Mathematics

21 pages, 1006 KiB

Open AccessArticle

TADocs: Teacher–Assistant Distillation for Improved Policy Transfer in 6G RAN Slicing

by Xian Mu, Yao Xu, Dagang Li and Mingzhu Liu

Mathematics 2024, 12(18), 2934; https://doi.org/10.3390/math12182934 (registering DOI) - 20 Sep 2024

Abstract

Network slicing is an advanced technology that significantly enhances network flexibility and efficiency. Recently, reinforcement learning (RL) has been applied to solve resource management challenges in 6G networks. However, RL-based network slicing solutions have not been widely adopted. One of the primary reasons [...] Read more.

Network slicing is an advanced technology that significantly enhances network flexibility and efficiency. Recently, reinforcement learning (RL) has been applied to solve resource management challenges in 6G networks. However, RL-based network slicing solutions have not been widely adopted. One of the primary reasons for this is the slow convergence of agents when the Service Level Agreement (SLA) weight parameters in Radio Access Network (RAN) slices change. Therefore, a solution is needed that can achieve rapid convergence while maintaining high accuracy. To address this, we propose a Teacher and Assistant Distillation method based on cosine similarity (TADocs). This method utilizes cosine similarity to precisely match the most suitable teacher and assistant models, enabling rapid policy transfer through policy distillation to adapt to the changing SLA weight parameters. The cosine similarity matching mechanism ensures that the student model learns from the appropriate teacher and assistant models, thereby maintaining high performance. Thanks to this efficient matching mechanism, the number of models that need to be maintained is greatly reduced, resulting in lower computational resource consumption. TADocs improves convergence speed by 81% while achieving an average accuracy of 98%. Full article

(This article belongs to the Special Issue Performance Modelling and Optimization in Future Networks)

19 pages, 4789 KiB

Open AccessArticle

Graph Neural Networks for Mesh Generation and Adaptation in Structural and Fluid Mechanics

by Ugo Pelissier, Augustin Parret-Fréaud, Felipe Bordeu and Youssef Mesri

Mathematics 2024, 12(18), 2933; https://doi.org/10.3390/math12182933 (registering DOI) - 20 Sep 2024

Abstract

The finite element discretization of computational physics problems frequently involves the manual generation of an initial mesh and the application of adaptive mesh refinement (AMR). This approach is employed to selectively enhance the accuracy of resolution in regions that encompass significant features throughout [...] Read more.

The finite element discretization of computational physics problems frequently involves the manual generation of an initial mesh and the application of adaptive mesh refinement (AMR). This approach is employed to selectively enhance the accuracy of resolution in regions that encompass significant features throughout the simulation process. In this paper, we introduce Adaptnet, a Graph Neural Networks (GNNs) framework for learning mesh generation and adaptation. The model is composed of two GNNs: the first one, Meshnet, learns mesh parameters commonly used in open-source mesh generators, to generate an initial mesh from a Computer Aided Design (CAD) file; while the second one, Graphnet, learns mesh-based simulations to predict the components of an Hessian-based metric to perform anisotropic mesh adaptation. Our approach is tested on structural (Deforming plate–Linear elasticity) and fluid mechanics (Flow around cylinders–steady-state Stokes) problems. Our findings demonstrate the model’s ability to precisely predict the dynamics of the system and adapt the mesh as needed. The adaptability of the model enables learning resolution-independent mesh-based simulations during training, allowing it to scale effectively to more intricate state spaces during inference. Full article

(This article belongs to the Special Issue Artificial Intelligence for Fluid Mechanics)

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27 pages, 1560 KiB

Open AccessArticle

Reputation-Driven Asynchronous Federated Learning for Optimizing Communication Efficiency in Big Data Labeling Systems

by Xuanzhu Sheng, Chao Yu, Yang Zhou and Xiaolong Cui

Mathematics 2024, 12(18), 2932; https://doi.org/10.3390/math12182932 (registering DOI) - 20 Sep 2024

Abstract

With the continuous improvement of the performance of artificial intelligence and neural networks, a new type of computing architecture-edge computing, came into being. However, when the scale of hybrid intelligent edge systems expands, there are redundant communications between the node and the parameter [...] Read more.

With the continuous improvement of the performance of artificial intelligence and neural networks, a new type of computing architecture-edge computing, came into being. However, when the scale of hybrid intelligent edge systems expands, there are redundant communications between the node and the parameter server; the cost of these redundant communications cannot be ignored. This paper proposes a reputation-based asynchronous model update scheme and formulates the federated learning scheme as an optimization problem. First, the explainable reputation consensus mechanism for hybrid intelligent labeling systems communication is proposed. Then, during the process of local intelligent data annotation, significant challenges in consistency, personalization, and privacy protection posed by the federated recommendation system prompted the development of a novel federated recommendation framework utilizing a graph neural network. Additionally, the method of information interaction model fusion was adopted to address data heterogeneity and enhance the uniformity of distributed intelligent annotation. Furthermore, to mitigate communication delays and overhead, an asynchronous federated learning mechanism was devised based on the proposed reputation consensus mechanism. This mechanism leverages deep reinforcement learning to optimize the selection of participating nodes, aiming to maximize system utility and streamline data sharing efficiency. Lastly, integrating the learned models into blockchain technology and conducting validation ensures the reliability and security of shared data. Numerical findings underscore that the proposed federated learning scheme achieves higher learning accuracy and enhances communication efficiency. Full article

(This article belongs to the Special Issue New Advances of Operations Research and Analysis)

17 pages, 339 KiB

Open AccessArticle

On Non-Commutative Multi-Rings with Involution

by Kaique M. A. Roberto, Kaique R. P. Santos and Hugo Luiz Mariano

Mathematics 2024, 12(18), 2931; https://doi.org/10.3390/math12182931 (registering DOI) - 20 Sep 2024

Abstract

The primary motivation for this work is to develop the concept of Marshall’s quotient applicable to non-commutative multi-rings endowed with involution, expanding upon the main ideas of the classical case—commutative and without involution—presented in Marshall’s seminal paper. We define two multiplicative properties to [...] Read more.

The primary motivation for this work is to develop the concept of Marshall’s quotient applicable to non-commutative multi-rings endowed with involution, expanding upon the main ideas of the classical case—commutative and without involution—presented in Marshall’s seminal paper. We define two multiplicative properties to address the involutive case and characterize their Marshall quotient. Moreover, this article presents various cases demonstrating that the “multi” version of rings with involution offers many examples, applications, and relatives in (multi)algebraic structures. Therefore, we established the first steps toward the development of an expansion of real algebra and real algebraic geometry to a non-commutative and involutive setting. Full article

(This article belongs to the Special Issue Algebraic Structures and Graph Theory, 2nd Edition)

19 pages, 1141 KiB

Open AccessArticle

On Convergence Rate of MRetrace

by Xingguo Chen, Wangrong Qin, Yu Gong, Shangdong Yang and Wenhao Wang

Mathematics 2024, 12(18), 2930; https://doi.org/10.3390/math12182930 (registering DOI) - 20 Sep 2024

Abstract

Off-policy is a key setting for reinforcement learning algorithms. In recent years, the stability of off-policy learning for value-based reinforcement learning has been guaranteed even when combined with linear function approximation and bootstrapping. Convergence rate analysis is currently a hot topic. However, the [...] Read more.

Off-policy is a key setting for reinforcement learning algorithms. In recent years, the stability of off-policy learning for value-based reinforcement learning has been guaranteed even when combined with linear function approximation and bootstrapping. Convergence rate analysis is currently a hot topic. However, the convergence rates of learning algorithms vary, and analyzing the reasons behind this remains an open problem. In this paper, we propose an essentially simplified version of a convergence rate to generate general off-policy temporal difference learning algorithms. We emphasize that the primary determinant influencing convergence rate is the minimum eigenvalue of the key matrix. Furthermore, we conduct a comparative analysis of the influencing factor across various off-policy learning algorithms in diverse numerical scenarios. The experimental findings validate the proposed determinant, which serves as a benchmark for the design of more efficient learning algorithms. Full article

(This article belongs to the Section Mathematics and Computer Science)

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16 pages, 860 KiB

Open AccessArticle

Robust Negative Binomial Regression via the Kibria–Lukman Strategy: Methodology and Application

by Adewale F. Lukman, Olayan Albalawi, Mohammad Arashi, Jeza Allohibi, Abdulmajeed Atiah Alharbi and Rasha A. Farghali

Mathematics 2024, 12(18), 2929; https://doi.org/10.3390/math12182929 (registering DOI) - 20 Sep 2024

Abstract

Count regression models, particularly negative binomial regression (NBR), are widely used in various fields, including biometrics, ecology, and insurance. Over-dispersion is likely when dealing with count data, and NBR has gained attention as an effective tool to address this challenge. However, multicollinearity among [...] Read more.

Count regression models, particularly negative binomial regression (NBR), are widely used in various fields, including biometrics, ecology, and insurance. Over-dispersion is likely when dealing with count data, and NBR has gained attention as an effective tool to address this challenge. However, multicollinearity among covariates and the presence of outliers can lead to inflated confidence intervals and inaccurate predictions in the model. This study proposes a comprehensive approach integrating robust and regularization techniques to handle the simultaneous impact of multicollinearity and outliers in the negative binomial regression model (NBRM). We investigate the estimators’ performance through extensive simulation studies and provide analytical comparisons. The simulation results and the theoretical comparisons demonstrate the superiority of the proposed robust hybrid KL estimator (M-NBKLE) with predictive accuracy and stability when multicollinearity and outliers exist. We illustrate the application of our methodology by analyzing a forestry dataset. Our findings complement and reinforce the simulation and theoretical results. Full article

(This article belongs to the Special Issue Application of Regression Models, Analysis and Bayesian Statistics)

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15 pages, 720 KiB

Open AccessArticle

Collaboration of Large and Small Models for Event Type Discovery in Completely Open Domains

by Jiaxu Li, Bin Ge, Hao Xu, Peixin Huang and Lihua Liu

Mathematics 2024, 12(18), 2928; https://doi.org/10.3390/math12182928 (registering DOI) - 20 Sep 2024

Abstract

Event type discovery in open domains aims to automate the induction of event types from completely unlabeled text data. Conventionally, small models utilize clustering techniques to address this task. Nonetheless, the fully unsupervised nature of these methods results in suboptimal performance by small [...] Read more.

Event type discovery in open domains aims to automate the induction of event types from completely unlabeled text data. Conventionally, small models utilize clustering techniques to address this task. Nonetheless, the fully unsupervised nature of these methods results in suboptimal performance by small models in this context. Recently, large language models (LLMs) have demonstrated excellent capabilities in contextual understanding, providing additional relevant information for specific task scenarios, albeit with challenges in precision and cost effectiveness. In this paper, we use LLM to guide the clustering of event texts and distill this process into a fine-tuning task for training smaller pre-trained language models. This approach enables effective event type discovery even in scenarios lacking annotated data. The study unfolds in three stages: in action acquisition, leveraging LLMs to extract type-relevant information from each event text, ensuring that the event representations are particular to task-specific details; in clustering refinement and dual-fine-tune, LLMs refine results from both task-agnostic and task-specific perspectives, with the refinement process designed as fine-tuning tasks under different viewpoints to adjust encoders; and in type generation, post-clustering, LLMs generate meaningful event type labels for each cluster. Experiments show that our method outperforms current state-of-the-art approaches and excels in event type discovery tasks even in completely open-domain with no labeled data. Full article

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21 pages, 4348 KiB

Open AccessArticle

A Novel Ensemble Method of Divide-and-Conquer Markov Boundary Discovery for Causal Feature Selection

by Hao Li, Jianjun Zhan, Haosen Wang and Zipeng Zhao

Mathematics 2024, 12(18), 2927; https://doi.org/10.3390/math12182927 (registering DOI) - 20 Sep 2024

Abstract

The discovery of Markov boundaries is highly effective at identifying features that are causally related to the target variable, providing strong interpretability and robustness. While there are numerous methods for discovering Markov boundaries in real-world applications, no single method is universally applicable to [...] Read more.

The discovery of Markov boundaries is highly effective at identifying features that are causally related to the target variable, providing strong interpretability and robustness. While there are numerous methods for discovering Markov boundaries in real-world applications, no single method is universally applicable to all datasets. Therefore, in order to balance precision and recall, we propose an ensemble framework of divide-and-conquer Markov boundary discovery algorithms based on U-I selection strategy. We put three divide-and-conquer Markov boundary methods into the framework to obtain an ensemble algorithm, focusing on judging controversial parent–child variables to further balance precision and recall. By combining multiple algorithms, the ensemble algorithm can leverage their respective strengths and more thoroughly analyze the cause-and-effect relationships of target variables through various perspectives. Furthermore, it can enhance the robustness of the algorithm and reduce dependence on a single algorithm. In the experiment, we select four advanced Markov boundary discovery algorithms as comparison algorithms and compare them on nine benchmark Bayesian networks and three real-world datasets. The results show that EDMB ranks first in the overall ranking, which illustrates the superiority of the integrated algorithm and the effectiveness of the adopted U-I selection strategy. The main contribution of this paper lies in proposing an ensemble framework for divide-and-conquer Markov boundary discovery algorithms, balancing precision and recall through the U-I selection strategy, and judging controversial parent–child variables to enhance algorithm performance and robustness. The advantage of the U-I selection strategy and its difference from existing methods is the ability to independently obtain the maximum precision and recall of multiple algorithms within the ensemble framework. By assessing controversial parent–child variables, it further balances precision and recall, leading to results that are closer to the true Markov boundary. Full article

(This article belongs to the Special Issue Computational Methods and Machine Learning for Causal Inference)

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15 pages, 6843 KiB

Open AccessArticle

TSPconv-Net: Transformer and Sparse Convolution for 3D Instance Segmentation in Point Clouds

by Xiaojuan Ning, Yule Liu, Yishu Ma, Zhiwei Lu, Haiyan Jin, Zhenghao Shi and Yinghui Wang

Mathematics 2024, 12(18), 2926; https://doi.org/10.3390/math12182926 (registering DOI) - 20 Sep 2024

Abstract

Current deep learning approaches for indoor 3D instance segmentation often rely on multilayer perceptrons (MLPs) for feature extraction. However, MLPs struggle to effectively capture the complex spatial relationships inherent in 3D scene data. To address this issue, we propose a novel and efficient [...] Read more.

Current deep learning approaches for indoor 3D instance segmentation often rely on multilayer perceptrons (MLPs) for feature extraction. However, MLPs struggle to effectively capture the complex spatial relationships inherent in 3D scene data. To address this issue, we propose a novel and efficient framework for 3D instance segmentation called TSPconv-Net. In contrast to existing methods that primarily depend on MLPs for feature extraction, our framework integrates a more robust feature extraction model comprising the offset-attention (OA) mechanism and submanifold sparse convolution (SSC). The proposed framework is an end-to-end network architecture. TSPconv-Net consists of a backbone network followed by a bounding box module. Specifically, the backbone network utilizes the OA mechanism to extract global features and employs SSC for local feature extraction. The bounding box module then conducts instance segmentation based on the extracted features. Experimental results demonstrate that our approach outperforms existing work on the S3DIS dataset while maintaining computational efficiency. TSPconv-Net achieves 68.6% mPrec, 52.5% mRec, and 60.1% mAP on the test set, surpassing 3D-BoNet by 3.0% mPrec, 5.4% mRec, and 2.6% mAP. Furthermore, it demonstrates high efficiency, completing computations in just 326 s. Full article

(This article belongs to the Special Issue Mathematical Computation for Pattern Recognition and Computer Vision)

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24 pages, 321 KiB

Open AccessArticle

Rough and T-Rough Sets Arising from Intuitionistic Fuzzy Ideals in BCK-Algebras

by Kholood M. Alsager and Sheza M. El-Deeb

Mathematics 2024, 12(18), 2925; https://doi.org/10.3390/math12182925 (registering DOI) - 20 Sep 2024

Abstract

This paper presents the novel concept of rough intuitionistic fuzzy ideals within the realm of BCK-algebras and investigates their fundamental properties. Furthermore, we introduce a set-valued homomorphism over a BCK-algebra, laying the foundation for the establishment of T-rough intuitionistic fuzzy ideals. The characterization [...] Read more.

This paper presents the novel concept of rough intuitionistic fuzzy ideals within the realm of BCK-algebras and investigates their fundamental properties. Furthermore, we introduce a set-valued homomorphism over a BCK-algebra, laying the foundation for the establishment of T-rough intuitionistic fuzzy ideals. The characterization of these innovative ideals is accomplished by employing the

(α, β)

-cut of intuitionistic fuzzy sets in the context of BCK-algebras. Full article

(This article belongs to the Special Issue Algebra and Discrete Mathematics 2023)

22 pages, 2742 KiB

Open AccessArticle

Simulation of Shock Waves in Methane: A Self-Consistent Continuum Approach Enhanced Using Machine Learning

by Zarina Maksudova, Liia Shakurova and Elena Kustova

Mathematics 2024, 12(18), 2924; https://doi.org/10.3390/math12182924 (registering DOI) - 20 Sep 2024

Abstract

This study presents a self-consistent one-temperature approach for modeling shock waves in single-component methane. The rigorous mathematical model takes into account the complex structure of CH₄ molecules with multiple vibrational modes and incorporates exact kinetic theory-based transport coefficients, including bulk viscosity. The [...] Read more.

This study presents a self-consistent one-temperature approach for modeling shock waves in single-component methane. The rigorous mathematical model takes into account the complex structure of CH₄ molecules with multiple vibrational modes and incorporates exact kinetic theory-based transport coefficients, including bulk viscosity. The effects of the bulk viscosity on gas-dynamic variables and transport terms are investigated in detail under varying degree of gas rarefaction. It is demonstrated that neglecting bulk viscosity significantly alters the shock front width and peak values of normal stress and heat flux, with the effect being more evident in denser gases. The study also evaluates limitations in the use of a constant specific heat ratio, revealing that this approach fails to accurately predict post-shock parameters in polyatomic gases, even at moderate Mach numbers. To enhance computational efficiency, a simplified approach based on a reduced vibrational spectrum is assessed. The results indicate that considering only the ground state leads to substantial errors in the fluid-dynamic variables across the shock front. Another approach explored involves the application of machine learning techniques to calculate vibrational energy and specific heat. Among the methods tested, the Feedforward Neural Network (FNN) proves to be the most effective, offering significant acceleration in calculations and providing one of the lowest errors. When integrated into the fluid-dynamic solver, the FNN approach yields nearly a three-fold increase in speed in numerical simulations of the shock wave structure. Full article

(This article belongs to the Special Issue Mathematical Modeling, Optimization and Machine Learning, 2nd Edition)

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20 pages, 5033 KiB

Open AccessFeature PaperArticle

Multi-Output Bayesian Support Vector Regression Considering Dependent Outputs

by Yanlin Wang, Zhijun Cheng and Zichen Wang

Mathematics 2024, 12(18), 2923; https://doi.org/10.3390/math12182923 (registering DOI) - 20 Sep 2024

Abstract

Multi-output regression aims to utilize the correlation between outputs to achieve information transfer between dependent outputs, thus improving the accuracy of predictive models. Although the Bayesian support vector machine (BSVR) can provide both the mean and the predicted variance distribution of the data [...] Read more.

Multi-output regression aims to utilize the correlation between outputs to achieve information transfer between dependent outputs, thus improving the accuracy of predictive models. Although the Bayesian support vector machine (BSVR) can provide both the mean and the predicted variance distribution of the data to be labeled, which has a large potential application value, its standard form is unable to handle multiple outputs at the same time. To solve this problem, this paper proposes a multi-output Bayesian support vector machine model (MBSVR), which uses a covariance matrix to describe the relationship between outputs and outputs and outputs and inputs simultaneously by introducing a semiparametric latent factor model (SLFM) in BSVR, realizing knowledge transfer between outputs and improving the accuracy of the model. MBSVR integrates and optimizes the parameters in BSVR and those in SLFM through Bayesian derivation to effectively deal with the multi-output problem on the basis of inheriting the advantages of BSVR. The effectiveness of the method is verified using two function cases and four high-dimensional real-world data with multi-output. Full article

(This article belongs to the Section Mathematics and Computer Science)

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18 pages, 6191 KiB

Open AccessArticle

Fast Analysis and Optimization of a Magnetic Gear Based on Subdomain Modeling

by Manh-Dung Nguyen, Woo-Sung Jung, Duy-Tinh Hoang, Yong-Joo Kim, Kyung-Hun Shin and Jang-Young Choi

Mathematics 2024, 12(18), 2922; https://doi.org/10.3390/math12182922 (registering DOI) - 20 Sep 2024

Abstract

This study presents a two-dimensional analytical method for fast optimization, taking into consideration the influence of the eddy current in a magnet and iron loss within a coaxial magnetic gear. Subdomain modeling was utilized to obtain vector potentials in the air-gap, magnet, and [...] Read more.

This study presents a two-dimensional analytical method for fast optimization, taking into consideration the influence of the eddy current in a magnet and iron loss within a coaxial magnetic gear. Subdomain modeling was utilized to obtain vector potentials in the air-gap, magnet, and modulation regions by solving Maxwell’s equations. After that, the magnet, rotor, and modulation losses were predicted and then compared using a finite element method simulation within three topologies with gear ratios ranging from five to six. The authors improved the machine performance, specifically the torque density, by employing a multi-objective function with particle swarm optimization. The flux density obtained using subdomain modeling in just 0.5 s benefits the optimization process, resulting in a torque-density optimal model after around 3 h. A 3/19/16 prototype targeting a low-speed, high-torque, permanent generator application was fabricated to verify the analytical and simulation results. Full article

(This article belongs to the Special Issue Mathematical Modelling and Numerical Analysis in Electrical Engineering, 2nd Edition)

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19 pages, 5928 KiB

Open AccessArticle

Design and Implementation of Digital PID Control for Mass-Damper Rectilinear Systems

by Humam Al-Baidhani and Marian K. Kazimierczuk

Mathematics 2024, 12(18), 2921; https://doi.org/10.3390/math12182921 (registering DOI) - 20 Sep 2024

Abstract

The mechanical systems were modeled using various combinations of mass-damper-spring elements to analyze the system dynamics and improve the system stability. Due to the marginal stability property of the mass-damper rectilinear system, a proper control law is required to control the mass position [...] Read more.

The mechanical systems were modeled using various combinations of mass-damper-spring elements to analyze the system dynamics and improve the system stability. Due to the marginal stability property of the mass-damper rectilinear system, a proper control law is required to control the mass position accurately, improve the relative stability, and enhance the dynamical response. In this paper, a mathematical model of the electromechanical system was first derived and analyzed. Next, a digital PID controller was developed based on the root locus technique, and a systematic design procedure is presented in detail. The proposed digital control system was simulated in MATLAB and compared with other control schemes to check their tracking performance and transient response characteristics. In addition, the digital PID control algorithm of the mass-damper rectilinear system was implemented via dSPACE platform to investigate the real-time control system performance and validate the control design methodology. It has been shown that the digital PID controller yields zero percentage overshoot, fast transient response, adequate stability margins, and zero steady-state error. Full article

(This article belongs to the Special Issue Modeling, Simulation and Control of Dynamical Systems)

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20 pages, 1314 KiB

Open AccessArticle

Upper Bounds for the Remainder Term in Boole’s Quadrature Rule and Applications to Numerical Analysis

by Muhammad Zakria Javed, Muhammad Uzair Awan, Bandar Bin-Mohsin and Savin Treanţă

Mathematics 2024, 12(18), 2920; https://doi.org/10.3390/math12182920 - 20 Sep 2024

Viewed by 151

Abstract

In the current study, we compute some upper bounds for the remainder term of Boole’s quadrature rule involving convex mappings. First, we build a new identity for first-order differentiable mapping, an auxiliary result to establish our required estimates. We provide several upper bounds [...] Read more.

In the current study, we compute some upper bounds for the remainder term of Boole’s quadrature rule involving convex mappings. First, we build a new identity for first-order differentiable mapping, an auxiliary result to establish our required estimates. We provide several upper bounds by utilizing the identity, convexity property, and bounded property of mappings and some well-known inequalities. Moreover, based on our primary findings, we deliver applications to the means, quadrature rule, special mappings, and non-linear analysis by developing a novel iterative scheme with cubic order of convergence. To the best of our knowledge, the current study is the first attempt to derive upper bounds for Boole’s scheme involving convex mappings. Full article

(This article belongs to the Special Issue Mathematical Inequalities and Fractional Calculus)

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23 pages, 24285 KiB

Open AccessArticle

Novel Hybrid Optimization Techniques for Enhanced Generalization and Faster Convergence in Deep Learning Models: The NestYogi Approach to Facial Biometrics

by Raoof Altaher and Hakan Koyuncu

Mathematics 2024, 12(18), 2919; https://doi.org/10.3390/math12182919 - 20 Sep 2024

Viewed by 110

Abstract

In the rapidly evolving field of biometric authentication, deep learning has become a cornerstone technology for face detection and recognition tasks. However, traditional optimizers often struggle with challenges such as overfitting, slow convergence, and limited generalization across diverse datasets. To address these issues, [...] Read more.

In the rapidly evolving field of biometric authentication, deep learning has become a cornerstone technology for face detection and recognition tasks. However, traditional optimizers often struggle with challenges such as overfitting, slow convergence, and limited generalization across diverse datasets. To address these issues, this paper introduces NestYogi, a novel hybrid optimization algorithm that integrates the adaptive learning capabilities of the Yogi optimizer, anticipatory updates of Nesterov momentum, and the generalization power of stochastic weight averaging (SWA). This combination significantly improves both the convergence rate and overall accuracy of deep neural networks, even when trained from scratch. Extensive data augmentation techniques, including noise and blur, were employed to ensure the robustness of the model across diverse conditions. NestYogi was rigorously evaluated on two benchmark datasets Labeled Faces in the Wild (LFW) and YouTube Faces (YTF), demonstrating superior performance with a detection accuracy reaching 98% and a recognition accuracy up to 98.6%, outperforming existing optimization strategies. These results emphasize NestYogi’s potential to overcome critical challenges in face detection and recognition, offering a robust solution for achieving state-of-the-art performance in real-world applications. Full article

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45 pages, 2062 KiB

Open AccessArticle

Exploring Metaheuristic Optimized Machine Learning for Software Defect Detection on Natural Language and Classical Datasets

by Aleksandar Petrovic, Luka Jovanovic, Nebojsa Bacanin, Milos Antonijevic, Nikola Savanovic, Miodrag Zivkovic, Marina Milovanovic and Vuk Gajic

Mathematics 2024, 12(18), 2918; https://doi.org/10.3390/math12182918 - 19 Sep 2024

Viewed by 271

Abstract

Software is increasingly vital, with automated systems regulating critical functions. As development demands grow, manual code review becomes more challenging, often making testing more time-consuming than development. A promising approach to improving defect detection at the source code level is the use of [...] Read more.

Software is increasingly vital, with automated systems regulating critical functions. As development demands grow, manual code review becomes more challenging, often making testing more time-consuming than development. A promising approach to improving defect detection at the source code level is the use of artificial intelligence combined with natural language processing (NLP). Source code analysis, leveraging machine-readable instructions, is an effective method for enhancing defect detection and error prevention. This work explores source code analysis through NLP and machine learning, comparing classical and emerging error detection methods. To optimize classifier performance, metaheuristic optimizers are used, and algorithm modifications are introduced to meet the study’s specific needs. The proposed two-tier framework uses a convolutional neural network (CNN) in the first layer to handle large feature spaces, with AdaBoost and XGBoost classifiers in the second layer to improve error identification. Additional experiments using term frequency–inverse document frequency (TF-IDF) encoding in the second layer demonstrate the framework’s versatility. Across five experiments with public datasets, the accuracy of the CNN was 0.768799. The second layer, using AdaBoost and XGBoost, further improved these results to 0.772166 and 0.771044, respectively. Applying NLP techniques yielded exceptional accuracies of 0.979781 and 0.983893 from the AdaBoost and XGBoost optimizers. Full article

(This article belongs to the Special Issue New Machine Learning and Deep Learning Techniques in Natural Language Processing)

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21 pages, 5960 KiB

Open AccessArticle

Effective SQL Injection Detection: A Fusion of Binary Olympiad Optimizer and Classification Algorithm

by Bahman Arasteh, Asgarali Bouyer, Seyed Salar Sefati and Razvan Craciunescu

Mathematics 2024, 12(18), 2917; https://doi.org/10.3390/math12182917 - 19 Sep 2024

Viewed by 261

Abstract

Since SQL injection allows attackers to interact with the database of applications, it is regarded as a significant security problem. By applying machine learning algorithms, SQL injection attacks can be identified. Problem: In the training stage of machine learning methods, effective features [...] Read more.

Since SQL injection allows attackers to interact with the database of applications, it is regarded as a significant security problem. By applying machine learning algorithms, SQL injection attacks can be identified. Problem: In the training stage of machine learning methods, effective features are used to develop an optimal classifier that is highly accurate. The specification of the features with the highest efficacy is considered to be an NP-complete combinatorial optimization challenge. Selecting the most effective features refers to the procedure of identifying the smallest and most effective features in the dataset. The rationale behind this paper is to optimize the accuracy, precision, and sensitivity parameters of the SQL injection attack detection method. Method: In this paper, a method for identifying SQL injection attacks was suggested. In the first step, a particular training dataset that included 13 features was developed. In the second step, to specify the best features of the dataset, a specific binary variety of the Olympiad optimization algorithm was developed. Various machine learning algorithms were used to create the optimal attack detector. Results: Based on the experiments carried out, the suggested SQL injection detector using an artificial neural network and the feature selector can achieve 99.35% accuracy, 100% precision, and 100% sensitivity. Owing to selecting about 30% of the effective features, the proposed method enhanced the efficacy of SQL injection detectors. Full article

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20 pages, 8696 KiB

Open AccessArticle

Reliability Modeling of Systems with Undetected Degradation Considering Time Delays, Self-Repair, and Random Operating Environments

by Hoang Pham

Mathematics 2024, 12(18), 2916; https://doi.org/10.3390/math12182916 - 19 Sep 2024

Viewed by 255

Abstract

In some settings, systems may not fail completely but instead undergo performance degradation, leading to reduced efficiency. A significant concern arises when a system transitions into a degraded state without immediate detection, with the degradation only becoming apparent after an unpredictable period. Undetected [...] Read more.

In some settings, systems may not fail completely but instead undergo performance degradation, leading to reduced efficiency. A significant concern arises when a system transitions into a degraded state without immediate detection, with the degradation only becoming apparent after an unpredictable period. Undetected degradation can result in failures with significant consequences. For instance, a minor crack in an oil pipeline might go unnoticed, eventually leading to a major leak, environmental harm, and costly cleanup efforts. Similarly, in the nuclear industry, undetected degradation in reactor cooling systems could cause overheating and potentially catastrophic failure. This paper focuses on reliability modeling for systems experiencing degradation, accounting for time delays associated with undetected degraded states, self-repair mechanisms, and varying operating environments. The paper presents a reliability model for degraded, time-dependent systems, incorporating various aspects of degradation. It first discusses the model assumptions and formulation, followed by numerical results obtained from system modeling using the developed program. Various scenarios are illustrated, incorporating time delays and different parameter values. Through computational analysis of these complex systems, we observe that the probability of the system being in the undetected degraded state tends to stabilize shortly after the initial degradation begins. The model is valuable for predicting and establishing an upper bound on the probability of the undetected, degraded state and the system’s overall reliability. Finally, the paper outlines potential avenues for future research. Full article

(This article belongs to the Special Issue Application of Mathematical Methods in Industrial Engineering and Management: 2nd Edition)

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17 pages, 306 KiB

Open AccessArticle

On LP-Kenmotsu Manifold with Regard to Generalized Symmetric Metric Connection of Type (α, β)

by Doddabhadrappla Gowda Prakasha, Nasser Bin Turki, Mathad Veerabhadraswamy Deepika and İnan Ünal

Mathematics 2024, 12(18), 2915; https://doi.org/10.3390/math12182915 - 19 Sep 2024

Viewed by 194

Abstract

In the current article, we examine Lorentzian para-Kenmotsu (shortly, LP-Kenmotsu) manifolds with regard to the generalized symmetric metric connection

\nabla^{G}

of type

(α, β)

. First, we obtain the expressions for curvature tensor, Ricci tensor and scalar curvature of [...] Read more.

In the current article, we examine Lorentzian para-Kenmotsu (shortly, LP-Kenmotsu) manifolds with regard to the generalized symmetric metric connection

\nabla^{G}

of type

(α, β)

. First, we obtain the expressions for curvature tensor, Ricci tensor and scalar curvature of an LP-Kenmotsu manifold with regard to the connection

\nabla^{G}

. Next, we analyze LP-Kenmotsu manifolds equipped with the connection

\nabla^{G}

that are locally symmetric, Ricci semi-symmetric, and

φ

-Ricci symmetric and also demonstrated that in all these situations the manifold is an Einstein one with regard to the connection

\nabla^{G}

. Moreover, we obtain some conclusions about projectively flat, projectively semi-symmetric and

φ

-projectively flat LP-Kenmotsu manifolds concerning the connection

\nabla^{G}

along with several consequences through corollaries. Ultimately, we provide a 5-dimensional LP-Kenmotsu manifold example to validate the derived expressions. Full article

(This article belongs to the Special Issue Differentiable Manifolds and Geometric Structures)

12 pages, 258 KiB

Open AccessArticle

Projective Vector Fields on Semi-Riemannian Manifolds

by Norah Alshehri and Mohammed Guediri

Mathematics 2024, 12(18), 2914; https://doi.org/10.3390/math12182914 - 19 Sep 2024

Viewed by 162

Abstract

This paper explores the properties of projective vector fields on semi-Riemannian manifolds. The main result establishes that if a projective vector field P on such a manifold is also a conformal vector field with potential function

ψ

and the vector field

ζ

dual [...] Read more.

This paper explores the properties of projective vector fields on semi-Riemannian manifolds. The main result establishes that if a projective vector field P on such a manifold is also a conformal vector field with potential function

ψ

and the vector field

ζ

dual to

d ψ

does not change its causal character, then P is homothetic, or

ζ

is a light-like vector field. Additionally, it is shown that a complete Riemannian manifold admits a projective vector field that is also conformal and non-Killing if and only if it is locally Euclidean. The paper also presents other results related to the characterization of Killing and parallel vector fields using the Ricci curvature and the Hessian of the function given by the inner product of the vector field. Full article

(This article belongs to the Special Issue Differentiable Manifolds and Geometric Structures)

15 pages, 285 KiB

Open AccessArticle

A Combined OCBA–AIC Method for Stochastic Variable Selection in Data Envelopment Analysis

by Qiang Deng

Mathematics 2024, 12(18), 2913; https://doi.org/10.3390/math12182913 - 19 Sep 2024

Viewed by 209

Abstract

This study introduces a novel approach to enhance variable selection in Data Envelopment Analysis (DEA), especially in stochastic environments where efficiency estimation is inherently complex. To address these challenges, we propose a game cross-DEA model to refine efficiency estimation. Additionally, we integrate the [...] Read more.

This study introduces a novel approach to enhance variable selection in Data Envelopment Analysis (DEA), especially in stochastic environments where efficiency estimation is inherently complex. To address these challenges, we propose a game cross-DEA model to refine efficiency estimation. Additionally, we integrate the Akaike Information Criterion (AIC) with the Optimal Computing Budget Allocation (OCBA) technique, creating a hybrid method named OCBA–AIC. This innovative method efficiently allocates computational resources for stochastic variable selection. Our numerical analysis indicates that OCBA–AIC surpasses existing methods, achieving a lower AIC value. We also present two real-world case studies that demonstrate the effectiveness of our approach in ranking suppliers and tourism companies under uncertainty by selecting the most suitable partners. This research enriches the understanding of efficiency measurement in DEA and makes a substantial contribution to the field of performance management and decision-making in stochastic contexts. Full article

21 pages, 2113 KiB

Open AccessArticle

Periodic Scheduling Optimization for Dual-Arm Cluster Tools with Arm Task and Residency Time Constraints via Petri Net Model

by Lei Gu, Naiqi Wu, Tan Li, Siwei Zhang and Wenyu Wu

Mathematics 2024, 12(18), 2912; https://doi.org/10.3390/math12182912 - 19 Sep 2024

Viewed by 198

Abstract

In order to improve quality assurance in wafer manufacturing, there are strict process requirements. Besides the well-known residency time constraints (RTCs), a dual-arm cluster tool also requires each robot arm to execute a specific set of tasks. We call such a tool an [...] Read more.

In order to improve quality assurance in wafer manufacturing, there are strict process requirements. Besides the well-known residency time constraints (RTCs), a dual-arm cluster tool also requires each robot arm to execute a specific set of tasks. We call such a tool an arm task-constrained dual-arm cluster tool (ATC-DACT). To do this, one of the arms is identified as the dirty one and the other as the clean one. The dirty one can deal with raw wafers, while the clean one can deal with processed wafers. This requirement raises a new problem for scheduling a cluster tool. This paper discusses the scheduling problem of ATC-DACTs with RTCs. Due to the arm task constraints, the proven, effective swap strategy is no longer applicable to ATC-DACTs, making the scheduling problem difficult. To address this problem, we explicitly describe the robot waiting as an event and build a Petri net (PN) model. Then, we propose a hybrid task sequence (HTS) as an operation strategy by combining the swap and backward strategies. Based on the HTS, the necessary and sufficient conditions for schedulability are established; also, a linear programming model is developed. We then develop an algorithm using these results to optimally schedule the system. Industrial case studies demonstrate the application of this method. Full article

(This article belongs to the Section Computational and Applied Mathematics)

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14 pages, 539 KiB

Open AccessArticle

Anti-Persistent Values of the Hurst Exponent Anticipate Mean Reversion in Pairs Trading: The Cryptocurrencies Market as a Case Study

by Mar Grande, Florentino Borondo, Juan Carlos Losada and Javier Borondo

Mathematics 2024, 12(18), 2911; https://doi.org/10.3390/math12182911 - 19 Sep 2024

Viewed by 210

Abstract

Pairs trading is a short-term speculation trading strategy based on matching a long position with a short position in two assets in the hope that their prices will return to their historical equilibrium. In this paper, we focus on identifying opportunities where mean [...] Read more.

Pairs trading is a short-term speculation trading strategy based on matching a long position with a short position in two assets in the hope that their prices will return to their historical equilibrium. In this paper, we focus on identifying opportunities where mean reversion will happen quickly, as the commission costs associated with keeping the positions open for an extended period of time can eliminate excess returns. To this end, we propose the use of the local Hurst exponent as a signal to open trades in the cryptocurrencies market. We conduct a natural experiment to show that the spread of pairs with anti-persistent values of Hurst revert to their mean significantly faster. Next, we verify that this effect is universal across pairs with different levels of co-movement. Finally, we back-test several pairs trading strategies that include

H < 0.5

as an indicator and check that all of them result in profits. Hence, we conclude that the Hurst exponent represents a meaningful indicator to detect pairs trading opportunities in the cryptocurrencies market. Full article

(This article belongs to the Special Issue Chaos Theory and Its Applications to Economic Dynamics)

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13 pages, 272 KiB

Open AccessArticle

Three Weak Solutions for a Critical Non-Local Problem with Strong Singularity in High Dimension

by Gabriel Neves Cunha, Francesca Faraci and Kaye Silva

Mathematics 2024, 12(18), 2910; https://doi.org/10.3390/math12182910 - 18 Sep 2024

Viewed by 239

Abstract

In this paper, we deal with a strongly singular problem involving a non-local operator, a critical nonlinearity, and a subcritical perturbation. We apply techniques from non-smooth analysis to the energy functional, in combination with the study of the topological properties of the sublevels [...] Read more.

In this paper, we deal with a strongly singular problem involving a non-local operator, a critical nonlinearity, and a subcritical perturbation. We apply techniques from non-smooth analysis to the energy functional, in combination with the study of the topological properties of the sublevels of its smooth part, to prove the existence of three weak solutions: two points of local minimum and a third one as a mountain pass critical point. Full article

(This article belongs to the Special Issue Problems and Methods in Nonlinear Analysis)

17 pages, 461 KiB

Open AccessArticle

LMKCDEY Revisited: Speeding Up Blind Rotation with Signed Evaluation Keys

by Yongwoo Lee

Mathematics 2024, 12(18), 2909; https://doi.org/10.3390/math12182909 - 18 Sep 2024

Viewed by 240

Abstract

Recently, Lee et al. introduced a novel blind rotation technique utilizing ring automorphisms also known as LMKCDEY. Among known prominent blind rotation methods, LMKCDEY stands out because of its minimal key size and efficient runtime for arbitrary secret keys, although Chillotti et al.’s [...] Read more.

Recently, Lee et al. introduced a novel blind rotation technique utilizing ring automorphisms also known as LMKCDEY. Among known prominent blind rotation methods, LMKCDEY stands out because of its minimal key size and efficient runtime for arbitrary secret keys, although Chillotti et al.’s approach, commonly referred to as CGGI, offers faster runtime when using binary or ternary secrets. In this paper, we propose an enhancement to LMKCDEY’s runtime by incorporating auxiliary keys that encrypt the negated values of secret key elements. Our method not only achieves faster execution than LMKCDEY but also maintains a smaller key size compared to the ternary version of CGGI. Moreover, the proposed technique is compatible with LMKCDEY with only minimal adjustments. Experimental results with OpenFHE demonstrate that our approach can improve bootstrapping runtime by 5–28%, depending on the chosen parameters. Full article

(This article belongs to the Special Issue New Advances in Applied Cryptography, Network Security and Data Privacy)

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17 pages, 690 KiB

Open AccessArticle

A Privacy-Preserving Electromagnetic-Spectrum-Sharing Trading Scheme Based on ABE and Blockchain

by Xing Pu, Ruixian Wang and Xin Lu

Mathematics 2024, 12(18), 2908; https://doi.org/10.3390/math12182908 - 18 Sep 2024

Viewed by 255

Abstract

The electromagnetic spectrum is a limited resource. With the widespread application of the electromagnetic spectrum in various fields, the contradiction between the demand for the electromagnetic spectrum and electromagnetic spectrum resources has become increasingly prominent. Spectrum sharing is an effective way to improve [...] Read more.

The electromagnetic spectrum is a limited resource. With the widespread application of the electromagnetic spectrum in various fields, the contradiction between the demand for the electromagnetic spectrum and electromagnetic spectrum resources has become increasingly prominent. Spectrum sharing is an effective way to improve the utilization of the electromagnetic spectrum. However, there are many challenges in existing distributed electromagnetic spectrum trading based on blockchain technology. Since a blockchain does not provide privacy protection, the risk of privacy leakage during the trading process makes electromagnetic spectrum owners unwilling to share. In addition, a blockchain only guarantees integrity, and the imperfect trading dispute resolution mechanism causes electromagnetic spectrum owners to be afraid to share. Therefore, we propose a privacy-preserving electromagnetic-spectrum-sharing trading scheme based on blockchain and ABE. The scheme not only designs an ABE fine-grained access control model in ciphertext form but also constructs a re-encryption algorithm that supports trading arbitration to achieve privacy protection for electromagnetic spectrum trading. Finally, we experimentally evaluated the efficiency of the proposed electromagnetic spectrum trading scheme. The experimental results show that the electromagnetic spectrum trading scheme we propose was highly efficient. Full article

(This article belongs to the Special Issue New Advances in Coding Theory and Cryptography, 2nd Edition)

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15 pages, 1428 KiB

Open AccessArticle

Incorporating Digital Footprints into Credit-Scoring Models through Model Averaging

by Linhui Wang, Jianping Zhu, Chenlu Zheng and Zhiyuan Zhang

Mathematics 2024, 12(18), 2907; https://doi.org/10.3390/math12182907 - 18 Sep 2024

Viewed by 268

Abstract

Digital footprints provide crucial insights into individuals’ behaviors and preferences. Their role in credit scoring is becoming increasingly significant. Therefore, it is crucial to combine digital footprint data with traditional data for personal credit scoring. This paper proposes a novel credit-scoring model. First, [...] Read more.

Digital footprints provide crucial insights into individuals’ behaviors and preferences. Their role in credit scoring is becoming increasingly significant. Therefore, it is crucial to combine digital footprint data with traditional data for personal credit scoring. This paper proposes a novel credit-scoring model. First, lasso-logistic regression is used to select key variables that significantly impact the prediction results. Then, digital footprint variables are categorized based on business understanding, and candidate models are constructed from various combinations of these groups. Finally, the optimal weight is selected by minimizing the Kullback–Leibler loss. Subsequently, the final prediction model is constructed. Empirical analysis validates the advantages and feasibility of the proposed method in variable selection, coefficient estimation, and predictive accuracy. Furthermore, the model-averaging method provides the weights for each candidate model, providing managerial implications to identify beneficial variable combinations for credit scoring. Full article

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25 pages, 1591 KiB

Open AccessArticle

An Attribute-Based End-to-End Policy-Controlled Signcryption Scheme for Secure Group Chat Communication

by Feng Yu, Linghui Meng, Xianxian Li, Daicen Jiang, Weidong Zhu and Zhihua Zeng

Mathematics 2024, 12(18), 2906; https://doi.org/10.3390/math12182906 - 18 Sep 2024

Viewed by 235

Abstract

Secure instant communication is an important topic of information security. A group chat is a highly convenient mode of instant communication. Increasingly, companies are adopting group chats as a daily office communication tool. However, a large volume of messages in group chat communication [...] Read more.

Secure instant communication is an important topic of information security. A group chat is a highly convenient mode of instant communication. Increasingly, companies are adopting group chats as a daily office communication tool. However, a large volume of messages in group chat communication can lead to message overload, causing group members to miss important information. Additionally, the communication operator’s server may engage in the unreliable behavior of stealing information from the group chat. To address these issues, this paper proposes an attribute-based end-to-end policy-controlled signcryption scheme, aimed at establishing a secure and user-friendly group chat communication mode. By using the linear secret sharing scheme (LSSS) with strong expressive power to construct the access structure in the signcryption technology, the sender can precisely control the recipients of the group chat information to avoid message overload. To minimize computational cost, a signcryption step with constant computational overhead is designed. Additionally, a message-sending mechanism combining “signcryption + encryption” is employed to prevent the operator server from maliciously stealing group chat information. Rigorous analysis shows that PCE-EtoE can resist adaptive chosen-ciphertext attacks under the standard model. Simulation results demonstrate that our theoretical derivation is correct, and that the PCE-EtoE scheme outperforms existing schemes in terms of computational cost, making it suitable for group chat communication. Full article

(This article belongs to the Special Issue Mathematical Methods Applied in Explainable Fake Multimedia Detection)

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17 pages, 5052 KiB

Open AccessArticle

A New Instance Segmentation Model for High-Resolution Remote Sensing Images Based on Edge Processing

by Xiaoying Zhang, Jie Shen, Huaijin Hu and Houqun Yang

Mathematics 2024, 12(18), 2905; https://doi.org/10.3390/math12182905 - 18 Sep 2024

Viewed by 263

Abstract

With the goal of addressing the challenges of small, densely packed targets in remote sensing images, we propose a high-resolution instance segmentation model named QuadTransPointRend Net (QTPR-Net). This model significantly enhances instance segmentation performance in remote sensing images. The model consists of two [...] Read more.

With the goal of addressing the challenges of small, densely packed targets in remote sensing images, we propose a high-resolution instance segmentation model named QuadTransPointRend Net (QTPR-Net). This model significantly enhances instance segmentation performance in remote sensing images. The model consists of two main modules: preliminary edge feature extraction (PEFE) and edge point feature refinement (EPFR). We also created a specific approach and strategy named TransQTA for edge uncertainty point selection and feature processing in high-resolution remote sensing images. Multi-scale feature fusion and transformer technologies are used in QTPR-Net to refine rough masks and fine-grained features for selected edge uncertainty points while balancing model size and accuracy. Based on experiments performed on three public datasets: NWPU VHR-10, SSDD, and iSAID, we demonstrate the superiority of QTPR-Net over existing approaches. Full article

(This article belongs to the Special Issue Advances in Computer Vision and Machine Learning, 2nd Edition)

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