Dynamic Entropy Research Articles

Dynamic maximum entropy provides accurate approximation of structured population dynamics.

Realistic models of biological processes typically involve interacting components on multiple scales, driven by changing environment and inherent stochasticity. Such models are often analytically and numerically intractable. We revisit a dynamic maximum entropy method that combines a static maximum entropy with a quasi-stationary approximation. This allows us to reduce stochastic non-equilibrium dynamics expressed by the Fokker-Planck equation to a simpler low-dimensional deterministic dynamics, without the need to track microscopic details. Although the method has been previously applied to a few (rather complicated) applications in population genetics, our main goal here is to explain and to better understand how the method works. We demonstrate the usefulness of the method for two widely studied stochastic problems, highlighting its accuracy in capturing important macroscopic quantities even in rapidly changing non-stationary conditions. For the Ornstein-Uhlenbeck process, the method recovers the exact dynamics whilst for a stochastic island model with migration from other habitats, the approximation retains high macroscopic accuracy under a wide range of scenarios in a dynamic environment.

Emotion identification by dynamic entropy and ensemble learning from electroencephalogram signals

AbstractEmotions are biologically based psychological states brought on by neurophysiologic changes, variously associated with thoughts, feelings, behavioral responses, and a degree of pleasure or displeasure. In order to assure active collaboration and trigger appropriate emotional input, accurate identification of human emotions is important. Poor generalization capacity induced by individual variations in emotion perceptions is indeed a concern in the current methods of emotion recognition. This work proposes a new dynamic pattern learning system based on entropy to allow electroencephalogram (EEG) signals for subject‐independent emotion recognition with strong generalization and classification through Recurrent Neural Network and Ensemble learning. First, dynamic entropy measurements are used to derive consecutive entropy values over time from EEG signals in quantitative EEG calculations. Experiment findings indicate that in order to distinguish negative and positive emotions, the highest average accuracy of 94.67% is achieved. In addition, the findings have completely shown that this approach produces outstanding performance for emotion detection across individuals relative to recent studies.

Fast identification method for thermal model parameters of Lithium-ion battery based on discharge temperature rise

An accurate thermal model of lithium-ion battery is extremely important for the safe operation of electric vehicles. The entropy coefficient is a key thermal characteristic of the battery, which is usually measured in advance. However, traditional measurement methods require a long test time or expensive equipment. In this paper, a novel thermal model parameter identification method with fast and continuous entropy coefficient identification is proposed, in which thermal parameters are obtained with lower time and equipment costs. First, a lumped thermal equivalent circuit model is established to describe the dynamic behaviors of battery temperature. Second, the thermal model parameters are identified based on experiments and calculations. The entropy coefficient is calculated based on temperature rise responses with different discharge currents. Finally, the identification results of the entropy coefficient are compared with traditional methods, which are found to be in good agreement. Furthermore, the thermal models are thoroughly verified under both galvanostatic discharge tests and dynamic profiles over the temperature range from 0 °C to 40 °C. Three kinds of thermal models with different entropy coefficient treatments are compared in terms of temperature errors, which indicates the superiority of the model with dynamic entropy coefficient, especially at high temperatures.

On cumulative residual Renyi's entropy for double truncated distribution

Recently, a new class of uncertainty measure, namely the dynamic cumulative residual Renyi's entropy, has been introduced and studied in the literature. In parallel to that here, we have defined cumulative residual Renyi's entropy for a doubly truncated random variable called interval cumulative residual Renyi's entropy (ICRRE). Several properties, including the effect of monotone transformation, and bounds of ICRRE are discussed. Furthermore, it is shown that the proposed measure uniquely determines the distribution function and obtained characterizations of some well-known life distributions. Finally, we have proposed four nonparametric estimators of ICRRE and compared their performance by using the Monte-Carlo simulation study. A real-life data set is also illustrated based on the best-proposed estimator.

Feasibility of Linear Parametric Estimation of Dynamic Information Measures to assess Physiological Stress from Short-Term Cardiovascular Variability.

Extensive efforts have been recently devoted to implement fast and reliable algorithms capable of assessing the physiological response of the organism to physiological stress. In this study, we propose the comparison between model-free and linear parametric methods as regards their ability to detect alterations in the dynamics and in the complexity of cardiovascular and respiratory variability evoked by postural and mental stress. Dynamic entropy (DE) and information storage (IS) measures were calculated on three physiological time-series, i.e. heart period, respiratory volume and systolic arterial pressure, on 61 healthy subjects monitored in resting conditions as well as during head-up tilt and while performing a mental arithmetic task. The results of the comparison suggest the feasibility of DE and IS measures computed from different physiological signals to discriminate among resting and stress states. If compared to the model-free algorithm, the faster linear method appears to be capable of detecting the same (or even more) statistically significant variations of DE or IS between resting and stress conditions, being thus in perspective more suitable for the integration within wearable devices. The computation of entropy indices extracted from multiple physiological signals acquired through wearables will allow a real-time stress assessment on people in daily-life situations.

Pseudo-random number generation based on digit isolation referenced to entropy buffers

Unpredictable pseudo-random number generators (PRNGs) are presented based on dissociated components with only coincidental interaction. The first components involve pointers taken from series of floating point numbers (float streams) arising from arithmetic. The pointers are formed by isolating generalized digits sufficiently far from the most significant digits in the float streams and may be combined into multi-digit pointers. The pointers indicate draw locations from the second component which are entropy decks having one or more cards corresponding to the elements used to assemble random numbers. Like playing cards, decks are cut and riffle-shuffled based on rules using digits appearing in the simulations. The various ordering states of the cards provide entropy to the PRNGs. The dual nature of the PRNGs is novel since they can operate either entirely on pointer variability to fixed decks or on shuffling variability using fixed pointer locations. Each component, pointers and dynamic entropy, is dissociated from the other and independently shown to pass stringent statistical tests with the other held as fixed; a “gold standard” mode involves changing the coincidental interaction between these two strong emulators of randomness by either cutting or shuffling prior to each draw. Gold standard modes may be useful in cryptography and in assessing tests themselves. One PRNG contains [Formula: see text] states in the entropy pool, another generates integers approximately 50% faster than the Advanced Encryption Standard (AES) PRNG with similar empirical performance, and a third generates full double-precision floats at speeds comparable to unsigned integer rates of the AES PRNG.

Bayesian Analysis of Dynamic Cumulative Residual Entropy for Lindley Distribution.

Dynamic cumulative residual (DCR) entropy is a valuable randomness metric that may be used in survival analysis. The Bayesian estimator of the DCR Rényi entropy (DCRRéE) for the Lindley distribution using the gamma prior is discussed in this article. Using a number of selective loss functions, the Bayesian estimator and the Bayesian credible interval are calculated. In order to compare the theoretical results, a Monte Carlo simulation experiment is proposed. Generally, we note that for a small true value of the DCRRéE, the Bayesian estimates under the linear exponential loss function are favorable compared to the others based on this simulation study. Furthermore, for large true values of the DCRRéE, the Bayesian estimate under the precautionary loss function is more suitable than the others. The Bayesian estimates of the DCRRéE work well when increasing the sample size. Real-world data is evaluated for further clarification, allowing the theoretical results to be validated.

Enhanced hierarchical symbolic dynamic entropy and maximum mean and covariance discrepancy-based transfer joint matching with Welsh loss for intelligent cross-domain bearing health monitoring

Domain adaptation (DA) as a critical and valuable tool is devoted to minimizing the distribution discrepancy across domains, which has been successfully utilized in intelligent bearing health monitoring. In particular, transfer joint matching (TJM) is a promising transfer learning strategy, especially when the domains differ considerably. In the TJM, the maximum mean discrepancy (MMD) is usually employed to assess the discrepancy of distributions in reproducing kernel Hilbert space (RKHS). However, the MMD has been proved to lose some useful statistical information in the RKHS. Hence, an improved TJM approach, called maximum mean and covariance discrepancy-based transfer joint matching with Welsh loss (MMCD-WTJM), is proposed in this article. In MMCD-WTJM, maximum mean and covariance discrepancy (MMCD) instead of MMD is incorporated into the TJM to match more statistical information in RKHS. Meanwhile, the Welsh loss function is incorporated into the TJM to enhance the stability of the model. Besides, we develop enhanced hierarchical symbolic dynamic entropy (EHSDE) to extract a more useful feature representation. Eventually, a novel hybrid cross-domain bearing fault identification based on EHSDE and MMCD-WTJM is developed. The analysis results of eight transfer bearing fault identification tasks demonstrate that the developed approach has an excellent capacity in intelligent bearing health monitoring under varying operation conditions and different machines. Compared with the existing entropy-based fault feature extraction approaches and domain adaptation-based transfer fault diagnosis methods, the presented bearing health monitoring scheme has remarkable strengths in recognition accuracy.

Multimodal MRI Analysis of Brain Metabolism in Maintenance Hemodialysis Patients Based on Cognitive Computing.

This paper investigates cognitive computation of brain metabolism in maintenance hemodialysis patients with multimodal MRI therapy assessment. This paper constructs a cross-individual emotion recognition method using dynamic sample entropy pattern learning. The cross-individual emotion recognition was carried out on subjects using the EEG emotion dataset SEED. The experimental results show that the proposed dynamic sample entropy-based pattern learning has better performance in cross-individual emotion recognition and exhibits better generalization and generalization ability when compared with the results of existing related studies. The constructed cognitive computing method for cross-individual emotion state recognition achieves optimization and innovation of EEG emotion pattern recognition, which can effectively predict people's mental emotion state from EEG signals. We also explore the value of diffusion-weighted magnetic resonance imaging and dynamic enhanced magnetic resonance imaging-based volumetric measurements in assessing the efficacy of neoadjuvant therapy in maintenance hemodialysis patients. We analyze and compare the results of different studies to find the best multimodal MRI to assess the efficacy of neoadjuvant therapy in maintenance hemodialysis patients. The use of ADC value growth rates to assess neoadjuvant efficacy provides the best diagnostic efficacy and allows the screening of patients who respond well to neoadjuvant therapy while avoiding the impact of two different b-value combinations commonly used to assess neoadjuvant efficacy.

Dynamic efficiency of China’s commodity futures market through the lens of high frequency data

In this paper, we use the permutation entropy algorithm to derive the static and dynamic permutation entropy of commodity futures, and to evaluate the effectiveness of main products in China’s commodity futures market. The intraday data of six varieties belonging to six categories in China’s commodity futures market are taken as samples. We find the following: (1) The return distribution of the main varieties shows high peaks, fat tails and asymmetry, and follows the biased random walk distribution characteristics; (2) The permutation entropy of all varieties decreases significantly in the same time window, during which the price volatility of major commodity markets rises. And the time window coincides with the impact time of COVID-19 epidemic; (3) By comparing the distribution of permutation entropy of main varieties in different stages of event shock, we found that the mean value of permutation entropy decreases significantly during the process of event shock, and the price fluctuates greatly. Therefore, the significant decrease of permutation entropy is a valuable warning signal for regulators and investors.

Thermodynamics and self-organization of strongly coupled Coulomb clusters: An experimental study

In this experimental work, the thermodynamics and self-organization of classical two-dimensional Coulomb clusters are studied as a function of the cluster size. The experiments are carried out in a DC glow discharge argon plasma in the dusty plasma experimental device for clusters with different number of particles. Hexagonal symmetry around each individual particle is quantified using the local orientational order parameter (|ψ6|) for all the configurations. The screened Coulomb coupling parameter, which plays a key role in determining the thermodynamic nature of a Coulomb cluster, is estimated using Langevin dynamics and found to be sensitive to the number of particles present in the cluster. In addition, the process of self-organization and the dynamics of individual particles of the cluster as it changes from a metastable state to the ground state are examined through the estimation of dynamic entropy. Our findings suggest an intimate link between the configurational ordering and the thermodynamics of a strongly coupled Coulomb cluster system—an insight that might be of practical value in analyzing and controlling the microdynamics of a wider class of finite systems.

English

In this paper, we obtain lower bounds for the variance of a function of random variables in terms of measures of reliability and entropy. Also based on the obtained characterization via the lower bounds for the variance of a function of random variable X, we find a characterization of the weighted function corresponding to density function f(x), in terms of Chernoff-type inequalities. Subsequently, we obtain monotonic relationships between variance residual life and dynamic cumulative residual entropy and between variance past lifetime and dynamic cumulative past entropy. Moreover, we find lower bounds for the variance of functions of weighted random variables with specific weight functions applicable in reliability under suitable conditions.

Evaluation of Cancer Progression Using Dynamic Entropy Changes and Thermography

Entropy is producing during any irreversible process. In the cancer cells, the entropy generation measures the irreversibility; so, the cancer cells have higher entropy generation than the healthy cells. The entropy generation rate shows the amount of robustness, progression, and invasion of the cancer cells. From a thermodynamic aspect, cancer's origin and growth is an irreversible process, and the thermodynamic variables such as the cell volume, temperature, and entropy will change during this process. In this paper, a procedure based on experimental data is proposed to calculate dynamic entropy generation in the tumoral tissues by dynamic thermography and measurement of tumor size. The dynamic changes in the volume, temperature, and entropy associated with tumor cells over time are tested and evaluated in this regard. An in vivo assay has been developed to measure and analyze these changes. This assay investigated the growth of 4T1 Breast Tumor in 55 BALB/c mice over time. Infrared thermography has been employed to evaluate dynamic temperature changes of the tumors. The computer code has been developed to gather important data from tumoral and healthy mice's images to compute considered temperature differences and entropy generation associated with tumoral tissues. To better evaluate tumor tissue, the Micro PET Images are used to verify volume changes of tumors. The relation between the volume and temperature gradient of tumor cells has detected by measuring during the experiment. The entropy of tumor cells was studying and calculating during the process of tumor changes. Results show that entropy generation as the main concept of thermodynamic is a strong tool for the analysis of cancer cells and has a strong relationship with cancer growth.

Dynamic Nature of High-Pressure Ice VII.

Starting from Shannon's definition of dynamic entropy, we propose a theory to describe the rare-event-determined dynamic states in condensed matter and their transitions and apply it to high-pressure ice VII. A dynamic intensive quantity named dynamic field, rather than the conventional thermodynamic intensive quantities such as temperature and pressure, is taken as the controlling variable. The dynamic entropy versus dynamic field curve demonstrates two dynamic states in the stability region of ice VII and dynamic ice VII. Their microscopic differences were assigned to the dynamic patterns of proton transfer. This study puts a similar dynamical theory used in earlier studies of glass models on a simpler and more fundamental basis, which could be applied to describe the dynamic states of more realistic condensed matter systems.

The Dynamic Entropy of Tumor Immune Infiltrates: The Impact of Recirculation, Antigen-Specific Interactions, and Retention on T Cells in Tumors.

Analysis of tumor infiltration using conventional methods reveals a snapshot view of lymphocyte interactions with the tumor environment. However, lymphocytes have the unique capacity for continued recirculation, exploring varied tissues for the presence of cognate antigens according to inflammatory triggers and chemokine gradients. We discuss the role of the inflammatory and cellular makeup of the tumor environment, as well as antigen expressed by cancer cells or cross-presented by stromal antigen presenting cells, on recirculation kinetics of T cells. We aim to discuss how current cancer therapies may manipulate lymphocyte recirculation versus retention to impact lymphocyte exclusion in the tumor.

Roller bearing fault diagnosis based on LMD and multi-scale symbolic dynamic information entropy

This paper presents a new fault feature extraction method based on the combination of local mean decomposition (LMD) and multi-scale symbolic dynamic information entropy (MSDE). The LMD method decomposes the multi-component signal into a finite number of product functions (PFs) to extract the characteristic information of the original signal. In this paper, the comparison of MSDE and the multi-scale sample entropy shows that the symbolic dynamic information entropy (SDE) has simple calculation and has better stability than sample entropy at multiscale. Entropy values of PFs that combine LMD and MSDE are extracted as the feature sets, which are inputted into the affinity propagation clustering model to identify the fault types and fault degree of roller bearings. This paper also discusses the influence of different filtering algorithms on the noise removal of bearing signal. Application results demonstrate the effectiveness of the proposed fault diagnosis method.

Dynamic entropy of human blood

Temperature control is a process that is used by biological systems to maintain a stable internal state for survival. People have an individually variable physiological temperature of about 36.6 °C, which can be modified by many undesirable factors. Based on an analysis of a time series of extracellular ionic fluxes that were obtained using the non-invasive solute-semiconductor interface technique, I show that this extremely specific (critical) temperature is encoded by a local minimum in the dynamic entropy of an isolated drop of human blood. Moreover, a dynamic zeroth-order normal fluid/“superfluid” nonequilibrium phase transition, which was reflected by a spontaneous symmetry breaking that occurred in the phase space, was revealed. The critical scaling of the dynamic measures for the covariates such as the spectral signature and Lyapunov exponent was also determined.

A New Health Condition Detection Method for Planetary Gears Based on Modified Distributed Compressed Sensing and Multiscale Symbol Dynamic Entropy

Planetary gear transmission system is an important transmission part of large machinery and is prone to failure. Aiming at the problem of how to extract fault information from vibration signals of nonlinear and nonstationary planetary gearboxes, a performance degradation evaluation index of planetary gearboxes based on improved distributed compressed sensing and modified multiscale symbolic dynamic entropy (DCSMDE) is proposed. DCSMDE combines distributed compression sensing with modified multiscale symbol dynamic entropy and solves the problem of strong nonlinearity and strong vibration signal coupling of the planetary transmission system from the homologous signals of multiple sensors. A distributed compression sensing parameter optimization algorithm based on Rényi entropy is proposed, which uses improved distributed compression sensing technology to simultaneously sample, compress, and denoise the multisource vibration data of rotating machinery. DCSMDE is used to calculate the reconstructed signal, extract the features with higher recognition characteristics, and use the change trend of the DCSMDE value to judge the working status of the planetary gearbox. Experimental results show that DCSMDE can be applied to dynamic evolution and fault identification of mechanical systems and accurately classify actual fault signals. It provides a new idea for the classification of planetary gear faults and the recognition of performance degradation.

Some Results on Quantile-based Dynamic Survival and Failure Tsallis Entropy

Non-additive entropy measures are important for many applications. In this paper, we introduce a quantile-based non-additive entropy measure, based on Tsallis entropy and study their properties. Some relationships of this measure with well-known reliability mea- sures and ageing classes are studied and some characterization results are presented. Also the concept of quantile-based shift independent entropy measures has been introduced and studied various properties.

On some characterization results of -norm dynamic survival entropies

The information based on entropy of uncertainty associated with the residual life of a random variable is implemented in various fields, e.g., information theory, statistical physics, reliability theory, statistics, demography and economics, etc. In this paper, we propose two new -norm dynamic survival entropy (RNDSE) and -norm weighted dynamic survival entropy (RNWDSE) based on the survival function and some results on stochastic ordering are studied in detail. Further, we have investigated the bounds on RNDSE and RNWDSE in terms of failure rate function. In addition, some relationships between RNDSE, RNWDSE and failure function have also been well established. Finally, in order to illustrate the applications of RNDSE and RNWDSE, some useful distributions like exponential, Rayleigh, Weibull, Pareto, finite range distributions and one new distribution called T-exponential have been characterized.