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Mathematics, Volume 12, Issue 13 (July-1 2024) – 227 articles

Cover Story (view full-size image): The theory of fiber bundles forms a fundamental and versatile basis for many applications in mathematics and physics. A special class are the principal bundles, where the fiber is a torsor—a free group-space homeomorphic to the group. Inspired by adiabatic quantum mechanics, this work considers group-spaces where the fibers are generalized to disjoint unions of torsors, called semi-torsors, which then form semi-principal bundles. These extend the principal bundles, and similarly support equivariant parallel transport. The main difference is that this parallel transport may now end up in a different group orbit, meaning that group translations can no longer describe the situation. This can be mediated by introducing frames of group-spaces, which supply the needed reference points and enable the passage to a (principal) frame bundle. View this paper
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12 pages, 955 KiB  
Article
Time-Series Prediction of Electricity Load for Charging Piles in a Region of China Based on Broad Learning System
by Liansong Yu and Xiaohu Ge
Mathematics 2024, 12(13), 2147; https://doi.org/10.3390/math12132147 - 8 Jul 2024
Viewed by 455
Abstract
This paper introduces a novel electricity load time-series prediction model, utilizing a broad learning system to tackle the challenge of low prediction accuracy caused by the unpredictable nature of electricity load sequences in a specific region of China. First, a correlation analysis with [...] Read more.
This paper introduces a novel electricity load time-series prediction model, utilizing a broad learning system to tackle the challenge of low prediction accuracy caused by the unpredictable nature of electricity load sequences in a specific region of China. First, a correlation analysis with mutual information is utilized to identify the key factors affecting the electricity load. Second, variational mode decomposition is employed to obtain different mode information, and then a broad learning system is utilized to build a prediction model with different mode information. Finally, particle swarm optimization is used to fuse the prediction models under different modes. Simulation experiments using real data validate the efficiency of the proposed method, demonstrating that it offers higher accuracy compared to advanced modeling techniques and can assist in optimal electricity-load scheduling decision-making. Additionally, the R2 of the proposed model is 0.9831, the PRMSE is 21.8502, the PMAE is 17.0097, and the PMAPE is 2.6468. Full article
(This article belongs to the Special Issue Complex Process Modeling and Control Based on AI Technology)
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30 pages, 10891 KiB  
Article
A Fuzzy-Based Approach for Flexible Modeling and Management of Freshwater Fish Farming
by Ahmed M. Gadallah, Sameh A. Elsayed, Shaymaa Mousa and Hesham A. Hefny
Mathematics 2024, 12(13), 2146; https://doi.org/10.3390/math12132146 - 8 Jul 2024
Viewed by 462
Abstract
Most populated developing countries having water resources, like Egypt, are interested in aquaculture since it supplies around 30% of the cheap protein consumed by customers. Increasing the production of aquaculture, specifically fish farming, in such countries represents an essential need. One candidate water [...] Read more.
Most populated developing countries having water resources, like Egypt, are interested in aquaculture since it supplies around 30% of the cheap protein consumed by customers. Increasing the production of aquaculture, specifically fish farming, in such countries represents an essential need. One candidate water resource for freshwater fish farming in Egypt is the Nile River (1530 km long). Yet, this represents a challenging task due to the existing variations in its water quality (WQ) parameters, such as dissolved oxygen, acidity, and temperature, at different sites. Climate change and pollution negatively affect many water quality parameters. This work provides a fuzzy-based approach for modeling WQ requirements for a set of fish types and evaluates the suitability of a water site for farming them. Thus, it greatly helps managing and planning fish farming in a set of water sites. It benefits from the flexibility of fuzzy logic to model the farming requirements of each fish type. Consequently, it evaluates and clusters the water sites with respect to their degrees of suitability for farming various fish types. The illustrative case study considers 27 freshwater sites spread along the Nile River and 17 freshwater fish types. The result incorporates a set of suitable clusters and a set of unsuitable ones for farming each fish type. It greatly helps managing and planning fish farming, to maximize the overall productivity and prevent probable catastrophic damage. In addition, it shows how to enhance each unsuitable site. We believe that eliminating the causes of pollution in the polluted freshwater sites along a water source could cause a significant boom in the cultivation of multiple freshwater fish types. Full article
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17 pages, 333 KiB  
Article
Multistep Iterative Methods for Solving Equations in Banach Space
by Ramandeep Behl, Ioannis K. Argyros, Sattam Alharbi, Hashim Alshehri and Michael Argyros
Mathematics 2024, 12(13), 2145; https://doi.org/10.3390/math12132145 - 8 Jul 2024
Viewed by 257
Abstract
The novelty of this article lies in the fact that we extend the use of a multistep method for developing a sequence whose limit solves a Banach space-valued equation. We suggest the error estimates, local convergence, and semi-local convergence, a radius of convergence, [...] Read more.
The novelty of this article lies in the fact that we extend the use of a multistep method for developing a sequence whose limit solves a Banach space-valued equation. We suggest the error estimates, local convergence, and semi-local convergence, a radius of convergence, the uniqueness of the required solution that can be computed under ω-continuity, and conditions on the first derivative, which is on the method. But, earlier studies used high-order derivatives, even though those derivatives do not appear in the body structure of the proposed method. In addition to this, they did not propose computable estimates and semi-local convergence. We checked the applicability of our study to three real-life problems for semi-local convergence and two problems chosen for local convergence. Based on the obtained results, we conclude that our approach improves its applicability and makes it suitable for challenges in applied science. Full article
(This article belongs to the Section Computational and Applied Mathematics)
19 pages, 357 KiB  
Article
Hidden Abstract Stack Markov Models with Learning Process
by Mete Özbaltan
Mathematics 2024, 12(13), 2144; https://doi.org/10.3390/math12132144 - 8 Jul 2024
Viewed by 282
Abstract
We present hidden abstract stack Markov models (HASMMs) with their learning process. The HASMMs we offer carry the more expressive nature of probabilistic context-free grammars (PCFGs) while allowing faster parameter fitting of hidden Markov models (HMMs). Both HMMs and PCFGs are widely utilized [...] Read more.
We present hidden abstract stack Markov models (HASMMs) with their learning process. The HASMMs we offer carry the more expressive nature of probabilistic context-free grammars (PCFGs) while allowing faster parameter fitting of hidden Markov models (HMMs). Both HMMs and PCFGs are widely utilized structured models, offering an effective formalism capable of describing diverse phenomena. PCFGs are better accommodated than HMMs such as for expressing natural language processing; however, HMMs outperform PCFGs for parameter fitting. We extend HMMs towards PCFGs for such applications, by associating each state of an HMM with an abstract stack, which can be thought of as the single-stack alphabet of pushdown automata (PDA). As a result, we leverage the expressive capabilities of PCFGs for such applications while mitigating the cubic complexity of parameter learning in the observation sequence length of PCFGs by adopting the bilinear complexity of HMMs. Full article
(This article belongs to the Section Mathematics and Computer Science)
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14 pages, 436 KiB  
Article
Novel Dynamic Defense Strategies in Networked Control Systems under Stochastic Jamming Attacks
by Hana Mejdi and Tahar Ezzedine
Mathematics 2024, 12(13), 2143; https://doi.org/10.3390/math12132143 - 8 Jul 2024
Viewed by 258
Abstract
In contemporary networked control systems (NCSs), ensuring robust and adaptive security measures against dynamic threats like jamming attacks is crucial. These attacks can disrupt the control signals, leading to degraded performance or even catastrophic failures. This paper introduces a novel approach to enhance [...] Read more.
In contemporary networked control systems (NCSs), ensuring robust and adaptive security measures against dynamic threats like jamming attacks is crucial. These attacks can disrupt the control signals, leading to degraded performance or even catastrophic failures. This paper introduces a novel approach to enhance NCS security by applying stochastic game theory to model and resolve interactions between a defender and a jammer. We develop a two-player zero-sum game where the defender employs mixed strategies to minimize the expected cost of maintaining system stability and control effectiveness in the face of potential jamming. Our model discretizes the state space and employs backward induction to dynamically update the value functions associated with various system states, reflecting the ongoing adjustment of strategies in response to the adversary’s actions. Utilizing linear programming in MATLAB, we optimize the defender’s mixed strategies to systematically mitigate the impact of jamming. The results from extensive simulations demonstrate the efficacy of our proposed strategies in attack scenarios, indicating a substantial enhancement in the resilience and performance of NCSs against jamming attacks. Specifically, the proposed method improved network state stability by 75%, reducing the fluctuation range by over 50% compared with systems without defense mechanisms. This study not only advances the theoretical framework for security in NCSs but also provides practical insights for the design of resilient control systems under uncertainty. Full article
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18 pages, 4444 KiB  
Article
Federated Transfer Fault Diagnosis Method Based on Variational Auto-Encoding with Few-Shot Learning
by Yang Ge and Yong Ren
Mathematics 2024, 12(13), 2142; https://doi.org/10.3390/math12132142 - 8 Jul 2024
Viewed by 245
Abstract
Achieving accurate equipment fault diagnosis relies heavily on the availability of extensive, high-quality training data, which can be difficult to obtain, particularly for models with new equipment. The challenge is further compounded by the need to protect sensitive data during the training process. [...] Read more.
Achieving accurate equipment fault diagnosis relies heavily on the availability of extensive, high-quality training data, which can be difficult to obtain, particularly for models with new equipment. The challenge is further compounded by the need to protect sensitive data during the training process. This paper introduces a pioneering federated transfer fault diagnosis method that integrates Variational Auto-Encoding (VAE) for robust feature extraction with few-shot learning capabilities. The proposed method adeptly navigates the complexities of data privacy, diverse working conditions, and the cross-equipment transfer of diagnostic models. By harnessing the generative power of VAE, our approach extracts pivotal features from signals, effectively curbing overfitting during training, a common issue when dealing with limited fault samples. We construct a federated learning model comprising an encoder, variational feature generator, decoder, classifier, and discriminator, fortified with an advanced training strategy that refines federated averaging and incorporates regularization when handling non-independent data distributions. This strategy ensures the privacy of data while enhancing the model’s ability to discern subtleties in fault signatures across different equipment and operational settings. Our experiments, conducted across various working conditions and devices, demonstrate that our method significantly outperforms traditional federated learning techniques in terms of fault recognition accuracy. The innovative integration of VAE within a federated learning framework not only bolsters the model’s adaptability and accuracy but also upholds stringent data privacy standards. Full article
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10 pages, 251 KiB  
Article
On Finsler Surfaces with Isotropic Main Scalar
by Akbar Tayebi and Wei Sin Koh
Mathematics 2024, 12(13), 2141; https://doi.org/10.3390/math12132141 - 8 Jul 2024
Viewed by 280
Abstract
Let (M,F) be a Finsler surface with the isotropic main scalar I=I(x). The well-known Berwald’s theorem states that F is a Berwald metric if and only if it has a constant main scalar [...] Read more.
Let (M,F) be a Finsler surface with the isotropic main scalar I=I(x). The well-known Berwald’s theorem states that F is a Berwald metric if and only if it has a constant main scalar I=constant. This ensures a kind of equality of two non-Riemannian quantities for Finsler surfaces. In this paper, we consider a positively curved Finsler surface and show that H=0 if and only if I=0. This provides an extension of Berwald’s theorem. It follows that F has an isotropic scalar flag curvature if and only if it is Riemannian. Our results yield an infrastructural development of some equalities for two-dimensional Finsler manifolds. Full article
(This article belongs to the Section Algebra, Geometry and Topology)
21 pages, 3083 KiB  
Article
The Assessment of the Overall Lifetime Performance Index of Chen Products with Multiple Components
by Shu-Fei Wu and Yu-Lun Huang
Mathematics 2024, 12(13), 2140; https://doi.org/10.3390/math12132140 - 8 Jul 2024
Viewed by 248
Abstract
Process capability indices are widely utilized to evaluate process performance and drive continuous improvements in quality and productivity. Among these indices, the the-larger-the-better lifetime performance index is particularly noteworthy. For products with multiple components, an overall lifetime performance index is used, since it [...] Read more.
Process capability indices are widely utilized to evaluate process performance and drive continuous improvements in quality and productivity. Among these indices, the the-larger-the-better lifetime performance index is particularly noteworthy. For products with multiple components, an overall lifetime performance index is used, since it is a monotonically increasing function of the overall conforming rate and the relationship with each individual lifetime performance index can be determined. For products with the lifetime of the ith component following the Chen distribution, we investigate the maximum likelihood estimator for the overall lifetime performance index and the individual lifetime performance index based on the progressive type I interval censoring sample. Their asymptotic distributions for all lifetime performance indices are also derived. Once the target level for the overall lifetime performance index is specified, the desired level of individual lifetime performance index can be specified. By using the maximum likelihood estimator as the test statistic, a testing procedure to test whether the overall lifetime performance index has reached the target level is developed. The power analysis of the testing procedure is shown with figures, and some findings are summarized. At last, we use one practical example with two components to demonstrate how to implement this testing algorithmic procedure to test if the overall production process has reached the pre-assigned target level. Full article
(This article belongs to the Special Issue Computational Mathematics and Numerical Analysis)
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12 pages, 6009 KiB  
Article
Modeling and Optimal Control of Infectious Diseases
by Mario Lefebvre
Mathematics 2024, 12(13), 2139; https://doi.org/10.3390/math12132139 - 7 Jul 2024
Viewed by 444
Abstract
We propose a stochastic model of infectious disease transmission that is more realistic than those found in the literature. The model is based on jump-diffusion processes. However, it is defined in such a way that the number of people susceptible to be infected [...] Read more.
We propose a stochastic model of infectious disease transmission that is more realistic than those found in the literature. The model is based on jump-diffusion processes. However, it is defined in such a way that the number of people susceptible to be infected decreases over time, which is the case for a population of fixed size. Next, we consider the problem of finding the optimal control of the proposed model. The dynamic programming equation satisfied by the value function is derived. Estimators of the various model parameters are obtained. Full article
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23 pages, 5296 KiB  
Article
Solving Dynamic Full-Truckload Vehicle Routing Problem Using an Agent-Based Approach
by Selin Çabuk and Rızvan Erol
Mathematics 2024, 12(13), 2138; https://doi.org/10.3390/math12132138 - 7 Jul 2024
Viewed by 359
Abstract
In today’s complex and dynamic transportation networks, increasing energy costs and adverse environmental impacts necessitate the efficient transport of goods or raw materials across a network to minimize all related costs through vehicle assignment and routing decisions. Vehicle routing problems under dynamic and [...] Read more.
In today’s complex and dynamic transportation networks, increasing energy costs and adverse environmental impacts necessitate the efficient transport of goods or raw materials across a network to minimize all related costs through vehicle assignment and routing decisions. Vehicle routing problems under dynamic and stochastic conditions are known to be very challenging in both mathematical modeling and computational complexity. In this study, a special variant of the full-truckload vehicle assignment and routing problem was investigated. First, a detailed analysis of the processes in a liquid transportation logistics firm with a large fleet of tanker trucks was conducted. Then, a new original problem with distinctive features compared with similar studies in the literature was formulated, including pickup/delivery time windows, nodes with different functions (pickup/delivery, washing facilities, and parking), a heterogeneous truck fleet, multiple trips per truck, multiple trailer types, multiple freight types, and setup times between changing freight types. This dynamic optimization problem was solved using an intelligent multi-agent model with agent designs that run on vehicle assignment and routing algorithms. To assess the performance of the proposed approach under varying environmental conditions (e.g., congestion factors and the ratio of orders with multiple trips) and different algorithmic parameter levels (e.g., the latest response time to orders and activating the interchange of trip assignments between vehicles), a detailed scenario analysis was conducted based on a set of designed simulation experiments. The simulation results indicate that the proposed dynamic approach is capable of providing good and efficient solutions in response to dynamic conditions. Furthermore, using longer latest response times and activating the interchange mechanism have significant positive impacts on the relevant costs, profitability, ratios of loaded trips over the total distance traveled, and the acceptance ratios of customer orders. Full article
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23 pages, 4312 KiB  
Article
Numerical Solution to the Time-Fractional Burgers–Huxley Equation Involving the Mittag-Leffler Function
by Afzaal Mubashir Hayat, Muhammad Bilal Riaz, Muhammad Abbas, Moataz Alosaimi, Adil Jhangeer and Tahir Nazir
Mathematics 2024, 12(13), 2137; https://doi.org/10.3390/math12132137 - 7 Jul 2024
Viewed by 370
Abstract
Fractional differential equations play a significant role in various scientific and engineering disciplines, offering a more sophisticated framework for modeling complex behaviors and phenomena that involve multiple independent variables and non-integer-order derivatives. In the current research, an effective cubic B-spline collocation method is [...] Read more.
Fractional differential equations play a significant role in various scientific and engineering disciplines, offering a more sophisticated framework for modeling complex behaviors and phenomena that involve multiple independent variables and non-integer-order derivatives. In the current research, an effective cubic B-spline collocation method is used to obtain the numerical solution of the nonlinear inhomogeneous time-fractional Burgers–Huxley equation. It is implemented with the help of a θ-weighted scheme to solve the proposed problem. The spatial derivative is interpolated using cubic B-spline functions, whereas the temporal derivative is discretized by the Atangana–Baleanu operator and finite difference scheme. The proposed approach is stable across each temporal direction as well as second-order convergent. The study investigates the convergence order, error norms, and graphical visualization of the solution for various values of the non-integer parameter. The efficacy of the technique is assessed by implementing it on three test examples and we find that it is more efficient than some existing methods in the literature. To our knowledge, no prior application of this approach has been made for the numerical solution of the given problem, making it a first in this regard. Full article
(This article belongs to the Special Issue Applications of Partial Differential Equations, 2nd Edition)
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32 pages, 1967 KiB  
Article
Different Statistical Inference Algorithms for the New Pareto Distribution Based on Type-II Progressively Censored Competing Risk Data with Applications
by Essam A. Ahmed, Tariq S. Alshammari and Mohamed S. Eliwa
Mathematics 2024, 12(13), 2136; https://doi.org/10.3390/math12132136 - 7 Jul 2024
Viewed by 282
Abstract
In this research, the statistical inference of unknown lifetime parameters is proposed in the presence of independent competing risks using a progressive Type-II censored dataset. The lifetime distribution associated with a failure mode is assumed to follow the new Pareto distribution, with consideration [...] Read more.
In this research, the statistical inference of unknown lifetime parameters is proposed in the presence of independent competing risks using a progressive Type-II censored dataset. The lifetime distribution associated with a failure mode is assumed to follow the new Pareto distribution, with consideration given to two distinct competing failure reasons. Maximum likelihood estimators (MLEs) for the unknown model parameters, as well as reliability and hazard functions, are derived, noting that they are not expressible in closed form. The Newton–Raphson, expectation maximization (EM), and stochastic expectation maximization (SEM) methods are employed to generate maximum likelihood (ML) estimations. Approximate confidence intervals for the unknown parameters, reliability, and hazard rate functions are constructed using the normal approximation of the MLEs and the normal approximation of the log-transformed MLEs. Additionally, the missing information principle is utilized to derive the closed form of the Fisher information matrix, which, in turn, is used with the delta approach to calculate confidence intervals for reliability and hazards. Bayes estimators are derived under both symmetric and asymmetric loss functions, with informative and non-informative priors considered, including independent gamma distributions for informative priors. The Monte Carlo Markov Chain sampling approach is employed to obtain the highest posterior density credible intervals and Bayesian point estimates for unknown parameters and reliability characteristics. A Monte Carlo simulation is conducted to assess the effectiveness of the proposed techniques, with the performances of the Bayes and maximum likelihood estimations examined using average values and mean squared errors as benchmarks. Interval estimations are compared in terms of average lengths and coverage probabilities. Real datasets are considered and examined for each topic to provide illustrative examples. Full article
(This article belongs to the Special Issue Application of the Bayesian Method in Statistical Modeling)
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38 pages, 1204 KiB  
Article
Frames of Group Sets and Their Application in Bundle Theory
by Eric J. Pap and Holger Waalkens
Mathematics 2024, 12(13), 2135; https://doi.org/10.3390/math12132135 - 7 Jul 2024
Viewed by 293
Abstract
We study fiber bundles where the fibers are not a group G but a free G-space with disjoint orbits. The fibers are then not torsors but disjoint unions of these; hence, we like to call them semi-torsors. Bundles of semi-torsors naturally generalize [...] Read more.
We study fiber bundles where the fibers are not a group G but a free G-space with disjoint orbits. The fibers are then not torsors but disjoint unions of these; hence, we like to call them semi-torsors. Bundles of semi-torsors naturally generalize principal bundles, and we call these semi-principal bundles. These bundles admit parallel transport in the same way that principal bundles do. The main difference is that lifts may end up in another group orbit, meaning that the change cannot be described by group translations alone. The study of such effects is facilitated by defining the notion of a basis of a G-set, in analogy with a basis of a vector space. The basis elements serve as reference points for the orbits so that parallel transport amounts to reordering the basis elements and scaling them with the appropriate group elements. These two symmetries of the bases are described by a wreath product group. The notion of basis also leads to a frame bundle, which is principal and so allows for a conventional treatment. In fact, the frame bundle functor is found to be a retraction from the semi-principal bundles to the principal bundles. The theory presented provides a mathematical framework for a unified description of geometric phases and exceptional points in adiabatic quantum mechanics. Full article
(This article belongs to the Section Algebra, Geometry and Topology)
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21 pages, 6141 KiB  
Article
Research on Magnetic Levitation Control Method under Elastic Track Conditions Based on Backstepping Method
by Pengxiang Zhu, Te Zhang, Danfeng Zhou, Jie Li, Yuxin Jin and Qicai Li
Mathematics 2024, 12(13), 2134; https://doi.org/10.3390/math12132134 - 7 Jul 2024
Viewed by 312
Abstract
The vehicle–guideway coupled self-excited vibration of maglev systems is a common control instability problem in maglev traffic while the train is suspended above flexible girders, and it seriously affects the suspension stability of maglev vehicles. In order to solve this problem, a nonlinear [...] Read more.
The vehicle–guideway coupled self-excited vibration of maglev systems is a common control instability problem in maglev traffic while the train is suspended above flexible girders, and it seriously affects the suspension stability of maglev vehicles. In order to solve this problem, a nonlinear dynamic model of a single-point maglev system with elastic track is established in this paper, and a new and more stable adaptive backstepping control method combined with magnetic flux feedback is designed. In order to verify the control effect of the designed control method, a maglev vehicle–guideway coupled experimental platform with elastic track is built, and experimental verifications under rigid and elastic conditions are carried out. The results show that, compared with the state feedback controller based on the feedback linearization controller, the adaptive backstepping control law proposed in this paper can achieve stable suspension under extremely low track stiffness, and that it shows good stability and anti-interference abilities under elastic conditions. This work has an important meaning regarding its potential to benefit the advancement of commercial maglev lines, which may significantly enhance the stability of the maglev system and reduce the cost of guideway construction. Full article
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15 pages, 280 KiB  
Article
New Extension of Darbo’s Fixed Point Theorem and Its Application to a System of Weighted-Fractional-Type Integral Equations
by Marija Paunović, Ana Savić, Hemanta Kalita, Sudip Deb and Vahid Parvaneh
Mathematics 2024, 12(13), 2133; https://doi.org/10.3390/math12132133 - 7 Jul 2024
Viewed by 278
Abstract
In this article, we introduce several new extensions of Darbo’s fixed point theorem with newly constructed contraction functions associated with the measure of noncompactness. We apply our new extensions to prove the existence of solutions for a system of weighted fractional integral equations [...] Read more.
In this article, we introduce several new extensions of Darbo’s fixed point theorem with newly constructed contraction functions associated with the measure of noncompactness. We apply our new extensions to prove the existence of solutions for a system of weighted fractional integral equations in Banach space BC(R+). At the end, we establish an example to show the applicability of our discovery. Full article
(This article belongs to the Special Issue Soft Computing and Fuzzy Mathematics: New Advances and Applications)
14 pages, 271 KiB  
Article
Parabolic Hessian Quotient Equation in Exterior Domain
by Huawei Zhao and Limei Dai
Mathematics 2024, 12(13), 2132; https://doi.org/10.3390/math12132132 - 7 Jul 2024
Viewed by 205
Abstract
This study mainly focuses on the parabolic Hessian quotient equation in the exterior domain. The existence and uniqueness of generalized parabolically symmetric solutions with generalized asymptotic behavior are proven using Perron’s method. Full article
(This article belongs to the Section Difference and Differential Equations)
23 pages, 4816 KiB  
Article
Updating Correlation-Enhanced Feature Learning for Multi-Label Classification
by Zhengjuan Zhou, Xianju Zheng, Yue Yu, Xin Dong and Shaolong Li
Mathematics 2024, 12(13), 2131; https://doi.org/10.3390/math12132131 - 7 Jul 2024
Viewed by 280
Abstract
In the domain of multi-label classification, label correlations play a crucial role in enhancing prediction precision. However, traditional methods heavily depend on ground-truth label sets, which can be incompletely tagged due to the diverse backgrounds of annotators and the significant cost associated with [...] Read more.
In the domain of multi-label classification, label correlations play a crucial role in enhancing prediction precision. However, traditional methods heavily depend on ground-truth label sets, which can be incompletely tagged due to the diverse backgrounds of annotators and the significant cost associated with procuring extensive labeled datasets. To address these challenges, this paper introduces a novel multi-label classification method called updating Correlation-enhanced Feature Learning (uCeFL), which extracts label correlations directly from the data instances, circumventing the dependency on potentially incomplete label sets. uCeFL initially computes a revised label matrix by multiplying the incomplete label matrix with the label correlations extracted from the data matrix. This revised matrix is then utilized to enrich the original data features, enabling a neural network to learn correlation-enhanced representations that capture intricate relationships between data features, labels, and their interactions. Notably, label correlations are not static; they are dynamically updated during the neural network’s training process. Extensive experiments carried out on various datasets emphasize the effectiveness of the proposed approach. By leveraging label correlations within data instances, along with the hierarchical learning capabilities of neural networks, it offers a significant improvement in multi-label classification, even in scenarios with incomplete labels. Full article
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22 pages, 806 KiB  
Article
Optimal Investment for Defined-Contribution Pension Plans with the Return of Premium Clause under Partial Information
by Zilan Liu, Huanying Zhang, Yijun Wang and Ya Huang
Mathematics 2024, 12(13), 2130; https://doi.org/10.3390/math12132130 - 7 Jul 2024
Viewed by 267
Abstract
The optimal investment problem for defined contribution (DC) pension plans with partial information is the subject of this paper. The purpose of the return of premium clauses is to safeguard the rights of DC pension plan participants who pass away during accumulation. We [...] Read more.
The optimal investment problem for defined contribution (DC) pension plans with partial information is the subject of this paper. The purpose of the return of premium clauses is to safeguard the rights of DC pension plan participants who pass away during accumulation. We assume that the market price of risk consists of observable and unobservable factors that follow the Ornstein-Uhlenbeck processes, and the pension fund managers estimate the unobservable component from known information through Bayesian learning. Considering maximizing the expected utility of fund wealth at the terminal time, optimal investment strategies and the corresponding value function are determined using the dynamical programming principle approach and the filtering technique. Additionally, fund managers forsake learning, which results in the presentation of suboptimal strategies and utility losses for comparative analysis. Lastly, numerical analyses are included to demonstrate the impact of model parameters on the optimal strategy. Full article
(This article belongs to the Section Financial Mathematics)
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18 pages, 5511 KiB  
Article
Global Sensitivity Analysis of Structural Reliability Using Cliff Delta
by Zdeněk Kala
Mathematics 2024, 12(13), 2129; https://doi.org/10.3390/math12132129 - 7 Jul 2024
Viewed by 328
Abstract
This paper introduces innovative sensitivity indices based on Cliff’s Delta for the global sensitivity analysis of structural reliability. These indices build on the Sobol’ method, using binary outcomes (success or failure), but avoid the need to calculate failure probability Pf and the [...] Read more.
This paper introduces innovative sensitivity indices based on Cliff’s Delta for the global sensitivity analysis of structural reliability. These indices build on the Sobol’ method, using binary outcomes (success or failure), but avoid the need to calculate failure probability Pf and the associated distributional assumptions of resistance R and load F. Cliff’s Delta, originally used for ordinal data, evaluates the dominance of resistance over load without specific assumptions. The mathematical formulations for computing Cliff’s Delta between R and F quantify structural reliability by assessing the random realizations of R > F using a double-nested-loop approach. The derived sensitivity indices, based on the squared value of Cliff’s Delta δC2, exhibit properties analogous to those in the Sobol’ sensitivity analysis, including first-order, second-order, and higher-order indices. This provides a framework for evaluating the contributions of input variables on structural reliability. The results demonstrate that the Cliff’s Delta method provides a more accurate estimate of Pf. In one case study, the Cliff’s Delta approach reduces the standard deviation of Pf estimates across various Monte Carlo run counts. This method is particularly significant for FEM applications, where repeated simulations of R or F are computationally intensive. The double-nested-loop algorithm of Cliff’s Delta maximizes the extraction of information about structural reliability from these simulations. However, the high computational demand of Cliff’s Delta is a disadvantage. Future research should optimize computational demands, especially for small values of Pf. Full article
(This article belongs to the Special Issue Sensitivity Analysis and Decision Making)
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12 pages, 391 KiB  
Article
SCC-GPT: Source Code Classification Based on Generative Pre-Trained Transformers
by Mohammad D. Alahmadi, Moayad Alshangiti and Jumana Alsubhi
Mathematics 2024, 12(13), 2128; https://doi.org/10.3390/math12132128 - 7 Jul 2024
Viewed by 278
Abstract
Developers often rely on online resources, such as Stack Overflow (SO), to seek assistance for programming tasks. To facilitate effective search and resource discovery, manual tagging of questions and posts with the appropriate programming language is essential. However, accurate tagging is not consistently [...] Read more.
Developers often rely on online resources, such as Stack Overflow (SO), to seek assistance for programming tasks. To facilitate effective search and resource discovery, manual tagging of questions and posts with the appropriate programming language is essential. However, accurate tagging is not consistently achieved, leading to the need for the automated classification of code snippets into the correct programming language as a tag. In this study, we introduce a novel approach to automated classification of code snippets from Stack Overflow (SO) posts into programming languages using generative pre-trained transformers (GPT). Our method, which does not require additional training on labeled data or dependency on pre-existing labels, classifies 224,107 code snippets into 19 programming languages. We employ the text-davinci-003 model of ChatGPT-3.5 and postprocess its responses to accurately identify the programming language. Our empirical evaluation demonstrates that our GPT-based model (SCC-GPT) significantly outperforms existing methods, achieving a median F1-score improvement that ranges from +6% to +31%. These findings underscore the effectiveness of SCC-GPT in enhancing code snippet classification, offering a cost-effective and efficient solution for developers who rely on SO for programming assistance. Full article
(This article belongs to the Special Issue AI-Augmented Software Engineering)
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29 pages, 412 KiB  
Article
Unsteady Magnetohydrodynamics PDE of Monge–Ampère Type: Symmetries, Closed-Form Solutions, and Reductions
by Andrei D. Polyanin and Alexander V. Aksenov
Mathematics 2024, 12(13), 2127; https://doi.org/10.3390/math12132127 - 6 Jul 2024
Viewed by 299
Abstract
The paper studies an unsteady equation with quadratic nonlinearity in second derivatives, that occurs in electron magnetohydrodynamics. In mathematics, such PDEs are referred to as parabolic Monge–Ampère equations. An overview of the Monge–Ampère type equations is given, in which their unusual qualitative features [...] Read more.
The paper studies an unsteady equation with quadratic nonlinearity in second derivatives, that occurs in electron magnetohydrodynamics. In mathematics, such PDEs are referred to as parabolic Monge–Ampère equations. An overview of the Monge–Ampère type equations is given, in which their unusual qualitative features are noted. For the first time, the Lie group analysis of the considered highly nonlinear PDE with three independent variables is carried out. An eleven-parameter transformation is found that preserves the form of the equation. Some one-dimensional reductions allowing to obtain self-similar and other invariant solutions that satisfy ordinary differential equations are described. A large number of new additive, multiplicative, generalized, and functional separable solutions are obtained. Special attention is paid to the construction of exact closed-form solutions, including solutions in elementary functions (in total, more than 30 solutions in elementary functions were obtained). Two-dimensional symmetry and non-symmetry reductions leading to simpler partial differential equations with two independent variables are considered (including stationary Monge–Ampère type equations, linear and nonlinear heat type equations, and nonlinear filtration equations). The obtained results and exact solutions can be used to evaluate the accuracy and analyze the adequacy of numerical methods for solving initial boundary value problems described by highly nonlinear partial differential equations. Full article
23 pages, 674 KiB  
Article
Characterizing Finite Groups through Equitable Graphs: A Graph-Theoretic Approach
by Alaa Altassan, Anwar Saleh, Marwa Hamed and Najat Muthana
Mathematics 2024, 12(13), 2126; https://doi.org/10.3390/math12132126 - 6 Jul 2024
Viewed by 259
Abstract
This paper introduces equitable graphs of Type I associated with finite groups. We investigate the connectedness and some graph-theoretic properties of these graphs for various groups. Furthermore, we establish the novel concepts of the equitable square-free number and the equitable group. Our study [...] Read more.
This paper introduces equitable graphs of Type I associated with finite groups. We investigate the connectedness and some graph-theoretic properties of these graphs for various groups. Furthermore, we establish the novel concepts of the equitable square-free number and the equitable group. Our study includes an analysis of the equitable graphs for specific equitable groups. Additionally, we determine the first, second and forgotten Zagreb topological indices for the equitable graphs of Type I constructed from certain groups. Finally, we derive the adjacency matrix for this graph type built from cyclic p-groups. Full article
(This article belongs to the Special Issue Algebraic Structures and Graph Theory, 2nd Edition)
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22 pages, 3578 KiB  
Article
A Hybrid News Recommendation Approach Based on Title–Content Matching
by Shuhao Jiang, Yizi Lu, Haoran Song, Zihong Lu and Yong Zhang
Mathematics 2024, 12(13), 2125; https://doi.org/10.3390/math12132125 - 6 Jul 2024
Viewed by 245
Abstract
Personalized news recommendation can alleviate the information overload problem, and accurate modeling of user interests is the core of personalized news recommendation. Existing news recommendation methods integrate the titles and contents of news articles that users have historically browsed to construct user interest [...] Read more.
Personalized news recommendation can alleviate the information overload problem, and accurate modeling of user interests is the core of personalized news recommendation. Existing news recommendation methods integrate the titles and contents of news articles that users have historically browsed to construct user interest models. However, this method ignores the phenomenon of “title–content mismatching” in news articles, which leads to the lack of precision in user interest modeling. Therefore, a hybrid news recommendation method based on title–content matching is proposed in this paper: (1) An interactive attention network is employed to model the correlation between title and content contexts, thereby enhancing the feature representation of both; (2) The degree of title–content matching is computed using a Siamese neural network, constructing a user interest model based on title–content matching; and (3) neural collaborative filtering (NCF) based on factorization machines (FM) is integrated, taking into account the perspective of the potential relationships between users for recommendation, leveraging the insensitivity of neural collaboration to news content to alleviate the impact of title–content mismatching on user feature modeling. The proposed model was evaluated on a real-world dataset, achieving an nDCG of 83.03%, MRR of 81.88%, AUC of 85.22%, and F1 Score of 35.10%. Compared to state-of-the-art news recommendation methods, our model demonstrated an average improvement of 0.65% in nDCG and 3% in MRR. These experimental results indicate that our approach effectively enhances the performance of news recommendation systems. Full article
(This article belongs to the Section Mathematics and Computer Science)
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21 pages, 3231 KiB  
Article
Designing Decentralized Multi-Variable Robust Controllers: A Multi-Objective Approach Considering Nearly Optimal Solutions
by Alberto Pajares, Xavier Blasco, Juan Manuel Herrero, Javier Sanchis and Raúl Simarro
Mathematics 2024, 12(13), 2124; https://doi.org/10.3390/math12132124 - 6 Jul 2024
Viewed by 283
Abstract
This article presents a new methodology for designing a robust, decentralized control structure that considers stochastic parametric uncertainty and uses a multi-objective approach. This design tunes the loop pairing and controller to be implemented. The proposed approach obtains the optimal and nearly optimal [...] Read more.
This article presents a new methodology for designing a robust, decentralized control structure that considers stochastic parametric uncertainty and uses a multi-objective approach. This design tunes the loop pairing and controller to be implemented. The proposed approach obtains the optimal and nearly optimal controllers relevant to the nominal scenario. Once obtained, the robustness of these solutions is analyzed. This methodology is compared with a traditional approach for selecting the most robust control pairings. The traditional approach obtains lightly robust controllers, i.e., the most robust controllers with an acceptable performance for the nominal scenario, and it obtains trade-offs between robustness and nominal performance. However, the traditional approach has a high computational cost because it is necessary to consider uncertainty in the optimization stage. The proposed approach mathematically guarantees the acquisition of at least one neighbor controller for each existing lightly robust controller. Therefore, this approach obtains solutions similar to lightly robust solutions with a significantly lower computational cost. Furthermore, the proposed approach provides the designer with more diversity and interesting solutions that are not lightly robust. The different approaches are compared using an example of a multi-variable process with two alternative control structures. The results show the usefulness of the proposed methodology. Full article
(This article belongs to the Special Issue Advanced Applications Based on Nonlinear Optimal and Robust Control)
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18 pages, 315 KiB  
Article
OLF-ML: An Offensive Language Framework for Detection, Categorization, and Offense Target Identification Using Text Processing and Machine Learning Algorithms
by MD. Nahid Hasan, Kazi Shadman Sakib, Taghrid Tahani Preeti, Jeza Allohibi, Abdulmajeed Atiah Alharbi and Jia Uddin
Mathematics 2024, 12(13), 2123; https://doi.org/10.3390/math12132123 - 6 Jul 2024
Viewed by 395
Abstract
The pervasiveness of offensive language on social media emphasizes the necessity of automated systems for identifying and categorizing content. To ensure a more secure online environment and improve communication, effective identification and categorization of this content is essential. However, existing research encounters challenges [...] Read more.
The pervasiveness of offensive language on social media emphasizes the necessity of automated systems for identifying and categorizing content. To ensure a more secure online environment and improve communication, effective identification and categorization of this content is essential. However, existing research encounters challenges such as limited datasets and biased model performance, hindering progress in this domain. To address these challenges, this research presents a comprehensive framework that simplifies the utilization of support vector machines (SVM), random forest (RF) and artificial neural networks (ANN). The proposed methodology yields notable gains in offensive language detection, automatic categorization of offensiveness, and offense target identification tasks by utilizing the Offensive Language Identification Dataset (OLID). The simulation results indicate that SVM performs exceptionally well, exhibiting excellent accuracy scores (77%, 88%, and 68%), precision scores (76%, 87%, and 67%), F1 scores (57%, 88%, and 68%), and recall rates (45%, 88%, and 68%), proving to be practically successful in identifying and moderating offensive content on social media. By applying sophisticated preprocessing and meticulous hyperparameter tuning, our model outperforms some earlier research in detecting and categorizing offensive language tasks. Full article
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15 pages, 842 KiB  
Article
A Physical Insight into Computational Fluid Dynamics and Heat Transfer
by Sergey I. Martynenko and Aleksey Yu. Varaksin
Mathematics 2024, 12(13), 2122; https://doi.org/10.3390/math12132122 - 6 Jul 2024
Viewed by 242
Abstract
Mathematical equations that describe all physical processes are valid only under certain assumptions. One of them is the minimum scales used for the given description. In fact, this prohibits the use of derivatives in the mathematical models of the physical processes. This article [...] Read more.
Mathematical equations that describe all physical processes are valid only under certain assumptions. One of them is the minimum scales used for the given description. In fact, this prohibits the use of derivatives in the mathematical models of the physical processes. This article represents a derivative-free approach for the mathematical modelling. The proposed approach for CFD and numerical heat transfer is based on the conservation and phenomenological laws, and physical constraints on the minimum problem-dependent spatial and temporal scales (for example, on the average free path of molecules and the average time of their collisions for gases). This leads to the derivative-free governing equations (the discontinuum approximation) that are very convenient for numerical simulation. The theoretical analysis of governing equations describing the fundamental conservation laws in the continuum and discontinuum approximations is given. The article demonstrates the derivative-free approach based on the correctly defined macroparameters (pressure, temperature, density, etc.) for the mathematical description of physical and chemical processes. This eliminates the finite-difference, finite-volume, finite-element or other approximations of the governing equations from the computational algorithms. Full article
(This article belongs to the Topic Fluid Mechanics, 2nd Edition)
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14 pages, 285 KiB  
Article
A Political Radicalization Framework Based on Moral Foundations Theory
by Ruben Interian
Mathematics 2024, 12(13), 2121; https://doi.org/10.3390/math12132121 - 6 Jul 2024
Viewed by 332
Abstract
Moral foundations theory proposes that individuals with conflicting political views base their behavior on different principles chosen from a small group of universal moral foundations. This study proposes using a set of widely accepted moral foundations (fairness, in-group loyalty, authority, and purity) as [...] Read more.
Moral foundations theory proposes that individuals with conflicting political views base their behavior on different principles chosen from a small group of universal moral foundations. This study proposes using a set of widely accepted moral foundations (fairness, in-group loyalty, authority, and purity) as proxies to determine the degree of radicalization of online communities. A fifth principle, care, is generally surpassed by others that are higher in the radicalized groups’ moral hierarchy. Moreover, the presented data-driven methodological framework proposes an alternative way to measure whether a community complies with a certain moral principle or foundation: not evaluating its speech, but its behavior through the interactions of its individuals, establishing a bridge between the structural features of the interaction network and the intensity of communities’ radicalization regarding the considered moral foundations. Two foundations were assessed using the network’s structural characteristics: in-group loyalty measured by group-level modularity, and authority evaluated using group domination, for detecting potential hierarchical substructures within the network. By analyzing a set of Pareto-optimal groups regarding a multidimensional moral relevance scale, the most radicalized communities were identified among those considered extreme in some of their attitudes or views. An application of the proposed framework is illustrated using real-world datasets. The radicalized communities’ behavior exhibited increasing isolation, and their authorities and leaders showed growing domination over their audience. Differences were also detected between users’ behavior and speech, showing that individuals tended to share more “extreme” in-group content than they publish: extreme views get more likes on social media. Full article
(This article belongs to the Special Issue Modeling and Simulation of Social-Behavioral Phenomena)
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17 pages, 385 KiB  
Article
Synthesis of Optimal Correction Functions in the Class of Disjunctive Normal Forms
by Anvar Kabulov, Abdussattar Baizhumanov and Islambek Saymanov
Mathematics 2024, 12(13), 2120; https://doi.org/10.3390/math12132120 - 5 Jul 2024
Viewed by 328
Abstract
The paper proposes to consider individual heuristics as unreliably operating parts of the information processing system. In a separate case, several different heuristics are adopted to solve the same problem, and the results obtained are adjusted in a certain way. In this case, [...] Read more.
The paper proposes to consider individual heuristics as unreliably operating parts of the information processing system. In a separate case, several different heuristics are adopted to solve the same problem, and the results obtained are adjusted in a certain way. In this case, problems arise that are close in methodology to the problems of synthesizing reliable circuits from unreliable elements or making a collective expert decision. The work solves the problem of constructing an optimal correction function based on control material; classes of functions of k-valued logic under monotonicity restrictions are studied. A theorem on the completeness of the class of monotonic functions of k-valued logic for arbitrary k is proved, and a basis in the given class is proved and constructed. The problem of constructing an optimal corrector in the class of disjunctive normal forms of k-valued functions is solved. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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22 pages, 6590 KiB  
Article
A New Strategy: Remaining Useful Life Prediction of Wind Power Bearings Based on Deep Learning under Data Missing Conditions
by Xuejun Li, Xu Lei, Lingli Jiang, Tongguang Yang and Zhenyu Ge
Mathematics 2024, 12(13), 2119; https://doi.org/10.3390/math12132119 - 5 Jul 2024
Viewed by 316
Abstract
With its formidable nonlinear mapping capabilities, deep learning has been widely applied in bearing remaining useful life (RUL) prediction. Given that equipment in actual work is subject to numerous disturbances, the collected data tends to exhibit random missing values. Furthermore, due to the [...] Read more.
With its formidable nonlinear mapping capabilities, deep learning has been widely applied in bearing remaining useful life (RUL) prediction. Given that equipment in actual work is subject to numerous disturbances, the collected data tends to exhibit random missing values. Furthermore, due to the dynamic nature of wind turbine environments, LSTM models relying on manually set parameters exhibit certain limitations. Considering these factors can lead to issues with the accuracy of predictive models when forecasting the remaining useful life (RUL) of wind turbine bearings. In light of this issue, a novel strategy for predicting the remaining life of wind turbine bearings under data scarcity conditions is proposed. Firstly, the average similarity (AS) is introduced to reconstruct the discriminator of the Generative Adversarial Imputation Nets (GAIN), and the adversarial process between the generative module and the discriminant is strengthened. Based on this, the dung beetle algorithm (DBO) is used to optimize multiple parameters of the long-term and short-term memory network (LSTM), and the complete data after filling is used as the input data of the optimized LSTM to realize the prediction of the remaining life of the wind power bearing. The effectiveness of the proposed method is verified by the full-life data test of bearings. The results show that, under the condition of missing data, the new strategy of AS-GAIN-LSTM is used to predict the RUL of wind turbine bearings, which has a more stable prediction performance. Full article
(This article belongs to the Topic AI and Data-Driven Advancements in Industry 4.0)
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21 pages, 377 KiB  
Article
Joint Statistical Inference for the Area under the ROC Curve and Youden Index under a Density Ratio Model
by Siyan Liu, Qinglong Tian, Yukun Liu and Pengfei Li
Mathematics 2024, 12(13), 2118; https://doi.org/10.3390/math12132118 - 5 Jul 2024
Viewed by 340
Abstract
The receiver operating characteristic (ROC) curve is a valuable statistical tool in medical research. It assesses a biomarker’s ability to distinguish between diseased and healthy individuals. The area under the ROC curve (AUC) and the Youden index (J [...] Read more.
The receiver operating characteristic (ROC) curve is a valuable statistical tool in medical research. It assesses a biomarker’s ability to distinguish between diseased and healthy individuals. The area under the ROC curve (AUC) and the Youden index (J) are common summary indices used to evaluate a biomarker’s diagnostic accuracy. Simultaneously examining AUC and J offers a more comprehensive understanding of the ROC curve’s characteristics. In this paper, we utilize a semiparametric density ratio model to link the distributions of a biomarker for healthy and diseased individuals. Under this model, we establish the joint asymptotic normality of the maximum empirical likelihood estimator of (AUC,J) and construct an asymptotically valid confidence region for (AUC,J). Furthermore, we propose a new test to determine whether a biomarker simultaneously exceeds prespecified target values of AUC0 and J0 with the null hypothesis H0:AUCAUC0 or JJ0 against the alternative hypothesis Ha:AUC>AUC0 and J>J0. Simulation studies and a real data example on Duchenne Muscular Dystrophy are used to demonstrate the effectiveness of our proposed method and highlight its advantages over existing methods. Full article
(This article belongs to the Special Issue Statistical Analysis and Data Science for Complex Data)
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