-sectional, observational study design.

RESULTS

No significant differences in H values were found between non-headache COVID-19 and control groups., while those with ongoing headache had significantly reduced H values, and those who had recovered from headache had elevated H values, relative to non-headache groups. Effects were greatest in temporal, sensorimotor, and insular brain regions. Reduced H in these regions was also associated with decreased BOLD activity and local functional connectivity.

CONCLUSIONS

These findings provide new insights into the neurophysiological mechanisms that underlie persistent post-COVID headache, with reduced BOLD scaling as a potential biomarker that is specific to this debilitating condition.

Entropy and fractal analysis of brain-related neurophysiological signals in Alzheimer's and Parkinson's disease

Brain-related neuronal recordings, such as local field potential, electroencephalogram and magnetoencephalogram, offer the opportunity to study the complexity of the human brain at different spatial and temporal scales. The complex properties of neuronal signals are intrinsically related to the concept of 'scale-free' behavior and irregular dynamic, which cannot be fully described through standard linear methods, but can be measured by nonlinear indexes. A remarkable application of these analysis methods on electrophysiological recordings is the deep comprehension of the pathophysiology of neurodegenerative diseases, that has been shown to be associated to changes in brain activity complexity. In particular, a decrease of global complexity has been associated to Alzheimer's disease, while a local increase of brain signals complexity characterizes Parkinson's disease. Despite the recent proliferation of studies using fractal and entropy-based analysis, the application of these techniques is still far from clinical practice, due to the lack of an agreement about their correct estimation and a conclusive and shared interpretation. Along with the aim of helping towards the realization of a multidisciplinary audience to approach nonlinear methods based on the concepts of fractality and irregularity, this survey describes the implementation and proper employment of the mostly known and applied indexes in the context of Alzheimer's and Parkinson's diseases.

Cell-autonomous diversification in bacteria arises from calcium dynamics self-organizing at a critical point

How dynamic bacterial calcium is regulated, with kinetics faster than typical mechanisms of cellular adaptation, is unknown. We discover bacterial calcium fluctuations are temporal-fractals resulting from a property known as self-organized criticality (SOC). SOC processes are poised at a phase transition separating ordered and chaotic dynamical regimes and are observed in many natural and anthropogenic systems. SOC in bacterial calcium emerges due to calcium channel coupling mediated via membrane voltage. Environmental or genetic perturbations modify calcium dynamics and the critical exponent suggesting a continuum of critical attractors. Moving along this continuum alters the collective information capacity of bacterial populations. We find that the stochastic transition from motile to sessile lifestyle is partially mediated by SOC-governed calcium fluctuations through the regulation of c-di-GMP. In summary, bacteria co-opt the physics of phase transitions to maintain dynamic calcium equilibrium, and this enables cell-autonomous population diversification during surface colonization by leveraging the stochasticity inherent at a boundary between phases.

Adaptive walking assistance does not impact long-range stride-to-stride autocorrelations in healthy people

Many studies have demonstrated in the past that the level of long-range autocorrelations in series of stride durations, characterizing natural gait variability, is impacted by external constraints, such as treadmill or metronome, or by pathologies, such as Parkinson's or Huntington's disease. Nevertheless, no one has analyzed the effects on this metric of a gait constrained by a robot-mediated walking assistance, which intrinsically tends to normalize the gait pattern. This paper focuses on the influence of a wearable active pelvis orthosis on the level of long-range autocorrelations in series of stride durations. Ten healthy participants, aged between 55 and 77 yr, performed four overground walking sessions, wearing this orthosis, and with different assistive parameters. This study showed that the adaptive assistance provided by this device has the potential of improving gait metrics that are typically affected by aging, such as the hip range of motion, walking speed, stride length, and stride duration, without impacting natural gait variability, i.e., the level of long-range autocorrelations in series of stride durations. This combination is virtuous toward the design of an assistive device for people with locomotion disorders resulting in deteriorated levels of long-range autocorrelations, such as patients with Parkinson's disease.NEW & NOTEWORTHY This study is the first that investigates the effects of a wearable active pelvis orthosis using an oscillator-based adaptive assistance on the level of long-range autocorrelations in series of stride durations during overground walking. It is also the first to compare the effects of different assistance settings on spatiotemporal gait metrics.

Using the photoplethysmography method to monitor age-related changes in the cardiovascular system

Introduction: Aging is a physiological process characterized by progressive changes in all organ systems. In the last few decades, the elderly population has been growing, so the scientific community is focusing on the investigation of the aging process, all in order to improve the quality of life in elderly. One of the biggest challenges in studying the impact of the aging on the human body represents the monitoring of the changes that inevitably occur in arterial blood vessels. Therefore, the medical community has invested a great deal of effort in studying and discovering new methods and tools that could be used to monitor the changes in arterial blood vessels caused by the aging process. The goal of our research was to develop a new diagnostic method using a photoplethysmographic sensor and to examine the impact of the aging process on the cardiovascular system in adults. Long-term recorded arterial blood flow waveforms were analyzed using detrended fluctuation analysis. Materials and Methods: The study included 117 respondents, aged 20-70 years. The waveform of the arterial blood flow was recorded for 5 min, with an optical sensor placed above the left common carotid artery, simultaneously with a single-channel ECG. For each cardiac cycle, the blood flow amplitude was determined, and a new time series was formed, which was analyzed non-linearly (DFA method). The values of the scalar coefficients α 1 and α 2, particularly their ratio (α 1/α 2) were obtained, which were then monitored in relation to the age of the subjects. Result: The values of the scalar ratio (α 1/α 2) were significantly different between the subjects older and younger than 50 years. The value of the α 1/α 2 decreased exponentially with the aging. In the population of middle-aged adults, this ratio had a value around 1, in young adults the value was exclusively higher than 1 and in older adults the value was exclusively lower than 1. Conclusion: The results of this study indicated that the aging led to a decrease in the α 1/α 2 in the population of healthy subjects. With this non-invasive method, changes in the cardiovascular system due to aging can be detected and monitored.

Nonlinear analysis of heart rate variability signals in meditative state: a review and perspective

INTRODUCTION

In recent times, an upsurge in the investigation related to the effects of meditation in reconditioning various cardiovascular and psychological disorders is seen. In majority of these studies, heart rate variability (HRV) signal is used, probably for its ease of acquisition and low cost. Although understanding the dynamical complexity of HRV is not an easy task, the advances in nonlinear analysis has significantly helped in analyzing the impact of meditation of heart regulations. In this review, we intend to present the various nonlinear approaches, scientific findings and their limitations to develop deeper insights to carry out further research on this topic.

RESULTS

Literature have shown that research focus on nonlinear domain is mainly concentrated on assessing predictability, fractality, and entropy-based dynamical complexity of HRV signal. Although there were some conflicting results, most of the studies observed a reduced dynamical complexity, reduced fractal dimension, and decimated long-range correlation behavior during meditation. However, techniques, such as multiscale entropy (MSE) and multifractal analysis (MFA) of HRV can be more effective in analyzing non-stationary HRV signal, which were hardly used in the existing research works on meditation.

CONCLUSIONS

After going through the literature, it is realized that there is a requirement of a more rigorous research to get consistent and new findings about the changes in HRV dynamics due to the practice of meditation. The lack of adequate standard open access database is a concern in drawing statistically reliable results. Albeit, data augmentation technique is an alternative option to deal with this problem, data from adequate number of subjects can be more effective. Multiscale entropy analysis is scantily employed in studying the effect of meditation, which probably need more attention along with multifractal analysis.

METHODS

Scientific databases, namely PubMed, Google Scholar, Web of Science, Scopus were searched to obtain the literature on "HRV analysis during meditation by nonlinear methods". Following an exclusion criteria, 26 articles were selected to carry out this scientific analysis.

Fractional Dynamics Foster Deep Learning of COPD Stage Prediction

Chronic obstructive pulmonary disease (COPD) is one of the leading causes of death worldwide. Current COPD diagnosis (i.e., spirometry) could be unreliable because the test depends on an adequate effort from the tester and testee. Moreover, the early diagnosis of COPD is challenging. The authors address COPD detection by constructing two novel physiological signals datasets (4432 records from 54 patients in the WestRo COPD dataset and 13824 medical records from 534 patients in the WestRo Porti COPD dataset). The authors demonstrate their complex coupled fractal dynamical characteristics and perform a fractional-order dynamics deep learning analysis to diagnose COPD. The authors found that the fractional-order dynamical modeling can extract distinguishing signatures from the physiological signals across patients with all COPD stages-from stage 0 (healthy) to stage 4 (very severe). They use the fractional signatures to develop and train a deep neural network that predicts COPD stages based on the input features (such as thorax breathing effort, respiratory rate, or oxygen saturation). The authors show that the fractional dynamic deep learning model (FDDLM) achieves a COPD prediction accuracy of 98.66% and can serve as a robust alternative to spirometry. The FDDLM also has high accuracy when validated on a dataset with different physiological signals.

Recruit-aged adults may preferentially weight task goals over deleterious cost functions during short duration loaded and imposed gait tasks

Optimal motor control that is stable and adaptable to perturbation is reflected in the temporal arrangement and regulation of gait variability. Load carriage and forced-marching are common military relevant perturbations to gait that have been implicated in the high incidence of musculoskeletal injuries in military populations. We investigated the interactive effects of load magnitude and locomotion pattern on motor variability, stride regulation and spatiotemporal complexity during gait in recruit-aged adults. We further investigated the influences of sex and task duration. Healthy adults executed trials of running and forced-marching with and without loads at 10% above their gait transition velocity. Spatiotemporal parameters were analyzed using a goal equivalent manifold approach. With load and forced-marching, individuals used a greater array of motor solutions to execute the task goal (maintain velocity). Stride-to-stride regulation became stricter as the task progressed. Participants exhibited optimal spatiotemporal complexity with significant but not meaningful differences between sexes. With the introduction of load carriage and forced-marching, individuals relied on a strategy that maximizes and regulates motor solutions that achieve the task goal of velocity specifically but compete with other task functions. The appended cost penalties may have deleterious effects during prolonged execution, potentially increasing the risk of musculoskeletal injuries.

Considerations for Applying Entropy Methods to Temporally Correlated Stochastic Datasets

The goal of this paper is to highlight considerations and provide recommendations for analytical issues that arise when applying entropy methods, specifically Sample Entropy (SampEn), to temporally correlated stochastic datasets, which are representative of a broad range of biomechanical and physiological variables. To simulate a variety of processes encountered in biomechanical applications, autoregressive fractionally integrated moving averaged (ARFIMA) models were used to produce temporally correlated data spanning the fractional Gaussian noise/fractional Brownian motion model. We then applied ARFIMA modeling and SampEn to the datasets to quantify the temporal correlations and regularity of the simulated datasets. We demonstrate the use of ARFIMA modeling for estimating temporal correlation properties and classifying stochastic datasets as stationary or nonstationary. We then leverage ARFIMA modeling to improve the effectiveness of data cleaning procedures and mitigate the influence of outliers on SampEn estimates. We also emphasize the limitations of SampEn to distinguish among stochastic datasets and suggest the use of complementary measures to better characterize the dynamics of biomechanical variables. Finally, we demonstrate that parameter normalization is not an effective procedure for increasing the interoperability of SampEn estimates, at least not for entirely stochastic datasets.

Model-based stationarity filtering of long-term memory data applied to resting-state blood-oxygen-level-dependent signal

Resting-state blood-oxygen-level-dependent (BOLD) signal acquired through functional magnetic resonance imaging is a proxy of neural activity and a key mechanism for assessing neurological conditions. Therefore, practical tools to filter out artefacts that can compromise the assessment are required. On the one hand, a variety of tailored methods to preprocess the data to deal with identified sources of noise (e.g., head motion, heart beating, and breathing, just to mention a few) are in place. But, on the other hand, there might be unknown sources of unstructured noise present in the data. Therefore, to mitigate the effects of such unstructured noises, we propose a model-based filter that explores the statistical properties of the underlying signal (i.e., long-term memory). Specifically, we consider autoregressive fractional integrative process filters. Remarkably, we provide evidence that such processes can model the signals at different regions of interest to attain stationarity. Furthermore, we use a principled analysis where a ground-truth signal with statistical properties similar to the BOLD signal under the injection of noise is retrieved using the proposed filters. Next, we considered preprocessed (i.e., the identified sources of noise removed) resting-state BOLD data of 98 subjects from the Human Connectome Project. Our results demonstrate that the proposed filters decrease the power in the higher frequencies. However, unlike the low-pass filters, the proposed filters do not remove all high-frequency information, instead they preserve process-related higher frequency information. Additionally, we considered four different metrics (power spectrum, functional connectivity using the Pearson's correlation, coherence, and eigenbrains) to infer the impact of such filter. We provided evidence that whereas the first three keep most of the features of interest from a neuroscience perspective unchanged, the latter exhibits some variations that could be due to the sporadic activity filtered out.

Fractal Structure of Brain Electrical Activity of Patients With Mental Disorders

This work was aimed at a comparative analysis of the degree of multifractality of electroencephalographic time series obtained from a group of healthy subjects and from patients with mental disorders. We analyzed long-term records of patients with paranoid schizophrenia and patients with depression. To evaluate the properties of multifractal scaling of various electroencephalographic time series, the method of maximum modulus of the wavelet transform and multifractal analysis of fluctuations without a trend were used. The stability of the width and position of the singularity spectrum for each of the test groups was revealed, and a relationship was established between the correlation and anticorrelation dynamics of successive values of the electroencephalographic time series and the type of mental disorders. It was shown that the main differences between the multifractal properties of brain activity in normal and pathological conditions lie in the different width of the multifractality spectrum and its location associated with the correlated or anticorrelated dynamics of the values of successive time series. It was found that the schizophrenia group is characterized by a greater degree of multifractality compared to the depression group. Thus, the degree of multifractality can be included in a set of tests for differential diagnosis and research of mental disorders.

Contribution of Phase Resetting to Statistical Persistence in Stride Intervals: A Modeling Study

Stride intervals in human walking fluctuate from one stride to the next, exhibiting statistical persistence. This statistical property is changed by aging, neural disorders, and experimental interventions. It has been hypothesized that the central nervous system is responsible for the statistical persistence. Human walking is a complex phenomenon generated through the dynamic interactions between the central nervous system and the biomechanical system. It has also been hypothesized that the statistical persistence emerges through the dynamic interactions during walking. In particular, a previous study integrated a biomechanical model composed of seven rigid links with a central pattern generator (CPG) model, which incorporated a phase resetting mechanism as sensory feedback as well as feedforward, trajectory tracking, and intermittent feedback controllers, and suggested that phase resetting contributes to the statistical persistence in stride intervals. However, the essential mechanisms remain largely unclear due to the complexity of the neuromechanical model. In this study, we reproduced the statistical persistence in stride intervals using a simplified neuromechanical model composed of a simple compass-type biomechanical model and a simple CPG model that incorporates only phase resetting and a feedforward controller. A lack of phase resetting induced a loss of statistical persistence, as observed for aging, neural disorders, and experimental interventions. These mechanisms were clarified based on the phase response characteristics of our model. These findings provide useful insight into the mechanisms responsible for the statistical persistence of stride intervals in human walking.

Monofractal analysis of functional magnetic resonance imaging: An introductory review

The following review will aid readers in providing an overview of scale-free dynamics and monofractal analysis, as well as its applications and potential in functional magnetic resonance imaging (fMRI) neuroscience and clinical research. Like natural phenomena such as the growth of a tree or crashing ocean waves, the brain expresses scale-invariant, or fractal, patterns in neural signals that can be measured. While neural phenomena may represent both monofractal and multifractal processes and can be quantified with many different interrelated parameters, this review will focus on monofractal analysis using the Hurst exponent (H). Monofractal analysis of fMRI data is an advanced analysis technique that measures the complexity of brain signaling by quantifying its degree of scale-invariance. As such, the H value of the blood oxygenation level-dependent (BOLD) signal specifies how the degree of correlation in the signal may mediate brain functions. This review presents a brief overview of the theory of fMRI monofractal analysis followed by notable findings in the field. Through highlighting the advantages and challenges of the technique, the article provides insight into how to best conduct fMRI fractal analysis and properly interpret the findings with physiological relevance. Furthermore, we identify the future directions necessary for its progression towards impactful functional neuroscience discoveries and widespread clinical use. Ultimately, this presenting review aims to build a foundation of knowledge among readers to facilitate greater understanding, discussion, and use of this unique yet powerful imaging analysis technique.

Multiple-Resampling Cross-Spectral Analysis: An Unbiased Tool for Estimating Fractal Connectivity With an Application to Neurophysiological Signals

Investigating scale-free (i.e., fractal) functional connectivity in the brain has recently attracted increasing attention. Although numerous methods have been developed to assess the fractal nature of functional coupling, these typically ignore that neurophysiological signals are assemblies of broadband, arrhythmic activities as well as oscillatory activities at characteristic frequencies such as the alpha waves. While contribution of such rhythmic components may bias estimates of fractal connectivity, they are also likely to represent neural activity and coupling emerging from distinct mechanisms. Irregular-resampling auto-spectral analysis (IRASA) was recently introduced as a tool to separate fractal and oscillatory components in the power spectrum of neurophysiological signals by statistically summarizing the power spectra obtained when resampling the original signal by several non-integer factors. Here we introduce multiple-resampling cross-spectral analysis (MRCSA) as an extension of IRASA from the univariate to the bivariate case, namely, to separate the fractal component of the cross-spectrum between two simultaneously recorded neural signals by applying the same principle. MRCSA does not only provide a theoretically unbiased estimate of the fractal cross-spectrum (and thus its spectral exponent) but also allows for computing the proportion of scale-free coupling between brain regions. As a demonstration, we apply MRCSA to human electroencephalographic recordings obtained in a word generation paradigm. We show that the cross-spectral exponent as well as the proportion of fractal coupling increases almost uniformly over the cortex during the rest-task transition, likely reflecting neural desynchronization. Our results indicate that MRCSA can be a valuable tool for scale-free connectivity studies in characterizing various cognitive states, while it also can be generalized to other applications outside the field of neuroscience.

Fractal-Based Analysis of fMRI BOLD Signal During Naturalistic Viewing Conditions

Background: Temporal fractals are characterized by prominent scale-invariance and self-similarity across time scales. Monofractal analysis quantifies this scaling behavior in a single parameter, the Hurst exponent (H). Higher H reflects greater correlation in the signal structure, which is taken as being more fractal. Previous fMRI studies have observed lower H during conventional tasks relative to resting state conditions, and shown that H is negatively correlated with task difficulty and novelty. To date, no study has investigated the fractal dynamics of BOLD signal during naturalistic conditions. Methods: We performed fractal analysis on Human Connectome Project 7T fMRI data (n = 72, 41 females, mean age 29.46 ± 3.76 years) to compare H across movie-watching and rest. Results: In contrast to previous work using conventional tasks, we found higher H values for movie relative to rest (mean difference = 0.014; p = 5.279 × 10^-7; 95% CI [0.009, 0.019]). H was significantly higher in movie than rest in the visual, somatomotor and dorsal attention networks, but was significantly lower during movie in the frontoparietal and default networks. We found no cross-condition differences in test-retest reliability of H. Finally, we found that H of movie-derived stimulus properties (e.g., luminance changes) were fractal whereas H of head motion estimates were non-fractal. Conclusions: Overall, our findings suggest that movie-watching induces fractal signal dynamics. In line with recent work characterizing connectivity-based brain state dynamics during movie-watching, we speculate that these fractal dynamics reflect the configuring and reconfiguring of brain states that occurs during naturalistic processing, and are markedly different than dynamics observed during conventional tasks.

Viscoelasticity and Noise Properties Reveal the Formation of Biomemory in Cells

Living cells are neither perfectly elastic nor liquid and return a viscoelastic response to external stimuli. Nanoindentation provides force–distance curves, allowing the investigation of cell mechanical properties, and yet, these curves can differ from point to point on the cell surface, revealing its inhomogeneous character. In the present work, we propose a mathematical method to estimate both viscoelastic and noise properties of cells as these are depicted on the values of the scaling exponents of relaxation function and power spectral density, respectively. The method uses as input the time derivative of the response force in a nanoindentation experiment. Generalized moments method and/or rescaled range analysis is used to study the resulting time series depending on their nonstationary or stationary nature. We conducted experiments in living Ulocladium chartarum spores. We found that spores in the approaching phase present a viscoelastic behavior with the corresponding scaling exponent in the range 0.25–0.52 and in the retracting phase present a liquid-like behavior with exponents in the range 0.67–0.85. This substantial difference of the scaling exponents in the two phases suggests the formation of biomemory as a response of the spores to the indenting AFM mechanical stimulus. The retracting phase may be described as a process driven by bluish noises, while the approaching one is driven by persistent noise.

Ontogenetic changes in activity, locomotion and behavioural complexity in tadpoles

Metamorphosis is a widespread developmental process that involves considerable changes in morphology, habitat use, ecology and behaviour between early developmental (larval) stages and adult forms. Among amphibians, anuran larvae (tadpoles) undergo massive morphological and ecological changes during their development, with early stages characterized by somatic growth, whereas more conspicuous changes (i.e. metamorphosis) occur later during development. In this study, we examined how locomotor and behavioural traits covary with morphology (body size) and metamorphosis (hindlimb and forelimb development) across developmental stages in spined toad (Bufo spinosus) tadpoles. As expected, we found that locomotion and behaviour undergo significant changes during tadpole development. These changes are curvilinear across developmental stages, with a phase of increasing activity and locomotion followed by a phase of stasis and/or reduction in locomotion and behavioural complexity. All the metrics we investigated indicate that the peak of activity and associated behaviour is situated at a pivotal stage when somatic growth decreases and significant morphological changes occur (i.e. hindlimb growth). Future studies that aim to investigate determinants of locomotion should include developmental stages as covariates in order to assess whether the sensitivity of locomotion to environmental variables changes across developmental stages.

Fast Hand Movements Unveil Multifractal Roots of Adaptation in the Visuomotor Cognitive System

Beyond apparent simplicity, visuomotor dexterity actually requires the coordination of multiple interactions across a complex system that links the brain, the body and the environment. Recent research suggests that a better understanding of how perceptive, cognitive and motor activities cohere to form executive control could be gained from multifractal formalisms applied to movement behavior. Rather than a central executive "talking" to encapsuled components, the multifractal intuition suggests that eye-hand coordination arises from multiplicative cascade dynamics across temporal scales of activity within the whole system, which is reflected in movement time series. Here we examined hand movements of sport students performing a visuomotor task in virtual reality (VR). The task involved hitting spatially arranged targets that lit up on a virtual board under critical time pressure. Three conditions were compared where the visual search field changed: whole board (Standard), half-board lower view field (LVF) and upper view field (UVF). Densely sampled (90 Hz) time series of hand motions captured by VR controllers were analyzed by a focus-based multifractal detrended fluctuation analysis (DFA). Multiplicative rather than additive interactions across temporal scales were evidenced by testing comparatively phase-randomized surrogates of experimental series, which confirmed nonlinear processes. As main results, it was demonstrated that: (i) the degree of multifractality in hand motion behavior was minimal in LVF, a familiar visual search field where subjects correlatively reached their best visuomotor response times (RTs); (ii) multifractality increased in the less familiar UVF, but interestingly only for the non-dominant hand; and (iii) multifractality increased further in Standard, for both hands indifferently; in Standard, the maximal expansion of the visual search field imposed the highest demand as evidenced by the worst visuomotor RTs. Our observations advocate for visuomotor dexterity best described by multiplicative cascades dynamics and a system-wide distributed control rather than a central executive. More importantly, multifractal metrics obtained from hand movements behavior, beyond the confines of the brain, offer a window on the fine organization of control architecture, with high sensitivity to hand-related control behavior under specific constraints. Appealing applications may be found in movement learning/rehabilitation, e.g., in hemineglect people, stroke patients, maturing children or athletes.

Separating scale-free and oscillatory components of neural activity in schizophrenia

INTRODUCTION

Alterations in narrow-band spectral power of electroencephalography (EEG) recordings are commonly reported in patients with schizophrenia (SZ). It is well established however that electrophysiological signals comprise a broadband scale-free (or fractal) component generated by mechanisms different from those producing oscillatory neural activity. Despite this known feature, it has not yet been investigated if spectral abnormalities found in SZ could be attributed to scale-free or oscillatory brain function.

METHODS

In this study, we analyzed resting-state EEG recordings of 14 SZ patients and 14 healthy controls. Scale-free and oscillatory components of the power spectral density (PSD) were separated, and band-limited power (BLP) of the original (mixed) PSD, as well as its fractal and oscillatory components, was estimated in five frequency bands. The scaling property of the fractal component was characterized by its spectral exponent in two distinct frequency ranges (1-13 and 13-30 Hz).

RESULTS

Analysis of the mixed PSD revealed a decrease of BLP in the delta band in SZ over the central regions; however, this difference could be attributed almost exclusively to a shift of power toward higher frequencies in the fractal component. Broadband neural activity expressed a true bimodal nature in all except frontal regions. Furthermore, both low- and high-range spectral exponents exhibited a characteristic topology over the cortex in both groups.

CONCLUSION

Our results imply strong functional significance of scale-free neural activity in SZ and suggest that abnormalities in PSD may emerge from alterations of the fractal and not only the oscillatory components of neural activity.

Scale-Free Coupled Dynamics in Brain Networks Captured by Bivariate Focus-Based Multifractal Analysis

While most connectivity studies investigate functional connectivity (FC) in a scale-dependent manner, coupled neural processes may also exhibit broadband dynamics, manifesting as power-law scaling of their measures of interdependence. Here we introduce the bivariate focus-based multifractal (BFMF) analysis as a robust tool for capturing such scale-free relations and use resting-state electroencephalography (EEG) recordings of 12 subjects to demonstrate its performance in reconstructing physiological networks. BFMF was employed to characterize broadband FC between 62 cortical regions in a pairwise manner, with all investigated connections being tested for true bivariate multifractality. EEG channels were also grouped to represent the activity of six resting-state networks (RSNs) in the brain, thus allowing for the analysis of within- and between- RSNs connectivity, separately. Most connections featured true bivariate multifractality, which could be attributed to the genuine scale-free coupling of neural dynamics. Bivariate multifractality showed a characteristic topology over the cortex that was highly concordant among subjects. Long-term autocorrelation was higher in within-RSNs, while the degree of multifractality was generally found stronger in between-RSNs connections. These results offer statistical evidence of the bivariate multifractal nature of functional coupling in the brain and validate BFMF as a robust method to capture such scale-independent coupled dynamics.

Neuromuscular response to a single session of whole-body vibration in children with cerebral palsy: A pilot study

BACKGROUND

Whole-body vibration (WBV) is a relative new intervention paradigm that could reduce spasticity and improve motor function in children with cerebral palsy (CP). We investigated neuromuscular response to a single session of side-alternating WBV with different amplitudes in children with CP.

METHODS

Ten children with spastic CP aged 7-17 years at GMFCS level I-III participated in this pilot study. Participants received two sessions of side-alternating WBV with the same frequency (20 Hz) but different amplitudes (low-amplitude: 1 mm and high-amplitude: 2 mm). Each session included six sets of 90 s of WBV and 90 s of rest. Before and after each WBV session, we used (a) the modified Ashworth scale to evaluate the spasticity of the participants' leg muscles, (b) a quiet standing task to analyze center-of-pressure (CoP) pattern and postural control, and (c) overground walking trials to assess spatiotemporal gait parameters and joint range-of-motion (RoM).

RESULTS

Both WBV sessions similarly reduced the spasticity of the ankle plantarflexors, improved long-range correlation of CoP profile during standing, and reduced muscle activity of tibialis anterior during walking. The high-amplitude WBV further increased ankle RoM during walking.

CONCLUSIONS

This study demonstrates that a single session of WBV with either a low or a high amplitude can reduce spasticity, enhance standing posture, and improve gait patterns in children with CP. It suggests that low-amplitude WBV may induce similar neuromuscular response as high-amplitude WBV in children with spastic CP and can provide positive outcomes for those who are not able to tolerate stronger vibration.

The dynamics of plant nutation

In this article we advance a cutting-edge methodology for the study of the dynamics of plant movements of nutation. Our approach, unlike customary kinematic analyses of shape, period, or amplitude, is based on three typical signatures of adaptively controlled processes and motions, as reported in the biological and behavioral dynamics literature: harmonicity, predictability, and complexity. We illustrate the application of a dynamical methodology to the bending movements of shoots of common beans (Phaseolus vulgaris L.) in two conditions: with and without a support to climb onto. The results herewith reported support the hypothesis that patterns of nutation are influenced by the presence of a support to climb in their vicinity. The methodology is in principle applicable to a whole range of plant movements.

Stochastic Resonance Reduces Sway and Gait Variability in Individuals With Unilateral Transtibial Amputation: A Pilot Study

Sub-threshold (imperceptible) vibration, applied to parts of the body, impacts how people move and perceive our world. Could this idea help someone who has lost part of their limb? Sub-threshold vibration was applied to the thigh of the affected limb of 20 people with unilateral transtibial amputation. Vibration conditions tested included two noise structures: pink and white. Center of pressure (COP) excursion (range and root-mean-square displacements) during quiet standing, and speed and spatial stride measures (mean and standard deviations of step length and width) during walking were assessed. Pink noise vibration decreased COP displacements in standing, and white noise vibration decreased sound limb step length standard deviation in walking. Sub-threshold vibration positively impacted aspects of both posture and gait; however, different noise structures had different effects. The current study represents foundational work in understanding the potential benefits of incorporating stochastic resonance as an intervention for individuals with amputation.

Temporal integration as "common currency" of brain and self-scale-free activity in resting-state EEG correlates with temporal delay effects on self-relatedness

The self is a multifaceted phenomenon that integrates information and experience across multiple time scales. How temporal integration on the psychological level of the self is related to temporal integration on the neuronal level remains unclear. To investigate temporal integration on the psychological level, we modified a well-established self-matching paradigm by inserting temporal delays. On the neuronal level, we indexed temporal integration in resting-state EEG by two related measures of scale-free dynamics, the power law exponent and autocorrelation window. We hypothesized that the previously established self-prioritization effect, measured as decreased response times or increased accuracy for self-related stimuli, would change with the insertion of different temporal delays between the paired stimuli, and that these changes would be related to temporal integration on the neuronal level. We found a significant self-prioritization effect on accuracy in all conditions with delays, indicating stronger temporal integration of self-related stimuli. Further, we observed a relationship between temporal integration on psychological and neuronal levels: higher degrees of neuronal integration, that is, higher power-law exponent and longer autocorrelation window, during resting-state EEG were related to a stronger increase in the self-prioritization effect across longer temporal delays. We conclude that temporal integration on the neuronal level serves as a template for temporal integration of the self on the psychological level. Temporal integration can thus be conceived as the "common currency" of neuronal and psychological levels of self.

Regional Hurst Exponent Reflects Impulsivity-Related Alterations in Fronto-Hippocampal Pathways Within the Waiting Impulsivity Network

In general, the Hurst exponent. is used as a measure of long-term memory of time series. In previous neuroimaging studies, H has been introduced as one important parameter to define resting-state networks, reflecting upon global scale-free properties emerging from a network. H has been examined in the waiting impulsivity (WI) network in an earlier study. We found that alterations of H in the anterior cingulate cortex (H^ACC) and the nucleus accumbens (H^NAcc) were lower in high impulsive (highIMP) compared to low impulsive (lowIMP) participants. Following up on those findings, we addressed the relation between altered fractality in H^ACC and H^NAcc and brain activation and neural network connectivity. To do so, brain activation maps were calculated, and network connectivity was determined using the Dynamic Causal Modeling (DCM) approach. Finally, 1–H scores were determined to quantify the alterations of H. This way, the focus of the analyses was placed on the potential effects of alterations of H on neural network activation and connectivity. Correlation analyses between the alterations of H^ACC/H^NAcc and activation maps and DCM estimates were performed. We found that the alterations of H predominantly correlated with fronto-hippocampal pathways and correlations were significant only in highIMP subjects. For example, alterations of H^ACC was associated with a decrease in neural activation in the right HC in combination with increased ACC-hippocampal connectivity. Alteration inH^NAcc, in return, was related to an increase in bilateral prefrontal activation in combination with increased fronto-hippocampal connectivity. The findings, that the WI network was related to H alteration in highIMP subjects indicated that impulse control was not reduced per se but lacked consistency. Additionally, H has been used to describe long-term memory processes before, e.g., in capital markets, energy future prices, and human memory. Thus, current findings supported the relation of H toward memory processing even when further prominent cognitive functions were involved.

A Novel Functional Link Network Stacking Ensemble with Fractal Features for Multichannel Fall Detection

Falls are a major health concern and result in high morbidity and mortality rates in older adults with high costs to health services. Automatic fall classification and detection systems can provide early detection of falls and timely medical aid. This paper proposes a novel Random Vector Functional Link (RVFL) stacking ensemble classifier with fractal features for classification of falls. The fractal Hurst exponent is used as a representative of fractal dimensionality for capturing irregularity of accelerometer signals for falls and other activities of daily life. The generalised Hurst exponents along with wavelet transform coefficients are leveraged as input feature space for a novel stacking ensemble of RVFLs composed with an RVFL neural network meta-learner. Novel fast selection criteria are presented for base classifiers founded on the proposed diversity indicator, obtained from the overall performance values during the training phase. The proposed features and the stacking ensemble provide the highest classification accuracy of 95.71% compared with other machine learning techniques, such as Random Forest (RF), Artificial Neural Network (ANN) and Support Vector Machine. The proposed ensemble classifier is 2.3× faster than a single Decision Tree and achieves the highest speedup in training time of 317.7× and 198.56× compared with a highly optimised ANN and RF ensemble, respectively. The significant improvements in training times of the order of 100× and high accuracy demonstrate that the proposed RVFL ensemble is a prime candidate for real-time, embedded wearable device–based fall detection systems.

Multifractal and Entropy-Based Analysis of Delta Band Neural Activity Reveals Altered Functional Connectivity Dynamics in Schizophrenia

Dynamic functional connectivity (DFC) was established in the past decade as a potent approach to reveal non-trivial, time-varying properties of neural interactions – such as their multifractality or information content –, that otherwise remain hidden from conventional static methods. Several neuropsychiatric disorders were shown to be associated with altered DFC, with schizophrenia (SZ) being one of the most intensely studied among such conditions. Here we analyzed resting-state electroencephalography recordings of 14 SZ patients and 14 age- and gender-matched healthy controls (HC). We reconstructed dynamic functional networks from delta band (0.5–4 Hz) neural activity and captured their spatiotemporal dynamics in various global network topological measures. The acquired network measure time series were made subject to dynamic analyses including multifractal analysis and entropy estimation. Besides group-level comparisons, we built a classifier to explore the potential of DFC features in classifying individual cases. We found stronger delta-band connectivity, as well as increased variance of DFC in SZ patients. Surrogate data testing verified the true multifractal nature of DFC in SZ, with patients expressing stronger long-range autocorrelation and degree of multifractality when compared to controls. Entropy analysis indicated reduced temporal complexity of DFC in SZ. When using these indices as features, an overall cross-validation accuracy surpassing 89% could be achieved in classifying individual cases. Our results imply that dynamic features of DFC such as its multifractal properties and entropy are potent markers of altered neural dynamics in SZ and carry significant potential not only in better understanding its pathophysiology but also in improving its diagnosis. The proposed framework is readily applicable for neuropsychiatric disorders other than schizophrenia.

On the application of entropic half-life and statistical persistence decay for quantification of time dependency in human gait

Entropic half-life (ENT½) and statistical persistence decay (SPD) was recently introduced as measures of time dependency in stride time intervals during walking. The present study investigated the effect of data length on ENT½ and SPD and additionally applied these measures to stride length and stride speed intervals. First, stride times were collected from subjects during one hour of treadmill walking. ENT½ and SPD were calculated from a range of stride numbers between 250 and 2500. Secondly, stride times, stride lengths and stride speeds were collected from subjects during 16 min of treadmill walking. ENT½ and SPD were calculated from the stride times, stride lengths and stride speeds. The ENT½ values reached a plateau between 1000 and 2500 strides whereas the SPD increased linearly with the number of included strides. This suggests that ENT½ can be compared if 1000 strides or more are included, but only SPD obtained from same number of strides should be compared. The ENT½ and SPD of the stride times were significantly longer compared to that of the stride lengths and stride speeds. This indicates that the time dependency is greater in the motor control of stride time compared to that of stride lengths and stride speeds.

Oceanic thermal structure mediates dive sequences in a foraging seabird

Changes in marine ecosystems are easier to detect in upper-level predators, like seabirds, which integrate trophic interactions throughout the food web.Here, we examined whether diving parameters and complexity in the temporal organization of diving behavior of little penguins (Eudyptula minor) are influenced by sea surface temperature (SST), water stratification, and wind speed-three oceanographic features influencing prey abundance and distribution in the water column.Using fractal time series analysis, we found that foraging complexity, expressed as the degree of long-range correlations or memory in the dive series, was associated with SST and water stratification throughout the breeding season, but not with wind speed. Little penguins foraging in warmer/more-stratified waters exhibited greater determinism (memory) in foraging sequences, likely as a response to prey aggregations near the thermocline. They also showed higher foraging efficiency, performed more dives and dove to shallower depths than those foraging in colder/less-stratified waters.Reductions in the long-term memory of dive sequences, or in other words increases in behavioral stochasticity, may suggest different strategies concerning the exploration-exploitation trade-off under contrasting environmental conditions.

Signatures of the autonomic nervous system and the heart's pacemaker cells in canine electrocardiograms and their applications to humans

Heart rate and heart rate variability (HRV) are mainly determined by the autonomic nervous system (ANS), which interacts with receptors on the sinoatrial node (SAN; the heart’s primary pacemaker), and by the “coupled-clock” system within the SAN cells. HRV changes are associated with cardiac diseases. However, the relative contributions of the ANS and SAN to HRV are not clear, impeding effective treatment. To discern the SAN’s contribution, we performed HRV analysis on canine electrocardiograms containing basal and ANS-blockade segments. We also analyzed human electrocardiograms of atrial fibrillation and heart failure patients, as well as healthy aged subjects. Finally, we used a mathematical model to simulate HRV under decreased “coupled-clock” regulation. We found that (a) in canines, the SAN and ANS contribute mainly to long- and short-term HRV, respectively; (b) there is evidence suggesting a similar relative SAN contribution in humans; (c) SAN features can be calculated from beat-intervals obtained in-vivo, without intervention; (d) ANS contribution can be modeled by sines embedded in white noise; (e) HRV changes associated with cardiac diseases and aging can be interpreted as deterioration of both SAN and ANS; and (f) SAN clock-coupling can be estimated from changes in HRV. This may enable future non-invasive diagnostic applications.

On Estimating the Hurst Parameter from Least-Squares Residuals. Case Study: Correlated Terrestrial Laser Scanner Range Noise

Many signals appear fractal and have self-similarity over a large range of their power spectral densities. They can be described by so-called Hermite processes, among which the first order one is called fractional Brownian motion (fBm), and has a wide range of applications. The fractional Gaussian noise (fGn) series is the successive differences between elements of a fBm series; they are stationary and completely characterized by two parameters: the variance, and the Hurst coefficient (H). From physical considerations, the fGn could be used to model the noise of observations coming from sensors working with, e.g., phase differences: due to the high recording rate, temporal correlations are expected to have long range dependency (LRD), decaying hyperbolically rather than exponentially. For the rigorous testing of deformations detected with terrestrial laser scanners (TLS), the correct determination of the correlation structure of the observations is mandatory. In this study, we show that the residuals from surface approximations with regression B-splines from simulated TLS data allow the estimation of the Hurst parameter of a known correlated input noise. We derive a simple procedure to filter the residuals in the presence of additional white noise or low frequencies. Our methodology can be applied to any kind of residuals, where the presence of additional noise and/or biases due to short samples or inaccurate functional modeling make the estimation of the Hurst coefficient with usual methods, such as maximum likelihood estimators, imprecise. We demonstrate the feasibility of our proposal with real observations from a white plate scanned by a TLS.

Scale-free functional brain dynamics during recovery from sport-related concussion

Studies using blood‐oxygenation‐level‐dependent functional magnetic resonance imaging (BOLD fMRI) have characterized how the resting brain is affected by concussion. The literature to date, however, has largely focused on measuring changes in the spatial organization of functional brain networks. In the present study, changes in the temporal dynamics of BOLD signals are examined throughout concussion recovery using scaling (or fractal) analysis. Imaging data were collected for 228 university‐level athletes, 61 with concussion and 167 athletic controls. Concussed athletes were scanned at the acute phase of injury (1–7 days postinjury), the subacute phase (8–14 days postinjury), medical clearance to return to sport (RTS), 1 month post‐RTS and 1 year post‐RTS. The wavelet leader multifractal approach was used to assess scaling (c₁) and multifractal (c₂) behavior. Significant longitudinal changes were identified for c₁, which was lowest at acute injury, became significantly elevated at RTS, and returned near control levels by 1 year post‐RTS. No longitudinal changes were identified for c₂. Secondary analyses showed that clinical measures of acute symptom severity and time to RTP were related to longitudinal changes in c₁. Athletes with both higher symptoms and prolonged recovery had elevated c₁ values at RTS, while athletes with higher symptoms but rapid recovery had reduced c₁ at acute injury. This study provides the first evidence for long‐term recovery of BOLD scale‐free brain dynamics after a concussion.

Co-actors Exhibit Similarity in Their Structure of Behavioural Variation That Remains Stable Across Range of Naturalistic Activities

Human behaviour, along with any natural/biological behaviour, has varying degrees of intrinsic 'noise' or variability. Many studies have shown that the structure or patterning of this variability is sensitive to changes in task and constraint. Furthermore, two or more humans interacting together often begin to exhibit similar structures of behavioural variability (i.e., the patterning of their behavioural fluctuations becomes aligned or matched) independent of any moment-to-moment synchronization (termed complexity matching). However, much of the previous work has focused on a subset of simple or contrived behaviours within the context of highly controlled laboratory tasks. In the current study, individuals and pairs performed five self-paced (unsupervised), semi-structured activities around a university campus. Empatica E4 wristbands and iPhones were used to record the participants' behavioural activity via accelerometers and GPS. The results revealed that the structure of variability in naturalistic human behaviour co-varies with the task-goal constraints, and that the patterning of the behavioural fluctuations exhibited by co-acting individuals does become aligned during the performance of everyday activities. The results also revealed that the degree of complexity matching that occurred between pairs remained invariant across activity type, indicating that this measure could be employed as a robust, task-independent index of interpersonal behaviour.

A perspective view on the nanomotion detection of living organisms and its features

The insurgence of newly arising, rapidly developing health threats, such as drug-resistant bacteria and cancers, is one of the most urgent public-health issues of modern times. This menace calls for the development of sensitive and reliable diagnostic tools to monitor the response of single cells to chemical or pharmaceutical stimuli. Recently, it has been demonstrated that all living organisms oscillate at a nanometric scale and that these oscillations stop as soon as the organisms die. These nanometric scale oscillations can be detected by depositing living cells onto a micro-fabricated cantilever and by monitoring its displacements with an atomic force microscope-based electronics. Such devices, named nanomotion sensors, have been employed to determine the resistance profiles of life-threatening bacteria within minutes, to evaluate, among others, the effect of chemicals on yeast, neurons, and cancer cells. The data obtained so far demonstrate the advantages of nanomotion sensing devices in rapidly characterizing microorganism susceptibility to pharmaceutical agents. Here, we review the key aspects of this technique, presenting its major applications. and detailing its working protocols.

Detrended Fluctuation Analysis in the prediction of type 2 diabetes mellitus in patients at risk: Model optimization and comparison with other metrics

Complexity analysis of glucose time series with Detrended Fluctuation Analysis (DFA) has been proved to be useful for the prediction of type 2 diabetes mellitus (T2DM) development. We propose a modified DFA algorithm, review some of its characteristics and compare it with other metrics derived from continuous glucose monitorization in this setting. Several issues of the DFA algorithm were evaluated: (1) Time windowing: the best predictive value was obtained including all time-windows from 15 minutes to 24 hours. (2) Influence of circadian rhythms: for 48-hour glucometries, DFA alpha scaling exponent was calculated on 24-hour sliding segments (1-hour gap, 23-hour overlap), with a median coefficient of variation of 3.2%, which suggests that analysing time series of at least 24-hour length avoids the influence of circadian rhythms. (3) Influence of pretreatment of the time series through integration: DFA without integration was more sensitive to the introduction of white noise and it showed significant predictive power to forecast the development of T2DM, while the pretreated time series did not. (4) Robustness of an interpolation algorithm for missing values: The modified DFA algorithm evaluates the percentage of missing values in a time series. Establishing a 2% error threshold, we estimated the number and length of missing segments that could be admitted to consider a time series as suitable for DFA analysis. For comparison with other metrics, a Principal Component Analysis was performed and the results neatly tease out four different components. The first vector carries information concerned with variability, the second represents mainly DFA alpha exponent, while the third and fourth vectors carry essentially information related to the two “pre-diabetic behaviours” (impaired fasting glucose and impaired glucose tolerance). The scaling exponent obtained with the modified DFA algorithm proposed has significant predictive power for the development of T2DM in a high-risk population compared with other variability metrics or with the standard DFA algorithm.

Biases in the Simulation and Analysis of Fractal Processes

Fractal processes have recently received a growing interest, especially in the domain of rehabilitation. More precisely, the evolution of fractality with aging and disease, suggesting a loss of complexity, has inspired a number of studies that tried, for example, to entrain patients with fractal rhythms. This kind of study requires relevant methods for generating fractal signals and for assessing the fractality of the series produced by participants. In the present work, we engaged a cross validation of three methods of generation and three methods of analysis. We generated exact fractal series with the Davies–Harte (DH) algorithm, the spectral synthesis method (SSM), and the ARFIMA simulation method. The series were analyzed by detrended fluctuation analysis (DFA), power spectral density (PSD) method, and ARFIMA modeling. Results show that some methods of generation present systematic biases: DH presented a strong bias toward white noise in fBm series close to the 1/f boundary and SSM produced series with a larger variability around the expected exponent, as compared with other methods. In contrast, ARFIMA simulations provided quite accurate series, without major bias. Concerning the methods of analysis, DFA tended to systematically underestimate fBm series. In contrast, PSD yielded overestimates for fBm series. With DFA, the variability of estimates tended to increase for fGn series as they approached the 1/f boundary and reached unacceptable levels for fBm series. The highest levels of variability were produced by PSD. Finally, ARFIMA methods generated the best series and provided the most accurate and less variable estimates.

The nucleus does not significantly affect the migratory trajectories of amoeba in two-dimensional environments

For a wide range of cells, from bacteria to mammals, locomotion movements are a crucial systemic behavior for cellular life. Despite its importance in a plethora of fundamental physiological processes and human pathologies, how unicellular organisms efficiently regulate their locomotion system is an unresolved question. Here, to understand the dynamic characteristics of the locomotion movements and to quantitatively study the role of the nucleus in the migration of Amoeba proteus we have analyzed the movement trajectories of enucleated and non-enucleated amoebas on flat two-dimensional (2D) surfaces using advanced non-linear physical-mathematical tools and computational methods. Our analysis shows that both non-enucleated and enucleated amoebas display the same kind of dynamic migration structure characterized by highly organized data sequences, super-diffusion, non-trivial long-range positive correlations, persistent dynamics with trend-reinforcing behavior, and move-step fluctuations with scale invariant properties. Our results suggest that the presence of the nucleus does not significantly affect the locomotion of amoeba in 2D environments.

Capturing the Forest but Missing the Trees: Microstates Inadequate for Characterizing Shorter-Scale EEG Dynamics

The brain is known to be active even when not performing any overt cognitive tasks, and often it engages in involuntary mind wandering. This resting state has been extensively characterized in terms of fMRI-derived brain networks. However, an alternate method has recently gained popularity: EEG microstate analysis. Proponents of microstates postulate that the brain discontinuously switches between four quasi-stable states defined by specific EEG scalp topologies at peaks in the global field potential (GFP). These microstates are thought to be “atoms of thought,” involved with visual, auditory, salience, and attention processing. However, this method makes some major assumptions by excluding EEG data outside the GFP peaks and then clustering the EEG scalp topologies at the GFP peaks, assuming that only one microstate is active at any given time. This study explores the evidence surrounding these assumptions by studying the temporal dynamics of microstates and its clustering space using tools from dynamical systems analysis, fractal, and chaos theory to highlight the shortcomings in microstate analysis. The results show evidence of complex and chaotic EEG dynamics outside the GFP peaks, which is being missed by microstate analysis. Furthermore, the winner-takes-all approach of only one microstate being active at a time is found to be inadequate since the dynamic EEG scalp topology does not always resemble that of the assigned microstate, and there is competition among the different microstate classes. Finally, clustering space analysis shows that the four microstates do not cluster into four distinct and separable clusters. Taken collectively, these results show that the discontinuous description of EEG microstates is inadequate when looking at nonstationary short-scale EEG dynamics.