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Similar to traditional imaging, virtual reality (VR) imagery encompasses nonstereoscopic (VR-2D) and stereoscopic (VR-3D) modes. Currently, Russell's emotional model has been extensively studied in traditional 2D and VR-3D modes, but there is limited comparative research between VR-2D and VR-3D modes. In this study, we investigate whether Russell's emotional model exhibits stronger brain activation states in VR-3D mode compared to VR-2D mode. By designing an experiment covering four emotional categories (high arousal–high pleasure (HAHV), high arousal–low pleasure (HALV), low arousal–low pleasure (LALV), and low arousal–high pleasure (LAHV)), EEG signals were collected from 30 healthy undergraduate and graduate students while watching videos in both VR modes. Initially, power spectral density (PSD) computations revealed distinct brain activation patterns in different emotional states across the two modes, with VR-3D videos inducing significantly higher brainwave energy, primarily in the frontal, temporal, and occipital regions. Subsequently, Differential entropy (DE) feature sets, selected via a dual ten-fold cross-validation Support Vector Machine (SVM) classifier, demonstrate satisfactory classification accuracy, particularly superior in the VR-3D mode. The paper subsequently presents a deep learning-based EEG emotion recognition framework, adeptly utilizing the frequency, spatial, and temporal information of EEG data to improve recognition accuracy. The contribution of each individual feature to the prediction probabilities is discussed through machine-learning interpretability based on Shapley values. The study reveals notable differences in brain activation states for identical emotions between the two modes, with VR-3D mode showing more pronounced activation. [ABSTRACT FROM AUTHOR]

In this work, we consider the design of power-constrained networked control systems (NCSs) and a differential entropy-based fault-detection mechanism. For the NCS design of the control loop, we consider faults in the plant gain and unstable plant pole locations, either due to natural causes or malicious intent. Since the power-constrained approach utilized in the NCS design is a stationary approach, we then discuss the finite-time approximation of the power constraints for the relevant control loop signals. The network under study is formed by two additive white Gaussian noise (AWGN) channels located on the direct and feedback paths of the closed control loop. The finite-time approximation of the controller output signal allows us to estimate its differential entropy, which is used in our proposed fault-detection mechanism. After fault detection, we propose a fault-identification mechanism that is capable of correctly discriminating faults. Finally, we discuss the extension of the contributions developed here to future research directions, such as fault recovery and control resilience. [ABSTRACT FROM AUTHOR]

Complex biological systems often undergo sudden qualitative changes during their dynamic evolution. These critical transitions are typically characterized by a catastrophic progression of the system. Identifying the critical point is critical to uncovering the underlying mechanisms of complex biological systems. However, the system may exhibit minimal changes in its state until the critical point is reached, and in the face of high throughput and strong noise data, traditional biomarkers may not be effective in distinguishing the critical state. In this study, we propose a novel approach, mutual information weighted entropy (MIWE), which uses mutual information between genes to build networks and identifies critical states by quantifying molecular dynamic differences at each stage through weighted differential entropy. The method is applied to one numerical simulation dataset and four real datasets, including bulk and single-cell expression datasets. The critical states of the system can be recognized and the robustness of MIWE method is verified by numerical simulation under the influence of different noises. Moreover, we identify two key transcription factors (TFs), CREB1 and CREB3, that regulate downstream signaling genes to coordinate cell fate commitment. The dark genes in the single-cell expression datasets are mined to reveal the potential pathway regulation mechanism. [ABSTRACT FROM AUTHOR]

The study of Shannon differential entropy function and its associated measures using quantile function are of recent interest among researchers. However, a bivariate extension of the same have not been considered so far. Recently, a new method of deriving bivariate quantile function and their properties in the context of reliability modeling is available in literature. Motivated by this, the present paper introduces and obtain some properties of quantile-based entropy function in the bivariate case. We also examine various properties of bivariate quantile entropy function for residual random variables. Finally, we illustrate the bivariate quantile-based residual entropy function using a suitable lifetime data. [ABSTRACT FROM AUTHOR]

We investigate the cumulative Tsallis entropy, an information measure recently introduced as a cumulative version of the classical Tsallis differential entropy, which is itself a generalization of the Boltzmann-Gibbs statistics. This functional is here considered as a perturbation of the expected mean residual life via some power weight function. This point of view leads to the introduction of the dual cumulative Tsallis entropy and of two families of coherent risk measures generalizing those built on mean residual life. We characterize the finiteness of the cumulative Tsallis entropy in terms of L p -spaces and show how they determine the underlying distribution. The range of the functional is exactly described under various constraints, with optimal bounds improving on all those previously available in the literature. Whereas the maximization of the Tsallis differential entropy gives rise to the classical q -Gaussian distribution which is a generalization of the Gaussian having a finite range or heavy tails, the maximization of the cumulative Tsallis entropy leads to an analogous perturbation of the Logistic distribution. [ABSTRACT FROM AUTHOR]

The generalized Kaiser–Bessel window function is defined via the modified Bessel function of the first kind and arises frequently in tomographic image reconstruction. In this paper, we study in details the properties of the Kaiser–Bessel distribution, which we define via the symmetric form of the generalized Kaiser–Bessel window function. The Kaiser–Bessel distribution resembles to the Bessel distribution of McKay of the first type, it is a platykurtic or sub-Gaussian distribution, it is not infinitely divisible in the classical sense and it is an extension of the Wigner's semicircle, parabolic and n-sphere distributions, as well as of the ultra-spherical (or hyper-spherical) and power semicircle distributions. We deduce the moments and absolute moments of this distribution and we find its characteristic and moment generating function in two different ways. In addition, we find its cumulative distribution function in three different ways and we deduce a recurrence relation for the moments and absolute moments. Moreover, by using a formula of Ismail and May on quotient of modified Bessel functions of the first kind, we deduce a closed-form expression for the differential entropy. We also prove that the Kaiser–Bessel distribution belongs to the family of log-concave and geometrically concave distributions, and we study in details the monotonicity and convexity properties of the probability density function with respect to the argument and each of the parameters. In the study of the monotonicity with respect to one of the parameters we complement a known result of Gronwall concerning the logarithmic derivative of modified Bessel functions of the first kind. Finally, we also present a modified method of moments to estimate the parameters of the Kaiser–Bessel distribution, and by using the classical rejection method we present two algorithms for sampling independent continuous random variables of Kaiser–Bessel distribution. The paper is closed with conclusions and proposals for future works. [ABSTRACT FROM AUTHOR]

The recent introduction of geometric partition entropy offered an alternative to differential Shannon entropy for the quantification of uncertainty as estimated from a sample drawn from a one-dimensional bounded continuous probability distribution. In addition to being a fresh perspective for the basis of continuous information theory, this new approach provided several improvements over traditional entropy estimators including its effectiveness on sparse samples and a proper incorporation of the impact from extreme outliers. However, a complimentary relationship exists between the new geometric approach and the basic form of its frequency-based predecessor that is leveraged here to define an entropy measure with no bias toward the sample size. This stable normalized measure is named the Boltzmann–Shannon interaction entropy (BSIE)) as it is defined in terms of a standard divergence between the measure-based and frequency-based distributions that can be associated with the two historical figures. This parameter-free measure can be accurately estimated in a computationally efficient manner, and we illustrate its utility as a quality metric for subsampling in the context of nonlinear polynomial regression. [ABSTRACT FROM AUTHOR]

We investigate the cumulative Tsallis entropy, an information measure recently introduced as a cumulative version of the classical Tsallis differential entropy, which is itself a generalization of the Boltzmann-Gibbs statistics. This functional is here considered as a perturbation of the expected mean residual life via some power weight function. This point of view leads to the introduction of the dual cumulative Tsallis entropy and of two families of coherent risk measures generalizing those built on mean residual life. We characterize the finiteness of the cumulative Tsallis entropy in terms of L p -spaces and show how they determine the underlying distribution. The range of the functional is exactly described under various constraints, with optimal bounds improving on all those previously available in the literature. Whereas the maximization of the Tsallis differential entropy gives rise to the classical q -Gaussian distribution which is a generalization of the Gaussian having a finite range or heavy tails, the maximization of the cumulative Tsallis entropy leads to an analogous perturbation of the Logistic distribution. [ABSTRACT FROM AUTHOR]

This paper explores the concept of residual extropy as an uncertainty measure for order statistics. We specifically derive the residual extropy for the ith-order statistic and establish its relationship with the residual extropy of the ith-order statistic from a random sample generated from a uniform distribution. By employing this approach, we obtain a formula for the residual extropy of order statistics applicable to general continuous distributions. In addition, we offer two lower bounds that can be applied in situations where obtaining closed-form expressions for the residual extropy of order statistics in diverse distributions proves to be challenging. Additionally, we investigate the monotonicity properties of the residual extropy of order statistics. Furthermore, we present other aspects of the residual extropy of order statistics, including its dependence on the position of order statistics and various features of the underlying distribution. [ABSTRACT FROM AUTHOR]

New technologies, such as electric vehicles, rooftop solar, and behind-the-meter storage, will lead to increased variation in electrical load, and the location and time of the penetration of these technologies are uncertain. Power quality, reliability, and protection issues can be the result if electric utilities do not consider the probability of load scenarios that have not yet occurred. The authors' approach to addressing these concerns started with collecting the electrical load data for an expansive and diverse set of distribution transformers. This provided approximately two-and-a-half years of data that were used to develop new methods that will enable engineers to address emerging issues. The efficacy of the methods was then assessed with a real-world test dataset that was not used in the development of the new methods. This resulted in an approach to efficiently generate stochastic electrical load forecasts for elements of distribution circuits. Methods are also described that use those forecasts for engineering analysis that predict the likelihood of distribution transformer failures and power quality events. 100% of the transformers identified as most likely to fail either did fail or identified a data correction opportunity. The accuracy of the power quality results was 92% while allowing for a balance between measures of efficiency and customer satisfaction. [ABSTRACT FROM AUTHOR]

The NP-hard maximum-entropy sampling problem (MESP) seeks a maximum (log-) determinant principal submatrix, of a given order, from an input covariance matrix C. We give an efficient dynamic-programming algorithm for MESP when C (or its inverse) is tridiagonal and generalize it to the situation where the support graph of C (or its inverse) is a spider graph with a constant number of legs (and beyond). We give a class of arrowhead covariance matrices C for which a natural greedy algorithm solves MESP. A mask M for MESP is a correlation matrix with which we pre-process C , by taking the Hadamard product M ∘ C. Upper bounds on MESP with M ∘ C give upper bounds on MESP with C. Most upper-bounding methods are much faster to apply, when the input matrix is tridiagonal, so we consider tridiagonal masks M (which yield tridiagonal M ∘ C). We make a detailed analysis of such tridiagonal masks, and develop a combinatorial local-search based upper-bounding method that takes advantage of fast computations on tridiagonal matrices. [ABSTRACT FROM AUTHOR]

In this paper, we present the derivation of Jeffreys divergence, generalized Fisher divergence, and the corresponding De Bruijn identities for space–time random field. First, we establish the connection between Jeffreys divergence and generalized Fisher information of a single space–time random field with respect to time and space variables. Furthermore, we obtain the Jeffreys divergence between two space–time random fields obtained by different parameters under the same Fokker–Planck equations. Then, the identities between the partial derivatives of the Jeffreys divergence with respect to space–time variables and the generalized Fisher divergence are found, also known as the De Bruijn identities. Later, at the end of the paper, we present three examples of the Fokker–Planck equations on space–time random fields, identify their density functions, and derive the Jeffreys divergence, generalized Fisher information, generalized Fisher divergence, and their corresponding De Bruijn identities. [ABSTRACT FROM AUTHOR]

(1) Background: Emotion recognition based on EEG signals is a rapidly growing and promising research field in affective computing. However, traditional methods have focused on single-channel features that reflect time-domain or frequency-domain information of the EEG, as well as bi-channel features that reveal channel-wise relationships across brain regions. Despite these efforts, the mechanism of mutual interactions between EEG rhythms under different emotional expressions remains largely unexplored. Currently, the primary form of information interaction between EEG rhythms is phase–amplitude coupling (PAC), which results in computational complexity and high computational cost. (2) Methods: To address this issue, we proposed a method of extracting inter-bands correlation (IBC) features via canonical correlation analysis (CCA) based on differential entropy ( D E ) features. This approach eliminates the need for surrogate testing and reduces computational complexity. (3) Results: Our experiments verified the effectiveness of IBC features through several tests, demonstrating that the more correlated features between EEG frequency bands contribute more to emotion classification accuracy. We then fused IBC features and traditional DE features at the decision level, which significantly improved the accuracy of emotion recognition on the SEED dataset and the local CUMULATE dataset compared to using a single feature alone. (4) Conclusions: These findings suggest that IBC features are a promising approach to promoting emotion recognition accuracy. By exploring the mutual interactions between EEG rhythms under different emotional expressions, our method can provide valuable insights into the underlying mechanisms of emotion processing and improve the performance of emotion recognition systems. [ABSTRACT FROM AUTHOR]

Every nonlinear system grows by increments, and the final probability distributions for components of that system emerge from an amalgamation of these increments. The resulting probability distribution depends on the constraints imposed on each increment by the physical and chemical processes that produce the system. Hence there is the potential that the observed probability distribution can reveal information on these processes. Complex systems that grow by competition between the supply and consumption of energy and mass have growth laws that are cumulative probability distributions for their component parts that reflect such competition. We show that the type of probability distribution is characteristic of the endowment of orogenic gold deposits with the sequence: Weibull → Fréchet → gamma → log normal representative of increasing endowment. Further, the differential entropy of the probability distribution is indicative of the quality of the deposit, with low-quality deposits represented by high entropy and high-quality deposits represented by low or negative entropy. The type of probability distribution gives an indication of the processes that operated to produce the deposit. These conclusions hold for mineralisation as well as for the associated alteration assemblages. We suggest that the probability distribution for the mineralisation or the alteration assemblage gives a good indication of the endowment and quality of a deposit from a single drill hole. A single drill hole from a deposit can provide information on endowment and organisation. Weibull → Fréchet → gamma → log normal probability distributions are representative of increasing gold endowment. The differential entropies of these distributions characterise the organisation of the system. [ABSTRACT FROM AUTHOR]

The increasing penetration of renewable-based generation in the distribution network adds randomness to the bus voltage due to its stochastic characteristics. Consequently, the distribution network faces voltage limit violations at multiple buses. In this scenario, the traditional voltage control method fails to maintain the voltage profile of the network due to its slow response time. A fast and dynamic voltage control technique can be achieved by utilizing the voltage-controlling capability of available DGs in the network with the information about the impact of DG-integrated bus on change in voltage at any bus in the network. Evaluating this information using the traditional probabilistic load flow method is computationally inefficient for real-time applications. Therefore, in this paper, a principal component analysis (PCA)-based novel probabilistic voltage sensitivity index (PVSI) is proposed. It ranks the DG-integrated buses by evaluating the impact of power perturbation at DG-integrated buses on changes in voltage at any bus in the network. The PVSI is analytically derived to reduce the computation time for ranking. Further, the proposed PVSI is validated on the 69-bus and the 141-bus distribution systems by comparing it with the traditional Monte Carlo simulation (MCS) and joint differential entropy (JDE) in terms of accuracy and computation time. From the simulation, it is observed that PVSI gives a similar ranking as both methods in less computation time. Due to the advantage in computation time, the proposed method enables the distribution system operator (DSO) to use this information for fast and dynamic voltage control in a real-time scenario. [ABSTRACT FROM AUTHOR]

The main aim of this article is to establish an effective criterion for a positive parametric topological entropy to differential equations with multivalued nonautonomous impulses on tori. The crucial tool for this goal consists in developing an appropriate Ivanov-like inequality for the lower estimate of a new kind of entropy by means of the logarithm of asymptotic Nielsen numbers for the compositions of a one-parameter family of multivalued admissible maps. This inequality is then applied to impulsive differential equations on tori via the associated Poincaré translation operators along their trajectories. The obtained results generalize in a significant way those in our recent papers, especially in the one with the same title (whence the indication by II), into a multivalued setting. Another nontrivial generalization can be regarded with respect to their simple reduction into a "nonparametric" case. [ABSTRACT FROM AUTHOR]

Electroencephalogram (EEG) signals exhibit low amplitude, complex background noise, randomness, and significant inter-individual differences, which pose challenges in extracting sufficient features and can lead to information loss during the mapping process from low-dimensional feature matrices to high-dimensional ones in emotion recognition algorithms. In this paper, we propose a Multi-scale Deformable Convolutional Interacting Attention Network based on Residual Network (MDCNAResnet) for EEG-based emotion recognition. Firstly, we extract differential entropy features from different channels of EEG signals and construct a three-dimensional feature matrix based on the relative positions of electrode channels. Secondly, we utilize deformable convolution (DCN) to extract high-level abstract features by replacing standard convolution with deformable convolution, enhancing the modeling capability of the convolutional neural network for irregular targets. Then, we develop the Bottom-Up Feature Pyramid Network (BU-FPN) to extract multi-scale data features, enabling complementary information from different levels in the neural network, while optimizing the feature extraction process using Efficient Channel Attention (ECANet). Finally, we combine the MDCNAResnet with a Bidirectional Gated Recurrent Unit (BiGRU) to further capture the contextual semantic information of EEG signals. Experimental results on the DEAP dataset demonstrate the effectiveness of our approach, achieving accuracies of 98.63% and 98.89% for Valence and Arousal dimensions, respectively. [ABSTRACT FROM AUTHOR]

We propose Choquet regularizers to measure and manage the level of exploration for reinforcement learning (RL) and reformulate the continuous-time entropy-regularized RL problem of H. Wang, T. Zariphopoulou, and X. Zhou [J. Mach. Learn. Res., 21 (2020), pp. 1--34] in which we replace the differential entropy used for regularization with a Choquet regularizer. We derive the Hamilton--Jacobi--Bellman equation of the problem and solve it explicitly in the linear-quadratic (LQ) case via maximizing statically a mean-variance constrained Choquet regularizer. Under the LQ setting, we derive explicit optimal distributions for several specific Choquet regularizers and conversely identify the Choquet regularizers that generate a number of broadly used exploratory samplers, such as\varepsilon-greedy, exponential, uniform, and Gaussian. [ABSTRACT FROM AUTHOR]

Response times (RT) distributions are routinely used by psychologists and neuroscientists in the assessment and modeling of human behavior and cognition. The statistical properties of RT distributions are valuable in uncovering unobservable psychological mechanisms. A potentially important statistical aspect of RT distributions is their entropy. However, to date, no valid measure of entropy on RT distributions has been developed, mainly because available extensions of discrete entropy measures to continuous distributions were fraught with problems and inconsistencies. The present work takes advantage of the cumulative residual entropy (CRE) function—a well-known differential entropy measure that can circumvent those problems. Applications of the CRE to RT distributions are presented along with concrete examples and simulations. In addition, a novel measure of instantaneous CRE is developed that captures the rate of entropy reduction (or information gain) from a stimulus as a function of processing time. Taken together, the new measures of entropy in RT distributions proposed here allow for stronger statistical inferences, as well as motivated theoretical interpretations of psychological constructs such as mental effort and processing efficiency. [ABSTRACT FROM AUTHOR]

A fundamental factor in relevant applications is the predictability of the life cycle of a coherent system consisting of more than one component. In this context, we examine how entropy can be applied to evaluate the degree of predictability. In particular, in order to calculate the Tsallis entropy of the past life, we consider a scenario in which all components of the system fail at a given time t and use the system signature to calculate the Tsallis entropy of the past life. We examine a number of analytical results, e.g., expressions, thresholds and orders for the measure at issue in our study. The results may provide insights into the predictability of a coherent system's life cycle. [ABSTRACT FROM AUTHOR]

We calculate differential Shannon entropies derived from time-dependent coordinate-space and momentum-space probability densities. This is performed for a prototype system of a coupled electron–nuclear motion. Two situations are considered, where one is a Born–Oppenheimer adiabatic dynamics, and the other is a diabatic motion involving strong non-adiabatic transitions. The information about coordinate- and momentum-space dynamics derived from the total and single-particle entropies is discussed and interpreted with the help of analytical models. From the entropies, we derive mutual information, which is a measure for the electron–nuclear correlation. In the adiabatic case, it is found that such correlations are manifested differently in coordinate- and momentum space. For the diabatic dynamics, we show that it is possible to decompose the entropies into state-specific contributions. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to investigate a parametric topological entropy for impulsive differential inclusions on tori. In this way, besides other matters, we would like to extend our recent results concerning impulsive differential equations as well as those on "nonparametric" topological entropy to impulsive differential inclusions. Parametric topological entropy, which is usually called a topological entropy for nonautonomous dynamical systems, is considered here via the compositions of associated multivalued Poincaré translation operators with the single-valued time-dependent impulsive maps. On compact polyhedra and, in particular on tori, parametric topological entropy for families of admissible multivalued maps can be estimated from below by means Ivanov-type inequality in terms of the asymptotic Nielsen and Lefschetz numbers which are, unlike the topological entropy, homotopy invariants. In the scalar case, an effective criterion for a positive parametric topological entropy can be given by topological degree arguments for equi-continuous impulsive maps. In a single-valued nonparametric case, a positive topological entropy usually signifies topological chaos. Some simple illustrative examples are provided. [ABSTRACT FROM AUTHOR]

Suppose we have n experts who have their prior opinion about the unknown probability q in the experiment with a binary outcome. It is known that experts' opinions are in conflict with each other. To model "conflicting" experts' opinions a prior distribution based on Selberg's integral is constructed. We prove a theorem regarding the limiting properties of the posterior distribution. Also, differential entropy and Kullback-Leibler (KL) divergence of such posterior are studied. [ABSTRACT FROM AUTHOR]

Objectives: In order to ensure the reliability of underwater gravity matching navigation,a suitability analysis method of gravity matching navigation based on multiple attribute decision making theory is proposed, which is to solve the defect of incomplete evaluation results caused by a single feature index as a suitability analysis criterion. Methods: First, six main characteristic parameters, such as standard deviation of gravity field, roughness, correlation coefficient, slope standard deviation, skew coefficient and differential entropy of gravitational anomalies, are used as attribute sets for weighted normalization, so that the decision index is obtained to rank the suitability of the matching region, and the most excellent suitability area is evaluated by constructing the relative fit.Second, in the same conditions, we compare the simulation results of gravity matching in each region to be matched. Results: The results show that the matching effect is more stable in the higher decision-making index area, and the most excellent suitability area could be directly screened, The matching degree of decision results with navigation results is as high as 80%, the decision- making results of the method have good consistency with the accuracy of the matching experiment. Conclusions: The reliability of the method is high, so it could solve the problem of less information of a single feature index, and provide an important guarantee for the long-term voyage of underwater submersibles. [ABSTRACT FROM AUTHOR]

In parallel with the concept of Rényi entropy for residual lifetime distributions, the Rényi entropy of inactivity time of lifetime distributions belonging to asymmetric distributions is a useful measure of independent interest. For a system that turns out to be inactive in time t, the past entropy is considered as an uncertainty measure for the past lifetime distribution. In this study, we consider a coherent system that includes n components and has the property that all the components of the system have failed at time t. To assess the predictability of the coherent system's lifetime, we use the system's signature to determine the Rényi entropy of its past lifetime. We study several analytical results, including expressions, bounds, and order properties for this measure. [ABSTRACT FROM AUTHOR]

Emotion recognition is one of the most researched fields in today's scientific world. It is a subject that is closely examined by disciplines such as neuroscience and psychology, and it is more and more involved in our daily lives, especially in human-computer interaction area. Although methods such as speech signals, facial expressions, body language, and facial expressions are used for emotion analysis, these methods do not give as reliable results as biological signals because they are open to manipulation. In this study, a new method for emotion recognition with electroencephalography (EEG) signals, which is a bioelectrical signal prepared with the help of virtual reality (VR) technology, is proposed. In this method, differential entropy (DE) and phase-locking value (PLV) properties of sub-bands of EEG signals were used to recognize positive and negative emotions with the help of a designed one-dimensional convolutional neural network (1D-CNN). The feature matrices obtained with the help of both features were tested ten times and average accuracy values were obtained. As a result of these tests, the highest average accuracy scores with DE and FKD features were obtained as 74.061±1.41% and 63.7590±1.72%, respectively, by combining all sub-band feature matrices. In addition, the higher accuracy rates of the tests of the high-frequency signal components obtained in the study compared to the low-frequency bands, supported the results of similar studies carried out in this area before. [ABSTRACT FROM AUTHOR]

In recent years, artificial intelligence (AI) technology has promoted the development of electroencephalogram (EEG) emotion recognition. However, existing methods often overlook the computational cost of EEG emotion recognition, and there is still room for improvement in the accuracy of EEG emotion recognition. In this study, we propose a novel EEG emotion recognition algorithm called FCAN–XGBoost, which is a fusion of two algorithms, FCAN and XGBoost. The FCAN module is a feature attention network (FANet) that we have proposed for the first time, which processes the differential entropy (DE) and power spectral density (PSD) features extracted from the four frequency bands of the EEG signal and performs feature fusion and deep feature extraction. Finally, the deep features are fed into the eXtreme Gradient Boosting (XGBoost) algorithm to classify the four emotions. We evaluated the proposed method on the DEAP and DREAMER datasets and achieved a four-category emotion recognition accuracy of 95.26% and 94.05%, respectively. Additionally, our proposed method reduces the computational cost of EEG emotion recognition by at least 75.45% for computation time and 67.51% for memory occupation. The performance of FCAN–XGBoost outperforms the state-of-the-art four-category model and reduces computational costs without losing classification performance compared with other models. [ABSTRACT FROM AUTHOR]

In recent years, there has been a growing interest in the study of emotion recognition through electroencephalogram (EEG) signals. One particular group of interest are individuals with hearing impairments, who may have a bias towards certain types of information when communicating with those in their environment. To address this, our study collected EEG signals from both hearing-impaired and non-hearing-impaired subjects while they viewed pictures of emotional faces for emotion recognition. Four kinds of feature matrices, symmetry difference, and symmetry quotient based on original signal and differential entropy (DE) were constructed, respectively, to extract the spatial domain information. The multi-axis self-attention classification model was proposed, which consists of local attention and global attention, combining the attention model with convolution through a novel architectural element for feature classification. Three-classification (positive, neutral, negative) and five-classification (happy, neutral, sad, angry, fearful) tasks of emotion recognition were carried out. The experimental results show that the proposed method is superior to the original feature method, and the multi-feature fusion achieved a good effect in both hearing-impaired and non-hearing-impaired subjects. The average classification accuracy for hearing-impaired subjects and non-hearing-impaired subjects was 70.2% (three-classification) and 50.15% (five-classification), and 72.05% (three-classification) and 51.53% (five-classification), respectively. In addition, by exploring the brain topography of different emotions, we found that the discriminative brain regions of the hearing-impaired subjects were also distributed in the parietal lobe, unlike those of the non-hearing-impaired subjects. [ABSTRACT FROM AUTHOR]

For a given system observed at time t, the past entropy serves as an uncertainty measure about the past life-time of the distribution. We consider a coherent system in which there are n components that have all failed at time t. To assess the predictability of the life-time of such a system, we use the signature vector to determine the entropy of its past life-time. We explore various analytical results, including expressions, bounds, and order properties, for this measure. Our results provide valuable insight into the predictability of the coherent system's life-time, which may be useful in a number of practical applications. [ABSTRACT FROM AUTHOR]

In this work, we reveal some distributional traits of concomitants of order statistics (COSs) arising from the extended Farlie–Gumbel–Morgenstern (FGM) bivariate distribution, which was developed and studied in recent work. The joint distribution and product moments of COSs for this family are discussed. Moreover, some useful recurrence relations between single and product moments of concomitants are obtained. In addition, the asymptotic behavior of the concomitant's rank for order statistics (OSs) is studied. The information measures, differential entropy, Kullback–Leibler (KL) distance, Fisher information number (FIN), and cumulative past inaccuracy (CPI) are theoretically and numerically studied. [ABSTRACT FROM AUTHOR]

In recent years, deep learning has gradually become a prevailing way in EEG-based emotion recognition research because it can extract features and classify emotions automatically. To fully exploit the underlying information in EEG signals, we propose an emotion recognition method based on cascaded convolutional recurrent neural networks. Firstly, the differential entropy features of each channel signal are transformed into four-dimensional structure data, which are able to contain temporal-spatial-frequency information integratively. Then, the cascaded VGG16 and long short-term memory (LSTM) networks are applied to learn the spatiotemporal information of the samples, and the hidden layer of the last node of LSTM is output to a linear transformation classifier to perform classification. On DEAP dataset, the proposed method gives out an average accuracy of 94.43% and 94.85% in arousal-based and valence-based classification, respectively. On SEED dataset, the method achieves average accuracy of 94.16%. Compared with the existing methods, our method demonstrates superior performances in emotion recognition. [ABSTRACT FROM AUTHOR]

In this article, we propose three nonparametric estimators for quantile-based Shannon differential entropy function for complete samples. Asymptotic properties of the estimators are established under suitable regularity conditions. Simulation study are carried out to compare the performance of the proposed estimators and with other important entropy estimators. The usefulness of the new estimators are also illustrated using real data sets. [ABSTRACT FROM AUTHOR]

Effect of dynamics of site energy disorder on charge transport in organic molecular semiconductors is not yet well-established. In order to study the relationship between the dynamics of site energy disorder and charge transport, we have performed a multiscale study on dialkyl substituted thienothiophene capped benzobisthiazole (BDHTT-BBT) and methyl-substituted dicyanovinyl-capped quinquethiophene (DCV5T-Me) molecular solids. In this study, we explore the structural dynamics and correlated charge transport by electronic structure calculations, molecular dynamics, and kinetic Monte-Carlo simulations. We have also proposed the differential entropy dependent diffusion and charge density equations to study the electric field drifted diffusion property and carrier density. In this investigation, we have addressed the transformation mechanism from dynamic to static disorder in the extended stacked molecular units. Here, the decrease in the charge transfer rate due to site energy fluctuations reveals the dispersion transport along the extended π-stacked molecules. Furthermore, the calculated current density for a different set of site energy difference values shows the validity and the limitations of the Einstein relation. Based on the calculated ideality factor, we have classified the charge transport in these molecules as either the Langevin or the Shockley-Read-Hall type mechanism. Through the calculated mobility, current density, and ideality factor analysis, we categorize the applicability of molecules of interest for photovoltaic or light emitting diode applications. [ABSTRACT FROM AUTHOR]

We derive some quantum central limit theorems for the expectation values of macroscopically coarse-grained observables, which are functions of coarse-grained Hermitian operators consisting of non-commuting variables. Thanks to the Hermiticity constraints, we obtain positive-definite distributions for the expectation values of observables. These probability distributions open some pathway for the emergence of classical behaviours in the limit of an infinitely large number of identical and non-interacting quantum constituents. This is in contradistinction to other mechanisms of classicality emergence due to environmental decoherence and consistent histories. The probability distributions thus derived also enable us to evaluate the non-trivial time-dependence of certain differential entropies. [ABSTRACT FROM AUTHOR]

In the teleparallel f (T) gravity scenario, we consider a five-dimensional thick brane. This scenario is interesting because this theory can provide explanations for inflation, radiation and dark matter under certain conditions. It is convenient to assume, for our study, a polynomial profile of the function f (T). Indeed, some polynomial profiles can produce internal structures for which a brane splitting occurs. For functions f (T) with this capability, geometrically contracted matter field configurations are obtained. These contractions of the matter field for the profiles of f (T) reproduce compact-like settings. To complement the study, we analyze the stability of the brane using the concept of Configurational Entropy (CE). The CE arguments are interesting because they tell us the most stable and likely configurations from the brane in this gravitational background. Therefore, we can indicate the best profile of the function f (T). [ABSTRACT FROM AUTHOR]

Because of its ability to objectively reflect people's emotional states, electroencephalogram (EEG) has been attracting increasing research attention for emotion classification. The classification method based on spatial-domain analysis is one of the research hotspots. However, most previous studies ignored the complementarity of information between different frequency bands, and the information in a single frequency band is not fully mined, which increases the computational time and the difficulty of improving classification accuracy. To address the above problems, this study proposes an emotion classification method based on dynamic simplifying graph convolutional (SGC) networks and a style recalibration module (SRM) for channels, termed SGC-SRM, with multi-band EEG data as input. Specifically, first, the graph structure is constructed using the differential entropy characteristics of each sub-band and the internal relationship between different channels is dynamically learned through SGC networks. Second, a convolution layer based on the SRM is introduced to recalibrate channel features to extract more emotion-related features. Third, the extracted sub-band features are fused at the feature level and classified. In addition, to reduce the redundant information between EEG channels and the computational time, (1) we adopt only 12 channels that are suitable for emotion classification to optimize the recognition algorithm, which can save approximately 90.5% of the time cost compared with using all channels; (2) we adopt information in the θ, α, β, and γ bands, consequently saving 23.3% of the time consumed compared with that in the full bands while maintaining almost the same level of classification accuracy. Finally, a subject-independent experiment is conducted on the public SEED dataset using the leave-one-subject-out cross-validation strategy. According to experimental results, SGC-SRM improves classification accuracy by 5.51–15.43% compared with existing methods. [ABSTRACT FROM AUTHOR]

The Gaussian law reigns supreme in the information theory of analog random variables. This paper showcases a number of information theoretic results which find elegant counterparts for Cauchy distributions. New concepts such as that of equivalent pairs of probability measures and the strength of real-valued random variables are introduced here and shown to be of particular relevance to Cauchy distributions. [ABSTRACT FROM AUTHOR]

The high cost of acquiring training data in the field of emotion recognition based on electroencephalogram (EEG) is a problem, making it difficult to establish a high-precision model from EEG signals for emotion recognition tasks. Given the outstanding performance of generative adversarial networks (GANs) in data augmentation in recent years, this paper proposes a task-driven method based on CWGAN to generate high-quality artificial data. The generated data are represented as multi-channel EEG data differential entropy feature maps, and a task network (emotion classifier) is introduced to guide the generator during the adversarial training. The evaluation results show that the proposed method can generate artificial data with clearer classifications and distributions that are more similar to the real data, resulting in obvious improvements in EEG-based emotion recognition tasks. [ABSTRACT FROM AUTHOR]

With the development of image recovery models, especially those based on adversarial and perceptual losses, the detailed texture portions of images are being recovered more naturally. However, these restored images are similar but not identical in detail texture to their reference images. With traditional image quality assessment methods, results with better subjective perceived quality often score lower in objective scoring. Assessment methods suffer from subjective and objective inconsistencies. This paper proposes a regional differential information entropy (RDIE) method for image quality assessment to address this problem. This approach allows better assessment of similar but not identical textural details and achieves good agreement with perceived quality. Neural networks are used to reshape the process of calculating information entropy, improving the speed and efficiency of the operation. Experiments conducted with this study's image quality assessment dataset and the PIPAL dataset show that the proposed RDIE method yields a high degree of agreement with people's average opinion scores compared with other image quality assessment metrics, proving that RDIE can better quantify the perceived quality of images. [ABSTRACT FROM AUTHOR]

The evaluation of the information entropy content in the data analysis is an effective role in the assessment of fatigue damage. Due to the connection between the generalized half-normal distribution and fatigue extension, the objective inference for the differential entropy of the generalized half-normal distribution is considered in this paper. The Bayesian estimates and associated credible intervals are discussed based on different non-informative priors including Jeffery, reference, probability matching, and maximal data information priors for the differential entropy measure. The Metropolis–Hastings samplers data sets are used to estimate the posterior densities and then compute the Bayesian estimates. For comparison purposes, the maximum likelihood estimators and asymptotic confidence intervals of the differential entropy are derived. An intensive simulation study is conducted to evaluate the performance of the proposed statistical inference methods. Two real data sets are analyzed by the proposed methodology for illustrative purposes as well. Finally, non-informative priors for the original parameters of generalized half-normal distribution based on the direct and transformation of the entropy measure are also proposed and compared. [ABSTRACT FROM AUTHOR]

The state of charge (SOC) is critical for the safety and reliable utilization of the battery. However, SOC estimation accuracy of lithium iron phosphate (LiFePO4) battery is a challenging task because of its flat voltage plateau and its performance is affected greatly by temperature. An improved open circuit voltage (OCV) combined with coulomb counting (CC) method based on the dual input model of ambient temperature and OCV is proposed. This approach is employed to obtain the initial value of SOC based on the dual input model over a wide range of temperature, and to establish SOC estimation model of modified CC with Simulink. The temperature entropy coefficient and differential analysis has been analyzed under different SOC conditions. The SOC maximum errors predicted by the proposed OCV-CC method maintain within 3.10%, while the maximum errors of the traditional OCV-CC increase from 4.78% to 23.64% under the temperature of 35°C ~−15°C. The results show the estimation accuracy of SOC using the proposed OCV-CC method is improved obviously, especially under low temperature. [ABSTRACT FROM AUTHOR]

Adult attention deficit/hyperactivity disorder (ADHD), schizophrenia (SCHZ), and bipolar disorder (BP) have common symptoms and differences, and the underlying neural mechanisms are still unclear. This article will thoroughly discuss the differences between ADHD, BP, and SCHZ (31 healthy control and 31 ADHD; 34 healthy control and 34 BP; 42 healthy control and 42 SCHZ) relative to healthy subjects in combination with three atlases (et al., the Brainnetome atlas, the Dosenbach atlas, the Power atlas) and seven entropies (et al., approximate entropy (ApEn), sample entropy (SaEn), permutation entropy (PeEn), fuzzy entropy (FuEn), differential entropy (DiffEn), range entropy (RaEn), and dispersion entropy (DispEn)), as well as the prominent significant brain regions, in the hope of giving information that is more suitable for analyzing different diseases' entropy. First, the reliability (et al., intraclass correlation coefficient [ICC]) of seven kinds of entropy is calculated and analyzed by using the MSC dataset (10 subjects and 100 sessions in total) and simulation data; then, seven types of entropy and multiscale entropy expanded based on seven kinds of entropy are used to explore the differences and brain regions of ADHD, BP, and SCHZ relative to healthy subjects; and finally, by verifying the classification performance of the seven information entropies on ADHD, BP, and SCHZ, the effectiveness of the seven entropy methods is evaluated through these three methods. The core brain regions that affect the classification are given, and DiffEn performed best on ADHD, SaEn for BP, and RaEn for SCHZ. [ABSTRACT FROM AUTHOR]

On the background of a brief survey panorama of results on the topic in the title, one new theorem is presented concerning a positive topological entropy (i.e. topological chaos) for the impulsive differential equations on the Cartesian product of compact intervals, which is positively invariant under the composition of the associated Poincaré translation operator with a multivalued upper semicontinuous impulsive mapping. [ABSTRACT FROM AUTHOR]

In this paper, we propose nonparametric kernel estimators for Shannon differential entropy function under length-biased sampling. Asymptotic properties of the estimators are established under suitable regularity conditions. A simulation study is accomplished to compare the performance of proposed estimators. The usefulness of the estimators are also examined using a real data. [ABSTRACT FROM AUTHOR]

Graph convolutional neural networks (GCN) have attracted much attention in the task of electroencephalogram (EEG) emotion recognition. However, most features of current GCNs do not take full advantage of the causal connection between the EEG signals in different frequency bands during the process of constructing the adjacency matrix. Based on the causal connectivity between the EEG channels obtained by Granger causality (GC) analysis, this paper proposes a multi-frequency band EEG graph feature extraction and fusion method for EEG emotion recognition. First, the original GC matrices between the EEG signals at each frequency band are calculated via GC analysis, and then they are adaptively converted to asymmetric binary GC matrices through an optimal threshold. Then, a kind of novel GC-based GCN feature (GC-GCN) is constructed by using differential entropy features and the binary GC matrices as the node values and adjacency matrices, respectively. Finally, on the basis of the GC-GCN features, a new multi-frequency band feature fusion method (GC-F-GCN) is proposed, which integrates the graph information of the EEG signals at different frequency bands for the same node. The experimental results demonstrate that the proposed GC-F-GCN method achieves better recognition performance than the state-of-the-art GCN methods, for which average accuracies of 97.91%, 98.46%, and 98.15% were achieved for the arousal, valence, and arousal–valence classifications, respectively. [ABSTRACT FROM AUTHOR]

The entropy power inequality (EPI) and the Brascamp-Lieb inequality (BLI) are fundamental inequalities concerning the differential entropies of linear transformations of random vectors. The EPI provides lower bounds for the differential entropy of linear transformations of random vectors with independent components. The BLI, on the other hand, provides upper bounds on the differential entropy of a random vector in terms of the differential entropies of some of its linear transformations. In this paper, we define a family of entropy functionals, which we show are subadditive. We then establish that Gaussians are extremal for these functionals by adapting a proof technique from Geng and Nair (2014). As a consequence, we obtain a new entropy inequality that generalizes both the BLI and EPI. By considering a variety of independence relations among the components of the random vectors appearing in these functionals, we also obtain families of inequalities that lie between the EPI and the BLI. [ABSTRACT FROM AUTHOR]

The flow of a fluid across a revolving disc has several technical and industrial uses. Examples of rotating disc flows include centrifugal pumps, viscometers, rotors, fans, turbines, and spinning discs. An important technology with implications for numerous treatments utilized in numerous sectors is the use of hybrid nanofluids (HNFs) to accelerate current advancements. Through investigation of ternary nanoparticle impacts on heat transfer (HT) and liquid movement, the thermal properties of tri-HNFs were to be ascertained in this study. Hall current, thermal radiation, and heat dissipation have all been studied in relation to the use of flow-describing equations. The ternary HNFs under research are composed of the nanomolecules aluminum oxide (Al2O3), copper oxide (CuO), silver (Ag), and water (H2O). For a number of significant physical characteristics, the physical situation is represented utilizing the boundary layer investigation, which produces partial differential equations (PDEs). The rheology of the movement is extended and computed in a revolving setting under the assumption that the movement is caused by a rotatingfloppy. Before the solution was found using the finite difference method, complicated generated PDEs were transformed into corresponding ODEs (Keller Box method). A rise in the implicated influencing factors has numerous notable physical impacts that have been seen and recorded. The Keller Box method (KBM) approach is also delivered for simulating the determination of nonlinear system problems faced in developing liquid and supplementary algebraic dynamics domains. The rate of entropy formation rises as the magnetic field parameter and radiation parameter increase. Entropy production rate decreases as the Brinkman number and Hall current parameter become more enriched. The thermal efficiency of ternary HNFs compared to conventional HNFs losses to a low of 4.8% and peaks to 5.2%. [ABSTRACT FROM AUTHOR]

The present study investigated the thermodynamic properties of Mefenamic acid tablets at three temperatures (25, 35, 45oC) based on the experimental sorption data studied earlier in a previous study. The net isosteric heat of adsorption and the differential entropy were found to decrease as the water activity increases. A 4th order polynomial equation described both of them. A linear enthalpy-entropy relationship is disclosed with 95.6 % correlation factor. The isokinetic temperature was differed significantly from the harmonic mean temperature implying the linear enthalpy-entropy compensation and enthalpy drawn adsorption process. The enthalpies associated to GAB's model (GAB: Guggenhein - Anderson and de Boer) were also investigated and discussed. [ABSTRACT FROM AUTHOR]