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Entropy, Volume 27, Issue 1 (January 2025) – 61 articles

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16 pages, 3019 KiB  
Article
Transient Voltage Information Entropy Difference Unit Protection Based on Fault Condition Attribute Fusion
by Zhenwei Guo, Ruiqiang Zhao, Zebo Huang, Yongyan Jiang, Haojie Li and Yingcai Deng
Entropy 2025, 27(1), 61; https://doi.org/10.3390/e27010061 (registering DOI) - 11 Jan 2025
Abstract
Transient protection has the advantage of ultra-high-speed action, but traditional transient protection is susceptible to the influence of two fault condition attributes, namely, transition resistance and initial angle of fault, and there are the problems of insufficient sensitivity and insufficient reliability under weak [...] Read more.
Transient protection has the advantage of ultra-high-speed action, but traditional transient protection is susceptible to the influence of two fault condition attributes, namely, transition resistance and initial angle of fault, and there are the problems of insufficient sensitivity and insufficient reliability under weak faults. To this end, the propagation characteristics of high-frequency components of transient voltage in bus and line systems are explored, and a new method of unit protection based on the entropy difference in transient voltage information is proposed. In order to solve the problem of single-ended transient protection not being able to reliably distinguish line faults from bus faults and adjacent line first-end faults, the difference between the entropy of line voltage and the entropy of bus voltage was introduced as a fault characteristic. Aimed at the susceptibility of transient protection to the influence of fault condition attributes, composite fault characteristics containing fault attribute information were obtained by integrating fault characteristics with fault condition attributes to overcome the adverse influence of fault condition attributes on transient protection and improve the reliability of the protection. The algorithm solved 38.9% of the original cross-data, 36.1% of the false actions, and 6.1% of the rejected actions. Finally, the accuracy and reliability of the proposed algorithm were verified by extensive ATP-Draw simulation tests. Full article
(This article belongs to the Section Multidisciplinary Applications)
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21 pages, 3693 KiB  
Article
An Efficient Retinal Fluid Segmentation Network Based on Large Receptive Field Context Capture for Optical Coherence Tomography Images
by Hang Qi, Weijiang Wang, Hua Dang, Yueyang Chen, Minli Jia and Xiaohua Wang
Entropy 2025, 27(1), 60; https://doi.org/10.3390/e27010060 (registering DOI) - 11 Jan 2025
Abstract
Optical Coherence Tomography (OCT) is a crucial imaging modality for diagnosing and monitoring retinal diseases. However, the accurate segmentation of fluid regions and lesions remains challenging due to noise, low contrast, and blurred edges in OCT images. Although feature modeling with wide or [...] Read more.
Optical Coherence Tomography (OCT) is a crucial imaging modality for diagnosing and monitoring retinal diseases. However, the accurate segmentation of fluid regions and lesions remains challenging due to noise, low contrast, and blurred edges in OCT images. Although feature modeling with wide or global receptive fields offers a feasible solution, it typically leads to significant computational overhead. To address these challenges, we propose LKMU-Lite, a lightweight U-shaped segmentation method tailored for retinal fluid segmentation. LKMU-Lite integrates a Decoupled Large Kernel Attention (DLKA) module that captures both local patterns and long-range dependencies, thereby enhancing feature representation. Additionally, it incorporates a Multi-scale Group Perception (MSGP) module that employs Dilated Convolutions with varying receptive field scales to effectively predict lesions of different shapes and sizes. Furthermore, a novel Aggregating-Shift decoder is proposed, reducing model complexity while preserving feature integrity. With only 1.02 million parameters and a computational complexity of 3.82 G FLOPs, LKMU-Lite achieves state-of-the-art performance across multiple metrics on the ICF and RETOUCH datasets, demonstrating both its efficiency and generalizability compared to existing methods. Full article
(This article belongs to the Section Signal and Data Analysis)
21 pages, 384 KiB  
Review
The Group-Algebraic Formalism of Quantum Probability and Its Applications in Quantum Statistical Mechanics
by Yan Gu and Jiao Wang
Entropy 2025, 27(1), 59; https://doi.org/10.3390/e27010059 - 10 Jan 2025
Viewed by 215
Abstract
We show that the theory of quantum statistical mechanics is a special model in the framework of the quantum probability theory developed by mathematicians, by extending the characteristic function in the classical probability theory to the quantum probability theory. As dynamical variables of [...] Read more.
We show that the theory of quantum statistical mechanics is a special model in the framework of the quantum probability theory developed by mathematicians, by extending the characteristic function in the classical probability theory to the quantum probability theory. As dynamical variables of a quantum system must respect certain commutation relations, we take the group generated by a Lie algebra constructed with these commutation relations as the bridge, so that the classical characteristic function defined in a Euclidean space is transformed to a normalized, non-negative definite function defined in this group. Indeed, on the quantum side, this group-theoretical characteristic function is equivalent to the density matrix; hence, it can be adopted to represent the state of a quantum ensemble. It is also found that this new representation may have significant advantages in applications. As two examples, we show its effectiveness and convenience in solving the quantum-optical master equation for a harmonic oscillator coupled with its thermal environment, and in simulating the quantum cat map, a paradigmatic model for quantum chaos. Other related issues are reviewed and discussed as well. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness V)
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21 pages, 954 KiB  
Article
Advanced Monte Carlo for Acquisition Sampling in Bayesian Optimization
by Javier Garcia-Barcos and Ruben Martinez-Cantin
Entropy 2025, 27(1), 58; https://doi.org/10.3390/e27010058 - 10 Jan 2025
Viewed by 193
Abstract
Optimizing complex systems usually involves costly and time-consuming experiments, where selecting the experiments to perform is fundamental. Bayesian optimization (BO) has proved to be a suitable optimization method in these situations thanks to its sample efficiency and principled way of learning from previous [...] Read more.
Optimizing complex systems usually involves costly and time-consuming experiments, where selecting the experiments to perform is fundamental. Bayesian optimization (BO) has proved to be a suitable optimization method in these situations thanks to its sample efficiency and principled way of learning from previous data, but it typically requires that experiments are sequentially performed. Fully distributed BO addresses the need for efficient parallel and asynchronous active search, especially where traditional centralized BO faces limitations concerning privacy in federated learning and resource utilization in high-performance computing settings. Boltzmann sampling is an embarrassingly parallel method that enables fully distributed BO using Monte Carlo sampling. However, it also requires sampling from a continuous acquisition function, which can be challenging even for advanced Monte Carlo methods due to its highly multimodal nature, constrained search space, and possibly numerically unstable values. We introduce a simplified version of Boltzmann sampling, and we analyze multiple Markov chain Monte Carlo (MCMC) methods with a numerically improved log EI implementation for acquisition sampling. Our experiments suggest that by introducing gradient information during MCMC sampling, methods such as the MALA or CyclicalSGLD improve acquisition sampling efficiency. Interestingly, a mixture of proposals for the Metropolis–Hastings approach proves to be effective despite its simplicity. Full article
(This article belongs to the Special Issue Advances in Bayesian Optimization and Deep Reinforcement Learning)
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13 pages, 603 KiB  
Article
The Structure of Bit-String Similarity Networks
by David M. Schneider and Damián H. Zanette
Entropy 2025, 27(1), 57; https://doi.org/10.3390/e27010057 - 10 Jan 2025
Viewed by 223
Abstract
We study the structural properties of networks formed by random sets of bit strings—namely the ordered arrays of binary variables representing, for instance, genetic information or cultural profiles. Two bit strings are connected by a network link when they are sufficiently similar to [...] Read more.
We study the structural properties of networks formed by random sets of bit strings—namely the ordered arrays of binary variables representing, for instance, genetic information or cultural profiles. Two bit strings are connected by a network link when they are sufficiently similar to each other, i.e., when their Hamming distance is below a certain threshold. Using both analytical and numerical techniques, we determine the degree distribution and the conditions for the existence of a giant component in this kind of network. In addition, we analyze their clustering, assortativity, and mean geodesic distance. We show that these properties combine features specific to random networks with characteristics that derive from the Hamming metrics implicit in the definition of similarity between bit strings. 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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15 pages, 2003 KiB  
Article
Invariant Representation Learning in Multimedia Recommendation with Modality Alignment and Model Fusion
by Xinghang Hu and Haiteng Zhang
Entropy 2025, 27(1), 56; https://doi.org/10.3390/e27010056 - 10 Jan 2025
Viewed by 215
Abstract
Multimedia recommendation systems aim to accurately predict user preferences from multimodal data. However, existing methods may learn a recommendation model from spurious features, i.e., appearing to be related to an outcome but actually having no causal relationship with the outcome, leading to poor [...] Read more.
Multimedia recommendation systems aim to accurately predict user preferences from multimodal data. However, existing methods may learn a recommendation model from spurious features, i.e., appearing to be related to an outcome but actually having no causal relationship with the outcome, leading to poor generalization ability. While previous approaches have adopted invariant learning to address this issue, they simply concatenate multimodal data without proper alignment, resulting in information loss or redundancy. To overcome these challenges, we propose a framework called M3-InvRL, designed to enhance recommendation system performance through common and modality-specific representation learning, invariant learning, and model merging. Specifically, our approach begins by learning modality-specific representations along with a common representation for each modality. To achieve this, we introduce a novel contrastive loss that aligns representations and imposes mutual information constraints to extract modality-specific features, thereby preventing generalization issues within the same representation space. Next, we generate invariant masks based on the identification of heterogeneous environments to learn invariant representations. Finally, we integrate both invariant-specific and shared invariant representations for each modality to train models and fuse them in the output space, reducing uncertainty and enhancing generalization performance. Experiments on real-world datasets demonstrate the effectiveness of our approach. Full article
(This article belongs to the Special Issue Causal Inference in Recommender Systems)
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28 pages, 1249 KiB  
Article
Unified Analysis of Viscoelasticity and Viscoplasticity Using the Onsager Variational Principle
by Kwang Soo Cho
Entropy 2025, 27(1), 55; https://doi.org/10.3390/e27010055 - 10 Jan 2025
Viewed by 198
Abstract
This study is the application of the Onsager variational principle to viscoelasticity and viscoplasticity with the minimization of the assumptions which are popularly used in conventional approaches. The conventional approaches assume Kröner–Lee decomposition, incompressible plastic deformation, flowing rule, stress equation and so on. [...] Read more.
This study is the application of the Onsager variational principle to viscoelasticity and viscoplasticity with the minimization of the assumptions which are popularly used in conventional approaches. The conventional approaches assume Kröner–Lee decomposition, incompressible plastic deformation, flowing rule, stress equation and so on. These assumptions have been accumulated by many researchers for a long time and have shown many successful cases. The large number of successful assumptions leads to the conjecture that the mechanics can be described with a smaller number of assumptions. This paper shows that this conjecture is correct by using the Onsager variational principle. Full article
(This article belongs to the Section Thermodynamics)
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35 pages, 1319 KiB  
Article
Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions
by Mladen Pavičić
Entropy 2025, 27(1), 54; https://doi.org/10.3390/e27010054 - 9 Jan 2025
Viewed by 218
Abstract
Quantum contextuality plays a significant role in supporting quantum computation and quantum information theory. The key tools for this are the Kochen–Specker and non-Kochen–Specker contextual sets. Traditionally, their representation has been predominantly operator-based, mainly focusing on specific constructs in dimensions ranging from three [...] Read more.
Quantum contextuality plays a significant role in supporting quantum computation and quantum information theory. The key tools for this are the Kochen–Specker and non-Kochen–Specker contextual sets. Traditionally, their representation has been predominantly operator-based, mainly focusing on specific constructs in dimensions ranging from three to eight. However, nearly all of these constructs can be represented as low-dimensional hypergraphs. This study demonstrates how to generate contextual hypergraphs in any dimension using various methods, particularly those that do not scale in complexity with increasing dimensions. Furthermore, we introduce innovative examples of hypergraphs extending to dimension 32. Our methodology reveals the intricate structural properties of hypergraphs, enabling precise quantifications of contextuality. Additionally, we investigate several promising applications of hypergraphs in quantum communication and quantum computation, paving the way for future breakthroughs in the field. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness V)
24 pages, 2736 KiB  
Article
Is Word Order Responsive to Morphology? Disentangling Cause and Effect in Morphosyntactic Change in Five Western European Languages
by Julie Nijs, Freek Van de Velde and Hubert Cuyckens
Entropy 2025, 27(1), 53; https://doi.org/10.3390/e27010053 - 9 Jan 2025
Viewed by 271
Abstract
This study examines the relationship between morphological complexity and word order rigidity, addressing a gap in the literature regarding causality in linguistic changes. While prior research suggests that the loss of inflectional morphology correlates with the adoption of fixed word order, this study [...] Read more.
This study examines the relationship between morphological complexity and word order rigidity, addressing a gap in the literature regarding causality in linguistic changes. While prior research suggests that the loss of inflectional morphology correlates with the adoption of fixed word order, this study shifts the focus from correlation to causation. By employing Kolmogorov complexity as a measure of linguistic complexity alongside Granger Causality to examine causal relationships, we analyzed data from Germanic and Romance languages over time. Our findings indicate that changes in morphological complexity are statistically more likely to cause shifts in word order rigidity than vice versa. The causal asymmetry is robustly borne out in Dutch and German, though waveringly in English, as well as in French and Italian. Nowhere, however, is the asymmetry reversed. Together, these results can be interpreted as supporting the idea that a decline in morphological complexity causally precedes a rise in syntactic complexity, though further investigation into the underlying factors contributing to the differing trends across languages is needed. Full article
(This article belongs to the Special Issue Complexity Characteristics of Natural Language)
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30 pages, 13292 KiB  
Article
Entropy-Based Stochastic Optimization of Multi-Energy Systems in Gas-to-Methanol Processes Subject to Modeling Uncertainties
by Xueteng Wang, Jiandong Wang, Mengyao Wei and Yang Yue
Entropy 2025, 27(1), 52; https://doi.org/10.3390/e27010052 - 9 Jan 2025
Viewed by 225
Abstract
In gas-to-methanol processes, optimizing multi-energy systems is a critical challenge toward efficient energy allocation. This paper proposes an entropy-based stochastic optimization method for a multi-energy system in a gas-to-methanol process, aiming to achieve optimal allocation of gas, steam, and electricity to ensure executability [...] Read more.
In gas-to-methanol processes, optimizing multi-energy systems is a critical challenge toward efficient energy allocation. This paper proposes an entropy-based stochastic optimization method for a multi-energy system in a gas-to-methanol process, aiming to achieve optimal allocation of gas, steam, and electricity to ensure executability under modeling uncertainties. First, mechanistic models are developed for major chemical equipments, including the desulfurization, steam boilers, air separation, and syngas compressors. Structural errors in these models under varying operating conditions result in noticeable model uncertainties. Second, Bayesian estimation theory and the Markov Chain Monte Carlo approach are employed to analyze the differences between historical data and model predictions under varying operating conditions, thereby quantifying modeling uncertainties. Finally, subject to constraints in the model uncertainties, equipment capacities, and energy balance, a multi-objective stochastic optimization model is formulated to minimize gas loss, steam loss, and operating costs. The entropy weight approach is then applied to filter the Pareto front solution set, selecting a final optimal solution with minimal subjectivity and preferences. Case studies using Aspen Hysys-based simulations show that optimization solutions considering model uncertainties outperform the counterparts from a standard deterministic optimization in terms of executability. Full article
(This article belongs to the Section Multidisciplinary Applications)
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25 pages, 974 KiB  
Article
Thompson Sampling for Non-Stationary Bandit Problems
by Han Qi, Fei Guo and Li Zhu
Entropy 2025, 27(1), 51; https://doi.org/10.3390/e27010051 - 9 Jan 2025
Viewed by 215
Abstract
Non-stationary multi-armed bandit (MAB) problems have recently attracted extensive attention. We focus on the abruptly changing scenario where reward distributions remain constant for a certain period and change at unknown time steps. Although Thompson sampling (TS) has shown success in non-stationary settings, there [...] Read more.
Non-stationary multi-armed bandit (MAB) problems have recently attracted extensive attention. We focus on the abruptly changing scenario where reward distributions remain constant for a certain period and change at unknown time steps. Although Thompson sampling (TS) has shown success in non-stationary settings, there is currently no regret bound analysis for TS with uninformative priors. To address this, we propose two algorithms, discounted TS and sliding-window TS, designed for sub-Gaussian reward distributions. For these algorithms, we establish an upper bound for the expected regret by bounding the expected number of times a suboptimal arm is played. We show that the regret upper bounds of both algorithms are O~(TBT), where T is the time horizon and BT is the number of breakpoints. This upper bound matches the lower bound for abruptly changing problems up to a logarithmic factor. Empirical comparisons with other non-stationary bandit algorithms highlight the competitive performance of our proposed methods. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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22 pages, 3874 KiB  
Article
Measuring Complexity in Manufacturing: Integrating Entropic Methods, Programming and Simulation
by Germán Herrera-Vidal, Jairo R. Coronado-Hernández, Ivan Derpich-Contreras, Breezy P. Martínez Paredes and Gustavo Gatica
Entropy 2025, 27(1), 50; https://doi.org/10.3390/e27010050 - 9 Jan 2025
Viewed by 305
Abstract
This research addresses complexity in manufacturing systems from an entropic perspective for production improvement. The main objective is to develop and validate a methodology that develops an entropic metric of complexity in an integral way in production environments, through simulation and programming techniques. [...] Read more.
This research addresses complexity in manufacturing systems from an entropic perspective for production improvement. The main objective is to develop and validate a methodology that develops an entropic metric of complexity in an integral way in production environments, through simulation and programming techniques. The methodological proposal is composed of six stages: (i) Case study, (ii) Hypothesis formulation, (iii) Discrete event simulation, (iv) Measurement of entropic complexity by applying Shannon’s information theory, (v) Entropy analysis, and (vi) Statistical analysis by ANOVA. The results confirm that factors such as production sequence and product volume significantly influence the structural complexity of the workstations, with station A being less complex (0.4154 to 0.9913 bits) compared to stations B and C, which reached up to 2.2084 bits. This analysis has shown that optimizing production scheduling can reduce bottlenecks and improve system efficiency. Furthermore, the developed methodology, validated in a case study of the metalworking sector, provides a quantitative framework that combines discrete event simulation and robust statistical analysis, offering an effective tool to anticipate and manage complexity in production. In synthesis, this research presents an innovative methodology to measure static and dynamic complexity in manufacturing systems, with practical application to improve efficiency and competitiveness in the industrial sector. Full article
(This article belongs to the Section Complexity)
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26 pages, 727 KiB  
Article
Generalized Adaptive Diversity Gradient Descent Bit-Flipping with a Finite State Machine
by Jovan Milojković, Srdjan Brkić, Predrag Ivaniš and Bane Vasić
Entropy 2025, 27(1), 49; https://doi.org/10.3390/e27010049 - 9 Jan 2025
Viewed by 253
Abstract
In this paper, we introduce a novel gradient descent bit-flipping algorithm with a finite state machine (GDBF-wSM) for iterative decoding of low-density parity-check (LDPC) codes. The algorithm utilizes a finite state machine to update variable node potentials—for each variable node, the corresponding finite [...] Read more.
In this paper, we introduce a novel gradient descent bit-flipping algorithm with a finite state machine (GDBF-wSM) for iterative decoding of low-density parity-check (LDPC) codes. The algorithm utilizes a finite state machine to update variable node potentials—for each variable node, the corresponding finite state machine adjusts the update value based on whether the node was a candidate for flipping in previous iterations. We also present a learnable framework that can optimize decoder parameters using a database of uncorrectable error patterns. The performance of the proposed algorithm is illustrated for various regular LDPC codes, both in a binary symmetric channel (BSC) and the channel with additive white Gaussian noise (AWGN). The numerical results indicate a performance improvement when comparing our algorithm to previously proposed GDBF-based approaches. Full article
(This article belongs to the Special Issue Information Theory and Coding for Wireless Communications II)
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13 pages, 811 KiB  
Article
Subdiffusion Equation with Fractional Caputo Time Derivative with Respect to Another Function in Modeling Superdiffusion
by Tadeusz Kosztołowicz
Entropy 2025, 27(1), 48; https://doi.org/10.3390/e27010048 - 9 Jan 2025
Viewed by 239
Abstract
Superdiffusion is usually defined as a random walk process of a molecule, in which the time evolution of the mean-squared displacement, σ2, of the molecule is a power function of time, σ2(t)∼t2/γ [...] Read more.
Superdiffusion is usually defined as a random walk process of a molecule, in which the time evolution of the mean-squared displacement, σ2, of the molecule is a power function of time, σ2(t)∼t2/γ, with γ∈(1,2). An equation with a Riesz-type fractional derivative of the order γ with respect to a spatial variable (a fractional superdiffusion equation) is often used to describe superdiffusion. However, this equation leads to the formula σ2(t)=κt2/γ with κ=∞, which, in practice, makes it impossible to define the parameter γ. Moreover, due to the nonlocal nature of this derivative, it is generally not possible to impose boundary conditions at a thin partially permeable membrane. We show a model of superdiffusion based on an equation in which there is a fractional Caputo time derivative with respect to another function, g; the spatial derivative is of the second order. By choosing the function in an appropriate way, we obtain the g-superdiffusion equation, in which Green’s function (GF) in the long time limit approaches GF for the fractional superdiffusion equation. GF for the g-superdiffusion equation generates σ2 with finite κ. In addition, the boundary conditions at a thin membrane can be given in a similar way as for normal diffusion or subdiffusion. As an example, the filtration process generated by a partially permeable membrane in a superdiffusive medium is considered. Full article
(This article belongs to the Section Statistical Physics)
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10 pages, 813 KiB  
Article
Using Entropy to Measure Religious Pluralism
by George Sturm
Entropy 2025, 27(1), 47; https://doi.org/10.3390/e27010047 - 9 Jan 2025
Viewed by 207
Abstract
This paper discusses a unique and revolutionary method that quantitatively evaluates the programming of a media outlet regarding religious pluralism. Using a “program appeal” score and entropy measures from information theory, the broadcast operator is able to determine if governmental compliance is being [...] Read more.
This paper discusses a unique and revolutionary method that quantitatively evaluates the programming of a media outlet regarding religious pluralism. Using a “program appeal” score and entropy measures from information theory, the broadcast operator is able to determine if governmental compliance is being met and whether certain programs are problematic. The theoretical foundation of this tool is presented and illustrated using real-life data. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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15 pages, 3782 KiB  
Article
Self-Assembly of Particles on a Curved Mesh
by Gabriele Costa and Santi Prestipino
Entropy 2025, 27(1), 46; https://doi.org/10.3390/e27010046 - 9 Jan 2025
Viewed by 212
Abstract
Discrete statistical systems offer a significant advantage over systems defined in the continuum, since they allow for an easier enumeration of microstates. We introduce a lattice-gas model on the vertices of a polyhedron called a pentakis icosidodecahedron and draw its exact phase diagram [...] Read more.
Discrete statistical systems offer a significant advantage over systems defined in the continuum, since they allow for an easier enumeration of microstates. We introduce a lattice-gas model on the vertices of a polyhedron called a pentakis icosidodecahedron and draw its exact phase diagram by the Wang–Landau method. Using different values for the couplings between first-, second-, and third-neighbor particles, we explore various interaction patterns for the model, ranging from softly repulsive to Lennard-Jones-like and SALR. We highlight the existence of sharp transitions between distinct low-temperature “phases”, featuring, among others, regular polyhedral, cluster-crystal-like, and worm-like structures. When attempting to reproduce the equation of state of the model by Monte Carlo simulation, we find hysteretic behavior near zero temperature, implying a bottleneck issue for Metropolis dynamics near phase-crossover points. Full article
(This article belongs to the Special Issue Dimensional Crossover in Classical and Quantum Systems)
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10 pages, 5000 KiB  
Article
Coexistence Demonstration and Wavelength Dependency Analysis of S-Band CV-QKD Signal with Fully Loaded C+L-Band DWDM Signals
by Tetsuo Kawakami, Hiroki Kawahara, Toshihiko Okamura and Wakako Maeda
Entropy 2025, 27(1), 45; https://doi.org/10.3390/e27010045 - 8 Jan 2025
Viewed by 236
Abstract
We demonstrated the coexistence of an S-band CV-QKD signal with fully loaded C+L-band classical signals for the first time. The secret key rate of the S-band QKD system was 986 kbps with the C+L-band WDM signals transmitted through a 20 km G.654.E fiber [...] Read more.
We demonstrated the coexistence of an S-band CV-QKD signal with fully loaded C+L-band classical signals for the first time. The secret key rate of the S-band QKD system was 986 kbps with the C+L-band WDM signals transmitted through a 20 km G.654.E fiber link. We also revealed that the S-band CV-QKD performance limiting factor under the C+L-band WDM condition is the spontaneous Raman scattering light similar to the C-band CV-QKD performance limiting factor, confirming the validity of estimating the wavelength dependency of the secret key rate under the WDM condition from the fiber loss and the spontaneous Raman scattering light power. These results show that the CV-QKD performance under the C+L band WDM conditions becomes comparable to that under the C-band WDM conditions by wavelength design in the S-band. Full article
(This article belongs to the Special Issue Continuous Variables for Quantum Key Distribution and Quantum Random Number Generators)
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25 pages, 55235 KiB  
Article
Towards Quality Assessment for Arbitrary Translational 6DoF Video: Subjective Quality Database and Objective Assessment Metric
by Chongchong Jin and Yeyao Chen
Entropy 2025, 27(1), 44; https://doi.org/10.3390/e27010044 - 7 Jan 2025
Viewed by 322
Abstract
Arbitrary translational Six Degrees of Freedom (6DoF) video represents a transitional stage towards immersive terminal videos, allowing users to freely switch viewpoints for a 3D scene experience. However, the increased freedom of movement introduces new distortions that significantly impact human visual perception quality. [...] Read more.
Arbitrary translational Six Degrees of Freedom (6DoF) video represents a transitional stage towards immersive terminal videos, allowing users to freely switch viewpoints for a 3D scene experience. However, the increased freedom of movement introduces new distortions that significantly impact human visual perception quality. Therefore, it is crucial to explore quality assessment (QA) to validate its application feasibility. In this study, we conduct subjective and objective QAs of arbitrary translational 6DoF videos. Subjectively, we establish an arbitrary translational 6DoF synthesized video quality database, specifically exploring path navigation in 3D space, which has often been limited to planar navigation in previous studies. We simulate path navigation distortion, rendering distortion, and compression distortion to create a subjective QA database. Objectively, based on the spatio-temporal distribution characteristics of various distortions, we propose a no-reference video quality assessment (VQA) metric for arbitrary translational 6DoF videos. The experimental results on the established subjective dataset fully demonstrate the effectiveness and superiority of the proposed objective method. Full article
(This article belongs to the Section Signal and Data Analysis)
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7 pages, 206 KiB  
Article
On the Differential and the Integral Value of Information
by Raphael D. Levine
Entropy 2025, 27(1), 43; https://doi.org/10.3390/e27010043 - 7 Jan 2025
Viewed by 230
Abstract
A quantitative expression for the value of information within the framework of information theory and of the maximal entropy formulation is discussed. We examine both a local, differential measure and an integral, global measure for the value of the change in information when [...] Read more.
A quantitative expression for the value of information within the framework of information theory and of the maximal entropy formulation is discussed. We examine both a local, differential measure and an integral, global measure for the value of the change in information when additional input is provided. The differential measure is a potential and as such carries a physical dimension. The integral value has the dimension of information. The differential measure can be used, for example, to discuss how the value of information changes with time or with other parameters of the problem. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
6 pages, 230 KiB  
Article
Operational Meaning of Classical Fidelity and Path Length in Kubo–Mori–Bogoliubov Fisher Geometry
by Lajos Diósi
Entropy 2025, 27(1), 42; https://doi.org/10.3390/e27010042 - 7 Jan 2025
Viewed by 282
Abstract
We show that the minimum entropy production in near-reversible quantum state transport along a path is a simple function of the path length measured according to the Fisher–KMB metrics. Hence, for the sharp values of path lengths, also called statistical lengths, we obtain [...] Read more.
We show that the minimum entropy production in near-reversible quantum state transport along a path is a simple function of the path length measured according to the Fisher–KMB metrics. Hence, for the sharp values of path lengths, also called statistical lengths, we obtain the operational meaning to quantify the residual irreversibility in near-reversible state transport. In the classical limit, the Bhattacharyya fidelity is found to have a sharp operational meaning after eighty years. Full article
(This article belongs to the Section Quantum Information)
27 pages, 365 KiB  
Article
Self-Normalized Moderate Deviations for Degenerate U-Statistics
by Lin Ge, Hailin Sang and Qi-Man Shao
Entropy 2025, 27(1), 41; https://doi.org/10.3390/e27010041 - 7 Jan 2025
Viewed by 226
Abstract
In this paper, we study self-normalized moderate deviations for degenerate U-statistics of order 2. Let {Xi,i≥1} be i.i.d. random variables and consider symmetric and degenerate kernel functions in the form [...] Read more.
In this paper, we study self-normalized moderate deviations for degenerate U-statistics of order 2. Let {Xi,i≥1} be i.i.d. random variables and consider symmetric and degenerate kernel functions in the form h(x,y)=∑l=1∞λlgl(x)gl(y), where λl>0, Egl(X1)=0, and gl(X1) is in the domain of attraction of a normal law for all l≥1. Under the condition ∑l=1∞λl<∞ and some truncated conditions for {gl(X1):l≥1}, we show that logP(∑1≤i≠j≤nh(Xi,Xj)max1≤l<∞λlVn,l2≥xn2)∼−xn22 for xn→∞ and xn=o(n), where Vn,l2=∑i=1ngl2(Xi). As application, a law of the iterated logarithm is also obtained. Full article
(This article belongs to the Special Issue The Random Walk Path of Pál Révész in Probability)
21 pages, 10962 KiB  
Article
Cryptanalysis of an Image Encryption Algorithm Using DNA Coding and Chaos
by Yuzhuo Zhao, Qiqin Shi and Qun Ding
Entropy 2025, 27(1), 40; https://doi.org/10.3390/e27010040 - 7 Jan 2025
Viewed by 299
Abstract
In recent years, many chaotic image encryption algorithms have been cracked by chosen plaintext attack. Therefore, the method of associating the key with the plaintext to resist the cryptanalysis has received extensive attention from designers. This paper proposes a new method of cryptanalysis [...] Read more.
In recent years, many chaotic image encryption algorithms have been cracked by chosen plaintext attack. Therefore, the method of associating the key with the plaintext to resist the cryptanalysis has received extensive attention from designers. This paper proposes a new method of cryptanalysis for image encryption algorithms with a key associated with plaintext. We broke an image encryption scheme using chaos and DNA encoding. Through our comprehensive security analysis, we found a security vulnerability in the mechanism of the association between the key and plaintext and proposed a breaking scheme. The experimental results show that the chosen plaintext attack can recover the cipher image to the plain image. The cryptanalysis scheme proposed in this paper can provide new ideas for subsequent cryptanalysis work and also provide some meaningful references for designers to improve the security of encryption algorithms when designing them. In addition, we also propose an improved logistic chaotic map with random bit-position scrambling. The improved chaotic map has a wider parameter range and a larger Lyapunov exponent. In the end, some suggestions are given to improve the original algorithm to resist such attacks. Full article
(This article belongs to the Topic Recent Trends in Nonlinear, Chaotic and Complex Systems)
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31 pages, 753 KiB  
Article
Reconstruction of Multiple Strings of Constant Weight from Prefix–Suffix Compositions
by Yaoyu Yang and Zitan Chen
Entropy 2025, 27(1), 39; https://doi.org/10.3390/e27010039 - 6 Jan 2025
Viewed by 305
Abstract
Motivated by studies of data retrieval in polymer-based storage systems, we consider the problem of reconstructing a multiset of binary strings that have the same length and the same weight from the compositions of their prefixes and suffixes of every possible length. We [...] Read more.
Motivated by studies of data retrieval in polymer-based storage systems, we consider the problem of reconstructing a multiset of binary strings that have the same length and the same weight from the compositions of their prefixes and suffixes of every possible length. We provide necessary and sufficient conditions for which unique reconstruction up to the reversal of the strings is possible. Additionally, we present two algorithms for reconstructing strings from the compositions of prefixes and suffixes of constant-length constant-weight strings. Full article
(This article belongs to the Special Issue Coding and Algorithms for DNA-Based Data Storage Systems)
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19 pages, 402 KiB  
Article
A Novel Hyper-Heuristic Algorithm with Soft and Hard Constraints for Causal Discovery Using a Linear Structural Equation Model
by Yinglong Dang, Xiaoguang Gao and Zidong Wang
Entropy 2025, 27(1), 38; https://doi.org/10.3390/e27010038 - 6 Jan 2025
Viewed by 369
Abstract
Artificial intelligence plays an indispensable role in improving productivity and promoting social development, and causal discovery is one of the extremely important research directions in this field. Acyclic directed graphs (DAGs) are the most commonly used tool in causal modeling because of their [...] Read more.
Artificial intelligence plays an indispensable role in improving productivity and promoting social development, and causal discovery is one of the extremely important research directions in this field. Acyclic directed graphs (DAGs) are the most commonly used tool in causal modeling because of their excellent interpretability and structural properties. However, in the face of insufficient data, the accuracy and efficiency of DAGs learning are greatly reduced, resulting in a false perception of causality. As intuitive expert knowledge, structural constraints control DAG learning by limiting the causal relationship between variables, which is expected to solve the above-mentioned problem. However, it is often impossible to build a DAG by relying on expert knowledge alone. To solve this problem, we propose the use of expert knowledge as a hard constraint and the structural prior gained via data learning as a soft constraint. In this paper, we propose a fitness-rate-rank-based multiarmed bandit (FRRMAB) hyper-heuristic that integrates soft and hard constraints into the DAG learning process. For a linear structural equation model (SEM), soft constraints are obtained via partial correlation analysis. The experimental results on different networks show that the proposed method has higher scalability and accuracy. Full article
(This article belongs to the Special Issue Causal Graphical Models and Their Applications)
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13 pages, 1876 KiB  
Article
Information Theoretical Analysis of Quantum Mixedness in a Finite Model of Interacting Fermions
by Diana Monteoliva, Angelo Plastino and Angel Ricardo Plastino
Entropy 2025, 27(1), 37; https://doi.org/10.3390/e27010037 - 6 Jan 2025
Viewed by 321
Abstract
In this study, we utilize information theory tools to investigate notable features of the quantum degree of mixedness (Cf) in a finite model of N interacting fermions. This model serves as a simplified proxy for an atomic nucleus, capturing its [...] Read more.
In this study, we utilize information theory tools to investigate notable features of the quantum degree of mixedness (Cf) in a finite model of N interacting fermions. This model serves as a simplified proxy for an atomic nucleus, capturing its essential features in a more manageable form compared to a realistic nuclear model, which would require the diagonalization of matrices with millions of elements, making the extraction of qualitative features a significant challenge. Specifically, we aim to correlate Cf with particle number fluctuations and temperature, using the paradigmatic Lipkin model. Our analysis reveals intriguing dependencies of Cf on the total fermion number, showcasing distinct behaviors at different temperatures. Notably, we find that the degree of quantum mixedness exhibits a strong dependence on the total fermion number, with varying trends across different temperature regimes. Remarkably, this dependence remains unaffected by the strength of the fermion–fermion interaction (as long as it is non-zero), underscoring the robustness of the observed phenomena. Through comprehensive numerical simulations, we provide illustrative graphs depicting these dependencies, offering valuable insights into the fundamental characteristics of quantum many-body fermion systems. Our findings illuminate the intricate dynamics of the degree of mixedness, a crucial quantum property, with potential implications for diverse fields ranging from condensed matter physics to quantum information science. 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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5 pages, 210 KiB  
Article
On the Komlós–Révész SLLN for Ψ-Mixing Sequences
by Zbigniew S. Szewczak
Entropy 2025, 27(1), 36; https://doi.org/10.3390/e27010036 - 4 Jan 2025
Viewed by 258
Abstract
The Komlós–Révész strong law of large numbers (SLLN) is proved for ψ-mixing sequences without a rate assumption. Full article
(This article belongs to the Special Issue The Random Walk Path of Pál Révész in Probability)
17 pages, 399 KiB  
Article
Greedy Algorithm for Deriving Decision Rules from Decision Tree Ensembles
by Evans Teiko Tetteh and Beata Zielosko
Entropy 2025, 27(1), 35; https://doi.org/10.3390/e27010035 - 4 Jan 2025
Viewed by 407
Abstract
This study introduces a greedy algorithm for deriving decision rules from decision tree ensembles, targeting enhanced interpretability and generalization in distributed data environments. Decision rules, known for their transparency, provide an accessible method for knowledge extraction from data, facilitating decision-making processes across diverse [...] Read more.
This study introduces a greedy algorithm for deriving decision rules from decision tree ensembles, targeting enhanced interpretability and generalization in distributed data environments. Decision rules, known for their transparency, provide an accessible method for knowledge extraction from data, facilitating decision-making processes across diverse fields. Traditional decision tree algorithms, such as CART and ID3, are employed to induce decision trees from bootstrapped datasets, which represent distributed data sources. Subsequently, a greedy algorithm is applied to derive decision rules that are true across multiple decision trees. Experiments are performed, taking into account knowledge representation and discovery perspectives. They show that, as the value of α, 0≤α<1, increases, shorter rules are obtained, and also it is possible to improve the classification accuracy of rule-based models. Full article
(This article belongs to the Special Issue Methods in Artificial Intelligence and Information Processing, Third Edition)
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7 pages, 216 KiB  
Article
An Erdős-Révész Type Law for the Length of the Longest Match of Two Coin-Tossing Sequences
by Karl Grill
Entropy 2025, 27(1), 34; https://doi.org/10.3390/e27010034 - 3 Jan 2025
Viewed by 295
Abstract
Consider a coin-tossing sequence, i.e., a sequence of independent variables, taking values 0 and 1 with probability 1/2. The famous Erdős-Rényi law of large numbers implies that the longest run of ones in the first n observations has a length [...] Read more.
Consider a coin-tossing sequence, i.e., a sequence of independent variables, taking values 0 and 1 with probability 1/2. The famous Erdős-Rényi law of large numbers implies that the longest run of ones in the first n observations has a length Rn that behaves like log(n), as n tends to infinity (throughout this article, log denotes logarithm with base 2). Erdős and Révész refined this result by providing a description of the Lévy upper and lower classes of the process Rn. In another direction, Arratia and Waterman extended the Erdős-Rényi result to the longest matching subsequence (with shifts) of two coin-tossing sequences, finding that it behaves asymptotically like 2log(n). The present paper provides some Erdős-Révész type results in this situation, obtaining a complete description of the upper classes and a partial result on the lower ones. Full article
(This article belongs to the Special Issue The Random Walk Path of Pál Révész in Probability)
9 pages, 283 KiB  
Article
On the Convergence Rate for the Longest at Most T-Contaminated Runs of Heads
by István Fazekas, Borbála Fazekas and László Fórián
Entropy 2025, 27(1), 33; https://doi.org/10.3390/e27010033 - 3 Jan 2025
Viewed by 266
Abstract
In this paper, we study the usual coin tossing experiment. We call a run at most T-contaminated, if it contains at most T tails. We approximate the distribution of the length of the longest at most T-contaminated runs. We offer a [...] Read more.
In this paper, we study the usual coin tossing experiment. We call a run at most T-contaminated, if it contains at most T tails. We approximate the distribution of the length of the longest at most T-contaminated runs. We offer a more precise approximation than the previous one. Full article
(This article belongs to the Special Issue The Random Walk Path of Pál Révész in Probability)
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23 pages, 575 KiB  
Article
Towards Secure Internet of Things: A Coercion-Resistant Attribute-Based Encryption Scheme with Policy Revocation
by Yuan Zhai, Tao Wang, Yanwei Zhou, Feng Zhu and Bo Yang
Entropy 2025, 27(1), 32; https://doi.org/10.3390/e27010032 - 2 Jan 2025
Viewed by 319
Abstract
With the development and application of the Internet of Things (IoT), the volume of data generated daily by IoT devices is growing exponentially. These IoT devices, such as smart wearable devices, produce data containing sensitive personal information. However, since IoT devices and users [...] Read more.
With the development and application of the Internet of Things (IoT), the volume of data generated daily by IoT devices is growing exponentially. These IoT devices, such as smart wearable devices, produce data containing sensitive personal information. However, since IoT devices and users often operate in untrusted external environments, their encrypted data remain vulnerable to potential privacy leaks and security threats from malicious coercion. Additionally, access control and management of these data remain critical issues. To address these challenges, this paper proposes a novel coercion-resistant ciphertext-policy attribute-based encryption scheme. The scheme leverages chameleon hashing to enhance deniable encryption, achieving coercion resistance, thereby enabling IoT data to resist coercion attacks. Moreover, the scheme employs attribute-based encryption to secure IoT data, enabling fine-grained access control and dynamic user access management, providing a secure and flexible solution for vast IoT data. We construct the scheme on a composite order bilinear group and provide formal proofs for its coercion resistance, correctness, and security. Finally, through experimental comparisons, we demonstrate the efficiency and feasibility of the proposed scheme. Full article
(This article belongs to the Special Issue Information Security and Data Privacy)
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