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For developing nations to achieve net-zero targets, macroeconomic linkages impacting the decoupling of emissions from economic growth must account for non-linear business cycles and economic shocks. This study aims to delineate decarbonization policy pathways for the Indian electricity sector in the aftermath of COVID-19 by analysing the long-term evolution of the economy–electricity–emissions (3E) nexus during the 2008 financial crisis and during COVID-19, covering the period of 1996Q2 to 2020Q3. Upon testing multiple theoretical 3E systems, it was found that a model internalizing trade, inflation, and stochasticity was able to minimize the reproduction errors from growth to recession phases, as well as predict the rebound effect from an economic crisis. This was revealed to be due to more information within the coefficients in a trade stochastic model. Our results confirm the existence of electricity-associated emission decoupling with capital formation in the long-run, post-crisis, while economic growth and inflation increase CO2 emissions. The main finding highlights the negative feedback loop of inflation->trade->emissions, which shows that GDP and emissions are not directly causal. This long-run macroeconomic dynamic death spiral causes decoupling to be inhibited, where fossil fuel imports should not be subsidized for economic shock rebound, and the risk hedging of energy transition investments should occur in the post-COVID-19 era. [ABSTRACT FROM AUTHOR]

Wind energy is a clean, sustainable, and renewable source. It is receiving a large amount of attention from governments and energy companies worldwide as it plays a significant role as an alternative source of energy in reducing carbon emissions. However, due to long-term operation in reduced and difficult weather conditions, wind turbine blades are always seriously damaged. Hence, damage detection in blade structure is essential to evaluate its operational condition and ensure its structural integrity and safety. We aim to use fractal, entropy, and chaos concepts as descriptors for the diagnosis of wind turbine blade condition. They are, respectively, estimated by the correlation dimension, approximate entropy, and the Lyapunov exponent. Formal statistical tests are performed to check how they are different across wind turbine blade conditions. The experimental results follow. First, the correlation dimension is not able to distinguish between all conditions of wind turbine blades. Second, approximate entropy is suitable to distinguish between healthy and erosion conditions and between healthy and mass imbalance conditions. Third, chaos is not a discriminative feature to distinguish between wind turbine blade conditions. Fourth, wind turbine blades with either erosion or mass imbalance exhibit less irregularity in their respective signals than healthy wind turbine blades. [ABSTRACT FROM AUTHOR]

Although auditory stimuli benefit patients with disorders of consciousness (DOC), the optimal stimulus remains unclear. We explored the most effective electroencephalography (EEG)-tracking method for eliciting brain responses to auditory stimuli and assessed its potential as a neural marker to improve DOC diagnosis. We collected 58 EEG recordings from patients with DOC to evaluate the classification model's performance and optimal auditory stimulus. Using non-linear dynamic analysis (approximate entropy [ApEn]), we assessed EEG responses to various auditory stimuli (resting state, preferred music, subject's own name [SON], and familiar music) in 40 patients. The diagnostic performance of the optimal stimulus-induced EEG classification for vegetative state (VS)/unresponsive wakefulness syndrome (UWS) and minimally conscious state (MCS) was compared with the Coma Recovery Scale-Revision in 18 patients using the machine learning cascade forward backpropagation neural network model. Regardless of patient status, preferred music significantly activated the cerebral cortex. Patients in MCS showed increased activity in the prefrontal pole and central, occipital, and temporal cortices, whereas those in VS/UWS showed activity in the prefrontal and anterior temporal lobes. Patients in VS/UWS exhibited the lowest preferred music-induced ApEn differences in the central, middle, and posterior temporal lobes compared with those in MCS. The resting state ApEn value of the prefrontal pole (0.77) distinguished VS/UWS from MCS with 61.11% accuracy. The cascade forward backpropagation neural network tested for ApEn values in the resting state and preferred music-induced ApEn differences achieved an average of 83.33% accuracy in distinguishing VS/UWS from MCS (based on K-fold cross-validation). EEG non-linear analysis quantifies cortical responses in patients with DOC, with preferred music inducing more intense EEG responses than SON and familiar music. Machine learning algorithms combined with auditory stimuli showed strong potential for improving DOC diagnosis. Future studies should explore the optimal multimodal sensory stimuli tailored for individual patients. Trial registration: The study is registered in the Chinese Registry of Clinical Trials (Approval no: KYLL-2023-414, Registration code: ChiCTR2300079310). [ABSTRACT FROM AUTHOR]

The study of the dynamics of foreign exchange rates is of paramount importance to economic policy makers for developing countries like India that depend on foreign exchange to meet a large part of their import obligations. This paper uses the concepts of entropy to study the regularity/irregularity of the returns from the Indian Foreign exchange (forex) markets particularly during periods of economic instability. We use the Approximate Entropy and Sample Entropy statistics which measure the level of repeatability in the data are used to quantify the randomness in the forex returns for four major currencies namely the US Dollar, the British pound, the EURO and the Japanese Yen with respect to the Indian Rupee from the time period 2006 to 2021. These statistics are chosen as they are both statistical measures for assessing the randomness or regularity of time series data and enable researchers to objectively evaluate the degree of randomness present in the returns series and understand the crucial underlying patters or behaviors. In this research we look at two periods of major financial upheavals, the subprime crisis also known as the Global Financial Crisis (GFC) during 2006-2007 and the recent Covid-19 pandemic during 2020-2021. Our empirical results overwhelmingly confirm our working hypothesis that regularity in the returns of the major Indian foreign exchange rates increases during times of financial crisis. This is evidenced by a decrease in the values of the sample entropy and approximate entropy before and after/during the financial crisis period for the majority of the exchange rates. Our empirical results also show that Sample Entropy is a better measure of regularity than Approximate Entropy for the Indian forex rates which is in agreement with the theoretical predictions. Understanding the returns from foreign exchange rates during financial crises has important policy implications for various stakeholders, including market participants, policymakers, and regulators. It enables them to formulate better risk management and hedging strategies. It also helps policy makers in crisis management and contingency planning and safeguard the stability of the financial system. Exchange rate movements are interconnected across global markets, and crises often have cross-border implications. Collaborating on crisis management strategies across countries can help foster stability in international markets. [ABSTRACT FROM AUTHOR]

A stroke represents a significant medical condition characterized by the sudden interruption of blood flow to the brain, leading to cellular damage or death. The impact of stroke on individuals can vary from mild impairments to severe disability. Treatment for stroke often focuses on gait rehabilitation. Notably, assessing muscle activation and kinematics patterns using electromyography (EMG) and stereophotogrammetry, respectively, during walking can provide information regarding pathological gait conditions. The concurrent measurement of EMG and kinematics can help in understanding disfunction in the contribution of specific muscles to different phases of gait. To this aim, complexity metrics (e.g., sample entropy; approximate entropy; spectral entropy) applied to EMG and kinematics have been demonstrated to be effective in identifying abnormal conditions. Moreover, the conditional entropy between EMG and kinematics can identify the relationship between gait data and muscle activation patterns. This study aims to utilize several machine learning classifiers to distinguish individuals with stroke from healthy controls based on kinematics and EMG complexity measures. The cubic support vector machine applied to EMG metrics delivered the best classification results reaching 99.85% of accuracy. This method could assist clinicians in monitoring the recovery of motor impairments for stroke patients. [ABSTRACT FROM AUTHOR]

Partial discharge (PD) fault diagnosis is of great importance for ensuring the safe and stable operation of power transformers. To address the issues of low accuracy in traditional PD fault diagnostic methods, this paper proposes a novel method for the power transformer PD fault diagnosis. It incorporates the approximate entropy (ApEn) of symplectic geometry mode decomposition (SGMD) into the optimized bidirectional long short-term memory (BILSTM) neural network. This method extracts dominant PD features employing SGMD and ApEn. Meanwhile, it improves the diagnostic accuracy with the optimized BILSTM by introducing the golden jackal optimization (GJO). Simulation studies evaluate the performance of FFT, EMD, VMD, and SGMD. The results show that SGMD–ApEn outperforms other methods in extracting dominant PD features. Experimental results verify the effectiveness and superiority of the proposed method by comparing different traditional methods. The proposed method improves PD fault recognition accuracy and provides a diagnostic rate of 98.6%, with lower noise sensitivity. [ABSTRACT FROM AUTHOR]

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Abstract Although auditory stimuli benefit patients with disorders of consciousness (DOC), the optimal stimulus remains unclear. We explored the most effective electroencephalography (EEG)-tracking method for eliciting brain responses to auditory stimuli and assessed its potential as a neural marker to improve DOC diagnosis. We collected 58 EEG recordings from patients with DOC to evaluate the classification model’s performance and optimal auditory stimulus. Using non-linear dynamic analysis (approximate entropy [ApEn]), we assessed EEG responses to various auditory stimuli (resting state, preferred music, subject’s own name [SON], and familiar music) in 40 patients. The diagnostic performance of the optimal stimulus-induced EEG classification for vegetative state (VS)/unresponsive wakefulness syndrome (UWS) and minimally conscious state (MCS) was compared with the Coma Recovery Scale-Revision in 18 patients using the machine learning cascade forward backpropagation neural network model. Regardless of patient status, preferred music significantly activated the cerebral cortex. Patients in MCS showed increased activity in the prefrontal pole and central, occipital, and temporal cortices, whereas those in VS/UWS showed activity in the prefrontal and anterior temporal lobes. Patients in VS/UWS exhibited the lowest preferred music-induced ApEn differences in the central, middle, and posterior temporal lobes compared with those in MCS. The resting state ApEn value of the prefrontal pole (0.77) distinguished VS/UWS from MCS with 61.11% accuracy. The cascade forward backpropagation neural network tested for ApEn values in the resting state and preferred music-induced ApEn differences achieved an average of 83.33% accuracy in distinguishing VS/UWS from MCS (based on K-fold cross-validation). EEG non-linear analysis quantifies cortical responses in patients with DOC, with preferred music inducing more intense EEG responses than SON and familiar music. Machine learning algorithms combined with auditory stimuli showed strong potential for improving DOC diagnosis. Future studies should explore the optimal multimodal sensory stimuli tailored for individual patients. Trial registration: The study is registered in the Chinese Registry of Clinical Trials (Approval no: KYLL-2023-414, Registration code: ChiCTR2300079310).

The examination of brain responses in individuals with a pornography addiction compared to those without sheds light on the neurobiological aspects associated with this behavior. Neuroscientific studies utilizing techniques such as electroencephalography (EEG) have shown that porn-addicted individuals may exhibit alterations in neural pathways related to reward processing and impulse control. In this paper, we analyzed the variations in the brain response of porn-addicted versus healthy individuals under five function tasks including baseline, emotional state, memorize task, executive task, and recall task. For this purpose, we analyzed the complexity of EEG signals using fractal theory, approximate entropy (ApEn), and sample entropy. The results showed that the EEG signals of porn-addicted teenagers are more complex than the ones for healthy individuals, which reflects a higher level of brain activity for porn-addicted teenagers. This method of analysis can be extended to examine the brain activity of other types of addiction versus healthy brains. [ABSTRACT FROM AUTHOR]

The influence of video games on the human brain has been a topic of extensive research and discussion. Video games, characterized by their dynamic and immersive qualities, have demonstrated the capacity to impact diverse cognitive processes. In this study, we conducted a detailed analysis of brain response variations to different genres of computer games, specifically focusing on boring, calm, horror, and funny games. To achieve this, we computed the sample entropy and approximate entropy of electroencephalograms (EEG) signals recorded from participants while they engaged with each type of game. Our findings revealed that EEG signals exhibited the highest complexity during the funny game and the lowest complexity during the calm game. This suggests that the brain is most active when playing the funny game and least active during the calm game. These results provide valuable insights into how different types of video game content can influence brain activity. The methodology employed in this study can be extended to explore brain activity under various conditions, potentially offering a broader understanding of how different stimuli impact cognitive processes. This approach can be useful in examining the effects of various interactive media on brain function and could inform the design of video games and other digital experiences to optimize cognitive engagement and mental well-being. [ABSTRACT FROM AUTHOR]

In order to evaluate the simulation effect of the model on the dynamic characteristics of the climate system, the approximate entropy method was used to analyze the complexity of surface air temperature (SAT) based on observational data (CN05.1) and the model-simulated data by the Beijing Climate Central Climate Model (BCC-CSM2-MR) in this study. We investigated whether the simulated climate model data exhibited complexity characteristics similar to real-world meteorological elements. In this scenario, we could assess the climate model's performance by comparing the complexity of observed and simulated data. The results indicate that the BCC-CSM2-MR model can accurately reflect the complexity of SAT in China. When considering the entire year, the model exhibited greater complexity in the simulated SAT than the observations in most regions of China, indicating an overestimation of complexity by the model. When examining different seasons, the model's complexity was similar to the observations in spring, summer, and winter, indicating a better performance during these seasons. In contrast, the simulated performance is poor during autumn, mainly due to an overestimation of complexity in Qinghai, south-central Xinjiang, and western Xizang. [ABSTRACT FROM AUTHOR]

Analysis of the brain activity in different mental tasks is an important area of research. We used complexity-based analysis to study the changes in brain activity in four mental tasks: relaxation, Stroop color-word, mirror image recognition, and arithmetic tasks. We used fractal theory, sample entropy, and approximate entropy to analyze the changes in electroencephalogram (EEG) signals between different tasks. Our analysis showed that by moving from relaxation to the Stroop color-word, arithmetic, and mirror image recognition tasks, the complexity of EEG signals increases, respectively, reflecting rising brain activity between these conditions. Furthermore, only the fractal theory could decode the significant changes in brain activity between different conditions. Similar analyses can be done to decode the brain activity in case of other conditions. [ABSTRACT FROM AUTHOR]

The analysis of extraocular muscles' activation is crucial for understanding eye movement patterns, providing insights into oculomotor control, and contributing to advancements in fields such as vision research, neurology, and biomedical engineering. Ten subjects went through the experiments, including normal watching, blinking, upward and downward movements of eyes, and eye movements to the left and right while their electromyogram (EMG) signals were recorded. We analyzed the complexity of recorded EMG signals using fractal theory, sample entropy, and approximate entropy (ApEn). The results showed that the techniques are able to decode the changes in the complexity of EMG signals between different eye movements. In other words, we can use these methods to study extraocular muscle activations in different conditions. [ABSTRACT FROM AUTHOR]

This study examines the market efficiency in the prices and volumes of transactions of 41 cryptocurrencies. Specifically, the correlation dimension (CD), Lyapunov Exponent (LE), and approximate entropy (AE) were estimated before and during the COVID-19 pandemic. Then, we applied Student's t-test and F-test to check whether the estimated nonlinear features differ across periods. The empirical results show that (i) the COVID-19 pandemic has not affected the means of CD, LE, and AE in prices, (ii) the variances of CD, LE, and AE estimated from prices are different across pre-pandemic and during pandemic periods, and specifically (iii) the variance of CD decreased during the pandemic; however, the variance of LE and the variance of AE increased during the pandemic period. Furthermore, the pandemic has not affected all three features estimated from the volume series. Our findings suggest that investing in cryptocurrencies is advantageous during a pandemic because their prices become more regular and stable, and the latter has not affected the volume of transactions. [ABSTRACT FROM AUTHOR]

Abstract Regularity is an important aspect of physical activity that can provide valuable insights into how individuals engage in physical activity over time. Accurate measurement of regularity not only advances our understanding of physical activity behavior but also facilitates the development of human activity modeling and forecasting. Furthermore, it can inform the design and implementation of tailored interventions to improve population health outcomes. In this paper, we aim to assess the regularity of physical activities through longitudinal sensor data, which reflects individuals’ all physical activities over an extended period. We explore three entropy models, including entropy rate, approximate entropy, and sample entropy, which can potentially offer a more comprehensive evaluation of physical activity regularity compared to metrics based solely on periodicity or stability. We propose a framework to validate the performance of entropy models on both synthesized and real-world physical activity data. The results indicate entropy rate is able to identify not only the magnitude and amount of noise but also macroscopic variations of physical activities, such as differences on duration and occurrence time. Simultaneously, entropy rate is highly correlated with the predictability of real-world samples, further highlighting its applicability in measuring human physical activity regularity. Leveraging entropy rate, we further investigate the regularity for 686 individuals. We find the composition of physical activities can partially explain the difference in regularity among individuals, and the majority of individuals exhibit temporal stability of regularity.

Amidst the recent technological breakthroughs and increased integration of Artificial Intelligence (AI) technologies across various domains, it is imperative to consider the myriad security threats posed by AI. One of the significant attack vectors on AI models is the backdoor attack, which involves maliciously manipulating the model’s behaviour by inserting hidden patterns or triggers into training datasets. In this paper our primary focus is on the defenses for the backdoor attacks mounted via poisoned training datasets. While many backdoor defense mechanisms have been proposed in the context of text, image, and audio domains, a majority of these defense mechanisms focus on training a specific model to detect backdoor triggers. Our current work proposes a novel model agnostic backdoor detection approach that utilizes complexity/entropy-based measures. In this study, we demonstrate the limitations of currently existing entropy measures – Sample Entropy and Approximate Entropy in detecting backdoor triggers in poisoned datasets. Consequently, we propose a novel modification of the Manhattan metric in the Entropy calculation and incorporate it in the complexity measures. This modified approach is shown to successfully detect backdoor triggers in datasets from not only the Natural Language Processing (NLP) domain, but also from the Financial and Geological domains. The effectiveness of the proposed approach was further substantiated with the high F1 scores in the range of 0.92 to 1.00 across the datasets, and with zero false negatives for the real-world datasets from the Financial and the Geological domains.

Anorexia nervosa is associated with impaired cognitive flexibility and central coherence, i.e., the ability to provide an overview of complex information. Therefore, the aim of the present study was to evaluate EEG features elicited from patients with anorexia nervosa and healthy controls during mental tasks (valid and invalid Aristotelian syllogisms and paradoxes). Particularly, we examined the combination of the most significant syllogisms with selected features (relative power of the time–frequency domain and wavelet-estimated EEG-specific waves, Higuchi fractal dimension (HFD), and information-oriented approximate entropy (AppEn)). We found that alpha, beta, gamma, theta waves, and AppEn are the most suitable measures, which, when combined with specific syllogisms, form a powerful tool for efficiently classifying healthy subjects and patients with AN. We assessed the performance of triadic combinations of "feature–classifier–syllogism" via machine learning techniques in correctly classifying new subjects in these two groups. The following triads attain the best classifications: (a) "AppEn-invalid-ensemble BT classifier" (accuracy 83.3%), (b) "Higuchi FD-valid-linear discriminant" (accuracy 75%), (c) "alpha amplitude-valid-SVM" (accuracy 83.3%), (d) "alpha RP-paradox-ensemble BT" (accuracy 85%), (e) "beta RP-valid-ensemble" (accuracy 85%), (f) "gamma RP-valid-SVM" (accuracy 85%), and (g) "theta RP-valid-KNN" (accuracy 80%). Our findings suggest that anorexia nervosa has a specific information-processing style across reasoning tasks in the brain as measured via EEG activity. Our findings also contribute to further supporting the view that entropy-oriented, i.e., information-based features (the AppEn measure used in this study) are promising diagnostic tools (biomarkers) in clinical applications related to medical classification problems. Furthermore, the main EEG-specific frequency waves are extremely enhanced and become powerful classification tools when combined with Aristotle's syllogisms. [ABSTRACT FROM AUTHOR]

Dissolved gas analysis (DGA) in transformer oil, which analyzes its gas content, is valuable for promptly detecting potential faults in oil-immersed transformers. Given the limitations of traditional transformer fault diagnostic methods, such as insufficient gas characteristic components and a high misjudgment rate for transformer faults, this study proposes a transformer fault diagnosis model based on multi-scale approximate entropy and optimized convolutional neural networks (CNNs). This study introduces an improved sparrow search algorithm (ISSA) for optimizing CNN parameters, establishing the ISSA-CNN transformer fault diagnosis model. The dissolved gas components in the transformer oil are analyzed, and the multi-scale approximate entropy of the gas content under different fault modes is calculated. The computed entropy values are then used as feature parameters for the ISSA-CNN model to derive diagnostic results. Experimental data analysis demonstrates that multi-scale approximate entropy effectively characterizes the dissolved gas components in the transformer oil, significantly improving the diagnostic efficiency. Comparative analysis with BPNN, ELM, and CNNs validates the effectiveness and superiority of the proposed ISSA-CNN diagnostic model across various evaluation metrics. [ABSTRACT FROM AUTHOR]

Regularity is an important aspect of physical activity that can provide valuable insights into how individuals engage in physical activity over time. Accurate measurement of regularity not only advances our understanding of physical activity behavior but also facilitates the development of human activity modeling and forecasting. Furthermore, it can inform the design and implementation of tailored interventions to improve population health outcomes. In this paper, we aim to assess the regularity of physical activities through longitudinal sensor data, which reflects individuals' all physical activities over an extended period. We explore three entropy models, including entropy rate, approximate entropy, and sample entropy, which can potentially offer a more comprehensive evaluation of physical activity regularity compared to metrics based solely on periodicity or stability. We propose a framework to validate the performance of entropy models on both synthesized and real-world physical activity data. The results indicate entropy rate is able to identify not only the magnitude and amount of noise but also macroscopic variations of physical activities, such as differences on duration and occurrence time. Simultaneously, entropy rate is highly correlated with the predictability of real-world samples, further highlighting its applicability in measuring human physical activity regularity. Leveraging entropy rate, we further investigate the regularity for 686 individuals. We find the composition of physical activities can partially explain the difference in regularity among individuals, and the majority of individuals exhibit temporal stability of regularity. [ABSTRACT FROM AUTHOR]

(1) Background: Vibrotactile stimulation has been studied for tremor, but there is little evidence for Essential Tremor (ET). (2) Methods: This research employed a dataset from a previous study, with data collected from 18 individuals subjected to four vibratory stimuli. To characterise tremor changes before, during, and after stimuli, time and frequency domain features were estimated from the signals. Correlation and regression analyses verified the relationship between features and clinical tremor scores. (3) Results: Individuals responded differently to vibrotactile stimulation. The 250 Hz stimulus was the only one that reduced tremor amplitude after stimulation. Compared to the baseline, the 250 Hz and random frequency stimulation reduced tremor peak power. The clinical scores and amplitude-based features were highly correlated, yielding accurate regression models (mean squared error of 0.09). (4) Conclusions: The stimulation frequency of 250 Hz has the greatest potential to reduce tremors in ET. The accurate regression model and high correlation between estimated features and clinical scales suggest that prediction models can automatically evaluate and control stimulus-induced tremor. A limitation of this research is the relatively reduced sample size. [ABSTRACT FROM AUTHOR]

Purpose: The kinetics of physiological responses to exercise have traditionally been characterized by estimating exponential equation parameters using iterative best-fit techniques of heart rate (HR) and gas exchange (respiratory rate, oxygen uptake (V̇O2), carbon dioxide output, and ventilation). In this study, we present a novel approach to characterizing the maturation of physiological responses to exercise in children by accounting for response uncertainty and variability. Methods: Thirty-seven early-pubertal (17 females, 20 males) and 44 late-pubertal (25 females, 19 males) participants performed three multiple brief exercise bouts (MBEB). MBEB consisted of ten 2-min bouts of cycle ergometry at constant work rate interspersed by 1-min rest. Exercise intensity was categorized as low, moderate, or high, corresponding to 40%, 60%, and 80% of peak work rate, and performed in random order on 3 separate days. We evaluated sample entropy (SampEn), approximate entropy, detrended fluctuation analysis, and average absolute local variability of HR and gas exchange. Results: SampEn of HR and gas-exchange responses to MBEB was greater in early- compared with late-pubertal participants (e.g., V̇O2 early-pubertal vs late-pubertal, 1.70 ± 0.023 vs 1.41 ± 0.027; P = 2.97 × 10−14), and decreased as MBEB intensity increased (e.g., 0.37 ± 0.01 HR for low-intensity compared with 0.21 ± 0.014 for high intensity, P = 3.56 × 10−17). Females tended to have higher SampEn than males (e.g., 1.61 ± 0.025 V̇O2 for females vs 1.46 ± 0.031 for males, P = 1.28 × 10−4). Average absolute local variability was higher in younger participants for both gas exchange and HR (e.g., early-pubertal vs late-pubertal V̇O2, 17.48 % ± 0.56% vs 10.24 % ± 0.34%; P = 1.18 × 10−21). Conclusions: The greater entropy in signal response to a known, quantifiable exercise perturbation in the younger children might represent maturation-dependent, enhanced competition among physiological controlling mechanisms that originate at the autonomic, subconscious, and cognitive levels. [ABSTRACT FROM AUTHOR]

Studying the activity of organs during aging is a very important research area. On the other hand, simultaneous analysis of the activities of various organs is important to understand how their activities are correlated. For the first time, this research analyzes the brain-heart correlation in younger and older subjects. We analyzed the sample entropy (SampEn) and approximate entropy (ApEn) of EEG and R-R signals (as heart rate variability (HRV)) of younger and older participants while they sat comfortably in an armchair with their eyes open. The results indicated that older subjects' EEG and R-R signals have greater values of sample and approximate entropies than younger subjects. Therefore, as subjects age, their EEG and R-R signals become more complex. This analysis can be extended to investigate the correlation between other physiological signals among different age groups. [ABSTRACT FROM AUTHOR]

Every year, droughts and floods cause significant damage to the economy and water resources of the UK. Numerous studies have been explored droughts and floods from various points of view, however few have pointed the variations in the patterns induced by climate change. The precipitation data of Central England in the UK was gathered from 1931 to 2020. The analysis was performed by application of fractal dimension, noise variance, Lyapunov exponent, approximate entropy, extreme climate indices, and Standard Precipitation Index. The cross-correlation results indicated the study area warming owing to CO 2 emissions on a global and local scale, implicating the climate change in the study area. Moreover, the mean maximum and minimum temperatures were affected by CO 2 emissions on global and local scales, respectively. The nonlinear dynamic analysis indicated that the duration and intensity of the dry and wet spells were increased due to climate change. In other words, the droughts' intensity and duration were augmented. However, the number of annual droughts and wetness's have remained unaffected by climate change. The results signified a weakening in the flash floods possibility and an increment in the flash floods severity owing to climate change. Moreover, climate change brought about an intensification in the rivers' inundation (fluvial floods) probability. The findings of the present study contribute to the understanding of the mechanism of climate change impacts on droughts and floods (flash, pluvial, and fluvial) patterns and furnished references for nonlinear dynamic studies of droughts and floods patterns. [ABSTRACT FROM AUTHOR]

The paper proposes a novel fault diagnosis method for hydroelectric units to address the challenge of achieving high-precision fault diagnosis due to the non-stationarity and non-linearity of vibration signals, which makes it difficult to extract single features. The method utilizes convolutional neural networks to extract vibration signal features, and employs empirical mode decomposition and approximate entropy to construct signal feature vectors, which are used to create a fusion feature vector. Furthermore, a BP neural network is trained with the fusion feature vector as input and the fault category as output to obtain a hydroelectric unit fault recognizer that can identify the unit's operating state as normal or with a specific fault type. The validity of the proposed method in signal feature mining and its high fault diagnosis accuracy are verified through rotor experimental data. [ABSTRACT FROM AUTHOR]

The prime objective of speech emotion recognition is to accurately recognize the emotion from the speech signal. It is a challenging task to accomplish. Speech emotion recognition (SER) has many applications, including medicine, online marketing, strengthening human–computer interaction (HCI), online education, and many more. Hence, it has been a topic of interest for many researchers for last three decades. The researchers used different methodologies to improve the classification accuracy of emotions. In this study, we tried to improve emotion classification accuracy using mel-frequency cepstral coefficient (MFCC)-based entropy features. First, we extracted the MFCC coefficient matrix from every speech of the EMO-DB, RAVDESS and SAVEE datasets, and then we calculated the proposed features: statistical mean ( MFCC mean ), MFCC-based approximate entropy ( MFCC AE ), and MFCC-based spectral entropy ( MFCC SE ), from the MFCC coefficient matrix of every utterance. The performance of the proposed features is accessed using the DNN classifier. We achieved a classification accuracy of 87.48%, 75.9%, and 79.64% using the combination of MFCC mean and MFCC SE features and obtained classification accuracies of 85.61%, 77.54%, and 76.26% using the combination of MFCC mean , MFCC AE , and MFCC SE features for the EMO-DB, RAVDESS, and SAVEE datasets, respectively. [ABSTRACT FROM AUTHOR]

In this study, a platform for a welding experiment, used to collect input and output electrical signals, was constructed, and the algorithm for the input pulsating energy interpolation line (IPEI) was given. Experiments with MAG surface straight line welding were conducted at various voltages. Analysis of the IPEI in relation to the welding current was performed while combining real-world welding occurrences with high-speed camera images of droplet transfer. It was established that the IPEI can be employed as a characteristic parameter to assess the stability of the short-circuiting transfer process in MAG welding. The three criteria for assessing the stability were the spectrum, approximation entropy, and coefficient of variation. A comparative analysis was conducted on each of these approaches. It was determined that the most effective technique is approximation entropy. The approximation entropy of the welding current and IPEI are also highly consistent, with a correlation coefficient as high as 0.9889. [ABSTRACT FROM AUTHOR]

Introduction: It is proved that there are differences between gait performed by females and males, which appear in movements of selected body parts. Despite numerous state-of-the-art studies related to the discriminative analysis of motion capture data, the question of whether measures of signal complexity and uncertainty can extract valuable features for the problem of sex distinction still remains open. It is the subject of the paper. Methods: Correlation dimension, as well as approximate and sample entropies, are selected to describe motion data. In the numerical experiments, the collected dataset with 884 samples of 25 females and 30 males was used. The measurements took place in the Human Motion Laboratory (HML), equipped with a highly precise motion capture system. Two variants of data representation were investigated-time series that contain joint rotations of taken skeleton model as well as positions of the markers attached to the human body. Finally, a comparative analysis between the populations of females and males using descriptive statistics, non-parametric estimation, and statistical hypotheses verification was carried out. Results: There are statistically significant sex differences extracted by the taken measures. In general, the movements of lower limbs result in greater values of correlation dimension and entropies for females, while selected upper body parts play a similar role for males. The dissimilarities are mainly observed in hip, ankle, shoulder, and head movements. Discussion: Correlation dimension and entropy measures provide robust and explainable features of motion capture data with a valuable description of the human locomotion system. Thus, beyond the importance of discovered differences between females and males, their interpretation and understanding are also known. [ABSTRACT FROM AUTHOR]

Globally, respiratory disorders are a great health burden, affecting as well as destroying human lives; pneumonia is one among them. Pneumonia stages can progress from mild stage to even towards deadly if it is misdiagnosed. Misdiagnosis happens as it exhibits the symptoms identical to other respiratory diseases. Respiratory sound (RS)-based detection of pneumonia could be the most perfect, convenient, as well as the economical solution to this serious problem. This paper presents a novel method to detect pneumonia based on RS. This study is carried out over 310 pneumonia RS and 318 healthy RS, recorded from a hospital. The noises from each RS are eliminated using the Butterworth band pass filter and sparsity-assisted signal smoothing algorithm. Approximate entropy, Shannon entropy, fractal dimension, and largest Lyapunov exponent are the nonlinear features, which are extracted from each denoised RS. The extracted features are inputted to support vector machine classifiers to distinguish pneumonia RS and healthy RS. This method discriminates against pneumonia and healthy RS with 99.8% classification accuracy, 99.8% sensitivity, 99.6% specificity, 99.6% positive predictive value, 99.6% F1-score, and area under curve value of 1.0. Future endeavours will be to examine the efficacy of the proposed algorithm to diagnose pneumonia from the real-time RS acquired from a pneumonia patient in a hospital. This proposed work could be a great support to clinicians in diagnosing pneumonia based on RS. [ABSTRACT FROM AUTHOR]

This study examines the relationship between physiological complexity, as measured by Approximate Entropy (ApEn) and Sample Entropy (SampEn), and fitness levels in female athletes. Our focus is on their association with maximal oxygen consumption ( V O 2 , m a x ). Our findings reveal a complex relationship between entropy metrics and fitness levels, indicating that higher fitness typically, though not invariably, correlates with greater entropy in physiological time series data; however, this is not consistent for all individuals. For Heart Rate (HR), entropy measures suggest stable patterns across fitness categories, while pulse oximetry ( S p O 2 ) data shows greater variability. For instance, the medium fitness group displayed an ApEn(HR) = 0.57 ± 0.13 with a coefficient of variation (CV) of 22.17 and ApEn( S p O 2 ) = 0.96 ± 0.49 with a CV of 46.08%, compared to the excellent fitness group with ApEn(HR) = 0.60 ± 0.09 with a CV of 15.19% and ApEn( S p O 2 ) = 0.85 ± 0.42 with a CV of 49.46%, suggesting broader physiological responses among more fit individuals. The larger standard deviations and CVs for S p O 2 entropy may indicate the body's proficient oxygen utilization at higher levels of physical demand. Our findings advocate for combining entropy metrics with wearable sensor technology for improved biomedical analysis and personalized healthcare. [ABSTRACT FROM AUTHOR]

For developing nations to achieve net-zero targets, macroeconomic linkages impacting the decoupling of emissions from economic growth must account for non-linear business cycles and economic shocks. This study aims to delineate decarbonization policy pathways for the Indian electricity sector in the aftermath of COVID-19 by analysing the long-term evolution of the economy–electricity–emissions (3E) nexus during the 2008 financial crisis and during COVID-19, covering the period of 1996Q2 to 2020Q3. Upon testing multiple theoretical 3E systems, it was found that a model internalizing trade, inflation, and stochasticity was able to minimize the reproduction errors from growth to recession phases, as well as predict the rebound effect from an economic crisis. This was revealed to be due to more information within the coefficients in a trade stochastic model. Our results confirm the existence of electricity-associated emission decoupling with capital formation in the long-run, post-crisis, while economic growth and inflation increase CO2 emissions. The main finding highlights the negative feedback loop of inflation->trade->emissions, which shows that GDP and emissions are not directly causal. This long-run macroeconomic dynamic death spiral causes decoupling to be inhibited, where fossil fuel imports should not be subsidized for economic shock rebound, and the risk hedging of energy transition investments should occur in the post-COVID-19 era.

Wind energy is a clean, sustainable, and renewable source. It is receiving a large amount of attention from governments and energy companies worldwide as it plays a significant role as an alternative source of energy in reducing carbon emissions. However, due to long-term operation in reduced and difficult weather conditions, wind turbine blades are always seriously damaged. Hence, damage detection in blade structure is essential to evaluate its operational condition and ensure its structural integrity and safety. We aim to use fractal, entropy, and chaos concepts as descriptors for the diagnosis of wind turbine blade condition. They are, respectively, estimated by the correlation dimension, approximate entropy, and the Lyapunov exponent. Formal statistical tests are performed to check how they are different across wind turbine blade conditions. The experimental results follow. First, the correlation dimension is not able to distinguish between all conditions of wind turbine blades. Second, approximate entropy is suitable to distinguish between healthy and erosion conditions and between healthy and mass imbalance conditions. Third, chaos is not a discriminative feature to distinguish between wind turbine blade conditions. Fourth, wind turbine blades with either erosion or mass imbalance exhibit less irregularity in their respective signals than healthy wind turbine blades.

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

Listening to music is experimentally associated with positive stress reduction effect on human organisms. However, the opinions of therapists about this complementary non-invasive therapy are still different. Purpose: The aim of our study was to investigate the effect of selected passive music therapy frequencies without vocals on selected cardio-vagal and complexity indices of short-term heart rate variability (HRV) in healthy youth, in terms of calming the human. Main methods: 30 probands (15 male, averaged age: 19.7±1.4 years, BMI: 23.3±3.8 kg/m² ) were examined during protocol (Silence baseline, Music 1 (20-1000 Hz), Silence 1, Music 2 (250-2000 Hz), Silence 2, Music 3 (1000-16000 Hz), and Silence 3). Evaluated HRV parameters in time, spectral, and geometrical domains represent indices of cardio-vagal and emotional regulation. Additionally, HRV complexity was calculated by approximate entropy and sample entropy (SampEn) and subjective characteristics of each phase by Likert scale. Results: the distance between subsequent R-waves in the electrocardiogram (RR intervals [ms]) and SampEn were significantly higher during Music 3 compared to Silence 3 (p=0.015, p=0.021, respectively). Geometrical cardio-vagal index was significantly higher during Music 2 than during Silence 2 (p=0.006). In the subjective perception of the healthy youths evaluated statistically through a Likert scale, the phases of music were perceived significantly more pleasant than the silent phases (p<0.001, p=0.008, p=0.003, respectively). Conclusions: Our findings revealed a rise of cardiovagal modulation and higher complexity assessed by short-term HRV indices suggesting positive relaxing effect music especially of higher frequency on human organism. [ABSTRACT FROM AUTHOR]

IntroductionIt is proved that there are differences between gait performed by females and males, which appear in movements of selected body parts. Despite numerous state-of-the-art studies related to the discriminative analysis of motion capture data, the question of whether measures of signal complexity and uncertainty can extract valuable features for the problem of sex distinction still remains open. It is the subject of the paper.MethodsCorrelation dimension, as well as approximate and sample entropies, are selected to describe motion data. In the numerical experiments, the collected dataset with 884 samples of 25 females and 30 males was used. The measurements took place in the Human Motion Laboratory (HML), equipped with a highly precise motion capture system. Two variants of data representation were investigated-time series that contain joint rotations of taken skeleton model as well as positions of the markers attached to the human body. Finally, a comparative analysis between the populations of females and males using descriptive statistics, non-parametric estimation, and statistical hypotheses verification was carried out.ResultsThere are statistically significant sex differences extracted by the taken measures. In general, the movements of lower limbs result in greater values of correlation dimension and entropies for females, while selected upper body parts play a similar role for males. The dissimilarities are mainly observed in hip, ankle, shoulder, and head movements.DiscussionCorrelation dimension and entropy measures provide robust and explainable features of motion capture data with a valuable description of the human locomotion system. Thus, beyond the importance of discovered differences between females and males, their interpretation and understanding are also known.

Partial discharge (PD) fault diagnosis is of great importance for ensuring the safe and stable operation of power transformers. To address the issues of low accuracy in traditional PD fault diagnostic methods, this paper proposes a novel method for the power transformer PD fault diagnosis. It incorporates the approximate entropy (ApEn) of symplectic geometry mode decomposition (SGMD) into the optimized bidirectional long short-term memory (BILSTM) neural network. This method extracts dominant PD features employing SGMD and ApEn. Meanwhile, it improves the diagnostic accuracy with the optimized BILSTM by introducing the golden jackal optimization (GJO). Simulation studies evaluate the performance of FFT, EMD, VMD, and SGMD. The results show that SGMD–ApEn outperforms other methods in extracting dominant PD features. Experimental results verify the effectiveness and superiority of the proposed method by comparing different traditional methods. The proposed method improves PD fault recognition accuracy and provides a diagnostic rate of 98.6%, with lower noise sensitivity.

Analysis of the changes in brain activity between rest and various conditions is an important area of research. We investigated the changes in brain activity among rest and multitask workload (SIMKAP multitasking test) by quantifying the complexity of EEG signals. The results showed that EEG signals have smaller fractal dimensions, sample entropy, and approximate entropy during the SIMKAP multitasking test than the rest. Therefore, the complexity of EEG signals was lower during the SIMKAP multitasking test than the rest. In further research, we can study the changes in brain activity among other conditions, which has great benefits in decoding brain activity in various conditions. [ABSTRACT FROM AUTHOR]

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Generalized anxiety disorder (GAD) is a highly prevalent disease characterized by chronic, pervasive, and intrusive worry. Previous resting-state functional MRI (fMRI) studies on GAD have mainly focused on conventional static linear features. Entropy analysis of resting-state functional magnetic resonance imaging (rs-fMRI) has recently been adopted to characterize brain temporal dynamics in some neuropsychological or psychiatric diseases. However, the nonlinear dynamic complexity of brain signals has been rarely explored in GAD. We measured the approximate entropy (ApEn) and sample entropy (SampEn) of the resting-state fMRI data from 38 GAD patients and 37 matched healthy controls (HCs). The brain regions with significantly different ApEn and SampEn values between the two groups were extracted. Using these brain regions as seed points, we also investigated whether there are differences in whole brain resting-state function connectivity (RSFC) pattern between GADs and HCs. Correlation analysis was subsequently conducted to investigate the association between brain entropy, RSFC and the severity of anxiety symptoms. A linear support vector machine (SVM) was used to assess the discriminative power of BEN and RSFC features among GAD patients and HCs. Compared to the HCs, patients with GAD showed increased levels of ApEn in the right angular cortex (AG) and increased levels of SampEn in the right middle occipital gyrus (MOG) as well as the right inferior occipital gyrus (IOG). Contrarily, compared to the HCs, patients with GAD showed decreased RSFC between the right AG and the right inferior parietal gyrus (IPG). The SVM-based classification model achieved 85.33 % accuracy (sensitivity: 89.19 %; specificity: 81.58 %; and area under the receiver operating characteristic curve: 0.9018). The ApEn of the right AG and the SVM-based decision value was positively correlated with the Hamilton Anxiety Scale (HAMA). This study used cross-sectional data and sample size was small. Patients with GAD showed increased level of nonlinear dynamical complexity of ApEn in the right AG and decreased linear features of RSFC in the right IPG. Combining the linear and nonlinear features of brain signals may be used to effectively diagnose psychiatric disorders. • A comprehensive analysis method, both brain entropy and RSFC analysis were adopted. • GAD patients showed increased BEN and decreased RSFC compared to HCs. • The SVM-based analysis achieved a correct classification rate of 85.33% assessing the discriminative power of GAD. • The increased BEN of the rAG and SVM-based decision value were associated with clinical response. [ABSTRACT FROM AUTHOR]

Anorexia nervosa is associated with impaired cognitive flexibility and central coherence, i.e., the ability to provide an overview of complex information. Therefore, the aim of the present study was to evaluate EEG features elicited from patients with anorexia nervosa and healthy controls during mental tasks (valid and invalid Aristotelian syllogisms and paradoxes). Particularly, we examined the combination of the most significant syllogisms with selected features (relative power of the time–frequency domain and wavelet-estimated EEG-specific waves, Higuchi fractal dimension (HFD), and information-oriented approximate entropy (AppEn)). We found that alpha, beta, gamma, theta waves, and AppEn are the most suitable measures, which, when combined with specific syllogisms, form a powerful tool for efficiently classifying healthy subjects and patients with AN. We assessed the performance of triadic combinations of “feature–classifier–syllogism” via machine learning techniques in correctly classifying new subjects in these two groups. The following triads attain the best classifications: (a) “AppEn-invalid-ensemble BT classifier” (accuracy 83.3%), (b) “Higuchi FD-valid-linear discriminant” (accuracy 75%), (c) “alpha amplitude-valid-SVM” (accuracy 83.3%), (d) “alpha RP-paradox-ensemble BT” (accuracy 85%), (e) “beta RP-valid-ensemble” (accuracy 85%), (f) “gamma RP-valid-SVM” (accuracy 85%), and (g) “theta RP-valid-KNN” (accuracy 80%). Our findings suggest that anorexia nervosa has a specific information-processing style across reasoning tasks in the brain as measured via EEG activity. Our findings also contribute to further supporting the view that entropy-oriented, i.e., information-based features (the AppEn measure used in this study) are promising diagnostic tools (biomarkers) in clinical applications related to medical classification problems. Furthermore, the main EEG-specific frequency waves are extremely enhanced and become powerful classification tools when combined with Aristotle’s syllogisms.

Dissolved gas analysis (DGA) in transformer oil, which analyzes its gas content, is valuable for promptly detecting potential faults in oil-immersed transformers. Given the limitations of traditional transformer fault diagnostic methods, such as insufficient gas characteristic components and a high misjudgment rate for transformer faults, this study proposes a transformer fault diagnosis model based on multi-scale approximate entropy and optimized convolutional neural networks (CNNs). This study introduces an improved sparrow search algorithm (ISSA) for optimizing CNN parameters, establishing the ISSA-CNN transformer fault diagnosis model. The dissolved gas components in the transformer oil are analyzed, and the multi-scale approximate entropy of the gas content under different fault modes is calculated. The computed entropy values are then used as feature parameters for the ISSA-CNN model to derive diagnostic results. Experimental data analysis demonstrates that multi-scale approximate entropy effectively characterizes the dissolved gas components in the transformer oil, significantly improving the diagnostic efficiency. Comparative analysis with BPNN, ELM, and CNNs validates the effectiveness and superiority of the proposed ISSA-CNN diagnostic model across various evaluation metrics.

(1) Background: Vibrotactile stimulation has been studied for tremor, but there is little evidence for Essential Tremor (ET). (2) Methods: This research employed a dataset from a previous study, with data collected from 18 individuals subjected to four vibratory stimuli. To characterise tremor changes before, during, and after stimuli, time and frequency domain features were estimated from the signals. Correlation and regression analyses verified the relationship between features and clinical tremor scores. (3) Results: Individuals responded differently to vibrotactile stimulation. The 250 Hz stimulus was the only one that reduced tremor amplitude after stimulation. Compared to the baseline, the 250 Hz and random frequency stimulation reduced tremor peak power. The clinical scores and amplitude-based features were highly correlated, yielding accurate regression models (mean squared error of 0.09). (4) Conclusions: The stimulation frequency of 250 Hz has the greatest potential to reduce tremors in ET. The accurate regression model and high correlation between estimated features and clinical scales suggest that prediction models can automatically evaluate and control stimulus-induced tremor. A limitation of this research is the relatively reduced sample size.

In this study, a platform for a welding experiment, used to collect input and output electrical signals, was constructed, and the algorithm for the input pulsating energy interpolation line (IPEI) was given. Experiments with MAG surface straight line welding were conducted at various voltages. Analysis of the IPEI in relation to the welding current was performed while combining real-world welding occurrences with high-speed camera images of droplet transfer. It was established that the IPEI can be employed as a characteristic parameter to assess the stability of the short-circuiting transfer process in MAG welding. The three criteria for assessing the stability were the spectrum, approximation entropy, and coefficient of variation. A comparative analysis was conducted on each of these approaches. It was determined that the most effective technique is approximation entropy. The approximation entropy of the welding current and IPEI are also highly consistent, with a correlation coefficient as high as 0.9889.

This study examines the relationship between physiological complexity, as measured by Approximate Entropy (ApEn) and Sample Entropy (SampEn), and fitness levels in female athletes. Our focus is on their association with maximal oxygen consumption (VO2,max). Our findings reveal a complex relationship between entropy metrics and fitness levels, indicating that higher fitness typically, though not invariably, correlates with greater entropy in physiological time series data; however, this is not consistent for all individuals. For Heart Rate (HR), entropy measures suggest stable patterns across fitness categories, while pulse oximetry (SpO2) data shows greater variability. For instance, the medium fitness group displayed an ApEn(HR) = 0.57±0.13 with a coefficient of variation (CV) of 22.17 and ApEn(SpO2) = 0.96±0.49 with a CV of 46.08%, compared to the excellent fitness group with ApEn(HR) = 0.60±0.09 with a CV of 15.19% and ApEn(SpO2) =0.85±0.42 with a CV of 49.46%, suggesting broader physiological responses among more fit individuals. The larger standard deviations and CVs for SpO2 entropy may indicate the body’s proficient oxygen utilization at higher levels of physical demand. Our findings advocate for combining entropy metrics with wearable sensor technology for improved biomedical analysis and personalized healthcare.