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Entropy, Volume 25, Issue 7 (July 2023) – 149 articles

Cover Story (view full-size image): Gear shifting is best known from car driving. On a flat highway, the highest gear gives the highest speed. When driving uphill, shifting to a lower gear may increase the speed and prevent stalling; the optimal gear number decreases with the increasing slope of the hill. Can living organisms shift gears? The answer is yes. Cells can engage in alternative pathways that enable them to continue making energy molecules (‘ATP’) when these contain more Gibbs energy, even though this uses more nutrient energy per energy molecule. The continued synthesis of the energy molecules enables the cells to utilize these for growth and survival when faced with thermodynamic challenges. View this paper
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17 pages, 18119 KiB  
Article
Friction and Stiffness Dependent Dynamics of Accumulation Landslides with Delayed Failure
by Srđan Kostić, Kristina Todorović, Žarko Lazarević and Dragan Prekrat
Entropy 2023, 25(7), 1109; https://doi.org/10.3390/e25071109 - 24 Jul 2023
Cited by 1 | Viewed by 959
Abstract
We propose a new model for landslide dynamics under the assumption of a delay failure mechanism. Delay failure is simulated as a delayed interaction between adjacent blocks, which mimics the relationship between the accumulation and feeder part of the accumulation slope. The conducted [...] Read more.
We propose a new model for landslide dynamics under the assumption of a delay failure mechanism. Delay failure is simulated as a delayed interaction between adjacent blocks, which mimics the relationship between the accumulation and feeder part of the accumulation slope. The conducted research consisted of three phases. Firstly, the real observed movements of the landslide were examined to exclude the existence or the statistically significant presence of background noise. Secondly, we propose a new mechanical model of an accumulation landslide dynamics, with introduced delay failure, and with variable friction law. Results obtained indicate the onset of a transition from an equilibrium state to an oscillatory regime if delayed failure is assumed for different cases of slope stiffness and state of homogeneity/heterogeneity of the slope. At the end, we examine the influence of different frictional properties (along the sliding surface) on the conditions for the onset of instability. Results obtained indicate that the increase of friction parameters leads to stabilization of sliding for homogeneous geological environment. Moreover, increase of certain friction parameters leads to the occurrence of irregular aperiodic behavior, which could be ascribed to the regime of fast irregular sliding along the slope. Full article
(This article belongs to the Section Complexity)
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33 pages, 804 KiB  
Article
Kolmogorov Entropy for Convergence Rate in Incomplete Functional Time Series: Application to Percentile and Cumulative Estimation in High Dimensional Data
by Ouahiba Litimein, Fatimah Alshahrani, Salim Bouzebda, Ali Laksaci and Boubaker Mechab
Entropy 2023, 25(7), 1108; https://doi.org/10.3390/e25071108 - 24 Jul 2023
Viewed by 1018
Abstract
The convergence rate for free-distribution functional data analyses is challenging. It requires some advanced pure mathematics functional analysis tools. This paper aims to bring several contributions to the existing functional data analysis literature. First, we prove in this work that Kolmogorov entropy is [...] Read more.
The convergence rate for free-distribution functional data analyses is challenging. It requires some advanced pure mathematics functional analysis tools. This paper aims to bring several contributions to the existing functional data analysis literature. First, we prove in this work that Kolmogorov entropy is a fundamental tool in characterizing the convergence rate of the local linear estimation. Precisely, we use this tool to derive the uniform convergence rate of the local linear estimation of the conditional cumulative distribution function and the local linear estimation conditional quantile function. Second, a central limit theorem for the proposed estimators is established. These results are proved under general assumptions, allowing for the incomplete functional time series case to be covered. Specifically, we model the correlation using the ergodic assumption and assume that the response variable is collected with missing at random. Finally, we conduct Monte Carlo simulations to assess the finite sample performance of the proposed estimators. Full article
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13 pages, 1538 KiB  
Article
Kaniadakis’s Information Geometry of Compositional Data
by Giovanni Pistone and Muhammad Shoaib
Entropy 2023, 25(7), 1107; https://doi.org/10.3390/e25071107 - 24 Jul 2023
Cited by 1 | Viewed by 956
Abstract
We propose to use a particular case of Kaniadakis’ logarithm for the exploratory analysis of compositional data following the Aitchison approach. The affine information geometry derived from Kaniadakis’ logarithm provides a consistent setup for the geometric analysis of compositional data. Moreover, the affine [...] Read more.
We propose to use a particular case of Kaniadakis’ logarithm for the exploratory analysis of compositional data following the Aitchison approach. The affine information geometry derived from Kaniadakis’ logarithm provides a consistent setup for the geometric analysis of compositional data. Moreover, the affine setup suggests a rationale for choosing a specific divergence, which we name the Kaniadakis divergence. Full article
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39 pages, 5033 KiB  
Article
Reasoning and Logical Proofs of the Fundamental Laws: “No Hope” for the Challengers of the Second Law of Thermodynamics
by Milivoje Kostic
Entropy 2023, 25(7), 1106; https://doi.org/10.3390/e25071106 - 24 Jul 2023
Cited by 1 | Viewed by 2189
Abstract
This comprehensive treatise is written for the special occasion of the author’s 70th birthday. It presents his lifelong endeavors and reflections with original reasoning and re-interpretations of the most critical and sometimes misleading issues in thermodynamics—since now, we have the advantage to look [...] Read more.
This comprehensive treatise is written for the special occasion of the author’s 70th birthday. It presents his lifelong endeavors and reflections with original reasoning and re-interpretations of the most critical and sometimes misleading issues in thermodynamics—since now, we have the advantage to look at the historical developments more comprehensively and objectively than the pioneers. Starting from Carnot (grand-father of thermodynamics to become) to Kelvin and Clausius (fathers of thermodynamics), and other followers, the most relevant issues are critically examined and put in historical and contemporary perspective. From the original reasoning of generalized “energy forcing and displacement” to the logical proofs of several fundamental laws, to the ubiquity of thermal motion and heat, and the indestructibility of entropy, including the new concept of “thermal roughness” and “inevitability of dissipative irreversibility,” to dissecting “Carnot true reversible-equivalency” and the critical concept of “thermal-transformer,” limited by the newly generalized “Carnot-Clausius heat-work reversible-equivalency (CCHWRE),” regarding the inter-complementarity of heat and work, and to demonstrating “No Hope” for the “Challengers” of the Second Law of thermodynamics, among others, are offered. It is hoped that the novel contributions presented here will enlighten better comprehension and resolve some of the fundamental issues, as well as promote collaboration and future progress. Full article
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11 pages, 1135 KiB  
Article
Kinetic Models of Wealth Distribution with Extreme Inequality: Numerical Study of Their Stability against Random Exchanges
by Asim Ghosh, Suchismita Banerjee, Sanchari Goswami, Manipushpak Mitra and Bikas K. Chakrabarti
Entropy 2023, 25(7), 1105; https://doi.org/10.3390/e25071105 - 24 Jul 2023
Cited by 2 | Viewed by 1398
Abstract
In view of some recent reports on global wealth inequality, where a small number (often a handful) of people own more wealth than 50% of the world’s population, we explored if kinetic exchange models of markets could ever capture features where a significant [...] Read more.
In view of some recent reports on global wealth inequality, where a small number (often a handful) of people own more wealth than 50% of the world’s population, we explored if kinetic exchange models of markets could ever capture features where a significant fraction of wealth can concentrate in the hands of a few as the market size N approaches infinity. One existing example of such a kinetic exchange model is the Chakraborti or Yard-Sale model; in the absence of tax redistribution, etc., all wealth ultimately condenses into the hands of a single individual (for any value of N), and the market dynamics stop. With tax redistribution, etc., steady-state dynamics are shown to have remarkable applicability in many cases in our extremely unequal world. We show that another kinetic exchange model (called the Banerjee model) has intriguing intrinsic dynamics, where only ten rich traders or agents possess about 99.98% of the total wealth in the steady state (without any tax, etc., like external manipulation) for any large N value. We will discuss the statistical features of this model using Monte Carlo simulations. We will also demonstrate that if each trader has a non-zero probability f of engaging in random exchanges, then these condensations of wealth (e.g., 100% in the hand of one agent in the Chakraborti model, or about 99.98% in the hands of ten agents in the Banerjee model) disappear in the large N limit. Moreover, due to the built-in possibility of random exchange dynamics in the earlier proposed Goswami–Sen model, where the exchange probability decreases with the inverse power of the wealth difference between trading pairs, one does not see any wealth condensation phenomena. In this paper, we explore these aspects of statistics of these intriguing models. Full article
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23 pages, 35184 KiB  
Article
Multivariate Modeling for Spatio-Temporal Radon Flux Predictions
by Sandra De Iaco, Claudia Cappello, Antonella Congedi and Monica Palma
Entropy 2023, 25(7), 1104; https://doi.org/10.3390/e25071104 - 24 Jul 2023
Cited by 1 | Viewed by 1289
Abstract
Nowadays, various fields in environmental sciences require the availability of appropriate techniques to exploit the information given by multivariate spatial or spatio-temporal observations. In particular, radon flux data which are of high interest to monitor greenhouse gas emissions and to assess human exposure [...] Read more.
Nowadays, various fields in environmental sciences require the availability of appropriate techniques to exploit the information given by multivariate spatial or spatio-temporal observations. In particular, radon flux data which are of high interest to monitor greenhouse gas emissions and to assess human exposure to indoor radon are determined by the deposit of uranium and radio (precursor elements). Furthermore, they are also affected by various atmospheric variables, such as humidity, temperature, precipitation and evapotranspiration. To this aim, a significant role can be recognized to the tools of multivariate geostatistics which supports the modeling and prediction of variables under study. In this paper, the spatio-temporal distribution of radon flux densities over the Veneto Region (Italy) and its estimation at unsampled points in space and time are discussed. In particular, the spatio-temporal linear coregionalization model is identified on the basis of the joint diagonalization of the empirical covariance matrices evaluated at different spatio-temporal lags and is used to produce predicted radon flux maps for different months. Probability maps, that the radon flux density in the upcoming months is greater than three historical statistics, are then built. This might be of interest especially in summer months when the risk of radon exhalation is higher. Moreover, a comparison with respect to alternative models in the univariate and multivariate context is provided. Full article
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18 pages, 961 KiB  
Article
Kernel-Free Quadratic Surface Regression for Multi-Class Classification
by Changlin Wang, Zhixia Yang, Junyou Ye and Xue Yang
Entropy 2023, 25(7), 1103; https://doi.org/10.3390/e25071103 - 24 Jul 2023
Viewed by 1226
Abstract
For multi-class classification problems, a new kernel-free nonlinear classifier is presented, called the hard quadratic surface least squares regression (HQSLSR). It combines the benefits of the least squares loss function and quadratic kernel-free trick. The optimization problem of HQSLSR is convex and unconstrained, [...] Read more.
For multi-class classification problems, a new kernel-free nonlinear classifier is presented, called the hard quadratic surface least squares regression (HQSLSR). It combines the benefits of the least squares loss function and quadratic kernel-free trick. The optimization problem of HQSLSR is convex and unconstrained, making it easy to solve. Further, to improve the generalization ability of HQSLSR, a softened version (SQSLSR) is proposed by introducing an ε-dragging technique, which can enlarge the between-class distance. The optimization problem of SQSLSR is solved by designing an alteration iteration algorithm. The convergence, interpretability and computational complexity of our methods are addressed in a theoretical analysis. The visualization results on five artificial datasets demonstrate that the obtained regression function in each category has geometric diversity and the advantage of the ε-dragging technique. Furthermore, experimental results on benchmark datasets show that our methods perform comparably to some state-of-the-art classifiers. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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19 pages, 578 KiB  
Article
Weighted Sum Secrecy Rate Maximization for Joint ITS- and IRS-Empowered System
by Shaochuan Yang, Kaizhi Huang, Hehao Niu, Yi Wang and Zheng Chu
Entropy 2023, 25(7), 1102; https://doi.org/10.3390/e25071102 - 24 Jul 2023
Viewed by 1063
Abstract
In this work, we investigate a novel intelligent surface-assisted multiuser multiple-input single-output multiple-eavesdropper (MU-MISOME) secure communication network where an intelligent reflecting surface (IRS) is deployed to enhance the secrecy performance and an intelligent transmission surface (ITS)-based transmitter is utilized to perform energy-efficient beamforming. [...] Read more.
In this work, we investigate a novel intelligent surface-assisted multiuser multiple-input single-output multiple-eavesdropper (MU-MISOME) secure communication network where an intelligent reflecting surface (IRS) is deployed to enhance the secrecy performance and an intelligent transmission surface (ITS)-based transmitter is utilized to perform energy-efficient beamforming. A weighted sum secrecy rate (WSSR) maximization problem is developed by jointly optimizing transmit power allocation, ITS beamforming, and IRS phase shift. To solve this problem, we transform the objective function into an approximated concave form by using the successive convex approximation (SCA) technique. Then, we propose an efficient alternating optimization (AO) algorithm to solve the reformulated problem in an iterative way, where Karush–Kuhn–Tucker (KKT) conditions, the alternating direction method of the multiplier (ADMM), and majorization–minimization (MM) methods are adopted to derive the closed-form solution for each subproblem. Finally, simulation results are given to verify the convergence and secrecy performance of the proposed schemes. Full article
(This article belongs to the Special Issue Quantum and Classical Physical Cryptography)
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19 pages, 4201 KiB  
Article
Critic Learning-Based Safe Optimal Control for Nonlinear Systems with Asymmetric Input Constraints and Unmatched Disturbances
by Chunbin Qin, Kaijun Jiang, Jishi Zhang and Tianzeng Zhu
Entropy 2023, 25(7), 1101; https://doi.org/10.3390/e25071101 - 24 Jul 2023
Viewed by 1313
Abstract
In this paper, the safe optimal control method for continuous-time (CT) nonlinear safety-critical systems with asymmetric input constraints and unmatched disturbances based on the adaptive dynamic programming (ADP) is investigated. Initially, a new non-quadratic form function is implemented to effectively handle the asymmetric [...] Read more.
In this paper, the safe optimal control method for continuous-time (CT) nonlinear safety-critical systems with asymmetric input constraints and unmatched disturbances based on the adaptive dynamic programming (ADP) is investigated. Initially, a new non-quadratic form function is implemented to effectively handle the asymmetric input constraints. Subsequently, the safe optimal control problem is transformed into a two-player zero-sum game (ZSG) problem to suppress the influence of unmatched disturbances, and a new Hamilton–Jacobi–Isaacs (HJI) equation is introduced by integrating the control barrier function (CBF) with the cost function to penalize unsafe behavior. Moreover, a damping factor is embedded in the CBF to balance safety and optimality. To obtain a safe optimal controller, only one critic neural network (CNN) is utilized to tackle the complex HJI equation, leading to a decreased computational load in contrast to the utilization of the conventional actor–critic network. Then, the system state and the parameters of the CNN are uniformly ultimately bounded (UUB) through the application of the Lyapunov stability method. Lastly, two examples are presented to confirm the efficacy of the presented approach. Full article
(This article belongs to the Section Complexity)
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17 pages, 1044 KiB  
Article
A Novel Trajectory Feature-Boosting Network for Trajectory Prediction
by Qingjian Ni, Wenqiang Peng, Yuntian Zhu and Ruotian Ye
Entropy 2023, 25(7), 1100; https://doi.org/10.3390/e25071100 - 23 Jul 2023
Viewed by 1568
Abstract
Trajectory prediction is an essential task in many applications, including autonomous driving, robotics, and surveillance systems. In this paper, we propose a novel trajectory prediction network, called TFBNet (trajectory feature-boosting network), that utilizes trajectory feature boosting to enhance prediction accuracy. TFBNet operates by [...] Read more.
Trajectory prediction is an essential task in many applications, including autonomous driving, robotics, and surveillance systems. In this paper, we propose a novel trajectory prediction network, called TFBNet (trajectory feature-boosting network), that utilizes trajectory feature boosting to enhance prediction accuracy. TFBNet operates by mapping the original trajectory data to a high-dimensional space, analyzing the change rules of the trajectory in this space, and finally aggregating the trajectory goals to generate the final trajectory. Our approach presents a new perspective on trajectory prediction. We evaluate TFBNet on five real-world datasets and compare it to state-of-the-art methods. Our results demonstrate that TFBNet achieves significant improvements in the ADE (average displacement error) and FDE (final displacement error) indicators, with increases of 46% and 52%, respectively. These results validate the effectiveness of our proposed approach and its potential to improve the performance of trajectory prediction models in various applications. Full article
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19 pages, 3411 KiB  
Article
Double-Layer Detection Model of Malicious PDF Documents Based on Entropy Method with Multiple Features
by Enzhou Song, Tao Hu, Peng Yi and Wenbo Wang
Entropy 2023, 25(7), 1099; https://doi.org/10.3390/e25071099 - 23 Jul 2023
Cited by 1 | Viewed by 960
Abstract
Traditional PDF document detection technology usually builds a rule or feature library for specific vulnerabilities and therefore is only fit for single detection targets and lacks anti-detection ability. To address these shortcomings, we build a double-layer detection model for malicious PDF documents based [...] Read more.
Traditional PDF document detection technology usually builds a rule or feature library for specific vulnerabilities and therefore is only fit for single detection targets and lacks anti-detection ability. To address these shortcomings, we build a double-layer detection model for malicious PDF documents based on an entropy method with multiple features. First, we address the single detection target problem with the fusion of 222 multiple features, including 130 basic features (such as objects, structure, content stream, metadata, etc.) and 82 dangerous features (such as suspicious and encoding function, etc.), which can effectively resist obfuscation and encryption. Second, we generate the best set of features (a total of 153) by creatively applying an entropy method based on RReliefF and MIC (EMBORAM) to PDF samples with 37 typical document vulnerabilities, which can effectively resist anti-detection methods, such as filling data and imitation attacks. Finally, we build a double-layer processing framework to detect samples efficiently through the AdaBoost-optimized random forest algorithm and the robustness-optimized support vector machine algorithm. Compared to the traditional static detection method, this model performs better for various evaluation criteria. The average time of document detection is 1.3 ms, while the accuracy rate reaches 95.9%. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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23 pages, 5510 KiB  
Article
Comparative Exergy and Environmental Assessment of the Residual Biomass Gasification Routes for Hydrogen and Ammonia Production
by Gabriel Gomes Vargas, Daniel Alexander Flórez-Orrego and Silvio de Oliveira Junior
Entropy 2023, 25(7), 1098; https://doi.org/10.3390/e25071098 - 22 Jul 2023
Cited by 4 | Viewed by 1980
Abstract
The need to reduce the dependency of chemicals on fossil fuels has recently motivated the adoption of renewable energies in those sectors. In addition, due to a growing population, the treatment and disposition of residual biomass from agricultural processes, such as sugar cane [...] Read more.
The need to reduce the dependency of chemicals on fossil fuels has recently motivated the adoption of renewable energies in those sectors. In addition, due to a growing population, the treatment and disposition of residual biomass from agricultural processes, such as sugar cane and orange bagasse, or even from human waste, such as sewage sludge, will be a challenge for the next generation. These residual biomasses can be an attractive alternative for the production of environmentally friendly fuels and make the economy more circular and efficient. However, these raw materials have been hitherto widely used as fuel for boilers or disposed of in sanitary landfills, losing their capacity to generate other by-products in addition to contributing to the emissions of gases that promote global warming. For this reason, this work analyzes and optimizes the biomass-based routes of biochemical production (namely, hydrogen and ammonia) using the gasification of residual biomasses. Moreover, the capture of biogenic CO2 aims to reduce the environmental burden, leading to negative emissions in the overall energy system. In this context, the chemical plants were designed, modeled, and simulated using Aspen plus™ software. The energy integration and optimization were performed using the OSMOSE Lua Platform. The exergy destruction, exergy efficiency, and general balance of the CO2 emissions were evaluated. As a result, the irreversibility generated by the gasification unit has a relevant influence on the exergy efficiency of the entire plant. On the other hand, an overall negative emission balance of −5.95 kgCO2/kgH2 in the hydrogen production route and −1.615 kgCO2/kgNH3 in the ammonia production route can be achieved, thus removing from the atmosphere 0.901 tCO2/tbiomass and 1.096 tCO2/tbiomass, respectively. Full article
(This article belongs to the Special Issue Thermodynamic Optimization of Industrial Energy Systems)
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17 pages, 4931 KiB  
Article
Chinese Few-Shot Named Entity Recognition and Knowledge Graph Construction in Managed Pressure Drilling Domain
by Siqing Wei, Yanchun Liang, Xiaoran Li, Xiaohui Weng, Jiasheng Fu and Xiaosong Han
Entropy 2023, 25(7), 1097; https://doi.org/10.3390/e25071097 - 22 Jul 2023
Cited by 1 | Viewed by 1415
Abstract
Managed pressure drilling (MPD) is the most effective means to ensure drilling safety, and MPD is able to avoid further deterioration of complex working conditions through precise control of the wellhead back pressure. The key to the success of MPD is the well [...] Read more.
Managed pressure drilling (MPD) is the most effective means to ensure drilling safety, and MPD is able to avoid further deterioration of complex working conditions through precise control of the wellhead back pressure. The key to the success of MPD is the well control strategy, which currently relies heavily on manual experience, hindering the automation and intelligence process of well control. In response to this issue, an MPD knowledge graph is constructed in this paper that extracts knowledge from published papers and drilling reports to guide well control. In order to improve the performance of entity extraction in the knowledge graph, a few-shot Chinese entity recognition model CEntLM-KL is extended from the EntLM model, in which the KL entropy is built to improve the accuracy of entity recognition. Through experiments on benchmark datasets, it has been shown that the proposed model has a significant improvement compared to the state-of-the-art methods. On the few-shot drilling datasets, the F-1 score of entity recognition reaches 33%. Finally, the knowledge graph is stored in Neo4J and applied for knowledge inference. Full article
(This article belongs to the Special Issue Entropy in Machine Learning Applications)
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20 pages, 1325 KiB  
Article
Feature Fusion Based on Graph Convolution Network for Modulation Classification in Underwater Communication
by Xiaohui Yao, Honghui Yang and Meiping Sheng
Entropy 2023, 25(7), 1096; https://doi.org/10.3390/e25071096 - 21 Jul 2023
Cited by 1 | Viewed by 1289
Abstract
Automatic modulation classification (AMC) of underwater acoustic communication signals is of great significance in national defense and marine military. Accurate modulation classification methods can make great contributions to accurately grasping the parameters and characteristics of enemy communication systems. While a poor underwater acoustic [...] Read more.
Automatic modulation classification (AMC) of underwater acoustic communication signals is of great significance in national defense and marine military. Accurate modulation classification methods can make great contributions to accurately grasping the parameters and characteristics of enemy communication systems. While a poor underwater acoustic channel makes it difficult to classify the modulation types correctly. Feature extraction and deep learning methods have proven to be effective methods for the modulation classification of underwater acoustic communication signals, but their performance is still limited by the complex underwater communication environment. Graph convolution networks (GCN) can learn the graph structured information of the data, making it an effective method for processing structured data. To improve the stability and robustness of AMC in underwater channels, we combined the feature extraction and deep learning methods by fusing the multi-domain features and deep features using GCN. The proposed method takes the relationships among the different multi-domain features and deep features into account. Firstly, a feature graph was built using the properties of the features. Secondly, multi-domain features were extracted from the received signals and deep features were extracted from the signals using a deep neural network. Thirdly, we constructed the input of GCN using these features and the graph. Then, the multi-domain features and deep features were fused by the GCN. Finally, we classified the modulation types using the output of GCN by way of a softmax layer. We conducted the experiments on a simulated dataset and a real-world dataset, respectively. The results show that the AMC based on GCN can achieve a significant improvement in performance compared to the current state-of-the-art methods. Our approach is robust in underwater acoustic channels. Full article
(This article belongs to the Special Issue Entropy and Information Theory in Acoustics III)
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11 pages, 295 KiB  
Article
Gas of Particles Obeying the Monotone Statistics
by Francesco Fidaleo
Entropy 2023, 25(7), 1095; https://doi.org/10.3390/e25071095 - 21 Jul 2023
Viewed by 858
Abstract
The present note is devoted to the detailed investigation of a concrete model satisfying the block-monotone statistics introduced in a previous paper (joint, with collaborators) of the author. The model under consideration indeed describes the free gas of massless particles in a one-dimensional [...] Read more.
The present note is devoted to the detailed investigation of a concrete model satisfying the block-monotone statistics introduced in a previous paper (joint, with collaborators) of the author. The model under consideration indeed describes the free gas of massless particles in a one-dimensional environment. This investigation can have consequences in two fundamental respects. The first one concerns the applicability of the (block-)monotone statistics to concrete physical models, yet completely unknown. Since the formula for the degeneracy of the energy-levels of the one-particle Hamiltonian of a free particle is very involved, the second aspect might be related to the, highly nontrivial, investigation of the expected thermodynamics of the free gas of particles obeying the block-monotone statistics in arbitrary spatial dimensions. A final section contains a comparison between the various (block, strict, and weak) monotone schemes with the Boltzmann statistics, which describes the gas of classical particles. It is seen that the block-monotone statistics, which takes into account the degeneracy of the energy-levels, seems the unique one having realistic physical applications. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness IV)
8 pages, 303 KiB  
Article
The Time Evolution of Mutual Information between Disjoint Regions in the Universe
by Biswajit Pandey
Entropy 2023, 25(7), 1094; https://doi.org/10.3390/e25071094 - 21 Jul 2023
Cited by 1 | Viewed by 1035
Abstract
We study the time evolution of mutual information between mass distributions in spatially separated but casually connected regions in an expanding universe. The evolution of mutual information is primarily determined by the configuration entropy rate, which depends on the dynamics of the expansion [...] Read more.
We study the time evolution of mutual information between mass distributions in spatially separated but casually connected regions in an expanding universe. The evolution of mutual information is primarily determined by the configuration entropy rate, which depends on the dynamics of the expansion and growth of density perturbations. The joint entropy between distributions from the two regions plays a negligible role in such evolution. Mutual information decreases with time in a matter-dominated universe, whereas it stays constant in a Λ-dominated universe. The ΛCDM model and some other models of dark energy predict a minimum in mutual information beyond which dark energy dominates the dynamics of the universe. Mutual information may have deeper connections to the dark energy and accelerated expansion of the universe. Full article
(This article belongs to the Special Issue Entropy, Time and Evolution II)
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12 pages, 283 KiB  
Article
The Necessary and Sufficient Conditions When Global and Local Fidelities Are Equal
by Seong-Kun Kim and Yonghae Lee
Entropy 2023, 25(7), 1093; https://doi.org/10.3390/e25071093 - 21 Jul 2023
Viewed by 911
Abstract
In the field of quantum information theory, the concept of quantum fidelity is employed to quantify the similarity between two quantum states. It has been observed that the fidelity between two states describing a bipartite quantum system AB is always less [...] Read more.
In the field of quantum information theory, the concept of quantum fidelity is employed to quantify the similarity between two quantum states. It has been observed that the fidelity between two states describing a bipartite quantum system AB is always less than or equal to the quantum fidelity between the states in subsystem A alone. While this fidelity inequality is well understood, determining the conditions under which the inequality becomes an equality remains an open question. In this paper, we present the necessary and sufficient conditions for the equality of fidelities between a bipartite system AB and subsystem A, considering pure quantum states. Moreover, we provide explicit representations of quantum states that satisfy the fidelity equality, based on our derived results. Full article
(This article belongs to the Special Issue Quantum Shannon Theory and Its Applications)
11 pages, 1562 KiB  
Article
Degree-Based Graph Entropy in Structure–Property Modeling
by Sourav Mondal and Kinkar Chandra Das
Entropy 2023, 25(7), 1092; https://doi.org/10.3390/e25071092 - 21 Jul 2023
Cited by 4 | Viewed by 1705
Abstract
Graph entropy plays an essential role in interpreting the structural information and complexity measure of a network. Let G be a graph of order n. Suppose dG(vi) is degree of the vertex vi for each [...] Read more.
Graph entropy plays an essential role in interpreting the structural information and complexity measure of a network. Let G be a graph of order n. Suppose dG(vi) is degree of the vertex vi for each i=1,2,,n. Now, the k-th degree-based graph entropy for G is defined as Id,k(G)=i=1ndG(vi)kj=1ndG(vj)klogdG(vi)kj=1ndG(vj)k, where k is real number. The first-degree-based entropy is generated for k=1, which has been well nurtured in last few years. As j=1ndG(vj)k yields the well-known graph invariant first Zagreb index, the Id,k for k=2 is worthy of investigation. We call this graph entropy as the second-degree-based entropy. The present work aims to investigate the role of Id,2 in structure property modeling of molecules. Full article
(This article belongs to the Special Issue Spectral Graph Theory, Topological Indices of Graph, and Entropy)
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50 pages, 3321 KiB  
Review
Non-Equilibrium Thermodynamics of Heat Transport in Superlattices, Graded Systems, and Thermal Metamaterials with Defects
by David Jou and Liliana Restuccia
Entropy 2023, 25(7), 1091; https://doi.org/10.3390/e25071091 - 20 Jul 2023
Cited by 2 | Viewed by 1307
Abstract
In this review, we discuss a nonequilibrium thermodynamic theory for heat transport in superlattices, graded systems, and thermal metamaterials with defects. The aim is to provide researchers in nonequilibrium thermodynamics as well as material scientists with a framework to consider in a systematic [...] Read more.
In this review, we discuss a nonequilibrium thermodynamic theory for heat transport in superlattices, graded systems, and thermal metamaterials with defects. The aim is to provide researchers in nonequilibrium thermodynamics as well as material scientists with a framework to consider in a systematic way several nonequilibrium questions about current developments, which are fostering new aims in heat transport, and the techniques for achieving them, for instance, defect engineering, dislocation engineering, stress engineering, phonon engineering, and nanoengineering. We also suggest some new applications in the particular case of mobile defects. Full article
(This article belongs to the Special Issue Thermodynamic Constitutive Theory and Its Application)
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11 pages, 812 KiB  
Article
Quantum Adversarial Transfer Learning
by Longhan Wang, Yifan Sun and Xiangdong Zhang
Entropy 2023, 25(7), 1090; https://doi.org/10.3390/e25071090 - 20 Jul 2023
Viewed by 1226
Abstract
Adversarial transfer learning is a machine learning method that employs an adversarial training process to learn the datasets of different domains. Recently, this method has attracted attention because it can efficiently decouple the requirements of tasks from insufficient target data. In this study, [...] Read more.
Adversarial transfer learning is a machine learning method that employs an adversarial training process to learn the datasets of different domains. Recently, this method has attracted attention because it can efficiently decouple the requirements of tasks from insufficient target data. In this study, we introduce the notion of quantum adversarial transfer learning, where data are completely encoded by quantum states. A measurement-based judgment of the data label and a quantum subroutine to compute the gradients are discussed in detail. We also prove that our proposal has an exponential advantage over its classical counterparts in terms of computing resources such as the gate number of the circuits and the size of the storage required for the generated data. Finally, numerical experiments demonstrate that our model can be successfully trained, achieving high accuracy on certain datasets. Full article
(This article belongs to the Topic Quantum Information and Quantum Computing)
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17 pages, 4797 KiB  
Article
Unstable Points, Ergodicity and Born’s Rule in 2d Bohmian Systems
by Athanasios C. Tzemos and George Contopoulos
Entropy 2023, 25(7), 1089; https://doi.org/10.3390/e25071089 - 20 Jul 2023
Cited by 3 | Viewed by 951
Abstract
We study the role of unstable points in the Bohmian flow of a 2d system composed of two non-interacting harmonic oscillators. In particular, we study the unstable points in the inertial frame of reference as well as in the frame of reference of [...] Read more.
We study the role of unstable points in the Bohmian flow of a 2d system composed of two non-interacting harmonic oscillators. In particular, we study the unstable points in the inertial frame of reference as well as in the frame of reference of the moving nodal points, in cases with 1, 2 and multiple nodal points. Then, we find the contributions of the ordered and chaotic trajectories in the Born distribution, and when the latter is accessible by an initial particle distribution which does not satisfy Born’s rule. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness IV)
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11 pages, 266 KiB  
Article
Upgrading the Fusion of Imprecise Classifiers
by Serafín Moral-García, María D. Benítez and Joaquín Abellán
Entropy 2023, 25(7), 1088; https://doi.org/10.3390/e25071088 - 19 Jul 2023
Viewed by 813
Abstract
Imprecise classification is a relatively new task within Machine Learning. The difference with standard classification is that not only is one state of the variable under study determined, a set of states that do not have enough information against them and cannot be [...] Read more.
Imprecise classification is a relatively new task within Machine Learning. The difference with standard classification is that not only is one state of the variable under study determined, a set of states that do not have enough information against them and cannot be ruled out is determined as well. For imprecise classification, a mode called an Imprecise Credal Decision Tree (ICDT) that uses imprecise probabilities and maximum of entropy as the information measure has been presented. A difficult and interesting task is to show how to combine this type of imprecise classifiers. A procedure based on the minimum level of dominance has been presented; though it represents a very strong method of combining, it has the drawback of an important risk of possible erroneous prediction. In this research, we use the second-best theory to argue that the aforementioned type of combination can be improved through a new procedure built by relaxing the constraints. The new procedure is compared with the original one in an experimental study on a large set of datasets, and shows improvement. Full article
(This article belongs to the Special Issue Selected Featured Papers from Entropy Editorial Board Members)
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14 pages, 4647 KiB  
Article
Low Noise Opto-Electro-Mechanical Modulator for RF-to-Optical Transduction in Quantum Communications
by Michele Bonaldi, Antonio Borrielli, Giovanni Di Giuseppe, Nicola Malossi, Bruno Morana, Riccardo Natali, Paolo Piergentili, Pasqualina Maria Sarro, Enrico Serra and David Vitali
Entropy 2023, 25(7), 1087; https://doi.org/10.3390/e25071087 - 19 Jul 2023
Cited by 2 | Viewed by 1429
Abstract
In this work, we present an Opto-Electro-Mechanical Modulator (OEMM) for RF-to-optical transduction realized via an ultra-coherent nanomembrane resonator capacitively coupled to an rf injection circuit made of a microfabricated read-out able to improve the electro-optomechanical interaction. This device configuration can be embedded in [...] Read more.
In this work, we present an Opto-Electro-Mechanical Modulator (OEMM) for RF-to-optical transduction realized via an ultra-coherent nanomembrane resonator capacitively coupled to an rf injection circuit made of a microfabricated read-out able to improve the electro-optomechanical interaction. This device configuration can be embedded in a Fabry–Perot cavity for electromagnetic cooling of the LC circuit in a dilution refrigerator exploiting the opto-electro-mechanical interaction. To this aim, an optically measured steady-state frequency shift of 380 Hz was seen with a polarization voltage of 30 V and a Q-factor of the assembled device above 106 at room temperature. The rf-sputtered titanium nitride layer can be made superconductive to develop efficient quantum transducers. Full article
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18 pages, 1826 KiB  
Article
Probing Intrinsic Neural Timescales in EEG with an Information-Theory Inspired Approach: Permutation Entropy Time Delay Estimation (PE-TD)
by Andrea Buccellato, Yasir Çatal, Patrizia Bisiacchi, Di Zang, Federico Zilio, Zhe Wang, Zengxin Qi, Ruizhe Zheng, Zeyu Xu, Xuehai Wu, Alessandra Del Felice, Ying Mao and Georg Northoff
Entropy 2023, 25(7), 1086; https://doi.org/10.3390/e25071086 - 19 Jul 2023
Cited by 1 | Viewed by 1346
Abstract
Time delays are a signature of many physical systems, including the brain, and considerably shape their dynamics; moreover, they play a key role in consciousness, as postulated by the temporo-spatial theory of consciousness (TTC). However, they are often not known a priori and [...] Read more.
Time delays are a signature of many physical systems, including the brain, and considerably shape their dynamics; moreover, they play a key role in consciousness, as postulated by the temporo-spatial theory of consciousness (TTC). However, they are often not known a priori and need to be estimated from time series. In this study, we propose the use of permutation entropy (PE) to estimate time delays from neural time series as a more robust alternative to the widely used autocorrelation window (ACW). In the first part, we demonstrate the validity of this approach on synthetic neural data, and we show its resistance to regimes of nonstationarity in time series. Mirroring yet another example of comparable behavior between different nonlinear systems, permutation entropy–time delay estimation (PE-TD) is also able to measure intrinsic neural timescales (INTs) (temporal windows of neural activity at rest) from hd-EEG human data; additionally, this replication extends to the abnormal prolongation of INT values in disorders of consciousness (DoCs). Surprisingly, the correlation between ACW-0 and PE-TD decreases in a state-dependent manner when consciousness is lost, hinting at potential different regimes of nonstationarity and nonlinearity in conscious/unconscious states, consistent with many current theoretical frameworks on consciousness. In summary, we demonstrate the validity of PE-TD as a tool to extract relevant time scales from neural data; furthermore, given the divergence between ACW and PE-TD specific to DoC subjects, we hint at its potential use for the characterization of conscious states. Full article
(This article belongs to the Special Issue Temporo-Spatial Theory of Consciousness (TTC))
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15 pages, 4993 KiB  
Article
EnRDeA U-Net Deep Learning of Semantic Segmentation on Intricate Noise Roads
by Xiaodong Yu, Ta-Wen Kuan, Shih-Pang Tseng, Ying Chen, Shuo Chen, Jhing-Fa Wang, Yuhang Gu and Tuoli Chen
Entropy 2023, 25(7), 1085; https://doi.org/10.3390/e25071085 - 19 Jul 2023
Cited by 5 | Viewed by 1580
Abstract
Road segmentation is beneficial to build a vision-controllable mission-oriented self-driving bot, e.g., the Self-Driving Sweeping Bot, or SDSB, for working in restricted areas. Using road segmentation, the bot itself and physical facilities may be protected and the sweeping efficiency of the SDSB promoted. [...] Read more.
Road segmentation is beneficial to build a vision-controllable mission-oriented self-driving bot, e.g., the Self-Driving Sweeping Bot, or SDSB, for working in restricted areas. Using road segmentation, the bot itself and physical facilities may be protected and the sweeping efficiency of the SDSB promoted. However, roads in the real world are generally exposed to intricate noise conditions as a result of changing weather and climate effects; these include sunshine spots, shadowing caused by trees or physical facilities, traffic obstacles and signs, and cracks or sealing signs resulting from long-term road usage, as well as different types of road materials, such as cement or asphalt; all of these factors greatly influence the effectiveness of road segmentation. In this work, we investigate the extension of Primordial U-Net by the proposed EnRDeA U-Net, which uses an input channel applying a Residual U-Net block as an encoder and an attention gate in the output channel as a decoder, to validate a dataset of intricate road noises. In addition, we carry out a detailed analysis of the nets’ features and segmentation performance to validate the intricate noises dataset on three U-Net extensions, i.e., the Primordial U-Net, Residual U-Net, and EnRDeA U-Net. Finally, the nets’ structures, parameters, training losses, performance indexes, etc., are presented and discussed in the experimental results. Full article
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21 pages, 366 KiB  
Article
Thermodynamics of Composition Graded Thermoelastic Solids
by Vito Antonio Cimmelli
Entropy 2023, 25(7), 1084; https://doi.org/10.3390/e25071084 - 19 Jul 2023
Viewed by 914
Abstract
We propose a thermodynamic model describing the thermoelastic behavior of composition graded materials. The compatibility of the model with the second law of thermodynamics is explored by applying a generalized Coleman–Noll procedure. For the material at hand, the specific entropy and the stress [...] Read more.
We propose a thermodynamic model describing the thermoelastic behavior of composition graded materials. The compatibility of the model with the second law of thermodynamics is explored by applying a generalized Coleman–Noll procedure. For the material at hand, the specific entropy and the stress tensor may depend on the gradient of the unknown fields, resulting in a very general theory. We calculate the speeds of coupled first- and second-sound pulses, propagating either trough nonequilibrium or equilibrium states. We characterize several different types of perturbations depending on the value of the material coefficients. Under the assumption that the deformation of the body can produce changes in its stoichiometry, altering locally the material composition, the possibility of propagation of pure stoichiometric waves is pointed out. Thermoelastic perturbations generated by the coupling of stoichiometric and thermal effects are analyzed as well. Full article
(This article belongs to the Special Issue Thermodynamic Constitutive Theory and Its Application)
17 pages, 2150 KiB  
Article
Synchronization Induced by Layer Mismatch in Multiplex Networks
by Md Sayeed Anwar, Sarbendu Rakshit, Jürgen Kurths and Dibakar Ghosh
Entropy 2023, 25(7), 1083; https://doi.org/10.3390/e25071083 - 19 Jul 2023
Cited by 2 | Viewed by 1030
Abstract
Heterogeneity among interacting units plays an important role in numerous biological and man-made complex systems. While the impacts of heterogeneity on synchronization, in terms of structural mismatch of the layers in multiplex networks, has been studied thoroughly, its influence on intralayer synchronization, in [...] Read more.
Heterogeneity among interacting units plays an important role in numerous biological and man-made complex systems. While the impacts of heterogeneity on synchronization, in terms of structural mismatch of the layers in multiplex networks, has been studied thoroughly, its influence on intralayer synchronization, in terms of parameter mismatch among the layers, has not been adequately investigated. Here, we study the intralayer synchrony in multiplex networks, where the layers are different from one other, due to parameter mismatch in their local dynamics. In such a multiplex network, the intralayer coupling strength for the emergence of intralayer synchronization decreases upon the introduction of impurity among the layers, which is caused by a parameter mismatch in their local dynamics. Furthermore, the area of occurrence of intralayer synchronization also widens with increasing mismatch. We analytically derive a condition under which the intralayer synchronous solution exists, and we even sustain its stability. We also prove that, in spite of the mismatch among the layers, all the layers of the multiplex network synchronize simultaneously. Our results indicate that a multiplex network with mismatched layers can induce synchrony more easily than a multiplex network with identical layers. Full article
(This article belongs to the Special Issue Synchronization in Complex Networks of Nonlinear Dynamical Systems)
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9 pages, 278 KiB  
Article
Thermodynamic Entropy as a Noether Invariant from Contact Geometry
by Alessandro Bravetti, Miguel Ángel García-Ariza and Diego Tapias
Entropy 2023, 25(7), 1082; https://doi.org/10.3390/e25071082 - 19 Jul 2023
Cited by 3 | Viewed by 1351
Abstract
We use a formulation of Noether’s theorem for contact Hamiltonian systems to derive a relation between the thermodynamic entropy and the Noether invariant associated with time-translational symmetry. In the particular case of thermostatted systems at equilibrium, we show that the total entropy of [...] Read more.
We use a formulation of Noether’s theorem for contact Hamiltonian systems to derive a relation between the thermodynamic entropy and the Noether invariant associated with time-translational symmetry. In the particular case of thermostatted systems at equilibrium, we show that the total entropy of the system plus the reservoir are conserved as a consequence thereof. Our results contribute to understanding thermodynamic entropy from a geometric point of view. Full article
(This article belongs to the Special Issue Geometric Structure of Thermodynamics: Theory and Applications)
28 pages, 1596 KiB  
Article
Decision Support System for Prioritization of Offshore Wind Farm Site by Utilizing Picture Fuzzy Combined Compromise Solution Group Decision Method
by Yuan Rong and Liying Yu
Entropy 2023, 25(7), 1081; https://doi.org/10.3390/e25071081 - 18 Jul 2023
Cited by 7 | Viewed by 1080
Abstract
The selection of offshore wind farm site (OWFS) has important strategic significance for vigorously developing offshore new energy and is deemed as a complicated uncertain multicriteria decision-making (MCDM) process. To further promote offshore wind power energy planning and provide decision support, this paper [...] Read more.
The selection of offshore wind farm site (OWFS) has important strategic significance for vigorously developing offshore new energy and is deemed as a complicated uncertain multicriteria decision-making (MCDM) process. To further promote offshore wind power energy planning and provide decision support, this paper proposes a hybrid picture fuzzy (PF) combined compromise solution (CoCoSo) technique for prioritization of OWFSs. To begin with, a fresh PF similarity measure is proffered to estimate the importance of experts. Next, the novel operational rules for PF numbers based upon the generalized Dombi norms are defined, and four novel generalized Dombi operators are propounded. Afterward, the PF preference selection index (PSI) method and PF stepwise weights assessment ratio analysis (SWARA) model are propounded to identify the objective and subjective weight of criteria, separately. In addition, the enhanced CoCoSo method is proffered via the similarity measure and new operators for ranking OWFSs with PF information. Lastly, the applicability and feasibility of the propounded PF-PSI-SWARA-CoCoSo method are adopted to ascertain the optimal OWFS. The comparison and sensibility investigations are also carried out to validate the robustness and superiority of our methodology. Results manifest that the developed methodology can offer powerful decision support for departments and managers to evaluate and choose the satisfying OWFSs. Full article
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24 pages, 2685 KiB  
Article
Wavelet-Based Multiscale Intermittency Analysis: The Effect of Deformation
by José M. Angulo and Ana E. Madrid
Entropy 2023, 25(7), 1080; https://doi.org/10.3390/e25071080 - 18 Jul 2023
Cited by 1 | Viewed by 895
Abstract
Intermittency represents a certain form of heterogeneous behavior that has interest in diverse fields of application, particularly regarding the characterization of system dynamics and for risk assessment. Given its intrinsic location-scale-dependent nature, wavelets constitute a useful functional tool for technical analysis of intermittency. [...] Read more.
Intermittency represents a certain form of heterogeneous behavior that has interest in diverse fields of application, particularly regarding the characterization of system dynamics and for risk assessment. Given its intrinsic location-scale-dependent nature, wavelets constitute a useful functional tool for technical analysis of intermittency. Deformation of the support may induce complex structural changes in a signal. In this paper, we study the effect of deformation on intermittency. Specifically, we analyze the interscale transfer of energy and its implications on different wavelet-based intermittency indicators, depending on whether the signal corresponds to a ‘level’- or a ‘flow’-type physical magnitude. Further, we evaluate the effect of deformation on the interscale distribution of energy in terms of generalized entropy and complexity measures. For illustration, various contrasting scenarios are considered based on simulation, as well as two segments corresponding to different regimes in a real seismic series before and after a significant earthquake. Full article
(This article belongs to the Section Signal and Data Analysis)
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