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Carbon trading has garnered considerable attention as a pivotal policy instrument for advancing carbon peaking and carbon neutrality, which are essential components of sustainable development. The capacity to precisely anticipate the cost of carbon trading has significant implications for the optimal deployment of market mechanisms, the economic advancement of technological innovations in corporate emissions reduction, and the facilitation of international energy policy adjustments. To this end, this paper proposes a novel and sustainable trading price prediction tool that employs a four-step process: decomposition, reconstruction, prediction, and integration. This innovative approach first utilizes the Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN), then reconstructs the decomposition set using multi-scale entropy (MSE), and finally uses the Long Short-Term Memory neural network model (LSTM) enhanced by the Grey Wolf Optimizer (GWO) to predict the carbon emission trading price. The experimental results demonstrate that the tool achieves high accuracy for both the EU carbon price series and the carbon price series of China's seven major carbon trading markets, with accuracy rates of 99.10% and 99.60% in Hubei and the EU carbon trading markets, respectively. This represents an improvement of approximately 3.1% over the ICEEMDAN-LSTM model and 0.91% over the ICEEMDAN-MSE-LSTM model, thereby contributing to more sustainable and efficient carbon trading practices. [ABSTRACT FROM AUTHOR]

Late-life depression (LLD) is associated with risk of dementia, yet intervention of LLD provides an opportunity to attenuate subsequent cognitive decline. Omega-3 polyunsaturated fatty acids (PUFAs) supplement is a potential intervention due to their beneficial effect in depressive symptoms and cognitive function. To explore the underlying neural mechanism, we used resting-state functional MRI (rs-fMRI) before and after omega-3 PUFAs supplement in older adults with LLD. A 52-week double-blind randomized controlled trial was conducted. We used multi-scale sample entropy to analyze rs-fMRI data. Comprehensive cognitive tests and inflammatory markers were collected to correlate with brain entropy changes. A total of 20 patients completed the trial with 11 under omega-3 PUFAs and nine under placebo. While no significant global cognitive improvement was observed, a marginal enhancement in processing speed was noted in the omega-3 PUFAs group. Importantly, participants receiving omega-3 PUFAs exhibited decreased brain entropy in left posterior cingulate gyrus (PCG), multiple visual areas, the orbital part of the right middle frontal gyrus, and the left Rolandic operculum. The brain entropy changes of the PCG in the omega-3 PUFAs group correlated with improvement of language function and attenuation of interleukin-6 levels. Sample size is small with only marginal clinical effect. These findings suggest that omega-3 PUFAs supplement may mitigate cognitive decline in LLD through anti-inflammatory mechanisms and modulation of brain entropy. Larger clinical trials are warranted to validate the potential therapeutic implications of omega-3 PUFAs for deterring cognitive decline in patients with late-life depression. • Brain entropy decreased in left posterior cingulate gyrus (PCC) and various brain regions after omega-3 PUFAs use in late-life depressed patients. • The reduction of brain entropy in left PCG correlated with improvement in language function and IL-6 level. • Only marginal improvement in processing speed was found clinically after omega-3 PUFAs supplement. • The anti-inflammatory and beneficial cognitive effects of omega-3 PUFAs in late-life depression are associated with brain entropy changes in left PCG. [ABSTRACT FROM AUTHOR]

In modern industrial production, high-temperature environments are commonplace, posing significant challenges to equipment stability, safety, and production efficiency. Machine vision, as an effective automated inspection technology, has attracted extensive attention in high-temperature settings. However, the unique conditions of high temperatures, such as significant thermal noise and optical interference, demand enhanced performance from machine vision systems. The second law of thermodynamics provides a theoretical foundation for understanding these challenges, emphasizing the increase of entropy in energy transformation and transfer processes, and guides the design and optimization of machine vision systems in high-temperature environments. This paper aims to comprehensively explore the application of machine vision based on the second law of thermodynamics in high-temperature industrial inspection, focusing on two core issues: the impact of thermodynamic parameters on the performance of machine vision systems and the technology for analyzing high-temperature industrial infrared images using multiscale entropy. By thoroughly analyzing how thermodynamic parameters influence the design and implementation of machine vision systems, and by developing infrared image processing algorithms adapted to high temperatures, this study seeks to enhance the efficiency and accuracy of machine vision technology in high-temperature industrial applications, providing theoretical support and technical guidance for the advancement of intelligent manufacturing. [ABSTRACT FROM AUTHOR]

The complexity of fMRI signals quantifies temporal dynamics of spontaneous neural activity, which has been increasingly recognized as providing important insights into cognitive functions and psychiatric disorders. However, its heritability and structural underpinnings are not well understood. Here, we utilize multi-scale sample entropy to extract resting-state fMRI complexity in a large healthy adult sample from the Human Connectome Project. We show that fMRI complexity at multiple time scales is heritable in broad brain regions. Heritability estimates are modest and regionally variable. We relate fMRI complexity to brain structure including surface area, cortical myelination, cortical thickness, subcortical volumes, and total brain volume. We find that surface area is negatively correlated with fine-scale complexity and positively correlated with coarse-scale complexity in most cortical regions, especially the association cortex. Most of these correlations are related to common genetic and environmental effects. We also find positive correlations between cortical myelination and fMRI complexity at fine scales and negative correlations at coarse scales in the prefrontal cortex, lateral temporal lobe, precuneus, lateral parietal cortex, and cingulate cortex, with these correlations mainly attributed to common environmental effects. We detect few significant associations between fMRI complexity and cortical thickness. Despite the non-significant association with total brain volume, fMRI complexity exhibits significant correlations with subcortical volumes in the hippocampus, cerebellum, putamen, and pallidum at certain scales. Collectively, our work establishes the genetic basis and structural correlates of resting-state fMRI complexity across multiple scales, supporting its potential application as an endophenotype for psychiatric disorders.

Introduction: Walking speed can affect gait stability and increase the risk of falling.Methods: In this study, we design a device to measure the distribution of the plantar pressure to investigate the impact of the walking speed on the stability of the human gait and movements of the body. We fused the entropy acquired at multiple scales with signals of the plantar pressure to evaluate the effects of the walking speed on the stability of the human gait. We simultaneously collected data on the motion-induced pressure from eight plantar regions to obtain the fused regional pressure. To verify their accuracy, we obtained data on the plantar pressure during walking by using the force table of the Qualisys system. We then extracted the peak points and intervals of the human stride from pressure signals fused over three regions, and analyzed the mechanics of their regional fusion by using the regional amplitude–pressure ratio to obtain the distribution of the plantar pressure at an asynchronous walking speed. Furthermore, we introduced multi-scale entropy to quantify the complexity of the gait and evaluate its stability at different walking speeds.Results: The results of experiments showed that increasing the speed from 2 to 6 km/h decreased the stability of the gait, with a 26.7% increase in the amplitude of pressure in the region of the forefoot. The hindfoot and forefoot regions were subjected to the minimal pressure at a speed of 2 km/h, while the most consistent stress was observed in regions of the forefoot, midfoot, and hindfoot. Moreover, the curve of entropy at a speed of 2 km/h exhibited a slow decline at a small scale and high stability at a large scale.Discussion: The multi-scale entropy increased the variation in the stability of the synchronous velocity of walking compared with the sample entropy and the analysis of regional fusion mechanics. Multi-scale entropy can thus be used to qualitatively assess the relationship between the speed and stability of the gait, and to identify the most stable gait speed that can ensure gait stability and posture control.

In this paper, we propose a contact-free wheat moisture monitoring system, termed Wi-Wheat+, to address the several limitations of the existing grain moisture detection technologies, such as time-consuming process, expensive equipment, low accuracy, and difficulty in real-time monitoring. The proposed system is based on Commodity WiFi and is easy to deploy. Leveraging WiFi CSI data, this paper proposes a feature extraction method based on multi-scale and multi-channel entropy. The feasibility and stability of the system are validated through experiments in both Line-Of-Sight (LOS) and Non-Line-Of-Sight (NLOS) scenarios, where ten types of wheat moisture content are tested using multi-class Support Vector Machine (SVM). Compared with the Wi-Wheat system proposed in our prior work, Wi-Wheat+ ​has higher efficiency, requiring only a simple training process, and can sense more wheat moisture content levels.

A novel and real-time fault diagnosis method based on current data reconstruction for rectifiers is proposed in this article. The symmetry of a 3-phase pulse-width modulation rectifier's topology can be used for fault diagnosis. The symmetry is broken when open-circuit faults happen, a similarity measurement algorithm based on current data reconstruction is used for fault detection. Fault characteristics for current lists and multi-scale entropy are proposed to locate different kinds of faults. The proposed diagnostic method doesn't need additional hardware devices and costs low. It is convenient to be embedded in an existing control system as a subprogram without significant adjustments. The experimental results show the effectiveness of the proposed diagnostic method for both single and multiple open-circuit faults. [ABSTRACT FROM AUTHOR]

The thermal protection structures of supersonic vehicles are vulnerable to damage in the extreme environment of high temperature. With advantages of the large propagation range and high sensitivity to damage, guided waves show great potential for structural health monitoring. However, guided waves are susceptible to ambient temperature change, resulting in low reliability of damage detection results. Therefore, this paper proposed a multi-scale entropy feature extraction method for structural damage detection. Firstly, to eliminate the influence of multi-mode guided waves, a sliding window was used to extract the wave packet of different signals to analyze disturbance caused by damage and temperature. Then, an ant colony optimization algorithm was introduced as a feature fusion method to improve the classification performance. To evaluate the performance of features selected by the ant colony optimization algorithm, K -means clustering algorithm, and silhouette coefficients were utilized to calculate the evaluation function and represent the characteristics of damage. Finally, a set of guided wave signals from 20°C to 40°C were obtained to investigate the influence of temperature variation on the damage feature extraction. The results show that the multi-scale entropy method based on the sliding window can effectively extract damage features in the condition of temperature change. [ABSTRACT FROM AUTHOR]

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.

The complexity of fMRI signals quantifies temporal dynamics of spontaneous neural activity, which has been increasingly recognized as providing important insights into cognitive functions and psychiatric disorders. However, its heritability and structural underpinnings are not well understood. Here, we utilize multi-scale sample entropy to extract resting-state fMRI complexity in a large healthy adult sample from the Human Connectome Project. We show that fMRI complexity at multiple time scales is heritable in broad brain regions. Heritability estimates are modest and regionally variable. We relate fMRI complexity to brain structure including surface area, cortical myelination, cortical thickness, subcortical volumes, and total brain volume. We find that surface area is negatively correlated with fine-scale complexity and positively correlated with coarse-scale complexity in most cortical regions, especially the association cortex. Most of these correlations are related to common genetic and environmental effects. We also find positive correlations between cortical myelination and fMRI complexity at fine scales and negative correlations at coarse scales in the prefrontal cortex, lateral temporal lobe, precuneus, lateral parietal cortex, and cingulate cortex, with these correlations mainly attributed to common environmental effects. We detect few significant associations between fMRI complexity and cortical thickness. Despite the non-significant association with total brain volume, fMRI complexity exhibits significant correlations with subcortical volumes in the hippocampus, cerebellum, putamen, and pallidum at certain scales. Collectively, our work establishes the genetic basis and structural correlates of resting-state fMRI complexity across multiple scales, supporting its potential application as an endophenotype for psychiatric disorders. • fMRI complexity at multiple time scales is heritable across most brain regions. • fMRI complexity is related to surface area (SA) and cortical myelination (CM). • SA-complexity correlations mainly relate to common genetic and environmental effects. • CM-complexity correlations are primarily associated with environmental correlations. • fMRI complexity at certain scales relates to the volumes of some subcortical areas. [ABSTRACT FROM AUTHOR]

Recently, tools developed for detecting human activities have been quite prominent in contributing to health issue prevention and long-term healthcare. For this occasion, the current study aimed to evaluate the performance of eye-movement complexity features (from multi-scale entropy analysis) compared to eye-movement conventional features (from basic statistical measurements) on detecting daily computer activities, comprising reading an English scientific paper, watching an English movie-trailer video, and typing English sentences. A total of 150 students participated in these computer activities. The participants' eye movements were captured using a desktop eye-tracker (GP3 HD Gazepoint™ Canada) while performing the experimental tasks. The collected eye-movement data were then processed to obtain 56 conventional and 550 complexity features of eye movement. A statistic test, analysis of variance (ANOVA), was performed to screen these features, which resulted in 45 conventional and 379 complexity features. These eye-movement features with four combinations were used to build 12 AI models using Support Vector Machine, Decision Tree, and Random Forest (RF). The comparisons of the models showed the superiority of complexity features (85.34% of accuracy) compared to conventional features (66.98% of accuracy). Furthermore, screening eye-movement features using ANOVA enhances 2.29% of recognition accuracy. This study proves the superiority of eye-movement complexity features. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Good sleep quality is essential to our life and work. The two major challenges in evaluating sleep quality are the scoring of sleep stages and sleep apnea detection. In addition to sleep apnea, hypopnea is also a respiratory event that occurs at an equal or even higher frequency compared to that of apnea. However, the two phenomena are not only different in terms of physical manifestation, there are also significant differences in the methods and means of clinical treatment. Therefore, in this study we propose an effective algorithm to distinguish between hypopnea and apnea events. We consider two aspects of feature extraction. On the one hand, from the original time-domain waveform of electrocardiogram signals, we extract the time difference sequence between the appearance of the R-R wave in two adjacent QRS waves (RR intervals) and explore the way they change when apnea and hypopnea event occur. On the other hand, considering that the degree of sequence disorder caused by hypopnea and apnea events is different, multi-scale entropy and complexity are chosen as the features that describe this change. The results obtained using the proposed algorithm show that the classification between hypopnea events and any type of apnea events all reach an accuracy rate greater than 90%. For obstructive apnea events, which occur most frequently among the three different types of apneas, the classification accuracy, sensitivity, specificity and F1-score were 91.78%, 92.21%, 91.30%, 92.20%, respectively. The classification results between central apnea events and hypopnea events reached an accuracy of 93.18%, sensitivity of 95.00%, specificity of 91.67% and F1-score of 92.68%. At the same time, the algorithm achieved an accuracy of 92.59%, sensitivity of 90.38%, specificity of 94.64% and F1-score of 92.16% when classifying mixed apnea and hypopnea events. In the classification of normal breathing, hypopnea events and apnea events, the total accuracy rate achieved was 91.92%, with that for normal breathing reaching 93.62%, for hypopnea events reaching 90.39%, and 91.91% for apnea events, with a Kappa coefficient of 0.99. The algorithm proposed in this study constitutes an efficient and convenient approach for apnea and hypopnea event detection and classification.

With the aging process, brain functions, such as attention, memory, and cognitive functions, degrade over time. In a super-aging society, the alteration of neural activity owing to aging is considered crucial for interventions for the prevention of brain dysfunction. The complexity of temporal neural fluctuations with temporal scale dependency plays an important role in optimal brain information processing, such as perception and thinking. Complexity analysis is a useful approach for detecting cortical alteration in healthy individuals, as well as in pathological conditions, such as senile psychiatric disorders, resulting in changes in neural activity interactions among a wide range of brain regions. Multi-fractal (MF) and multi-scale entropy (MSE) analyses are known methods for capturing the complexity of temporal scale dependency of neural activity in the brain. MF and MSE analyses exhibit high accuracy in detecting changes in neural activity and are superior with regard to complexity detection when compared with other methods. In addition to complex temporal fluctuations, functional connectivity reflects the integration of information of brain processes in each region, described as mutual interactions of neural activity among brain regions. Thus, we hypothesized that the complementary relationship between functional connectivity and complexity could improve the ability to detect the alteration of spatiotemporal patterns observed on electroencephalography (EEG) with respect to aging. To prove this hypothesis, this study investigated the relationship between the complexity of neural activity and functional connectivity in aging based on EEG findings. Concretely, MF and MSE analyses were performed to evaluate the temporal complexity profiles, and phase lag index analyses assessing the unique profile of functional connectivity were performed based on the EEGs conducted for young and older participants. Subsequently, these profiles were combined through machine learning. We found that the complementary relationship between complexity and functional connectivity improves the classification accuracy among aging participants. Thus, the outcome of this study could be beneficial in formulating interventions for the prevention of age-related brain dysfunction. [ABSTRACT FROM AUTHOR]

Tourette syndrome (TS) is a childhood-onset neuropsychiatric disorder characterized by the presence of multiple motor and vocal tics. Because of its varied clinical expressions and lack of reliable diagnostic biomarker, present TS diagnosis still depends on qualitative descriptions of symptoms. Our study aimed to investigate whether the complexity of resting state brain activity can serve as a potential biomarker for TS diagnosis, since it has been used successfully in various neuropsychiatric disorders, including two common TS comorbidities: attention-deficit hyperactivity disorder (ADHD) and obsessive–compulsive disorder (OCD). In the current study, we used both univariate analysis and multivariate searchlight analysis with both linear and non-linear classification methods to explore the group differences in the complexity of resting state brain blood oxygen level-dependent (BOLD) signals between 25 TS boys without comorbidity and 25 sex, age and educational years matched healthy controls (HCs). We also investigated the relation between symptom severity in TS patients (YGTSS scores) and complexity indices derived from different analysis methods. We found: i) univariate analysis revealed reduced complexity in TS patients in the left cerebellum, left superior frontal gyrus, and left medial frontal gyrus; ii) multivariate analysis with non-linear classification method achieved the highest performance (accuracy: 0.94, sensitivity: 0.96, specificity: 0.92, AUC: 0.95) in bilateral supplementary motor areas; iii) significant correlations were found between complexity index derived from multivariate analysis with non-linear classification method and Tic severity (YGTSS scores) in the left cerebellum (r = 0.523, with YGTSS phonic) and in the right supplementary motor area (r = 0.767, with YGTSS motor). Taken together, these results suggested that complexity of resting state BOLD activity is a highly effective index for differentiating TS patients from normal controls. It has a good potential to be a quantitative biomarker for TS diagnosis. [ABSTRACT FROM AUTHOR]

With the aging process, brain functions, such as attention, memory, and cognitive functions, degrade over time. In a super-aging society, the alteration of neural activity owing to aging is considered crucial for interventions for the prevention of brain dysfunction. The complexity of temporal neural fluctuations with temporal scale dependency plays an important role in optimal brain information processing, such as perception and thinking. Complexity analysis is a useful approach for detecting cortical alteration in healthy individuals, as well as in pathological conditions, such as senile psychiatric disorders, resulting in changes in neural activity interactions among a wide range of brain regions. Multi-fractal (MF) and multi-scale entropy (MSE) analyses are known methods for capturing the complexity of temporal scale dependency of neural activity in the brain. MF and MSE analyses exhibit high accuracy in detecting changes in neural activity and are superior with regard to complexity detection when compared with other methods. In addition to complex temporal fluctuations, functional connectivity reflects the integration of information of brain processes in each region, described as mutual interactions of neural activity among brain regions. Thus, we hypothesized that the complementary relationship between functional connectivity and complexity could improve the ability to detect the alteration of spatiotemporal patterns observed on electroencephalography (EEG) with respect to aging. To prove this hypothesis, this study investigated the relationship between the complexity of neural activity and functional connectivity in aging based on EEG findings. Concretely, MF and MSE analyses were performed to evaluate the temporal complexity profiles, and phase lag index analyses assessing the unique profile of functional connectivity were performed based on the EEGs conducted for young and older participants. Subsequently, these profiles were combined through machine learning. We found that the complementary relationship between complexity and functional connectivity improves the classification accuracy among aging participants. Thus, the outcome of this study could be beneficial in formulating interventions for the prevention of age-related brain dysfunction.

Fault diagnosis of critical rotating machinery components is necessary to ensure safe operation. However, the commonly used rotating machinery fault diagnosis methods are generally based on the single-channel signal processing method, which is not suitable for processing multi-channel signals. Thus, to extract features and carry out the intelligent diagnosis of multi-channel signals, a novel method for rotating machinery fault diagnosis is proposed. Firstly, a novel nonlinear dynamics technique named the multivariate generalized refined composite multi-scale sample entropy was presented and applied to extract fusion entropy features of multi-channel signals. Secondly, a practical manifold learning known as supervised isometric mapping was introduced to map the high-dimensional fusion entropy features in a low-dimensional space. In a third step, the Harris hawks optimization-based support vector machine was applied to carry out the intelligent fault recognition. Finally, aiming to verify the effectiveness of the proposed method and present its advantages, it was applied to analyze the rotating machinery system bearing and gear data. The experimental results have shown that the method at hand can accurately identify various faults in both the bearings and gears. Furthermore, in addition to being suitable for multi-channel signal fault diagnosis, it had higher recognition accuracy compared to other multi-channel or single-channel methods. [ABSTRACT FROM AUTHOR]

The present study explored multi-scale entropy (MSE) analysis to investigate the entropy of resting state fMRI signals across multiple time scales. MSE analysis was developed to distinguish random noise from complex signals since the entropy of the former decreases with longer time scales while the latter signal maintains its entropy due to a "self-resemblance" across time scales. A long resting state BOLD fMRI (rs-fMRI) scan with 1000 data points was performed on five healthy young volunteers to investigate the spatial and temporal characteristics of entropy across multiple time scales. A shorter rs-fMRI scan with 240 data points was performed on a cohort of subjects consisting of healthy young (age 23 ± 2 years, n = 8) and aged volunteers (age 66 ± 3 years, n = 8) to investigate the effect of healthy aging on the entropy of rs-fMRI. The results showed that MSE of gray matter, rather than white matter, resembles closely that of f (-1) noise over multiple time scales. By filtering out high frequency random fluctuations, MSE analysis is able to reveal enhanced contrast in entropy between gray and white matter, as well as between age groups at longer time scales. Our data support the use of MSE analysis as a validation metric for quantifying the complexity of rs-fMRI signals.

Fatigue is a major challenge when moving steady-state visual evoked potential (SSVEP)-based brain-computer interfaces (BCIs) from the laboratory into real-life applications, as it leads to user's discomfort and system performance degradation. To study and eventually reduce the fatigue, the first step is to know the fatigue level for which a reliable and objective method to the assessment would be very important and helpful. This paper considers the synchronization of brain activities at multiple time scales as such a measure. Specifically, we propose an objective fatigue index based on the multi-scale entropy (MSE) of subjects' electroencephalogram (EEG) and validate it through an experimental study on 12 subjects. Main results show that the proposed fatigue index is significantly correlated with the subjective fatigue index and it can be used to distinguish the “alert”and “fatigue”states with 97% accuracy, which is significantly better than the existing fatigue indices based on different EEG spectrum, such as θ, α, and β. The proposed fatigue index would provide an assessment tool for the smart wearable BCI in real-life applications and an ergonomic evaluation method for other human-machine cooperation.

Aiming at the problem that when support vector machine ( SVM) was applied to bearing fault classification, the traditional intelligent algorithm optimization of SVM parameters had problems such as slow optimization speed, more adjustment parameters, and easy to fall into local optimal values, a fault diagnosis method based on CEEMDAN and SSA-SVM was proposed. The fault feature extraction and SVM parameter optimization of rolling bearings were studied. A new swarm intelligence optimization algorithm sparrow search algorithm (SSA) was introduced to optimize the parameters of the SVM to improve the optimization speed and the accuracy of bearing fault classification. Firstly, the complete ensemble empirical mode decomposition with adaptive noise ( CEEMDAN) algorithm was used to decompose the signal to obtain several intrinsic mode functions ( IMF) . Then the correlation coefficient method was used to select the useful IMF components and recombine them. Finally, the multi-scale entropy of the reconstructed signal was calculated as the feature vector and inputted into the SVM optimized by SSA for fault classification. The results indicate that this method can accurately obtain fault information and has high recognition accuracy. Comparing with SVM optimized by PSO and GA, t his method has better fault diagnosis and classification performance. [ABSTRACT FROM AUTHOR]

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.

Weld quality directly affects the performance and reliability of structural parts and can be critically ensured by online monitoring. In this study, local mean decomposition (LMD), an adaptive time-frequency analysis is used to analyze the current signals of welding, and then combined with deep belief network (DBN) to classify the weld quality. Firstly, the current signals are decomposed by LMD into a series of product functions. Each product function is a complex signal, and its complexity is calculated by multi-scale entropy to select the most relevant product function with weld quality. Finally, DBN is applied to classify weld quality into four types. This method has a higher classification and recognition rate compared with principal component analysis and extreme learning machine classification. Thus, LMD is a potentially effective method to diagnose weld quality. [ABSTRACT FROM AUTHOR]

In traumatic brain injury (TBI), preliminary retrospective work on signal entropy suggests an association with global outcome. The goal of this study was to provide multi-center validation of the association between multi-scale entropy (MSE) of cardiovascular and cerebral physiological signals, with six-month outcome. Using the Collaborative European NeuroTrauma Effectiveness Research in TBI (CENTER-TBI) high-resolution intensive care unit (ICU) cohort, we selected patients with a minimum of 72 h of physiological recordings and a documented six-month Glasgow Outcome Scale Extended (GOSE) score. The 10-sec summary data for heart rate (HR), mean arterial pressure (MAP), intracranial pressure (ICP), and pulse amplitude of ICP (AMP) were derived across the first 72 h of data. The MSE complexity index (MSE-Ci) was determined for HR, MAP, ICP, and AMP, with the association between MSE and dichotomized six-month outcomes assessed using Mann-Whitney U testing and logistic regression analysis. A total of 160 patients had a minimum of 72 h of recording and a documented outcome. Decreased HR MSE-Ci (7.3 [interquartile range (IQR) 5.4 to 10.2] vs. 5.1 [IQR 3.1 to 7.0]; p = 0.002), lower ICP MSE-Ci (11.2 [IQR 7.5 to 14.2] vs. 7.3 [IQR 6.1 to 11.0]; p = 0.009), and lower AMP MSE-Ci (10.9 [IQR 8.0 to 13.7] vs. 8.7 [IQR 6.6 to 11.0]; p = 0.022), were associated with death. Similarly, lower HR MSE-Ci (8.0 [IQR 6.2 to 10.9] vs. 6.2 [IQR 3.9 to 8.7]; p = 0.003) and lower ICP MSE-Ci (11.4 [IQR 8.6 to 14.4)] vs. 9.2 [IQR 6.0 to 13.5]), were associated with unfavorable outcome. Logistic regression analysis confirmed that lower HR MSE-Ci and ICP MSE-Ci were associated with death and unfavorable outcome at six months. These findings suggest that a reduction in cardiovascular and cerebrovascular system entropy is associated with worse outcomes. Further work in the field of signal complexity in TBI multi-modal monitoring is required. [ABSTRACT FROM AUTHOR]

Mild cognitive impairment (MCI) is characterized as a transitional phase between cognitive decline associated with normal aging and Alzheimer’s disease (AD). Resting-state functional magnetic resonance imaging (fMRI) measuring blood oxygenation level-dependent (BOLD) signals provides complementary information considered essential for understanding disease progression. Previous studies suggested that multi-scale entropy (MSE) analysis quantifying the complexity of BOLD signals is a novel and promising method for investigating neurodegeneration associated with cognitive decline in different stages of MCI. Therefore, the current study used MSE to explore the changes in the complexity of resting-state brain BOLD signals in patients with early MCI (EMCI) and late MCI (LMCI). We recruited 345 participants’ data from the Alzheimer’s Disease Neuroimaging Initiative database, including 176 normal control (NC) subjects, 87 patients with EMCI and 82 patients with LMCI. We observed a significant reduction of brain signal complexity toward regularity in the left fusiform gyrus region in the EMCI group and in the rostral anterior cingulate cortex in the LMCI group. Our results extend prior work by revealing that significant reductions of brain BOLD signal complexity can be detected in different stages of MCI independent of age, sex and regional atrophy. Notably, the reduction of BOLD signal complexity in the rostral anterior cingulate cortex was significantly associated with greater risk of progression to AD. The present study thus identified MSE as a potential imaging biomarker for the early diagnosis of pre-clinical Alzheimer’s disease and provides further insights into the neuropathology of cognitive decline in prodromal AD.

Mild cognitive impairment (MCI) is characterized as a transitional phase between cognitive decline associated with normal aging and Alzheimer's disease (AD). Resting-state functional magnetic resonance imaging (fMRI) measuring blood oxygenation level-dependent (BOLD) signals provides complementary information considered essential for understanding disease progression. Previous studies suggested that multi-scale entropy (MSE) analysis quantifying the complexity of BOLD signals is a novel and promising method for investigating neurodegeneration associated with cognitive decline in different stages of MCI. Therefore, the current study used MSE to explore the changes in the complexity of resting-state brain BOLD signals in patients with early MCI (EMCI) and late MCI (LMCI). We recruited 345 participants' data from the Alzheimer's Disease Neuroimaging Initiative database, including 176 normal control (NC) subjects, 87 patients with EMCI and 82 patients with LMCI. We observed a significant reduction of brain signal complexity toward regularity in the left fusiform gyrus region in the EMCI group and in the rostral anterior cingulate cortex in the LMCI group. Our results extend prior work by revealing that significant reductions of brain BOLD signal complexity can be detected in different stages of MCI independent of age, sex and regional atrophy. Notably, the reduction of BOLD signal complexity in the rostral anterior cingulate cortex was significantly associated with greater risk of progression to AD. The present study thus identified MSE as a potential imaging biomarker for the early diagnosis of pre-clinical Alzheimer's disease and provides further insights into the neuropathology of cognitive decline in prodromal AD. [ABSTRACT FROM AUTHOR]

Introduction: Walking speed can affect gait stability and increase the risk of falling. Methods: In this study, we design a device to measure the distribution of the plantar pressure to investigate the impact of the walking speed on the stability of the human gait and movements of the body. We fused the entropy acquired at multiple scales with signals of the plantar pressure to evaluate the effects of the walking speed on the stability of the human gait. We simultaneously collected data on the motion-induced pressure from eight plantar regions to obtain the fused regional pressure. To verify their accuracy, we obtained data on the plantar pressure during walking by using the force table of the Qualisys system. We then extracted the peak points and intervals of the human stride from pressure signals fused over three regions, and analyzed the mechanics of their regional fusion by using the regional amplitude-pressure ratio to obtain the distribution of the plantar pressure at an asynchronous walking speed. Furthermore, we introduced multi-scale entropy to quantify the complexity of the gait and evaluate its stability at different walking speeds. Results: The results of experiments showed that increasing the speed from 2 to 6 km/h decreased the stability of the gait, with a 26.7% increase in the amplitude of pressure in the region of the forefoot. The hindfoot and forefoot regions were subjected to the minimal pressure at a speed of 2 km/h, while the most consistent stress was observed in regions of the forefoot, midfoot, and hindfoot. Moreover, the curve of entropy at a speed of 2 km/h exhibited a slow decline at a small scale and high stability at a large scale. Discussion: The multi-scale entropy increased the variation in the stability of the synchronous velocity of walking compared with the sample entropy and the analysis of regional fusion mechanics. Multi-scale entropy can thus be used to qualitatively assess the relationship between the speed and stability of the gait, and to identify the most stable gait speed that can ensure gait stability and posture control., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2024 Hu, Li, Wei, Zhao, Tang and Wei.)

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Summary: Faults of lithium batteries in their early stage in electric vehicles (EVs) are usually undetectable, and their characteristics are difficult to be extracted by conventional methods. This paper presents a novel synergistic diagnosis scheme for multiple battery faults using the modified multi‐scale entropy (MMSE). The proposed MMSE can effectively extract the multi‐scale features of complex battery signals in the early stages of battery faults as well as overcome the shortage of the coarse‐grained mode in the standard multi‐scale entropy. The simulation results on experimental data and the real‐world operational vehicles show that the proposed method can effectively detect and locate multiple battery faults/abnormities before they trigger the alarm thresholds. The defined sensitivity factor can implement real‐time evaluation on abnormities with high efficiency and stability, and the developed variable‐calculation‐window diagnosis scheme can synchronously detect and locate different fault types in real time. Furthermore, feasibility, stability, reliability, versatility, robustness, and practicality of the proposed method are separately verified using multiple sets of real‐world operation data. More importantly, the proposed method also provides feasibility to effectively prevent battery thermal runaway caused by multiple battery abnormities/faults. The applications of multi‐scale entropy theory is the first of its kind to battery fault diagnosis on the real‐world operational vehicles. [ABSTRACT FROM AUTHOR]

Highlights • An adaptive scaling factor method based on k -means algorithm is proposed. • Different genders have an impact on fatigue driving detection. • Adaptive multi-scale entropy has higher accuracy than single-scale entropy. • The accuracy of fatigue driving detection based on the forehead reached 95.37%. • The effectiveness of the method was verified by the epileptic dataset. Abstract Fatigue driving is one of the main factors that causes traffic accidents. In the current non-linear analysis methods, the entropy feature extraction methods can be well applied to detection of driving fatigue. However, all of these methods analyzed the EEG data on a single scale signal and there is also no effective way to determine the signal multi-scale information. In addition, most of the current researches choose all the electrodes, which is not conducive to practical application. Based on the forehead EEG data, an adaptive multi-scale entropy feature extraction algorithm is proposed by combining with an adaptive scaling factor (ASF) obtaining algorithm and entropy feature extraction method. Firstly, ASF algorithm is used to extract the scale factor of the signal. Secondly, this factor is used to reconstruct the signal to get new signal data. Finally, the entropy features are extracted for classification. The experimental results show that the proposed adaptive multi-scale entropy feature algorithm is effective in the detection of fatigue driving based on using forehead EEG data. So the effectiveness of this feature extraction algorithm is proved. [ABSTRACT FROM AUTHOR]

Emphatic doctor-patient communication has been associated with improved psycho-physiological well-being involving cardiovascular and neuroendocrine responses. Nevertheless, a comprehensive assessment of heartbeat linear and nonlinear dynamics throughout the communication of a life-threatening disease has not been performed yet. To this extent, we studied linear heartbeat dynamics through the extraction of time-frequency domain measurements, as well as heartbeat nonlinear and complex dynamics through novel approaches to compute multi-scale and multi-lag series analyses: namely, the multi-scale distribution entropy and lagged Poincaré plot symbolic analysis. Heart rate variability series were recorded from 54 healthy female subjects who were blind to the aim of the experiment. Participants were randomly assigned into two groups: 27 subjects watched a video where an oncologist discloses the diagnosis of a cancer metastasis to a patient, whereas the remaining 27 watched the same video including four additional supportive comments by the clinician. Considering differences between the beginning and the end of each communication video, results from non-parametric Wilcoxon tests demonstrated that, at a group level, significant differences occurred in heartbeat linear and nonlinear dynamics, with lower complexity during nonsupportive communication. Furthermore, a support vector machine algorithm, validated using a leave-one-subject-out procedure, was able to discern the supportive experience at a single-subject level with an accuracy of 83.33% when nonlinear features were considered, dropping to 51.85% when using standard HRV features only. In conclusion, heartbeat nonlinear and complex dynamics can be a viable tool for the psycho-physiological evaluation of supportive doctor-patient communication. Graphical Abstract Scheme of the three main stages of the study: signal acquisition during doctor-patient communication, ECG signal processing and pattern recognition results. [ABSTRACT FROM AUTHOR]

As alternative entropy estimators, multiscale entropy (MSE) and permutation entropy (PE) are utilized for quantification of the brain function and its signal variability. In this context, their applications are primarily focused on two specific domains: (1) the effect of brain pathology on its function (2) the study of altered states of consciousness. As a result, there is a paucity of research on applicability of these measures in more naturalistic scenarios. In addition, the utility of these measures for quantification of the brain function and with respect to its signal entropy is not well studied. These shortcomings limit the interpretability of the measures when used for quantification of the brain signal entropy. The present study addresses these limitations by comparing MSE and PE with entropy of human subjects’ EEG recordings, who watched short movie clips with negative, neutral, and positive content. The contribution of the present study is threefold. First, it identifies a significant anti-correlation between MSE and entropy. In this regard, it also verifies that such an anti-correlation is stronger in the case of negative rather than positive or neutral affects. Second, it finds that MSE significantly differentiates between these three affective states. Third, it observes that the use of PE does not warrant such significant differences. These results highlight the level of association between brain’s entropy in response to affective stimuli on the one hand and its quantification in terms of MSE and PE on the other hand. This, in turn, allows for more informed conclusions on the utility of MSE and PE for the study and analysis of the brain signal variability in naturalistic scenarios.

Feature extraction is one of the challenging problems in fault diagnosis, and it has a direct bearing on the accuracy of fault diagnosis. Therefore, in this paper, a new method based on ensemble empirical mode decomposition (EEMD), wavelet semi-soft threshold (WSST) signal reconstruction, and multi-scale entropy (MSE) is proposed. First, the EEMD method is applied to decompose the vibration signal into intrinsic mode functions (IMFs), and then, the high-frequency IMFs, which contain more noise information, are screened by the Pearson correlation coefficient. Then, the WSST method is applied for denoising the high-frequency part of the signal to reconstruct the signal. Secondly, the MSE method is applied for calculating the MSE values of the reconstructed signal, to construct an eigenvector with the complexity measure. Finally, the eigenvector is input to a support vector machine (SVM) to find the fault diagnosis results. The experimental results prove that the proposed method, with a better classification performance, can better solve the problem of the effective signal and noise mixed in high-frequency signals. Based on the proposed method, the fault types can be accurately identified with an average classification accuracy of 100%.

The human resting-state is characterized by spatially coherent brain activity at a low temporal frequency. The default mode network (DMN), one of so-called resting-state networks, has been associated with cognitive processes that are directed toward the self, such as introspection and autobiographic memory. The DMN’s integrity appears to be crucial for mental health. For example, patients with Alzheimer’s disease or other psychiatric conditions show disruptions of functional connectivity within the brain regions of the DMN. However, in prodromal or early stages of Alzheimer’s disease, physiological alterations are sometimes elusive, despite manifested cognitive impairment. While functional connectivity assesses the signal correlation between brain areas, multi-scale entropy (MSE) measures the complexity of the blood-oxygen level dependent signal within an area and thus might show local changes before connectivity is affected. Hence, we investigated alterations of functional connectivity and MSE within the DMN in fifteen mild Alzheimer’s disease patients as compared to fourteen controls. Potential associations of MSE with functional connectivity and cognitive abilities [i.e., mini-mental state examination (MMSE)] were assessed. A moderate decrease of DMN functional connectivity between posterior cingulate cortex and right hippocampus in Alzheimer’s disease was found, whereas no differences were evident for whole-network functional connectivity. In contrast, the Alzheimer’s disease group yielded lower global DMN-MSE than the control group. The most pronounced regional effects were localized in left and right hippocampi, and this was true for most scales. Moreover, MSE significantly correlated with functional connectivity, and DMN-MSE correlated positively with the MMSE in Alzheimer’s disease. Most interestingly, the right hippocampal MSE was positively associated with semantic memory performance. Thus, our results suggested that cognitive decline in Alzheimer’s disease is reflected by decreased signal complexity in DMN nodes, which might further lead to disrupted DMN functional connectivity. Additionally, altered entropy in Alzheimer’s disease found in the majority of the scales indicated a disturbance of both local information processing and information transfer between distal areas. Conclusively, a loss of nodal signal complexity potentially impairs synchronization across nodes and thus preempts functional connectivity changes. MSE presents a putative functional marker for cognitive decline that might be more sensitive than functional connectivity alone.

We present the results of the analysis of the effect of a bodily-contact communication medium on the brain activity of the individuals during verbal communication. Our results suggest that the communicated content that is mediated through such a device induces a significant effect on electroencephalogram (EEG) time series of human subjects. Precisely, we find a significant reduction of overall power of the EEG signals of the individuals. This observation that is supported by the analysis of the permutation entropy (PE) of the EEG time series of brain activity of the participants suggests the positive effect of such a medium on the stress relief and the induced sense of relaxation. Additionally, multiscale entropy (MSE) analysis of our data implies that such a medium increases the level of complexity that is exhibited by EEG time series of our participants, thereby suggesting their sustained sense of involvement in their course of communication. These findings that are in accord with the results reported by cognitive neuroscience research suggests that the use of such a medium can be beneficial as a complementary step in treatment of developmental disorders, attentiveness of schoolchildren and early child development, as well as scenarios where intimate physical interaction over distance is desirable (e.g., distance-parenting).

The goal of this study was to investigate the parameters affecting exergame performance using multi-scale entropy analysis, with the aim of informing the design of exergames for personalized balance training. Test subjects’ center of pressure (COP) displacement data were recorded during exergame play to examine their balance ability at varying difficulty levels of a balance-based exergame; the results of a multi-scale entropy-based analysis were then compared to traditional COP indicators. For games involving static posture frames, variation in posture frame travel time was found to significantly affect the complexity of both the anterior-posterior (MSE-AP) and medio-lateral (MSE-ML) components of balancing movements. However, in games involving dynamic posture frames, only MSE-AP was found to be sensitive to the variation of parameters, namely foot-lifting speed. Findings were comparable to the COP data published by Sun et al., indicating that the use of complexity data is a feasible means of distinguishing between different parameter sets and of understanding how human design considerations must be taken into account in exergame development. Not only can this method be used as another assessment index in the future, it can also be used in the optimization of parameters within the virtual environments of exergames.

The human resting-state is characterized by spatially coherent brain activity at a low temporal frequency. The default mode network (DMN), one of so-called resting-state networks, has been associated with cognitive processes that are directed toward the self, such as introspection and autobiographic memory. The DMN's integrity appears to be crucial for mental health. For example, patients with Alzheimer's disease or other psychiatric conditions show disruptions of functional connectivity within the brain regions of the DMN. However, in prodromal or early stages of Alzheimer's disease, physiological alterations are sometimes elusive, despite manifested cognitive impairment. While functional connectivity assesses the signal correlation between brain areas, multi-scale entropy (MSE) measures the complexity of the blood-oxygen level dependent signal within an area and thus might show local changes before connectivity is affected. Hence, we investigated alterations of functional connectivity and MSE within the DMN in fifteen mild Alzheimer's disease patients as compared to fourteen controls. Potential associations of MSE with functional connectivity and cognitive abilities [i.e., mini-mental state examination (MMSE)] were assessed. A moderate decrease of DMN functional connectivity between posterior cingulate cortex and right hippocampus in Alzheimer's disease was found, whereas no differences were evident for whole-network functional connectivity. In contrast, the Alzheimer's disease group yielded lower global DMN-MSE than the control group. The most pronounced regional effects were localized in left and right hippocampi, and this was true for most scales. Moreover, MSE significantly correlated with functional connectivity, and DMN-MSE correlated positively with the MMSE in Alzheimer's disease. Most interestingly, the right hippocampal MSE was positively associated with semantic memory performance. Thus, our results suggested that cognitive decline in Alzheimer's disease is reflected by decreased signal complexity in DMN nodes, which might further lead to disrupted DMN functional connectivity. Additionally, altered entropy in Alzheimer's disease found in the majority of the scales indicated a disturbance of both local information processing and information transfer between distal areas. Conclusively, a loss of nodal signal complexity potentially impairs synchronization across nodes and thus preempts functional connectivity changes. MSE presents a putative functional marker for cognitive decline that might be more sensitive than functional connectivity alone. [ABSTRACT FROM AUTHOR]

We present the results of the analysis of the effect of a bodily-contact communication medium on the brain activity of the individuals during verbal communication. Our results suggest that the communicated content that is mediated through such a device induces a significant effect on electroencephalogram (EEG) time series of human subjects. Precisely, we find a significant reduction of overall power of the EEG signals of the individuals. This observation that is supported by the analysis of the permutation entropy (PE) of the EEG time series of brain activity of the participants suggests the positive effect of such a medium on the stress relief and the induced sense of relaxation. Additionally, multiscale entropy (MSE) analysis of our data implies that such a medium increases the level of complexity that is exhibited by EEG time series of our participants, thereby suggesting their sustained sense of involvement in their course of communication. These findings that are in accord with the results reported by cognitive neuroscience research suggests that the use of such a medium can be beneficial as a complementary step in treatment of developmental disorders, attentiveness of schoolchildren and early child development, as well as scenarios where intimate physical interaction over distance is desirable (e.g., distance-parenting). [ABSTRACT FROM AUTHOR]

• A leakage identification method for coal mine air supply pipeline systems is proposed. • The above method is realized by the joint noise reduction algorithm and ELM. • The joint noise reduction method comprises POVMD and wavelet denoising. • The separation point of low- and high-frequency modes is identified by MIE values. • Thresholds in the wavelet denoising method vary according to the decomposition layer. This work presents a leakage identification framework for the coal mine air supply pipeline system based on joint noise reduction and extreme learning machine (ELM). First, leakage vibration signals from a pipeline system are sampled. Then, vibration signals are decomposed by parameter-optimized variational mode decomposition (POVMD), where the mode number is determined via the energy difference principle, and the separation point of low- and high-frequency modes are identified by mutual information entropy. Next, the wavelet denoising method based on an improved threshold function is implemented on high-frequency modes. Then denoised vibration signals are reconstructed by denoised high-frequency modes and low-frequency modes. Subsequently, multi-scale entropy values are extracted and fed into ELM for training and testing. In the laboratory environment, the ELM model with 132 hidden nodes and the Sigmoid function shows the highest testing accuracy (94.17%), indicating that the proposed method is more practical and effective than other methods. [ABSTRACT FROM AUTHOR]

Complex network approaches for nonlinear time series analysis are still under fast developments. In this work, we propose a set of entropy measures to characterize the multi-scale transition networks which are constructed from nonlinear time series. These entropy measures compare the distances between an empirical distribution P to a uniform distribution P e , which are achieved via the multi-scale node transition matrix from different perspectives of out-link transitions, and in-link transitions, respectively. In addition, the entropy measures show convergence to zeros for white noise while non-zero values for deterministic chaotic processes. In correlated stochastic processes, the convergence rates are influenced by the correlation length. We show that entropy measures based on transition complexity are able to capture different dynamical states, i.e., tracking routes to chaos and dynamical hysteresis. In the experimental EEG analysis, we show that epileptic brain states are successfully distinguished from healthy control by all entropy measures. • We propose entropy measures to characterize multi-scale transition networks. • The measures compare distance of an empirical and a uniform distribution. • The measures are convergent to zeros for white noise but non-zeros for chaos. • The measures are able to track routes to chaos and dynamical hysteresis. • EEGs of epileptic states are successfully distinguished from healthy controls. [ABSTRACT FROM AUTHOR]

The present study aimed to compare various entropy measures to assess the dynamics and complexity of center of pressure (COP) displacements. Perturbing balance tests are often used in healthy subjects to imitate either pathological conditions or to test the sensitivity of postural analysis techniques. Eleven healthy adult subjects were asked to stand in normal stance in three experimental conditions while the visuo-kinesthetic input was altered. COP displacement was recorded using a force plate. Three entropy measures [Sample Entropy (SE), Multi-Scale Entropy (MSE), and Multivariate Multi Scale Entropy (MMSE)] describing COP regularity at different scales were compared to traditional measures of COP variability. The analyses of the COP trajectories revealed that suppression of vision produced minor changes in COP displacement and in the COP characteristics. The comparison with the reference analysis showed that the entropy measures analysis techniques are more sensitive in the incremented time series compared to the classical parameters and entropy measures of original time series. Non-linear methods appear to be an additional valuable tool for analysis of the dynamics of posture especially when applied on incremental time series.

Using 1000 successive points of a pulse wave velocity (PWV) series, we previously distinguished healthy from diabetic subjects with multi-scale entropy (MSE) using a scale factor of 10. One major limitation is the long time for data acquisition (i.e., 20 min). This study aimed at validating the sensitivity of a novel method, short time MSE (sMSE) that utilized a substantially smaller sample size (i.e., 600 consecutive points), in differentiating the complexity of PWV signals both in simulation and in human subjects that were divided into four groups: healthy young (Group 1; n = 24) and middle-aged (Group 2; n = 30) subjects without known cardiovascular disease and middle-aged individuals with well-controlled (Group 3; n = 18) and poorly-controlled (Group 4; n = 22) diabetes mellitus type 2. The results demonstrated that although conventional MSE could differentiate the subjects using 1000 consecutive PWV series points, sensitivity was lost using only 600 points. Simulation study revealed consistent results. By contrast, the novel sMSE method produced significant differences in entropy in both simulation and testing subjects. In conclusion, this study demonstrated that using a novel sMSE approach for PWV analysis, the time for data acquisition can be substantially reduced to that required for 600 cardiac cycles (~10 min) with remarkable preservation of sensitivity in differentiating among healthy, aged, and diabetic populations.