From physiological complexity to data interactions-A case study of recordings from exercise monitoring.

The popularity of nonlinear analysis has been growing simultaneously with the technology of effort monitoring. Therefore, considering the simple methods of physiological data collection and the approaches from the information domain, we proposed integrating univariate and bivariate analysis for the rest and effort comparison. Two sessions separated by an intensive training program were studied. Nine subjects participated in the first session (S1) and seven in the second session (S2). The protocol included baseline (BAS), exercise, and recovery phase. During all phases, electrocardiogram (ECG) was recorded. For the analysis, we selected corresponding data lengths of BAS and exercise usually lasting less than 5 min. We found the utility of the differences between original data and their surrogates for sample entropy Sdiff and Kullback-Leibler divergence KLDdiff. Sdiff of heart rate variability was negative in BAS and exercise but its sensitivity for phases discrimination was not satisfactory. We studied the bivariate analysis of RR intervals and corresponding QT peaks by Interlayer Mutual Information (IMI) and average edge overlap (AVO) markers. While the IMI parameter decreases in exercise conditions, AVO increased in effort compared to BAS. These findings conclude that researchers should consider a bivariate analysis of extracted RR intervals and corresponding QT datasets, when only ECG is recorded during tests.

Quantitative Analysis of Mother Wavelet Function Selection for Wearable Sensors-Based Human Activity Recognition.

Recent advancements in the Internet of Things (IoT) wearable devices such as wearable inertial sensors have increased the demand for precise human activity recognition (HAR) with minimal computational resources. The wavelet transform, which offers excellent time-frequency localization characteristics, is well suited for HAR recognition systems. Selecting a mother wavelet function in wavelet analysis is critical, as optimal selection improves the recognition performance. The activity time signals data have different periodic patterns that can discriminate activities from each other. Therefore, selecting a mother wavelet function that closely resembles the shape of the recognized activity's sensor (inertial) signals significantly impacts recognition performance. This study uses an optimal mother wavelet selection method that combines wavelet packet transform with the energy-to-Shannon-entropy ratio and two classification algorithms: decision tree (DT) and support vector machines (SVM). We examined six different mother wavelet families with different numbers of vanishing points. Our experiments were performed on eight publicly available ADL datasets: MHEALTH, WISDM Activity Prediction, HARTH, HARsense, DaLiAc, PAMAP2, REALDISP, and HAR70+. The analysis demonstrated in this paper can be used as a guideline for optimal mother wavelet selection for human activity recognition.

The EEG-Based Fusion Entropy-Featured Identification of Isometric Contraction Forces under the Same Action.

This study explores the important role of assessing force levels in accurately controlling upper limb movements in human-computer interfaces. It uses a new method that combines entropy to improve the recognition of force levels. This research aims to differentiate between different levels of isometric contraction forces using electroencephalogram (EEG) signal analysis. It integrates eight different entropy measures: power spectrum entropy (PSE), singular spectrum entropy (SSE), logarithmic energy entropy (LEE), approximation entropy (AE), sample entropy (SE), fuzzy entropy (FE), alignment entropy (PE), and envelope entropy (EE). The findings emphasize two important advances: first, including a wide range of entropy features significantly improves classification efficiency; second, the fusion entropy method shows exceptional accuracy in classifying isometric contraction forces. It achieves an accuracy rate of 91.73% in distinguishing between 15% and 60% maximum voluntary contraction (MVC) forces, along with 69.59% accuracy in identifying variations across 15%, 30%, 45%, and 60% MVC. These results illuminate the efficacy of employing fusion entropy in EEG signal analysis for isometric contraction detection, heralding new opportunities for advancing motor control and facilitating fine motor movements through sophisticated human-computer interface technologies.

Biomechanical Assessment Methods Used in Chronic Stroke: A Scoping Review of Non-Linear Approaches.

Non-linear and dynamic systems analysis of human movement has recently become increasingly widespread with the intention of better reflecting how complexity affects the adaptability of motor systems, especially after a stroke. The main objective of this scoping review was to summarize the non-linear measures used in the analysis of kinetic, kinematic, and EMG data of human movement after stroke. PRISMA-ScR guidelines were followed, establishing the eligibility criteria, the population, the concept, and the contextual framework. The examined studies were published between 1 January 2013 and 12 April 2023, in English or Portuguese, and were indexed in the databases selected for this research: PubMed®, Web of Science®, Institute of Electrical and Electronics Engineers®, Science Direct® and Google Scholar®. In total, 14 of the 763 articles met the inclusion criteria. The non-linear measures identified included entropy (n = 11), fractal analysis (n = 1), the short-term local divergence exponent (n = 1), the maximum Floquet multiplier (n = 1), and the Lyapunov exponent (n = 1). These studies focused on different motor tasks: reaching to grasp (n = 2), reaching to point (n = 1), arm tracking (n = 2), elbow flexion (n = 5), elbow extension (n = 1), wrist and finger extension upward (lifting) (n = 1), knee extension (n = 1), and walking (n = 4). When studying the complexity of human movement in chronic post-stroke adults, entropy measures, particularly sample entropy, were preferred. Kinematic assessment was mainly performed using motion capture systems, with a focus on joint angles of the upper limbs.

How ATP suppresses the fibrillation of amyloid peptides: analysis of the free-energy contributions.

Recent experiments have revealed that adenosine triphosphate (ATP) suppresses the fibrillation of amyloid peptides - a process closely linked to neurodegenerative diseases such as Alzheimer's and Parkinson's. Apart from the adsorption of ATP onto amyloid peptides, the molecular understanding is still limited, leaving the underlying mechanism for the fibrillation suppression by ATP largely unclear, especially in regards to the molecular energetics. Here we provide an explanation at the molecular scale by quantifying the free energies using all-atom molecular dynamics simulations. We found that the changes of the free energies due to the addition of ATP lead to a significant equilibrium shift towards monomeric peptides in agreement with experiments. Despite ATP being a highly charged species, the decomposition of the free energies reveals that the van der Waals interactions with the peptide are decisive in determining the relative stabilization of the monomeric state. While the phosphate moiety exhibits strong electrostatic interactions, the compensation by the water solvent results in a minor, overall Coulomb contribution. Our quantitative analysis of the free energies identifies which intermolecular interactions are responsible for the suppression of the amyloid fibril formation by ATP and offers a promising method to analyze the roles of similarly complex cosolvents in aggregation processes.

Edge-based relative entropy as a sensitive indicator of critical transitions in biological systems.

BACKGROUND: Disease progression in biosystems is not always a steady process but is occasionally abrupt. It is important but challenging to signal critical transitions in complex biosystems. METHODS: In this study, based on the theoretical framework of dynamic network biomarkers (DNBs), we propose a model-free method, edge-based relative entropy (ERE), to identify temporal key biomolecular associations/networks that may serve as DNBs and detect early-warning signals of the drastic state transition during disease progression in complex biological systems. Specifically, by combining gene‒gene interaction (edge) information with the relative entropy, the ERE method converts gene expression values into network entropy values, quantifying the dynamic change in a biomolecular network and indicating the qualitative shift in the system state. RESULTS: The proposed method was validated using simulated data and real biological datasets of complex diseases. The applications show that for certain diseases, the ERE method helps to reveal so-called "dark genes" that are non-differentially expressed but with high ERE values and of essential importance in both gene regulation and prognosis. CONCLUSIONS: The proposed method effectively identified the critical transition states of complex diseases at the network level. Our study not only identified the critical transition states of various cancers but also provided two types of new prognostic biomarkers, positive and negative edge biomarkers, for further practical application. The method in this study therefore has great potential in personalized disease diagnosis.

Modulatory effects of low-intensity retinal ultrasound stimulation on rapid and non-rapid eye movement sleep.

Prior investigations have established that the manipulation of neural activity has the potential to influence both rapid eye movement and non-rapid eye movement sleep. Low-intensity retinal ultrasound stimulation has shown effectiveness in the modulation of neural activity. Nevertheless, the specific effects of retinal ultrasound stimulation on rapid eye movement and non-rapid eye movement sleep, as well as its potential to enhance overall sleep quality, remain to be elucidated. Here, we found that: In healthy mice, retinal ultrasound stimulation: (i) reduced total sleep time and non-rapid eye movement sleep ratio; (ii) changed relative power and sample entropy of the delta (0.5-4 Hz) in non-rapid eye movement sleep; and (iii) enhanced relative power of the theta (4-8 Hz) and reduced theta-gamma coupling strength in rapid eye movement sleep. In Alzheimer's disease mice with sleep disturbances, retinal ultrasound stimulation: (i) reduced the total sleep time; (ii) altered the relative power of the gamma band during rapid eye movement sleep; and (iii) enhanced the coupling strength of delta-gamma in non-rapid eye movement sleep and weakened the coupling strength of theta-fast gamma. The results indicate that retinal ultrasound stimulation can modulate rapid eye movement and non-rapid eye movement-related neural activity; however, it is not beneficial to the sleep quality of healthy and Alzheimer's disease mice.

Spatio-temporal evolution of sports tourism industry integration: A empirical analysis of Xinjiang in China.

Since the issuance of the "Guiding Opinions on Vigorously Developing Sports Tourism" in 2016, the integration of sports and tourism has become a strategy in regional economic development. It creates new economic growth points, enhances local images, and promotes cultural communication. In the context of the "Tourism Makes Xinjiang Thrive" strategy, quantitatively investigating the integration of the sports and tourism industries helps people to better understand their interaction which can serve as the valuable input in policy-making for the comprehensive development of a region. This paper uses entropy weight method, stochastic frontier analysis and coupling coordination model to quantitatively analyze the effect of sports tourism industry integration in Xinjiang from the perspective of integration path. Meanwhile, the Dagum Gini coefficient and nuclear density estimation were used to analyze the regional differences and dynamic evolution of industrial integration quality. The result shows that (1) The sports and tourism integration quality in Xinjiang has not reached the optimal goal of complete integration. In the process of mutual industrial promotion, tourism promotes a higher degree of integration with the sports industry. (2) The industrial integration quality shows a phenomenon of "imbalance and inadequacy" among the regions. The regions with high quality of industrial integration were Urumqi, Ili, Kashgar, Altay and Changji, which have rich sports tourism resources. (3) The overall spatial difference in the quality of industrial integration presented a fluctuation downtrend. The difference between the tourism industrial belts was very significant.

Permutation entropy analysis of EEG signals for distinguishing eyes-open and eyes-closed brain states: Comparison of different approaches.

Developing reliable methodologies to decode brain state information from electroencephalogram (EEG) signals is an open challenge, crucial to implementing EEG-based brain-computer interfaces (BCIs). For example, signal processing methods that identify brain states could allow motor-impaired patients to communicate via non-invasive, EEG-based BCIs. In this work, we focus on the problem of distinguishing between the states of eyes closed (EC) and eyes open (EO), employing quantities based on permutation entropy (PE). An advantage of PE analysis is that it uses symbols (ordinal patterns) defined by the ordering of the data points (disregarding the actual values), hence providing robustness to noise and outliers due to motion artifacts. However, we show that for the analysis of multichannel EEG recordings, the performance of PE in discriminating the EO and EC states depends on the symbols' definition and how their probabilities are estimated. Here, we study the performance of PE-based features for EC/EO state classification in a dataset of N=107 subjects with one-minute 64-channel EEG recordings in each state. We analyze features obtained from patterns encoding temporal or spatial information, and we compare different approaches to estimate their probabilities (by averaging over time, over channels, or by "pooling"). We find that some PE-based features provide about 75% classification accuracy, comparable to the performance of features extracted with other statistical analysis techniques. Our work highlights the limitations of PE methods in distinguishing the eyes' state, but, at the same time, it points to the possibility that subject-specific training could overcome these limitations.

Multicentric intelligent cardiotocography signal interpretation using deep semi-supervised domain adaptation via minimax entropy and domain invariance.

BACKGROUND AND OBJECTIVE: Obstetricians use Cardiotocography (CTG), which is the continuous recording of fetal heart rate and uterine contraction, to assess fetal health status. Deep learning models for intelligent fetal monitoring trained on extensively labeled and identically distributed CTG records have achieved excellent performance. However, creation of these training sets requires excessive time and specialist labor for the collection and annotation of CTG signals. Previous research has demonstrated that multicenter studies can improve model performance. However, models trained on cross-domain data may not generalize well to target domains due to variance in distribution among datasets. Hence, this paper conducted a multicenter study with Deep Semi-Supervised Domain Adaptation (DSSDA) for intelligent interpretation of antenatal CTG signals. This approach helps to align cross-domain distribution and transfer knowledge from a label-rich source domain to a label-scarce target domain. METHODS: We proposed a DSSDA framework that integrated Minimax Entropy and Domain Invariance (DSSDA-MMEDI) to reduce inter-domain gaps and thus achieve domain invariance. The networks were developed using GoogLeNet to extract features from CTG signals, with fully connected, softmax layers for classification. We designed a Dynamic Gradient-driven strategy based on Mutual Information (DGMI) to unify the losses from Minimax Entropy (MME), Domain Invariance (DI), and supervised cross-entropy during iterative learning. RESULTS: We validated our DSSDA model on two datasets collected from collaborating healthcare institutions and mobile terminals as the source and target domains, which contained 16,355 and 3,351 CTG signals, respectively. Compared to the results achieved with deep learning networks without DSSDA, DSSDA-MMEDI significantly improved sensitivity and F1-score by over 6%. DSSDA-MMEDI also outperformed other state-of-the-art DSSDA approaches for CTG signal interpretation. Ablation studies were performed to determine the unique contribution of each component in our DSSDA mechanism. CONCLUSIONS: The proposed DSSDA-MMEDI is feasible and effective for alignment of cross-domain data and automated interpretation of multicentric antenatal CTG signals with minimal annotation cost.

An integrated model for rice supplier selection strategies and a comparative analysis of fuzzy multicriteria decision-making approaches based on the fuzzy entropy weight method for evaluating rice suppliers.

Rice, being a staple food in many countries, necessitates the identification of reliable suppliers to ensure a steady supply. Consequently, it is vital to establish trustworthy vendors for various types of this essential grain who can meet stringent product quality standards. This study aims to identify, analyze, rank, and select primary rice suppliers. The study emphasizes the importance of selecting and managing suitable providers to meet customer demands, proposes a ranking model for rice suppliers, and introduces developed fuzzy MCDM techniques. It proposes an integrated model for selecting rice suppliers, considering factors related to the processes before, during, and after selecting providers within a defined framework. The outcomes shows that rice supplier selection strategy can efficiently identify reliable rice suppliers, improve buyer value, reduce procurement risk, enhance efficiency, and establish strong supply chain relationships in complex decision-making processes. To assess suppliers, the study introduces two advanced integrated approaches and compares them. The fuzzy entropy weight method (EWM) was used to determine the criteria weights. The ranking of rice suppliers was achieved using a fuzzy multi-objective optimization based on ratio analysis (MOORA), fuzzy complex proportional assessment (COPRAS), and combinations of these two methods in different approaches. The methodology supports decision-makers in a rapidly evolving global environment by assisting importers, traders, suppliers, procurement, and logistics management, particularly for non-rice-cultivating countries in rice importation and supplier selection. The numerical analysis is grounded in a real-world case study of selecting rice suppliers in Jordan. The findings reveal that the various strategies yield both similar and different results. Furthermore, the integrated method is considered the most accurate for evaluating rice imports and suppliers, aligning closely with the reality of the current situation.

Understanding the Reversible Binding of a Multichain Protein-Protein Complex through Free-Energy Calculations.

We demonstrate that the binding affinity of a multichain protein-protein complex, insulin dimer, can be accurately predicted using a streamlined route of standard binding free-energy calculations. We find that chains A and C, which do not interact directly during binding, stabilize the insulin monomer structures and reduce the binding affinity of the two monomers, therefore enabling their reversible association. Notably, we confirm that although classical methods can estimate the binding affinity of the insulin dimer, conventional molecular dynamics, enhanced sampling algorithms, and classical geometrical routes of binding free-energy calculations may not fully capture certain aspects of the role played by the noninteracting chains in the binding dynamics. Therefore, this study not only elucidates the role of noninteracting chains in the reversible binding of the insulin dimer but also offers a methodological guide for investigating the reversible binding of multichain protein-protein complexes utilizing streamlined free-energy calculations.

Entropy Tug-of-War Determines Solvent Effects in the Liquid-Liquid Phase Separation of a Globular Protein.

Liquid-liquid phase separation (LLPS) plays a key role in the compartmentalization of cells via the formation of biomolecular condensates. Here, we combined atomistic molecular dynamics (MD) simulations and terahertz (THz) spectroscopy to determine the solvent entropy contribution to the formation of condensates of the human eye lens protein γD-Crystallin. The MD simulations reveal an entropy tug-of-war between water molecules that are released from the protein droplets and those that are retained within the condensates, two categories of water molecules that were also assigned spectroscopically. A recently developed THz-calorimetry method enables quantitative comparison of the experimental and computational entropy changes of the released water molecules. The strong correlation mutually validates the two approaches and opens the way to a detailed atomic-level understanding of the different driving forces underlying the LLPS.

Short-term forecasting approach of single well production based on multi-intelligent agent hybrid model.

The short-term prediction of single well production can provide direct data support for timely guiding the optimization and adjustment of oil well production parameters and studying and judging oil well production conditions. In view of the coupling effect of complex factors on the daily output of a single well, a short-term prediction method based on a multi-agent hybrid model is proposed, and a short-term prediction process of single well output is constructed. First, CEEMDAN method is used to decompose and reconstruct the original data set, and the sliding window method is used to compose the data set with the obtained components. Features of components by decomposition are described as feature vectors based on values of fuzzy entropy and autocorrelation coefficient, through which those components are divided into two groups using cluster algorithm for prediction with two sub models. Optimized online sequential extreme learning machine and the deep learning model based on encoder-decoder structure using self-attention are developed as sub models to predict the grouped data, and the final predicted production comes from the sum of prediction values by sub models. The validity of this method for short-term production prediction of single well daily oil production is verified. The statistical value of data deviation and statistical test methods are introduced as the basis for comparative evaluation, and comparative models are used as the reference model to evaluate the prediction effect of the above multi-agent hybrid model. Results indicated that the proposed hybrid model has performed better with MAE value of 0.0935, 0.0694 and 0.0593 in three cases, respectively. By comparison, the short-term prediction method of single well production based on multi-agent hybrid model has considerably improved the statistical value of prediction deviation of selected oil well data in different periods. Through statistical test, the multi-agent hybrid model is superior to the comparative models. Therefore, the short-term prediction method of single well production based on a multi-agent hybrid model can effectively optimize oilfield production parameters and study and judge oil well production conditions.

Constructing an evaluation model for the comprehensive level of sustainable development of provincial competitive sports in China based on DPSIR and MCDM.

This study focuses on the objective assessment of sport development in socio-economic environments, considering the challenges faced by the industry. These challenges include disparities in regional investments, limited market participation, slow progress towards sports professionalization, and insufficient technological innovations. To tackle these challenges, we suggest implementing an integrated evaluation model that follows the DPSIR (Drivers, Pressures, States, Impacts, Responses) framework and incorporates comprehensive socioeconomic indicators. Subsequently, we utilized the Entropy power method and TOPSIS (Order Preference Technique for Similarity to an Ideal Solution, TOPSIS) analysis to comprehensively assess the progress of competitive sports development in 31 provinces and cities in China. Additionally, we recommended further developments in competitive sports and proposed precise strategies for promoting its growth. The framework and methodology developed in this paper provide an objective and scientifically based set of decision-making guidelines that can be adopted by government agencies and related industries in order to create successful plans that promote the sustainable growth of competitive sport. This is expected to bolster the nation's global influence, enhance social unity, and fuel economic expansion. The findings of this study offer policymakers valuable insights regarding competitive sports and can advance the development of the sports sector in China, thus making it a crucial driver of regional socio-economic progress.

The entropy rate of Linear Additive Markov Processes.

This work derives a theoretical value for the entropy of a Linear Additive Markov Process (LAMP), an expressive but simple model able to generate sequences with a given autocorrelation structure. Our research establishes that the theoretical entropy rate of a LAMP model is equivalent to the theoretical entropy rate of the underlying first-order Markov Chain. The LAMP model captures complex relationships and long-range dependencies in data with similar expressibility to a higher-order Markov process. While a higher-order Markov process has a polynomial parameter space, a LAMP model is characterised only by a probability distribution and the transition matrix of an underlying first-order Markov Chain. This surprising result can be explained by the information balance between the additional structure imposed by the next state distribution of the LAMP model, and the additional randomness of each new transition. Understanding the entropy of the LAMP model provides a tool to model complex dependencies in data while retaining useful theoretical results. To emphasise the practical applications, we use the LAMP model to estimate the entropy rate of the LastFM, BrightKite, Wikispeedia and Reuters-21578 datasets. We compare estimates calculated using frequency probability estimates, a first-order Markov model and the LAMP model, also considering two approaches to ensure the transition matrix is irreducible. In most cases the LAMP entropy rates are lower than those of the alternatives, suggesting that LAMP model is better at accommodating structural dependencies in the processes, achieving a more accurate estimate of the true entropy.

Coupling coordination and underlying mechanisms of urbanization development and land use efficiency in the Gansu section of the Yellow River Basin.

This swift progression of urbanization has led to increasingly prominent conflicts over the use of land, particularly around its supply and demand. Researchers, both in China and internationally, have underscored the inherent interconnection between urbanization and land utilization. This relationship has gradually become more complex with the development of urbanization. With the implementation of the Yellow River Basin's strategy to preserve the environment while ensuring high-quality development, the Yellow River Basin has become a focal point of attention for numerous scholars. This study centers on the 57 county-level administrative divisions within the Gansu segment of the Yellow River Basin. We employed an extensive array of methodologies, such as GIS technology, the entropy method, data envelopment analysis, the coupling coordination degree model, and the panel vector autoregressive model. We established an index system and a measurement model to evaluate the degree of urbanization and the efficiency of land use. We also investigated the coupling coordinated dynamics between these two variables, to further explore the dynamic interplay between urbanization and land use and reveal their underlying mechanisms. The conclusions are as follows. The urbanization level and efficiency of land use in the Gansu section of the Yellow River Basin have exhibited a consistent upward trajectory, albeit at levels that are not particularly high, indicating substantial room for improvement in the future. The level of coupling coordination between urbanization and land use efficiency in the Gansu section of the Yellow River Basin has shown a generally upward trend. However, the overall coordination level remains relatively low, characterized by an imbalance, with "high coupling but low coordination". Regarding spatial distribution patterns, considerable disparities exist in the level of coordination development, which generally decreases from the eastern toward the western regions. A strong reciprocal and interactive relationship exists between the urbanization level and land use efficiency. An elevated level of economic urbanization can initially stimulate land use efficiency. Similarly, the improvement in the level of population urbanization, social urbanization, and ecological urbanization tends to exert a restraining influence on the augmentation of land use efficiency. Conversely, the enhancement of land use efficiency makes a distinct contribution to promoting the elevation of the urbanization level.

Evaluating the metropolitan public health preparedness for pandemics using entropy-TOPSIS-IF.

Introduction: Metropolitan governance's efficacy is regularly gauged by its capability for public health preparedness, a critical component, particularly in the post-pandemic climate, as global cities reassess their mitigation abilities. This process has broader implications, curbing mortality rates and amplifying sustainability. Current methodologies for preparedness assessment lean primarily on either Subjective Evaluation-Based Assessment (SBA), predicated on experts' input on various capacity indicators, or they opt for Data-Based quantitative Assessments (DBA), chiefly utilizing public statistic data. Methods: The manuscript discusses an urgent need for integrating both SBA and DBA to adequately measure Metropolitan Public Health Pandemics Preparedness (MPHPP), thus proposing a novel entropy-TOPSIS-IF model for comprehensive evaluation of MPHPP. Within this proposed model, experts' subjective communication is transformed into quantitative data via the aggregation of fuzzy decisions, while objective data is collected from public statistics sites. Shannon's entropy and TOPSIS methods are enacted on these data sets to ascertain the optimal performer after normalization and data isotropy. Results and discussion: The core contribution of the entropy-TOPSIS-IF model lies in its assessment flexibility, making it universally applicable across various contexts, regardless of the availability of expert decisions or quantitative data. To illustrate the efficacy of the entropy-TOPSIS-IF model, a numerical application is presented, examining three Chinese metropolises through chosen criteria according to the evaluations of three experts. A sensitivity analysis is provided to further affirm the stability and robustness of the suggested MPHPP evaluation model.