The Multiscale Entropy Algorithm and Its Variants: A Review

Towards discovery and implementation of neurophysiologic biomarkers of Alzheimer's disease using entropy methods

Alzheimer's disease (AD) is a prevalent and debilitating neurodegenerative disease that leads to substantial loss of quality of life. Therapies currently available for AD do not modify the disease course and have limited efficacy in symptom control. As such, novel and precise therapies tailored to individual patients' neurophysiologic profiles are needed. Functional neuroimaging tools have demonstrated substantial potential to provide quantifiable insight into brain function in various neurologic disorders, particularly AD. Entropy, a novel analysis for better understanding the nonlinear nature of neurophysiological data, has demonstrated consistent accuracy in disease detection. This literature review characterizes the use of entropy-based analyses from functional neuroimaging tools, including electroencephalography (EEG) and magnetoencephalography (MEG), in patients with AD for disease detection, therapeutic response measurement, and providing clinical insights.

Mixbiotic society measures: Assessment of community well-going as living system

Social isolation and fragmentation represent global challenges, with the former stemming from a lack of interaction and the latter from exclusive mobs-both rooted in communication issues. Addressing these challenges, the philosophical realm introduces the concept of the "mixbiotic society." In this framework, individuals with diverse freedoms and values mix together in physical proximity with diverse mingling, recognizing their respective "fundamental incapacities" and uniting in solidarity. This study aims to provide novel measures to balance freedom and solidarity, specifically the intermediate between isolation and mobbing, within a mixbiotic society. To achieve this, we introduce simplified measures to evaluate dynamic communication patterns. These measures complement traditional social network analysis of static structures and conventional entropy-based assessments of dynamic patterns. Our specific hypothesis posits that the measures corresponding to four distinct phases are established by representing communication patterns as multidimensional vectors. These measures include the mean of Euclidean distance to quantify "mobism" for fragmentation, the relative distance change for "atomism" indicating isolation, and a composite measure derived from multiplying the mean and variance of cosine similarity for "mixism," reflecting the well-going state of a mixbiotic society. Additionally, nearly negligible measures correspond to "nihilism." Through the evaluation of seven real-society datasets (high school, primary school, workplace, village, conference, online community, and email), we demonstrate the utility of the "mixism" measure in assessing freedom and solidarity in society. These measures can be employed to typify communities on a radar chart and a communication trajectory graph. The superiority of the measures lies in their ability to evaluate dynamic patterns, ease of calculation, and easily interpretable meanings compared to conventional analyses. As a future development, alongside additional validation using diverse datasets, the mixbiotic society measures will be employed to analyze social issues and applied in the fields of digital democracy and platform cooperativism.

Multi-scale dynamics by adjusting the leaking rate to enhance the performance of deep echo state networks

Introduction

The deep echo state network (Deep-ESN) architecture, which comprises a multi-layered reservoir layer, exhibits superior performance compared to conventional echo state networks (ESNs) owing to the divergent layer-specific time-scale responses in the Deep-ESN. Although researchers have attempted to use experimental trial-and-error grid searches and Bayesian optimization methods to adjust the hyperparameters, suitable guidelines for setting hyperparameters to adjust the time scale of the dynamics in each layer from the perspective of dynamical characteristics have not been established. In this context, we hypothesized that evaluating the dependence of the multi-time-scale dynamical response on the leaking rate as a typical hyperparameter of the time scale in each neuron would help to achieve a guideline for optimizing the hyperparameters of the Deep-ESN.

Method

First, we set several leaking rates for each layer of the Deep-ESN and performed multi-scale entropy (MSCE) analysis to analyze the impact of the leaking rate on the dynamics in each layer. Second, we performed layer-by-layer cross-correlation analysis between adjacent layers to elucidate the structural mechanisms to enhance the performance.

Results

As a result, an optimum task-specific leaking rate value for producing layer-specific multi-time-scale responses and a queue structure with layer-to-layer signal transmission delays for retaining past applied input enhance the Deep-ESN prediction performance.

Discussion

These findings can help to establish ideal design guidelines for setting the hyperparameters of Deep-ESNs.

Modern neurophysiological techniques indexing normal or abnormal brain aging

Brain aging is associated with a decline in cognitive performance, motor function and sensory perception, even in the absence of neurodegeneration. The underlying pathophysiological mechanisms remain incompletely understood, though alterations in neurogenesis, neuronal senescence and synaptic plasticity are implicated. Recent years have seen advancements in neurophysiological techniques such as electroencephalography (EEG), magnetoencephalography (MEG), event-related potentials (ERP) and transcranial magnetic stimulation (TMS), offering insights into physiological and pathological brain aging. These methods provide real-time information on brain activity, connectivity and network dynamics. Integration of Artificial Intelligence (AI) techniques promise as a tool enhancing the diagnosis and prognosis of age-related cognitive decline. Our review highlights recent advances in these electrophysiological techniques (focusing on EEG, ERP, TMS and TMS-EEG methodologies) and their application in physiological and pathological brain aging. Physiological aging is characterized by changes in EEG spectral power and connectivity, ERP and TMS parameters, indicating alterations in neural activity and network function. Pathological aging, such as in Alzheimer's disease, is associated with further disruptions in EEG rhythms, ERP components and TMS measures, reflecting underlying neurodegenerative processes. Machine learning approaches show promise in classifying cognitive impairment and predicting disease progression. Standardization of neurophysiological methods and integration with other modalities are crucial for a comprehensive understanding of brain aging and neurodegenerative disorders. Advanced network analysis techniques and AI methods hold potential for enhancing diagnostic accuracy and deepening insights into age-related brain changes.

Statistical Interdependence between Daily Precipitation and Extreme Daily Temperature in Regions of Mexico and Colombia

We study the statistical interdependence between daily precipitation and daily extreme temperature for regions of Mexico (14 climatic stations, period 1960-2020) and Colombia (7 climatic stations, period 1973-2020) using linear (cross-correlation and coherence) and nonlinear (global phase synchronization index, mutual information, and cross-sample entropy) synchronization metrics. The information shared between these variables is relevant and exhibits changes when comparing regions with different climatic conditions. We show that precipitation and temperature records from La Mojana are characterized by high persistence, while data from Mexico City exhibit lower persistence (less memory). We find that the information exchange and the level of coupling between the precipitation and temperature are higher for the case of the La Mojana region (Colombia) compared to Mexico City (Mexico), revealing that regions where seasonal changes are almost null and with low temperature gradients (less local variability) tend to display higher synchrony compared to regions where seasonal changes are very pronounced. The interdependence characterization between precipitation and temperature represents a robust option to characterize and analyze the collective dynamics of the system, applicable in climate change studies, as well as in changes not easily identifiable in future scenarios.

Seizure detection using nonlinear measures over EEG frequency bands and deep learning classifiers

Epilepsy is a brain disorder that causes patients to suffer from convulsions, which affects their behavior and way of life. Epilepsy can be detected with electroencephalograms (EEGs), which record brain neural activity. Traditional approaches for detecting epileptic seizures from an EEG signal are time-consuming and annoying. To supersede these traditional methods, a myriad of automated seizure detection frameworks based on machine learning techniques have recently been developed. Feature extraction and classification are the two essential phases for seizure detection. The classifier assigns the proper class label after feature extraction lowers the input pattern space while maintaining useful features. This paper proposes a new feature extraction method based on calculating nonlinear features from the most relevant EEG frequency bands. The EEG signal is first decomposed into smaller time segments from which a vector of nonlinear features is computed and supplied to machine learning (ML) and deep learning (DL) classifiers. Experiments on the Bonn dataset reveals an accuracy of 99.7% reached in classifying normal and ictal EEG signals; and an accuracy of 98.8% in the discrimination of ictal and interictal EEG signals. Furthermore, a performance of 100% is achieved on the Hauz Khas dataset. The classification results of the proposed approach were compared to those from published state of the art techniques. Our results are equivalent to or better than some recent studies appeared in the literature.

Benefits of Zero-Phase or Linear Phase Filters to Design Multiscale Entropy: Theory and Application

In various applications, multiscale entropy (MSE) is often used as a feature to characterize the complexity of the signals in order to classify them. It consists of estimating the sample entropies (SEs) of the signal under study and its coarse-grained (CG) versions, where the CG process amounts to (1) filtering the signal with an average filter whose order is the scale and (2) decimating the filter output by a factor equal to the scale. In this paper, we propose to derive a new variant of the MSE. Its novelty stands in the way to get the sequences at different scales by avoiding distortions during the decimation step. To this end, a linear-phase or null-phase low-pass filter whose cutoff frequency is well suited to the scale is used. Interpretations on how the MSE behaves and illustrations with a sum of sinusoids, as well as white and pink noises, are given. Then, an application to detect attentional tunneling is presented. It shows the benefit of the new approach in terms of p value when one aims at differentiating the set of MSEs obtained in the attentional tunneling state from the set of MSEs obtained in the nominal state. It should be noted that CG versions can be replaced not only for the MSE but also for other variants.

Multiscale Entropy-Based Feature Extraction for the Detection of Instability Inception in Axial Compressors

The detection of instability inception is favorable to avoid compressor instability. In this paper, a multiscale entropy-based feature extraction is developed for the detection of the instability inception in axial compressors. Nonlinear and statistical features of the short-time instability inception are extracted by generally combining multiscale entropy and statistical features. First, nonlinear features are extracted by refined composite multiscale entropy to avoid the inaccurate estimation or undefined entropy of multiscale entropy for short time series. Second, the time-domain-based statistical features are chosen to capture more information on instability inception, and the dominant statistical features are determined by random forests implemented with the mean decrease accuracy algorithm at each time scale. The obtained refined composite dominant statistical features are regarded as weighting factors and integrated with the refined composite multiscale entropy to generate a combined feature. Finally, numerical simulation results on two synthetic noise datasets and a compressor instability model dataset are presented to demonstrate the effectiveness, efficiency, and robustness of the combined features under different conditions.

NLDyn - An open source MATLAB toolbox for the univariate and multivariate nonlinear dynamical analysis of physiological data

BACKGROUND AND OBJECTIVE

We present NLDyn, an open-source MATLAB toolbox tailored for in-depth analysis of nonlinear dynamics in biomedical signals. Our objective is to offer a user-friendly yet comprehensive platform for researchers to explore the intricacies of time series data.

METHODS

NLDyn integrates approximately 80 distinct methods, encompassing both univariate and multivariate nonlinear dynamics, setting it apart from existing solutions. This toolbox combines state-of-the-art nonlinear dynamical techniques with advanced multivariate entropy methods, providing users with powerful analytical capabilities. NLDyn enables analyses with or without a sliding window, and users can easily access and customize default parameters.

RESULTS

NLDyn generates results that are both exportable and visually informative, facilitating seamless integration into research and presentations. Its ongoing development ensures it remains at the forefront of nonlinear dynamics analysis.

CONCLUSIONS

NLDyn is a valuable resource for researchers in the biomedical field, offering an intuitive interface and a wide array of nonlinear analysis tools. Its integration of advanced techniques empowers users to gain deeper insights from their data. As we continually refine and expand NLDyn's capabilities, we envision it becoming an indispensable tool for the exploration of complex dynamics in biomedical signals.

Simplicial complex entropy for time series analysis

The complex behavior of many systems in nature requires the application of robust methodologies capable of identifying changes in their dynamics. In the case of time series (which are sensed values of a system during a time interval), several methods have been proposed to evaluate their irregularity. However, for some types of dynamics such as stochastic and chaotic, new approaches are required that can provide a better characterization of them. In this paper we present the simplicial complex approximate entropy, which is based on the conditional probability of the occurrence of elements of a simplicial complex. Our results show that this entropy measure provides a wide range of values with details not easily identifiable with standard methods. In particular, we show that our method is able to quantify the irregularity in simulated random sequences and those from low-dimensional chaotic dynamics. Furthermore, it is possible to consistently differentiate cardiac interbeat sequences from healthy subjects and from patients with heart failure, as well as to identify changes between dynamical states of coupled chaotic maps. Our results highlight the importance of the structures revealed by the simplicial complexes, which holds promise for applications of this approach in various contexts.

Evaluation of skin sympathetic nervous activity for classification of intracerebral hemorrhage and outcome prediction

Classification and outcome prediction of intracerebral hemorrhage (ICH) is critical for improving the survival rate of patients. Early or delayed neurological deterioration is common in ICH patients, which may lead to changes in the autonomic nervous system (ANS). Therefore, we proposed a new framework for ICH classification and outcome prediction based on skin sympathetic nervous activity (SKNA) signals. A customized measurement device presented in our previous papers was used to collect data. 117 subjects (50 healthy control subjects and 67 ICH patients) were recruited for this study to obtain their 5-min electrocardiogram (ECG) and SKNA signals. We extracted the signal's time-domain, frequency-domain, and nonlinear features and analyzed their differences between healthy control subjects and ICH patients. Subsequently, we established the ICH classification and outcome evaluation model based on the eXtreme Gradient Boosting (XGBoost). In addition, heart rate variability (HRV) as an ANS assessment method was also included as a comparison method in this study. The results showed significant differences in most features of the SKNA signal between healthy control subjects and ICH patients. The ICH patients with good outcomes have a higher change rate and complexity of SKNA signal than those with bad outcomes. In addition, the accuracy of the model for ICH classification and outcome prediction based on the SKNA signal was more than 91% and 83%, respectively. The ICH classification and outcome prediction based on the SKNA signal proved to be a feasible method in this study. Furthermore, the features of change rate and complexity, such as entropy measures, can be used to characterize the difference in SKNA signals of different groups. The method can potentially provide a new tool for rapid classification and outcome prediction of ICH patients. Index Terms-intracerebral hemorrhage (ICH), skin sympathetic nervous activity (SKNA), classification, outcome prediction, cardiovascular and cerebrovascular diseases.

A framework based on the information domain to measure coupling changes in electrophysiological signals

Objectives.In this paper, the features of physiological signals of healthy dataset are extracted using the linear and non-linear techniques, and a comparison has been made on healthy young and old subjects to study the aging and gender-related changes in the contribution of Heart Rate (HR), Blood Pressure (BP), and Respiration (RESP).Methods. To quantify the coupling changes in cardiovascular, cardiorespiratory, and vasculorespiratory complexity, an information domain approach based on compensated transfer entropy (cTE) is proposed.Result. The results show that there is a substantial decrease in the flow of information from BP tro the time interval between successive R-peaks (RR) and from RR to BP. There is also a significant decrease in the flow of information from RESP to BP and RESP to RR but there is no significant change in the information flow from BP to RESP and RR to RESP.Conclusion. We have done linear and non-linear analysis on the healthy datasets of young and old subjects. As already existed techniques lacks in studying complex behaviours of electrophysiological signals so to overcome these limitations, we have proposed compensated transfer entropy (cTE). We conducted an investigation to determine the degree to which recordings of RESP, BP, and HR can be utilized to predict changes in the other parameters. Specifically, the proposed analysis examined the relationship between these variables and assessed their consistency across different age groups and genders. By analyzing the data, we aimed to gain insights into the interdependencies and predictive potential of these physiological measures in relation to each other.

Multiscale Diffusion Entropy Analysis for the Detection of Crucial Events in Cardiac Pathology

The significance of crucial events in explaining the dynamics of a physiological system has only been recently emerging. Crucial events are yet to be fully understood and implemented in clinical applications of physiological signal processing. This paper proposes the application of modified diffusion entropy (MDEA) and novel multiscale diffusion entropy analyses (MSDEA) on measuring the temporal complexity of the ECG time series to improve crucial events detection performance. Thirty samples of each of three groups of ECG datasets from PhysioNet with recordings of cardiac arrhythmia (ARR), congestive heart failure (CHF) and normal sinus rhythm (NSR) were analyzed using MDEA with stripes followed by MSDEA. Healthy NSR ECGs showed an approximate 15% greater inverse power law (IPL) and scaling δ indices than pathologic CHF and ARR signals. Additionally, the scaling indices for the pathologic groups showed higher standard deviations, indicating that crucial events determined by MDEA reveal latent differences in ECG complexity that could better be investigated across multiple time scales of temporally decomposed signals using MSDEA which combines multiscale entropy (MSE) and MDEA. Hence, MSDEA showed an improved, clearer discrimination between the healthy and pathological cardiac signals (p<0.0005) characterized by a range of NSR complexity indices twice the range of the pathological values associated with ARR and CHF across twenty temporal scales as well as more reliable trend lines (R2>=0.95).Clinical Relevance- This research proposes a novel and enhanced diagnostic discrimination across healthy and pathologic cardiac conditions based on biomedical signal processing of ECG recordings utilizing the principle of crucial events detection.

Multiscale Entropy Algorithms to Analyze Complexity and Variability of Trunk Accelerations Time Series in Subjects with Parkinson's Disease

The aim of this study was to assess the ability of multiscale sample entropy (MSE), refined composite multiscale entropy (RCMSE), and complexity index (CI) to characterize gait complexity through trunk acceleration patterns in subjects with Parkinson's disease (swPD) and healthy subjects, regardless of age or gait speed. The trunk acceleration patterns of 51 swPD and 50 healthy subjects (HS) were acquired using a lumbar-mounted magneto-inertial measurement unit during their walking. MSE, RCMSE, and CI were calculated on 2000 data points, using scale factors (τ) 1-6. Differences between swPD and HS were calculated at each τ, and the area under the receiver operating characteristics, optimal cutoff points, post-test probabilities, and diagnostic odds ratios were calculated. MSE, RCMSE, and CIs showed to differentiate swPD from HS. MSE in the anteroposterior direction at τ4 and τ5, and MSE in the ML direction at τ4 showed to characterize the gait disorders of swPD with the best trade-off between positive and negative posttest probabilities and correlated with the motor disability, pelvic kinematics, and stance phase. Using a time series of 2000 data points, a scale factor of 4 or 5 in the MSE procedure can yield the best trade-off in terms of post-test probabilities when compared to other scale factors for detecting gait variability and complexity in swPD.

Information-theoretical analysis of statistical measures for multiscale dynamics

Multiscale entropy (MSE) has been widely used to examine nonlinear systems involving multiple time scales, such as biological and economic systems. Conversely, Allan variance has been used to evaluate the stability of oscillators, such as clocks and lasers, ranging from short to long time scales. Although these two statistical measures were developed independently for different purposes in different fields, their interest lies in examining the multiscale temporal structures of physical phenomena under study. We demonstrate that from an information-theoretical perspective, they share some foundations and exhibit similar tendencies. We experimentally confirmed that similar properties of the MSE and Allan variance can be observed in low-frequency fluctuations (LFF) in chaotic lasers and physiological heartbeat data. Furthermore, we calculated the condition under which this consistency between the MSE and Allan variance exists, which is related to certain conditional probabilities. Heuristically, natural physical systems including the aforementioned LFF and heartbeat data mostly satisfy this condition, and hence, the MSE and Allan variance demonstrate similar properties. As a counterexample, we demonstrate an artificially constructed random sequence, for which the MSE and Allan variance exhibit different trends.

Heart Rate Complexity and Autonomic Modulation Are Associated with Psychological Response Inhibition in Healthy Subjects

BACKGROUND

the ability to suppress/regulate impulsive reactions has been identified as common factor underlying the performance in all executive function tasks. We analyzed the HRV signals (power of high (HF) and low (LF) frequency, Sample Entropy (SampEn), and Complexity Index (CI)) during the execution of cognitive tests to assess flexibility, inhibition abilities, and rule learning.

METHODS

we enrolled thirty-six healthy subjects, recording five minutes of resting state and two tasks of increasing complexity based on 220 visual stimuli with 12 × 12 cm red and white squares on a black background.

RESULTS

at baseline, CI was negatively correlated with age, and LF was negatively correlated with SampEn. In Task 1, the CI and LF/HF were negatively correlated with errors. In Task 2, the reaction time positively correlated with the CI and the LF/HF ratio errors. Using a binary logistic regression model, age, CI, and LF/HF ratio classified performance groups with a sensitivity and specificity of 73 and 71%, respectively.

CONCLUSIONS

this study performed an important initial exploration in defining the complex relationship between CI, sympathovagal balance, and age in regulating impulsive reactions during cognitive tests. Our approach could be applied in assessing cognitive decline, providing additional information on the brain-heart interaction.

Neural complexity is a common denominator of human consciousness across diverse regimes of cortical dynamics

What is the common denominator of consciousness across divergent regimes of cortical dynamics? Does consciousness show itself in decibels or in bits? To address these questions, we introduce a testbed for evaluating electroencephalogram (EEG) biomarkers of consciousness using dissociations between neural oscillations and consciousness caused by rare genetic disorders. Children with Angelman syndrome (AS) exhibit sleep-like neural dynamics during wakefulness. Conversely, children with duplication 15q11.2-13.1 syndrome (Dup15q) exhibit wake-like neural dynamics during non-rapid eye movement (NREM) sleep. To identify highly generalizable biomarkers of consciousness, we trained regularized logistic regression classifiers on EEG data from wakefulness and NREM sleep in children with AS using both entropy measures of neural complexity and spectral (i.e., neural oscillatory) EEG features. For each set of features, we then validated these classifiers using EEG from neurotypical (NT) children and abnormal EEGs from children with Dup15q. Our results show that the classification performance of entropy-based EEG biomarkers of conscious state is not upper-bounded by that of spectral EEG features, which are outperformed by entropy features. Entropy-based biomarkers of consciousness may thus be highly adaptable and should be investigated further in situations where spectral EEG features have shown limited success, such as detecting covert consciousness or anesthesia awareness.

The Diagnosis of Congestive Heart Failure Based on Generalized Multiscale Entropy-Wavelet Leaders

Congestive heart failure (CHF) is a chronic heart condition associated with debilitating symptoms that can lead to mortality. The electrocardiogram (ECG) is a noninvasive and simple diagnostic method that can show detectable changes in CHF. However, manual diagnosis of ECG signals is often erroneous due to the small amplitude and duration of the ECG signals. This paper presents a CHF diagnosis method based on generalized multiscale entropy (MSE)-wavelet leaders (WL) and extreme learning machine (ELM). Firstly, ECG signals from normal sinus rhythm (NSR) and congestive heart failure (CHF) patients are pre-processed. Then, parameters such as segmentation time and scale factor are chosen, and the multifractal spectrum features and number of ELM hidden layer nodes are determined. Two different data sets (A, B) were used for training and testing. In both sets, the balanced data set (B) had the highest accuracy of 99.72%, precision, sensitivity, specificity, and F1 score of 99.46%, 100%, 99.44%, and 99.73%, respectively. The unbalanced data set (A) attained an accuracy of 99.56%, precision of 99.44%, sensitivity of 99.81%, specificity of 99.17%, and F1 score of 99.62%. Finally, increasing the number of ECG segments and different algorithms validated the probability of detection of the unbalanced data set. The results indicate that our proposed method requires a lower number of ECG segments and does not require the detection of R waves. Moreover, the method can improve the probability of detection of unbalanced data sets and provide diagnostic assistance to cardiologists by providing a more objective and faster interpretation of ECG signals.

Complexity of locomotion activities in an outside-of-the-lab wearable motion capture dataset

Gait complexity is widely used to understand risk factors for injury, rehabilitation, the performance of assistive devices, and other matters of clinical interest. We analyze the complexity of out-of-the-lab locomotion activities via measures that have previously been used in gait analysis literature, as well as measures from other domains of data analysis. We categorize these broadly as quantifying either the intrinsic dimensionality, the variability, or the regularity, periodicity, or self-similarity of the data from a nonlinear dynamical systems perspective. We perform this analysis on a novel full-body motion capture dataset collected in out-of-the-lab conditions for a variety of indoor environments. This is a unique dataset with a large amount (over 24 h total) of data from participants behaving without low-level instructions in out-of-the-lab indoor environments. We show that reasonable complexity measures can yield surprising, and even profoundly contradictory, results. We suggest that future complexity analysis can use these guidelines to be more specific and intentional about what aspect of complexity a quantitative measure expresses. This will become more important as wearable motion capture technology increasingly allows for comparison of ecologically relevant behavior with lab-based measurements.

On the Genuine Relevance of the Data-Driven Signal Decomposition-Based Multiscale Permutation Entropy

Ordinal pattern-based approaches have great potential to capture intrinsic structures of dynamical systems, and therefore, they continue to be developed in various research fields. Among these, the permutation entropy (PE), defined as the Shannon entropy of ordinal probabilities, is an attractive time series complexity measure. Several multiscale variants (MPE) have been proposed in order to bring out hidden structures at different time scales. Multiscaling is achieved by combining linear or nonlinear preprocessing with PE calculation. However, the impact of such a preprocessing on the PE values is not fully characterized. In a previous study, we have theoretically decoupled the contribution of specific signal models to the PE values from that induced by the inner correlations of linear preprocessing filters. A variety of linear filters such as the autoregressive moving average (ARMA), Butterworth, and Chebyshev were tested. The current work is an extension to nonlinear preprocessing and especially to data-driven signal decomposition-based MPE. The empirical mode decomposition, variational mode decomposition, singular spectrum analysis-based decomposition and empirical wavelet transform are considered. We identify possible pitfalls in the interpretation of PE values induced by these nonlinear preprocessing, and hence, we contribute to improving the PE interpretation. The simulated dataset of representative processes such as white Gaussian noise, fractional Gaussian processes, ARMA models and synthetic sEMG signals as well as real-life sEMG signals are tested.

PV System Failures Diagnosis Based on Multiscale Dispersion Entropy

Photovoltaic (PV) system diagnosis is a growing research domain likewise solar energy's ongoing significant expansion. Indeed, efficient Fault Detection and Diagnosis (FDD) tools are crucial to guarantee reliability, avoid premature aging and improve the profitability of PV plants. In this paper, an on-line diagnosis method using the PV plant electrical output is presented. This entirely signal-based method combines variational mode decomposition (VMD) and multiscale dispersion entropy (MDE) for the purpose of detecting and isolating faults in a real grid-connected PV plant. The present method seeks a low-cost design, an ease of implementation and a low computation cost. Taking into account the innovation of applying these techniques to PV FDD, the VMD and MDE procedures as well as parameters identification are carefully detailed. The proposed FFD approach performance is assessed on a real rooftop PV plant with experimentally induced faults, and the first results reveal the MDE approach has good suitability for PV plants diagnosis.

Temporal complexity of EEG encodes human alertness

OBJECTIVE

Automatic human alertness monitoring has recently become an important research topic with important applications in many areas such as the detection of drivers' fatigue, monitoring of monotonous tasks that require a high level of alertness such as traffic control and nuclear power plant monitoring, and sleep staging. In this study, we propose that balanced dynamics of Electroencephalography (EEG) (so called EEG temporal complexity) is a potentially useful feature for identifying human alertness states. Recently, a new signal entropy measure, called Range Entropy (RangeEn), was proposed to overcome some limitations of two of the most widely used entropy measures, namely Approximate Entropy (ApEn) and Sample Entropy (SampEn), and showed its relevance for the study of time domain EEG complexity. In this paper, we investigated whether the RangeEn holds discriminating information associated with human alertness states, namely Awake, Drowsy, and Sleep and compare its performance against those of SampEn and ApEn.

APPROACH

We used EEG data from 60 healthy subjects of both sexes and different ages acquired during whole night sleeps. Using a 30-second sliding window, we computed the three entropy measures of EEG and performed statistical analyses to evaluate the ability of these entropy measures to discriminate among the different human alertness states.

MAIN RESULTS

Although the three entropy measures contained useful information about human alertness, RangeEn showed a higher discriminative capability compared to ApEn and SampEn especially when using EEG within the Beta frequency band.

SIGNIFICANCE

Our findings highlight the EEG temporal complexity evolution through the human alertness states. This relationship can potentially be exploited for the development of automatic human alertness monitoring systems and diagnostic tools for different neurological and sleep disorders, including insomnia.

Quantification of Small-Scale Heterogeneity at the Core–Mantle Boundary Using Sample Entropy of SKS and SPdKS Synthetic Waveforms

Qualitative and quantitative analysis of seismic waveforms sensitive to the core–mantle boundary (CMB) region reveal the presence of ultralow-velocity zones (ULVZs) that have a strong decrease in compressional (P) and shear (S) wave velocity, and an increase in density within thin structures. However, understanding their physical origin and relation to the other large-scale structures in the lowermost mantle are limited due to an incomplete mapping of ULVZs at the CMB. The SKS and SPdKS seismic waveforms is routinely used to infer ULVZ presence, but has thus far only been used in a limited epicentral distance range. As the SKS/SPdKS wavefield interacts with a ULVZ it generates additional seismic arrivals, thus increasing the complexity of the recorded wavefield. Here, we explore utilization of the multi-scale sample entropy method to search for ULVZ structures. We investigate the feasibility of this approach through analysis of synthetic seismograms computed for PREM, 1-, 2.5-, and 3-D ULVZs as well as heterogeneous structures with a strong increase in velocity in the lowermost mantle in 1- and 2.5-D. We find that the sample entropy technique may be useful across a wide range of epicentral distances from 100° to 130°. Such an analysis, when applied to real waveforms, could provide coverage of roughly 85% by surface area of the CMB.

Predicting Box-Office Markets with Machine Learning Methods

The accurate prediction of gross box-office markets is of great benefit for investment and management in the movie industry. In this work, we propose a machine learning-based method for predicting the movie box-office revenue of a country based on the empirical comparisons of eight methods with diverse combinations of economic factors. Specifically, we achieved a prediction performance of the relative root mean squared error of 0.056 in the US and of 0.183 in China for the two case studies of movie markets in time-series forecasting experiments from 2013 to 2016. We concluded that the support-vector-machine-based method using gross domestic product reached the best prediction performance and satisfies the easily available information of economic factors. The computational experiments and comparison studies provided evidence for the effectiveness and advantages of our proposed prediction strategy. In the validation process of the predicted total box-office markets in 2017, the error rates were 0.044 in the US and 0.066 in China. In the consecutive predictions of nationwide box-office markets in 2018 and 2019, the mean relative absolute percentage errors achieved were 0.041 and 0.035 in the US and China, respectively. The precise predictions, both in the training and validation data, demonstrate the efficiency and versatility of our proposed method.

A Multi-Scale Entropy Approach to Study Collapse and Anomalous Diffusion in Shared Mobility Systems

In this paper, we study the phenomena of collapse and anomalous diffusion in shared mobility systems. In particular, we focus on a fleet of vehicles moving through a stations network and analyse the effect of self-journeys in system stability, using a mathematical simplex under stochastic flows. With a birth-death process approach, we find analytical upper bounds for random walk and we monitor how the system collapses by super diffusing under different randomization conditions. Using the multi-scale entropy metric, we show that real data from a bike-sharing fleet in the city of Salamanca (Spain) present a complex behaviour with more of a 1/f signal than a disorganized system with a white noise signal.

EMD-based analysis of complexity with dissociated EEG amplitude and frequency information: a data-driven robust tool -for Autism diagnosis- compared to multi-scale entropy approach

OBJECTIVE

Autism spectrum disorder (ASD) is usually characterised by altered social skills, repetitive behaviours, and difficulties in verbal/nonverbal communication. It has been reported that electroencephalograms (EEGs) in ASD are characterised by atypical complexity. The most commonly applied method in studies of ASD EEG complexity is multiscale entropy (MSE), where the sample entropy is evaluated across several scales. However, the accuracy of MSE-based classifications between ASD and neurotypical EEG activities is poor owing to several shortcomings in scale extraction and length, the overlap between amplitude and frequency information, and sensitivity to frequency. The present study proposes a novel, nonlinear, non-stationary, adaptive, data-driven, and accurate method for the classification of ASD and neurotypical groups based on EEG complexity and entropy without the shortcomings of MSE.

APPROACH

The proposed method is as follows: (a) each ASD and neurotypical EEG (122 subjects × 64 channels) is decomposed using empirical mode decomposition (EMD) to obtain the intrinsic components (intrinsic mode functions). (b) The extracted components are normalised through the direct quadrature procedure. (c) The Hilbert transforms of the components are computed. (d) The analytic counterparts of components (and normalised components) are found. (e) The instantaneous frequency function of each analytic normalised component is calculated. (f) The instantaneous amplitude function of each analytic component is calculated. (g) The Shannon entropy values of the instantaneous frequency and amplitude vectors are computed. (h) The entropy values are classified using a neural network (NN). (i) The achieved accuracy is compared to that obtained with MSE-based classification. (j) The consistency of the results of entropy 3D mapping with clinical data is assessed.

MAIN RESULTS

The results demonstrate that the proposed method outperforms MSE (accuracy: 66.4%), with an accuracy of 93.5%. Moreover, the entropy 3D mapping results are more consistent with the available clinical data regarding brain topography in ASD.

SIGNIFICANCE

This study presents a more robust alternative to MSE, which can be used for accurate classification of ASD/neurotypical as well as for the examination of EEG entropy across brain zones in ASD.

Diagnostic Developments in Differentiating Unresponsive Wakefulness Syndrome and the Minimally Conscious State

When treating patients with a disorder of consciousness (DOC), it is essential to obtain an accurate diagnosis as soon as possible to generate individualized treatment programs. However, accurately diagnosing patients with DOCs is challenging and prone to errors when differentiating patients in a Vegetative State/Unresponsive Wakefulness Syndrome (VS/UWS) from those in a Minimally Conscious State (MCS). Upwards of ~40% of patients with a DOC can be misdiagnosed when specifically designed behavioral scales are not employed or improperly administered. To improve diagnostic accuracy for these patients, several important neuroimaging and electrophysiological technologies have been proposed. These include Positron Emission Tomography (PET), functional Magnetic Resonance Imaging (fMRI), Electroencephalography (EEG), and Transcranial Magnetic Stimulation (TMS). Here, we review the different ways in which these techniques can improve diagnostic differentiation between VS/UWS and MCS patients. We do so by referring to studies that were conducted within the last 10 years, which were extracted from the PubMed database. In total, 55 studies met our criteria (clinical diagnoses of VS/UWS from MCS as made by PET, fMRI, EEG and TMS- EEG tools) and were included in this review. By summarizing the promising results achieved in understanding and diagnosing these conditions, we aim to emphasize the need for more such tools to be incorporated in standard clinical practice, as well as the importance of data sharing to incentivize the community to meet these goals.

Gait analysis under the lens of statistical physics

Human gait is a fundamental activity, essential for the survival of the individual, and an emergent property of the interactions between complex physical and cognitive processes. Gait is altered in many situations, due both to external constraints, as e.g. paced walk, and to physical and neurological pathologies. Its study is therefore important as a way of improving the quality of life of patients, but also as a door to understanding the inner working of the human nervous system. In this review we explore how four statistical physics concepts have been used to characterise normal and pathological gait: entropy, maximum Lyapunov exponent, multi-fractal analysis and irreversibility. Beyond some basic definitions, we present the main results that have been obtained in this field, as well as a discussion of the main limitations researchers have dealt and will have to deal with. We finally conclude with some biomedical considerations and avenues for further development.

Variational Embedding Multiscale Sample Entropy: A Tool for Complexity Analysis of Multichannel Systems

Entropy-based methods have received considerable attention in the quantification of structural complexity of real-world systems. Among numerous empirical entropy algorithms, conditional entropy-based methods such as sample entropy, which are associated with amplitude distance calculation, are quite intuitive to interpret but require excessive data lengths for meaningful evaluation at large scales. To address this issue, we propose the variational embedding multiscale sample entropy (veMSE) method and conclusively demonstrate its ability to operate robustly, even with several times shorter data than the existing conditional entropy-based methods. The analysis reveals that veMSE also exhibits other desirable properties, such as the robustness to the variation in embedding dimension and noise resilience. For rigor, unlike the existing multivariate methods, the proposed veMSE assigns a different embedding dimension to every data channel, which makes its operation independent of channel permutation. The veMSE is tested on both stimulated and real world signals, and its performance is evaluated against the existing multivariate multiscale sample entropy methods. The proposed veMSE is also shown to exhibit computational advantages over the existing amplitude distance-based entropy methods.

The Refined Composite Downsampling Permutation Entropy Is a Relevant Tool in the Muscle Fatigue Study Using sEMG Signals

Surface electromyography (sEMG) is a valuable technique that helps provide functional and structural information about the electric activity of muscles. As sEMG measures output of complex living systems characterized by multiscale and nonlinear behaviors, Multiscale Permutation Entropy (MPE) is a suitable tool for capturing useful information from the ordinal patterns of sEMG time series. In a previous work, a theoretical comparison in terms of bias and variance of two MPE variants—namely, the refined composite MPE (rcMPE) and the refined composite downsampling (rcDPE), was addressed. In the current paper, we assess the superiority of rcDPE over MPE and rcMPE, when applied to real sEMG signals. Moreover, we demonstrate the capacity of rcDPE in quantifying fatigue levels by using sEMG data recorded during a fatiguing exercise. The processing of four consecutive temporal segments, during biceps brachii exercise maintained at 70% of maximal voluntary contraction until exhaustion, shows that the 10th-scale of rcDPE was capable of better differentiation of the fatigue segments. This scale actually brings the raw sEMG data, initially sampled at 10 kHz, to the specific 0–500 Hz sEMG spectral band of interest, which finally reveals the inner complexity of the data. This study promotes good practices in the use of MPE complexity measures on real data.

Neurofeedback Training Based on Motor Imagery Strategies Increases EEG Complexity in Elderly Population

Neurofeedback training (NFT) has shown promising results in recent years as a tool to address the effects of age-related cognitive decline in the elderly. Since previous studies have linked reduced complexity of electroencephalography (EEG) signal to the process of cognitive decline, we propose the use of non-linear methods to characterise changes in EEG complexity induced by NFT. In this study, we analyse the pre- and post-training EEG from 11 elderly subjects who performed an NFT based on motor imagery (MI-NFT). Spectral changes were studied using relative power (RP) from classical frequency bands (delta, theta, alpha, and beta), whilst multiscale entropy (MSE) was applied to assess EEG-induced complexity changes. Furthermore, we analysed the subject's scores from Luria tests performed before and after MI-NFT. We found that MI-NFT induced a power shift towards rapid frequencies, as well as an increase of EEG complexity in all channels, except for C3. These improvements were most evident in frontal channels. Moreover, results from cognitive tests showed significant enhancement in intellectual and memory functions. Therefore, our findings suggest the usefulness of MI-NFT to improve cognitive functions in the elderly and encourage future studies to use MSE as a metric to characterise EEG changes induced by MI-NFT.

EntropyHub: An open-source toolkit for entropic time series analysis

An increasing number of studies across many research fields from biomedical engineering to finance are employing measures of entropy to quantify the regularity, variability or randomness of time series and image data. Entropy, as it relates to information theory and dynamical systems theory, can be estimated in many ways, with newly developed methods being continuously introduced in the scientific literature. Despite the growing interest in entropic time series and image analysis, there is a shortage of validated, open-source software tools that enable researchers to apply these methods. To date, packages for performing entropy analysis are often run using graphical user interfaces, lack the necessary supporting documentation, or do not include functions for more advanced entropy methods, such as cross-entropy, multiscale cross-entropy or bidimensional entropy. In light of this, this paper introduces EntropyHub, an open-source toolkit for performing entropic time series analysis in MATLAB, Python and Julia. EntropyHub (version 0.1) provides an extensive range of more than forty functions for estimating cross-, multiscale, multiscale cross-, and bidimensional entropy, each including a number of keyword arguments that allows the user to specify multiple parameters in the entropy calculation. Instructions for installation, descriptions of function syntax, and examples of use are fully detailed in the supporting documentation, available on the EntropyHub website- www.EntropyHub.xyz. Compatible with Windows, Mac and Linux operating systems, EntropyHub is hosted on GitHub, as well as the native package repository for MATLAB, Python and Julia, respectively. The goal of EntropyHub is to integrate the many established entropy methods into one complete resource, providing tools that make advanced entropic time series analysis straightforward and reproducible.

Parameter Analysis of Multiscale Two-Dimensional Fuzzy and Dispersion Entropy Measures Using Machine Learning Classification

Two-dimensional fuzzy entropy, dispersion entropy, and their multiscale extensions (MFuzzyEn2D and MDispEn2D, respectively) have shown promising results for image classifications. However, these results rely on the selection of key parameters that may largely influence the entropy values obtained. Yet, the optimal choice for these parameters has not been studied thoroughly. We propose a study on the impact of these parameters in image classification. For this purpose, the entropy-based algorithms are applied to a variety of images from different datasets, each containing multiple image classes. Several parameter combinations are used to obtain the entropy values. These entropy values are then applied to a range of machine learning classifiers and the algorithm parameters are analyzed based on the classification results. By using specific parameters, we show that both MFuzzyEn2D and MDispEn2D approach state-of-the-art in terms of image classification for multiple image types. They lead to an average maximum accuracy of more than 95% for all the datasets tested. Moreover, MFuzzyEn2D results in a better classification performance than that extracted by MDispEn2D as a majority. Furthermore, the choice of classifier does not have a significant impact on the classification of the extracted features by both entropy algorithms. The results open new perspectives for these entropy-based measures in textural analysis.

Effects of ECG Data Length on Heart Rate Variability among Young Healthy Adults

The relationship between the robustness of HRV derived by linear and nonlinear methods to the required minimum data lengths has yet to be well understood. The normal electrocardiography (ECG) data of 14 healthy volunteers were applied to 34 HRV measures using various data lengths, and compared with the most prolonged (2000 R peaks or 750 s) by using the Mann-Whitney U test, to determine the 0.05 level of significance. We found that SDNN, RMSSD, pNN50, normalized LF, the ratio of LF and HF, and SD1 of the Poincaré plot could be adequately computed by small data size (60-100 R peaks). In addition, parameters of RQA did not show any significant differences among 60 and 750 s. However, longer data length (1000 R peaks) is recommended to calculate most other measures. The DFA and Lyapunov exponent might require an even longer data length to show robust results. Conclusions: Our work suggests the optimal minimum data sizes for different HRV measures which can potentially improve the efficiency and save the time and effort for both patients and medical care providers.

Multiscale Entropy Analysis of Heart Rate Variability in Neonatal Patients with and without Seizures

The complex physiological dynamics of neonatal seizures make their detection challenging. A timely diagnosis and treatment, especially in intensive care units, are essential for a better prognosis and the mitigation of possible adverse effects on the newborn's neurodevelopment. In the literature, several electroencephalographic (EEG) studies have been proposed for a parametric characterization of seizures or their detection by artificial intelligence techniques. At the same time, other sources than EEG, such as electrocardiography, have been investigated to evaluate the possible impact of neonatal seizures on the cardio-regulatory system. Heart rate variability (HRV) analysis is attracting great interest as a valuable tool in newborns applications, especially where EEG technologies are not easily available. This study investigated whether multiscale HRV entropy indexes could detect abnormal heart rate dynamics in newborns with seizures, especially during ictal events. Furthermore, entropy measures were analyzed to discriminate between newborns with seizures and seizure-free ones. A cohort of 52 patients (33 with seizures) from the Helsinki University Hospital public dataset has been evaluated. Multiscale sample and fuzzy entropy showed significant differences between the two groups (p-value < 0.05, Bonferroni multiple-comparison post hoc correction). Moreover, interictal activity showed significant differences between seizure and seizure-free patients (Mann-Whitney Test: p-value < 0.05). Therefore, our findings suggest that HRV multiscale entropy analysis could be a valuable pre-screening tool for the timely detection of seizure events in newborns.

Effect of Walking Speeds on Complexity of Plantar Pressure Patterns

Various walking speeds may induce different responses on the plantar pressure patterns. Current methods used to analyze plantar pressure patterns are linear and ignore nonlinear features. The purpose of this study was to analyze the complexity of plantar pressure images after walking at various speeds using nonlinear bidimensional multiscale entropy (MSE2D). Twelve participants (age: 27.1 ± 5.8 years; height: 170.3 ± 10.0 cm; and weight: 63.5 ± 13.5 kg) were recruited for walking at three speeds (slow at 1.8 mph, moderate at 3.6 mph, and fast at 5.4 mph) for 20 minutes. A plantar pressure measurement system was used to measure plantar pressure patterns. Complexity index (CI), a summation of MSE2D from all time scales, was used to quantify the changes of complexity of plantar pressure images. The analysis of variance with repeated measures and Fisher’s least significant difference correction were used to examine the results of this study. The results showed that CI of plantar pressure images of 1.8 mph (1.780) was significantly lower compared with 3.6 (1.790) and 5.4 mph (1.792). The results also showed that CI significantly increased from the 1st min (1.780) to the 10th min (1.791) and 20th min (1.791) with slow walking (1.8 mph). Our results indicate that slow walking at 1.8 mph may not be good for postural control compared with moderate walking (3.6 mph) and fast walking (5.4 mph). This study demonstrates that bidimensional multiscale entropy is able to quantify complexity changes of plantar pressure images after different walking speeds.

The Impact of Linear Filter Preprocessing in the Interpretation of Permutation Entropy

Permutation Entropy (PE) is a powerful tool for measuring the amount of information contained within a time series. However, this technique is rarely applied directly on raw signals. Instead, a preprocessing step, such as linear filtering, is applied in order to remove noise or to isolate specific frequency bands. In the current work, we aimed at outlining the effect of linear filter preprocessing in the final PE values. By means of the Wiener-Khinchin theorem, we theoretically characterize the linear filter's intrinsic PE and separated its contribution from the signal's ordinal information. We tested these results by means of simulated signals, subject to a variety of linear filters such as the moving average, Butterworth, and Chebyshev type I. The PE results from simulations closely resembled our predicted results for all tested filters, which validated our theoretical propositions. More importantly, when we applied linear filters to signals with inner correlations, we were able to theoretically decouple the signal-specific contribution from that induced by the linear filter. Therefore, by providing a proper framework of PE linear filter characterization, we improved the PE interpretation by identifying possible artifact information introduced by the preprocessing steps.

Aberrant EEG signal variability at a specific temporal scale in major depressive disorder

OBJECTIVE

Signal variability is linked to irregularities in time series caused by intrinsic nonlinearities of the neural system and can be measured on variable temporal scales over short time series. By measuring refined complex multiscale permutation entropy (RCMPE) from resting-state electroencephalography (EEG) data, we investigated the presence of a specific range of time scales characterizing major depressive disorder (MDD).

METHOD

We used an EEG dataset acquired from 22 MDD patients and 22 healthy controls in the eyes-closed (EC) and eyes-open (EO) states available on the PRED + CT website. Signal variability in both the EC and EO states was compared between the two groups, and their relationship to depressive symptom severity was examined.

RESULTS

In the EC state, the RCMPE was higher in the MDD group than in the control group on a coarse temporal scale, approximately 20-32 ms, at almost all sensors. It also showed a negative correlation with depressive symptom severity on a fine temporal scale, approximately 2-26 ms, in the frontal, right temporal, and left parietal sensor areas in MDD. The EO state revealed a group difference but no relationship with depressive symptom severity.

CONCLUSION

Our results suggested that the diagnosis of MDD as a trait and the severity of depressive symptoms as a state are linked to EEG signal variability on the coarse temporal scale and the fine scale in the resting state, respectively.

SIGNIFICANCE

Signal variability reflects different characteristics of depression depending on the temporal scale.

Heart Rate Variability in Psychology: A Review of HRV Indices and an Analysis Tutorial

The use of heart rate variability (HRV) in research has been greatly popularized over the past decades due to the ease and affordability of HRV collection, coupled with its clinical relevance and significant relationships with psychophysiological constructs and psychopathological disorders. Despite the wide use of electrocardiograms (ECG) in research and advancements in sensor technology, the analytical approach and steps applied to obtain HRV measures can be seen as complex. Thus, this poses a challenge to users who may not have the adequate background knowledge to obtain the HRV indices reliably. To maximize the impact of HRV-related research and its reproducibility, parallel advances in users' understanding of the indices and the standardization of analysis pipelines in its utility will be crucial. This paper addresses this gap and aims to provide an overview of the most up-to-date and commonly used HRV indices, as well as common research areas in which these indices have proven to be very useful, particularly in psychology. In addition, we also provide a step-by-step guide on how to perform HRV analysis using an integrative neurophysiological toolkit, NeuroKit2.

The Systematic Bias of Entropy Calculation in the Multi-Scale Entropy Algorithm

Entropy indicates irregularity or randomness of a dynamic system. Over the decades, entropy calculated at different scales of the system through subsampling or coarse graining has been used as a surrogate measure of system complexity. One popular multi-scale entropy analysis is the multi-scale sample entropy (MSE), which calculates entropy through the sample entropy (SampEn) formula at each time scale. SampEn is defined by the “logarithmic likelihood” that a small section (within a window of a length m) of the data “matches” with other sections will still “match” the others if the section window length increases by one. “Match” is defined by a threshold of r times standard deviation of the entire time series. A problem of current MSE algorithm is that SampEn calculations at different scales are based on the same matching threshold defined by the original time series but data standard deviation actually changes with the subsampling scales. Using a fixed threshold will automatically introduce systematic bias to the calculation results. The purpose of this paper is to mathematically present this systematic bias and to provide methods for correcting it. Our work will help the large MSE user community avoiding introducing the bias to their multi-scale SampEn calculation results.

Automatic classification of excitation location of snoring sounds

STUDY OBJECTIVES

For surgical treatment of patients with obstructive sleep apnea-hypopnea syndrome, it is crucial to locate accurately the obstructive sites in the upper airway; however, noninvasive methods for locating the obstructive sites have not been well explored. Snoring, as the cardinal symptom of obstructive sleep apnea-hypopnea syndrome, should contain information that reflects the state of the upper airway. Through the classification of snores produced at four different locations, this study aimed to test the hypothesis that snores generated by various obstructive sites differ.

METHODS

We trained and tested our model on a public data set that comprised 219 participants. For each snore episode, an acoustic and a physiological feature were extracted and concatenated, forming a 59-dimensional fusion feature. A principal component analysis and a support machine vector were used for dimensional reduction and snore classification. The performance of the proposed model was evaluated using several metrics: sensitivity, precision, specificity, area under the receiver operating characteristic curve, and F1 score.

RESULTS

The unweighted average values of sensitivity, precision, specificity, area under the curve, and F1 were 86.36%, 89.09%, 96.4%, 87.9%, and 87.63%, respectively. The model achieved 98.04%, 80.56%, 72.73%, and 94.12% sensitivity for types V (velum), O (oropharyngeal), T (tongue), and E (epiglottis) snores.

CONCLUSIONS

The characteristics of snores are related to the state of the upper airway. The machine-learning-based model can be used to locate the vibration sites in the upper airway.

Brain Dynamics Altered by Photic Stimulation in Patients with Alzheimer's Disease and Mild Cognitive Impairment

Individuals with mild cognitive impairment (MCI) are at high risk of developing Alzheimer's disease (AD). Repetitive photic stimulation (PS) is commonly used in routine electroencephalogram (EEG) examinations for rapid assessment of perceptual functioning. This study aimed to evaluate neural oscillatory responses and nonlinear brain dynamics under the effects of PS in patients with mild AD, moderate AD, severe AD, and MCI, as well as healthy elderly controls (HC). EEG power ratios during PS were estimated as an index of oscillatory responses. Multiscale sample entropy (MSE) was estimated as an index of brain dynamics before, during, and after PS. During PS, EEG harmonic responses were lower and MSE values were higher in the AD subgroups than in HC and MCI groups. PS-induced changes in EEG complexity were less pronounced in the AD subgroups than in HC and MCI groups. Brain dynamics revealed a "transitional change" between MCI and Mild AD. Our findings suggest a deficiency in brain adaptability in AD patients, which hinders their ability to adapt to repetitive perceptual stimulation. This study highlights the importance of combining spectral and nonlinear dynamical analysis when seeking to unravel perceptual functioning and brain adaptability in the various stages of neurodegenerative diseases.

Entropy Analysis in Gait Research: Methodological Considerations and Recommendations

The usage of entropy analysis in gait research has grown considerably the last two decades. The present paper reviews the application of different entropy analyses in gait research and provides recommendations for future studies. While single-scale entropy analysis such as approximate and sample entropy can be used to quantify regularity/predictability/probability, they do not capture the structural richness and component entanglement characterized by a complex system operating across multiple spatial and temporal scales. Thus, for quantification of complexity, either multiscale entropy or refined composite multiscale entropy is recommended. For both single- and multiscale-scale entropy analyses, care should be made when selecting the input parameters of tolerance window r, vector length m, time series length N and number of scales. This selection should be based on the proposed research question and the type of data collected and not copied from previous studies. Parameter consistency should be investigated and published along with the main results to ensure transparency and enable comparisons between studies. Furthermore, since the interpretation of the absolute size of both single- and multiscale entropy analyses outcomes is not straightforward, comparisons should always be made with a control condition or group.

Using Bidimensional Multiscale Entropy Analysis of Ultrasound Images to Assess the Effect of Various Walking Intensities on Plantar Soft Tissues

Walking performance is usually assessed by linear analysis of walking outcome measures. However, human movements consist of both linear and nonlinear complexity components. The purpose of this study was to use bidimensional multiscale entropy analysis of ultrasound images to evaluate the effects of various walking intensities on plantar soft tissues. Twelve participants were recruited to perform six walking protocols, consisting of three speeds (slow at 1.8 mph, moderate at 3.6 mph, and fast at 5.4 mph) for two durations (10 and 20 min). A B-mode ultrasound was used to assess plantar soft tissues before and after six walking protocols. Bidimensional multiscale entropy (MSE_2D) and the Complexity Index (CI) were used to quantify the changes in irregularity of the ultrasound images of the plantar soft tissues. The results showed that the CI of ultrasound images after 20 min walking increased when compared to before walking (CI₄: 0.39 vs. 0.35; CI₅: 0.48 vs. 0.43, p < 0.05). When comparing 20 and 10 min walking protocols at 3.6 mph, the CI was higher after 20 min walking than after 10 min walking (CI₄: 0.39 vs. 0.36, p < 0.05; and CI₅: 0.48 vs. 0.44, p < 0.05). This is the first study to use bidimensional multiscale entropy analysis of ultrasound images to assess plantar soft tissues after various walking intensities.

Improvement of Statistical Performance of Ordinal Multiscale Entropy Techniques Using Refined Composite Downsampling Permutation Entropy

Multiscale Permutation Entropy (MPE) analysis is a powerful ordinal tool in the measurement of information content of time series. MPE refinements, such as Composite MPE (cMPE) and Refined Composite MPE (rcMPE), greatly increase the precision of the entropy estimation by modifying the original method. Nonetheless, these techniques have only been proposed as algorithms, and are yet to be described from the theoretical perspective. Therefore, the purpose of this article is two-fold. First, we develop the statistical theory behind cMPE and rcMPE. Second, we propose an alternative method, Refined Composite Downsampling Permutation Entropy (rcDPE) to further increase the entropy estimation’s precision. Although cMPE and rcMPE outperform MPE when applied on uncorrelated noise, the results are higher than our predictions due to inherent redundancies found in the composite algorithms. The rcDPE method, on the other hand, not only conforms to our theoretical predictions, but also greatly improves over the other methods, showing the smallest bias and variance. By using MPE, rcMPE and rcDPE to classify faults in bearing vibration signals, rcDPE outperforms the multiscaling methods, enhancing the difference between faulty and non-faulty signals, provided we apply a proper anti-aliasing low-pass filter at each time scale.

Age-related alterations on the capacities to navigate on a bike: use of a simulator and entropy measures

Studying the impact of age is important to understand the phenomenon of aging and the disorders that are associated with it. In this work, we analyze age-related alterations on the capacities to navigate on a bike. For this purpose, we use CycléoONE, a bike simulator, and entropy measures. We thus record navigation data (handlebar angle and speed) during the ride. They are processed with two cross-distribution entropy methods (time-shift multiscale cross-distribution entropy and multiscale cross-distribution entropy). We also analyze the time series with a detrended cross-correlation analysis to determine which method can best underline age-related alterations. Our results show that methods based on cross-distribution entropy may be efficient to stress the decrease in navigation capacities with age. The results are very encouraging for our future goal of adding medical benefits to a leisure equipment. They also show the value of using virtual reality to study the impact of age. Graphical Abstract This study deals with the use of the signal processing methods (multiscale cross-entropy and multiscale cross-correlation) applied on naviagtion data, acquired with a bike simulator, to study the impact of age on two populations (young healthy subjects and older adults with loss of autonomy).

Effect of Different Local Vibration Frequencies on the Multiscale Regularity of Plantar Skin Blood Flow

Local vibration has shown promise in improving skin blood flow (SBF). However, there is no consensus on the selection of the best vibration frequency. An important reason may be that previous studies utilized time- and frequency-domain parameters to characterize vibration-induced SBF responses. These parameters are unable to characterize the structural features of the SBF response to local vibrations, thus contributing to the inconsistent findings seen in vibration research. The objective of this study was to provide evidence that nonlinear dynamics of SBF responses would be an important aspect for assessing the effect of local vibration on SBF. Local vibrations at 100 Hz, 35 Hz, and 0 Hz (sham vibration) with an amplitude of 1 mm were randomly applied to the right first metatarsal head of 12 healthy participants for 10 min. SBF at the same site was measured for 10 min before and after local vibration. The degree of regularity of SBF was quantified using a multiscale sample entropy algorithm. The results showed that 100 Hz vibration significantly increased multiscale regularity of SBF but 35 Hz and 0 Hz (sham vibration) did not. The significant increase of regularity of SBF after 100 Hz vibration was mainly attributed to increased regularity of SBF oscillations within the frequency interval at 0.0095–0.15 Hz. These findings support the use of multiscale regularity to assess effectiveness of local vibration on improving skin blood flow.