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Volume 26
Issue 4
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Entropy, Volume 26, Issue 4 (April 2024) – 74 articles

Cover Story (view full-size image): The Lorenz attractor reminds us of the "Butterfly Effect", which illustrates the essence of chaos, showing sensitive dependence to initial conditions, i.e., small changes in initial conditions can lead to dramatic variations in the long run. Chaotic data are statistically indistinguishable from randomness; therefore, such a distinction should be based on algebraic and/or topological arguments. Visibility and phase space reconstruction graphs are powerful tools for representing the dynamics of complex systems, as different dynamics generate different types of networks. Evaluating the claims that these methods can distinguish chaos from randomness in terms of the degree distributions of the associated networks, we conclude that such a distinction does not hold in general. View this paper
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22 pages, 1607 KiB  
Article
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
Viewed by 1430
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, [...] Read more.
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 1dB compared to the existing CE precoding algorithm and has an acceptable computational complexity. This performance advantage also exists when it comes to DCE precoding. Full article
(This article belongs to the Special Issue Information Theory for MIMO Systems)
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21 pages, 527 KiB  
Article
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
Cited by 5 | Viewed by 1498
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 by Capalbo et al., our construction is simpler and may be closer to being implementable in practice, due to the [...] Read more.
We construct an infinite family of bounded-degree bipartite unique neighbour expander graphs with arbitrarily unbalanced sides. Although weaker than the lossless expanders constructed by Capalbo 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)
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20 pages, 8265 KiB  
Article
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
Cited by 1 | Viewed by 1072
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Computational Thermodynamics and Its Applications)
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25 pages, 632 KiB  
Article
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
Cited by 1 | Viewed by 1664
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Discrete Math in Coding Theory)
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17 pages, 1472 KiB  
Article
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
Viewed by 1235
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Quantum Computing in the NISQ Era)
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19 pages, 601 KiB  
Article
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
Cited by 1 | Viewed by 3076
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Advances in Complex Networks and Their Applications, from COMPLEX NETWORKS 2023)
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9 pages, 196 KiB  
Opinion
Friston, Free Energy, and Psychoanalytic Psychotherapy
by Jeremy Holmes
Entropy 2024, 26(4), 343; https://doi.org/10.3390/e26040343 - 18 Apr 2024
Cited by 1 | Viewed by 2093
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue From Functional Imaging to Free Energy—Dedicated to Professor Karl Friston on the Occasion of His 65th Birthday)
13 pages, 19897 KiB  
Article
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
Viewed by 1279
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Statistical Methods for Earthquake Hazard Assessment and Risk Analysis)
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21 pages, 11315 KiB  
Article
Distinction of Chaos from Randomness Is Not Possible from the Degree Distribution of the Visibility and Phase Space Reconstruction Graphs
by 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
Cited by 2 | Viewed by 2241
Abstract
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 [...] Read more.
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. Full article
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14 pages, 4741 KiB  
Article
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
Cited by 1 | Viewed by 1404
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 [...] Read more.
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, TiZrHfNbMo0.1 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 f 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. Full article
(This article belongs to the Special Issue Recent Advances in Refractory High Entropy Alloys)
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29 pages, 6017 KiB  
Review
Advances in Adjoint Functions of Connection Number in Water Resources Complex Systems: A Systematic Review
by 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
Viewed by 1204
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 [...] Read more.
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. Full article
(This article belongs to the Topic Complex Systems and Artificial Intelligence)
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18 pages, 928 KiB  
Article
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
Viewed by 1449
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 g(Y). It communicates with a decoder that possesses side information Y and aims [...] Read more.
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 g(Y). It communicates with a decoder that possesses side information Y and aims to retrieve f(X,Y) 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 R*(g); in particular, it covers the case where PX,Y 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 g(Y) and R*(g). 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. Full article
(This article belongs to the Special Issue Extremal and Additive Combinatorial Aspects in Information Theory)
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14 pages, 736 KiB  
Article
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
Cited by 2 | Viewed by 1312
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 [...] Read more.
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 (TΔS) 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. Full article
(This article belongs to the Collection Foundations and Ubiquity of Classical Thermodynamics)
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28 pages, 604 KiB  
Article
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
Viewed by 1656
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Quantum Mechanics and the Challenge of Time)
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19 pages, 2693 KiB  
Article
Bayesian Non-Parametric Inference for Multivariate Peaks-over-Threshold Models
by Peter Trubey and Bruno Sansó
Entropy 2024, 26(4), 335; https://doi.org/10.3390/e26040335 - 14 Apr 2024
Viewed by 1430
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Bayesianism)
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25 pages, 3940 KiB  
Article
Improvement of Z-Weighted Function Based on Fifth-Order Nonlinear Multi-Order Weighted Method for Shock Capturing of Hyperbolic Conservation Laws
by 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
Viewed by 1010
Abstract
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 [...] Read more.
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 τ 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 τ 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. Full article
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21 pages, 13702 KiB  
Review
Dynamical Tunneling in More than Two Degrees of Freedom
by Srihari Keshavamurthy
Entropy 2024, 26(4), 333; https://doi.org/10.3390/e26040333 - 14 Apr 2024
Cited by 1 | Viewed by 1283
Abstract
Recent progress towards understanding the mechanism of dynamical tunneling in Hamiltonian systems with three or more degrees of freedom (DoF) is reviewed. In contrast to systems with two degrees of freedom, the three or more degrees of freedom case presents several challenges. Specifically, [...] Read more.
Recent progress towards understanding the mechanism of dynamical tunneling in Hamiltonian systems with three or more degrees of freedom (DoF) is reviewed. In contrast to systems with two degrees of freedom, the three or more degrees of freedom case presents several challenges. Specifically, in higher-dimensional phase spaces, multiple mechanisms for classical transport have significant implications for the evolution of initial quantum states. In this review, the importance of features on the Arnold web, a signature of systems with three or more DoF, to the mechanism of resonance-assisted tunneling is illustrated using select examples. These examples represent relevant models for phenomena such as intramolecular vibrational energy redistribution in isolated molecules and the dynamics of Bose–Einstein condensates trapped in optical lattices. Full article
(This article belongs to the Special Issue Tunneling in Complex Systems)
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26 pages, 2852 KiB  
Article
Benefits of Zero-Phase or Linear Phase Filters to Design Multiscale Entropy: Theory and Application
by Eric Grivel, Bastien Berthelot, Gaetan Colin, Pierrick Legrand and Vincent Ibanez
Entropy 2024, 26(4), 332; https://doi.org/10.3390/e26040332 - 14 Apr 2024
Cited by 1 | Viewed by 1350
Abstract
In various applications, multiscale entropy (MSE) is often used as a feature to characterize the complexity of the signals in order to classify them. It consists of estimating the sample entropies (SEs) of the signal under study and its coarse-grained (CG) versions, where [...] Read more.
In various applications, multiscale entropy (MSE) is often used as a feature to characterize the complexity of the signals in order to classify them. It consists of estimating the sample entropies (SEs) of the signal under study and its coarse-grained (CG) versions, where the CG process amounts to (1) filtering the signal with an average filter whose order is the scale and (2) decimating the filter output by a factor equal to the scale. In this paper, we propose to derive a new variant of the MSE. Its novelty stands in the way to get the sequences at different scales by avoiding distortions during the decimation step. To this end, a linear-phase or null-phase low-pass filter whose cutoff frequency is well suited to the scale is used. Interpretations on how the MSE behaves and illustrations with a sum of sinusoids, as well as white and pink noises, are given. Then, an application to detect attentional tunneling is presented. It shows the benefit of the new approach in terms of p value when one aims at differentiating the set of MSEs obtained in the attentional tunneling state from the set of MSEs obtained in the nominal state. It should be noted that CG versions can be replaced not only for the MSE but also for other variants. Full article
(This article belongs to the Special Issue Ordinal Pattern-Based Entropies: New Ideas and Challenges)
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19 pages, 17411 KiB  
Article
Multi-Time-Scale Optimal Scheduling Strategy for Marine Renewable Energy Based on Deep Reinforcement Learning Algorithm
by Ren Xu, Fei Lin, Wenyi Shao, Haoran Wang, Fanping Meng and Jun Li
Entropy 2024, 26(4), 331; https://doi.org/10.3390/e26040331 - 14 Apr 2024
Viewed by 1221
Abstract
Surrounded by the Shandong Peninsula, the Bohai Sea and Yellow Sea possess vast marine energy resources. An analysis of actual meteorological data from these regions indicates significant seasonality and intra-day uncertainty in wind and photovoltaic power generation. The challenge of scheduling to leverage [...] Read more.
Surrounded by the Shandong Peninsula, the Bohai Sea and Yellow Sea possess vast marine energy resources. An analysis of actual meteorological data from these regions indicates significant seasonality and intra-day uncertainty in wind and photovoltaic power generation. The challenge of scheduling to leverage the complementary characteristics of various renewable energy sources for maintaining grid stability is substantial. In response, we have integrated wave energy with offshore photovoltaic and wind power generation and propose a day-ahead and intra-day multi-time-scale rolling optimization scheduling strategy for the complementary dispatch of these three energy sources. Using real meteorological data from this maritime area, we employed a CNN-LSTM neural network to predict the power generation and load demand of the area on both day-ahead 24 h and intra-day 1 h time scales, with the DDPG algorithm applied for refined electricity management through rolling optimization scheduling of the forecast data. Simulation results demonstrate that the proposed strategy effectively meets load demands through complementary scheduling of wave power, wind power, and photovoltaic power generation based on the climatic characteristics of the Bohai and Yellow Sea regions, reducing the negative impacts of the seasonality and intra-day uncertainty of these three energy sources on the grid. Additionally, compared to the day-ahead scheduling strategy alone, the day-ahead and intra-day rolling optimization scheduling strategy achieved a reduction in system costs by 16.1% and 22% for a typical winter day and a typical summer day, respectively. Full article
(This article belongs to the Topic New Results on Mathematical Methods–Models and Their Applications to Energy Systems)
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25 pages, 363 KiB  
Article
Major Role of Multiscale Entropy Evolution in Complex Systems and Data Science
by Shahid Nawaz, Muhammad Saleem, Fedor V. Kusmartsev and Dalaver H. Anjum
Entropy 2024, 26(4), 330; https://doi.org/10.3390/e26040330 - 12 Apr 2024
Viewed by 1438
Abstract
Complex systems are prevalent in various disciplines encompassing the natural and social sciences, such as physics, biology, economics, and sociology. Leveraging data science techniques, particularly those rooted in artificial intelligence and machine learning, offers a promising avenue for comprehending the intricacies of complex [...] Read more.
Complex systems are prevalent in various disciplines encompassing the natural and social sciences, such as physics, biology, economics, and sociology. Leveraging data science techniques, particularly those rooted in artificial intelligence and machine learning, offers a promising avenue for comprehending the intricacies of complex systems without necessitating detailed knowledge of underlying dynamics. In this paper, we demonstrate that multiscale entropy (MSE) is pivotal in describing the steady state of complex systems. Introducing the multiscale entropy dynamics (MED) methodology, we provide a framework for dissecting system dynamics and uncovering the driving forces behind their evolution. Our investigation reveals that the MED methodology facilitates the expression of complex system dynamics through a Generalized Nonlinear Schrödinger Equation (GNSE) that thus demonstrates its potential applicability across diverse complex systems. By elucidating the entropic underpinnings of complexity, our study paves the way for a deeper understanding of dynamic phenomena. It offers insights into the behavior of complex systems across various domains. Full article
(This article belongs to the Special Issue Nonlinear Dynamical Behaviors in Complex Systems)
49 pages, 542 KiB  
Article
Functional Formulation of Quantum Theory of a Scalar Field in a Metric with Lorentzian and Euclidean Signatures
by Zbigniew Haba
Entropy 2024, 26(4), 329; https://doi.org/10.3390/e26040329 - 12 Apr 2024
Viewed by 995
Abstract
We study the Schrödinger equation in quantum field theory (QFT) in its functional formulation. In this approach, quantum correlation functions can be expressed as classical expectation values over (complex) stochastic processes. We obtain a stochastic representation of the Schrödinger time evolution on Wentzel–Kramers–Brillouin [...] Read more.
We study the Schrödinger equation in quantum field theory (QFT) in its functional formulation. In this approach, quantum correlation functions can be expressed as classical expectation values over (complex) stochastic processes. We obtain a stochastic representation of the Schrödinger time evolution on Wentzel–Kramers–Brillouin (WKB) states by means of the Wiener integral. We discuss QFT in a flat expanding metric and in de Sitter space-time. We calculate the evolution kernel in an expanding flat metric in the real-time formulation. We discuss a field interaction in pseudoRiemannian and Riemannian metrics showing that an inversion of the signature leads to some substantial simplifications of the singularity problems in QFT. Full article
(This article belongs to the Section Astrophysics, Cosmology, and Black Holes)
18 pages, 985 KiB  
Article
CAC: Confidence-Aware Co-Training for Weakly Supervised Crack Segmentation
by Fengjiao Liang, Qingyong Li, Xiaobao Li, Yang Liu and Wen Wang
Entropy 2024, 26(4), 328; https://doi.org/10.3390/e26040328 - 12 Apr 2024
Viewed by 1354
Abstract
Automatic crack segmentation plays an essential role in maintaining the structural health of buildings and infrastructure. Despite the success in fully supervised crack segmentation, the costly pixel-level annotation restricts its application, leading to increased exploration in weakly supervised crack segmentation (WSCS). However, WSCS [...] Read more.
Automatic crack segmentation plays an essential role in maintaining the structural health of buildings and infrastructure. Despite the success in fully supervised crack segmentation, the costly pixel-level annotation restricts its application, leading to increased exploration in weakly supervised crack segmentation (WSCS). However, WSCS methods inevitably bring in noisy pseudo-labels, which results in large fluctuations. To address this problem, we propose a novel confidence-aware co-training (CAC) framework for WSCS. This framework aims to iteratively refine pseudo-labels, facilitating the learning of a more robust segmentation model. Specifically, a co-training mechanism is designed and constructs two collaborative networks to learn uncertain crack pixels, from easy to hard. Moreover, the dynamic division strategy is designed to divide the pseudo-labels based on the crack confidence score. Among them, the high-confidence pseudo-labels are utilized to optimize the initialization parameters for the collaborative network, while low-confidence pseudo-labels enrich the diversity of crack samples. Extensive experiments conducted on the Crack500, DeepCrack, and CFD datasets demonstrate that the proposed CAC significantly outperforms other WSCS methods. Full article
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11 pages, 1078 KiB  
Article
Unveiling Human Values: Analyzing Emotions behind Arguments
by Amir Reza Jafari, Praboda Rajapaksha, Reza Farahbakhsh, Guanlin Li and Noel Crespi
Entropy 2024, 26(4), 327; https://doi.org/10.3390/e26040327 - 12 Apr 2024
Viewed by 1381
Abstract
Detecting the underlying human values within arguments is essential across various domains, ranging from social sciences to recent computational approaches. Identifying these values remains a significant challenge due to their vast numbers and implicit usage in discourse. This study explores the potential of [...] Read more.
Detecting the underlying human values within arguments is essential across various domains, ranging from social sciences to recent computational approaches. Identifying these values remains a significant challenge due to their vast numbers and implicit usage in discourse. This study explores the potential of emotion analysis as a key feature in improving the detection of human values and information extraction from this field. It aims to gain insights into human behavior by applying intensive analyses of different levels of human values. Additionally, we conduct experiments that integrate extracted emotion features to improve human value detection tasks. This approach holds the potential to provide fresh insights into the complex interactions between emotions and values within discussions, offering a deeper understanding of human behavior and decision making. Uncovering these emotions is crucial for comprehending the characteristics that underlie various values through data-driven analyses. Our experiment results show improvement in the performance of human value detection tasks in many categories. Full article
(This article belongs to the Special Issue Advances in Complex Networks and Their Applications, from COMPLEX NETWORKS 2023)
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13 pages, 279 KiB  
Article
Corrections to the Bekenstein–Hawking Entropy of the HNUTKN Black Hole Due to Lorentz-Breaking Fermionic Einstein–Aether Theory
by Xia Tan, Cong Wang and Shu-Zheng Yang
Entropy 2024, 26(4), 326; https://doi.org/10.3390/e26040326 - 11 Apr 2024
Cited by 1 | Viewed by 1065
Abstract
A hot NUT–Kerr–Newman black hole is a general stationary axisymmetric black hole. In this black hole spacetime, the dynamical equations of fermions at the horizon are modified by considering Lorentz breaking. The corrections to the Hawking temperature and Bekenstein–Hawking entropy at the horizon [...] Read more.
A hot NUT–Kerr–Newman black hole is a general stationary axisymmetric black hole. In this black hole spacetime, the dynamical equations of fermions at the horizon are modified by considering Lorentz breaking. The corrections to the Hawking temperature and Bekenstein–Hawking entropy at the horizon of the black hole are studied in depth. Based on the semiclassical theory correction, the Bekenstein–Hawking entropy of this black hole is quantum-corrected by considering the perturbation effect of the Planck constant ℏ. The latter part of this paper presents a detailed discussion of the obtained results and their physical implications. Full article
(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology, 4th Edition)
14 pages, 595 KiB  
Article
Enhancing Zero-Shot Stance Detection with Contrastive and Prompt Learning
by Zhenyin Yao, Wenzhong Yang and Fuyuan Wei
Entropy 2024, 26(4), 325; https://doi.org/10.3390/e26040325 - 11 Apr 2024
Cited by 2 | Viewed by 1325
Abstract
In social networks, the occurrence of unexpected events rapidly catalyzes the widespread dissemination and further evolution of network public opinion. The advent of zero-shot stance detection aligns more closely with the characteristics of stance detection in today’s digital age, where the absence of [...] Read more.
In social networks, the occurrence of unexpected events rapidly catalyzes the widespread dissemination and further evolution of network public opinion. The advent of zero-shot stance detection aligns more closely with the characteristics of stance detection in today’s digital age, where the absence of training examples for specific models poses significant challenges. This task necessitates models with robust generalization abilities to discern target-related, transferable stance features within training data. Recent advances in prompt-based learning have showcased notable efficacy in few-shot text classification. Such methods typically employ a uniform prompt pattern across all instances, yet they overlook the intricate relationship between prompts and instances, thereby failing to sufficiently direct the model towards learning task-relevant knowledge and information. This paper argues for the critical need to dynamically enhance the relevance between specific instances and prompts. Thus, we introduce a stance detection model underpinned by a gated multilayer perceptron (gMLP) and a prompt learning strategy, which is tailored for zero-shot stance detection scenarios. Specifically, the gMLP is utilized to capture semantic features of instances, coupled with a control gate mechanism to modulate the influence of the gate on prompt tokens based on the semantic context of each instance, thereby dynamically reinforcing the instance–prompt connection. Moreover, we integrate contrastive learning to empower the model with more discriminative feature representations. Experimental evaluations on the VAST and SEM16 benchmark datasets substantiate our method’s effectiveness, yielding a 1.3% improvement over the JointCL model on the VAST dataset. Full article
(This article belongs to the Special Issue Methods in Artificial Intelligence and Information Processing II)
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13 pages, 1657 KiB  
Article
Harnessing Information Thermodynamics: Conversion of DNA Information into Mechanical Work in RNA Transcription and Nanopore Sequencing
by Tatsuaki Tsuruyama
Entropy 2024, 26(4), 324; https://doi.org/10.3390/e26040324 - 11 Apr 2024
Viewed by 1360
Abstract
Recent advancements in information thermodynamics have revealed that information can be directly converted into mechanical work. Specifically, RNA transcription and nanopore sequencing serve as prime examples of this conversion, by reading information from a DNA template. This paper introduces an information thermodynamic model [...] Read more.
Recent advancements in information thermodynamics have revealed that information can be directly converted into mechanical work. Specifically, RNA transcription and nanopore sequencing serve as prime examples of this conversion, by reading information from a DNA template. This paper introduces an information thermodynamic model in which these molecular motors can move along the DNA template by converting the information read from the template DNA into their own motion. This process is a stochastic one, characterized by significant fluctuations in forward movement and is described by the Fokker–Planck equation, based on drift velocity and diffusion coefficients. In the current study, it is hypothesized that by utilizing the sequence information of the template DNA as mutual information, the fluctuations can be reduced, thereby biasing the forward movement on DNA and, consequently, reducing reading errors. Further research into the conversion of biological information by molecular motors could unveil new applications, insights, and important findings regarding the characteristics of information processing in biology. Full article
(This article belongs to the Special Issue Entropy in Cell Biology and Biophysics: From Gene Expression Regulation to Molecular Motors)
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21 pages, 1514 KiB  
Article
Minimum Information Variability in Linear Langevin Systems via Model Predictive Control
by Adrian-Josue Guel-Cortez, Eun-jin Kim and Mohamed W. Mehrez
Entropy 2024, 26(4), 323; https://doi.org/10.3390/e26040323 - 10 Apr 2024
Viewed by 1492
Abstract
Controlling the time evolution of a probability distribution that describes the dynamics of a given complex system is a challenging problem. Achieving success in this endeavour will benefit multiple practical scenarios, e.g., controlling mesoscopic systems. Here, we propose a control approach blending the [...] Read more.
Controlling the time evolution of a probability distribution that describes the dynamics of a given complex system is a challenging problem. Achieving success in this endeavour will benefit multiple practical scenarios, e.g., controlling mesoscopic systems. Here, we propose a control approach blending the model predictive control technique with insights from information geometry theory. Focusing on linear Langevin systems, we use model predictive control online optimisation capabilities to determine the system inputs that minimise deviations from the geodesic of the information length over time, ensuring dynamics with minimum “geometric information variability”. We validate our methodology through numerical experimentation on the Ornstein–Uhlenbeck process and Kramers equation, demonstrating its feasibility. Furthermore, in the context of the Ornstein–Uhlenbeck process, we analyse the impact on the entropy production and entropy rate, providing a physical understanding of the effects of minimum information variability control. Full article
(This article belongs to the Special Issue Entropies, Information Geometry and Fluctuations in Non-equilibrium Systems II)
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21 pages, 15331 KiB  
Article
Characterizing Microheterogeneity in Liquid Mixtures via Local Density Fluctuations
by Michael Lass, Tobias Kenter, Christian Plessl and Martin Brehm
Entropy 2024, 26(4), 322; https://doi.org/10.3390/e26040322 - 9 Apr 2024
Cited by 1 | Viewed by 1396
Abstract
We present a novel approach to characterize and quantify microheterogeneity and microphase separation in computer simulations of complex liquid mixtures. Our post-processing method is based on local density fluctuations of the different constituents in sampling spheres of varying size. It can be easily [...] Read more.
We present a novel approach to characterize and quantify microheterogeneity and microphase separation in computer simulations of complex liquid mixtures. Our post-processing method is based on local density fluctuations of the different constituents in sampling spheres of varying size. It can be easily applied to both molecular dynamics (MD) and Monte Carlo (MC) simulations, including periodic boundary conditions. Multidimensional correlation of the density distributions yields a clear picture of the domain formation due to the subtle balance of different interactions. We apply our approach to the example of force field molecular dynamics simulations of imidazolium-based ionic liquids with different side chain lengths at different temperatures, namely 1-ethyl-3-methylimidazolium chloride, 1-hexyl-3-methylimidazolium chloride, and 1-decyl-3-methylimidazolium chloride, which are known to form distinct liquid domains. We put the results into the context of existing microheterogeneity analyses and demonstrate the advantages and sensitivity of our novel method. Furthermore, we show how to estimate the configuration entropy from our analysis, and we investigate voids in the system. The analysis has been implemented into our program package TRAVIS and is thus available as free software. Full article
(This article belongs to the Special Issue Computational Physics and Chemistry Contributions to the Investigation of Ionic Liquids)
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23 pages, 7030 KiB  
Article
Research on a Framework for Chinese Argot Recognition and Interpretation by Integrating Improved MECT Models
by Mingfeng Li, Xin Li, Mianning Hu and Deyu Yuan
Entropy 2024, 26(4), 321; https://doi.org/10.3390/e26040321 - 6 Apr 2024
Viewed by 1553
Abstract
In underground industries, practitioners frequently employ argots to communicate discreetly and evade surveillance by investigative agencies. Proposing an innovative approach using word vectors and large language models, we aim to decipher and understand the myriad of argots in these industries, providing crucial technical [...] Read more.
In underground industries, practitioners frequently employ argots to communicate discreetly and evade surveillance by investigative agencies. Proposing an innovative approach using word vectors and large language models, we aim to decipher and understand the myriad of argots in these industries, providing crucial technical support for law enforcement to detect and combat illicit activities. Specifically, positional differences in semantic space distinguish argots, and pre-trained language models’ corpora are crucial for interpreting them. Expanding on these concepts, the article assesses the semantic coherence of word vectors in the semantic space based on the concept of information entropy. Simultaneously, we devised a labeled argot dataset, MNGG, and developed an argot recognition framework named CSRMECT, along with an argot interpretation framework called LLMResolve. These frameworks leverage the MECT model, the large language model, prompt engineering, and the DBSCAN clustering algorithm. Experimental results demonstrate that the CSRMECT framework outperforms the current optimal model by 10% in terms of the F1 value for argot recognition on the MNGG dataset, while the LLMResolve framework achieves a 4% higher accuracy in interpretation compared to the current optimal model.The related experiments undertaken also indicate a potential correlation between vector information entropy and model performance. Full article
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38 pages, 19811 KiB  
Article
Multi-Modal Latent Diffusion
by Mustapha Bounoua, Giulio Franzese and Pietro Michiardi
Entropy 2024, 26(4), 320; https://doi.org/10.3390/e26040320 - 5 Apr 2024
Cited by 5 | Viewed by 1874
Abstract
Multimodal datasets are ubiquitous in modern applications, and multimodal Variational Autoencoders are a popular family of models that aim to learn a joint representation of different modalities. However, existing approaches suffer from a coherence–quality tradeoff in which models with good generation quality lack [...] Read more.
Multimodal datasets are ubiquitous in modern applications, and multimodal Variational Autoencoders are a popular family of models that aim to learn a joint representation of different modalities. However, existing approaches suffer from a coherence–quality tradeoff in which models with good generation quality lack generative coherence across modalities and vice versa. In this paper, we discuss the limitations underlying the unsatisfactory performance of existing methods in order to motivate the need for a different approach. We propose a novel method that uses a set of independently trained and unimodal deterministic autoencoders. Individual latent variables are concatenated into a common latent space, which is then fed to a masked diffusion model to enable generative modeling. We introduce a new multi-time training method to learn the conditional score network for multimodal diffusion. Our methodology substantially outperforms competitors in both generation quality and coherence, as shown through an extensive experimental campaign. Full article
(This article belongs to the Special Issue Deep Generative Modeling: Theory and Applications)
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