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This study focuses on developing a medical testing equipment management system based on artificial intelligence. The system integrates advanced sensor technology to monitor patient's physiological characteristics data in real-time, such as heart rate, blood pressure, body temperature, etc. and processes the data through a differential entropy analysis algorithm to extract key health indicators. Then, this study constructed a deep learning neural network model to predict the changing trend of patient health status and optimized the configuration and use of medical detection equipment accordingly. This paper proposes a feature extraction method based on neural network model, which can effectively identify abnormal patterns in physiological signals and provide high-quality input data for subsequent prediction models. Simulation results show that the proposed neural network model has high accuracy and practicability in predicting patients' health status. The model can assist healthcare workers in identifying potential health risks in time to improve treatment results and patients' quality of life. [ABSTRACT FROM AUTHOR]

Decoding human internal emotional states based on EEG (Electroencephalogram) and surrounding physiological signals is key in the field of emotional computing, but the performance of machine learning models using EEG or surrounding physiological signal modes may be limited. In this study, a multi-mode fusion strategy is proposed based on the single mode method. The differential entropy, statistical and complexity features are extracted from each EEG fragment, and these features are properly integrated with the surrounding physiological signals. Multiple modal features recorded in the DEAP (Database for Emotion Analysis using Physiological Signals) data set are incorporated in the proposed method. In terms of titer, the experimental accuracy of single EEG feature is 49.21%, the classification accuracy of two types of feature fusion is 56.39%, 55.24% and 56.98%, and the experimental accuracy of three types of mode fusion is 56.98%. In terms of arousal, the experimental accuracy of single EEG feature is 49.34%, the classification accuracy of two types of feature fusion is 54.53%, 54.53% and 59.39%, and the experimental accuracy of three types of feature fusion is 55.48%. The experimental results show that the classification accuracy of multi-modal features after the fusion of EEG features and peripheral physiological features is the highest, and the classification accuracy is improved by 7.77% and 10.05%, respectively, compared with the single EEG features. [ABSTRACT FROM AUTHOR]

Alzheimer's disease (AD) stands out as the most prevalent neurological brain disorder, and its diagnosis relies on various laboratory techniques. The electroencephalogram (EEG) emerges as a valuable tool for identifying AD, offering a quick, cost-effective, and readily accessible means of detecting early-stage dementia. Detecting AD in its early stages is crucial, as early intervention yields more successful outcomes and entails fewer risks than treating the disease at a later stage. The objective of this research is to create an advanced diagnosis system for AD using machine learning (ML) and EEG data. The proposed system utilizes a multilayer perceptron (MLP) and a deep neural network with bidirectional long short-term memory (BiLSTM) as the classifier. The feature extraction process involves incorporating Hjorth parameters, power spectral density (PSD), differential asymmetry (DASM), and differential entropy (DE). The BiLSTM classifier, particularly when combined with DE, exhibits outstanding performance with an accuracy of 97.27%. This amalgamation of DE and the deep neural network surpasses current state-of-the-art techniques, underscoring the substantial potential of this approach for precise and advanced diagnosis of AD. [ABSTRACT FROM AUTHOR]

AbstractVariance-based Sobol’ sensitivity is one of the most well-known measures in global sensitivity analysis (GSA). However, uncertainties with certain distributions, such as highly skewed distributions or those with a heavy tail, cannot be adequately characterised using the second central moment only. Entropy-based GSA can consider the entire probability density function, but its application has been limited because it is difficult to estimate. Here we present a novel derivative-based upper bound for conditional entropies, to efficiently rank uncertain variables and to work as a proxy for entropy-based total effect indices. To overcome the non-desirable issue of negativity for differential entropies as sensitivity indices, we discuss an exponentiation of the total effect entropy and its proxy. Numerical verifications demonstrate that the upper bound is tight for monotonic functions and it provides the same input variable ranking as the entropy-based indices for about three-quarters of the 1000 random functions tested. We found that the new entropy proxy performs similarly to the variance-based proxies for a river flood physics model with 8 inputs of different distributions, and these two proxies are equivalent in the special case of linear functions with Gaussian inputs. We expect the new entropy proxy to increase the variable screening power of derivative-based GSA and to complement Sobol’-indices proxy for a more diverse type of distributions. [ABSTRACT FROM AUTHOR]

In this research, we delve into the localization patterns of fermionic fields within a braneworld setting, employing a modified gravity model denoted as f (Q). Our investigation revolves around two specific models, f 1 (Q) = Q + k Q n and f 2 (Q) = Q + k 1 Q 2 + k 2 Q 3 , where we systematically vary the parameters n and k 1 , 2 . Through an in-depth analysis encompassing the effective potential, massless, and massive modes, we elucidate how deviations from the conventional Symmetric Teleparallel Equivalent of General Relativity (STEGR) gravity impact the localization of fermionic fields. To ensure greater precision, our methodology integrates probabilistic measures such as Shannon entropy and relative probability. Moreover, we gauge the stability of these models employing Differential Configurational Entropy (DCE), revealing a compelling correlation between the most stable configurations and the emergence of novel structures within the background scalar field. This work significantly contributes to our understanding of the gravitational modifications' intricate influence on fermionic field localization within braneworld scenarios. By shedding light on these dynamics, it advances the broader comprehension of the interplay between gravity modifications and fermionic field behaviors in these theoretical frameworks. [ABSTRACT FROM AUTHOR]

Stimulated by the need of describing useful notions related to information measures, we introduce the 'pdf-related distributions'. These are defined in terms of transformation of absolutely continuous random variables through their own probability density functions. We investigate their main characteristics, with reference to the general form of the distribution, the quantiles, and some related notions of reliability theory. This allows us to obtain a characterization of the pdf-related distribution being uniform for distributions of exponential and Laplace type as well. We also face the problem of stochastic comparing the pdf-related distributions by resorting to suitable stochastic orders. Finally, the given results are used to analyse properties and to compare some useful information measures, such as the differential entropy and the varentropy. [ABSTRACT FROM AUTHOR]

We deal with two-dimensional copulas from the perspective of their differential entropy. We formulate a problem of finding a copula with maximum differential entropy when some copula values are given. As expected, the solution is a copula with a piecewise constant density (a checkerboard copula). This allows us to simplify the optimization of the continuous objective function, the differential entropy, to an optimization of finitely many density values. We present several ideas to simplify this problem. It has a feasible numerical solution. We also present several instances that admit closed-form solutions. [ABSTRACT FROM AUTHOR]

With increasing remote work and online learning, there is a growing demand for image encryption algorithms with sufficient capacity and efficiency. In this paper, we propose an effective multiimage encryption algorithm. By coupling the Sine map and some useful mathematical functions, we design a two-dimensional hyperchaotic system (2D SFCM). After evaluating different chaos indicators, it is found that the Lyapunov exponent and the permutation entropy of 2D SFCM are significantly higher than those of other chaotic mappings. Additionally, its sample entropy has an average value of 1.916. These results indicate that the chaotic sequences generated by 2D SFCM exhibit a high level of randomness. The pseudo-random sequences generated by this chaotic system are combined with image encryption algorithms to shuffle 3D images by accessing pixels from different planes. Using randomly determined pixel points, cyclic diffusion is performed on each plane to ensure that the pixel information at any point extends to the whole 3D image. Experimental results demonstrate that the proposed algorithm exhibits good key sensitivity and robustness. Numerical results show that the algorithm has considerable capabilities in resisting common attacks. Compared to related algorithms, our algorithm shows certain advantages in terms of information entropy and resistance to differential attacks. [ABSTRACT FROM AUTHOR]

Electroencephalography (EEG) signals are crucial for investigating brain function and cognitive processes. This study aims to address the challenges of efficiently recording and analyzing high-dimensional EEG signals while listening to music to recognize emotional states. We propose a method combining Bidirectional Long Short-Term Memory (Bi-LSTM) networks with attention mechanisms for EEG signal processing. Using wearable EEG devices, we collected brain activity data from participants listening to music. The data was preprocessed, segmented, and Differential Entropy (DE) features were extracted. We then constructed and trained a Bi-LSTM model to enhance key feature extraction and improve emotion recognition accuracy. Experiments were conducted on the SEED and DEAP datasets. The Bi-LSTM-AttGW model achieved 98.28% accuracy on the SEED dataset and 92.46% on the DEAP dataset in multi-class emotion recognition tasks, significantly outperforming traditional models such as SVM and EEG-Net. This study demonstrates the effectiveness of combining Bi-LSTM with attention mechanisms, providing robust technical support for applications in brain–computer interfaces (BCI) and affective computing. Future work will focus on improving device design, incorporating multimodal data, and further enhancing emotion recognition accuracy, aiming to achieve practical applications in real-world scenarios. [ABSTRACT FROM AUTHOR]

In this paper, we have derived and studied new probability distributions by extending the 2‐dimensional Rayleigh distribution (RD). First, we extend the RD to 3 dimensions and then generalize it to k dimensions for any positive integer k ≥ 3. The distributions are named the 3‐dimensional Rayleigh distribution (3‐DRD) and k‐dimensional Rayleigh distribution (k‐DRD), respectively. For both 3‐DRD and k‐DRD, detailed mathematical and statistical properties including derivations of the corresponding cumulative distribution, probability density, survival, and hazard functions, moments, moment generating functions, mode, skewness, kurtosis, and differential entropy are obtained in closed forms. Parameter estimation is done for both models using the maximum likelihood estimation method and some statistical properties of the estimator are discussed for each case. Interestingly, the commonly known Normal, Rayleigh, Maxwell–Boltzmann, chi‐square, gamma, and Erlang distributions are related to the newly developed extended RDs as special cases. For the 3‐DRD, plots of cumulative distribution, probability density, survival, and hazard functions are exhibited, a simulation study is carried out, and random samples are generated using the standard accept–reject (AR) algorithm to check the efficiency of the maximum likelihood estimates of the parameter. Moreover, the new 3‐DRD model is fitted to one simulated and three real datasets, revealing good performance compared to four existing Rayleigh‐based distributions. This study will contribute new knowledge to the field of applied statistics and probability, and the findings will be used as a basis for future research in the field. [ABSTRACT FROM AUTHOR]

• Machine learning classifiers identified EEG responses to familiar/non-familiar videos in healthy controls and patients with disorders of consciousness (DOC) • Gamma and beta bands contributed to better performances in healthy controls, while no clear trend was found in patients with DOC. • Identifiable EEG responses to familiar/non-familiar stimuli were consistent with the clinical progress of most patients with DOC. To investigate the differences in the brain responses of healthy controls (HC) and patients with disorders of consciousness (DOC) to familiar and non-familiar audiovisual stimuli and their consistency with the clinical progress. EEG responses of 19 HC and 19 patients with DOC were recorded while watching emotionally-valenced familiar and non-familiar videos. Differential entropy of the EEG recordings was used to train machine learning models aimed to distinguish brain responses to stimuli type. The consistency of brain responses with the clinical progress of the patients was also evaluated. Models trained using data from HC outperformed those for patients. However, the performance of the models for patients was not influenced by their clinical condition. The models were successfully trained for over 75% of participants, regardless of their clinical condition. More than 75% of patients whose CRS-R scores increased post-study displayed distinguishable brain responses to both stimuli. Responses to emotionally-valenced stimuli enabled modelling classifiers that were sensitive to the familiarity of the stimuli, regardless of the clinical condition of the participants and were consistent with their clinical progress in most cases. EEG responses are sensitive to familiarity of emotionally-valenced stimuli in HC and patients with DOC. [ABSTRACT FROM AUTHOR]

The lognormal moment sequence is considered. Using the fractional moments technique, it is first proved that the lognormal has the largest differential entropy among the infinite positively supported probability densities with the same lognormal-moments. Then, relying on previous theoretical results on entropy convergence obtained by the authors concerning the indeterminate Stieltjes moment problem, the lognormal distribution is accurately reconstructed by the maximum entropy technique using only its integer moment sequence, although it is not uniquely determined by moments. [ABSTRACT FROM AUTHOR]

The entropy-based goodness-of-fit tests have gained prominence due to their easiness and accuracy. In this paper, the goodness of fit test problem is developed for widely used Exponential distribution under imprecise conditions. To this aim, a novel concept called fuzzy differential entropy is introduced to measure the degree of uncertainty for fuzzy random variables. Then, the fuzzy empirical differential entropy proposed to estimate the new fuzzy information measure. We consider the Vasicek estimator of entropy and use the α-pessimistic approach to propose an entropy-based goodness of fit test for the fuzzy Exponential distribution. The practical applicability and superiority of the proposed test over other fuzzy goodness-of-fit tests were demonstrated through Monte Carlo simulation using a numerical example and two real-life applications. [ABSTRACT FROM AUTHOR]

Context. Observations of ionic, atomic, or molecular lines are performed to improve our understanding of the interstellar medium (ISM). However, the potential of a line to constrain the physical conditions of the ISM is difficult to assess quantitatively, because of the complexity of the ISM physics. The situation is even more complex when trying to assess which combinations of lines are the most useful. Therefore, observation campaigns usually try to observe as many lines as possible for as much time as possible. Aims. We have searched for a quantitative statistical criterion to evaluate the full constraining power of a (combination of) tracer(s) with respect to physical conditions. Our goal with such a criterion is twofold. First, we want to improve our understanding of the statistical relationships between ISM tracers and physical conditions. Secondly, by exploiting this criterion, we aim to propose a method that helps observers to make their observation proposals; for example, by choosing to observe the lines with the highest constraining power given limited resources and time. Methods. We propose an approach based on information theory, in particular the concepts of conditional differential entropy and mutual information. The best (combination of) tracer(s) is obtained by comparing the mutual information between a physical parameter and different sets of lines. The presented analysis is independent of the choice of the estimation algorithm (e.g., neural network or χ2 minimization). We applied this method to simulations of radio molecular lines emitted by a photodissociation region similar to the Horsehead Nebula. In this simulated data, we considered the noise properties of a state-of-the-art single dish telescope such as the IRAM 30m telescope. We searched for the best lines to constrain the visual extinction, AVtot, or the ultraviolet illumination field, G0. We ran this search for different gas regimes, namely translucent gas, filamentary gas, and dense cores. Results. The most informative lines change with the physical regime (e.g., cloud extinction). However, the determination of the optimal (combination of) line(s) to constrain a physical parameter such as the visual extinction depends not only on the radiative transfer of the lines and chemistry of the associated species, but also on the achieved mean signal-to-noise ratio. The short integration time of the CO isotopologue J = 1 − 0 lines already yields much information on the total column density for a large range of (AVtot, G0) space. The best set of lines to constrain the visual extinction does not necessarily combine the most informative individual lines. Precise constraints on the radiation field are more difficult to achieve with molecular lines. They require spectral lines emitted at the cloud surface (e.g., [CII] and [CI] lines). Conclusions. This approach allows one to better explore the knowledge provided by ISM codes, and to guide future observation campaigns. [ABSTRACT FROM AUTHOR]

In models with insufficient initial information, parameter estimation can be subject to statistical uncertainty, potentially resulting in suboptimal decision-making; however, delaying implementation to gather more information can also incur costs. This paper examines an extension of information-theoretic approaches designed to address this classical dilemma, focusing on balancing the expected profits and the information needed to be obtained about all of the possible outcomes. Initially utilized in binary outcome scenarios, these methods leverage information measures to harmonize competing objectives efficiently. Building upon the foundations laid by existing research, this methodology is expanded to encompass experiments with multiple outcome categories using Dirichlet processes. The core of our approach is centered around weighted entropy measures, particularly in scenarios dictated by Dirichlet distributions, which have not been extensively explored previously. We innovatively adapt the technique initially applied to binary case to Dirichlet distributions/processes. The primary contribution of our work is the formulation of a sequential minimization strategy for the main term of an asymptotic expansion of differential entropy, which scales with sample size, for non-binary outcomes. This paper provides a theoretical grounding, extended empirical applications, and comprehensive proofs, setting a robust framework for further interdisciplinary applications of information-theoretic paradigms in sequential decision-making. [ABSTRACT FROM AUTHOR]

Background/Objectives: There have been attempts to detect depression using medical-grade electroencephalograph (EEG) data based on a machine learning approach. EEG has garnered interest as a method for assessing brainwaves by attaching electrodes to the scalp to obtain electrical activity in the brain. Recently, machine learning has been applied to the EEG data to detect depression, with encouraging results. Specifically, studies using medical-grade EEG data have shown that depression can be accurately detected. However, there is a need to expand the range of applications by achieving a score with machine learning using simpler consumer-grade brain wave sensors. At present, a sufficient score has not been achieved.; Methods: To improve the score of depression detection, we quantified various EEG indices to train models such as power spectrum, asymmetry, complexity, and functional connectivity. In addition, feature selection was performed to ensure that the model learns only promising EEG indices for depression detection. The feature selection methods were Light Gradient Boosting Machine (LightGBM) feature importance, mutual information, ReliefF and ElasticNet coefficients. The selected EEG indices were learned by the LightGBM model, which is reported to be as accurate as the latest deep learning models. In cross-validation, the independence of test and training data was ensured to avoid excessively calculated score; Results: The results showed that the Macro F1 score was 91.59%, suggesting that a consumer-grade EEG can detect depression. In addition, analysis of the EEG indices selected by feature selection indicated that the Macro F1 score was about 80% for single EEG indices such as differential entropy in the frequency band β and functional connectivity in the left frontal region in the frequency band 1–128 Hz; Conclusions: Although the data were obtained from a consumer-grade EEG, the results suggest that these EEG indices are promising for detection depression. [ABSTRACT FROM AUTHOR]

Approximate Bayesian computation (ABC) methods are applicable to statistical models specified by generative processes with analytically intractable likelihoods. These methods try to approximate the posterior density of a model parameter by comparing the observed data with additional process‐generated simulated data sets. For computational benefit, only the values of certain well‐chosen summary statistics are usually compared, instead of the whole data set. Most ABC procedures are computationally expensive, justified only heuristically, and have poor asymptotic properties. In this article, we introduce a new empirical likelihood‐based approach to the ABC paradigm called ABCel. The proposed procedure is computationally tractable and approximates the target log posterior of the parameter as a sum of two functions of the data—namely, the mean of the optimal log‐empirical likelihood weights and the estimated differential entropy of the summary functions. We rigorously justify the procedure via direct and reverse information projections onto appropriate classes of probability densities. Past applications of empirical likelihood in ABC demanded constraints based on analytically tractable estimating functions that involve both the data and the parameter; although by the nature of the ABC problem such functions may not be available in general. In contrast, we use constraints that are functions of the summary statistics only. Equally importantly, we show that our construction directly connects to the reverse information projection and estimate the relevant differential entropy by a k‐NN estimator. We show that ABCel is posterior consistent and has highly favorable asymptotic properties. Its construction justifies the use of simple summary statistics like moments, quantiles, and so forth, which in practice produce accurate approximation of the posterior density. We illustrate the performance of the proposed procedure in a range of applications. [ABSTRACT FROM AUTHOR]

Casing treatments improve compressor stability but often at the expense of compressor efficiency. In this study, the differential entropy generation rate (DEGR) was applied to both efficiency evaluation and stall margin estimation. Rotor 67 was used as the compressor in this study and the simulation results were analyzed to correlate the distribution of the DEGR with the flow structures in the rotor at three rotating speeds. The characteristics of the DEGR at each speed were analyzed, exhibiting the characteristics of the flow structures at peak efficiency (PE) and near stall (NS) flow conditions. Loss analysis was conducted on the peak efficiency operating condition, particularly at 100% rotating speed. The critical state of the DEGR was investigated to identify stall occurrences on the near-stall condition. It was thus concluded that the DEGR can be a unified measure of both efficiency and stall margin. This theoretical exploration was subsequently applied to the design of casing treatments with two objectives: enhancing peak efficiency at 100% rotating speed and improving stability margins at all speeds. Two casing treatments were designed, with two circumferential grooves positioned axially at different locations. Their mechanisms for reducing the high DEGR area in the peak efficiency condition of 100% speed and suppressing an increase in DEGR during approaching stall were investigated, respectively. The results indicated that the presence of a groove near the leading edge of the blade tip can effectively suppress stall at all speeds. In order to achieve peak efficiency at high speeds, the extent of casing treatment coverage above the shock wave plays a crucial role in minimizing losses. [ABSTRACT FROM AUTHOR]

Electroencephalography (EEG) is a physiological signal directly generated by the central nervous system. Brain rhythm is closely related to a person's emotional state and is widely used for EEG emotion recognition. In previous studies, the rhythm specificity between different brain channels was seldom explored. In this paper, the rhythm specificity of brain channels is studied to improve the accuracy of EEG emotion recognition. Variational mode decomposition is used to decompose rhythm signals and enhance features, and two kinds of information entropy, i.e., differential entropy (DE) and dispersion entropy (DispEn) are extracted. The rhythm being used to get the best result of single channel emotion recognition is selected as the representative rhythm, and the remove one method is employed to obtain rhythm information entropy feature. In the experiment, the DEAP database was used for EEG emotion recognition in valence-arousal space. The results showed that the best result of rhythm DE feature classification in the valence dimension is 77.04%, and the best result of rhythm DispEn feature classification in the arousal dimension is 79.25%. [ABSTRACT FROM AUTHOR]

The objective of this study is to derive the thermodynamic characteristics from sorption isotherm data for canola. The semi‐gravimetric method was utilized at three different temperatures (25, 40, and 55°C) and seven air relative humidity levels within the range of 11%–90%. The observed data indicated that the equilibrium moisture content of the sample decreased as the temperature increased. The "GAB and BET" models were applied to fit the empirical data, which demonstrated a Type III isotherm, and the monolayer water content was subsequently determined using these models. Thermodynamic properties such as "isosteric heat," "net isosteric heat," "differential entropy," "net integral entropy," and "net integral enthalpy" were determined from isothermal sorption curves. The results show that as moisture content increases, both the sorption isosteric heat and the differential entropy of sorption decrease. This indicates that at higher moisture levels, the energy required for additional moisture adsorption and the changes in entropy are reduced. Similarly, the net isosteric heat of sorption and the net integral enthalpy of sorption also decrease with increasing moisture content, consistent with the observed reductions in isosteric heat and differential entropy. The specific absorption surface area for each temperature was determined by calculating the monolayer moisture content using both the "GAB and BET models." The net integral entropy had an increasing trend in the range of 4%–4.5% (db%), while it decreased in the range of 4.5%–6.8% of moisture content. In addition, the spreading pressure at three levels of temperature was reported. Finally, an empirical relation was employed to illustrate the cumulative energy requirement for drying versus moisture content. The results indicated that at low moisture content levels, the drying process required significantly higher energy. Practical applications: Moisture sorption isotherms are essential for understanding the interaction between water and food ingredients. This knowledge is vital for improving food processing methods such as drying, mixing, cooling, and storage. In industry, isotherms can help determine the best drying method to maintain food quality, identify the optimal mixing conditions to ensure consistency, establish cooling protocols to prevent spoilage, and set storage guidelines to extend shelf life. In addition, understanding thermodynamic properties is crucial for regulating moisture absorption and release, achieving the desired food texture, managing surface characteristics, and calculating the energy needed for effective dehydration processes. [ABSTRACT FROM AUTHOR]

Shannon differential entropy is extensively applied in the literature as a measure of dispersion or uncertainty. Nonetheless, there are other measurements, such as the cumulative residual Tsallis entropy (CRTE), that reveal interesting effects in several fields. Motivated by this, we study and compute Tsallis measures for the concomitants of the generalized order statistics (CGOS) from the iterated Farlie-Gumbel-Morgenstern (IFGM) bivariate family. Some newly introduced information measures are also being considered for CGOS within the framework of the IFGM family, including Tsallis entropy, CRTE, and an alternative measure of CRTE of order η. Applications of these results are given for order statistics and record values with uniform, exponential, and power marginals distributions. In addition, the empirical cumulative Tsallis entropy is suggested as a method to calculate the new information measure. Finally, a real-world data set has been analyzed for illustrative purposes, and the performance is quite satisfactory [ABSTRACT FROM AUTHOR]

We consider a Markov model of learning consisting of three states: the state of knowledge transfer, the training state, and the state of knowledge control. Taking into account of training time within this model allows one to obtain additional information about competencies of students, to estimate the values of latent parameters, and to improve the learning process. [ABSTRACT FROM AUTHOR]

We calculate the average differential entropy of a q-component Gaussian mixture in R n . For simplicity, all components have covariance matrix σ 2 1 , while the means { W i } i = 1 q are i.i.d. Gaussian vectors with zero mean and covariance s 2 1 . We obtain a series expansion in μ = s 2 / σ 2 for the average differential entropy up to order O (μ 2) , and we provide a recipe to calculate higher-order terms. Our result provides an analytic approximation with a quantifiable order of magnitude for the error, which is not achieved in previous literature. [ABSTRACT FROM AUTHOR]

The new mathematical connection of De Donder's differential entropy production with the differential changes of thermodynamic potentials (Helmholtz free energy, enthalpy, and Gibbs free energy) was obtained through the linear sequence of equations (direct, straightforward path), in which we use rigorous thermodynamic definitions of the partial molar thermodynamic properties. This new connection uses a global approach to the problem of reversibility and irreversibility, which is vital to global learners' view and standardizes the linking procedure for thermodynamic potentials (Helmholtz free energy, enthalpy, and and Gibbs free energy)—preferably to the sensing learners. It is shown that De Donder's differential entropy production in an isolated composite system is equal to the differential change in total entropy and that De Donder's equation agrees with Clausius' inequality. The useful work of the irreversible process is discussed, which with the decrease of irreversibility tends towards the hypothetical maximum useful work of the reversible process. [ABSTRACT FROM AUTHOR]

Emotion recognition based on EEG signals has become an important challenge in the field of emotional computing and human-computer interaction. In order to obtain better emotion recognition performance, a key issue is how to effectively combine time, space and frequency dimension information in EEG signals. This paper proposes a hybrid network model (ECA-ResNet-LSTM) combining attention residual networks and long short-term memory networks. By integrating time, space and frequency information in EEG signals, this model can effectively improve the accuracy of emotion recognition. Firstly, the differential entropy features of EEG signals in different frequency bands after time-domain segmentation are extracted, and the differential entropy features extracted from different channels are transformed into a four-dimensional feature matrix. Then, the spatial and frequency information in the EEG signal is extracted through ECA ResNet, and attention mechanisms are introduced to redistribute the weights of more relevant frequency band information. LSTM extracts time related information from the output of ECA ResNet. Finally, the experimental results show that in DEAP dataset, the accuracy of awakening and valence dimension binary classification reaches 97.15% and 96.13%, respectively, and the accuracy of awakening valence dimension four classification reaches 95.96%; In SEED dataset, the accuracy of positive neutral negative three classification reaches 96.64%. Compared with the existing mainstream emotion, the classification accuracy of the recognition model has been significantly improved. [ABSTRACT FROM AUTHOR]

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The high-accuracy detection of multiple distinct human emotions is crucial for advancing affective computing, mental health diagnostics, and human–computer interaction. The integration of deep learning networks with entropy measures holds significant potential in neuroscience and medicine, especially for analyzing EEG-based emotion states. This study proposes a method combining ResNet18 with differential entropy to identify five types of human emotions (happiness, sadness, fear, disgust, and neutral) from EEG signals. Our approach first calculates the differential entropy of EEG signals to capture the complexity and variability of the emotional states. Then, the ResNet18 network is employed to learn feature representations from the differential entropy measures, which effectively captures the intricate spatiotemporal dynamics inherent in emotional EEG patterns using residual connections. To validate the efficacy of our method, we conducted experiments on the SEED-V dataset, achieving an average accuracy of 95.61%. Our findings demonstrate that the combination of ResNet18 with differential entropy is highly effective in classifying multiple distinct human emotions from EEG signals. This method shows robust generalization and broad applicability, indicating its potential for extension to various pattern recognition tasks across different domains. [ABSTRACT FROM AUTHOR]

Emotional EEG (electroencephalogram) signal is a non‑stationary time series with low signal‑to‑noise ratio. Traditional feature extraction and classification methods are difficult to extract and classify the effective features of different emotional states. In regard to the above situation, a deep learning model that automatically fuses different frequency bands and time‑frequency characteristics of EEG signals is proposed. Firstly, the preprocessed data is processed in frequency bands, and the differential entropy features of each frequency band are extracted. Then, the squeeze excitation module connected in the network assigns weight to the differential entropy features of different frequency bands to obtain the valuable information of the input data, and then uses the improved dense connection network for feature fusion and classification recognition to ensure the maximum information transmission between the network layers. Finally, the algorithm is verified by using the SEED emotional EEG of three classification dataset, and the classification accuracy is 96. 03%, which is higher than the existing baseline learning algorithm. The proposed algorithm further enhances network feature extraction capabilities and demonstrates faster convergence, which is of great significance for improving the performance of the classifier. [ABSTRACT FROM AUTHOR]

Introduction Fisher information is a measure of the information inside a random variable about an unknown parameter. Mutual information shows the dependence between two variables and relative entropy shows the difference between the two probability distributions. Material and Methods In this paper, Fisher information is generalized for mutual information and relative entropy and the monotonicity properties of Fisher information are examined. Then concepts such as information correlation and information correlation coefficient are introduced. Results and discussion It is shown that Shannon differential entropy, which measures the behavior of a random variable, and conditional Fisher information are used to determine the probability of estimation error. Conclusion In this paper, with the help of Fisher's information structure, some concepts of information theory were generalized. For a Markov chain, it was shown that when the statistic moves away from the estimated parameter, the mutual Fisher information decreases, and when the Fisher information is conditioned on closer values, it is higher than when it is conditioned on more distant values. Two open problems are proposed for researchers who are interested in this topic. In cases where a topological group acts on random variables, the criteria mentioned in this paper should be analyzed. Also, with the help of the convolution function, the criteria mentioned in the paper can be examined for linear combinations of random variables. [ABSTRACT FROM AUTHOR]

The Self-Exciting Threshold Autoregressive model (SETAR) is non-linear and considers threshold values to model time series affected by regimes. It is extended through the Multivariate SETAR (MSETAR) model, where the threshold variable can also be a multivariate process. The stationary marginal density (smd) of an MSETAR process of order one corresponds to a Unified Skew-Normal density. In this paper, the smd of an MSETAR of order one process was considered to compute explicit expressions of differential entropy and Kullback–Leibler and Jeffrey's divergences between two MSETAR(1) processes. In addition, two asymptotic tests based on divergences were built for statistical significance testing of the disparity between MSETAR(1) processes and the threshold coefficient matrix. Information measures considered involved high-dimensional integrals that likewise depended on multivariate cumulative density normal function. To solve these integrals, Genz's algorithm was considered based on Cholesky decomposition and Monte Carlo approximation. Some numerical experiments and applications to fish condition factor and Chilean economic perception time series illustrate performance. [ABSTRACT FROM AUTHOR]

Emotion recognition research has attracted great interest in various research fields, and electroencephalography (EEG) is considered a promising tool for extracting emotion-related information. However, traditional EEG-based emotion recognition methods ignore the spatial correlation between electrodes. To address this problem, this paper proposes an EEG-based emotion recognition method combining differential entropy feature matrix (DEFM) and 2D-CNN-LSTM. In this work, first, the one-dimensional EEG vector sequence is converted into a two-dimensional grid matrix sequence, which corresponds to the distribution of brain regions of the EEG electrode positions, and can better characterize the spatial correlation between the EEG signals of multiple adjacent electrodes. Then, the EEG signal is divided into equal time windows, and the differential entropy (DE) of each electrode in this time window is calculated, it is combined with a two-dimensional grid matrix and differential entropy to obtain a new data representation that can capture the spatiotemporal correlation of the EEG signal, which is called DEFM. Secondly, we use 2D-CNN-LSTM to accurately identify the emotional categories contained in the EEG signals and finally classify them through the fully connected layer. Experiments are conducted on the widely used DEAP dataset. Experimental results show that the method achieves an average classification accuracy of 91.92% and 92.31% for valence and arousal, respectively. The method performs outstandingly in emotion recognition. This method effectively combines the temporal and spatial correlation of EEG signals, improves the accuracy and robustness of EEG emotion recognition, and has broad application prospects in the field of emotion classification and recognition based on EEG signals. [ABSTRACT FROM AUTHOR]

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 paper, a tight lower bound for the differential entropy of the Gaussian mixture model is presented. First, the probability model of mixed Gaussian distribution that is created by mixing both discrete and continuous random variables is investigated in order to represent symmetric bimodal Gaussian distribution using the hyperbolic cosine function, on which a tighter upper bound is set. Then, this tight upper bound is used to derive a tight lower bound for the differential entropy of the Gaussian mixture model introduced. The proposed lower bound allows to maintain its tightness over the entire range of the model’s parameters and shows more tightness when compared with other bounds that lose their tightness over certain parameter ranges. The presented results are then extended to introduce a more general tight lower bound for asymmetric bimodal Gaussian distribution, in which the two modes have a symmetric mean but differ in terms of their weights. [ABSTRACT FROM AUTHOR]

Abstract 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.

In this paper, a tight lower bound for the differential entropy of the Gaussian mixture model is presented. First, the probability model of mixed Gaussian distribution that is created by mixing both discrete and continuous random variables is investigated in order to represent symmetric bimodal Gaussian distribution using the hyperbolic cosine function, on which a tighter upper bound is set. Then, this tight upper bound is used to derive a tight lower bound for the differential entropy of the Gaussian mixture model introduced. The proposed lower bound allows to maintain its tightness over the entire range of the model's parameters and shows more tightness when compared with other bounds that lose their tightness over certain parameter ranges. The presented results are then extended to introduce a more general tight lower bound for asymmetric bimodal Gaussian distribution, in which the two modes have a symmetric mean but differ in terms of their weights.

In the present article, the differential entropy rate and the rate distortion function (RDF) are computed for certain nonstationary real Gaussian autoregressive moving average (ARMA) vector sources. [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]

A fundamental NP-hard combinatorial-optimization in the area of statistical designs is the maximum-entropy sampling problem (MESP), which seeks to maximize Shannon's "differential entropy" over all subsets of a prespecified cardinality from a set of n Gaussian random variables. This problem has applications in many areas, such as the redesign of environmental-monitoring networks. Most algorithms for exact solution of MESP are branch-and-bound based, and one of the best upper bounds is based on Anstrecher's recent concave "linx relaxation" of differential entropy. A key paradigm for improving bounds is by "masking" the covariance of the random variables with a correlation matrix. The main result establishes that in the best case, the linx bound can be improved by an amount that is at least linear in n by masking. These and other recent results on the hot topic of MESP are leading to practical algorithms for exact solution of meaningful design problems in applied areas such as environmental statistics. The maximum-entropy sampling problem is the NP-hard problem of maximizing the (log) determinant of an order-s principal submatrix of a given order n covariance matrix C. Exact algorithms are based on a branch-and-bound framework. The problem has wide applicability in spatial statistics and in particular in environmental monitoring. Probably the best upper bound for the maximum empirically is Anstreicher's scaled "linx" bound. An earlier methodology for potentially improving any upper-bounding method is by masking, that is, applying the bounding method to C ∘ M , where M is any correlation matrix. We establish that the linx bound can be improved via masking by an amount that is at least linear in n, even when optimal scaling parameters are used. We also extend an earlier result that the linx bound is convex in the logarithm of a scaling parameter, making a full characterization of its behavior and providing an efficient means of calculating its limiting behavior in all cases. Funding: J. Lee was supported by the Air Force Office of Scientific Research [Grant FA9550-19-1-0175]. M. Fampa was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grants 303898/2016-0 and 434683/2018-3]. [ABSTRACT FROM AUTHOR]

It is proven that a conjecture of Tao (2010) holds true for log-concave random variables on the integers: For every $n \geq 1$ , if $X_1,\ldots,X_n$ are i.i.d. integer-valued, log-concave random variables, then \begin{equation*} H(X_1+\cdots +X_{n+1}) \geq H(X_1+\cdots +X_{n}) + \frac {1}{2}\log {\Bigl (\frac {n+1}{n}\Bigr)} - o(1) \end{equation*} as $H(X_1) \to \infty$ , where $H(X_1)$ denotes the (discrete) Shannon entropy. The problem is reduced to the continuous setting by showing that if $U_1,\ldots,U_n$ are independent continuous uniforms on $(0,1)$ , then \begin{equation*} h(X_1+\cdots +X_n + U_1+\cdots +U_n) = H(X_1+\cdots +X_n) + o(1), \end{equation*} as $H(X_1) \to \infty$ , where $h$ stands for the differential entropy. Explicit bounds for the $o(1)$ -terms are provided. [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 use of residues resulting from the processing of agricultural products is an widely studied topic, which is justified by the need to reduce costs and by the search for productive sustainability, which has as one of its principles the full use production, reducing waste and therefore increasing the amount of products extracted per unit of area. Residual seeds, resulting from the production of fruit pulps, are rich in nutrients and with the potential to be further improved by the application of germination, increasing the protein content and the content of bioactive compounds. However, in the germination process, the product acquires a high water content, requiring immediate drying and control of the water adsorption kinetics after dehydration. Therefore, the objective of this study was to determine the water adsorption isotherms of germinated seeds flours from pumpkins of three varieties at temperatures of 15, 25 and 35 °C, to obtain the most appropriate mathematical model to describe the hygroscopic behavior and to determine the thermodynamic properties of water adsorption, through the values of the integral isosteric heat, differential entropy, differential enthalpy and Gibbs free energy for the studied conditions. The GAB and Peleg models fit the experimental data well. With increasing water activity, there was a reduction in isosteric heat and entropy. The enthalpy-entropy compensation theory was confirmed. Gibbs free energy was negative for all temperatures, increasing with increasing equilibrium water content, demonstrating that it is a spontaneous process. [ABSTRACT FROM AUTHOR]

Accurate detection of spectrum holes is a useful requirement for cognitive radios that improves the efficiency of spectrum usage. The authors propose three novel, simple, and entropy‐based detectors for spectrum sensing in cognitive radio. The authors evaluate the probability of detection of these three detectors: Vasicek's entropy detector, truncated Vasicek's entropy detector, and Van Es' entropy detector, over a predefined probability of false‐alarm. In particular, the authors provide the approximate and asymptotic test statistics for these detectors in the presence and absence of Nakagami‐m fading, noise variance uncertainty, and optimised detection threshold. Furthermore, the authors provide a detailed comparison study among all the detectors via Monte Carlo simulations and justify authors results through real‐world data. The authors' experimental results establish a superior performance of truncated Vasicek's entropy detector over Vasicek's entropy detector, energy detector, differential entropy detector and Van Es' entropy detector in practically viable scenarios. [ABSTRACT FROM AUTHOR]

Moisture adsorption and desorption isotherms of gelatin extracted from whitefish skin powder (FSGP) at different temperatures across a wide range of water activity were determined along with their thermodynamic properties. Nine mathematical models were utilized for fitting the experimental data and simulating the adsorption and desorption behavior. The thermodynamic properties were determined and fitted to the experimental data. The results showed that Peleg and GAB models were the best fit for FSGP. The energies involved in the adsorption and desorption process of FSGP indicated a stronger dependence on equilibrium moisture content (Xe). When Xe decreased, there was a consistent trend of increasing thermodynamic properties. Both the moisture adsorption and desorption behaviors of FSGP were, therefore, non-spontaneous processes. Linear correlations between the changes in enthalpy and entropy for adsorption and desorption were observed, indicating the presence of enthalpy–entropy compensation for FSGP. For preserving FSGP quality, it should be stored with Xw ≤ 8 (gw/gdm, d.b.) at temperatures below 53 °C and an RH of 50% to avoid it becoming rubbery. These findings are crucial for providing insight into the optimal drying and storage conditions. [ABSTRACT FROM AUTHOR]