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Volume 25
Issue 9
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Entropy, Volume 25, Issue 9 (September 2023) – 122 articles

Cover Story (view full-size image): Separating frequency hopping signals blindly raises the question of whether each frequency originates from an individual source or whether multiple frequencies are transmitted by the same source. In this work, carrier frequencies and DOAs are estimated for signals transmitted by stationary and spatially sparse sources observed over a Spatial Channel Model. These two estimates are paired to ascertain which source(s) transmit which frequency(ies), thus achieving blind source separation. In a multipath scenario, a signal transmitted by one source may appear to be coming from different directions, leading to erroneous DOA estimation. A filtering technique is developed to refine DOA estimates for sources whose intermittent activity follows a hidden Markov model. View this paper
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16 pages, 6322 KiB  
Article
Response Analysis of the Three-Degree-of-Freedom Vibroimpact System with an Uncertain Parameter
by Guidong Yang, Zichen Deng, Lin Du and Zicheng Lin
Entropy 2023, 25(9), 1365; https://doi.org/10.3390/e25091365 - 21 Sep 2023
Viewed by 697
Abstract
The inherent non-smoothness of the vibroimpact system leads to complex behaviors and a strong sensitivity to parameter changes. Unfortunately, uncertainties and errors in system parameters are inevitable in mechanical engineering. Therefore, investigations of dynamical behaviors for vibroimpact systems with stochastic parameters are highly [...] Read more.
The inherent non-smoothness of the vibroimpact system leads to complex behaviors and a strong sensitivity to parameter changes. Unfortunately, uncertainties and errors in system parameters are inevitable in mechanical engineering. Therefore, investigations of dynamical behaviors for vibroimpact systems with stochastic parameters are highly essential. The present study aims to analyze the dynamical characteristics of the three-degree-of-freedom vibroimpact system with an uncertain parameter by means of the Chebyshev polynomial approximation method. Specifically, the vibroimpact system model considered is one with unilateral constraint. Firstly, the three-degree-of-freedom vibroimpact system with an uncertain parameter is transformed into an equivalent deterministic form using the Chebyshev orthogonal approximation. Then, the ensemble means responses of the stochastic vibroimpact system are derived. Numerical simulations are performed to verify the effectiveness of the approximation method. Furthermore, the periodic and chaos motions under different system parameters are investigated, and the bifurcations of the vibroimpact system are analyzed with the Poincaré map. The results demonstrate that both the restitution coefficient and the random factor can induce the appearance of the periodic bifurcation. It is worth noting that the bifurcations fundamentally differ between the stochastic and deterministic systems. The former has a bifurcation interval, while the latter occurs at a critical point. Full article
(This article belongs to the Special Issue Nonlinear Dynamical Behaviors in Complex Systems)
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11 pages, 990 KiB  
Article
Entropy-Based Multifractal Testing of Heart Rate Variability during Cognitive-Autonomic Interplay
by Laurent M. Arsac
Entropy 2023, 25(9), 1364; https://doi.org/10.3390/e25091364 - 21 Sep 2023
Viewed by 708
Abstract
Entropy-based and fractal-based metrics derived from heart rate variability (HRV) have enriched the way cardiovascular dynamics can be described in terms of complexity. The most commonly used multifractal testing, a method using q moments to explore a range of fractal scaling in small-sized [...] Read more.
Entropy-based and fractal-based metrics derived from heart rate variability (HRV) have enriched the way cardiovascular dynamics can be described in terms of complexity. The most commonly used multifractal testing, a method using q moments to explore a range of fractal scaling in small-sized and large-sized fluctuations, is based on detrended fluctuation analysis, which examines the power–law relationship of standard deviation with the timescale in the measured signal. A more direct testing of a multifractal structure exists based on the Shannon entropy of bin (signal subparts) proportion. This work aims to reanalyze HRV during cognitive tasks to obtain new markers of HRV complexity provided by entropy-based multifractal spectra using the method proposed by Chhabra and Jensen in 1989. Inter-beat interval durations (RR) time series were obtained in 28 students comparatively in baseline (viewing a video) and during three cognitive tasks: Stroop color and word task, stop-signal, and go/no-go. The new HRV estimators were extracted from the f/α singularity spectrum of the RR magnitude increment series, established from q-weighted stable (log–log linear) power laws, namely: (i) the whole spectrum width (MF) calculated as αmax − αmin; the specific width representing large-sized fluctuations (MFlarge) calculated as α0 − αq+; and small-sized fluctuations (MFsmall) calculated as αq− − α0. As the main results, cardiovascular dynamics during Stroop had a specific MF signature while MFlarge was rather specific to go/no-go. The way these new HRV markers could represent different aspects of a complete picture of the cognitive–autonomic interplay is discussed, based on previously used entropy- and fractal-based markers, and the introduction of distribution entropy (DistEn), as a marker recently associated specifically with complexity in the cardiovascular control. Full article
(This article belongs to the Special Issue Assessing Complexity in Physiological Systems through Biomedical Signals Analysis II)
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12 pages, 7072 KiB  
Article
Effects of Nonextensive Electrons on Dust–Ion Acoustic Waves in a Collisional Dusty Plasma with Negative Ions
by Zhipeng Liu
Entropy 2023, 25(9), 1363; https://doi.org/10.3390/e25091363 - 21 Sep 2023
Viewed by 836
Abstract
The effects of nonextensive electrons on nonlinear ion acoustic waves in dusty negative ion plasmas with ion–dust collisions are investigated. Analytical results show that both solitary and shock waves are supported in this system. The wave propagation is governed by a Korteweg–de Vries [...] Read more.
The effects of nonextensive electrons on nonlinear ion acoustic waves in dusty negative ion plasmas with ion–dust collisions are investigated. Analytical results show that both solitary and shock waves are supported in this system. The wave propagation is governed by a Korteweg–de Vries Burgers-type equation. The coefficients of this equation are modified by the nonextensive parameter q. Numerical calculations indicate that the amplitude of solitary wave and oscillatory shock can be obviously modified by the nonextensive electrons, but the monotonic shock is little affected. Full article
(This article belongs to the Special Issue Nonadditive Entropies and Nonextensive Statistical Mechanics—Dedicated to Professor Constantino Tsallis on the Occasion of His 80th Birthday)
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18 pages, 3774 KiB  
Article
A Quantum Model of Trust Calibration in Human–AI Interactions
by Luisa Roeder, Pamela Hoyte, Johan van der Meer, Lauren Fell, Patrick Johnston, Graham Kerr and Peter Bruza
Entropy 2023, 25(9), 1362; https://doi.org/10.3390/e25091362 - 20 Sep 2023
Viewed by 1163
Abstract
This exploratory study investigates a human agent’s evolving judgements of reliability when interacting with an AI system. Two aims drove this investigation: (1) compare the predictive performance of quantum vs. Markov random walk models regarding human reliability judgements of an AI system and [...] Read more.
This exploratory study investigates a human agent’s evolving judgements of reliability when interacting with an AI system. Two aims drove this investigation: (1) compare the predictive performance of quantum vs. Markov random walk models regarding human reliability judgements of an AI system and (2) identify a neural correlate of the perturbation of a human agent’s judgement of the AI’s reliability. As AI becomes more prevalent, it is important to understand how humans trust these technologies and how trust evolves when interacting with them. A mixed-methods experiment was developed for exploring reliability calibration in human–AI interactions. The behavioural data collected were used as a baseline to assess the predictive performance of the quantum and Markov models. We found the quantum model to better predict the evolving reliability ratings than the Markov model. This may be due to the quantum model being more amenable to represent the sometimes pronounced within-subject variability of reliability ratings. Additionally, a clear event-related potential response was found in the electroencephalographic (EEG) data, which is attributed to the expectations of reliability being perturbed. The identification of a trust-related EEG-based measure opens the door to explore how it could be used to adapt the parameters of the quantum model in real time. Full article
(This article belongs to the Special Issue Quantum Decision-Making: From Cognitive Psychology and Social Science to Artificial Intelligent Systems)
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54 pages, 8483 KiB  
Article
Quantum and Quantum-Inspired Stereographic K Nearest-Neighbour Clustering
by Alonso Viladomat Jasso, Ark Modi, Roberto Ferrara, Christian Deppe, Janis Nötzel, Fred Fung and Maximilian Schädler
Entropy 2023, 25(9), 1361; https://doi.org/10.3390/e25091361 - 20 Sep 2023
Viewed by 1123
Abstract
Nearest-neighbour clustering is a simple yet powerful machine learning algorithm that finds natural application in the decoding of signals in classical optical-fibre communication systems. Quantum k-means clustering promises a speed-up over the classical k-means algorithm; however, it has been shown to [...] Read more.
Nearest-neighbour clustering is a simple yet powerful machine learning algorithm that finds natural application in the decoding of signals in classical optical-fibre communication systems. Quantum k-means clustering promises a speed-up over the classical k-means algorithm; however, it has been shown to not currently provide this speed-up for decoding optical-fibre signals due to the embedding of classical data, which introduces inaccuracies and slowdowns. Although still not achieving an exponential speed-up for NISQ implementations, this work proposes the generalised inverse stereographic projection as an improved embedding into the Bloch sphere for quantum distance estimation in k-nearest-neighbour clustering, which allows us to get closer to the classical performance. We also use the generalised inverse stereographic projection to develop an analogous classical clustering algorithm and benchmark its accuracy, runtime and convergence for decoding real-world experimental optical-fibre communication data. This proposed ‘quantum-inspired’ algorithm provides an improvement in both the accuracy and convergence rate with respect to the k-means algorithm. Hence, this work presents two main contributions. Firstly, we propose the general inverse stereographic projection into the Bloch sphere as a better embedding for quantum machine learning algorithms; here, we use the problem of clustering quadrature amplitude modulated optical-fibre signals as an example. Secondly, as a purely classical contribution inspired by the first contribution, we propose and benchmark the use of the general inverse stereographic projection and spherical centroid for clustering optical-fibre signals, showing that optimizing the radius yields a consistent improvement in accuracy and convergence rate. Full article
(This article belongs to the Special Issue Quantum Information: From Fundamental Aspects to Practical Applications)
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22 pages, 4600 KiB  
Article
Community-Based Matrix Factorization (CBMF) Approach for Enhancing Quality of Recommendations
by Srilatha Tokala, Murali Krishna Enduri, T. Jaya Lakshmi and Hemlata Sharma
Entropy 2023, 25(9), 1360; https://doi.org/10.3390/e25091360 - 20 Sep 2023
Viewed by 928
Abstract
Matrix factorization is a long-established method employed for analyzing and extracting valuable insight recommendations from complex networks containing user ratings. The execution time and computational resources demanded by these algorithms pose limitations when confronted with large datasets. Community detection algorithms play a crucial [...] Read more.
Matrix factorization is a long-established method employed for analyzing and extracting valuable insight recommendations from complex networks containing user ratings. The execution time and computational resources demanded by these algorithms pose limitations when confronted with large datasets. Community detection algorithms play a crucial role in identifying groups and communities within intricate networks. To overcome the challenge of extensive computing resources with matrix factorization techniques, we present a novel framework that utilizes the inherent community information of the rating network. Our proposed approach, named Community-Based Matrix Factorization (CBMF), has the following steps: (1) Model the rating network as a complex bipartite network. (2) Divide the network into communities. (3) Extract the rating matrices pertaining only to those communities and apply MF on these matrices in parallel. (4) Merge the predicted rating matrices belonging to communities and evaluate the root mean square error (RMSE). In our experimentation, we use basic MF, SVD++, and FANMF for matrix factorization, and the Louvain algorithm is used for community division. The experimental evaluation on six datasets shows that the proposed CBMF enhances the quality of recommendations in each case. In the MovieLens 100K dataset, RMSE has been reduced to 0.21 from 1.26 using SVD++ by dividing the network into 25 communities. A similar reduction in RMSE is observed for the datasets of FilmTrust, Jester, Wikilens, Good Books, and Cell Phone. Full article
(This article belongs to the Special Issue Foundations of Network Analysis)
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26 pages, 526 KiB  
Article
A New Truncated Lindley-Generated Family of Distributions: Properties, Regression Analysis, and Applications
by Mohamed Hussein, Gabriela M. Rodrigues, Edwin M. M. Ortega, Roberto Vila and Howaida Elsayed
Entropy 2023, 25(9), 1359; https://doi.org/10.3390/e25091359 - 20 Sep 2023
Viewed by 868
Abstract
We present the truncated Lindley-G (TLG) model, a novel class of probability distributions with an additional shape parameter, by composing a unit distribution called the truncated Lindley distribution with a parent distribution function G(x). The proposed model’s characteristics [...] Read more.
We present the truncated Lindley-G (TLG) model, a novel class of probability distributions with an additional shape parameter, by composing a unit distribution called the truncated Lindley distribution with a parent distribution function G(x). The proposed model’s characteristics including critical points, moments, generating function, quantile function, mean deviations, and entropy are discussed. Also, we introduce a regression model based on the truncated Lindley–Weibull distribution considering two systematic components. The model parameters are estimated using the maximum likelihood method. In order to investigate the behavior of the estimators, some simulations are run for various parameter settings, censoring percentages, and sample sizes. Four real datasets are used to demonstrate the new model’s potential. Full article
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16 pages, 1341 KiB  
Article
A Novel Joint Channel Estimation and Symbol Detection Receiver for Orthogonal Time Frequency Space in Vehicular Networks
by Xiaoqi Zhang, Haifeng Wen, Ziyu Yan, Weijie Yuan, Jun Wu and Zhongjie Li
Entropy 2023, 25(9), 1358; https://doi.org/10.3390/e25091358 - 20 Sep 2023
Cited by 1 | Viewed by 900
Abstract
A vehicular network embodies a specialized variant of wireless network systems, characterized by its capability to facilitate inter-vehicular communication and connectivity with the encompassing infrastructure. With the rapid development of wireless communication technology, high-speed and reliable communication has become increasingly important in vehicular [...] Read more.
A vehicular network embodies a specialized variant of wireless network systems, characterized by its capability to facilitate inter-vehicular communication and connectivity with the encompassing infrastructure. With the rapid development of wireless communication technology, high-speed and reliable communication has become increasingly important in vehicular networks. It has been demonstrated that orthogonal time frequency space (OTFS) modulation proves effective in addressing the challenges posed by high-mobility environments, as it transforms the time-varying channels into the delay-Doppler domain. Motivated by this, in this paper, we focus on the theme of integrated sensing and communication (ISAC)-assisted OTFS receiver design, which aims to perform sensing channel estimation and communication symbol detection. Specifically, the estimation of the sensing channel is accomplished through the utilization of a deep residual denoising network (DRDN), while the communication symbol detection is performed by orthogonal approximate message passing (OAMP) processing. The numerical results demonstrate that the proposed ISAC system exhibits superior performance and robustness compared to traditional methods, with a lower complexity as well. The proposed system has great potential for future applications in wireless communication systems, especially in challenging scenarios with high mobility and interference. Full article
(This article belongs to the Special Issue Delay-Doppler Domain Communications for Future Wireless Networks)
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13 pages, 340 KiB  
Article
Nonlinear Fokker–Planck Equations, H-Theorem and Generalized Entropy of a Composed System
by Luiz R. Evangelista and Ervin K. Lenzi
Entropy 2023, 25(9), 1357; https://doi.org/10.3390/e25091357 - 20 Sep 2023
Cited by 1 | Viewed by 835
Abstract
We investigate the dynamics of a system composed of two different subsystems when subjected to different nonlinear Fokker–Planck equations by considering the H–theorem. We use the H–theorem to obtain the conditions required to establish a suitable dependence for the system’s interaction that agrees [...] Read more.
We investigate the dynamics of a system composed of two different subsystems when subjected to different nonlinear Fokker–Planck equations by considering the H–theorem. We use the H–theorem to obtain the conditions required to establish a suitable dependence for the system’s interaction that agrees with the thermodynamics law when the nonlinearity in these equations is the same. In this framework, we also consider different dynamical aspects of each subsystem and investigate a possible expression for the entropy of the composite system. Full article
(This article belongs to the Special Issue Twenty Years of Kaniadakis Entropy: Current Trends and Future Perspectives)
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11 pages, 265 KiB  
Article
Quantum Mechanics Is Compatible with Counterfactual Definiteness
by Janne V. Kujala and Ehtibar N. Dzhafarov
Entropy 2023, 25(9), 1356; https://doi.org/10.3390/e25091356 - 20 Sep 2023
Viewed by 787
Abstract
Counterfactual definiteness (CFD) means that if some property is measured in some context, then the outcome of the measurement would have been the same had this property been measured in a different context. A context includes all other measurements made together with the [...] Read more.
Counterfactual definiteness (CFD) means that if some property is measured in some context, then the outcome of the measurement would have been the same had this property been measured in a different context. A context includes all other measurements made together with the one in question, and the spatiotemporal relations among them. The proviso for CFD is non-disturbance: any physical influence of the contexts on the property being measured is excluded by the laws of nature, so that no one measuring this property has a way of ascertaining its context. It is usually claimed that in quantum mechanics CFD does not hold, because if one assigns the same value to a property in all contexts it is measured in, one runs into a logical contradiction, or at least contravenes quantum theory and experimental evidence. We show that this claim is not substantiated if one takes into account that only one of the possible contexts can be a factual context, all other contexts being counterfactual. With this in mind, any system of random variables can be viewed as satisfying CFD. The concept of CFD is closely related to but distinct from that of noncontextuality, and it is the latter property that may or may not hold for a system, in particular being contravened by some quantum systems. Full article
(This article belongs to the Special Issue Quantum Contextuality and Non-locality: Foundations, Applications and Extensions)
51 pages, 7091 KiB  
Article
Exact and Soft Successive Refinement of the Information Bottleneck
by Hippolyte Charvin, Nicola Catenacci Volpi and Daniel Polani
Entropy 2023, 25(9), 1355; https://doi.org/10.3390/e25091355 - 19 Sep 2023
Cited by 1 | Viewed by 1025
Abstract
The information bottleneck (IB) framework formalises the essential requirement for efficient information processing systems to achieve an optimal balance between the complexity of their representation and the amount of information extracted about relevant features. However, since the representation complexity affordable by real-world systems [...] Read more.
The information bottleneck (IB) framework formalises the essential requirement for efficient information processing systems to achieve an optimal balance between the complexity of their representation and the amount of information extracted about relevant features. However, since the representation complexity affordable by real-world systems may vary in time, the processing cost of updating the representations should also be taken into account. A crucial question is thus the extent to which adaptive systems can leverage the information content of already existing IB-optimal representations for producing new ones, which target the same relevant features but at a different granularity. We investigate the information-theoretic optimal limits of this process by studying and extending, within the IB framework, the notion of successive refinement, which describes the ideal situation where no information needs to be discarded for adapting an IB-optimal representation’s granularity. Thanks in particular to a new geometric characterisation, we analytically derive the successive refinability of some specific IB problems (for binary variables, for jointly Gaussian variables, and for the relevancy variable being a deterministic function of the source variable), and provide a linear-programming-based tool to numerically investigate, in the discrete case, the successive refinement of the IB. We then soften this notion into a quantification of the loss of information optimality induced by several-stage processing through an existing measure of unique information. Simple numerical experiments suggest that this quantity is typically low, though not entirely negligible. These results could have important implications for (i) the structure and efficiency of incremental learning in biological and artificial agents, (ii) the comparison of IB-optimal observation channels in statistical decision problems, and (iii) the IB theory of deep neural networks. Full article
(This article belongs to the Special Issue Theory and Application of the Information Bottleneck Method)
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18 pages, 5417 KiB  
Article
Degradation-Sensitive Health Indicator Construction for Precise Insulation Degradation Monitoring of Electromagnetic Coils
by Yue Sun, Kai Wang, Aidong Xu, Beiye Guan, Ruiqi Li, Bo Zhang and Xiufang Zhou
Entropy 2023, 25(9), 1354; https://doi.org/10.3390/e25091354 - 19 Sep 2023
Viewed by 863
Abstract
Electromagnetic coils are indispensable components for energy conversion and transformation in various systems across industries. However, electromagnetic coil insulation failure occurs frequently, which can lead to serious consequences. To facilitate predictive maintenance for industrial systems, it is essential to monitor insulation degradation prior [...] Read more.
Electromagnetic coils are indispensable components for energy conversion and transformation in various systems across industries. However, electromagnetic coil insulation failure occurs frequently, which can lead to serious consequences. To facilitate predictive maintenance for industrial systems, it is essential to monitor insulation degradation prior to the formation of turn-to-turn shorts. This paper experimentally investigates coil insulation degradation from both macro and micro perspectives. At the macro level, an evaluation index based on a weighted linear combination of trend, monotonicity and robustness is proposed to construct a degradation-sensitive health indicator (DSHI) based on high-frequency electrical response parameters for precise insulation degradation monitoring. While at the micro level, a coil finite element analysis and twisted pair accelerated degradation test are conducted to obtain the actual turn-to-turn insulation status. The correlation analysis between macroscopic and microscopic effects of insulation degradation is used to verify the proposed DSHI-based method. Further, it helps to determine the threshold of DSHI. This breakthrough opens new possibilities for predictive maintenance for industrial equipment that incorporates coils. Full article
(This article belongs to the Special Issue Signal Processing for Fault Detection and Diagnosis in Electric Machines and Energy Conversion Systems)
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18 pages, 1098 KiB  
Article
CLIP-Driven Prototype Network for Few-Shot Semantic Segmentation
by Shi-Cheng Guo, Shang-Kun Liu, Jing-Yu Wang, Wei-Min Zheng and Cheng-Yu Jiang
Entropy 2023, 25(9), 1353; https://doi.org/10.3390/e25091353 - 18 Sep 2023
Cited by 2 | Viewed by 1866
Abstract
Recent research has shown that visual–text pretrained models perform well in traditional vision tasks. CLIP, as the most influential work, has garnered significant attention from researchers. Thanks to its excellent visual representation capabilities, many recent studies have used CLIP for pixel-level tasks. We [...] Read more.
Recent research has shown that visual–text pretrained models perform well in traditional vision tasks. CLIP, as the most influential work, has garnered significant attention from researchers. Thanks to its excellent visual representation capabilities, many recent studies have used CLIP for pixel-level tasks. We explore the potential abilities of CLIP in the field of few-shot segmentation. The current mainstream approach is to utilize support and query features to generate class prototypes and then use the prototype features to match image features. We propose a new method that utilizes CLIP to extract text features for a specific class. These text features are then used as training samples to participate in the model’s training process. The addition of text features enables model to extract features that contain richer semantic information, thus making it easier to capture potential class information. To better match the query image features, we also propose a new prototype generation method that incorporates multi-modal fusion features of text and images in the prototype generation process. Adaptive query prototypes were generated by combining foreground and background information from the images with the multi-modal support prototype, thereby allowing for a better matching of image features and improved segmentation accuracy. We provide a new perspective to the task of few-shot segmentation in multi-modal scenarios. Experiments demonstrate that our proposed method achieves excellent results on two common datasets, PASCAL-5i and COCO-20i. Full article
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12 pages, 9384 KiB  
Article
The Intricacies of Sprott-B System with Fractional-Order Derivatives: Dynamical Analysis, Synchronization, and Circuit Implementation
by Rending Lu, Prasina Alexander, Hayder Natiq, Anitha Karthikeyan, Sajad Jafari and Jiri Petrzela
Entropy 2023, 25(9), 1352; https://doi.org/10.3390/e25091352 - 17 Sep 2023
Viewed by 843
Abstract
Studying simple chaotic systems with fractional-order derivatives improves modeling accuracy, increases complexity, and enhances control capabilities and robustness against noise. This paper investigates the dynamics of the simple Sprott-B chaotic system using fractional-order derivatives. This study involves a comprehensive dynamical analysis conducted through [...] Read more.
Studying simple chaotic systems with fractional-order derivatives improves modeling accuracy, increases complexity, and enhances control capabilities and robustness against noise. This paper investigates the dynamics of the simple Sprott-B chaotic system using fractional-order derivatives. This study involves a comprehensive dynamical analysis conducted through bifurcation diagrams, revealing the presence of coexisting attractors. Additionally, the synchronization behavior of the system is examined for various derivative orders. Finally, the integer-order and fractional-order electronic circuits are implemented to validate the theoretical findings. This research contributes to a deeper understanding of the Sprott-B system and its fractional-order dynamics, with potential applications in diverse fields such as chaos-based secure communications and nonlinear control systems. Full article
(This article belongs to the Special Issue Chaos and Complexity in Fractional Order Systems and Their Applications)
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15 pages, 2398 KiB  
Review
It’s Time for Entropic Clocks: The Roles of Random Chain Protein Sequences in Timing Ion Channel Processes Underlying Action Potential Properties
by Esraa Nsasra, Irit Dahan, Jerry Eichler and Ofer Yifrach
Entropy 2023, 25(9), 1351; https://doi.org/10.3390/e25091351 - 17 Sep 2023
Cited by 1 | Viewed by 933
Abstract
In recent years, it has become clear that intrinsically disordered protein segments play diverse functional roles in many cellular processes, thus leading to a reassessment of the classical structure–function paradigm. One class of intrinsically disordered protein segments is entropic clocks, corresponding to unstructured [...] Read more.
In recent years, it has become clear that intrinsically disordered protein segments play diverse functional roles in many cellular processes, thus leading to a reassessment of the classical structure–function paradigm. One class of intrinsically disordered protein segments is entropic clocks, corresponding to unstructured random protein chains involved in timing cellular processes. Such clocks were shown to modulate ion channel processes underlying action potential generation, propagation, and transmission. In this review, we survey the role of entropic clocks in timing intra- and inter-molecular binding events of voltage-activated potassium channels involved in gating and clustering processes, respectively, and where both are known to occur according to a similar ‘ball and chain’ mechanism. We begin by delineating the thermodynamic and timing signatures of a ‘ball and chain’-based binding mechanism involving entropic clocks, followed by a detailed analysis of the use of such a mechanism in the prototypical Shaker voltage-activated K+ channel model protein, with particular emphasis on ion channel clustering. We demonstrate how ‘chain’-level alternative splicing of the Kv channel gene modulates entropic clock-based ‘ball and chain’ inactivation and clustering channel functions. As such, the Kv channel model system exemplifies how linkage between alternative splicing and intrinsic disorder enables the functional diversity underlying changes in electrical signaling. Full article
(This article belongs to the Special Issue Entropy in Biological Systems)
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20 pages, 14749 KiB  
Article
FBANet: Transfer Learning for Depression Recognition Using a Feature-Enhanced Bi-Level Attention Network
by Huayi Wang, Jie Zhang, Yaocheng Huang and Bo Cai
Entropy 2023, 25(9), 1350; https://doi.org/10.3390/e25091350 - 17 Sep 2023
Viewed by 1043
Abstract
The House-Tree-Person (HTP) sketch test is a psychological analysis technique designed to assess the mental health status of test subjects. Nowadays, there are mature methods for the recognition of depression using the HTP sketch test. However, existing works primarily rely on manual analysis [...] Read more.
The House-Tree-Person (HTP) sketch test is a psychological analysis technique designed to assess the mental health status of test subjects. Nowadays, there are mature methods for the recognition of depression using the HTP sketch test. However, existing works primarily rely on manual analysis of drawing features, which has the drawbacks of strong subjectivity and low automation. Only a small number of works automatically recognize depression using machine learning and deep learning methods, but their complex data preprocessing pipelines and multi-stage computational processes indicate a relatively low level of automation. To overcome the above issues, we present a novel deep learning-based one-stage approach for depression recognition in HTP sketches, which has a simple data preprocessing pipeline and calculation process with a high accuracy rate. In terms of data, we use a hand-drawn HTP sketch dataset, which contains drawings of normal people and patients with depression. In the model aspect, we design a novel network called Feature-Enhanced Bi-Level Attention Network (FBANet), which contains feature enhancement and bi-level attention modules. Due to the limited size of the collected data, transfer learning is employed, where the model is pre-trained on a large-scale sketch dataset and fine-tuned on the HTP sketch dataset. On the HTP sketch dataset, utilizing cross-validation, FBANet achieves a maximum accuracy of 99.07% on the validation dataset, with an average accuracy of 97.71%, outperforming traditional classification models and previous works. In summary, the proposed FBANet, after pre-training, demonstrates superior performance on the HTP sketch dataset and is expected to be a method for the auxiliary diagnosis of depression. Full article
(This article belongs to the Special Issue Entropy: The Cornerstone of Machine Learning)
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17 pages, 376 KiB  
Article
Bounds on the Probability of Undetected Error for q-Ary Codes
by Xuan Wang, Huizhou Liu and Patrick Solé
Entropy 2023, 25(9), 1349; https://doi.org/10.3390/e25091349 - 17 Sep 2023
Viewed by 707
Abstract
We study the probability of an undetected error for general q-ary codes. We give upper and lower bounds on this quantity, by the Linear Programming and the Polynomial methods, as a function of the length, size, and minimum distance. Sharper bounds are [...] Read more.
We study the probability of an undetected error for general q-ary codes. We give upper and lower bounds on this quantity, by the Linear Programming and the Polynomial methods, as a function of the length, size, and minimum distance. Sharper bounds are obtained in the important special case of binary Hamming codes. Finally, several examples are given to illustrate the results of this paper. Full article
(This article belongs to the Special Issue Discrete Math in Coding Theory)
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18 pages, 8885 KiB  
Article
Physics-Based Differentiable Rendering for Efficient and Plausible Fluid Modeling from Monocular Video
by Yunchi Cen, Qifan Zhang and Xiaohui Liang
Entropy 2023, 25(9), 1348; https://doi.org/10.3390/e25091348 - 17 Sep 2023
Viewed by 1249
Abstract
Realistic fluid models play an important role in computer graphics applications. However, efficiently reconstructing volumetric fluid flows from monocular videos remains challenging. In this work, we present a novel approach for reconstructing 3D flows from monocular inputs through a physics-based differentiable renderer coupled [...] Read more.
Realistic fluid models play an important role in computer graphics applications. However, efficiently reconstructing volumetric fluid flows from monocular videos remains challenging. In this work, we present a novel approach for reconstructing 3D flows from monocular inputs through a physics-based differentiable renderer coupled with joint density and velocity estimation. Our primary contributions include the proposed efficient differentiable rendering framework and improved coupled density and velocity estimation strategy. Rather than relying on automatic differentiation, we derive the differential form of the radiance transfer equation under single scattering. This allows the direct computation of the radiance gradient with respect to density, yielding higher efficiency compared to prior works. To improve temporal coherence in the reconstructed flows, subsequent fluid densities are estimated via a coupled strategy that enables smooth and realistic fluid motions suitable for applications that require high efficiency. Experiments on synthetic and real-world data demonstrated our method’s capacity to reconstruct plausible volumetric flows with smooth dynamics efficiently. Comparisons to prior work on fluid motion reconstruction from monocular video revealed over 50–170x speedups across multiple resolutions. Full article
(This article belongs to the Special Issue Differential Equations and Networks for Description of Natural and Social Systems: Methodology and Applications)
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16 pages, 2398 KiB  
Article
A Novel Edge Cache-Based Private Set Intersection Protocol via Lightweight Oblivious PRF
by Jing Zhang, Li Yang, Yongli Tang, Minglu Jin and Shujing Wang
Entropy 2023, 25(9), 1347; https://doi.org/10.3390/e25091347 - 16 Sep 2023
Viewed by 978
Abstract
With the rapid development of edge computing and the Internet of Things, the problem of information resource sharing can be effectively solved through multi-party collaboration, but the risk of data leakage is also increasing. To address the above issues, we propose an efficient [...] Read more.
With the rapid development of edge computing and the Internet of Things, the problem of information resource sharing can be effectively solved through multi-party collaboration, but the risk of data leakage is also increasing. To address the above issues, we propose an efficient multi-party private set intersection (MPSI) protocol via a multi-point oblivious pseudorandom function (OPRF). Then, we apply it to work on a specific commercial application: edge caching. The proposed MPSI uses oblivious transfer (OT) together with a probe-and-XOR of strings (PaXoS) as the main building blocks. It not only provides one-sided malicious security, but also achieves a better balance between communication and computational overhead. From the communication pattern perspective, the client only needs to perform OT with the leader and send a data structure PaXoS to the designated party, making the protocol extremely efficient. Moreover, in the setting of edge caching, many parties hold a set of items containing an identity and its associated value. All parties can identify a set of the most frequently accessed common items without revealing the underlying data. Full article
(This article belongs to the Special Issue Information-Theoretic Privacy in Retrieval, Computing, and Learning)
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9 pages, 654 KiB  
Article
Taxes, Inequality, and Equal Opportunities
by José Roberto Iglesias, Ben-Hur Francisco Cardoso and Sebastián Gonçalves
Entropy 2023, 25(9), 1346; https://doi.org/10.3390/e25091346 - 16 Sep 2023
Viewed by 810
Abstract
Extreme inequality represents a grave challenge for impoverished individuals and poses a threat to economic growth and stability. Despite the fulfillment of affirmative action measures aimed at promoting equal opportunities, they often prove inadequate in effectively reducing inequality. Mathematical models and simulations have [...] Read more.
Extreme inequality represents a grave challenge for impoverished individuals and poses a threat to economic growth and stability. Despite the fulfillment of affirmative action measures aimed at promoting equal opportunities, they often prove inadequate in effectively reducing inequality. Mathematical models and simulations have demonstrated that even when equal opportunities are present, wealth tends to concentrate in the hands of a privileged few, leaving the majority of the population in dire poverty. This phenomenon, known as condensation, has been shown to be an inevitable outcome in economic models that rely on fair exchange. In light of the escalating levels of inequality in the 21st century and the significant state intervention necessitated by the recent COVID-19 pandemic, an increasing number of scholars are abandoning neo-liberal ideologies. Instead, they propose a more robust role for the state in the economy, utilizing mechanisms such as taxation, regulation, and universal allocations. This paper begins with the assumption that state intervention is essential to effectively reduce inequality and to revitalize the economy. Subsequently, it conducts a comparative analysis of various taxation and redistribution mechanisms, with a particular emphasis on their impact on inequality indices, including the Gini coefficient. Specifically, it compares the effects of fortune and consumption-based taxation, as well as universal redistribution mechanisms or targeted redistribution mechanisms aimed at assisting the most economically disadvantaged individuals. The results suggest that fortune taxation are more effective than consumption-based taxation to reduce inequality. Full article
(This article belongs to the Special Issue Statistical Physics and Its Applications in Economics and Social Sciences)
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15 pages, 2968 KiB  
Article
Accelerating Quantum Decay by Multiple Tunneling Barriers
by Ermanno Pinotti and Stefano Longhi
Entropy 2023, 25(9), 1345; https://doi.org/10.3390/e25091345 - 16 Sep 2023
Viewed by 999
Abstract
A quantum particle constrained between two high potential barriers provides a paradigmatic example of a system sustaining quasi-bound (or resonance) states. When the system is prepared in one of such quasi-bound states, the wave function approximately maintains its shape but decays in time [...] Read more.
A quantum particle constrained between two high potential barriers provides a paradigmatic example of a system sustaining quasi-bound (or resonance) states. When the system is prepared in one of such quasi-bound states, the wave function approximately maintains its shape but decays in time in a nearly exponential manner radiating into the surrounding space, the lifetime being of the order of the reciprocal of the width of the resonance peak in the transmission spectrum. Naively, one could think that adding more lateral barriers would preferentially slow down or prevent the quantum decay since tunneling is expected to become less probable and due to quantum backflow induced by multiple scattering processes. However, this is not always the case and in the early stage of the dynamics quantum decay can be accelerated (rather than decelerated) by additional lateral barriers, even when the barrier heights are arbitrarily large. The decay acceleration originates from resonant tunneling effects and is associated to large deviations from an exponential decay law. We discuss such a counterintuitive phenomenon by considering the hopping dynamics of a quantum particle on a tight-binding lattice with on-site potential barriers. Full article
(This article belongs to the Special Issue Tunneling in Complex Systems)
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10 pages, 431 KiB  
Article
Insecurity of Quantum Blockchains Based on Entanglement in Time
by Piotr Zawadzki
Entropy 2023, 25(9), 1344; https://doi.org/10.3390/e25091344 - 16 Sep 2023
Viewed by 781
Abstract
In this study, the security implications of utilizing the concept of entanglement in time in the quantum representation of a blockchain data structure are investigated. The analysis reveals that the fundamental idea underlying this representation relies on an uncertain interpretation of experimental results. [...] Read more.
In this study, the security implications of utilizing the concept of entanglement in time in the quantum representation of a blockchain data structure are investigated. The analysis reveals that the fundamental idea underlying this representation relies on an uncertain interpretation of experimental results. A different perspective is provided by adopting the Copenhagen interpretation, which explains the observed correlations in the experiment without invoking the concept of entanglement in time. According to this interpretation, the qubits responsible for these correlations are not entangled, posing a challenge to the security foundation of the data structure. The study incorporates theoretical analysis, numerical simulations, and experiments using real quantum hardware. By employing a dedicated circuit for detecting genuine entanglement, the existence of entanglement in the process of generating a quantum blockchain is conclusively excluded. Full article
(This article belongs to the Special Issue Quantum Correlations, Contextuality, and Quantum Nonlocality)
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21 pages, 4909 KiB  
Article
Short-Term Prediction of Multi-Energy Loads Based on Copula Correlation Analysis and Model Fusions
by Min Xie, Shengzhen Lin, Kaiyuan Dong and Shiping Zhang
Entropy 2023, 25(9), 1343; https://doi.org/10.3390/e25091343 - 16 Sep 2023
Viewed by 776
Abstract
To improve the accuracy of short-term multi-energy load prediction models for integrated energy systems, the historical development law of the multi-energy loads must be considered. Moreover, understanding the complex coupling correlation of the different loads in the multi-energy systems, and accounting for other [...] Read more.
To improve the accuracy of short-term multi-energy load prediction models for integrated energy systems, the historical development law of the multi-energy loads must be considered. Moreover, understanding the complex coupling correlation of the different loads in the multi-energy systems, and accounting for other load-influencing factors such as weather, may further improve the forecasting performance of such models. In this study, a two-stage fuzzy optimization method is proposed for the feature selection and identification of the multi-energy loads. To enrich the information content of the prediction input feature, we introduced a copula correlation feature analysis in the proposed framework, which extracts the complex dynamic coupling correlation of multi-energy loads and applies Akaike information criterion (AIC) to evaluate the adaptability of the different copula models presented. Furthermore, we combined a NARX neural network with Bayesian optimization and an extreme learning machine model optimized using a genetic algorithm (GA) to effectively improve the feature fusion performances of the proposed multi-energy load prediction model. The effectiveness of the proposed short-term prediction model was confirmed by the experimental results obtained using the multi-energy load time-series data of an actual integrated energy system. Full article
(This article belongs to the Special Issue Entropy Theory in Energy and Power Systems)
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22 pages, 8773 KiB  
Article
A Novel Clustering Method Based on Adjacent Grids Searching
by Zhimeng Li, Wen Zhong, Weiwen Liao, Jian Zhao, Ming Yu and Gaiyun He
Entropy 2023, 25(9), 1342; https://doi.org/10.3390/e25091342 - 15 Sep 2023
Viewed by 864
Abstract
Clustering is used to analyze the intrinsic structure of a dataset based on the similarity of datapoints. Its widespread use, from image segmentation to object recognition and information retrieval, requires great robustness in the clustering process. In this paper, a novel clustering method [...] Read more.
Clustering is used to analyze the intrinsic structure of a dataset based on the similarity of datapoints. Its widespread use, from image segmentation to object recognition and information retrieval, requires great robustness in the clustering process. In this paper, a novel clustering method based on adjacent grid searching (CAGS) is proposed. The CAGS consists of two steps: a strategy based on adaptive grid-space construction and a clustering strategy based on adjacent grid searching. In the first step, a multidimensional grid space is constructed to provide a quantization structure of the input dataset. The noise and cluster halo are automatically distinguished according to grid density. Moreover, the adaptive grid generating process solves the common problem of grid clustering, in which the number of cells increases sharply with the dimension. In the second step, a two-stage traversal process is conducted to accomplish the cluster recognition. The cluster cores with arbitrary shapes can be found by concealing the halo points. As a result, the number of clusters will be easily identified by CAGS. Therefore, CAGS has the potential to be widely used for clustering datasets with different characteristics. We test the clustering performance of CAGS through six different types of datasets: dataset with noise, large-scale dataset, high-dimensional dataset, dataset with arbitrary shapes, dataset with large differences in density between classes, and dataset with high overlap between classes. Experimental results show that CAGS, which performed best on 10 out of 11 tests, outperforms the state-of-the-art clustering methods in all the above datasets. Full article
(This article belongs to the Section Multidisciplinary Applications)
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17 pages, 3041 KiB  
Article
On the Effect of Imperfect Reference Signal Phase Recovery on Performance of PSK System Influenced by TWDP Fading
by Goran T. Djordjevic, Dejan N. Milic, Bata Vasic, Jarosław Makal and Bane Vasic
Entropy 2023, 25(9), 1341; https://doi.org/10.3390/e25091341 - 15 Sep 2023
Viewed by 829
Abstract
We examine the effects of imperfect phase estimation of a reference signal on the bit error rate and mutual information over a communication channel influenced by fading and thermal noise. The Two-Wave Diffuse-Power (TWDP) model is utilized for statistical characterization of propagation environment [...] Read more.
We examine the effects of imperfect phase estimation of a reference signal on the bit error rate and mutual information over a communication channel influenced by fading and thermal noise. The Two-Wave Diffuse-Power (TWDP) model is utilized for statistical characterization of propagation environment where there are two dominant line-of-sight components together with diffuse ones. We derive novel analytical expression of the Fourier series for probability density function arising from the composite received signal phase. Further, the expression for the bit error rate is presented and numerically evaluated. We develop efficient analytical, numerical and simulation methods for estimating the value of the error floor and identifying the range of acceptable signal-to-noise ratio (SNR) values in cases when the floor is present during the detection of multilevel phase-shift keying (PSK) signals. In addition, we use Monte Carlo simulations in order to evaluate the mutual information for modulation orders two, four and eight, and identify its dependence on receiver hardware imperfections under the given channel conditions. Our results expose direct correspondence between bit error rate and mutual information value on one side, and the parameters of TWDP channel, SNR and phase noise standard deviation on the other side. The results illustrate that the error floor values are strongly influenced by the phase noise when signals propagate over a TWDP channel. In addition, the phase noise considerably affects the mutual information. Full article
(This article belongs to the Special Issue Information Theory and Coding for Wireless Communications II)
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12 pages, 378 KiB  
Article
Evolution of Robustness in Growing Random Networks
by Melvyn Tyloo
Entropy 2023, 25(9), 1340; https://doi.org/10.3390/e25091340 - 15 Sep 2023
Viewed by 760
Abstract
Networks are widely used to model the interaction between individual dynamic systems. In many instances, the total number of units and interaction coupling are not fixed in time, and instead constantly evolve. In networks, this means that the number of nodes and edges [...] Read more.
Networks are widely used to model the interaction between individual dynamic systems. In many instances, the total number of units and interaction coupling are not fixed in time, and instead constantly evolve. In networks, this means that the number of nodes and edges both change over time. Various properties of coupled dynamic systems, such as their robustness against noise, essentially depend on the structure of the interaction network. Therefore, it is of considerable interest to predict how these properties are affected when the network grows as well as their relationship to the growth mechanism. Here, we focus on the time evolution of a network’s Kirchhoff index. We derive closed-form expressions for its variation in various scenarios, including the addition of both edges and nodes. For the latter case, we investigate the evolution where single nodes with one or two edges connecting to existing nodes are added recursively to a network. In both cases, we derive the relations between the properties of the nodes to which the new node connects along with the global evolution of network robustness. In particular, we show how different scalings of the Kirchhoff index can be obtained as a function of the number of nodes. We illustrate and confirm this theory via numerical simulations of randomly growing networks. Full article
(This article belongs to the Special Issue Complexity, Entropy and the Physics of Information)
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14 pages, 609 KiB  
Article
Secrecy Capacity Region of the AWGN MAC with External Eavesdropper and Feedback
by Haoheng Yuan, Guangfen Xie and Bin Dai
Entropy 2023, 25(9), 1339; https://doi.org/10.3390/e25091339 - 15 Sep 2023
Cited by 1 | Viewed by 603
Abstract
For the point-to-point additive white Gaussian noise (AWGN) channel with an eavesdropper and feedback, it has already been shown that the secrecy capacity can be achieved by a secret key-based feedback scheme, where the channel feedback is used for secret sharing, and then [...] Read more.
For the point-to-point additive white Gaussian noise (AWGN) channel with an eavesdropper and feedback, it has already been shown that the secrecy capacity can be achieved by a secret key-based feedback scheme, where the channel feedback is used for secret sharing, and then encrypting the transmitted message by the shared key. By secret sharing, any capacity-achieving coding scheme for the AWGN channel without feedback can be secure by itself, which indicates that the capacity of the same model without the secrecy constraint also affords an achievable secrecy rate to the AWGN channel with an eavesdropper and feedback. Then it is natural to ask: is the secret key-based feedback scheme still the optimal scheme for the AWGN multiple-access channel (MAC) with an external eavesdropper and channel feedback (AWGN-MAC-E-CF), namely, achieving the secrecy capacity region of the AWGN-MAC-E-CF? In this paper, we show that the answer to the aforementioned question is no, and propose the optimal feedback coding scheme for the AWGN-MAC-E-CF, which combines an existing linear feedback scheme for the AWGN MAC with feedback and the secret key scheme in the literature. This paper provides a way to find optimal coding schemes for AWGN multi-user channels in the presence of an external eavesdropper and channel feedback. Full article
(This article belongs to the Special Issue Coding and Entropy)
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15 pages, 360 KiB  
Article
Quasi-Hyperbolically Symmetric γ-Metric
by Luis Herrera, Alicia Di Prisco, Justo Ospino and Jaume Carot
Entropy 2023, 25(9), 1338; https://doi.org/10.3390/e25091338 - 15 Sep 2023
Cited by 1 | Viewed by 726
Abstract
We carry out a systematic study on the motion of test particles in the region inner to the naked singularity of a quasi-hyperbolically symmetric γ-metric. The geodesic equations are written and analyzed in detail. The obtained results are contrasted with the corresponding [...] Read more.
We carry out a systematic study on the motion of test particles in the region inner to the naked singularity of a quasi-hyperbolically symmetric γ-metric. The geodesic equations are written and analyzed in detail. The obtained results are contrasted with the corresponding results obtained for the axially symmetric γ-metric and the hyperbolically symmetric black hole. As in this latter case, it is found that test particles experience a repulsive force within the horizon (naked singularity), which prevents them from reaching the center. However, in the present case, this behavior is affected by the parameter γ which measures the departure from the hyperbolical symmetry. These results are obtained for radially moving particles as well as for particles moving in the θ−r subspace. The possible relevance of these results in the explanation of extragalactic jets is revealed. Full article
(This article belongs to the Special Issue Selected Featured Papers from Entropy Editorial Board Members)
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15 pages, 5173 KiB  
Article
Dynamic Causal Modeling and Online Collaborative Forecasting of Air Quality in Hong Kong and Macao
by Cheng He, Jia Ren and Wenjian Liu
Entropy 2023, 25(9), 1337; https://doi.org/10.3390/e25091337 - 15 Sep 2023
Cited by 1 | Viewed by 1186
Abstract
The Hong Kong and Macao Special Administrative Regions, situated within China’s Guangdong–Hong Kong–Macao Greater Bay Area, significantly influence and are impacted by their air quality conditions. Rapid urbanization, high population density, and air pollution from diverse factors present challenges, making the health of [...] Read more.
The Hong Kong and Macao Special Administrative Regions, situated within China’s Guangdong–Hong Kong–Macao Greater Bay Area, significantly influence and are impacted by their air quality conditions. Rapid urbanization, high population density, and air pollution from diverse factors present challenges, making the health of the atmospheric environment in these regions a research focal point. This study offers three key contributions: (1) It applied an interpretable dynamic Bayesian network (DBN) to construct a dynamic causal model of air quality in Hong Kong and Macao, amidst complex, unstable, multi-dimensional, and uncertain factors over time. (2) It investigated the dynamic interaction between meteorology and air quality sub-networks, and both qualitatively and quantitatively identified, evaluated, and understood the causal relationships between air pollutants and their determinants. (3) It facilitated an online collaborative forecast of air pollutant concentrations, enabling pollution warnings. The findings proposed that a DBN-based dynamic causal model can effectively explain and manage complex atmospheric environmental systems in Hong Kong and Macao. This method offers crucial insights for decision-making and the management of atmospheric environments not only in these regions but also for neighboring cities and regions with similar geographical contexts. Full article
(This article belongs to the Special Issue Information Network Mining and Applications)
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19 pages, 2924 KiB  
Article
Exploring Focus and Depth-Induced Saliency Detection for Light Field
by Yani Zhang, Fen Chen, Zongju Peng, Wenhui Zou and Changhe Zhang
Entropy 2023, 25(9), 1336; https://doi.org/10.3390/e25091336 - 15 Sep 2023
Cited by 1 | Viewed by 857
Abstract
An abundance of features in the light field has been demonstrated to be useful for saliency detection in complex scenes. However, bottom-up saliency detection models are limited in their ability to explore light field features. In this paper, we propose a light field [...] Read more.
An abundance of features in the light field has been demonstrated to be useful for saliency detection in complex scenes. However, bottom-up saliency detection models are limited in their ability to explore light field features. In this paper, we propose a light field saliency detection method that focuses on depth-induced saliency, which can more deeply explore the interactions between different cues. First, we localize a rough saliency region based on the compactness of color and depth. Then, the relationships among depth, focus, and salient objects are carefully investigated, and the focus cue of the focal stack is used to highlight the foreground objects. Meanwhile, the depth cue is utilized to refine the coarse salient objects. Furthermore, considering the consistency of color smoothing and depth space, an optimization model referred to as color and depth-induced cellular automata is improved to increase the accuracy of saliency maps. Finally, to avoid interference of redundant information, the mean absolute error is chosen as the indicator of the filter to obtain the best results. The experimental results on three public light field datasets show that the proposed method performs favorably against the state-of-the-art conventional light field saliency detection approaches and even light field saliency detection approaches based on deep learning. Full article
(This article belongs to the Section Signal and Data Analysis)
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