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Entropy, Volume 24, Issue 6 (June 2022) – 104 articles

Cover Story (view full-size image): Voronoi diagrams generated by a random set of points were studied. Dividing the edges of Voronoi cells into random parts yielded positional ordering of Voronoi cells, reminiscent of the formation of lamellae and spherulites in semicrystalline polymers. Shannon entropy of the patterns showed a tendency to attain values typical for random patterns. Shannon entropy and the continuous measure of symmetry demonstrated asymptotic behavior, while approaching the saturation values with the increase in the number of the iteration steps. Shannon entropy is not an unambiguous measure of order in the 2D patterns; more symmetrical patterns may demonstrate higher values of Shannon entropy. View this paper
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16 pages, 1214 KiB  
Article
Using Background Knowledge from Preceding Studies for Building a Random Forest Prediction Model: A Plasmode Simulation Study
by Lorena Hafermann, Nadja Klein, Geraldine Rauch, Michael Kammer and Georg Heinze
Entropy 2022, 24(6), 847; https://doi.org/10.3390/e24060847 - 20 Jun 2022
Cited by 1 | Viewed by 2430
Abstract
There is an increasing interest in machine learning (ML) algorithms for predicting patient outcomes, as these methods are designed to automatically discover complex data patterns. For example, the random forest (RF) algorithm is designed to identify relevant predictor variables out of a large [...] Read more.
There is an increasing interest in machine learning (ML) algorithms for predicting patient outcomes, as these methods are designed to automatically discover complex data patterns. For example, the random forest (RF) algorithm is designed to identify relevant predictor variables out of a large set of candidates. In addition, researchers may also use external information for variable selection to improve model interpretability and variable selection accuracy, thereby prediction quality. However, it is unclear to which extent, if at all, RF and ML methods may benefit from external information. In this paper, we examine the usefulness of external information from prior variable selection studies that used traditional statistical modeling approaches such as the Lasso, or suboptimal methods such as univariate selection. We conducted a plasmode simulation study based on subsampling a data set from a pharmacoepidemiologic study with nearly 200,000 individuals, two binary outcomes and 1152 candidate predictor (mainly sparse binary) variables. When the scope of candidate predictors was reduced based on external knowledge RF models achieved better calibration, that is, better agreement of predictions and observed outcome rates. However, prediction quality measured by cross-entropy, AUROC or the Brier score did not improve. We recommend appraising the methodological quality of studies that serve as an external information source for future prediction model development. Full article
(This article belongs to the Special Issue Improving Predictive Models with Expert Knowledge)
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18 pages, 1285 KiB  
Article
Reliable Semantic Communication System Enabled by Knowledge Graph
by Shengteng Jiang, Yueling Liu, Yichi Zhang, Peng Luo, Kuo Cao, Jun Xiong, Haitao Zhao and Jibo Wei
Entropy 2022, 24(6), 846; https://doi.org/10.3390/e24060846 - 20 Jun 2022
Cited by 18 | Viewed by 3480
Abstract
Semantic communication is a promising technology used to overcome the challenges of large bandwidth and power requirements caused by the data explosion. Semantic representation is an important issue in semantic communication. The knowledge graph, powered by deep learning, can improve the accuracy of [...] Read more.
Semantic communication is a promising technology used to overcome the challenges of large bandwidth and power requirements caused by the data explosion. Semantic representation is an important issue in semantic communication. The knowledge graph, powered by deep learning, can improve the accuracy of semantic representation while removing semantic ambiguity. Therefore, we propose a semantic communication system based on the knowledge graph. Specifically, in our system, the transmitted sentences are converted into triplets by using the knowledge graph. Triplets can be viewed as basic semantic symbols for semantic extraction and restoration and can be sorted based on semantic importance. Moreover, the proposed communication system adaptively adjusts the transmitted contents according to channel quality and allocates more transmission resources to important triplets to enhance communication reliability. Simulation results show that the proposed system significantly enhances the reliability of the communication in the low signal-to-noise regime compared to the traditional schemes. Full article
(This article belongs to the Special Issue Information Theoretic Methods for Future Communication Systems)
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14 pages, 2947 KiB  
Article
Research on Hyper-Parameter Optimization of Activity Recognition Algorithm Based on Improved Cuckoo Search
by Yu Tong and Bo Yu
Entropy 2022, 24(6), 845; https://doi.org/10.3390/e24060845 - 20 Jun 2022
Cited by 5 | Viewed by 1617
Abstract
Activity recognition methods often include some hyper-parameters based on experience, which greatly affects their effectiveness in activity recognition. However, the existing hyper-parameter optimization algorithms are mostly for continuous hyper-parameters, and rarely for the optimization of integer hyper-parameters and mixed hyper-parameters. To solve the [...] Read more.
Activity recognition methods often include some hyper-parameters based on experience, which greatly affects their effectiveness in activity recognition. However, the existing hyper-parameter optimization algorithms are mostly for continuous hyper-parameters, and rarely for the optimization of integer hyper-parameters and mixed hyper-parameters. To solve the problem, this paper improved the traditional cuckoo algorithm. The improved algorithm can optimize not only continuous hyper-parameters, but also integer hyper-parameters and mixed hyper-parameters. This paper validated the proposed method with the hyper-parameters in Least Squares Support Vector Machine (LS-SVM) and Long-Short-Term Memory (LSTM), and compared the activity recognition effects before and after optimization on the smart home activity recognition data set. The results show that the improved cuckoo algorithm can effectively improve the performance of the model in activity recognition. Full article
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15 pages, 317 KiB  
Article
A Testable Theory for the Emergence of the Classical World
by Stuart Kauffman and Sudip Patra
Entropy 2022, 24(6), 844; https://doi.org/10.3390/e24060844 - 20 Jun 2022
Cited by 5 | Viewed by 1709
Abstract
The transition from the quantum to the classical world is not yet understood. Here, we take a new approach. Central to this is the understanding that measurement and actualization cannot occur except on some specific basis. However, we have no established theory for [...] Read more.
The transition from the quantum to the classical world is not yet understood. Here, we take a new approach. Central to this is the understanding that measurement and actualization cannot occur except on some specific basis. However, we have no established theory for the emergence of a specific basis. Our framework entails the following: (i) Sets of N entangled quantum variables can mutually actualize one another. (ii) Such actualization must occur in only one of the 2N possible bases. (iii) Mutual actualization progressively breaks symmetry among the 2N bases. (iv) An emerging “amplitude” for any basis can be amplified by further measurements in that basis, and it can decay between measurements. (v) The emergence of any basis is driven by mutual measurements among the N variables and decoherence with the environment. Quantum Zeno interactions among the N variables mediates the mutual measurements. (vi) As the number of variables, N, increases, the number of Quantum Zeno mediated measurements among the N variables increases. We note that decoherence alone does not yield a specific basis. (vii) Quantum ordered, quantum critical, and quantum chaotic peptides that decohere at nanosecond versus femtosecond time scales can be used as test objects. (viii) By varying the number of amino acids, N, and the use of quantum ordered, critical, or chaotic peptides, the ratio of decoherence to Quantum Zeno effects can be tuned. This enables new means to probe the emergence of one among a set of initially entangled bases via weak measurements after preparing the system in a mixed basis condition. (ix) Use of the three stable isotopes of carbon, oxygen, and nitrogen and the five stable isotopes of sulfur allows any ten atoms in the test protein to be discriminably labeled and the basis of emergence for those labeled atoms can be detected by weak measurements. We present an initial mathematical framework for this theory, and we propose experiments. Full article
20 pages, 7315 KiB  
Article
Multi-Scale Mixed Attention Network for CT and MRI Image Fusion
by Yang Liu, Binyu Yan, Rongzhu Zhang, Kai Liu, Gwanggil Jeon and Xiaoming Yang
Entropy 2022, 24(6), 843; https://doi.org/10.3390/e24060843 - 19 Jun 2022
Cited by 6 | Viewed by 2095
Abstract
Recently, the rapid development of the Internet of Things has contributed to the generation of telemedicine. However, online diagnoses by doctors require the analyses of multiple multi-modal medical images, which are inconvenient and inefficient. Multi-modal medical image fusion is proposed to solve this [...] Read more.
Recently, the rapid development of the Internet of Things has contributed to the generation of telemedicine. However, online diagnoses by doctors require the analyses of multiple multi-modal medical images, which are inconvenient and inefficient. Multi-modal medical image fusion is proposed to solve this problem. Due to its outstanding feature extraction and representation capabilities, convolutional neural networks (CNNs) have been widely used in medical image fusion. However, most existing CNN-based medical image fusion methods calculate their weight maps by a simple weighted average strategy, which weakens the quality of fused images due to the effect of inessential information. In this paper, we propose a CNN-based CT and MRI image fusion method (MMAN), which adopts a visual saliency-based strategy to preserve more useful information. Firstly, a multi-scale mixed attention block is designed to extract features. This block can gather more helpful information and refine the extracted features both in the channel and spatial levels. Then, a visual saliency-based fusion strategy is used to fuse the feature maps. Finally, the fused image can be obtained via reconstruction blocks. The experimental results of our method preserve more textual details, clearer edge information and higher contrast when compared to other state-of-the-art methods. Full article
(This article belongs to the Special Issue Entropy Algorithms Using Deep Learning for Signal Processing)
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25 pages, 534 KiB  
Article
Examining Supervised Machine Learning Methods for Integer Link Weight Prediction Using Node Metadata
by Larissa Mori, Kaleigh O’Hara, Toyya A. Pujol and Mario Ventresca
Entropy 2022, 24(6), 842; https://doi.org/10.3390/e24060842 - 18 Jun 2022
Cited by 3 | Viewed by 1886
Abstract
With the goal of understanding if the information contained in node metadata can help in the task of link weight prediction, we investigate herein whether incorporating it as a similarity feature (referred to as metadata similarity) between end nodes of a link [...] Read more.
With the goal of understanding if the information contained in node metadata can help in the task of link weight prediction, we investigate herein whether incorporating it as a similarity feature (referred to as metadata similarity) between end nodes of a link improves the prediction accuracy of common supervised machine learning methods. In contrast with previous works, instead of normalizing the link weights, we treat them as count variables representing the number of interactions between end nodes, as this is a natural representation for many datasets in the literature. In this preliminary study, we find no significant evidence that metadata similarity improved the prediction accuracy of the four empirical datasets studied. To further explore the role of node metadata in weight prediction, we synthesized weights to analyze the extreme case where the weights depend solely on the metadata of the end nodes, while encoding different relationships between them using logical operators in the generation process. Under these conditions, the random forest method performed significantly better than other methods in 99.07% of cases, though the prediction accuracy was significantly degraded for the methods analyzed in comparison to the experiments with the original weights. Full article
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14 pages, 471 KiB  
Article
Multi-User Measurement-Device-Independent Quantum Key Distribution Based on GHZ Entangled State
by Ximing Hua, Min Hu and Banghong Guo
Entropy 2022, 24(6), 841; https://doi.org/10.3390/e24060841 - 18 Jun 2022
Cited by 7 | Viewed by 1941
Abstract
As a multi-particle entangled state, the Greenberger–Horne–Zeilinger (GHZ) state plays an important role in quantum theory and applications. In this study, we propose a flexible multi-user measurement-device-independent quantum key distribution (MDI-QKD) scheme based on a GHZ entangled state. Our scheme can distribute quantum [...] Read more.
As a multi-particle entangled state, the Greenberger–Horne–Zeilinger (GHZ) state plays an important role in quantum theory and applications. In this study, we propose a flexible multi-user measurement-device-independent quantum key distribution (MDI-QKD) scheme based on a GHZ entangled state. Our scheme can distribute quantum keys among multiple users while being resistant to detection attacks. Our simulation results show that the secure distance between each user and the measurement device can reach more than 280 km while reducing the complexity of the quantum network. Additionally, we propose a method to expand our scheme to a multi-node with multi-user network, which can further enhance the communication distance between the users at different nodes. Full article
(This article belongs to the Special Issue Quantum Information and Computation)
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9 pages, 1470 KiB  
Article
Effects of Spatial Nonlocality versus Nonlocal Causality for Bound Electrons in External Fields
by Ivan P. Christov
Entropy 2022, 24(6), 840; https://doi.org/10.3390/e24060840 - 18 Jun 2022
Cited by 2 | Viewed by 1807 | Correction
Abstract
Using numerically exact solution of the time-dependent Schrödinger equation together with time-dependent quantum Monte Carlo (TDQMC) calculations, here we compare the effects of spatial nonlocality versus nonlocal causality for the ground state and for real-time evolution of two entangled electrons in parabolic potential [...] Read more.
Using numerically exact solution of the time-dependent Schrödinger equation together with time-dependent quantum Monte Carlo (TDQMC) calculations, here we compare the effects of spatial nonlocality versus nonlocal causality for the ground state and for real-time evolution of two entangled electrons in parabolic potential in one spatial dimension. It was found that the spatial entanglement quantified by the linear quantum entropy is predicted with good accuracy using the spatial nonlocality, parameterized naturally within the TDQMC approach. At the same time, the nonlocal causality predicted by the exact solution leads to only small oscillations in the quantum trajectories which belong to the idler electron as the driven electron is subjected to a strong high frequency electric field, without interaction between the electrons. Full article
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15 pages, 1138 KiB  
Article
Twin-Field Quantum Digital Signature with Fully Discrete Phase Randomization
by Jiayao Wu, Chen He, Jiahui Xie, Xiaopeng Liu and Minghui Zhang
Entropy 2022, 24(6), 839; https://doi.org/10.3390/e24060839 - 18 Jun 2022
Viewed by 1485
Abstract
Quantum digital signatures (QDS) are able to verify the authenticity and integrity of a message in modern communication. However, the current QDS protocols are restricted by the fundamental rate-loss bound and the secure signature distance cannot be further improved. We propose a twin-field [...] Read more.
Quantum digital signatures (QDS) are able to verify the authenticity and integrity of a message in modern communication. However, the current QDS protocols are restricted by the fundamental rate-loss bound and the secure signature distance cannot be further improved. We propose a twin-field quantum digital signature (TF-QDS) protocol with fully discrete phase randomization and investigate its performance under the two-intensity decoy-state setting. For better performance, we optimize intensities of the signal state and the decoy state for each given distance. Numerical simulation results show that our TF-QDS with as few as six discrete random phases can give a higher signature rate and a longer secure transmission distance compared with current quantum digital signatures (QDSs), such as BB84-QDS and measurement-device-independent QDS (MDI-QDS). Moreover, we provide a clear comparison among some possible TF-QDSs constructed by different twin-field key generation protocols (TF-KGPs) and find that the proposed TF-QDS exhibits the best performance. Conclusively, the advantages of the proposed TF-QDS protocol in signature rate and secure transmission distance are mainly due to the single-photon interference applied in the measurement module and precise matching of discrete phases. Besides, our TF-QDS shows the feasibility of experimental implementation with current devices in practical QDS system. Full article
(This article belongs to the Section Quantum Information)
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26 pages, 449 KiB  
Article
A Generic Formula and Some Special Cases for the Kullback–Leibler Divergence between Central Multivariate Cauchy Distributions
by Nizar Bouhlel and David Rousseau
Entropy 2022, 24(6), 838; https://doi.org/10.3390/e24060838 - 17 Jun 2022
Cited by 4 | Viewed by 2353
Abstract
This paper introduces a closed-form expression for the Kullback–Leibler divergence (KLD) between two central multivariate Cauchy distributions (MCDs) which have been recently used in different signal and image processing applications where non-Gaussian models are needed. In this overview, the MCDs are surveyed and [...] Read more.
This paper introduces a closed-form expression for the Kullback–Leibler divergence (KLD) between two central multivariate Cauchy distributions (MCDs) which have been recently used in different signal and image processing applications where non-Gaussian models are needed. In this overview, the MCDs are surveyed and some new results and properties are derived and discussed for the KLD. In addition, the KLD for MCDs is showed to be written as a function of Lauricella D-hypergeometric series FD(p). Finally, a comparison is made between the Monte Carlo sampling method to approximate the KLD and the numerical value of the closed-form expression of the latter. The approximation of the KLD by Monte Carlo sampling method are shown to converge to its theoretical value when the number of samples goes to the infinity. Full article
(This article belongs to the Special Issue Information and Divergence Measures)
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16 pages, 308 KiB  
Article
Belavkin–Staszewski Relative Entropy, Conditional Entropy, and Mutual Information
by Yuan Zhai, Bo Yang and Zhengjun Xi
Entropy 2022, 24(6), 837; https://doi.org/10.3390/e24060837 - 17 Jun 2022
Cited by 6 | Viewed by 1973
Abstract
Belavkin–Staszewski relative entropy can naturally characterize the effects of the possible noncommutativity of quantum states. In this paper, two new conditional entropy terms and four new mutual information terms are first defined by replacing quantum relative entropy with Belavkin–Staszewski relative entropy. Next, their [...] Read more.
Belavkin–Staszewski relative entropy can naturally characterize the effects of the possible noncommutativity of quantum states. In this paper, two new conditional entropy terms and four new mutual information terms are first defined by replacing quantum relative entropy with Belavkin–Staszewski relative entropy. Next, their basic properties are investigated, especially in classical-quantum settings. In particular, we show the weak concavity of the Belavkin–Staszewski conditional entropy and obtain the chain rule for the Belavkin–Staszewski mutual information. Finally, the subadditivity of the Belavkin–Staszewski relative entropy is established, i.e., the Belavkin–Staszewski relative entropy of a joint system is less than the sum of that of its corresponding subsystems with the help of some multiplicative and additive factors. Meanwhile, we also provide a certain subadditivity of the geometric Rényi relative entropy. Full article
(This article belongs to the Special Issue Quantum Information and Computation)
18 pages, 5388 KiB  
Article
Nonlinear Modeling Study of Aerodynamic Characteristics of an X38-like Vehicle at Strong Viscous Interaction Regions
by Dingwu Jiang, Pei Wang, Jin Li and Meiliang Mao
Entropy 2022, 24(6), 836; https://doi.org/10.3390/e24060836 - 17 Jun 2022
Cited by 3 | Viewed by 1686
Abstract
Strong viscous interaction and multiple flow regimes exist when vehicles fly at high altitude and high Mach number conditions. The Navier–Stokes(NS) solver is no longer applicable in the above situation. Instead, the direct simulation Monte Carlo (DSMC) method or Boltzmann model equation solvers [...] Read more.
Strong viscous interaction and multiple flow regimes exist when vehicles fly at high altitude and high Mach number conditions. The Navier–Stokes(NS) solver is no longer applicable in the above situation. Instead, the direct simulation Monte Carlo (DSMC) method or Boltzmann model equation solvers are usually needed. However, they are computationally more expensive than the NS solver. Therefore, it is of great engineering value to establish the aerodynamic prediction model of vehicles at high altitude and high Mach number conditions. In this paper, the hypersonic aerodynamic characteristics of an X38-like vehicle in typical conditions from 70 km to 110 km are simulated using the unified gas kinetic scheme (UGKS), which is applicable for all flow regimes. The contributions of pressure and viscous stress on the force coefficients are analyzed. The viscous interaction parameters, Mach number, and angle of attack are used as independent variables, and the difference between the force coefficients calculated by UGKS and the Euler solver is used as a dependent variable to establish a nonlinear viscous interaction model between them in the range of 70–110 km. The evaluation of the model is completed using the correlation coefficient and the relative orthogonal distance. The conventional viscous interaction effect and rarefied effect are both taken into account in the model. The model can be used to quickly obtain the hypersonic aerodynamic characteristics of X38-like vehicle in a wide range, which is meaningful for engineering design. Full article
(This article belongs to the Special Issue Kinetic Theory-Based Methods in Fluid Dynamics)
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20 pages, 382 KiB  
Article
Quantum Models à la Gabor for the Space-Time Metric
by Gilles Cohen-Tannoudji, Jean-Pierre Gazeau, Célestin Habonimana and Juma Shabani
Entropy 2022, 24(6), 835; https://doi.org/10.3390/e24060835 - 16 Jun 2022
Cited by 2 | Viewed by 1598
Abstract
As an extension of Gabor signal processing, the covariant Weyl-Heisenberg integral quantization is implemented to transform functions on the eight-dimensional phase space x,k into Hilbertian operators. The x=xμ values are space-time variables, and the k=kμ [...] Read more.
As an extension of Gabor signal processing, the covariant Weyl-Heisenberg integral quantization is implemented to transform functions on the eight-dimensional phase space x,k into Hilbertian operators. The x=xμ values are space-time variables, and the k=kμ values are their conjugate frequency-wave vector variables. The procedure is first applied to the variables x,k and produces essentially canonically conjugate self-adjoint operators. It is next applied to the metric field gμν(x) of general relativity and yields regularized semi-classical phase space portraits gˇμν(x). The latter give rise to modified tensor energy density. Examples are given with the uniformly accelerated reference system and the Schwarzschild metric. Interesting probabilistic aspects are discussed. Full article
(This article belongs to the Special Issue Quantum Structures and Logics)
24 pages, 767 KiB  
Article
Spiking Neural P Systems with Membrane Potentials, Inhibitory Rules, and Anti-Spikes
by Yuping Liu and Yuzhen Zhao
Entropy 2022, 24(6), 834; https://doi.org/10.3390/e24060834 - 16 Jun 2022
Cited by 5 | Viewed by 1965
Abstract
Spiking neural P systems (SN P systems for short) realize the high abstraction and simulation of the working mechanism of the human brain, and adopts spikes for information encoding and processing, which are regarded as one of the third-generation neural network models. In [...] Read more.
Spiking neural P systems (SN P systems for short) realize the high abstraction and simulation of the working mechanism of the human brain, and adopts spikes for information encoding and processing, which are regarded as one of the third-generation neural network models. In the nervous system, the conduction of excitation depends on the presence of membrane potential (also known as the transmembrane potential difference), and the conduction of excitation on neurons is the conduction of action potentials. On the basis of the SN P systems with polarizations, in which the neuron-associated polarization is the trigger condition of the rule, the concept of neuronal membrane potential is introduced into systems. The obtained variant of the SN P system features charge accumulation and computation within neurons in quantity, as well as transmission between neurons. In addition, there are inhibitory synapses between neurons that inhibit excitatory transmission, and as such, synapses cause postsynaptic neurons to generate inhibitory postsynaptic potentials. Therefore, to make the model better fit the biological facts, inhibitory rules and anti-spikes are also adopted to obtain the spiking neural P systems with membrane potentials, inhibitory rules, and anti-spikes (referred to as the MPAIRSN P systems). The Turing universality of the MPAIRSN P systems as number generating and accepting devices is demonstrated. On the basis of the above working mechanism of the system, a small universal MPAIRSN P system with 95 neurons for computing functions is designed. The comparisons with other SN P models conclude that fewer neurons are required by the MPAIRSN P systems to realize universality. Full article
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28 pages, 429 KiB  
Article
On the Inertial Range Bounds of K-41-like Magnetohydrodynamics Turbulence
by Tesfalem Abate Tegegn
Entropy 2022, 24(6), 833; https://doi.org/10.3390/e24060833 - 16 Jun 2022
Viewed by 1307
Abstract
The spectral slope of magnetohydrodynamic (MHD) turbulence varies depending on the spectral theory considered; 3/2 is the spectral slope in Kraichnan–Iroshnikov–Dobrowolny (KID) theory, 5/3 in Marsch–Matthaeus–Zhou and Goldreich–Sridhar theories, also called Kolmogorov-like (K-41-like) MHD theory, the combination [...] Read more.
The spectral slope of magnetohydrodynamic (MHD) turbulence varies depending on the spectral theory considered; 3/2 is the spectral slope in Kraichnan–Iroshnikov–Dobrowolny (KID) theory, 5/3 in Marsch–Matthaeus–Zhou and Goldreich–Sridhar theories, also called Kolmogorov-like (K-41-like) MHD theory, the combination of the 5/3 and 3/2 scales in Biskamp, and so on. A rigorous mathematical proof to any of these spectral theories is of great scientific interest. Motivated by the 2012 work of A. Biryuk and W. Craig (Physica D 241(2012) 426–438), we establish inertial range bounds for K-41-like phenomenon in MHD turbulent flow through a mathematical rigor; a range of wave numbers in which the spectral slope of MHD turbulence is proportional to 5/3 is established and the upper and lower bounds of this range are explicitly formulated. We also have shown that the Leray weak solution of the standard MHD model is bonded in the Fourier space, the spectral energy of the system is bounded and its average over time decreases in time. Full article
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16 pages, 1104 KiB  
Article
Does Social Distancing Matter for Infectious Disease Propagation? An SEIR Model and Gompertz Law Based Cellular Automaton
by Szymon Biernacki and Krzysztof Malarz
Entropy 2022, 24(6), 832; https://doi.org/10.3390/e24060832 - 15 Jun 2022
Cited by 3 | Viewed by 1668
Abstract
In this paper, we present stochastic synchronous cellular automaton defined on a square lattice. The automaton rules are based on the SEIR (susceptible → exposed → infected → recovered) model with probabilistic parameters gathered from real-world data on human mortality and the characteristics [...] Read more.
In this paper, we present stochastic synchronous cellular automaton defined on a square lattice. The automaton rules are based on the SEIR (susceptible → exposed → infected → recovered) model with probabilistic parameters gathered from real-world data on human mortality and the characteristics of the SARS-CoV-2 disease. With computer simulations, we show the influence of the radius of the neighborhood on the number of infected and deceased agents in the artificial population. The increase in the radius of the neighborhood favors the spread of the pandemic. However, for a large range of interactions of exposed agents (who neither have symptoms of the disease nor have been diagnosed by appropriate tests), even isolation of infected agents cannot prevent successful disease propagation. This supports aggressive testing against disease as one of the useful strategies to prevent large peaks of infection in the spread of SARS-CoV-2-like diseases. Full article
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18 pages, 1282 KiB  
Article
Colored Texture Analysis Fuzzy Entropy Methods with a Dermoscopic Application
by Mirvana Hilal, Andreia S. Gaudêncio, Pedro G. Vaz, João Cardoso and Anne Humeau-Heurtier
Entropy 2022, 24(6), 831; https://doi.org/10.3390/e24060831 - 15 Jun 2022
Cited by 8 | Viewed by 1945
Abstract
Texture analysis is a subject of intensive focus in research due to its significant role in the field of image processing. However, few studies focus on colored texture analysis and even fewer use information theory concepts. Entropy measures have been proven competent for [...] Read more.
Texture analysis is a subject of intensive focus in research due to its significant role in the field of image processing. However, few studies focus on colored texture analysis and even fewer use information theory concepts. Entropy measures have been proven competent for gray scale images. However, to the best of our knowledge, there are no well-established entropy methods that deal with colored images yet. Therefore, we propose the recent colored bidimensional fuzzy entropy measure, FuzEnC2D, and introduce its new multi-channel approaches, FuzEnV2D and FuzEnM2D, for the analysis of colored images. We investigate their sensitivity to parameters and ability to identify images with different irregularity degrees, and therefore different textures. Moreover, we study their behavior with colored Brodatz images in different color spaces. After verifying the results with test images, we employ the three methods for analyzing dermoscopic images of malignant melanoma and benign melanocytic nevi. FuzEnC2D, FuzEnV2D, and FuzEnM2D illustrate a good differentiation ability between the two—similar in appearance—pigmented skin lesions. The results outperform those of a well-known texture analysis measure. Our work provides the first entropy measure studying colored images using both single and multi-channel approaches. Full article
(This article belongs to the Special Issue Entropy Algorithms for the Analysis of Biomedical Signals)
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17 pages, 5053 KiB  
Article
Novel Optimization Design Methods of Highly Loaded Compressor Cascades Considering Endwall Effect
by Bo Liu, Qidong Chen, Jun Li and Xiaochen Mao
Entropy 2022, 24(6), 830; https://doi.org/10.3390/e24060830 - 15 Jun 2022
Viewed by 1463
Abstract
The endwall effect has a great impact on the aerodynamic performance of compressor blades. Based on three conventional near-endwall blade modeling methods of bowed blade, endbend blade and leading-edge strake blade (LESB), two combined optimization design methods of highly loaded blades have been [...] Read more.
The endwall effect has a great impact on the aerodynamic performance of compressor blades. Based on three conventional near-endwall blade modeling methods of bowed blade, endbend blade and leading-edge strake blade (LESB), two combined optimization design methods of highly loaded blades have been developed considering the endwall effect in the current study, i.e., the bowed blade combined with the LESB (bowed LESB blade) and the endbend blade combined with the LESB (endbend LESB blade). Optimization designs were conducted for a compressor cascade with low solidity by using the two combined modeling methods and the three conventional modeling methods, and the optimization results were compared and analyzed in detail. The results showed that the five optimization modelling methods could all improve the performance for the original cascade, and the optimized cascade with the bowed LESB modeling method has the best aerodynamic performance. The total pressure loss of the optimal bowed LESB cascade was only 40.3% of that in the original cascade while reducing the solidity of the original cascade from 1.53 to 1.25 and keeping the static pressure rise and diffusion factor at the same level as the original one. Among the optimal cascades, the radial migration height of the low-energy fluid and the corresponding vortex have great effects on the aerodynamic performance, and the optimal bowed LESB cascade is superior to the other optimal cascades in this aspect. Full article
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15 pages, 2198 KiB  
Article
Supernovae and the Arrow of Time
by Snezhana I. Abarzhi, Desmon L. Hill, Annie Naveh, Kurt C. Williams and Cameron E. Wright
Entropy 2022, 24(6), 829; https://doi.org/10.3390/e24060829 - 14 Jun 2022
Cited by 3 | Viewed by 1983
Abstract
Supernovae are explosions of stars and are a central problem in astrophysics. Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities develop during the star’s explosion and lead to intense interfacial RT/RM mixing of the star materials. We handle the mathematical challenges of the RT/RM problem [...] Read more.
Supernovae are explosions of stars and are a central problem in astrophysics. Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities develop during the star’s explosion and lead to intense interfacial RT/RM mixing of the star materials. We handle the mathematical challenges of the RT/RM problem based on the group theory approach. We directly link the conservation laws governing RT/RM dynamics to the symmetry-based momentum model, derive the model parameters, and find the analytical solutions and characteristics of RT/RM dynamics with variable accelerations in the linear, nonlinear and mixing regimes. The theory outcomes explain the astrophysical observations and yield the design of laboratory experiments. They suggest that supernova evolution is a non-equilibrium process directed by the arrow of time. Full article
(This article belongs to the Special Issue The Second Law and Asymmetry of Time)
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24 pages, 766 KiB  
Article
Robust Finite-Time Stability for Uncertain Discrete-Time Stochastic Nonlinear Systems with Time-Varying Delay
by Xikui Liu, Wencong Li, Jiqiu Wang and Yan Li
Entropy 2022, 24(6), 828; https://doi.org/10.3390/e24060828 - 14 Jun 2022
Cited by 6 | Viewed by 1499
Abstract
The main concern of this paper is finite-time stability (FTS) for uncertain discrete-time stochastic nonlinear systems (DSNSs) with time-varying delay (TVD) and multiplicative noise. First, a Lyapunov–Krasovskii function (LKF) is constructed, using the forward difference, and less conservative stability criteria are obtained. By [...] Read more.
The main concern of this paper is finite-time stability (FTS) for uncertain discrete-time stochastic nonlinear systems (DSNSs) with time-varying delay (TVD) and multiplicative noise. First, a Lyapunov–Krasovskii function (LKF) is constructed, using the forward difference, and less conservative stability criteria are obtained. By solving a series of linear matrix inequalities (LMIs), some sufficient conditions for FTS of the stochastic system are found. Moreover, FTS is presented for a stochastic nominal system. Lastly, the validity and improvement of the proposed methods are shown with two simulation examples. Full article
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25 pages, 3795 KiB  
Article
Analysis of Chaotic Dynamics by the Extended Entropic Chaos Degree
by Kei Inoue
Entropy 2022, 24(6), 827; https://doi.org/10.3390/e24060827 - 14 Jun 2022
Cited by 1 | Viewed by 1541
Abstract
The Lyapunov exponent is the most-well-known measure for quantifying chaos in a dynamical system. However, its computation for any time series without information regarding a dynamical system is challenging because the Jacobian matrix of the map generating the dynamical system is required. The [...] Read more.
The Lyapunov exponent is the most-well-known measure for quantifying chaos in a dynamical system. However, its computation for any time series without information regarding a dynamical system is challenging because the Jacobian matrix of the map generating the dynamical system is required. The entropic chaos degree measures the chaos of a dynamical system as an information quantity in the framework of Information Dynamics and can be directly computed for any time series even if the dynamical system is unknown. A recent study introduced the extended entropic chaos degree, which attained the same value as the total sum of the Lyapunov exponents under typical chaotic conditions. Moreover, an improved calculation formula for the extended entropic chaos degree was recently proposed to obtain appropriate numerical computation results for multidimensional chaotic maps. This study shows that all Lyapunov exponents of a chaotic map can be estimated to calculate the extended entropic chaos degree and proposes a computational algorithm for the extended entropic chaos degree; furthermore, this computational algorithm was applied to one and two-dimensional chaotic maps. The results indicate that the extended entropic chaos degree may be a viable alternative to the Lyapunov exponent for both one and two-dimensional chaotic dynamics. Full article
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40 pages, 1510 KiB  
Review
Kinetic Theory of Polydisperse Granular Mixtures: Influence of the Partial Temperatures on Transport Properties—A Review
by Moisés García Chamorro, Rubén Gómez González and Vicente Garzó
Entropy 2022, 24(6), 826; https://doi.org/10.3390/e24060826 - 14 Jun 2022
Cited by 5 | Viewed by 2228
Abstract
It is well-recognized that granular media under rapid flow conditions can be modeled as a gas of hard spheres with inelastic collisions. At moderate densities, a fundamental basis for the determination of the granular hydrodynamics is provided by the Enskog kinetic equation conveniently [...] Read more.
It is well-recognized that granular media under rapid flow conditions can be modeled as a gas of hard spheres with inelastic collisions. At moderate densities, a fundamental basis for the determination of the granular hydrodynamics is provided by the Enskog kinetic equation conveniently adapted to account for inelastic collisions. A surprising result (compared to its molecular gas counterpart) for granular mixtures is the failure of the energy equipartition, even in homogeneous states. This means that the partial temperatures Ti (measuring the mean kinetic energy of each species) are different to the (total) granular temperature T. The goal of this paper is to provide an overview on the effect of different partial temperatures on the transport properties of the mixture. Our analysis addresses first the impact of energy nonequipartition on transport which is only due to the inelastic character of collisions. This effect (which is absent for elastic collisions) is shown to be significant in important problems in granular mixtures such as thermal diffusion segregation. Then, an independent source of energy nonequipartition due to the existence of a divergence of the flow velocity is studied. This effect (which was already analyzed in several pioneering works on dense hard-sphere molecular mixtures) affects to the bulk viscosity coefficient. Analytical (approximate) results are compared against Monte Carlo and molecular dynamics simulations, showing the reliability of kinetic theory for describing granular flows. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
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14 pages, 2267 KiB  
Article
Research on Fault Diagnosis of Rolling Bearings Based on Variational Mode Decomposition Improved by the Niche Genetic Algorithm
by Ruimin Shi, Bukang Wang, Zongyan Wang, Jiquan Liu, Xinyu Feng and Lei Dong
Entropy 2022, 24(6), 825; https://doi.org/10.3390/e24060825 - 14 Jun 2022
Cited by 7 | Viewed by 1773
Abstract
Due to the influence of signal-to-noise ratio in the early failure stage of rolling bearings in rotating machinery, it is difficult to effectively extract feature information. Variational Mode Decomposition (VMD) has been widely used to decompose vibration signals which can reflect more fault [...] Read more.
Due to the influence of signal-to-noise ratio in the early failure stage of rolling bearings in rotating machinery, it is difficult to effectively extract feature information. Variational Mode Decomposition (VMD) has been widely used to decompose vibration signals which can reflect more fault omens. In order to improve the efficiency and accuracy, a method to optimize VMD by using the Niche Genetic Algorithm (NGA) is proposed in this paper. In this method, the optimal Shannon entropy of modal components in a VMD algorithm is taken as the optimization objective, by using the NGA to constantly update and optimize the combination of influencing parameters composed of α and K so as to minimize the local minimum entropy. According to the obtained optimization results, the optimal input parameters of the VMD algorithm were set. The method mentioned is applied to the fault extraction of a simulated signal and a measured signal of a rolling bearing. The decomposition process of the rolling-bearing fault signal was transferred to the variational frame by the NGA-VMD algorithm, and several eigenmode function components were obtained. The energy feature extracted from the modal component containing the main fault information was used as the input vector of a particle swarm optimized support vector machine (PSO-SVM) and used to identify the fault type of the rolling bearing. The analysis results of the simulation signal and measured signal show that: the NGA-VMD algorithm can decompose the vibration signal of a rolling bearing accurately and has a better robust performance and correct recognition rate than the VMD algorithm. It can highlight the local characteristics of the original sample data and reduce the interference of the parameters selected artificially in the VMD algorithm on the processing results, improving the fault-diagnosis efficiency of rolling bearings. Full article
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11 pages, 535 KiB  
Article
Entropy Production in Non-Markovian Collision Models: Information Backflow vs. System-Environment Correlations
by Hüseyin T. Şenyaşa, Şahinde Kesgin, Göktuğ Karpat and Barış Çakmak
Entropy 2022, 24(6), 824; https://doi.org/10.3390/e24060824 - 14 Jun 2022
Cited by 3 | Viewed by 1867
Abstract
We investigate the irreversible entropy production of a qubit in contact with an environment modelled by a microscopic collision model in both Markovian and non-Markovian regimes. Our main goal is to contribute to the discussions on the relationship between non-Markovian dynamics and negative [...] Read more.
We investigate the irreversible entropy production of a qubit in contact with an environment modelled by a microscopic collision model in both Markovian and non-Markovian regimes. Our main goal is to contribute to the discussions on the relationship between non-Markovian dynamics and negative entropy production rates. We employ two different types of collision models that do or do not keep the correlations established between the system and the incoming environmental particle, while both of them pertain to their non-Markovian nature through information backflow from the environment to the system. We observe that as the former model, where the correlations between the system and environment are preserved, gives rise to negative entropy production rates in the transient dynamics, the latter one always maintains positive rates, even though the convergence to the steady-state value is slower as compared to the corresponding Markovian dynamics. Our results suggest that the mechanism underpinning the negative entropy production rates is not solely non-Markovianity through information backflow, but rather the contribution to it through established system-environment correlations. Full article
(This article belongs to the Special Issue Quantum Collision Models)
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28 pages, 1093 KiB  
Article
Effective Field Theory of Random Quantum Circuits
by Yunxiang Liao and Victor Galitski
Entropy 2022, 24(6), 823; https://doi.org/10.3390/e24060823 - 13 Jun 2022
Cited by 2 | Viewed by 2242
Abstract
Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such features have already been experimentally demonstrated in noisy [...] Read more.
Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such features have already been experimentally demonstrated in noisy intermediate-scale quantum (NISQ) devices. On the theory side, properties of random quantum circuits have been studied on a case-by-case basis and for certain specific systems, and a hallmark of quantum chaos—universal Wigner–Dyson level statistics—has been derived. This work develops an effective field theory for a large class of random quantum circuits. The theory has the form of a replica sigma model and is similar to the low-energy approach to diffusion in disordered systems. The method is used to explicitly derive the universal random matrix behavior of a large family of random circuits. In particular, we rederive the Wigner–Dyson spectral statistics of the brickwork circuit model by Chan, De Luca, and Chalker [Phys. Rev. X 8, 041019 (2018)] and show within the same calculation that its various permutations and higher-dimensional generalizations preserve the universal level statistics. Finally, we use the replica sigma model framework to rederive the Weingarten calculus, which is a method of evaluating integrals of polynomials of matrix elements with respect to the Haar measure over compact groups and has many applications in the study of quantum circuits. The effective field theory derived here provides both a method to quantitatively characterize the quantum dynamics of random Floquet systems (e.g., calculating operator and entanglement spreading) and a path to understanding the general fundamental mechanism behind quantum chaos and thermalization in these systems. Full article
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12 pages, 3316 KiB  
Article
Prisoner’s Dilemma Game with Cooperation-Defection Dominance Strategies on Correlational Multilayer Networks
by Qin Li, Guopeng Zhao and Minyu Feng
Entropy 2022, 24(6), 822; https://doi.org/10.3390/e24060822 - 13 Jun 2022
Cited by 4 | Viewed by 1621
Abstract
As multilayer networks are widely applied in modern society, numerous studies have shown the impact of a multilayer network structure and the network nature on the proportion of cooperators in the network. In this paper, we use Barabási–Albert scale-free networks (BA) and Watts [...] Read more.
As multilayer networks are widely applied in modern society, numerous studies have shown the impact of a multilayer network structure and the network nature on the proportion of cooperators in the network. In this paper, we use Barabási–Albert scale-free networks (BA) and Watts and Strogatz networks (WS) to build a multilayer network structure, and we propose a new strategy-updating rule called “cooperation-defection dominance”, which can be likened to dominant and recessive traits in biogenetics. With the newly constructed multilayer network structure and the strategy-updating rules, based on the simulation results, we find that in the BA-BA network, the cooperation dominance strategy can make the networks with different rs show a cooperative trend, while the defection dominance strategy only has an obvious effect on the network cooperation with a larger r. When the BA network is connected to the WS network, we find that the effect of strategy on the proportion of cooperators in the network decreases, and the main influencing factor is the structure of the network. In the three-layer network, the cooperation dominance strategy has a greater impact on the BA network, and the proportion of the cooperators is enhanced more than under the natural evolution strategy, but the promotion effect is still smaller than that of the two-layer BA network because of the WS network. Under the defection dominance strategy, the WS layer appears different from the first two strategies, and we conclude through simulation that when the payoff parameter is at the middle level, its cooperator proportion will be suppressed, and we deduce that the proportion of cooperators and defectors, as well as the payoff, play an important role. Full article
(This article belongs to the Section Statistical Physics)
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2 pages, 993 KiB  
Correction
Correction: Kasza et al. New, Spherical Solutions of Non-Relativistic, Dissipative Hydrodynamics. Entropy 2022, 24, 514
by Gábor Kasza, László P. Csernai and Tamás Csörgő
Entropy 2022, 24(6), 821; https://doi.org/10.3390/e24060821 - 13 Jun 2022
Viewed by 1035
Abstract
In the original publication [...] Full article
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17 pages, 855 KiB  
Article
Efficiency Fluctuations in a Quantum Battery Charged by a Repeated Interaction Process
by Felipe Barra
Entropy 2022, 24(6), 820; https://doi.org/10.3390/e24060820 - 13 Jun 2022
Cited by 6 | Viewed by 1758
Abstract
A repeated interaction process assisted by auxiliary thermal systems charges a quantum battery. The charging energy is supplied by switching on and off the interaction between the battery and the thermal systems. The charged state is an equilibrium state for the repeated interaction [...] Read more.
A repeated interaction process assisted by auxiliary thermal systems charges a quantum battery. The charging energy is supplied by switching on and off the interaction between the battery and the thermal systems. The charged state is an equilibrium state for the repeated interaction process, and the ergotropy characterizes its charge. The working cycle consists in extracting the ergotropy and charging the battery again. We discuss the fluctuating efficiency of the process, among other fluctuating properties. These fluctuations are dominated by the equilibrium distribution and depend weakly on other process properties. Full article
(This article belongs to the Special Issue Quantum Collision Models)
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33 pages, 5329 KiB  
Concept Paper
Competency in Navigating Arbitrary Spaces as an Invariant for Analyzing Cognition in Diverse Embodiments
by Chris Fields and Michael Levin
Entropy 2022, 24(6), 819; https://doi.org/10.3390/e24060819 - 12 Jun 2022
Cited by 39 | Viewed by 9504
Abstract
One of the most salient features of life is its capacity to handle novelty and namely to thrive and adapt to new circumstances and changes in both the environment and internal components. An understanding of this capacity is central to several fields: the [...] Read more.
One of the most salient features of life is its capacity to handle novelty and namely to thrive and adapt to new circumstances and changes in both the environment and internal components. An understanding of this capacity is central to several fields: the evolution of form and function, the design of effective strategies for biomedicine, and the creation of novel life forms via chimeric and bioengineering technologies. Here, we review instructive examples of living organisms solving diverse problems and propose competent navigation in arbitrary spaces as an invariant for thinking about the scaling of cognition during evolution. We argue that our innate capacity to recognize agency and intelligence in unfamiliar guises lags far behind our ability to detect it in familiar behavioral contexts. The multi-scale competency of life is essential to adaptive function, potentiating evolution and providing strategies for top-down control (not micromanagement) to address complex disease and injury. We propose an observer-focused viewpoint that is agnostic about scale and implementation, illustrating how evolution pivoted similar strategies to explore and exploit metabolic, transcriptional, morphological, and finally 3D motion spaces. By generalizing the concept of behavior, we gain novel perspectives on evolution, strategies for system-level biomedical interventions, and the construction of bioengineered intelligences. This framework is a first step toward relating to intelligence in highly unfamiliar embodiments, which will be essential for progress in artificial intelligence and regenerative medicine and for thriving in a world increasingly populated by synthetic, bio-robotic, and hybrid beings. Full article
(This article belongs to the Special Issue The Role of Information in Cultural Evolution)
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13 pages, 959 KiB  
Article
Maximum Power Point Tracking Control for Non-Gaussian Wind Energy Conversion System by Using Survival Information Potential
by Liping Yin, Lanlan Lai, Zhengju Zhu and Tao Li
Entropy 2022, 24(6), 818; https://doi.org/10.3390/e24060818 - 11 Jun 2022
Cited by 4 | Viewed by 1837
Abstract
In this paper, a wind energy conversion system is studied to improve the conversion efficiency and maximize power output. Firstly, a nonlinear state space model is established with respect to shaft current, turbine rotational speed and power output in the wind energy conversion [...] Read more.
In this paper, a wind energy conversion system is studied to improve the conversion efficiency and maximize power output. Firstly, a nonlinear state space model is established with respect to shaft current, turbine rotational speed and power output in the wind energy conversion system. As the wind velocity can be descried as a non-Gaussian variable on the system model, the survival information potential is adopted to measure the uncertainty of the stochastic tracking error between the actual wind turbine rotation speed and the reference one. Secondly, to minimize the stochastic tracking error, the control input is obtained by recursively optimizing the performance index function which is constructed with consideration of both survival information potential and control input constraints. To avoid those complex probability formulation, a data driven method is adopted in the process of calculating the survival information potential. Finally, a simulation example is given to illustrate the efficiency of the proposed maximum power point tracking control method. The results demonstrate that by following this method, the actual wind turbine rotation speed can track the reference speed with less time, less overshoot and higher precision, and thus the power output can still be guaranteed under the influence of non-Gaussian wind noises. Full article
(This article belongs to the Topic Advances in Nonlinear Dynamics: Methods and Applications)
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