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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]

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]

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]

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]

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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]

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]

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 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]

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]

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.

We calculate the average differential entropy of a q-component Gaussian mixture in Rn. For simplicity, all components have covariance matrix σ21, while the means {Wi}i=1q are i.i.d. Gaussian vectors with zero mean and covariance s21. We obtain a series expansion in μ=s2/σ2 for the average differential entropy up to order O(μ2), 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.

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.

This paper proposes a path strategy for VR+music combination therapy in future development and introduces an emotion recognition model based on EEG signals to address its inability to quantify the therapeutic effect of emotional intervention. EEG signal feature extraction involves extracting the differential entropy of the signal as a feature and smoothing it in a time series using a linear dynamic system. On this basis, the SVN-KNN-based emotion EEG recognition algorithm is further proposed, and the KNN algorithm is weighted and adjusted by using the inter-class sample density, which avoids the interference of the imbalanced distribution of the number of samples on the performance of the classifier and improves the generalization ability of the classification model. In the VR+music combination therapy experiment, the PSD of the theta, alpha, and beta EEG bands of the patients in the observation group was higher than that before the experiment. The difference between the observation group and the control group in the CERQ-C scores after the experiment in the factors of self-blame, contemplation, blaming others, acceptance, and rational analysis was statistically highly significant (P

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]

This article introduces the Differential Entropy-based Compactness Index (DECI), a new metric for synthetically describing the spatial distribution of point clouds. DECI is founded on the differential entropy (DE) of point clouds, and if they depict a moving object distribution, the index enables real-time monitoring. Historical data analysis allows for the study of DECI trends and average values in defined intervals. Multiple practical applications are suggested, including risk assessment, congestion measurement, traffic control (including autonomous systems), infrastructure planning, crowd density, and health analysis. DECI's real-time and historical insights are valuable for decision-making and system optimization and hold potential as a feature in machine learning applications. [ABSTRACT FROM AUTHOR]

In this study, the effectiveness of an experimental clinical technique for the reproduction of attachments during an orthodontic treatment with clear aligners was evaluated using a new index (CorAl) for quality assessment that exploits the differential entropy of point clouds. The procedure involves the use of a pre-drilled template and a second pre-loaded template with a high-viscosity composite and is compared with the standard technique. Attachment planning was conducted on four prototypes of dental arches with extracted teeth which were divided into two groups according to the proposed operating procedures. Digital scans were utilized to capture dental impressions for both the purposes of virtual planning and to reproduce the clinical outcomes post-procedure. The point clouds obtained after the reproduction of the attachments were aligned with those from the virtual planning, and the deviation analysis was conducted using the quality index of the CorAl method. Though no significant discrepancies were found among the groups regarding morphological flaws, detachments, or maximum defect values, the differential entropy analysis revealed that the experimental technique offers good alignment in attachment placement. The outcome supports that the innovative procedure of the clinical reproduction of attachments proved to be reliable and operationally simple, with additional benefits derived from using the CorAl index. The advantages of CorAl include the use of a single comparison index, no problem of comparison commutativity, noise immunity, low influence from the presence of holes, and point cloud densities. This allows for the drawing of quality maps that show areas with the highest deviation. [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]

An extension of Shannon's entropy power inequality when one of the summands is Gaussian was provided by Costa in 1985, known as Costa's concavity inequality. We consider the additive Gaussian noise channel with a more realistic assumption, i.e. the input and noise components are not independent and their dependence structure follows the well-known multivariate Gaussian copula. Two generalizations for the first- and second-order derivatives of the differential entropy of the output signal for dependent multivariate random variables are derived. It is shown that some previous results in the literature are particular versions of our results. Using these derivatives, concavity of the entropy power, under certain mild conditions, is proved. Finally, special one-dimensional versions of our general results are described which indeed reveal an extension of the one-dimensional case of Costa's concavity inequality to the dependent case. An illustrative example is also presented. [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]

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]

Cognitive radio (CR) systems are configured to dynamically assess the spectrum utilisation and contribute towards an improved spectrum efficiency. Hence, accurate detection of the incumbent signal in a given channel, popularly known as spectrum sensing (SS), is essential for CR. Here, in the domain of SS, the authors introduce a new goodness‐of‐fit test (GoFT) founded on p‐norm of the observations at the receiver node. To capture the heavy‐tailed nature of noise distribution in practical communication channels, the authors utilise generalised Gaussian distribution (GGD) as a noise model. A novel p‐norm detector (PND) and a geometric power detector (GPD) is proposed and corresponding probability density function (PDF) under GGD is derived. Via Monte Carlo simulations, the authors show a match of the derived PDFs with the simulation results. Using Neyman‐Pearson framework the performances of PND and GPD are compared with an existing differential entropy detector (DED), the well‐known energy detector (ED) and joint correlation and energy detector (CED) under GGD noise model. Evaluation of proposed PND and GPD utilising Monte Carlo simulations indicate a superior performance. Further, the experiments employing real‐world data establish superiority of the proposed detectors as compared to existing techniques. The authors derive and implement an optimised threshold for PND, providing further improvement in performance. [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]

(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]