Journal Description
Entropy
Entropy
is an international and interdisciplinary peer-reviewed open access journal of entropy and information studies, published monthly online by MDPI. The International Society for the Study of Information (IS4SI) and Spanish Society of Biomedical Engineering (SEIB) are affiliated with Entropy and their members receive a discount on the article processing charge.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, SCIE (Web of Science), MathSciNet, Inspec, PubMed, PMC, Astrophysics Data System, and other databases.
- Journal Rank: JCR - Q2 (Physics, Multidisciplinary) / CiteScore - Q1 (Mathematical Physics)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 20.8 days after submission; acceptance to publication is undertaken in 2.9 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Testimonials: See what our editors and authors say about Entropy.
- Companion journals for Entropy include: Foundations, Thermo and MAKE.
Impact Factor:
2.7 (2022);
5-Year Impact Factor:
2.6 (2022)
Latest Articles
LF3PFL: A Practical Privacy-Preserving Federated Learning Algorithm Based on Local Federalization Scheme
Entropy 2024, 26(5), 353; https://doi.org/10.3390/e26050353 - 23 Apr 2024
Abstract
In the realm of federated learning (FL), the exchange of model data may inadvertently expose sensitive information of participants, leading to significant privacy concerns. Existing FL privacy-preserving techniques, such as differential privacy (DP) and secure multi-party computing (SMC), though offering viable solutions, face
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In the realm of federated learning (FL), the exchange of model data may inadvertently expose sensitive information of participants, leading to significant privacy concerns. Existing FL privacy-preserving techniques, such as differential privacy (DP) and secure multi-party computing (SMC), though offering viable solutions, face practical challenges including reduced performance and complex implementations. To overcome these hurdles, we propose a novel and pragmatic approach to privacy preservation in FL by employing localized federated updates (LF3PFL) aimed at enhancing the protection of participant data. Furthermore, this research refines the approach by incorporating cross-entropy optimization, carefully fine-tuning measurement, and improving information loss during the model training phase to enhance both model efficacy and data confidentiality. Our approach is theoretically supported and empirically validated through extensive simulations on three public datasets: CIFAR-10, Shakespeare, and MNIST. We evaluate its effectiveness by comparing training accuracy and privacy protection against state-of-the-art techniques. Our experiments, which involve five distinct local models (Simple-CNN, ModerateCNN, Lenet, VGG9, and Resnet18), provide a comprehensive assessment across a variety of scenarios. The results clearly demonstrate that LF3PFL not only maintains competitive training accuracies but also significantly improves privacy preservation, surpassing existing methods in practical applications. This balance between privacy and performance underscores the potential of localized federated updates as a key component in future FL privacy strategies, offering a scalable and effective solution to one of the most pressing challenges in FL.
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(This article belongs to the Special Issue Information Security and Data Privacy)
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DiffFSRE: Diffusion-Enhanced Prototypical Network for Few-Shot Relation Extraction
by
Yang Chen and Bowen Shi
Entropy 2024, 26(5), 352; https://doi.org/10.3390/e26050352 - 23 Apr 2024
Abstract
Supervised learning methods excel in traditional relation extraction tasks. However, the quality and scale of the training data heavily influence their performance. Few-shot relation extraction is gradually becoming a research hotspot whose objective is to learn and extract semantic relationships between entities with
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Supervised learning methods excel in traditional relation extraction tasks. However, the quality and scale of the training data heavily influence their performance. Few-shot relation extraction is gradually becoming a research hotspot whose objective is to learn and extract semantic relationships between entities with only a limited number of annotated samples. In recent years, numerous studies have employed prototypical networks for few-shot relation extraction. However, these methods often suffer from overfitting of the relation classes, making it challenging to generalize effectively to new relationships. Therefore, this paper seeks to utilize a diffusion model for data augmentation to address the overfitting issue of prototypical networks. We propose a diffusion model-enhanced prototypical network framework. Specifically, we design and train a controllable conditional relation generation diffusion model on the relation extraction dataset, which can generate the corresponding instance representation according to the relation description. Building upon the trained diffusion model, we further present a pseudo-sample-enhanced prototypical network, which is able to provide more accurate representations for prototype classes, thereby alleviating overfitting and better generalizing to unseen relation classes. Additionally, we introduce a pseudo-sample-aware attention mechanism to enhance the model’s adaptability to pseudo-sample data through a cross-entropy loss, further improving the model’s performance. A series of experiments are conducted to prove our method’s effectiveness. The results indicate that our proposed approach significantly outperforms existing methods, particularly in low-resource one-shot environments. Further ablation analyses underscore the necessity of each module in the model. As far as we know, this is the first research to employ a diffusion model for enhancing the prototypical network through data augmentation in few-shot relation extraction.
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(This article belongs to the Special Issue Natural Language Processing and Data Mining)
Open AccessArticle
An Efficient Image Cryptosystem Utilizing Difference Matrix and Genetic Algorithm
by
Honglian Shen and Xiuling Shan
Entropy 2024, 26(5), 351; https://doi.org/10.3390/e26050351 - 23 Apr 2024
Abstract
Aiming at addressing the security and efficiency challenges during image transmission, an efficient image cryptosystem utilizing difference matrix and genetic algorithm is proposed in this paper. A difference matrix is a typical combinatorial structure that exhibits properties of discretization and approximate uniformity. It
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Aiming at addressing the security and efficiency challenges during image transmission, an efficient image cryptosystem utilizing difference matrix and genetic algorithm is proposed in this paper. A difference matrix is a typical combinatorial structure that exhibits properties of discretization and approximate uniformity. It can serve as a pseudo-random sequence, offering various scrambling techniques while occupying a small storage space. The genetic algorithm generates multiple ciphertext images with strong randomness through local crossover and mutation operations, then obtains high-quality ciphertext images through multiple iterations using the optimal preservation strategy. The whole encryption process is divided into three stages: first, the difference matrix is generated; second, it is utilized for initial encryption to ensure that the resulting ciphertext image has relatively good initial randomness; finally, multiple rounds of local genetic operations are used to optimize the output. The proposed cryptosystem is demonstrated to be effective and robust through simulation experiments and statistical analyses, highlighting its superiority over other existing algorithms.
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(This article belongs to the Topic AI and Computational Methods for Modelling, Simulations and Optimizing of Advanced Systems: Innovations in Complexity)
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Open AccessArticle
Planetary Energy Flow and Entropy Production Rate by Earth from 2002 to 2023
by
Elijah Thimsen
Entropy 2024, 26(5), 350; https://doi.org/10.3390/e26050350 - 23 Apr 2024
Abstract
In this work, satellite data from the Clouds and Earth’s Radiant Energy System (CERES) and Moderate Resolution Imaging Spectroradiometer (MODIS) instruments are analyzed to determine how the global absorbed sunlight and global entropy production rates have changed from 2002 to 2023. The data
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In this work, satellite data from the Clouds and Earth’s Radiant Energy System (CERES) and Moderate Resolution Imaging Spectroradiometer (MODIS) instruments are analyzed to determine how the global absorbed sunlight and global entropy production rates have changed from 2002 to 2023. The data is used to test hypotheses derived from the Maximum Power Principle (MPP) and Maximum Entropy Production Principle (MEP) about the evolution of Earth’s surface and atmosphere. The results indicate that both the rate of absorbed sunlight and global entropy production have increased over the last 20 years, which is consistent with the predictions of both hypotheses. Given the acceptance of the MPP or MEP, some peripheral extensions and nuances are discussed.
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(This article belongs to the Collection Disorder and Biological Physics)
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Efficient Constant Envelope Precoding for Massive MU-MIMO Downlink via Majorization-Minimization Method
by
Rui Liang, Hui Li, Yingli Dong and Guodong Xue
Entropy 2024, 26(4), 349; https://doi.org/10.3390/e26040349 - 21 Apr 2024
Abstract
The practical implementation of massive multi-user multi-input–multi-output (MU-MIMO) downlink communication systems power amplifiers that are energy efficient; otherwise, the power consumption of the base station (BS) will be prohibitive. Constant envelope (CE) precoding is gaining increasing interest for its capability to utilize low-cost,
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The practical implementation of massive multi-user multi-input–multi-output (MU-MIMO) downlink communication systems power amplifiers that are energy efficient; otherwise, the power consumption of the base station (BS) will be prohibitive. Constant envelope (CE) precoding is gaining increasing interest for its capability to utilize low-cost, high-efficiency nonlinear radio frequency amplifiers. Our work focuses on the topic of CE precoding in massive MU-MIMO systems and presents an efficient CE precoding algorithm. This algorithm uses an alternating minimization (AltMin) framework to optimize the CE precoded signal and precoding factor, aiming to minimize the difference between the received signal and the transmit symbol. For the optimization of the CE precoded signal, we provide a powerful approach that integrates the majorization-minimization (MM) method and the fast iterative shrinkage-thresholding (FISTA) method. This algorithm combines the characteristics of the massive MU-MIMO channel with the second-order Taylor expansion to construct the surrogate function in the MM method, in which minimizing this surrogate function is the worst-case of the system. Specifically, we expand the suggested CE precoding algorithm to involve the discrete constant envelope (DCE) precoding case. In addition, we thoroughly examine the exact property, convergence, and computational complexity of the proposed algorithm. Simulation results demonstrate that the proposed CE precoding algorithm can achievean uncoded biterror rate (BER) performance gain of roughly compared to the existing CE precoding algorithm and has an acceptable computational complexity. This performance advantage also exists when it comes to DCE precoding.
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(This article belongs to the Special Issue Information Theory for MIMO Systems)
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Bipartite Unique Neighbour Expanders via Ramanujan Graphs
by
Ron Asherov and Irit Dinur
Entropy 2024, 26(4), 348; https://doi.org/10.3390/e26040348 - 20 Apr 2024
Abstract
We construct an infinite family of bounded-degree bipartite unique neighbour expander graphs with arbitrarily unbalanced sides. Although weaker than the lossless expanders constructed byCapalbo et al.,our construction is simpler and may be closer to being implementable in practice, due to the smaller constants.
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We construct an infinite family of bounded-degree bipartite unique neighbour expander graphs with arbitrarily unbalanced sides. Although weaker than the lossless expanders constructed byCapalbo et al.,our construction is simpler and may be closer to being implementable in practice, due to the smaller constants. We construct these graphs by composing bipartite Ramanujan graphs with a fixed-size gadget in a way that generalises the construction of unique neighbour expanders by Alon and Capalbo. For the analysis of our construction, we prove a strong upper bound on average degrees in small induced subgraphs of bipartite Ramanujan graphs. Our bound generalises Kahale’s average degree bound to bipartite Ramanujan graphs, and may be of independent interest. Surprisingly, our bound strongly relies on the exact Ramanujan-ness of the graph and is not known to hold for nearly-Ramanujan graphs.
Full article
(This article belongs to the Special Issue Extremal and Additive Combinatorial Aspects in Information Theory)
Open AccessArticle
Simulation of Natural Convection with Sinusoidal Temperature Distribution of Heat Source at the Bottom of an Enclosed Square Cavity
by
Min Zeng, Zhiqiang Wang, Ying Xu and Qiang Ma
Entropy 2024, 26(4), 347; https://doi.org/10.3390/e26040347 - 19 Apr 2024
Abstract
The lattice Boltzmann method is employed in the current study to simulate the heat transfer characteristics of sinusoidal-temperature-distributed heat sources at the bottom of a square cavity under various conditions, including different amplitudes, phase angles, initial positions, and angular velocities. Additionally, a machine
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The lattice Boltzmann method is employed in the current study to simulate the heat transfer characteristics of sinusoidal-temperature-distributed heat sources at the bottom of a square cavity under various conditions, including different amplitudes, phase angles, initial positions, and angular velocities. Additionally, a machine learning-based model is developed to accurately predict the Nusselt number in such a sinusoidal temperature distribution of heat source at the bottom of a square cavity. The results indicate that (1) in the phase angle range from 0 to π, Nu basically shows a decreasing trend with an increase in phase angle. The decline in Nu at an accelerated rate is consistently observed when the phase angle reaches 4π/16. The corresponding Nu decreases as the amplitude increases at the same phase angle. (2) The initial position of the sinusoidal-temperature-distributed heat source Lc significantly impacts the convective heat transfer in the cavity. Moreover, the decline in Nu was further exacerbated when Lc reached 7/16. (3) The optimal overall heat transfer effect was achieved when the angular velocity of the non-uniform heat source reached π. As the angular velocity increases, the local Nu in the square cavity exhibits a gradual and oscillatory decline. Notably, it is observed that Nu at odd multiples of π surpasses that at even multiples of π. Furthermore, the current work integrates LBM with machine learning, enabling the development of a precise and efficient prediction model for simulating Nu under specific operational conditions. This research provides valuable insights into the application of machine learning in the field of heat transfer.
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(This article belongs to the Special Issue Computational Thermodynamics and Its Applications)
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Evaluating the Gilbert–Varshamov Bound for Constrained Systems
by
Keshav Goyal and Han Mao Kiah
Entropy 2024, 26(4), 346; https://doi.org/10.3390/e26040346 - 19 Apr 2024
Abstract
We revisit the well-known Gilbert–Varshamov (GV) bound for constrained systems. In 1991, Kolesnik and Krachkovsky showed that the GV bound can be determined via the solution of an optimization problem. Later, in 1992, Marcus and Roth modified the optimization problem and improved the
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We revisit the well-known Gilbert–Varshamov (GV) bound for constrained systems. In 1991, Kolesnik and Krachkovsky showed that the GV bound can be determined via the solution of an optimization problem. Later, in 1992, Marcus and Roth modified the optimization problem and improved the GV bound in many instances. In this work, we provide explicit numerical procedures to solve these two optimization problems and, hence, compute the bounds. We then show that the procedures can be further simplified when we plot the respective curves. In the case where the graph presentation comprises a single state, we provide explicit formulas for both bounds.
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(This article belongs to the Special Issue Discrete Math in Coding Theory)
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Hybrid Classical–Quantum Branch-and-Bound Algorithm for Solving Integer Linear Problems
by
Claudio Sanavio, Edoardo Tignone and Elisa Ercolessi
Entropy 2024, 26(4), 345; https://doi.org/10.3390/e26040345 - 19 Apr 2024
Abstract
Quantum annealers are suited to solve several logistic optimization problems expressed in the QUBO formulation. However, the solutions proposed by the quantum annealers are generally not optimal, as thermal noise and other disturbing effects arise when the number of qubits involved in the
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Quantum annealers are suited to solve several logistic optimization problems expressed in the QUBO formulation. However, the solutions proposed by the quantum annealers are generally not optimal, as thermal noise and other disturbing effects arise when the number of qubits involved in the calculation is too large. In order to deal with this issue, we propose the use of the classical branch-and-bound algorithm, that divides the problem into sub-problems which are described by a lower number of qubits. We analyze the performance of this method on two problems, the knapsack problem and the traveling salesman problem. Our results show the advantages of this method, that balances the number of steps that the algorithm has to make with the amount of error in the solution found by the quantum hardware that the user is willing to risk. The results are obtained using the commercially available quantum hardware D-Wave Advantage, and they outline the strategy for a practical application of the quantum annealers.
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(This article belongs to the Special Issue Quantum Computing in the NISQ Era)
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Multilingual Hate Speech Detection: A Semi-Supervised Generative Adversarial Approach
by
Khouloud Mnassri, Reza Farahbakhsh and Noel Crespi
Entropy 2024, 26(4), 344; https://doi.org/10.3390/e26040344 - 18 Apr 2024
Abstract
Social media platforms have surpassed cultural and linguistic boundaries, thus enabling online communication worldwide. However, the expanded use of various languages has intensified the challenge of online detection of hate speech content. Despite the release of multiple Natural Language Processing (NLP) solutions implementing
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Social media platforms have surpassed cultural and linguistic boundaries, thus enabling online communication worldwide. However, the expanded use of various languages has intensified the challenge of online detection of hate speech content. Despite the release of multiple Natural Language Processing (NLP) solutions implementing cutting-edge machine learning techniques, the scarcity of data, especially labeled data, remains a considerable obstacle, which further requires the use of semisupervised approaches along with Generative Artificial Intelligence (Generative AI) techniques. This paper introduces an innovative approach, a multilingual semisupervised model combining Generative Adversarial Networks (GANs) and Pretrained Language Models (PLMs), more precisely mBERT and XLM-RoBERTa. Our approach proves its effectiveness in the detection of hate speech and offensive language in Indo-European languages (in English, German, and Hindi) when employing only 20% annotated data from the HASOC2019 dataset, thereby presenting significantly high performances in each of multilingual, zero-shot crosslingual, and monolingual training scenarios. Our study provides a robust mBERT-based semisupervised GAN model (SS-GAN-mBERT) that outperformed the XLM-RoBERTa-based model (SS-GAN-XLM) and reached an average F1 score boost of 9.23% and an accuracy increase of 5.75% over the baseline semisupervised mBERT model.
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(This article belongs to the Special Issue Advances in Complex Networks and Their Applications, from COMPLEX NETWORKS 2023)
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Open AccessOpinion
Friston, Free Energy, and Psychoanalytic Psychotherapy
by
Jeremy Holmes
Entropy 2024, 26(4), 343; https://doi.org/10.3390/e26040343 - 18 Apr 2024
Abstract
This paper outlines the ways in which Karl Friston’s work illuminates the everyday practice of psychotherapists. These include (a) how the strategic ambiguity of the therapist’s stance brings, via ‘transference’, clients’ priors to light; (b) how the unstructured and negative capability of the
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This paper outlines the ways in which Karl Friston’s work illuminates the everyday practice of psychotherapists. These include (a) how the strategic ambiguity of the therapist’s stance brings, via ‘transference’, clients’ priors to light; (b) how the unstructured and negative capability of the therapy session reduces the salience of priors, enabling new top-down models to be forged; (c) how fostering self-reflection provides an additional step in the free energy minimization hierarchy; and (d) how Friston and Frith’s ‘duets for one’ can be conceptualized as a relational zone in which collaborative free energy minimization takes place without sacrificing complexity.
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(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)
Open AccessArticle
Time-Varying GPS Displacement Network Modeling by Sequential Monte Carlo
by
Suchanun Piriyasatit, Ercan Engin Kuruoglu and Mehmet Sinan Ozeren
Entropy 2024, 26(4), 342; https://doi.org/10.3390/e26040342 - 18 Apr 2024
Abstract
Geodetic observations through high-rate GPS time-series data allow the precise modeling of slow ground deformation at the millimeter level. However, significant attention has been devoted to utilizing these data for various earth science applications, including to determine crustal velocity fields and to detect
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Geodetic observations through high-rate GPS time-series data allow the precise modeling of slow ground deformation at the millimeter level. However, significant attention has been devoted to utilizing these data for various earth science applications, including to determine crustal velocity fields and to detect significant displacement from earthquakes. The relationships inherent in these GPS displacement observations have not been fully explored. This study employs the sequential Monte Carlo method, specifically particle filtering (PF), to develop a time-varying analysis of the relationships among GPS displacement time-series within a network, with the aim of uncovering network dynamics. Additionally, we introduce a proposed graph representation to enhance the understanding of these relationships. Using the 1-Hz GEONET GNSS network data of the Tohoku-Oki Mw9.0 2011 as a demonstration, the results demonstrate successful parameter tracking that clarifies the observations’ underlying dynamics. These findings have potential applications in detecting anomalous displacements in the future.
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(This article belongs to the Special Issue Statistical Methods for Earthquake Hazard Assessment and Risk Analysis)
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Distinction of Chaos from Randomness Is Not Possible from the Degree Distribution of the Visibility and Phase Space Reconstruction Graphs
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Alexandros K. Angelidis, Konstantinos Goulas, Charalampos Bratsas, Georgios C. Makris, Michael P. Hanias, Stavros G. Stavrinides and Ioannis E. Antoniou
Entropy 2024, 26(4), 341; https://doi.org/10.3390/e26040341 - 17 Apr 2024
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We investigate whether it is possible to distinguish chaotic time series from random time series using network theory. In this perspective, we selected four methods to generate graphs from time series: the natural, the horizontal, the limited penetrable horizontal visibility graph, and the
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We investigate whether it is possible to distinguish chaotic time series from random time series using network theory. In this perspective, we selected four methods to generate graphs from time series: the natural, the horizontal, the limited penetrable horizontal visibility graph, and the phase space reconstruction method. These methods claim that the distinction of chaos from randomness is possible by studying the degree distribution of the generated graphs. We evaluated these methods by computing the results for chaotic time series from the 2D Torus Automorphisms, the chaotic Lorenz system, and a random sequence derived from the normal distribution. Although the results confirm previous studies, we found that the distinction of chaos from randomness is not generally possible in the context of the above methodologies.
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Open AccessArticle
Irradiation-Hardening Model of TiZrHfNbMo0.1 Refractory High-Entropy Alloys
by
Yujun Fan, Xuejiao Wang, Yangyang Li, Aidong Lan and Junwei Qiao
Entropy 2024, 26(4), 340; https://doi.org/10.3390/e26040340 - 17 Apr 2024
Abstract
In order to find more excellent structural materials resistant to radiation damage, high-entropy alloys (HEAs) have been developed due to their characteristics of limited point defect diffusion such as lattice distortion and slow diffusion. Specially, refractory high-entropy alloys (RHEAs) that can adapt to
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In order to find more excellent structural materials resistant to radiation damage, high-entropy alloys (HEAs) have been developed due to their characteristics of limited point defect diffusion such as lattice distortion and slow diffusion. Specially, refractory high-entropy alloys (RHEAs) that can adapt to a high-temperature environment are badly needed. In this study, RHEAs are selected for irradiation and nanoindentation experiments. We combined the mechanistic model for the depth-dependent hardness of ion-irradiated metals and the introduction of the scale factor to modify the irradiation-hardening model in order to better describe the nanoindentation indentation process in the irradiated layer. Finally, it can be found that, with the increase in irradiation dose, a more serious lattice distortion caused by a higher defect density limits the expansion of the plastic zone.
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(This article belongs to the Special Issue Recent Advances in Refractory High Entropy Alloys)
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Open AccessReview
Advances in Adjoint Functions of Connection Number in Water Resources Complex Systems: A Systematic Review
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Liangguang Zhou, Juliang Jin, Rongxing Zhou, Yi Cui, Chengguo Wu, Yuliang Zhou, Shibao Dai and Yuliang Zhang
Entropy 2024, 26(4), 339; https://doi.org/10.3390/e26040339 - 16 Apr 2024
Abstract
The adjoint function of connection number has unique advantages in solving uncertainty problems of water resource complex systems, and has become an important frontier and research hotspot in the uncertainty research of water resource complex problems. However, in the rapid evolution of the
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The adjoint function of connection number has unique advantages in solving uncertainty problems of water resource complex systems, and has become an important frontier and research hotspot in the uncertainty research of water resource complex problems. However, in the rapid evolution of the adjoint function, some problems greatly limit the application of the adjoint function in the research of water resources. Therefore, based on bibliometric analysis, development, practical application issues, and prospects of the hot directions are analyzed. It is found that the development of the connection number of water resource set pair analysis can be divided into three stages: (1) relatively sluggish development before 2005, (2) a period of rapid advancement in adjoint function research spanning from 2005 to 2017, and (3) a subsequent surge post-2018. The introduction of the adjoint function of connection number promotes the continuous development of set pair analysis of water resources. Set pair potential and partial connection number are the crucial research directions of the adjoint function. Subtractive set pair potential has rapidly developed into a relatively independent and important trajectory. The research on connection entropy is comparatively less, which needs to be further strengthened, while that on adjacent connection number is even less. The adjoint function of set pair potential can be divided into three major categories: division set pair potential, exponential set pair potential, and subtraction set pair potential. The subtraction set pair potential, which retains the original dimension and quantity variation range of the connection number, is widely used in water resources and other fields. Coupled with the partial connection number, a series of new connection number adjoint functions have been developed. The partial connection number can be mainly divided into two categories: total partial connection number, and semi-partial connection number. Among these, the calculation expression and connotation of total partial connection numbers have not yet reached a consensus, accompanied by the slow development of high-order partial connection numbers. Semi-partial connection number can describe the mutual migration movement between different components of the connection number, which develops rapidly. With the limitations and current situation described above, promoting the exploration and application of the adjoint function of connection number in the field of water resources and other fields of complex systems has become the focus of future research.
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(This article belongs to the Topic Complex Systems and Artificial Intelligence)
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Open AccessArticle
Side Information Design in Zero-Error Coding for Computing
by
Nicolas Charpenay, Maël Le Treust and Aline Roumy
Entropy 2024, 26(4), 338; https://doi.org/10.3390/e26040338 - 16 Apr 2024
Abstract
We investigate the zero-error coding for computing problems with encoder side information. An encoder provides access to a source X and is furnished with side information . It communicates with a decoder that possesses side information Y and aims
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We investigate the zero-error coding for computing problems with encoder side information. An encoder provides access to a source X and is furnished with side information . It communicates with a decoder that possesses side information Y and aims to retrieve with zero probability of error, where f and g are assumed to be deterministic functions. In previous work, we determined a condition that yields an analytic expression for the optimal rate ; in particular, it covers the case where is full support. In this article, we review this result and study the side information design problem, which consists of finding the best trade-offs between the quality of the encoder’s side information and . We construct two greedy algorithms that give an achievable set of points in the side information design problem, based on partition refining and coarsening. One of them runs in polynomial time.
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(This article belongs to the Special Issue Extremal and Additive Combinatorial Aspects in Information Theory)
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Open AccessArticle
On the Supposed Mass of Entropy and That of Information
by
Didier Lairez
Entropy 2024, 26(4), 337; https://doi.org/10.3390/e26040337 - 15 Apr 2024
Abstract
In the theory of special relativity, energy can be found in two forms: kinetic energy and rest mass. The potential energy of a body is actually stored in the form of rest mass, the interaction energy too, but temperature is not. Information acquired
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In the theory of special relativity, energy can be found in two forms: kinetic energy and rest mass. The potential energy of a body is actually stored in the form of rest mass, the interaction energy too, but temperature is not. Information acquired about a dynamical system can be potentially used to extract useful work from it. Hence, the “mass–energy–information equivalence principle” that has been recently proposed. In this paper, it is first recalled that for a thermodynamic system made of non-interacting entities at constant temperature, the internal energy is also constant. So, the energy involved in a variation in entropy ( ) differs from a change in the potential energy stored or released and cannot be associated to a corresponding variation in mass of the system, even if it is expressed in terms of the quantity of information. This debate gives us the opportunity to deepen the notion of entropy seen as a quantity of information, to highlight the difference between logical irreversibility (a state-dependent property) and thermodynamical irreversibility (a path-dependent property), and to return to the nature of the link between energy and information that is dynamical.
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(This article belongs to the Collection Foundations and Ubiquity of Classical Thermodynamics)
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Open AccessArticle
Dwell Times, Wavepacket Dynamics, and Quantum Trajectories for Particles with Spin 1/2
by
Bill Poirier and Richard Lombardini
Entropy 2024, 26(4), 336; https://doi.org/10.3390/e26040336 - 14 Apr 2024
Abstract
The theoretical connections between quantum trajectories and quantum dwell times, previously explored in the context of 1D time-independent stationary scattering applications, are here generalized for multidimensional time-dependent wavepacket applications for particles with spin 1/2. In addition to dwell times, trajectory-based dwell time distributions
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The theoretical connections between quantum trajectories and quantum dwell times, previously explored in the context of 1D time-independent stationary scattering applications, are here generalized for multidimensional time-dependent wavepacket applications for particles with spin 1/2. In addition to dwell times, trajectory-based dwell time distributions are also developed, and compared with previous distributions based on the dwell time operator and the flux–flux correlation function. Dwell time distributions are of interest, in part because they may be of experimental relevance. In addition to standard unipolar quantum trajectories, bipolar quantum trajectories are also considered, and found to relate more directly to the dwell time (and other quantum time) quantities of greatest relevance for scattering applications. Detailed calculations are performed for a benchmark 3D spin-1/2 particle application, considered previously in the context of computing quantum arrival times.
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(This article belongs to the Special Issue Quantum Mechanics and the Challenge of Time)
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Bayesian Non-Parametric Inference for Multivariate Peaks-over-Threshold Models
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Peter Trubey and Bruno Sansó
Entropy 2024, 26(4), 335; https://doi.org/10.3390/e26040335 - 14 Apr 2024
Abstract
We consider a constructive definition of the multivariate Pareto that factorizes the random vector into a radial component and an independent angular component. The former follows a univariate Pareto distribution, and the latter is defined on the surface of the positive orthant of
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We consider a constructive definition of the multivariate Pareto that factorizes the random vector into a radial component and an independent angular component. The former follows a univariate Pareto distribution, and the latter is defined on the surface of the positive orthant of the infinity norm unit hypercube. We propose a method for inferring the distribution of the angular component by identifying its support as the limit of the positive orthant of the unit p-norm spheres and introduce a projected gamma family of distributions defined through the normalization of a vector of independent random gammas to the space. This serves to construct a flexible family of distributions obtained as a Dirichlet process mixture of projected gammas. For model assessment, we discuss scoring methods appropriate to distributions on the unit hypercube. In particular, working with the energy score criterion, we develop a kernel metric that produces a proper scoring rule and presents a simulation study to compare different modeling choices using the proposed metric. Using our approach, we describe the dependence structure of extreme values in the integrated vapor transport (IVT), data describing the flow of atmospheric moisture along the coast of California. We find clear but heterogeneous geographical dependence.
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(This article belongs to the Special Issue Bayesianism)
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Open AccessArticle
Improvement of Z-Weighted Function Based on Fifth-Order Nonlinear Multi-Order Weighted Method for Shock Capturing of Hyperbolic Conservation Laws
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Jinwei Bai, Zhenguo Yan, Meiliang Mao, Yankai Ma and Dingwu Jiang
Entropy 2024, 26(4), 334; https://doi.org/10.3390/e26040334 - 14 Apr 2024
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Based on a 5-point stencil and three 3-point stencils, a nonlinear multi-order weighted method adaptive to 5-3-3-3 stencils for shock capturing is presented in this paper. The form of the weighting function is the same as JS (Jiang–Shu) weighting; however, the smoothness indicator
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Based on a 5-point stencil and three 3-point stencils, a nonlinear multi-order weighted method adaptive to 5-3-3-3 stencils for shock capturing is presented in this paper. The form of the weighting function is the same as JS (Jiang–Shu) weighting; however, the smoothness indicator of the 5-point stencil adopts a special design with a higher-order leading term similar to the in Z weighting. The design maintains that the nonlinear weights satisfy sufficient conditions for the scheme to avoid degradation even near extreme points. By adjusting the linear weights to a specific value and using the in Z weighting, the method can be degraded to Z weighting. Analysis of linear weights shows that they do not affect the accuracy in the smooth region, and they can also adjust the resolution and discontinuity-capturing capability. Numerical tests of different hyperbolic conservation laws are conducted to test the performance of the newly designed nonlinear weights based on the weighted compact nonlinear scheme. The numerical results show that there are no obvious oscillations near the discontinuity, and the resolution of both the discontinuity and smooth regions is better than that of Z weights.
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