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Entropy
Volume 26
Issue 12
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Entropy, Volume 26, Issue 12 (December 2024) – 132 articles

Cover Story (view full-size image): Kinetic theory refers to the physical and mathematical approaches to a systematic deduction of the macroscopic behavior of many-particle systems from first principles, that is, starting from the microscopic equations of motion. This work presents kinetic theory based upon the Landau equation, describing the one-particle function in a weak interaction limit for self-propelled particles with alignment interactions. Self-propelled particles—driven units that break the conservation of momentum on a particle scale—are the epitome of active matter. This paper illustrates such particles that interact with nematic symmetry. The relevant equations can be brought into a diagrammatic form (first three orders are shown), allowing us to quantitatively extract accurate predictions for agent-based simulations. View this paper
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15 pages, 24936 KiB  
Article
A Model and Quantitative Framework for Evaluating Iterative Steganography
by Marcin Pery and Robert Waszkowski
Entropy 2024, 26(12), 1130; https://doi.org/10.3390/e26121130 - 23 Dec 2024
Viewed by 297
Abstract
This study presents a detailed characterization of iterative steganography, a unique class of information-hiding techniques, and proposes a formal mathematical model for their description. A novel quantitative measure, the Incremental Information Function (IIF), is introduced to evaluate the process of information gain in [...] Read more.
This study presents a detailed characterization of iterative steganography, a unique class of information-hiding techniques, and proposes a formal mathematical model for their description. A novel quantitative measure, the Incremental Information Function (IIF), is introduced to evaluate the process of information gain in iterative steganographic methods. The IIF offers a comprehensive framework for analyzing the step-by-step process of embedding information into a cover medium, focusing on the cumulative effects of each iteration in the encoding and decoding cycles. The practical application and efficacy of the proposed method are demonstrated using detailed case studies in video steganography. These examples highlight the utility of the IIF in delineating the properties and characteristics of iterative steganographic techniques. The findings reveal that the IIF effectively captures the incremental nature of information embedding and serves as a valuable tool for assessing the robustness and capacity of steganographic systems. This research provides significant insights into the field of information hiding, particularly in the development and evaluation of advanced steganographic methods. The IIF emerges as an innovative and practical analytical tool for researchers, offering a quantitative approach to understanding and optimizing iterative steganographic techniques. Full article
(This article belongs to the Section Signal and Data Analysis)
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20 pages, 549 KiB  
Article
Transpiling Quantum Assembly Language Circuits to a Qudit Form
by Denis A. Drozhzhin, Anastasiia S. Nikolaeva, Evgeniy O. Kiktenko and Aleksey K. Fedorov
Entropy 2024, 26(12), 1129; https://doi.org/10.3390/e26121129 - 23 Dec 2024
Viewed by 340
Abstract
In this paper, we introduce the workflow for converting qubit circuits represented by Open Quantum Assembly format (OpenQASM, also known as QASM) into the qudit form for execution on qudit hardware and provide a method for translating qudit experiment results back into qubit [...] Read more.
In this paper, we introduce the workflow for converting qubit circuits represented by Open Quantum Assembly format (OpenQASM, also known as QASM) into the qudit form for execution on qudit hardware and provide a method for translating qudit experiment results back into qubit results. We present the comparison of several qudit transpilation regimes, which differ in decomposition of multicontrolled gates: qubit as ordinary qubit transpilation and execution, qutrit with d=3 levels and single qubit in qudit, and ququart with d=4 levels and 2 qubits per ququart. We provide several examples of transpiling circuits for trapped ion qudit processors, which demonstrate potential advantages of qudits. Full article
(This article belongs to the Special Issue Quantum Computing with Trapped Ions)
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12 pages, 261 KiB  
Article
Fundamental Limits of an Irreversible Heat Engine
by Rui Fu
Entropy 2024, 26(12), 1128; https://doi.org/10.3390/e26121128 - 23 Dec 2024
Viewed by 321
Abstract
We investigated the optimal performance of an irreversible Stirling-like heat engine described by both overdamped and underdamped models within the framework of stochastic thermodynamics. By establishing a link between energy dissipation and Wasserstein distance, we derived the upper bound of maximal power that [...] Read more.
We investigated the optimal performance of an irreversible Stirling-like heat engine described by both overdamped and underdamped models within the framework of stochastic thermodynamics. By establishing a link between energy dissipation and Wasserstein distance, we derived the upper bound of maximal power that can be delivered over a complete engine cycle for both models. Additionally, we analytically developed an optimal control strategy to achieve this upper bound of maximal power and determined the efficiency at maximal power in the overdamped scenario. Full article
(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)
18 pages, 564 KiB  
Article
Refining the Allostatic Self-Efficacy Theory of Fatigue and Depression Using Causal Inference
by Alexander J. Hess, Dina von Werder, Olivia K. Harrison, Jakob Heinzle and Klaas Enno Stephan
Entropy 2024, 26(12), 1127; https://doi.org/10.3390/e26121127 - 23 Dec 2024
Viewed by 390
Abstract
Allostatic self-efficacy (ASE) represents a computational theory of fatigue and depression. In brief, it postulates that (i) fatigue is a feeling state triggered by a metacognitive diagnosis of loss of control over bodily states (persistently elevated interoceptive surprise); and that (ii) generalization of [...] Read more.
Allostatic self-efficacy (ASE) represents a computational theory of fatigue and depression. In brief, it postulates that (i) fatigue is a feeling state triggered by a metacognitive diagnosis of loss of control over bodily states (persistently elevated interoceptive surprise); and that (ii) generalization of low self-efficacy beliefs beyond bodily control induces depression. Here, we converted ASE theory into a structural causal model (SCM). This allowed identification of empirically testable hypotheses regarding causal relationships between the variables of interest. Applying conditional independence tests to questionnaire data from healthy volunteers, we sought to identify contradictions to the proposed SCM. Moreover, we estimated two causal effects proposed by ASE theory using three different methods. Our analyses identified specific aspects of the proposed SCM that were inconsistent with the available data. This enabled formulation of an updated SCM that can be tested against future data. Second, we confirmed the predicted negative average causal effect from metacognition of allostatic control to fatigue across all three different methods of estimation. Our study represents an initial attempt to refine and formalize ASE theory using methods from causal inference. Our results confirm key predictions from ASE theory but also suggest revisions which require empirical verification in future studies. Full article
(This article belongs to the Special Issue From Functional Imaging to Free Energy—Dedicated to Professor Karl Friston on the Occasion of His 65th Birthday)
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42 pages, 984 KiB  
Review
Applications of Entropy in Data Analysis and Machine Learning: A Review
by Salomé A. Sepúlveda-Fontaine and José M. Amigó
Entropy 2024, 26(12), 1126; https://doi.org/10.3390/e26121126 - 23 Dec 2024
Viewed by 971
Abstract
Since its origin in the thermodynamics of the 19th century, the concept of entropy has also permeated other fields of physics and mathematics, such as Classical and Quantum Statistical Mechanics, Information Theory, Probability Theory, Ergodic Theory and the Theory of Dynamical Systems. Specifically, [...] Read more.
Since its origin in the thermodynamics of the 19th century, the concept of entropy has also permeated other fields of physics and mathematics, such as Classical and Quantum Statistical Mechanics, Information Theory, Probability Theory, Ergodic Theory and the Theory of Dynamical Systems. Specifically, we are referring to the classical entropies: the Boltzmann–Gibbs, von Neumann, Shannon, Kolmogorov–Sinai and topological entropies. In addition to their common name, which is historically justified (as we briefly describe in this review), another commonality of the classical entropies is the important role that they have played and are still playing in the theory and applications of their respective fields and beyond. Therefore, it is not surprising that, in the course of time, many other instances of the overarching concept of entropy have been proposed, most of them tailored to specific purposes. Following the current usage, we will refer to all of them, whether classical or new, simply as entropies. In particular, the subject of this review is their applications in data analysis and machine learning. The reason for these particular applications is that entropies are very well suited to characterize probability mass distributions, typically generated by finite-state processes or symbolized signals. Therefore, we will focus on entropies defined as positive functionals on probability mass distributions and provide an axiomatic characterization that goes back to Shannon and Khinchin. Given the plethora of entropies in the literature, we have selected a representative group, including the classical ones. The applications summarized in this review nicely illustrate the power and versatility of entropy in data analysis and machine learning. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Applications—In Honor of Professor Osvaldo Anibal Rosso's 70th Birthday)
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17 pages, 5027 KiB  
Article
Ornstein–Uhlenbeck Adaptation as a Mechanism for Learning in Brains and Machines
by Jesús García Fernández, Nasir Ahmad and Marcel van Gerven
Entropy 2024, 26(12), 1125; https://doi.org/10.3390/e26121125 - 22 Dec 2024
Viewed by 501
Abstract
Learning is a fundamental property of intelligent systems, observed across biological organisms and engineered systems. While modern intelligent systems typically rely on gradient descent for learning, the need for exact gradients and complex information flow makes its implementation in biological and neuromorphic systems [...] Read more.
Learning is a fundamental property of intelligent systems, observed across biological organisms and engineered systems. While modern intelligent systems typically rely on gradient descent for learning, the need for exact gradients and complex information flow makes its implementation in biological and neuromorphic systems challenging. This has motivated the exploration of alternative learning mechanisms that can operate locally and do not rely on exact gradients. In this work, we introduce a novel approach that leverages noise in the parameters of the system and global reinforcement signals. Using an Ornstein–Uhlenbeck process with adaptive dynamics, our method balances exploration and exploitation during learning, driven by deviations from error predictions, akin to reward prediction error. Operating in continuous time, Ornstein–Uhlenbeck adaptation (OUA) is proposed as a general mechanism for learning in dynamic, time-evolving environments. We validate our approach across a range of different tasks, including supervised learning and reinforcement learning in feedforward and recurrent systems. Additionally, we demonstrate that it can perform meta-learning, adjusting hyper-parameters autonomously. Our results indicate that OUA provides a promising alternative to traditional gradient-based methods, with potential applications in neuromorphic computing. It also hints at a possible mechanism for noise-driven learning in the brain, where stochastic neurotransmitter release may guide synaptic adjustments. Full article
(This article belongs to the Special Issue Bayesian Inference and Mathematical Modeling in Complex Biological Systems)
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14 pages, 1997 KiB  
Article
Shannon Entropy Analysis of a Nuclear Fuel Pin Under Deep Burnup
by Wojciech R. Kubiński, Jan K. Ostrowski and Krzysztof W. Fornalski
Entropy 2024, 26(12), 1124; https://doi.org/10.3390/e26121124 - 22 Dec 2024
Viewed by 474
Abstract
This paper analyzes the behavior of the entropy of a nuclear fuel rod under deep burnup conditions, beyond standard operational ranges, reaching up to 60 years. The evolution of the neutron source distribution in a pressurized water reactor (PWR) fuel pin was analyzed [...] Read more.
This paper analyzes the behavior of the entropy of a nuclear fuel rod under deep burnup conditions, beyond standard operational ranges, reaching up to 60 years. The evolution of the neutron source distribution in a pressurized water reactor (PWR) fuel pin was analyzed using the Monte Carlo method and Shannon information entropy. To maintain proper statistics, a novel scaling method was developed, adjusting the neutron population based on the fission rate. By integrating reactor physics with information theory, this work aimed at the deeper understanding of nuclear fuel behavior under extreme burnup conditions. The results show a “U-shaped” entropy evolution: an initial decrease due to self-organization, followed by stabilization and eventual increase due to degradation. A minimum entropy state is reached after approximately 45 years of pin operation, showing a steady-state condition with no entropy change. This point may indicate a physical limit for fuel utilization. Beyond this point, entropy rises, reflecting system degradation and lower energy efficiency. The results show that entropy analysis can provide valuable insights into fuel behavior and operational limits. The proposed scaling method may also serve to control a Monte Carlo simulation, especially for the analysis of long-life reactors. Full article
(This article belongs to the Special Issue Insight into Entropy)
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23 pages, 6972 KiB  
Article
A Multi-Source Circular Geodesic Voting Model for Image Segmentation
by Shuwang Zhou, Minglei Shu and Chong Di
Entropy 2024, 26(12), 1123; https://doi.org/10.3390/e26121123 - 22 Dec 2024
Viewed by 263
Abstract
Image segmentation is a crucial task in artificial intelligence fields such as computer vision and medical imaging. While convolutional neural networks (CNNs) have achieved notable success by learning representative features from large datasets, they often lack geometric priors and global object information, limiting [...] Read more.
Image segmentation is a crucial task in artificial intelligence fields such as computer vision and medical imaging. While convolutional neural networks (CNNs) have achieved notable success by learning representative features from large datasets, they often lack geometric priors and global object information, limiting their accuracy in complex scenarios. Variational methods like active contours provide geometric priors and theoretical interpretability but require manual initialization and are sensitive to hyper-parameters. To overcome these challenges, we propose a novel segmentation approach, named PolarVoting, which combines the minimal path encoding rich geometric features and CNNs which can provide efficient initialization. The introduced model involves two main steps: firstly, we leverage the PolarMask model to extract multiple source points for initialization, and secondly, we construct a voting score map which implicitly contains the segmentation mask via a modified circular geometric voting (CGV) scheme. This map embeds global geometric information for finding accurate segmentation. By integrating neural network representation with geometric priors, the PolarVoting model enhances segmentation accuracy and robustness. Extensive experiments on various datasets demonstrate that the proposed PolarVoting method outperforms both PolarMask and traditional single-source CGV models. It excels in challenging imaging scenarios characterized by intensity inhomogeneity, noise, and complex backgrounds, accurately delineating object boundaries and advancing the state of image segmentation. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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45 pages, 447 KiB  
Article
Revisions of the Phenomenological and Statistical Statements of the Second Law of Thermodynamics
by Grzegorz Marcin Koczan and Roberto Zivieri
Entropy 2024, 26(12), 1122; https://doi.org/10.3390/e26121122 - 22 Dec 2024
Viewed by 433
Abstract
The status of the Second Law of Thermodynamics, even in the 21st century, is not as certain as when Arthur Eddington wrote about it a hundred years ago. It is not only about the truth of this law, but rather about its strict [...] Read more.
The status of the Second Law of Thermodynamics, even in the 21st century, is not as certain as when Arthur Eddington wrote about it a hundred years ago. It is not only about the truth of this law, but rather about its strict and exhaustive formulation. In the previous article, it was shown that two of the three most famous thermodynamic formulations of the Second Law of Thermodynamics are non-exhaustive. However, the status of the statistical approach, contrary to common and unfounded opinions, is even more difficult. It is known that Boltzmann did not manage to completely and correctly derive the Second Law of Thermodynamics from statistical mechanics, even though he probably did everything he could in this regard. In particular, he introduced molecular chaos into the extension of the Liouville equation, obtaining the Boltzmann equation. By using the H theorem, Boltzmann transferred the Second Law of Thermodynamics thesis to the molecular chaos hypothesis, which is not considered to be fully true. Therefore, the authors present a detailed and critical review of the issue of the Second Law of Thermodynamics and entropy from the perspective of phenomenological thermodynamics and statistical mechanics, as well as kinetic theory. On this basis, Propositions 1–3 for the statements of the Second Law of Thermodynamics are formulated in the original part of the article. Proposition 1 is based on resolving the misunderstanding of the Perpetuum Mobile of the Second Kind by introducing the Perpetuum Mobile of the Third Kind. Proposition 2 specifies the structure of allowed thermodynamic processes by using the Inequality of Heat and Temperature Proportions inspired by Eudoxus of Cnidus’s inequalities defining real numbers. Proposition 3 is a Probabilistic Scheme of the Second Law of Thermodynamics that, like a game, shows the statistical tendency for entropy to increase, even though the possibility of it decreasing cannot be completely ruled out. Proposition 3 is, in some sense, free from Loschmidt’s irreversibility paradox. Full article
(This article belongs to the Special Issue Trends in the Second Law of Thermodynamics)
12 pages, 285 KiB  
Article
Problem of Existence of Joint Distribution on Quantum Logic
by Oľga Nánásiová, Karla Čipková and Michal Zákopčan
Entropy 2024, 26(12), 1121; https://doi.org/10.3390/e26121121 - 21 Dec 2024
Viewed by 306
Abstract
This paper deals with the topics of modeling joint distributions on a generalized probability space. An algebraic structure known as quantum logic is taken as the basic model. There is a brief summary of some earlier published findings concerning a function s-map, [...] Read more.
This paper deals with the topics of modeling joint distributions on a generalized probability space. An algebraic structure known as quantum logic is taken as the basic model. There is a brief summary of some earlier published findings concerning a function s-map, which is a mathematical tool suitable for constructing virtual joint probabilities of even non-compatible propositions. The paper completes conclusions published in 2020 and extends the results for three or more random variables if the marginal distributions are known. The existence of a (n+1)-variate joint distribution is shown in special cases when the quantum logic consists of at most n blocks of Boolean algebras. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness V)
11 pages, 809 KiB  
Article
Computing Entropy for Long-Chain Alkanes Using Linear Regression: Application to Hydroisomerization
by Shrinjay Sharma, Richard Baur, Marcello Rigutto, Erik Zuidema, Umang Agarwal, Sofia Calero, David Dubbeldam and Thijs J. H. Vlugt
Entropy 2024, 26(12), 1120; https://doi.org/10.3390/e26121120 - 21 Dec 2024
Viewed by 389
Abstract
Entropies for alkane isomers longer than C10 are computed using our recently developed linear regression model for thermochemical properties which is based on second-order group contributions. The computed entropies show excellent agreement with experimental data and data from Scott’s tables which are [...] Read more.
Entropies for alkane isomers longer than C10 are computed using our recently developed linear regression model for thermochemical properties which is based on second-order group contributions. The computed entropies show excellent agreement with experimental data and data from Scott’s tables which are obtained from a statistical mechanics-based correlation. Entropy production and heat input are calculated for the hydroisomerization of C7 isomers in various zeolites (FAU-, ITQ-29-, BEA-, MEL-, MFI-, MTW-, and MRE-types) at 500 K at chemical equilibrium. Small variations in these properties are observed because of the differences in reaction equilibrium distributions for these zeolites. The effect of chain length on heat input and entropy production is also studied for the hydroisomerization of C7, C8, C10, and C14 isomers in MTW-type zeolite at 500 K. For longer chains, both heat input and entropy production increase. Enthalpies and absolute entropies of C7 hydroisomerization reaction products in MTW-type zeolite increase with higher temperatures. These findings highlight the accuracy of our linear regression model in computing entropies for alkanes and provide insight for designing and optimizing zeolite-catalyzed hydroisomerization processes. Full article
(This article belongs to the Special Issue The Entropy Production—as Cornerstone in Applied Nonequilibrium Thermodynamics—Dedicated to Professor Signe Kjelstrup on the Occasion of Her 75th Birthday)
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21 pages, 10983 KiB  
Review
Machine Learning Advances in High-Entropy Alloys: A Mini-Review
by Yibo Sun and Jun Ni
Entropy 2024, 26(12), 1119; https://doi.org/10.3390/e26121119 - 20 Dec 2024
Viewed by 414
Abstract
The efficacy of machine learning has increased exponentially over the past decade. The utilization of machine learning to predict and design materials has become a pivotal tool for accelerating materials development. High-entropy alloys are particularly intriguing candidates for exemplifying the potency of machine [...] Read more.
The efficacy of machine learning has increased exponentially over the past decade. The utilization of machine learning to predict and design materials has become a pivotal tool for accelerating materials development. High-entropy alloys are particularly intriguing candidates for exemplifying the potency of machine learning due to their superior mechanical properties, vast compositional space, and intricate chemical interactions. This review examines the general process of developing machine learning models. The advances and new algorithms of machine learning in the field of high-entropy alloys are presented in each part of the process. These advances are based on both improvements in computer algorithms and physical representations that focus on the unique ordering properties of high-entropy alloys. We also show the results of generative models, data augmentation, and transfer learning in high-entropy alloys and conclude with a summary of the challenges still faced in machine learning high-entropy alloys today. Full article
(This article belongs to the Special Issue Exploring Complexity: Short-Range Order in Medium and High-Entropy Materials)
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16 pages, 1635 KiB  
Article
EXIT Charts for Low-Density Algebra-Check Codes
by Zuo Tang, Jing Lei and Ying Huang
Entropy 2024, 26(12), 1118; https://doi.org/10.3390/e26121118 - 20 Dec 2024
Viewed by 269
Abstract
This paper focuses on the Low-Density Algebra-Check (LDAC) code, a novel low-rate channel code derived from the Low-Density Parity-Check (LDPC) code with expanded algebra-check constraints. A method for optimizing LDAC code design using Extrinsic Information Transfer (EXIT) charts is presented. Firstly, an iterative [...] Read more.
This paper focuses on the Low-Density Algebra-Check (LDAC) code, a novel low-rate channel code derived from the Low-Density Parity-Check (LDPC) code with expanded algebra-check constraints. A method for optimizing LDAC code design using Extrinsic Information Transfer (EXIT) charts is presented. Firstly, an iterative decoding model for LDAC is established according to its structure, and a method for plotting EXIT curves of the algebra-check node decoder is proposed. Then, the performance of two types of algebra-check nodes under different conditions is analyzed via EXIT curves. Finally, a low-rate LDAC code with enhanced coding gain is constructed, demonstrating the effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Advanced New Physical Layer Technologies for Next-Generation Wireless Communications)
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21 pages, 5924 KiB  
Article
Parallel Bayesian Optimization of Thermophysical Properties of Low Thermal Conductivity Materials Using the Transient Plane Source Method in the Body-Fitted Coordinate
by Huijuan Su, Jianye Kang, Yan Li, Mingxin Lyu, Yanhua Lai and Zhen Dong
Entropy 2024, 26(12), 1117; https://doi.org/10.3390/e26121117 - 20 Dec 2024
Viewed by 387
Abstract
The transient plane source (TPS) method heat transfer model was established. A body-fitted coordinate system is proposed to transform the unstructured grid structure to improve the speed of solving the heat transfer direct problem of the winding probe. A parallel Bayesian optimization algorithm [...] Read more.
The transient plane source (TPS) method heat transfer model was established. A body-fitted coordinate system is proposed to transform the unstructured grid structure to improve the speed of solving the heat transfer direct problem of the winding probe. A parallel Bayesian optimization algorithm based on a multi-objective hybrid strategy (MHS) is proposed based on an inverse problem. The efficiency of the thermophysical properties inversion was improved. The results show that the meshing method of 30° is the best. The transformation of body-fitted mesh is related to the orthogonality and density of the mesh. Compared with parameter inversion the computational fluid dynamics (CFD) software, the absolute values of the relative deviations of different materials are less than 0.03%. The calculation speeds of the body-fitted grid program are more than 36% and 91% higher than those of the CFD and self-developed unstructured mesh programs, respectively. The application of body-fitted coordinate system effectively improves the calculation speed of the TPS method. The MHS is more competitive than other algorithms in parallel mode, both in terms of accuracy and speed. The accuracy of the inversion is less affected by the number of initial samples, time range, and parallel points. The number of parallel points increased from 2 to 6, reducing the computation time by 66.6%. Adding parallel points effectively accelerates the convergence of algorithms. Full article
(This article belongs to the Section Thermodynamics)
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17 pages, 1972 KiB  
Article
A DNA Data Storage Method Using Spatial Encoding Based Lossless Compression
by Esra Şatır
Entropy 2024, 26(12), 1116; https://doi.org/10.3390/e26121116 - 20 Dec 2024
Viewed by 410
Abstract
With the rapid increase in global data and rapid development of information technology, DNA sequences have been collected and manipulated on computers. This has yielded a new and attractive field of bioinformatics, DNA storage, where DNA has been considered as a great potential [...] Read more.
With the rapid increase in global data and rapid development of information technology, DNA sequences have been collected and manipulated on computers. This has yielded a new and attractive field of bioinformatics, DNA storage, where DNA has been considered as a great potential storage medium. It is known that one gram of DNA can store 215 GB of data, and the data stored in the DNA can be preserved for tens of thousands of years. In this study, a lossless and reversible DNA data storage method was proposed. The proposed approach employs a vector representation of each DNA base in a two-dimensional (2D) spatial domain for both encoding and decoding. The structure of the proposed method is reversible, rendering the decompression procedure possible. Experiments were performed to investigate the capacity, compression ratio, stability, and reliability. The obtained results show that the proposed method is much more efficient in terms of capacity than other known algorithms in the literature. Full article
(This article belongs to the Special Issue Coding and Algorithms for DNA-Based Data Storage Systems)
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23 pages, 564 KiB  
Article
Lossless Image Compression Using Context-Dependent Linear Prediction Based on Mean Absolute Error Minimization
by Grzegorz Ulacha and Mirosław Łazoryszczak
Entropy 2024, 26(12), 1115; https://doi.org/10.3390/e26121115 - 20 Dec 2024
Viewed by 446
Abstract
This paper presents a method for lossless compression of images with fast decoding time and the option to select encoder parameters for individual image characteristics to increase compression efficiency. The data modeling stage was based on linear and nonlinear prediction, which was complemented [...] Read more.
This paper presents a method for lossless compression of images with fast decoding time and the option to select encoder parameters for individual image characteristics to increase compression efficiency. The data modeling stage was based on linear and nonlinear prediction, which was complemented by a simple block for removing the context-dependent constant component. The prediction was based on the Iterative Reweighted Least Squares (IRLS) method which allowed the minimization of mean absolute error. Two-stage compression was used to encode prediction errors: an adaptive Golomb and a binary arithmetic coding. High compression efficiency was achieved by using an author’s context-switching algorithm, which allows several prediction models tailored to the individual characteristics of each image area. In addition, an analysis of the impact of individual encoder parameters on efficiency and encoding time was conducted, and the efficiency of the proposed solution was shown against competing solutions, showing a 9.1% improvement in the bit average of files for the entire test base compared to JPEG-LS. Full article
(This article belongs to the Section Signal and Data Analysis)
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36 pages, 2037 KiB  
Article
Contextual Fine-Tuning of Language Models with Classifier-Driven Content Moderation for Text Generation
by Matan Punnaivanam and Palani Velvizhy
Entropy 2024, 26(12), 1114; https://doi.org/10.3390/e26121114 - 20 Dec 2024
Viewed by 573
Abstract
In today’s digital age, ensuring the appropriateness of content for children is crucial for their cognitive and emotional development. The rise of automated text generation technologies, such as Large Language Models like LLaMA, Mistral, and Zephyr, has created a pressing need for effective [...] Read more.
In today’s digital age, ensuring the appropriateness of content for children is crucial for their cognitive and emotional development. The rise of automated text generation technologies, such as Large Language Models like LLaMA, Mistral, and Zephyr, has created a pressing need for effective tools to filter and classify suitable content. However, the existing methods often fail to effectively address the intricate details and unique characteristics of children’s literature. This study aims to bridge this gap by developing a robust framework that utilizes fine-tuned language models, classification techniques, and contextual story generation to generate and classify children’s stories based on their suitability. Employing a combination of fine-tuning techniques on models such as LLaMA, Mistral, and Zephyr, alongside a BERT-based classifier, we evaluated the generated stories against established metrics like ROUGE, METEOR, and BERT Scores. The fine-tuned Mistral-7B model achieved a ROUGE-1 score of 0.4785, significantly higher than the base model’s 0.3185, while Zephyr-7B-Beta achieved a METEOR score of 0.4154 compared to its base counterpart’s score of 0.3602. The results indicated that the fine-tuned models outperformed base models, generating content more aligned with human standards. Moreover, the BERT Classifier exhibited high precision (0.95) and recall (0.97) for identifying unsuitable content, further enhancing the reliability of content classification. These findings highlight the potential of advanced language models in generating age-appropriate stories and enhancing content moderation strategies. This research has broader implications for educational technology, content curation, and parental control systems, offering a scalable approach to ensuring children’s exposure to safe and enriching narratives. Full article
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17 pages, 6381 KiB  
Article
Sample Augmentation Using Enhanced Auxiliary Classifier Generative Adversarial Network by Transformer for Railway Freight Train Wheelset Bearing Fault Diagnosis
by Jing Zhao, Junfeng Li, Zonghao Yuan, Tianming Mu, Zengqiang Ma and Suyan Liu
Entropy 2024, 26(12), 1113; https://doi.org/10.3390/e26121113 - 20 Dec 2024
Viewed by 376
Abstract
Diagnosing faults in wheelset bearings is critical for train safety. The main challenge is that only a limited amount of fault sample data can be obtained during high-speed train operations. This scarcity of samples impacts the training and accuracy of deep learning models [...] Read more.
Diagnosing faults in wheelset bearings is critical for train safety. The main challenge is that only a limited amount of fault sample data can be obtained during high-speed train operations. This scarcity of samples impacts the training and accuracy of deep learning models for wheelset bearing fault diagnosis. Studies show that the Auxiliary Classifier Generative Adversarial Network (ACGAN) demonstrates promising performance in addressing this issue. However, existing ACGAN models have drawbacks such as complexity, high computational expenses, mode collapse, and vanishing gradients. Aiming to address these issues, this paper presents the Transformer and Auxiliary Classifier Generative Adversarial Network (TACGAN), which increases the diversity, complexity and entropy of generated samples, and maximizes the entropy of the generated samples. The transformer network replaces traditional convolutional neural networks (CNNs), avoiding iterative and convolutional structures, thereby reducing computational expenses. Moreover, an independent classifier is integrated to prevent the coupling problem, where the discriminator is simultaneously identified and classified in the ACGAN. Finally, the Wasserstein distance is employed in the loss function to mitigate mode collapse and vanishing gradients. Experimental results using the train wheelset bearing datasets demonstrate the accuracy and effectiveness of the TACGAN. Full article
(This article belongs to the Section Multidisciplinary Applications)
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26 pages, 1215 KiB  
Article
Network Coding-Enhanced Polar Codes for Relay-Assisted Visible Light Communication Systems
by Congduan Li, Mingyang Zhong, Yiqian Zhang, Dan Song, Nanfeng Zhang and Jingfeng Yang
Entropy 2024, 26(12), 1112; https://doi.org/10.3390/e26121112 - 19 Dec 2024
Viewed by 531
Abstract
This paper proposes a novel polar coding scheme tailored for indoor visible light communication (VLC) systems. Simulation results demonstrate a significant reduction in bit error rate (BER) compared to uncoded transmission, with a coding gain of at least 5 dB. Furthermore, the reliable [...] Read more.
This paper proposes a novel polar coding scheme tailored for indoor visible light communication (VLC) systems. Simulation results demonstrate a significant reduction in bit error rate (BER) compared to uncoded transmission, with a coding gain of at least 5 dB. Furthermore, the reliable communication area of the VLC system is substantially extended. Building on this foundation, this study explores the joint design of polar codes and physical-layer network coding (PNC) for VLC systems. Simulation results illustrate that the BER of our scheme closely approaches that of the conventional VLC relay scheme. Moreover, our approach doubles the throughput, cuts equipment expenses in half, and boosts effective bit rates per unit time-slot twofold. This proposed design noticeably advances the performance of VLC systems and is particularly well-suited for scenarios with low-latency demands. Full article
(This article belongs to the Special Issue Advances in Modern Channel Coding)
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14 pages, 290 KiB  
Article
Bayesian Assessment of Corrosion-Related Failures in Steel Pipelines
by Fabrizio Ruggeri, Enrico Cagno, Franco Caron, Mauro Mancini and Antonio Pievatolo
Entropy 2024, 26(12), 1111; https://doi.org/10.3390/e26121111 - 19 Dec 2024
Viewed by 331
Abstract
The probability of gas escapes from steel pipelines due to different types of corrosion is studied with real failure data from an urban gas distribution network. Both the design and maintenance of the network are considered, identifying and estimating (in a Bayesian framework) [...] Read more.
The probability of gas escapes from steel pipelines due to different types of corrosion is studied with real failure data from an urban gas distribution network. Both the design and maintenance of the network are considered, identifying and estimating (in a Bayesian framework) an elementary multinomial model in the first case, and a more sophisticated non-homogeneous Poisson process in the second case. Special attention is paid to the elicitation of the experts’ opinions. We conclude that the corrosion process behaves quite differently depending on the type of corrosion, and that, in most cases, cathodically protected pipes should be installed. Full article
(This article belongs to the Special Issue Bayesianism)
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20 pages, 5238 KiB  
Article
A Novel Video Compression Approach Based on Two-Stage Learning
by Dan Shao, Ning Wang, Pu Chen, Yu Liu and Lin Lin
Entropy 2024, 26(12), 1110; https://doi.org/10.3390/e26121110 - 19 Dec 2024
Viewed by 439
Abstract
In recent years, the rapid growth of video data posed challenges for storage and transmission. Video compression techniques provided a viable solution to this problem. In this study, we proposed a bidirectional coding video compression model named DeepBiVC, which was based on two-stage [...] Read more.
In recent years, the rapid growth of video data posed challenges for storage and transmission. Video compression techniques provided a viable solution to this problem. In this study, we proposed a bidirectional coding video compression model named DeepBiVC, which was based on two-stage learning. Firstly, we conducted preprocessing on the video data by segmenting the video flow into groups of continuous image frames, with each group comprising five frames. Then, in the first stage, we developed an image compression module based on an invertible neural network (INN) model to compress the first and last frames of each group. In the second stage, we designed a video compression module that compressed the intermediate frames using bidirectional optical flow estimation. Experimental results indicated that DeepBiVC outperformed other state-of-the-art video compression methods regarding PSNR and MS-SSIM metrics. Specifically, on the VUG dataset at bpp = 0.3, DeepBiVC achieved a PSNR of 37.16 and an MS-SSIM of 0.98. Full article
(This article belongs to the Special Issue Information Theory and Coding for Image/Video Processing)
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17 pages, 4585 KiB  
Article
Effects of Temperature and Random Forces in Phase Transformation of Multi-Stable Systems
by Giuseppe Florio, Stefano Giordano and Giuseppe Puglisi
Entropy 2024, 26(12), 1109; https://doi.org/10.3390/e26121109 - 18 Dec 2024
Viewed by 419
Abstract
Multi-stable behavior at the microscopic length-scale is fundamental for phase transformation phenomena observed in many materials. These phenomena can be driven not only by external mechanical forces but are also crucially influenced by disorder and thermal fluctuations. Disorder, arising from structural defects or [...] Read more.
Multi-stable behavior at the microscopic length-scale is fundamental for phase transformation phenomena observed in many materials. These phenomena can be driven not only by external mechanical forces but are also crucially influenced by disorder and thermal fluctuations. Disorder, arising from structural defects or fluctuations in external stimuli, disrupts the homogeneity of the material and can significantly alter the system’s response, often leading to the suppression of cooperativity in the phase transition. Temperature can further introduce novel effects, modifying energy barriers and transition rates. The study of the effects of fluctuations requires the use of a framework that naturally incorporates the interaction of the system with the environment, such as Statistical Mechanics to account for the role of temperature. In the case of complex phenomena induced by disorder, advanced methods such as the replica method (to derive analytical formulas) or refined numerical methods based, for instance, on Monte Carlo techniques, may be needed. In particular, employing models that incorporate the main features of the physical system under investigation and allow for analytical results that can be compared with experimental data is of paramount importance for describing many realistic physical phenomena, which are often studied while neglecting the critical effect of randomness or by utilizing numerical techniques. Additionally, it is fundamental to efficiently derive the macroscopic material behavior from microscale properties, rather than relying solely on phenomenological approaches. In this perspective, we focus on a paradigmatic model that includes both nearest-neighbor interactions with multi-stable (elastic) energy terms and linear long-range interactions, capable of ensuring the presence of an ordered phase. Specifically, to study the effect of environmental noise on the control of the system, we include random fluctuation in external forces. We numerically analyze, on a small-size system, how the interplay of temperature and disorder can significantly alter the system’s phase transition behavior. Moreover, by mapping the model onto a modified version of the Random Field Ising Model, we utilize the replica method approach in the thermodynamic limit to justify the numerical results through analytical insights. Full article
(This article belongs to the Special Issue A Journey Through Complex Landscapes—Dedicated to Professor Giorgio Parisi to Celebrate the Nobel Prize & His 75th Birthday)
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19 pages, 2992 KiB  
Article
Asymmetric Cyclic Controlled Quantum Teleportation via Multiple-Qubit Entangled State in a Noisy Environment
by Hanxuan Zhou
Entropy 2024, 26(12), 1108; https://doi.org/10.3390/e26121108 - 18 Dec 2024
Viewed by 448
Abstract
In this paper, by using eleven entangled quantum states as a quantum channel, we propose a cyclic and asymmetric novel protocol for four participants in which both Alice and Bob can transmit two-qubit states, and Charlie can transmit three-qubit states with the assistance [...] Read more.
In this paper, by using eleven entangled quantum states as a quantum channel, we propose a cyclic and asymmetric novel protocol for four participants in which both Alice and Bob can transmit two-qubit states, and Charlie can transmit three-qubit states with the assistance of the supervisor David, who provides a guarantee for communication security. This protocol is based on GHZ state measurement (GHZ), single-qubit measurement (SM), and unitary operations (UO) to implement the communication task. The analysis demonstrates that the success probability of the proposed protocol can reach 100%. Furthermore, considering that in actual production environments, it is difficult to avoid the occurrence of noise in quantum channels, this paper also analyzes the changes in fidelity in four types of noisy scenarios: bit-flip noise, phase-flip noise, bit-phase-flip noise, and depolarizing noise. Showing that communication quality only depends on the amplitude parameters of the initial state and decoherence rate. Additionally, we give a comparison with previous similar schemes in terms of achieved method and intrinsic efficiency, which illustrates the superiority of our protocol. Finally, in response to the vulnerability of quantum channels to external attacks, a security analysis was conducted, and corresponding defensive measures were proposed. Full article
(This article belongs to the Section Quantum Information)
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15 pages, 726 KiB  
Article
W-Class States—Identification and Quantification of Bell-CHSH Inequalities’ Violation
by Joanna K. Kalaga, Wiesław Leoński and Jan Peřina, Jr.
Entropy 2024, 26(12), 1107; https://doi.org/10.3390/e26121107 - 18 Dec 2024
Cited by 3 | Viewed by 416
Abstract
We discuss a family of W-class states describing three-qubit systems. For such systems, we analyze the relations between the entanglement measures and the nonlocality parameter for a two-mode mixed state related to the two-qubit subsystem. We find the conditions determining the boundary values [...] Read more.
We discuss a family of W-class states describing three-qubit systems. For such systems, we analyze the relations between the entanglement measures and the nonlocality parameter for a two-mode mixed state related to the two-qubit subsystem. We find the conditions determining the boundary values of the negativity, parameterized by concurrence, for violating the Bell-CHSH inequality. Additionally, we derive the value ranges of the mixedness measure, parameterized by concurrence and negativity for the qubit–qubit mixed state, guaranteeing the violation and non-violation of the Bell-CHSH inequality. Full article
(This article belongs to the Special Issue Entropy in Classical and Quantum Information Theory with Applications)
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16 pages, 297 KiB  
Article
The Boltzmann Equation and Its Place in the Edifice of Statistical Mechanics
by Charlotte Werndl and Roman Frigg
Entropy 2024, 26(12), 1106; https://doi.org/10.3390/e26121106 - 18 Dec 2024
Viewed by 398
Abstract
It is customary to classify approaches in statistical mechanics (SM) as belonging either to Boltzmanninan SM (BSM) or Gibbsian SM (GSM). It is, however, unclear how the Boltzmann equation (BE) fits into either of these approaches. To discuss the relation between BE and [...] Read more.
It is customary to classify approaches in statistical mechanics (SM) as belonging either to Boltzmanninan SM (BSM) or Gibbsian SM (GSM). It is, however, unclear how the Boltzmann equation (BE) fits into either of these approaches. To discuss the relation between BE and BSM, we first present a version of BSM that differs from standard presentation in that it uses local field variables to individuate macro-states, and we then show that BE is a special case of BSM thus understood. To discuss the relation between BE and GSM, we focus on the BBGKY hierarchy and note the version of the BE that follows from the hierarchy is “Gibbsian” only in the minimal sense that it operates with an invariant measure on the state space of the full system. Full article
(This article belongs to the Special Issue Time and Temporal Asymmetries)
13 pages, 370 KiB  
Article
Enumerating Finitary Processes
by Benjamin D. Johnson, James P. Crutchfield, Christopher J. Ellison and Carl S. McTague
Entropy 2024, 26(12), 1105; https://doi.org/10.3390/e26121105 - 17 Dec 2024
Viewed by 284
Abstract
We show how to efficiently enumerate a class of finite-memory stochastic processes using the causal representation of ϵ-machines. We characterize ϵ-machines in the language of automata theory and adapt a recent algorithm for generating accessible deterministic finite automata, pruning this over-large [...] Read more.
We show how to efficiently enumerate a class of finite-memory stochastic processes using the causal representation of ϵ-machines. We characterize ϵ-machines in the language of automata theory and adapt a recent algorithm for generating accessible deterministic finite automata, pruning this over-large class down to that of ϵ-machines. As an application, we exactly enumerate topological ϵ-machines up to eight states and six-letter alphabets. Full article
(This article belongs to the Section Complexity)
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11 pages, 586 KiB  
Article
Stochastic Gradient Descent for Kernel-Based Maximum Correntropy Criterion
by Tiankai Li, Baobin Wang, Chaoquan Peng and Hong Yin
Entropy 2024, 26(12), 1104; https://doi.org/10.3390/e26121104 - 17 Dec 2024
Viewed by 409
Abstract
Maximum correntropy criterion (MCC) has been an important method in machine learning and signal processing communities since it was successfully applied in various non-Gaussian noise scenarios. In comparison with the classical least squares method (LS), which takes only the second-order moment of models [...] Read more.
Maximum correntropy criterion (MCC) has been an important method in machine learning and signal processing communities since it was successfully applied in various non-Gaussian noise scenarios. In comparison with the classical least squares method (LS), which takes only the second-order moment of models into consideration and belongs to the convex optimization problem, MCC captures the high-order information of models that play crucial roles in robust learning, which is usually accompanied by solving the non-convexity optimization problems. As we know, the theoretical research on convex optimizations has made significant achievements, while theoretical understandings of non-convex optimization are still far from mature. Motivated by the popularity of the stochastic gradient descent (SGD) for solving nonconvex problems, this paper considers SGD applied to the kernel version of MCC, which has been shown to be robust to outliers and non-Gaussian data in nonlinear structure models. As the existing theoretical results for the SGD algorithm applied to the kernel MCC are not well established, we present the rigorous analysis for the convergence behaviors and provide explicit convergence rates under some standard conditions. Our work can fill the gap between optimization process and convergence during the iterations: the iterates need to converge to the global minimizer while the obtained estimator cannot ensure the global optimality in the learning process. Full article
(This article belongs to the Special Issue Advances in Probabilistic Machine Learning)
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21 pages, 793 KiB  
Article
An Entropy Dynamics Approach to Inferring Fractal-Order Complexity in the Electromagnetics of Solids
by Basanta R. Pahari and William Oates
Entropy 2024, 26(12), 1103; https://doi.org/10.3390/e26121103 - 17 Dec 2024
Viewed by 478
Abstract
A fractal-order entropy dynamics model is developed to create a modified form of Maxwell’s time-dependent electromagnetic equations. The approach uses an information-theoretic method by combining Shannon’s entropy with fractional moment constraints in time and space. Optimization of the cost function leads to a [...] Read more.
A fractal-order entropy dynamics model is developed to create a modified form of Maxwell’s time-dependent electromagnetic equations. The approach uses an information-theoretic method by combining Shannon’s entropy with fractional moment constraints in time and space. Optimization of the cost function leads to a time-dependent Bayesian posterior density that is used to homogenize the electromagnetic fields. Self-consistency between maximizing entropy, inference of Bayesian posterior densities, and a fractal-order version of Maxwell’s equations are developed. We first give a set of relationships for fractal derivative definitions and their relationship to divergence, curl, and Laplacian operators. The fractal-order entropy dynamic framework is then introduced to infer the Bayesian posterior and its application to modeling homogenized electromagnetic fields in solids. The results provide a methodology to help understand complexity from limited electromagnetic data using maximum entropy by formulating a fractal form of Maxwell’s electromagnetic equations. Full article
(This article belongs to the Section Statistical Physics)
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14 pages, 546 KiB  
Article
Routing Algorithm Within the Multiple Non-Overlapping Paths’ Approach for Quantum Key Distribution Networks
by Evgeniy O. Kiktenko, Andrey Tayduganov and Aleksey K. Fedorov
Entropy 2024, 26(12), 1102; https://doi.org/10.3390/e26121102 - 16 Dec 2024
Viewed by 471
Abstract
We develop a novel key routing algorithm for quantum key distribution (QKD) networks that utilizes a distribution of keys between remote nodes, i.e., not directly connected by a QKD link, through multiple non-overlapping paths. This approach focuses on the security of a QKD [...] Read more.
We develop a novel key routing algorithm for quantum key distribution (QKD) networks that utilizes a distribution of keys between remote nodes, i.e., not directly connected by a QKD link, through multiple non-overlapping paths. This approach focuses on the security of a QKD network by minimizing potential vulnerabilities associated with individual trusted nodes. The algorithm ensures a balanced allocation of the workload across the QKD network links, while aiming for the _target key generation rate between directly connected and remote nodes. We present the results of testing the algorithm on two QKD network models consisting of 6 and 10 nodes. The testing demonstrates the ability of the algorithm to distribute secure keys among the nodes of the network in an all-to-all manner, ensuring that the information-theoretic security of the keys between remote nodes is maintained even when one of the trusted nodes is compromised. These results highlight the potential of the algorithm to improve the performance of QKD networks. Full article
(This article belongs to the Special Issue Quantum Communications Networks: Trends and Challenges)
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11 pages, 441 KiB  
Article
Symplectic Bregman Divergences
by Frank Nielsen
Entropy 2024, 26(12), 1101; https://doi.org/10.3390/e26121101 - 16 Dec 2024
Viewed by 432
Abstract
We present a generalization of Bregman divergences in finite-dimensional symplectic vector spaces that we term symplectic Bregman divergences. Symplectic Bregman divergences are derived from a symplectic generalization of the Fenchel–Young inequality which relies on the notion of symplectic subdifferentials. The symplectic Fenchel–Young inequality [...] Read more.
We present a generalization of Bregman divergences in finite-dimensional symplectic vector spaces that we term symplectic Bregman divergences. Symplectic Bregman divergences are derived from a symplectic generalization of the Fenchel–Young inequality which relies on the notion of symplectic subdifferentials. The symplectic Fenchel–Young inequality is obtained using the symplectic Fenchel transform which is defined with respect to the symplectic form. Since symplectic forms can be built generically from pairings of dual systems, we obtain a generalization of Bregman divergences in dual systems obtained by equivalent symplectic Bregman divergences. In particular, when the symplectic form is derived from an inner product, we show that the corresponding symplectic Bregman divergences amount to ordinary Bregman divergences with respect to composite inner products. Some potential applications of symplectic divergences in geometric mechanics, information geometry, and learning dynamics in machine learning are touched upon. Full article
(This article belongs to the Special Issue Information Geometry for Data Analysis)
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