Pedaling Asymmetry Reflected by Bilateral EMG Complexity in Chronic Stroke.

This study examines pedaling asymmetry using the electromyogram (EMG) complexity of six bilateral lower limb muscles for chronic stroke survivors. Fifteen unilateral chronic stroke and twelve healthy participants joined passive and volitional recumbent pedaling tasks using a self-modified stationary bike with a constant speed of 25 revolutions per minute. The fuzzy approximate entropy (fApEn) was adopted in EMG complexity estimation. EMG complexity values of stroke participants during pedaling were smaller than those of healthy participants (p = 0.002). For chronic stroke participants, the complexity of paretic limbs was smaller than that of non-paretic limbs during the passive pedaling task (p = 0.005). Additionally, there was a significant correlation between clinical scores and the paretic EMG complexity during passive pedaling (p = 0.022, p = 0.028), indicating that the paretic EMG complexity during passive movement might serve as an indicator of stroke motor function status. This study suggests that EMG complexity is an appropriate quantitative tool for measuring neuromuscular characteristics in lower limb dynamic movement tasks for chronic stroke survivors.

A Novel Fault Diagnosis Method for a Power Transformer Based on Multi-Scale Approximate Entropy and Optimized Convolutional Networks.

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.

Partial Discharge Fault Diagnosis in Power Transformers Based on SGMD Approximate Entropy and Optimized BILSTM.

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.

Data-Driven Identification of Stroke through Machine Learning Applied to Complexity Metrics in Multimodal Electromyography and Kinematics.

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.

Long-term memory in Staphylococcus aureus α-hemolysin ion channel kinetics.

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  ß-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 ([Formula: see text] = 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.

Beta-blockers and mechanical dyssynchrony in heart failure assessed by radionuclide ventriculography.

BACKGROUND: Radionuclide ventriculography (RNVG) can be used to quantify mechanical dyssynchrony and may be a valuable adjunct in the assessment of heart failure with reduced ejection fraction (HFrEF). The study aims to investigate the effect of beta-blockers on mechanical dyssynchrony using novel RNVG phase parameters. METHODS: A retrospective study was carried out in a group of 98 patients with HFrEF. LVEF and dyssynchrony were assessed pre and post beta-blockade. Dyssynchrony was assessed using synchrony, entropy, phase standard deviation, approximate entropy, and sample entropy from planar RNVG phase images. Subgroups split by ischemic etiology were also investigated. RESULTS: An improvement in dyssynchrony and LVEF was measured six months post beta-blockade for both ischemic and non-ischemic groups. CONCLUSIONS: A significant improvement in dyssynchrony and LVEF was measured post beta-blockade using novel measures of dyssynchrony.

Catching wandering minds with tapping fingers: neural and behavioral insights into task-unrelated cognition.

When the human mind wanders, it engages in episodes during which attention is focused on self-generated thoughts rather than on external task demands. Although the sustained attention to response task is commonly used to examine relationships between mind wandering and executive functions, limited executive resources are required for optimal task performance. In the current study, we aimed to investigate the relationship between mind wandering and executive functions more closely by employing a recently developed finger-tapping task to monitor fluctuations in attention and executive control through task performance and periodical experience sampling during concurrent functional magnetic resonance imaging (fMRI) and pupillometry. Our results show that mind wandering was preceded by increases in finger-tapping variability, which was correlated with activity in dorsal and ventral attention networks. The entropy of random finger-tapping sequences was related to activity in frontoparietal regions associated with executive control, demonstrating the suitability of this paradigm for studying executive functioning. The neural correlates of behavioral performance, pupillary dynamics, and self-reported attentional state diverged, thus indicating a dissociation between direct and indirect markers of mind wandering. Together, the investigation of these relationships at both the behavioral and neural level provided novel insights into the identification of underlying mechanisms of mind wandering.

The complexity analysis of cerebral oxygen saturation during pneumoperitoneum and Trendelenburg position: a retrospective cohort study.

BACKGROUND: The human brain is a highly complex and nonlinear system, nonlinear complexity measures such as approximate entropy (ApEn) and sample entropy (SampEn) can better reveal characteristics of brain dynamics. However, no studies report complexity of perioperative physiological signals to reveal how brain complexity associates with age, varies along with the development of surgery and postoperative neurological complications. AIM: This study examined the complexity of intraoperative regional cerebral oxygen saturation (rSO2), aiming to reveal brain dynamics during surgery. METHODS: This retrospective cohort study enrolled patients who scheduled for robot-assisted urological surgery. Intraoperative rSO2 was continuously monitored throughout the surgery. Postoperative delirium (POD) was diagnosed by the Confusion Assessment Method. ApEn and SampEn were used to characterize the complexity of rSO2. Pearson correlation coefficients were used to measure the correlation between complexity of rSO2 and age. The association between complexity of rSO2 and POD was examined using T tests. RESULTS: A total of 68 patients (mean [SD] age, 63.0 (12.0) years; 47 (69.1%) males) were include in this analysis. There was a significant reverse relationship between the complexity of rSO2 and age (The correlation coefficients range between - 0.32 and - 0.28, all p < 0.05). Patients ≥ 75 years showed significantly lower complexity of rSO2 than the other two groups. Older age remained an independent factor influencing complexity of rSO2 after adjusting for a number of covariates. Six patients (8.8%) developed POD, and POD patients had lower complexity of rSO2 compared with non-POD patients. CONCLUSIONS: The complexity of rSO2 may serve as a new candidate marker of aging and POD prediction.

Effects of Motor Task Difficulty on Postural Control Complexity during Dual Tasks in Young Adults: A Nonlinear Approach.

Few studies have evaluated the effect of a secondary motor task on the standing posture based on nonlinear analysis. However, it is helpful to extract information related to the complexity, stability, and adaptability to the environment of the human postural system. This study aimed to analyze the effect of two motor tasks with different difficulty levels in motor performance complexity on the static standing posture in healthy young adults. Thirty-five healthy participants (23.08 ± 3.92 years) performed a postural single task (ST: keep a quiet standing posture) and two motor dual tasks (DT). i.e., mot-DT(A)­perform the ST while performing simultaneously an easy motor task (taking a smartphone out of a bag, bringing it to the ear, and putting it back in the bag)­and mot-DT(T)­perform the ST while performing a concurrent difficult motor task (typing on the smartphone keyboard). The approximate entropy (ApEn), Lyapunov exponent (LyE), correlation dimension (CoDim), and fractal dimension (detrending fluctuation analysis, DFA) for the mediolateral (ML) and anterior-posterior (AP) center-of-pressure (CoP) displacement were measured with a force plate while performing the tasks. A significant difference was found between the two motor dual tasks in ApEn, DFA, and CoDim-AP (p < 0.05). For the ML CoP direction, all nonlinear variables in the study were significantly different (p < 0.05) between ST and mot-DT(T), showing impairment in postural control during mot-DT(T) compared to ST. Differences were found across ST and mot-DT(A) in ApEn-AP and DFA (p < 0.05). The mot-DT(T) was associated with less effectiveness in postural control, a lower number of degrees of freedom, less complexity and adaptability of the dynamic system than the postural single task and the mot-DT(A).

Comparative Analysis of Preference in Contemporary and Earlier Texts Using Entropy Measures.

Research in computational textual aesthetics has shown that there are textual correlates of preference in prose texts. The present study investigates whether textual correlates of preference vary across different time periods (contemporary texts versus texts from the 19th and early 20th centuries). Preference is operationalized in different ways for the two periods, in terms of canonization for the earlier texts, and through sales figures for the contemporary texts. As potential textual correlates of preference, we measure degrees of (un)predictability in the distributions of two types of low-level observables, parts of speech and sentence length. Specifically, we calculate two entropy measures, Shannon Entropy as a global measure of unpredictability, and Approximate Entropy as a local measure of surprise (unpredictability in a specific context). Preferred texts from both periods (contemporary bestsellers and canonical earlier texts) are characterized by higher degrees of unpredictability. However, unlike canonicity in the earlier texts, sales figures in contemporary texts are reflected in global (text-level) distributions only (as measured with Shannon Entropy), while surprise in local distributions (as measured with Approximate Entropy) does not have an additional discriminating effect. Our findings thus suggest that there are both time-invariant correlates of preference, and period-specific correlates.

ECG Approximate Entropy in the Elderly during Cycling Exercise.

Approximate entropy (ApEn) is used as a nonlinear measure of heart-rate variability (HRV) in the analysis of ECG time-series recordings. Previous studies have reported that HRV can differentiate between frail and pre-frail people. In this study, EEGs and ECGs were recorded from 38 elderly adults while performing a three-stage cycling routine. Before and after cycling stages, 5-min resting-state EEGs (rs-EEGs) and ECGs were also recorded under the eyes-open condition. Applying the K-mean classifier to pre-exercise rs-ECG ApEn values and body weights revealed nine females with EEG power which was far higher than that of the other subjects in all cycling stages. The breathing of those females was more rapid than that of other subjects and their average heart rate was faster. Those females also presented higher degrees of asymmetry in the alpha and theta bands (stronger power levels in the right frontal electrode), indicating stressful responses during the experiment. It appears that EEG delta activity could be used in conjunction with a very low ECG frequency power as a predictor of bursts in the heart rate to facilitate the monitoring of elderly adults at risk of heart failure. A resting ECG ApEn index in conjunction with the subject's weight or BMI is recommended for screening high-risk candidates prior to exercise interventions.

Exploring the Potential of Machine Learning for the Diagnosis of Balance Disorders Based on Centre of Pressure Analyses.

Balance disorders are caused by several factors related to functionality deficits in one or multiple sensory systems such as vision, vestibular, and somatosensory systems. Patients usually have difficulty explaining their dizziness, often using ambiguous words to describe their symptoms. A common practice by clinicians is to objectively evaluate the patient's dizziness by applying the Sensory Organization Test (SOT), which measures the contribution of each sensory system (vestibular, visual, somatosensory). The SOT protocol can record up to 2000 measurements in 20 s to generate the Equilibrium Score (EQS) with its five load sensors. EQS is an indicator that reflects how well a patient can maintain balance. However, its calculation only considers two instances from these 2000 measurements that reflect the maximum anterior and posterior sway angle during the test performance; therefore, there is an opportunity to perform further analysis. This article aims to use the Centre of Pressure (COP) time series generated by the SOT and describes a methodology to pre-process and reduce the dimensionality of this raw data and use it as an input for machine learning algorithms to diagnose patients with balance disorder impairments. After applying this methodology to data from 475 patients, the logistic regression model (LR) produced the highest f1-score with 76.47%, and the support vector machine (SVM) performed almost as well, with an f1-score of 76.19%.

Sensorimotor Cortical Activity during Respiratory Arousals in Obstructive Sleep Apnea.

Intensity of respiratory cortical arousals (RCA) is a pathophysiologic trait in obstructive sleep apnea (OSA) patients. We investigated the brain oscillatory features related to respiratory arousals in moderate and severe OSA. Raw electroencephalography (EEG) data recorded during polysomnography (PSG) of 102 OSA patients (32 females, mean age 51.6 ± 12 years) were retrospectively analyzed. Among all patients, 47 had moderate (respiratory distress index, RDI = 15−30/h) and 55 had severe (RDI > 30/h) OSA. Twenty RCA per sleep stage in each patient were randomly selected and a total of 10131 RCAs were analyzed. EEG signals obtained during, five seconds before and after the occurrence of each arousal were analyzed. The entropy (approximate (ApEn) and spectral (SpEn)) during each sleep stage (N1, N2 and REM) and area under the curve (AUC) of the EEG signal during the RCA was computed. Severe OSA compared to moderate OSA patients showed a significant decrease (p < 0.0001) in the AUC of the EEG signal during the RCA. Similarly, a significant decrease in spectral entropy, both before and after the RCA was observed, was observed in severe OSA patients when compared to moderate OSA patients. Contrarily, the approximate entropy showed an inverse pattern. The highest increase in approximate entropy was found in sleep stage N1. In conclusion, the dynamic range of sensorimotor cortical activity during respiratory arousals is sleep-stage specific, dependent on the frequency of respiratory events and uncoupled from autonomic activation. These findings could be useful for differential diagnosis of severe OSA from moderate OSA.

Cost-Sensitive KNN Algorithm for Cancer Prediction Based on Entropy Analysis.

Early diagnosis of cancer is beneficial in the formulation of the best treatment plan; it can improve the survival rate and the quality of patient life. However, imaging detection and needle biopsy usually used not only find it difficult to effectively diagnose tumors at early stage, but also do great harm to the human body. Since the changes in a patient's health status will cause changes in blood protein indexes, if cancer can be diagnosed by the changes in blood indexes in the early stage of cancer, it can not only conveniently track and detect the treatment process of cancer, but can also reduce the pain of patients and reduce the costs. In this paper, 39 serum protein markers were taken as research objects. The difference of the entropies of serum protein marker sequences in different types of patients was analyzed, and based on this, a cost-sensitive analysis model was established for the purpose of improving the accuracy of cancer recognition. The results showed that there were significant differences in entropy of different cancer patients, and the complexity of serum protein markers in normal people was higher than that in cancer patients. Although the dataset was rather imbalanced, containing 897 instances, including 799 normal instances, 44 liver cancer instances, and 54 ovarian cancer instances, the accuracy of our model still reached 95.21%. Other evaluation indicators were also stable and satisfactory; precision, recall, F1 and AUC reach 0.807, 0.833, 0.819 and 0.92, respectively. This study has certain theoretical and practical significance for cancer prediction and clinical application and can also provide a research basis for the intelligent medical treatment.

Novel Application of Multiscale Cross-Approximate Entropy for Assessing Early Changes in the Complexity between Systolic Blood Pressure and ECG R-R Intervals in Diabetic Rats.

Cardiac autonomic neuropathy (CAN) is a common complication of diabetes mellitus, and can be assessed using heart rate variability (HRV) and the correlations between systolic blood pressure (SBP) and ECG R-R intervals (RRIs), namely baroreflex sensitivity (BRS). In this study, we propose a novel parameter for the nonlinear association between SBP and RRIs based on multiscale cross-approximate entropy (MS-CXApEn). Sixteen male adult Wistar Kyoto rats were equally divided into two groups: streptozotocin-induced diabetes and age-matched controls. RRIs and SBP were acquired in control rats and the diabetic rats at the onset of hyperglycemia and insulin-treated euglycemia to determine HRV by the ratio of low-frequency to high-frequency power (LF/HF) and Poincaré plot as SSR (SD1/SD2), BRS, and MS-CXApEn. SSR and BRS were not significantly different among the three groups. The LF/HF was significantly higher in the hyperglycemic diabetics than those in the controls and euglycemic diabetic rats. MS-CXApEn was higher in the diabetic hyperglycemic rats than the control rats from scales 2 to 10, and approached the values of controls in diabetic euglycemic rats at scales 9 and 10. Conclusions: We propose MS-CXApEn as a novel parameter to quantify the dynamic nonlinear interactions between SBP and RRIs that reveals more apparent changes in early diabetic rats. Furthermore, changes in this parameter were related to correction of hyperglycemia and could be useful for detecting and assessing CAN in early diabetes.

Discriminating Bacterial Infection from Other Causes of Fever Using Body Temperature Entropy Analysis.

Body temperature is usually employed in clinical practice by strict binary thresholding, aiming to classify patients as having fever or not. In the last years, other approaches based on the continuous analysis of body temperature time series have emerged. These are not only based on absolute thresholds but also on patterns and temporal dynamics of these time series, thus providing promising tools for early diagnosis. The present study applies three time series entropy calculation methods (Slope Entropy, Approximate Entropy, and Sample Entropy) to body temperature records of patients with bacterial infections and other causes of fever in search of possible differences that could be exploited for automatic classification. In the comparative analysis, Slope Entropy proved to be a stable and robust method that could bring higher sensitivity to the realm of entropy tools applied in this context of clinical thermometry. This method was able to find statistically significant differences between the two classes analyzed in all experiments, with sensitivity and specificity above 70% in most cases.

CEGH: A Hybrid Model Using CEEMD, Entropy, GRU, and History Attention for Intraday Stock Market Forecasting.

Intraday stock time series are noisier and more complex than other financial time series with longer time horizons, which makes it challenging to predict. We propose a hybrid CEGH model for intraday stock market forecasting. The CEGH model contains four stages. First, we use complete ensemble empirical mode decomposition (CEEMD) to decompose the original intraday stock market data into different intrinsic mode functions (IMFs). Then, we calculate the approximate entropy (ApEn) values and sample entropy (SampEn) values of each IMF to eliminate noise. After that, we group the retained IMFs into four groups and predict the comprehensive signals of those groups using a feedforward neural network (FNN) or gate recurrent unit with history attention (GRU-HA). Finally, we obtain the final prediction results by integrating the prediction results of each group. The experiments were conducted on the U.S. and China stock markets to evaluate the proposed model. The results demonstrate that the CEGH model improved forecasting performance considerably. The creation of a collaboration between CEEMD, entropy-based denoising, and GRU-HA is our major contribution. This hybrid model could improve the signal-to-noise ratio of stock data and extract global dependence more comprehensively in intraday stock market forecasting.

Approximate Entropy in Canonical and Non-Canonical Fiction.

Computational textual aesthetics aims at studying observable differences between aesthetic categories of text. We use Approximate Entropy to measure the (un)predictability in two aesthetic text categories, i.e., canonical fiction ('classics') and non-canonical fiction (with lower prestige). Approximate Entropy is determined for series derived from sentence-length values and the distribution of part-of-speech-tags in windows of texts. For comparison, we also include a sample of non-fictional texts. Moreover, we use Shannon Entropy to estimate degrees of (un)predictability due to frequency distributions in the entire text. Our results show that the Approximate Entropy values can better differentiate canonical from non-canonical texts compared with Shannon Entropy, which is not true for the classification of fictional vs. expository prose. Canonical and non-canonical texts thus differ in sequential structure, while inter-genre differences are a matter of the overall distribution of local frequencies. We conclude that canonical fictional texts exhibit a higher degree of (sequential) unpredictability compared with non-canonical texts, corresponding to the popular assumption that they are more 'demanding' and 'richer'. In using Approximate Entropy, we propose a new method for text classification in the context of computational textual aesthetics.

Monitoring the Evolution of Asynchrony between Mean Arterial Pressure and Mean Cerebral Blood Flow via Cross-Entropy Methods.

Cerebrovascular control is carried out by multiple nonlinear mechanisms imposing a certain degree of coupling between mean arterial pressure (MAP) and mean cerebral blood flow (MCBF). We explored the ability of two nonlinear tools in the information domain, namely cross-approximate entropy (CApEn) and cross-sample entropy (CSampEn), to assess the degree of asynchrony between the spontaneous fluctuations of MAP and MCBF. CApEn and CSampEn were computed as a function of the translation time. The analysis was carried out in 23 subjects undergoing recordings at rest in supine position (REST) and during active standing (STAND), before and after surgical aortic valve replacement (SAVR). We found that at REST the degree of asynchrony raised, and the rate of increase in asynchrony with the translation time decreased after SAVR. These results are likely the consequence of the limited variability of MAP observed after surgery at REST, more than the consequence of a modified cerebrovascular control, given that the observed differences disappeared during STAND. CApEn and CSampEn can be utilized fruitfully in the context of the evaluation of cerebrovascular control via the noninvasive acquisition of the spontaneous MAP and MCBF variability.

Information sharing among cryptocurrencies: Evidence from mutual information and approximate entropy during COVID-19.

In this paper, we use mutual information approach to investigate the information sharing between cryptocurrencies during the COVID-19 crisis. We also use the approximate entropy to study their dynamics before COVID-19 and during the pandemic. Results from the mutual information measure indicate a rise in information sharing and ordering in the cryptocurrency markets in the pandemic period, while the evidence from the approximate entropy estimates indicates a rise in randomness during the COVID-19 period. Our results provide new insights on the information sharing of cryptocurrencies and their reaction to shocks such as the COVID-19 pandemic.