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Volume 24
Issue 7
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Entropy, Volume 24, Issue 7 (July 2022) – 163 articles

Cover Story (view full-size image): Permutation entropy (PE) is a popular tool to analyze time series in order to either estimate the degree of randomness of a time series source or to detect changes in its dynamics. However, most works that rely on PE neglect the crucial problem of considering the statistical significance of a PE assessment, or, equivalently, of estimating its uncertainty—a task that is hardly feasible in most cases. A new, viable approach to carry out this estimation exploits the technique of surrogate data generation. Using the technique as a proxy generator of the source’s dynamics allows us to assess its statistical properties. View this paper
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15 pages, 1829 KiB  
Article
LGCCT: A Light Gated and Crossed Complementation Transformer for Multimodal Speech Emotion Recognition
by Feng Liu, Si-Yuan Shen, Zi-Wang Fu, Han-Yang Wang, Ai-Min Zhou and Jia-Yin Qi
Entropy 2022, 24(7), 1010; https://doi.org/10.3390/e24071010 - 21 Jul 2022
Cited by 14 | Viewed by 2970
Abstract
Semantic-rich speech emotion recognition has a high degree of popularity in a range of areas. Speech emotion recognition aims to recognize human emotional states from utterances containing both acoustic and linguistic information. Since both textual and audio patterns play essential roles in speech [...] Read more.
Semantic-rich speech emotion recognition has a high degree of popularity in a range of areas. Speech emotion recognition aims to recognize human emotional states from utterances containing both acoustic and linguistic information. Since both textual and audio patterns play essential roles in speech emotion recognition (SER) tasks, various works have proposed novel modality fusing methods to exploit text and audio signals effectively. However, most of the high performance of existing models is dependent on a great number of learnable parameters, and they can only work well on data with fixed length. Therefore, minimizing computational overhead and improving generalization to unseen data with various lengths while maintaining a certain level of recognition accuracy is an urgent application problem. In this paper, we propose LGCCT, a light gated and crossed complementation transformer for multimodal speech emotion recognition. First, our model is capable of fusing modality information efficiently. Specifically, the acoustic features are extracted by CNN-BiLSTM while the textual features are extracted by BiLSTM. The modality-fused representation is then generated by the cross-attention module. We apply the gate-control mechanism to achieve the balanced integration of the original modality representation and the modality-fused representation. Second, the degree of attention focus can be considered, as the uncertainty and the entropy of the same token should converge to the same value independent of the length. To improve the generalization of the model to various testing-sequence lengths, we adopt the length-scaled dot product to calculate the attention score, which can be interpreted from a theoretical view of entropy. The operation of the length-scaled dot product is cheap but effective. Experiments are conducted on the benchmark dataset CMU-MOSEI. Compared to the baseline models, our model achieves an 81.0% F1 score with only 0.432 M parameters, showing an improvement in the balance between performance and the number of parameters. Moreover, the ablation study signifies the effectiveness of our model and its scalability to various input-sequence lengths, wherein the relative improvement is almost 20% of the baseline without a length-scaled dot product. Full article
(This article belongs to the Topic Complex Systems and Artificial Intelligence)
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12 pages, 4466 KiB  
Article
Exposing Deep Representations to a Recurrent Expansion with Multiple Repeats for Fuel Cells Time Series Prognosis
by Tarek Berghout, Mohamed Benbouzid, Toufik Bentrcia, Yassine Amirat and Leïla-Hayet Mouss
Entropy 2022, 24(7), 1009; https://doi.org/10.3390/e24071009 - 21 Jul 2022
Cited by 5 | Viewed by 2177
Abstract
The green conversion of proton exchange membrane fuel cells (PEMFCs) has received particular attention in both stationary and transportation applications. However, the poor durability of PEMFC represents a major problem that hampers its commercial application since dynamic operating conditions, including physical deterioration, have [...] Read more.
The green conversion of proton exchange membrane fuel cells (PEMFCs) has received particular attention in both stationary and transportation applications. However, the poor durability of PEMFC represents a major problem that hampers its commercial application since dynamic operating conditions, including physical deterioration, have a serious impact on the cell performance. Under these circumstances, prognosis and health management (PHM) plays an important role in prolonging durability and preventing damage propagation via the accurate planning of a condition-based maintenance (CBM) schedule. In this specific topic, health deterioration modeling with deep learning (DL) is the widely studied representation learning tool due to its adaptation ability to rapid changes in data complexity and drift. In this context, the present paper proposes an investigation of further deeper representations by exposing DL models themselves to recurrent expansion with multiple repeats. Such a recurrent expansion of DL (REDL) allows new, more meaningful representations to be explored by repeatedly using generated feature maps and responses to create new robust models. The proposed REDL, which is designed to be an adaptive learning algorithm, is tested on a PEMFC deterioration dataset and compared to its deep learning baseline version under time series analysis. Using multiple numeric and visual metrics, the results support the REDL learning scheme by showing promising performances. Full article
(This article belongs to the Special Issue Fault Diagnosis Methods Based on Information Theory or Machine Learning: From Theory to Application)
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13 pages, 2590 KiB  
Article
Generalized Maximum Complex Correntropy Augmented Adaptive IIR Filtering
by Haotian Zheng and Guobing Qian
Entropy 2022, 24(7), 1008; https://doi.org/10.3390/e24071008 - 21 Jul 2022
Cited by 3 | Viewed by 1653
Abstract
Augmented IIR filter adaptive algorithms have been considered in many studies, which are suitable for proper and improper complex-valued signals. However, lots of augmented IIR filter adaptive algorithms are developed under the mean square error (MSE) criterion. It is an ideal optimality criterion [...] Read more.
Augmented IIR filter adaptive algorithms have been considered in many studies, which are suitable for proper and improper complex-valued signals. However, lots of augmented IIR filter adaptive algorithms are developed under the mean square error (MSE) criterion. It is an ideal optimality criterion under Gaussian noises but fails to model the behavior of non-Gaussian noise found in practice. Complex correntropy has shown robustness under non-Gaussian noises in the design of adaptive filters as a similarity measure for the complex random variables. In this paper, we propose a new augmented IIR filter adaptive algorithm based on the generalized maximum complex correntropy criterion (GMCCC-AIIR), which employs the complex generalized Gaussian density function as the kernel function. Stability analysis provides the bound of learning rate. Simulation results verify its superiority. Full article
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16 pages, 5424 KiB  
Article
Experimental Diagnosis on Combustion Characteristic of Shock Wave Focusing Initiation Engine
by Shida Xu, Feilong Song, Xin Chen, Hesong Zhang, Xingkui Yang and Jianping Zhou
Entropy 2022, 24(7), 1007; https://doi.org/10.3390/e24071007 - 21 Jul 2022
Cited by 1 | Viewed by 1751
Abstract
A shock wave focusing initiation engine was assembled and tested in an experimental program. The effective pyrolysis rate of the pre-combustor was evaluated over a range of supplementary fuel ratio in this paper. Results highlight two operational modes of the resonant cavity: (1) [...] Read more.
A shock wave focusing initiation engine was assembled and tested in an experimental program. The effective pyrolysis rate of the pre-combustor was evaluated over a range of supplementary fuel ratio in this paper. Results highlight two operational modes of the resonant cavity: (1) pulsating combustion mode, (2) stable combustion mode. The appearance of the two combustion modes is jointly affected by the flow and the structural characteristic value of the combustion chamber. This paper uses images, time-frequency analysis, and nonlinear time series analysis methods to identify and distinguish these two combustion modes. It is believed that the interaction between the combustion chamber and the supply plenum is the probable reason for different combustion modes. The experiment has found that structural parameters and import flow parameters have an impact on the initiation of the combustion chamber. Increasing the injection pressure can appropriately broaden the fuel-rich boundary of initiation. Low equivalence ratio and high injection pressure can also appropriately increase the combustion working frequency in a small range. From the perspective of pressure utilization, under the premise of ensuring successful initiation, injection pressure should not be too high. Full article
(This article belongs to the Section Thermodynamics)
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18 pages, 1240 KiB  
Article
Entropy-Argumentative Concept of Computational Phonetic Analysis of Speech Taking into Account Dialect and Individuality of Phonation
by Viacheslav Kovtun, Oksana Kovtun and Andriy Semenov
Entropy 2022, 24(7), 1006; https://doi.org/10.3390/e24071006 - 20 Jul 2022
Cited by 7 | Viewed by 1709
Abstract
In this article, the concept (i.e., the mathematical model and methods) of computational phonetic analysis of speech with an analytical description of the phenomenon of phonetic fusion is proposed. In this concept, in contrast to the existing methods, the problem of multicriteria of [...] Read more.
In this article, the concept (i.e., the mathematical model and methods) of computational phonetic analysis of speech with an analytical description of the phenomenon of phonetic fusion is proposed. In this concept, in contrast to the existing methods, the problem of multicriteria of the process of cognitive perception of speech by a person is strictly formally presented using the theoretical and analytical apparatus of information (entropy) theory, pattern recognition theory and acoustic theory of speech formation. The obtained concept allows for determining reliably the individual phonetic alphabet inherent in a person, taking into account their inherent dialect of speech and individual features of phonation, as well as detecting and correcting errors in the recognition of language units. The experiments prove the superiority of the proposed scientific result over such common Bayesian concepts of decision making using the Euclidean-type mismatch metric as a method of maximum likelihood and a method of an ideal observer. The analysis of the speech signal carried out in the metric based on the proposed concept allows, in particular, for establishing reliably the phonetic saturation of speech, which objectively characterizes the environment of speech signal propagation and its source. Full article
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17 pages, 1399 KiB  
Article
Evolution of Cohesion between USA Financial Sector Companies before, during, and Post-Economic Crisis: Complex Networks Approach
by Vojin Stević, Marija Rašajski and Marija Mitrović Dankulov
Entropy 2022, 24(7), 1005; https://doi.org/10.3390/e24071005 - 20 Jul 2022
Viewed by 2029
Abstract
Various mathematical frameworks play an essential role in understanding the economic systems and the emergence of crises in them. Understanding the relation between the structure of connections between the system’s constituents and the emergence of a crisis is of great importance. In this [...] Read more.
Various mathematical frameworks play an essential role in understanding the economic systems and the emergence of crises in them. Understanding the relation between the structure of connections between the system’s constituents and the emergence of a crisis is of great importance. In this paper, we propose a novel method for the inference of economic systems’ structures based on complex networks theory utilizing the time series of prices. Our network is obtained from the correlation matrix between the time series of companies’ prices by imposing a threshold on the values of the correlation coefficients. The optimal value of the threshold is determined by comparing the spectral properties of the threshold network and the correlation matrix. We analyze the community structure of the obtained networks and the relation between communities’ inter and intra-connectivity as indicators of systemic risk. Our results show how an economic system’s behavior is related to its structure and how the crisis is reflected in changes in the structure. We show how regulation and deregulation affect the structure of the system. We demonstrate that our method can identify high systemic risks and measure the impact of the actions taken to increase the system’s stability. Full article
(This article belongs to the Special Issue Statistical Methods for Complex Systems)
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23 pages, 771 KiB  
Article
Application of Statistical K-Means Algorithm for University Academic Evaluation
by Daohua Yu, Xin Zhou, Yu Pan, Zhendong Niu and Huafei Sun
Entropy 2022, 24(7), 1004; https://doi.org/10.3390/e24071004 - 20 Jul 2022
Cited by 5 | Viewed by 2416
Abstract
With the globalization of higher education, academic evaluation is increasingly valued by the scientific and educational circles. Although the number of published papers of academic evaluation methods is increasing, previous research mainly focused on the method of assigning different weights for various indicators, [...] Read more.
With the globalization of higher education, academic evaluation is increasingly valued by the scientific and educational circles. Although the number of published papers of academic evaluation methods is increasing, previous research mainly focused on the method of assigning different weights for various indicators, which can be subjective and limited. This paper investigates the evaluation of academic performance by using the statistical K-means (SKM) algorithm to produce clusters. The core idea is mapping the evaluation data from Euclidean space to Riemannian space in which the geometric structure can be used to obtain accurate clustering results. The method can adapt to different indicators and make full use of big data. By using the K-means algorithm based on statistical manifolds, the academic evaluation results of universities can be obtained. Furthermore, through simulation experiments on the top 20 universities of China with the traditional K-means, GMM and SKM algorithms, respectively, we analyze the advantages and disadvantages of different methods. We also test the three algorithms on a UCI ML dataset. The simulation results show the advantages of the SKM algorithm. Full article
(This article belongs to the Special Issue Information and Divergence Measures)
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17 pages, 336 KiB  
Article
Robust Self-Testing of Four-Qubit Symmetric States
by Daipengwei Bao, Xiaoqing Tan, Qingshan Xu, Haozhen Wang and Rui Huang
Entropy 2022, 24(7), 1003; https://doi.org/10.3390/e24071003 - 20 Jul 2022
Cited by 1 | Viewed by 1799
Abstract
Quantum verification has been highlighted as a significant challenge on the road to scalable technology, especially with the rapid development of quantum computing. To verify quantum states, self-testing is proposed as a device-independent concept, which is based only on the observed statistics. Previous [...] Read more.
Quantum verification has been highlighted as a significant challenge on the road to scalable technology, especially with the rapid development of quantum computing. To verify quantum states, self-testing is proposed as a device-independent concept, which is based only on the observed statistics. Previous studies focused on bipartite states and some multipartite states, including all symmetric states, but only in the case of three qubits. In this paper, we first give a criterion for the self-testing of a four-qubit symmetric state with a special structure and the robustness analysis based on vector norm inequalities. Then we generalize the idea to a family of parameterized four-qubit symmetric states through projections onto two subsystems. Full article
(This article belongs to the Special Issue Quantum Information and Computation)
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13 pages, 855 KiB  
Article
Axisymmetric Fractional Diffusion with Mass Absorption in a Circle under Time-Harmonic Impact
by Yuriy Povstenko and Tamara Kyrylych
Entropy 2022, 24(7), 1002; https://doi.org/10.3390/e24071002 - 20 Jul 2022
Cited by 1 | Viewed by 1664
Abstract
The axisymmetric time-fractional diffusion equation with mass absorption is studied in a circle under the time-harmonic Dirichlet boundary condition. The Caputo derivative of the order 0<α≤2 is used. The investigated equation can be considered as the time-fractional generalization of [...] Read more.
The axisymmetric time-fractional diffusion equation with mass absorption is studied in a circle under the time-harmonic Dirichlet boundary condition. The Caputo derivative of the order 0<α≤2 is used. The investigated equation can be considered as the time-fractional generalization of the bioheat equation and the Klein–Gordon equation. Different formulations of the problem for integer values of the time-derivatives α=1 and α=2 are also discussed. The integral transform technique is employed. The outcomes of numerical calculations are illustrated graphically for different values of the parameters. Full article
(This article belongs to the Special Issue Dynamical Systems, Differential Equations and Applications)
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16 pages, 3612 KiB  
Article
Constructal Optimizations of Line-to-Line Vascular Channels with Turbulent Convection Heat Transfer
by Daoguang Lin, Zhihui Xie, Gang Nan, Pan Jiang and Yanlin Ge
Entropy 2022, 24(7), 999; https://doi.org/10.3390/e24070999 - 19 Jul 2022
Cited by 1 | Viewed by 1660
Abstract
The multi-scale line-to-line vascular channels (LVCs) widely exist in nature because of their excellent transmission characteristics. In this paper, models of LVCs with turbulent convection heat transfer are established. Based on constructal theory and the entropy generation minimization principle, the constructal optimizations of [...] Read more.
The multi-scale line-to-line vascular channels (LVCs) widely exist in nature because of their excellent transmission characteristics. In this paper, models of LVCs with turbulent convection heat transfer are established. Based on constructal theory and the entropy generation minimization principle, the constructal optimizations of LVCs with any order are conducted by taking the angles at bifurcations as the optimization variables. The heat flux on the channel wall per unit length is fixed and uniform. The areas occupied by vasculature and the total volumes of channels are fixed. The analytical expressions of the optimal angles, dimensionless total entropy generation rate and entropy generation number (EGN) of LVCs with any order versus dimensionless mass flow rate are obtained, respectively. The results indicate that the dimensionless total entropy generation rate of LVCs with any order can be significantly decreased by optimizing the angles of LVCs, which is significantly more when the order of LVCs is higher. As the dimensionless mass flow rate increases, the optimal angles of LVCs with any order remain unchanged first, then the optimal angles at the entrance (root) increase, and the other optimal angles decrease continuously and finally tend to the respective stable values. The optimal angles of LVCs continue to increase from the entrance to the outlet (crown), i.e., the LVCs with a certain order gradually spread out from the root to the crown. The dimensionless total entropy generation rate and EGN of LVCs first decrease and then increase with the growth of the dimensionless mass flow rate. There is optimal dimensionless mass flow rate, making the dimensionless total entropy generation rate and the EGN reach their respective minimums. The results obtained herein can provide some new theoretical guidelines of thermal design and management for the practical applications of LVCs. Full article
(This article belongs to the Topic Heat Exchanger Design and Heat Pump Efficiency)
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16 pages, 3300 KiB  
Article
A Statistical Journey through the Topological Determinants of the β2 Adrenergic Receptor Dynamics
by Luisa Di Paola, Humanath Poudel, Mauro Parise, Alessandro Giuliani and David M. Leitner
Entropy 2022, 24(7), 998; https://doi.org/10.3390/e24070998 - 19 Jul 2022
Cited by 6 | Viewed by 2265
Abstract
Activation of G-protein-coupled receptors (GPCRs) is mediated by molecular switches throughout the transmembrane region of the receptor. In this work, we continued along the path of a previous computational study wherein energy transport in the β2 Adrenergic Receptor (β2-AR) was examined and allosteric [...] Read more.
Activation of G-protein-coupled receptors (GPCRs) is mediated by molecular switches throughout the transmembrane region of the receptor. In this work, we continued along the path of a previous computational study wherein energy transport in the β2 Adrenergic Receptor (β2-AR) was examined and allosteric switches were identified in the molecular structure through the reorganization of energy transport networks during activation. In this work, we further investigated the allosteric properties of β2-AR, using Protein Contact Networks (PCNs). In this paper, we report an extensive statistical analysis of the topological and structural properties of β2-AR along its molecular dynamics trajectory to identify the activation pattern of this molecular system. The results show a distinct character to the activation that both helps to understand the allosteric switching previously identified and confirms the relevance of the network formalism to uncover relevant functional features of protein molecules. Full article
(This article belongs to the Special Issue Biological Statistical Mechanics II)
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13 pages, 413 KiB  
Article
Ponder: Enabling Balloon-Borne Based Solar Unmanned Aerial Vehicle’s Take Off Diagnosis under Little Data
by Yanfei Hu, Yingkui Jiao, Yujie Shang, Shuailou Li and Yanpeng Hu
Entropy 2022, 24(7), 997; https://doi.org/10.3390/e24070997 - 19 Jul 2022
Viewed by 1431
Abstract
Balloon-borne based solar unmanned aerial vehicle (short for BS-UAV) has been researched prevalently due to the promising application area of near-space (i.e., 20–100 km above the ground) and the advantages of taking off. However, BS-UAV encounters serious fault in its taking off phase. [...] Read more.
Balloon-borne based solar unmanned aerial vehicle (short for BS-UAV) has been researched prevalently due to the promising application area of near-space (i.e., 20–100 km above the ground) and the advantages of taking off. However, BS-UAV encounters serious fault in its taking off phase. The fault in taking off hinders the development of BS-UAV and causes great loss to human property. Thus, timely diagnosing the running state of BS-UAV in taking off phase is of great importance. Unfortunately, due to lack of fault data in the taking off phase, timely diagnosing the running state becomes a key challenge. In this paper, we propose Ponder to diagnose the running state of BS-UAV in the taking off phase. The key idea of Ponder is to take full advantage of existing data and complement fault data first and then diagnose current states. First, we compress existing data into a low-dimensional space. Then, we cluster the low-dimensional data into normal and outlier clusters. Third, we generate fault data with different aggression at different clusters. Finally, we diagnose fault state for each sampling at the taking off phase. With three datasets collected on real-world flying at different times, we show that Ponder outperforms existing diagnosing methods. In addition, we demonstrate Ponder’s effectiveness over time. We also show the comparable overhead. Full article
(This article belongs to the Section Multidisciplinary Applications)
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11 pages, 1136 KiB  
Article
Regge Models of Proton Diffractive Dissociation Based on Factorisation and Structure Functions
by László Jenkovszky, Rainer Schicker and István Szanyi
Entropy 2022, 24(7), 1001; https://doi.org/10.3390/e24071001 - 19 Jul 2022
Cited by 2 | Viewed by 1687
Abstract
Recent results by the authors on proton diffractive dissociation (single, double and central) in the low-mass resonance region with emphasis on the LHC kinematics are reviewed and updated. Based on the previous ideas that the contribution of the inelastic proton–Pomeron vertex can be [...] Read more.
Recent results by the authors on proton diffractive dissociation (single, double and central) in the low-mass resonance region with emphasis on the LHC kinematics are reviewed and updated. Based on the previous ideas that the contribution of the inelastic proton–Pomeron vertex can be described by the proton structure function, the contribution of the inelastic Pomeron–Pomeron vertex appearing in central diffraction is now described by a Pomeron structure function. Full article
(This article belongs to the Special Issue Zimányi School: Hydrodynamics and Thermodynamics in High Energy Particle and Nuclear Physics)
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12 pages, 308 KiB  
Article
Construction of Binary Quantum Error-Correcting Codes from Orthogonal Array
by Shanqi Pang, Hanxiao Xu and Mengqian Chen
Entropy 2022, 24(7), 1000; https://doi.org/10.3390/e24071000 - 19 Jul 2022
Cited by 7 | Viewed by 1894
Abstract
By using difference schemes, orthogonal partitions and a replacement method, some new methods to construct pure quantum error-correcting codes are provided from orthogonal arrays. As an application of these methods, we construct several infinite series of quantum error-correcting codes including some optimal ones. [...] Read more.
By using difference schemes, orthogonal partitions and a replacement method, some new methods to construct pure quantum error-correcting codes are provided from orthogonal arrays. As an application of these methods, we construct several infinite series of quantum error-correcting codes including some optimal ones. Compared with the existing binary quantum codes, more new codes can be constructed, which have a lower number of terms (i.e., the number of computational basis states) for each of their basis states. Full article
(This article belongs to the Special Issue Quantum Information and Computation)
15 pages, 39539 KiB  
Article
Multi-Image Encryption Method via Computational Integral Imaging Algorithm
by Xiaowu Li, Chuying Yu and Junfeng Guo
Entropy 2022, 24(7), 996; https://doi.org/10.3390/e24070996 - 18 Jul 2022
Cited by 12 | Viewed by 1991
Abstract
Under the framework of computational integral imaging, a multi-image encryption scheme based on the DNA-chaos algorithm is proposed. In this scheme, multiple images are merged to one image by a computational integral imaging algorithm, which significantly improves the efficiency of image encryption. Meanwhile, [...] Read more.
Under the framework of computational integral imaging, a multi-image encryption scheme based on the DNA-chaos algorithm is proposed. In this scheme, multiple images are merged to one image by a computational integral imaging algorithm, which significantly improves the efficiency of image encryption. Meanwhile, the computational integral imaging algorithm can merge images at different depth distances, thereby the different depth distances of multiple images can also be used as keys to increase the security of the encryption method. In addition, the high randomness of the chaos algorithm is combined to address the outline effect caused by the DNA encryption algorithm. We have experimentally verified the proposed multi-image encryption scheme. The entropy value of the encrypted image is 7.6227, whereas the entropy value of the merge image with two input images is 3.2886, which greatly reduces the relevance of the image. The simulation results also confirm that the proposed encryption scheme has high key security and can protect against various attacks. Full article
(This article belongs to the Special Issue Computational Imaging and Image Encryption with Entropy)
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26 pages, 3146 KiB  
Review
Differential Expression Analysis of Single-Cell RNA-Seq Data: Current Statistical Approaches and Outstanding Challenges
by Samarendra Das, Anil Rai and Shesh N. Rai
Entropy 2022, 24(7), 995; https://doi.org/10.3390/e24070995 - 18 Jul 2022
Cited by 12 | Viewed by 6822
Abstract
With the advent of single-cell RNA-sequencing (scRNA-seq), it is possible to measure the expression dynamics of genes at the single-cell level. Through scRNA-seq, a huge amount of expression data for several thousand(s) of genes over million(s) of cells are generated in a single [...] Read more.
With the advent of single-cell RNA-sequencing (scRNA-seq), it is possible to measure the expression dynamics of genes at the single-cell level. Through scRNA-seq, a huge amount of expression data for several thousand(s) of genes over million(s) of cells are generated in a single experiment. Differential expression analysis is the primary downstream analysis of such data to identify gene markers for cell type detection and also provide inputs to other secondary analyses. Many statistical approaches for differential expression analysis have been reported in the literature. Therefore, we critically discuss the underlying statistical principles of the approaches and distinctly divide them into six major classes, i.e., generalized linear, generalized additive, Hurdle, mixture models, two-class parametric, and non-parametric approaches. We also succinctly discuss the limitations that are specific to each class of approaches, and how they are addressed by other subsequent classes of approach. A number of challenges are identified in this study that must be addressed to develop the next class of innovative approaches. Furthermore, we also emphasize the methodological challenges involved in differential expression analysis of scRNA-seq data that researchers must address to draw maximum benefit from this recent single-cell technology. This study will serve as a guide to genome researchers and experimental biologists to objectively select options for their analysis. Full article
(This article belongs to the Section Entropy Reviews)
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22 pages, 1179 KiB  
Article
Evaluating Ecohydrological Model Sensitivity to Input Variability with an Information-Theory-Based Approach
by Mozhgan A. Farahani, Alireza Vahid and Allison E. Goodwell
Entropy 2022, 24(7), 994; https://doi.org/10.3390/e24070994 - 18 Jul 2022
Cited by 6 | Viewed by 2727
Abstract
Ecohydrological models vary in their sensitivity to forcing data and use available information to different extents. We focus on the impact of forcing precision on ecohydrological model behavior particularly by quantizing, or binning, time-series forcing variables. We use rate-distortion theory to quantize time-series [...] Read more.
Ecohydrological models vary in their sensitivity to forcing data and use available information to different extents. We focus on the impact of forcing precision on ecohydrological model behavior particularly by quantizing, or binning, time-series forcing variables. We use rate-distortion theory to quantize time-series forcing variables to different precisions. We evaluate the effect of different combinations of quantized shortwave radiation, air temperature, vapor pressure deficit, and wind speed on simulated heat and carbon fluxes for a multi-layer canopy model, which is forced and validated with eddy covariance flux tower observation data. We find that the model is more sensitive to radiation than meteorological forcing input, but model responses also vary with seasonal conditions and different combinations of quantized inputs. While any level of quantization impacts carbon flux similarly, specific levels of quantization influence heat fluxes to different degrees. This study introduces a method to optimally simplify forcing time series, often without significantly decreasing model performance, and could be applied within a sensitivity analysis framework to better understand how models use available information. Full article
(This article belongs to the Special Issue Complexity and Nonlinear Dynamics in the Geosciences: Methods and Applications)
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16 pages, 471 KiB  
Article
Essential Conditions for the Full Synergy of Probability of Occurrence Distributions
by Rubem P. Mondaini and Simão C. de Albuquerque Neto
Entropy 2022, 24(7), 993; https://doi.org/10.3390/e24070993 - 18 Jul 2022
Cited by 3 | Viewed by 1455
Abstract
In this contribution, we specify the conditions for assuring the validity of the synergy of the distribution of probabilities of occurrence. We also study the subsequent restriction on the maximal extension of the strict concavity region on the parameter space of Sharma–Mittal entropy [...] Read more.
In this contribution, we specify the conditions for assuring the validity of the synergy of the distribution of probabilities of occurrence. We also study the subsequent restriction on the maximal extension of the strict concavity region on the parameter space of Sharma–Mittal entropy measures, which has been derived in a previous paper in this journal. The present paper is then a necessary complement to that publication. Some applications of the techniques introduced here are applied to protein domain families (Pfam databases, versions 27.0 and 35.0). The results will show evidence of their usefulness for testing the classification work performed with methods of alignment that are used by expert biologists. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines III)
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11 pages, 1663 KiB  
Article
Polarization Attack on Continuous-Variable Quantum Key Distribution with a Local Local Oscillator
by Yun Shao, Yan Pan, Heng Wang, Yaodi Pi, Yang Li, Li Ma, Yichen Zhang, Wei Huang and Bingjie Xu
Entropy 2022, 24(7), 992; https://doi.org/10.3390/e24070992 - 18 Jul 2022
Cited by 4 | Viewed by 2120
Abstract
The estimation of phase noise of continuous-variable quantum key distribution protocol with a local local oscillator (LLO CVQKD), as a major process in quantifying the secret key rate, is closely relevant to the intensity of the phase reference. However, the transmission of the [...] Read more.
The estimation of phase noise of continuous-variable quantum key distribution protocol with a local local oscillator (LLO CVQKD), as a major process in quantifying the secret key rate, is closely relevant to the intensity of the phase reference. However, the transmission of the phase reference through the insecure quantum channel is prone to be exploited by the eavesdropper (Eve) to mount attacks. Here, we introduce a polarization attack scheme against the phase reference. Presently, in a practical LLO CVQKD system, only part of the phase reference pulses are measured to compensate for the polarization drift of the quantum signal pulses in a compensation cycle due to the limited polarization measurement rate, while the other part of the phase reference pulses are not measured. We show that Eve can control the phase noise by manipulating the polarization direction of the unmeasured phase reference to hide her attack on the quantum signal. Simulations show that Eve can obtain partial or total key rates information shared between Alice and Bob as the transmission distance increases. Improving the polarization measurement rate to 100% or monitoring the phase reference intensity in real-time is of great importance to protect the LLO CVQKD from polarization attack. Full article
(This article belongs to the Special Issue Quantum Communication)
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15 pages, 1547 KiB  
Article
Dense-Frequency Signal-Detection Based on the Primal–Dual Splitting Method
by Jiaoyu Zheng, Zheng Liao, Xiaoyang Ma, Yanlin Jin and Huangqi Ma
Entropy 2022, 24(7), 991; https://doi.org/10.3390/e24070991 - 18 Jul 2022
Cited by 1 | Viewed by 1696
Abstract
Aiming to solve the problem of dense-frequency signals in the power system caused by the growing proportion of new energy, this paper proposes a dense-frequency signal-detection method based on the primal–dual splitting method. After establishing the Taylor–Fourier model of the signal, the proposed [...] Read more.
Aiming to solve the problem of dense-frequency signals in the power system caused by the growing proportion of new energy, this paper proposes a dense-frequency signal-detection method based on the primal–dual splitting method. After establishing the Taylor–Fourier model of the signal, the proposed method uses the sparse property of the coefficient matrix to obtain the convex optimization form of the model. Then, the optimal solution of the estimated phasor is obtained by iterating over the fixed-point equation, finally acquiring the optimal estimation result for the dense signal. When representing the Taylor–Fourier model as a convex optimization form, the introduction of measuring-error entropy makes the solution of the model more rigorous. It can be further verified through simulation experiments that the estimation accuracy of the primal–dual splitting method proposed in this paper for dense signals can meet the M-class PMU accuracy requirements. Full article
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11 pages, 2965 KiB  
Article
On Entanglement-Assisted Multistatic Radar Techniques
by Ivan B. Djordjevic
Entropy 2022, 24(7), 990; https://doi.org/10.3390/e24070990 - 17 Jul 2022
Cited by 6 | Viewed by 2340
Abstract
Entanglement-based quantum sensors have much better sensitivity than corresponding classical sensors in a noisy and lossy regime. In our recent paper, we showed that the entanglement-assisted (EA) joint monostatic–bistatic quantum radar performs much better than conventional radars. Here, we propose an entanglement-assisted (EA) [...] Read more.
Entanglement-based quantum sensors have much better sensitivity than corresponding classical sensors in a noisy and lossy regime. In our recent paper, we showed that the entanglement-assisted (EA) joint monostatic–bistatic quantum radar performs much better than conventional radars. Here, we propose an entanglement-assisted (EA) multistatic radar that significantly outperforms EA bistatic, coherent state-based quantum, and classical radars. The proposed EA multistatic radar employs multiple entangled transmitters performing transmit-side optical phase conjugation, multiple coherent detection-based receivers serving as EA detectors, and a joint detector. Full article
(This article belongs to the Special Issue Information Theory and Coding for Wireless Communications)
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19 pages, 606 KiB  
Article
The Residual ISI for Which the Convolutional Noise Probability Density Function Associated with the Blind Adaptive Deconvolution Problem Turns Approximately Gaussian
by Monika Pinchas
Entropy 2022, 24(7), 989; https://doi.org/10.3390/e24070989 - 17 Jul 2022
Viewed by 1739
Abstract
In a blind adaptive deconvolution problem, the convolutional noise observed at the output of the deconvolution process, in addition to the required source signal, is—according to the literature—assumed to be a Gaussian process when the deconvolution process (the blind adaptive equalizer) is deep [...] Read more.
In a blind adaptive deconvolution problem, the convolutional noise observed at the output of the deconvolution process, in addition to the required source signal, is—according to the literature—assumed to be a Gaussian process when the deconvolution process (the blind adaptive equalizer) is deep in its convergence state. Namely, when the convolutional noise sequence or, equivalently, the residual inter-symbol interference (ISI) is considered small. Up to now, no closed-form approximated expression is given for the residual ISI, where the Gaussian model can be used to describe the convolutional noise probability density function (pdf). In this paper, we use the Maximum Entropy density technique, Lagrange’s Integral method, and quasi-moment truncation technique to obtain an approximated closed-form equation for the residual ISI where the Gaussian model can be used to approximately describe the convolutional noise pdf. We will show, based on this approximated closed-form equation for the residual ISI, that the Gaussian model can be used to approximately describe the convolutional noise pdf just before the equalizer has converged, even at a residual ISI level where the “eye diagram” is still very closed, namely, where the residual ISI can not be considered as small. Full article
(This article belongs to the Special Issue Applications of Information Theory in Statistics)
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18 pages, 1046 KiB  
Article
A Bregman-Split-Based Compressive Sensing Method for Dynamic Harmonic Estimation
by Aobing Chi, Chengbi Zeng, Yufu Guo and Hong Miao
Entropy 2022, 24(7), 988; https://doi.org/10.3390/e24070988 - 17 Jul 2022
Cited by 1 | Viewed by 1466
Abstract
In order to overcome the spectral interference of the conventional Fourier transform in the International Electrotechnical Commission framework, this paper introduces a Bregman-split-based compressive sensing (BSCS) method to estimate the Taylor–Fourier coefficients in a multi-frequency dynamic phasor model. Considering the DDC component estimation, [...] Read more.
In order to overcome the spectral interference of the conventional Fourier transform in the International Electrotechnical Commission framework, this paper introduces a Bregman-split-based compressive sensing (BSCS) method to estimate the Taylor–Fourier coefficients in a multi-frequency dynamic phasor model. Considering the DDC component estimation, this paper transforms the phasor problem into a compressive sensing model based on the regularity and sparsity of the dynamic harmonic signal distribution. It then derives an optimized hybrid regularization algorithm with the Bregman split method to reconstruct the dynamic phasor estimation. The accuracy of the model was verified by using the cross entropy to measure the distribution differences of values. Composite tests derived from the dynamic phasor test conditions were then used to verify the potentialities of the BSCS method. Simulation results show that the algorithm can alleviate the impact of dynamic signals on phasor estimation and significantly improve the estimation accuracy, which provides a theoretical basis for P-class phasor measurement units (PMUs). Full article
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20 pages, 9362 KiB  
Article
Damage Detection of Regular Civil Buildings Using Modified Multi-Scale Symbolic Dynamic Entropy
by Tzu-Kang Lin, Dong-You Lee, Yu-Chung Hsu and Kai-Wei Kuo
Entropy 2022, 24(7), 987; https://doi.org/10.3390/e24070987 - 17 Jul 2022
Cited by 1 | Viewed by 1464
Abstract
Based on the examination of the fundamental characteristics of structures, structural health monitoring (SHM) has received increased attention in recent years. Studies have shown that the SHM method using entropy analysis can precisely identify the damaged location of the structure, which is very [...] Read more.
Based on the examination of the fundamental characteristics of structures, structural health monitoring (SHM) has received increased attention in recent years. Studies have shown that the SHM method using entropy analysis can precisely identify the damaged location of the structure, which is very helpful for the daily inspection or maintenance of civil structures. Although entropy analysis has shown excellent accuracy, it still consumes too much time and too many resources in terms of data processing. To improve the dilemma, in this study, modified multi-scale symbolic dynamic entropy (MMSDE) is adopted to identify the damaged location of the civil structure. A damage index (DI) based on the entropy diagram is also proposed to clearly indicate the damage location. A seven-story numerical model was created to verify the efficiency of the proposed SHM system. The results of the analysis of each case of damage show that the MMSDE curve for the damaged floor is lower than that for the healthy floor, and the structural damage can be correctly diagnosed by the damage index. Subsequently, a scaled-down steel benchmark experiment, including 15 damage cases, was conducted to verify the practical performance of the SHM system. The confusion matrix was used to further evaluate the SHM system. The results demonstrated that the MMSD-based system can quickly diagnose structural safety with reliability and accuracy. It can be used in the field of long-term structural health monitoring in the near future. Full article
(This article belongs to the Special Issue Multiscale Entropy Approaches and Their Applications III)
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31 pages, 802 KiB  
Article
Three-Way Decision Models Based on Ideal Relations in Multi-Attribute Decision-Making
by Xiaozhi Chen and Ligeng Zou
Entropy 2022, 24(7), 986; https://doi.org/10.3390/e24070986 - 17 Jul 2022
Cited by 3 | Viewed by 1568
Abstract
In recent years, research on applications of three-way decision (e.g., TWD) has attracted the attention of many scholars. In this paper, we combine TWD with multi-attribute decision-making (MADM). First, we utilize the essential idea of TOPSIS in MADM theory to propose a pair [...] Read more.
In recent years, research on applications of three-way decision (e.g., TWD) has attracted the attention of many scholars. In this paper, we combine TWD with multi-attribute decision-making (MADM). First, we utilize the essential idea of TOPSIS in MADM theory to propose a pair of new ideal relation models based on TWD, namely, the three-way ideal superiority model and the three-way ideal inferiority model. Second, in order to reduce errors caused by the subjectivity of decision-makers, we develop two new methods to calculate the state sets for the two proposed ideal relation models. Third, we employ aggregate relative loss functions to calculate the thresholds of each object, divide all objects into three different territories and sort all objects. Then, we use a concrete example of building appearance selection to verify the rationality and feasibility of our proposed models. Furthermore, we apply comparative analysis, Spearman’s rank correlation analysis and experiment analysis to illustrate the consistency and superiority of our methods. Full article
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32 pages, 624 KiB  
Article
An Algorithmic Approach to Emergence
by Charles Alexandre Bédard and Geoffroy Bergeron
Entropy 2022, 24(7), 985; https://doi.org/10.3390/e24070985 - 16 Jul 2022
Cited by 1 | Viewed by 2132
Abstract
We suggest a quantitative and objective notion of emergence. Our proposal uses algorithmic information theory as a basis for an objective framework in which a bit string encodes observational data. A plurality of drops in the Kolmogorov structure function of such a [...] Read more.
We suggest a quantitative and objective notion of emergence. Our proposal uses algorithmic information theory as a basis for an objective framework in which a bit string encodes observational data. A plurality of drops in the Kolmogorov structure function of such a string is seen as the hallmark of emergence. Our definition offers some theoretical results, in addition to extending the notions of coarse-graining and boundary conditions. Finally, we confront our proposal with applications to dynamical systems and thermodynamics. Full article
(This article belongs to the Section Complexity)
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14 pages, 3210 KiB  
Article
Driving Behavior Recognition Algorithm Combining Attention Mechanism and Lightweight Network
by Lili Wang, Wenjie Yao, Chen Chen and Hailu Yang
Entropy 2022, 24(7), 984; https://doi.org/10.3390/e24070984 - 16 Jul 2022
Cited by 7 | Viewed by 1746
Abstract
In actual driving scenes, recognizing and preventing drivers’ non-standard driving behavior is helpful in reducing traffic accidents. To resolve the problems of various driving behaviors, a large range of action, and the low recognition accuracy of traditional detection methods, in this paper, a [...] Read more.
In actual driving scenes, recognizing and preventing drivers’ non-standard driving behavior is helpful in reducing traffic accidents. To resolve the problems of various driving behaviors, a large range of action, and the low recognition accuracy of traditional detection methods, in this paper, a driving behavior recognition algorithm was proposed that combines an attention mechanism and lightweight network. The attention module was integrated into the YOLOV4 model after improving the feature extraction network, and the structure of the attention module was also improved. According to the 20,000 images of the Kaggle dataset, 10 typical driving behaviors were analyzed, processed, and recognized. The comparison and ablation experimental results showed that the fusion of an improved attention mechanism and lightweight network model had good performance in accuracy, model size, and FLOPs. Full article
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15 pages, 14830 KiB  
Article
Consensus, Polarization and Hysteresis in the Three-State Noisy q-Voter Model with Bounded Confidence
by Maciej Doniec, Arkadiusz Lipiecki and Katarzyna Sznajd-Weron
Entropy 2022, 24(7), 983; https://doi.org/10.3390/e24070983 - 16 Jul 2022
Cited by 9 | Viewed by 2125
Abstract
In this work, we address the question of the role of the influence of group size on the emergence of various collective social phenomena, such as consensus, polarization and social hysteresis. To answer this question, we study the three-state noisy q-voter model [...] Read more.
In this work, we address the question of the role of the influence of group size on the emergence of various collective social phenomena, such as consensus, polarization and social hysteresis. To answer this question, we study the three-state noisy q-voter model with bounded confidence, in which agents can be in one of three states: two extremes (leftist and rightist) and centrist. We study the model on a complete graph within the mean-field approach and show that, depending on the size q of the influence group, saddle-node bifurcation cascades of different length appear and different collective phenomena are possible. In particular, for all values of q>1, social hysteresis is observed. Furthermore, for small values of q∈(1,4), disagreement, polarization and domination of centrists (a consensus understood as the general agreement, not unanimity) can be achieved but not the domination of extremists. The latter is possible only for larger groups of influence. Finally, by comparing our model to others, we discuss how a small change in the rules at the microscopic level can dramatically change the macroscopic behavior of the model. Full article
(This article belongs to the Special Issue Modern Trends in Sociophysics)
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28 pages, 17111 KiB  
Article
Rate-Distortion-Based Stego: A Large-Capacity Secure Steganography Scheme for Hiding Digital Images
by Yi-Lun Pan and Ja-Ling Wu
Entropy 2022, 24(7), 982; https://doi.org/10.3390/e24070982 - 15 Jul 2022
Cited by 2 | Viewed by 2720
Abstract
Steganography is one of the most crucial methods for information hiding, which embeds secret data on an ordinary file or a cover message for avoiding detection. We designed a novel rate-distortion-based large-capacity secure steganographic system, called rate-distortion-based Stego (RD-Stego), to effectively solve the [...] Read more.
Steganography is one of the most crucial methods for information hiding, which embeds secret data on an ordinary file or a cover message for avoiding detection. We designed a novel rate-distortion-based large-capacity secure steganographic system, called rate-distortion-based Stego (RD-Stego), to effectively solve the above requirement. The considered effectiveness of our system design includes embedding capacity, adaptability to chosen cover attacks, and the stability of the trained model. The proposed stego scheme can hide multiple three-channel color images and QR codes within another three-channel color image with low visual distortion. Empirically, with a certain degree of robustness against the chosen cover attack, we state that the system offers up to 192+ bits-per-pixel (bpp) embedding of a payload and leaks no secret-related information. Moreover, to provide theoretical foundations for our cost function design, a mutual information-based explanation of the choices of regulation processes is herein included. Finally, we justify our system’s claimed advantages through a series of experiments with publicly available benchmark datasets. Full article
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20 pages, 8423 KiB  
Article
Quantitative Identification of Internal and External Wire Rope Damage Based on VMD-AWT Noise Reduction and PSO-SVM
by Jie Tian, Pengbo Li, Wei Wang, Jianwu Ma, Ganggang Sun and Hongyao Wang
Entropy 2022, 24(7), 981; https://doi.org/10.3390/e24070981 - 15 Jul 2022
Cited by 4 | Viewed by 1842
Abstract
As a common load-bearing component, mining wire rope produces different types of damage during a long period of operation, especially in the case of damage inside the wire rope, which cannot be identified by the naked eye, and it is difficult to accurately [...] Read more.
As a common load-bearing component, mining wire rope produces different types of damage during a long period of operation, especially in the case of damage inside the wire rope, which cannot be identified by the naked eye, and it is difficult to accurately detect such damage using the present technology. In this study we designed a non-destructive testing device based on leakage magnetism, which can effectively detect the internal defects of wire rope damage, and carried out simulation analysis to lay a theoretical foundation for the subsequent experiments. To address the noise reduction problem in the design process, a variational mode decomposition–adaptive wavelet thresholding noise reduction method is proposed, which can improve the signal-to-noise ratio and also calculate the wavelet energy entropy in the reconstructed signal to construct multi-dimensional feature vectors. For the quantitative identification of system damage, a particle swarm optimization–support vector machine algorithm is proposed. Moreover, based on the signal following the noise reduction step, seven different feature vectors, namely, the waveform area, peak value, peak-valley value, wavelet energy entropy classification, and identification of internal and external damage defects, have been determined. The results show that the device can be used to effectively identify internal damage defects. In addition, the comparative analysis showed that the algorithm can reduce the system noise and effectively identify internal and external damage defects with a certain superiority. Full article
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