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Volume 12
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Mathematics, Volume 12, Issue 13 (July-1 2024) – 143 articles

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22 pages, 3812 KiB  
Article
Enhancing Fault Diagnosis in Mechanical Systems with Graph Neural Networks Addressing Class Imbalance
by Wenhao Lu, Wei Wang, Xuefei Qin and Zhiqiang Cai
Mathematics 2024, 12(13), 2064; https://doi.org/10.3390/math12132064 (registering DOI) - 1 Jul 2024
Abstract
Recent advancements in intelligent diagnosis rely heavily on data-driven methods. However, these methods often encounter challenges in adequately addressing class imbalances in the context of the fault diagnosis of mechanical systems. This paper proposes the MeanRadius-SMOTE graph neural network (MRS-GNN), a novel framework [...] Read more.
Recent advancements in intelligent diagnosis rely heavily on data-driven methods. However, these methods often encounter challenges in adequately addressing class imbalances in the context of the fault diagnosis of mechanical systems. This paper proposes the MeanRadius-SMOTE graph neural network (MRS-GNN), a novel framework designed to synthesize node representations in GNNs to effectively mitigate this issue. Through integrating the MeanRadius-SMOTE oversampling technique into the GNN architecture, the MRS-GNN demonstrates an enhanced capability to learn from under-represented classes while preserving the intrinsic connectivity patterns of the graph data. Comprehensive testing on various datasets demonstrates the superiority of the MRS-GNN over traditional methods in terms of classification accuracy and handling class imbalances. The experimental results on three publicly available fault diagnosis datasets show that the MRS-GNN improves the classification accuracy by 18 percentage points compared to some popular methods. Furthermore, the MRS-GNN exhibits a higher robustness in extreme imbalance scenarios, achieving an AUC-ROC value of 0.904 when the imbalance rate is 0.4. This framework not only enhances the fault diagnosis accuracy but also offers a scalable solution applicable to diverse mechanical and complex systems, demonstrating its utility and adaptability in various operating environments and fault conditions. Full article
(This article belongs to the Special Issue System Reliability and Quality Management in Industrial Engineering, 2nd Edition)
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26 pages, 12239 KiB  
Article
Deep Learning-Based Intelligent Diagnosis of Lumbar Diseases with Multi-Angle View of Intervertebral Disc
by Kaisi (Kathy) Chen, Lei Zheng, Honghao Zhao and Zihang Wang
Mathematics 2024, 12(13), 2062; https://doi.org/10.3390/math12132062 (registering DOI) - 1 Jul 2024
Abstract
The diagnosis of degenerative lumbar spine disease mainly relies on clinical manifestations and imaging examinations. However, the clinical manifestations are sometimes not obvious, and the diagnosis of medical imaging is usually time-consuming and highly relies on the doctor’s personal experiences. Therefore, a smart [...] Read more.
The diagnosis of degenerative lumbar spine disease mainly relies on clinical manifestations and imaging examinations. However, the clinical manifestations are sometimes not obvious, and the diagnosis of medical imaging is usually time-consuming and highly relies on the doctor’s personal experiences. Therefore, a smart diagnostic technology that can assist doctors in manual diagnosis has become particularly urgent. Taking advantage of the development of artificial intelligence, a series of solutions have been proposed for the diagnosis of spinal diseases by using deep learning methods. The proposed methods produce appealing results, but the majority of these approaches are based on sagittal and axial images separately, which limits the capability of different deep learning methods due to the insufficient use of data. In this article, we propose a two-stage classification process that fully utilizes image data. In particular, in the first stage, we used the Mask RCNN model to identify the lumbar spine in the spine image, locate the position of the vertebra and disc, and complete rough classification. In the fine classification stage, a multi-angle view of the intervertebral disc is generated by splicing the sagittal and axial slices of the intervertebral disc up and down based on the key position identified in the first stage, which provides more pieces of information to the deep learning methods for classification. The experimental results reveal substantial performance enhancements with the synthesized multi-angle view, achieving an F1 score of 96.67%. This represents a performance increase of approximately 15% over the sagittal images at 84.48% and nearly 14% over the axial images at 83.15%. This indicates that the proposed paradigm is feasible and more effective in identifying spinal-related degenerative diseases through medical images. Full article
(This article belongs to the Special Issue Algorithms and Models for Bioinformatics and Biomedical Applications)
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9 pages, 795 KiB  
Article
The Prediction of Stability in the Time-Delayed Milling Process of Spiral Bevel Gears Based on an Improved Full-Discretization Method
by Chong Tian, Taiyong Wang and Ying Tian
Mathematics 2024, 12(13), 2061; https://doi.org/10.3390/math12132061 (registering DOI) - 1 Jul 2024
Abstract
Spiral bevel gear drives are widely used in mechanical transmission devices due to their compact structure, smooth transmission, and cost-effectiveness. With the continuous improvement in mechanical product quality, higher and higher requirements are set for the precision, smoothness, and power density of gear [...] Read more.
Spiral bevel gear drives are widely used in mechanical transmission devices due to their compact structure, smooth transmission, and cost-effectiveness. With the continuous improvement in mechanical product quality, higher and higher requirements are set for the precision, smoothness, and power density of gear transmission devices. Chatter can lead to poor workpiece surface finish on spiral bevel gears, excessive tool wear, and even damage to machine tools. Therefore, the effective prediction of milling chatter during the processing of spiral bevel gears is essential. Regenerative chatter is one of the most fundamental types of vibration in machining processes. This paper presents an improved fully discrete algorithm for predicting the stability of time-delayed cutting in the milling process of spiral bevel gears. The method is validated using single- and double-degree-of-freedom models, demonstrating its accuracy and computational efficiency. The results show that the proposed method improves computational efficiency while ensuring accuracy. Full article
(This article belongs to the Section Engineering Mathematics)
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10 pages, 279 KiB  
Article
Studies on the Marchenko–Pastur Law
by Ayed. R. A. Alanzi, Ohud A. Alqasem, Maysaa Elmahi Abd Elwahab and Raouf Fakhfakh
Mathematics 2024, 12(13), 2060; https://doi.org/10.3390/math12132060 (registering DOI) - 1 Jul 2024
Abstract
In free probability, the theory of Cauchy–Stieltjes Kernel (CSK) families has recently been introduced. This theory is about a set of probability measures defined using the Cauchy kernel similarly to natural exponential families in classical probability that are defined by means of the [...] Read more.
In free probability, the theory of Cauchy–Stieltjes Kernel (CSK) families has recently been introduced. This theory is about a set of probability measures defined using the Cauchy kernel similarly to natural exponential families in classical probability that are defined by means of the exponential kernel. Within the context of CSK families, this article presents certain features of the Marchenko–Pastur law based on the Fermi convolution and the t-deformed free convolution. The Marchenko–Pastur law holds significant theoretical and practical implications in various fields, particularly in the analysis of random matrices and their applications in statistics, signal processing, and machine learning. In the specific context of CSK families, our study of the Marchenko–Pastur law is summarized as follows: Let K+(μ)={Qmμ(dx);m∈(m0μ,m+μ)} be the CSK family generated by a non-degenerate probability measure μ with support bounded from above. Denote by Qmμ•s the Fermi convolution power of order s>0 of the measure Qmμ. We prove that if Qmμ•s∈K+(μ), then μ is of the Marchenko–Pastur type law. The same result is obtained if we replace the Fermi convolution • with the t-deformed free convolution t. Full article
(This article belongs to the Section Probability and Statistics)
20 pages, 12301 KiB  
Article
High-Precision Drilling by Anchor-Drilling Robot Based on Hybrid Visual Servo Control in Coal Mine
by Mengyu Lei, Xuhui Zhang, Wenjuan Yang, Jicheng Wan, Zheng Dong, Chao Zhang and Guangming Zhang
Mathematics 2024, 12(13), 2059; https://doi.org/10.3390/math12132059 (registering DOI) - 1 Jul 2024
Abstract
Rock bolting is a commonly used method for stabilizing the surrounding rock in coal-mine roadways. It involves installing rock bolts after drilling, which penetrate unstable rock layers, binding loose rocks together, enhancing the stability of the surrounding rock, and controlling its deformation. Although [...] Read more.
Rock bolting is a commonly used method for stabilizing the surrounding rock in coal-mine roadways. It involves installing rock bolts after drilling, which penetrate unstable rock layers, binding loose rocks together, enhancing the stability of the surrounding rock, and controlling its deformation. Although recent progress in drilling and anchoring equipment has significantly enhanced the efficiency of roof support in coal mines and improved safety measures, how to deal with drilling rigs’ misalignment with the through-hole center remains a big issue, which may potentially compromise the quality of drilling and consequently affect the effectiveness of bolt support or even result in failure. To address this challenge, this article presents a robotic teleoperation system alongside a hybrid visual servo control strategy. Addressing the demand for high precision and efficiency in aligning the drilling rigs with the center of the drilling hole, a hybrid control strategy is introduced combining position-based and image-based visual servo control. The former facilitates an effective approach to the target area, while the latter ensures high-precision alignment with the center of the drilling hole. The robot teleoperation system employs the binocular vision measurement system to accurately determine the position and orientation of the drilling-hole center, which serves as the designated target position for the drilling rig. Leveraging the displacement and angle sensor information installed on each joint of the manipulator, the system utilizes the kinematic model of the manipulator to compute the spatial position of the end-effector. It dynamically adjusts the spatial pose of the end-effector in real time, aligning it with the target position relative to its current location. Additionally, it utilizes monocular vision information to fine-tune the movement speed and direction of the end-effector, ensuring rapid and precise alignment with the target drilling-hole center. Experimental results demonstrate that this method can control the maximum alignment error within 7 mm, significantly enhancing the alignment accuracy compared to manual control. Compared with the manual control method, the average error of this method is reduced by 41.2%, and the average duration is reduced by 4.3 s. This study paves a new path for high-precision drilling and anchoring of tunnel roofs, thereby improving the quality and efficiency of roof support while mitigating the challenges associated with significant errors and compromised safety during manual control processes. Full article
(This article belongs to the Special Issue Mathematics for Visual Computing: Acquisition, Processing, Analysis and Rendering of Visual Information)
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12 pages, 257 KiB  
Article
Suzuki–Ćirić-Type Nonlinear Contractions Employing a Locally ζ-Transitive Binary Relation with Applications to Boundary Value Problems
by Doaa Filali and Faizan Ahmad Khan
Mathematics 2024, 12(13), 2058; https://doi.org/10.3390/math12132058 (registering DOI) - 30 Jun 2024
Abstract
This article is devoted to enhancing a class of generalized Suzuki-type nonlinear contractions following Pant to a class of Suzuki–Ćirić-type nonlinear contractions via comparison functions via a locally ζ-transitive relation and implemented the same to ascertain certain fixed-point results. The outcomes presented [...] Read more.
This article is devoted to enhancing a class of generalized Suzuki-type nonlinear contractions following Pant to a class of Suzuki–Ćirić-type nonlinear contractions via comparison functions via a locally ζ-transitive relation and implemented the same to ascertain certain fixed-point results. The outcomes presented herewith unify and generalize a few existing findings. An illustrative examples is offered to explain our findings. Our outcomes assist us in figuring out the unique solution to a boundary value problem. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications II)
22 pages, 1738 KiB  
Article
Improving Graph Collaborative Filtering from the Perspective of User–Item Interaction Directly Using Contrastive Learning
by Jifeng Dong, Yu Zhou, Shufeng Hao, Ding Feng, Haixia Zheng and Zhenhuan Xu
Mathematics 2024, 12(13), 2057; https://doi.org/10.3390/math12132057 (registering DOI) - 30 Jun 2024
Abstract
Graph contrastive learning has demonstrated significant superiority for collaborative filtering. These methods typically use augmentation technology to generate contrastive views, and then train graph neural networks with contrastive learning as an auxiliary task. Although these methods are very effective, they do not consider [...] Read more.
Graph contrastive learning has demonstrated significant superiority for collaborative filtering. These methods typically use augmentation technology to generate contrastive views, and then train graph neural networks with contrastive learning as an auxiliary task. Although these methods are very effective, they do not consider using contrastive learning from the perspective of user–item interaction. As a result, they do not fully leverage the potential of contrastive learning. It is well known that contrastive learning can maximize the consistency of positive pairs and minimize the agreement of negative pairs. Collaborative filtering expects high consistency between users and the items they like and low consistency between users and the items they dislike. If we treat the items that users like as positive examples and the items they dislike as negative examples, contrastive learning can work very well with the goal of collaborative filtering. Based on the above understanding, we propose a new objective function called DCL loss, which improves graph collaborative filtering from the perspective of user–item interaction when Directly using Contrastive Learning. Extensive experiments have shown that when a model adopts DCL loss as its objective function, both its recommendation performance and training efficiency exhibit significant improvements. Full article
24 pages, 1324 KiB  
Article
Dual-Objective Reinforcement Learning-Based Adaptive Traffic Signal Control for Decarbonization and Efficiency Optimization
by Gongquan Zhang, Fangrong Chang, Helai Huang and Zilong Zhou
Mathematics 2024, 12(13), 2056; https://doi.org/10.3390/math12132056 (registering DOI) - 30 Jun 2024
Abstract
To improve traffic efficiency, adaptive traffic signal control (ATSC) systems have been widely developed. However, few studies have proactively optimized the air environmental issues in the development of ATSC. To fill this research gap, this study proposes an optimized ATSC algorithm to take [...] Read more.
To improve traffic efficiency, adaptive traffic signal control (ATSC) systems have been widely developed. However, few studies have proactively optimized the air environmental issues in the development of ATSC. To fill this research gap, this study proposes an optimized ATSC algorithm to take into consideration both traffic efficiency and decarbonization. The proposed algorithm is developed based on the deep reinforcement learning (DRL) framework with dual goals (DRL-DG) for traffic control system optimization. A novel network structure combining Convolutional Neural Networks and Long Short-Term Memory Networks is designed to map the intersection traffic state to a Q-value, accelerating the learning process. The reward mechanism involves a multi-objective optimization function, employing the entropy weight method to balance the weights among dual goals. Based on a representative intersection in Changsha, Hunan Province, China, a simulated intersection scenario is constructed to train and test the proposed algorithm. The result shows that the ATSC system optimized by the proposed DRL-DG results in a reduction of more than 71% in vehicle waiting time and 46% in carbon emissions compared to traditional traffic signal control systems. It converges faster and achieves a balanced dual-objective optimization compared to the prevailing DRL-based ATSC. Full article
(This article belongs to the Special Issue Advances in Perception, Control and Optimization Methods in Intelligent Transportation Systems)
26 pages, 882 KiB  
Article
Reservoir Slope Stability Analysis under Dynamic Fluctuating Water Level Using Improved Radial Movement Optimisation (IRMO) Algorithm
by Liangxing Jin, Chunwa Luo, Junjie Wei and Pingting Liu
Mathematics 2024, 12(13), 2055; https://doi.org/10.3390/math12132055 (registering DOI) - 30 Jun 2024
Abstract
External water level fluctuation is the major trigger causing reservoir slope failure, and therefore it is of great significance for the safety assessment and corresponding safety management of reservoir slopes. In this work, the seepage effects stemming from fluctuating external water levels are [...] Read more.
External water level fluctuation is the major trigger causing reservoir slope failure, and therefore it is of great significance for the safety assessment and corresponding safety management of reservoir slopes. In this work, the seepage effects stemming from fluctuating external water levels are given special analysis and then incorporated into the rigorous limit equilibrium method for assessing the stability of reservoir slope. An advanced metaheuristic intelligent algorithm, the improved radial movement optimisation (IRMO), is introduced to efficiently locate the critical failure surface and associated minimum factor of safety. Consequently, the effect of water level fluctuation directions, changing rates, and soil permeability coefficient on reservoir stability are investigated by the proposed method in three cases. It is found that the clay slope behaved more sensitively in stability fluctuation compared to the silty slope. With the dropping of external water, the higher dropping speed and lower soil permeability coefficient have worse impacts on the slope stability. The critical pool level during reservoir water dropping could be effectively obtained through the analysis. The results indicate that the IRMO-based method herein could effectively realise the stability analysis of the reservoir slope in a dynamic fluctuating reservoir water level, which could provide applicable technology for following preventions. Full article
(This article belongs to the Topic Physical Monitoring and Healthy Controlling of Geotechnical Engineering)
29 pages, 1442 KiB  
Article
Optimal Markup Pricing Strategies in a Green Supply Chain under Different Power Structures
by Senbiao Li and Shuxiao Sun
Mathematics 2024, 12(13), 2054; https://doi.org/10.3390/math12132054 (registering DOI) - 30 Jun 2024
Abstract
Fixed-dollar and flexible markups are two markup pricing strategies commonly adopted in the retail industry, but their impacts on green behaviors of enterprises remain unknown. This paper investigates how the two markup pricing strategies influence firms’ managerial behaviors in a green supply chain, [...] Read more.
Fixed-dollar and flexible markups are two markup pricing strategies commonly adopted in the retail industry, but their impacts on green behaviors of enterprises remain unknown. This paper investigates how the two markup pricing strategies influence firms’ managerial behaviors in a green supply chain, considering three power structures: Manufacturer Stackelberg, Retailer Stackelberg, and Vertical Nash. We find that the retailer’s pricing strategy choice is jointly affected by power structures and consumer sensitivity to product green levels. Particularly under Manufacturer Stackelberg, the fixed-markup strategy makes the retailer earn a higher profit. However, under Vertical Nash, the retailer’s pricing strategy depends on consumer sensitivity to green levels. When consumers are less sensitive to green levels, a flexible-dollar markup strategy is more profitable for the retailer; otherwise, the fixed-markup strategy is better. Additionally, for the manufacturer, the green levels of the product and the firm profit are always higher when the retailer adopts a fixed-dollar markup strategy under Manufacturer Stackelberg and Vertical Nash. Interestingly, if the retailer adopts a flexible-dollar markup strategy, the manufacturer has the “late-mover advantage” only when consumer sensitivity to the green level is high. Furthermore, the supply chain achieves the highest profit when the manufacturer acts as the leader under the fixed markup strategy. Full article
(This article belongs to the Special Issue Mathematical Modelling and Optimization of Service Supply Chain, 2nd Edition)
21 pages, 2072 KiB  
Article
Dynamical Behaviors and Abundant New Soliton Solutions of Two Nonlinear PDEs via an Efficient Expansion Method in Industrial Engineering
by Ibrahim Alraddadi, M. Akher Chowdhury, M. S. Abbas, K. El-Rashidy, J. R. M. Borhan, M. Mamun Miah and Mohammad Kanan
Mathematics 2024, 12(13), 2053; https://doi.org/10.3390/math12132053 (registering DOI) - 30 Jun 2024
Abstract
In this study, we discuss the dynamical behaviors and extract new interesting wave soliton solutions of the two significant well-known nonlinear partial differential equations (NPDEs), namely, the Korteweg–de Vries equation (KdVE) and the Jaulent–Miodek hierarchy equation (JMHE). This investigation has applications in pattern [...] Read more.
In this study, we discuss the dynamical behaviors and extract new interesting wave soliton solutions of the two significant well-known nonlinear partial differential equations (NPDEs), namely, the Korteweg–de Vries equation (KdVE) and the Jaulent–Miodek hierarchy equation (JMHE). This investigation has applications in pattern recognition, fluid dynamics, neural networks, mechanical systems, ecological systems, control theory, economic systems, bifurcation analysis, and chaotic phenomena. In addition, bifurcation analysis and the chaotic behavior of the KdVE and JMHE are the main issues of the present research. As a result, in this study, we obtain very effective advanced exact traveling wave solutions with the aid of the proposed mathematical method, and the solutions involve rational functions, hyperbolic functions, and trigonometric functions that play a vital role in illustrating and developing the models involving the KdVE and the JMHE. These new exact wave solutions lead to utilizing real problems and give an advanced explanation of our mentioned mathematical models that we did not yet have. Some of the attained solutions of the two equations are graphically displayed with 3D, 2D, and contour panels of different shapes, like periodic, singular periodic, kink, anti-kink, bell, anti-bell, soliton, and singular soliton wave solutions. The solutions obtained in this study of our considered equations can lead to the acceptance of our proposed method, effectively utilized to investigate the solutions for the mathematical models of various important complex problems in natural science and engineering. Full article
(This article belongs to the Special Issue Exact Solutions and Numerical Solutions of Differential Equations)
25 pages, 749 KiB  
Article
A Model for Developing a Mobile Payment Service Framework
by Amy H. I. Lee and He-Yau Kang
Mathematics 2024, 12(13), 2052; https://doi.org/10.3390/math12132052 (registering DOI) - 30 Jun 2024
Abstract
The rise of wireless communication has spurred the global adoption of mobile payment services, a trend that is significantly reducing the use of cash. This shift, driven by new technologies and lifestyle changes, not only presents opportunities for businesses but also enhances consumers’ [...] Read more.
The rise of wireless communication has spurred the global adoption of mobile payment services, a trend that is significantly reducing the use of cash. This shift, driven by new technologies and lifestyle changes, not only presents opportunities for businesses but also enhances consumers’ daily activities. Consumers’ and businesses’ willingness to adopt mobile payment services has increased due to factors such as easier access to new technologies, convenience, changing lifestyle choices, and economic conditions. Despite challenges such as limited access to technology, security concerns, and high transaction fees, the potential benefits of mobile payment services are promising. Therefore, this research aims to construct a suitable model for developing a mobile payment service framework that both consumers and businesses are willing to adopt. The proposed model integrates the Delphi method, interpretive structural modeling (ISM), quality function deployment (QFD), an analytic network process (ANP), and fuzzy set theory. To demonstrate the practical application of the model, a case study of developing a mobile payment service framework is presented, showcasing how the model can be used to address real-world challenges and enhance the adoption of mobile payment services. The case study results show that ease of use, system and service quality, and reliability are the most important customer requirements, and encryption, edge computing, authentication, and interoperability are the most important engineering characteristics. Full article
(This article belongs to the Special Issue Fuzzy Applications in Industrial Engineering, 3rd Edition)
17 pages, 307 KiB  
Article
An NTRU-like Message Recoverable Signature Algorithm
by Tingle Shen, Li Miao, Bin Hua and Shuai Li
Mathematics 2024, 12(13), 2051; https://doi.org/10.3390/math12132051 (registering DOI) - 30 Jun 2024
Abstract
An important feature of Nyberg-Rueppel type digital signature algorithms is message recovery, this signature algorithm can recover the original information from the signature directly by the verifier in the verification phase after signing the message. However, this algorithm is currently vulnerable to quantum [...] Read more.
An important feature of Nyberg-Rueppel type digital signature algorithms is message recovery, this signature algorithm can recover the original information from the signature directly by the verifier in the verification phase after signing the message. However, this algorithm is currently vulnerable to quantum attacks and its security cannot be guaranteed. Number Theory Research Unit (NTRU) is an efficient public-key cryptosystem and is considered to be one of the best quantum-resistant encryption schemes. This paper proposes an NTRU-like message recoverable signature algorithm to meet the key agreement requirements in the post-quantum world. This algorithm, designed for the Internet of Things (IoT), constructs a secure system using the Group-Based Message Recoverable Signature Algorithm (NR-GTRU), by integrating a Group-Based NTRU-Like Public-Key Cryptosystem (GTRU) with an efficient Nyberg-Rueppel type of NTRU digital signature algorithm (NR-NTRU). This signature algorithm, resistant to quantum algorithm attacks, offers higher security at the cost of a slight efficiency reduction compared to traditional NTRU signature algorithms, and features Nyberg-Rueppel message recovery, making it well-suited for IoT applications. Full article
(This article belongs to the Topic Recent Advances in Security, Privacy, and Trust)
19 pages, 342 KiB  
Article
On a Local and Nonlocal Second-Order Boundary Value Problem with In-Homogeneous Cauchy–Neumann Boundary Conditions—Applications in Engineering and Industry
by Tudor Barbu, Alain Miranville and Costică Moroşanu
Mathematics 2024, 12(13), 2050; https://doi.org/10.3390/math12132050 (registering DOI) - 30 Jun 2024
Viewed by 120
Abstract
A qualitative study for a second-order boundary value problem with local or nonlocal diffusion and a cubic nonlinear reaction term, endowed with in-homogeneous Cauchy–Neumann (Robin) boundary conditions, is addressed in the present paper. Provided that the initial data meet appropriate regularity conditions, the [...] Read more.
A qualitative study for a second-order boundary value problem with local or nonlocal diffusion and a cubic nonlinear reaction term, endowed with in-homogeneous Cauchy–Neumann (Robin) boundary conditions, is addressed in the present paper. Provided that the initial data meet appropriate regularity conditions, the existence of solutions to the nonlocal problem is given at the beginning in a function space suitably chosen. Next, under certain assumptions on the known data, we prove the well posedness (the existence, a priori estimates, regularity, uniqueness) of the classical solution to the local problem. At the end, we present a particularization of the local and nonlocal problems, with applications for image processing (reconstruction, segmentation, etc.). Some conclusions are given, as well as new directions to extend the results and methods presented in this paper. Full article
(This article belongs to the Special Issue Mathematical Modeling in Industrial Engineering and Electrical Engineering, 2nd Edition)
20 pages, 773 KiB  
Article
Fractional Adaptive Resonance Theory (FRA-ART): An Extension for a Stream Clustering Method with Enhanced Data Representation
by Yingwen Zhu, Ping Li, Qian Zhang, Yi Zhu and Jun Yang
Mathematics 2024, 12(13), 2049; https://doi.org/10.3390/math12132049 (registering DOI) - 30 Jun 2024
Viewed by 127
Abstract
Clustering data streams has become a hot topic and has been extensively applied to many real-world applications. Compared with traditional clustering, data stream clustering is more challenging. Adaptive Resonance Theory (ART) is a powerful (online) clustering method, it can automatically adjust to learn [...] Read more.
Clustering data streams has become a hot topic and has been extensively applied to many real-world applications. Compared with traditional clustering, data stream clustering is more challenging. Adaptive Resonance Theory (ART) is a powerful (online) clustering method, it can automatically adjust to learn both abstract and concrete information, and can respond to arbitrarily large non-stationary databases while having fewer parameters, low computational complexity, and less sensitivity to noise, but its limited feature representation hinders its application to complex data streams. In this paper, considering its advantages and disadvantages, we present its flexible extension for stream clustering, called fractional adaptive resonance theory (FRA-ART). FRA-ART enhances data representation by fractionally exponentiating input features using self-interactive basis functions (SIBFs) and incorporating feature interaction through cross-interactive basis functions (CIBFs) at the cost only of introducing an additionally adjustable fractional order. Both SIBFs and CIBFs can be precomputed using existing algorithms, making FRA-ART easily adaptable to any ART variant. Finally, comparative experiments on five data stream datasets, including artificial and real-world datasets, demonstrate FRA-ART’s superior robustness and comparable or improved performance in terms of accuracy, normalized mutual information, rand index, and cluster stability compared to ART and the state-of-the-art G-Stream algorithm. Full article
(This article belongs to the Special Issue Machine Learning Methods and Mathematical Modeling with Applications)
21 pages, 3616 KiB  
Article
Deep Smooth Random Sampling and Association Attention for Air Quality Anomaly Detection
by Peng Wang, Minhang Li, Xiaoying Zhi, Xiliang Liu, Zhixiang He, Ziyue Di, Xiang Zhu, Yanchen Zhu, Wenqiong Cui, Wenyu Deng and Wenhan Fan
Mathematics 2024, 12(13), 2048; https://doi.org/10.3390/math12132048 (registering DOI) - 30 Jun 2024
Viewed by 132
Abstract
Real-time monitoring and timely warning of air quality are vital components of building livable cities and implementing the “Healthy China” strategy. Real-time, efficient, and accurate detection of air quality anomalies holds great significance. However, almost all existing methods for air quality anomaly detection [...] Read more.
Real-time monitoring and timely warning of air quality are vital components of building livable cities and implementing the “Healthy China” strategy. Real-time, efficient, and accurate detection of air quality anomalies holds great significance. However, almost all existing methods for air quality anomaly detection often overlook the imbalanced distribution of data. In addition, many traditional methods cannot learn both pointwise representation and pairwise association, so they cannot solve complex features. This study proposes an anomaly detection method for air quality monitoring based on Deep Smooth Random Sampling and Association Attention in Transformer (DSRS-AAT). Firstly, based on the third geographical law, the more similar the geographical environment, the closer the geographical target features are. We cluster sites according to the surrounding geographic features to fully explore latent feature associations. Then, we employ Deep Smooth Random Sampling to rebalance the air quality datasets. Meanwhile, the Transformer with association attention considers both prior associations and series associations to distinguish anomaly patterns. Experiments are carried out with real data from 95 monitoring stations in Haikou City, China. Final results demonstrate that the proposed DSRS-AAT improves the effectiveness of anomaly detection and provides interpretability analysis for traceability, owing to a significant improvement with the baselines (OmniAnomaly, THOC, etc.). The proposed method effectively enhances the effectiveness of air quality anomaly detection and provides a reference value for real-time monitoring and early warning of urban air quality. Full article
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20 pages, 459 KiB  
Article
Optimal Reinsurance and Derivative-Based Investment Decisions for Insurers with Mean-Variance Preference
by Haiying Zhou and Huainian Zhu
Mathematics 2024, 12(13), 2047; https://doi.org/10.3390/math12132047 (registering DOI) - 30 Jun 2024
Abstract
In our study, we investigate reinsurance issues and optimal investment related to derivatives trading for a mean-variance insurer, employing game theory. Our primary objective is to identify strategies that are time-consistent. In particular, the insurer has the flexibility to purchase insurance in proportion [...] Read more.
In our study, we investigate reinsurance issues and optimal investment related to derivatives trading for a mean-variance insurer, employing game theory. Our primary objective is to identify strategies that are time-consistent. In particular, the insurer has the flexibility to purchase insurance in proportion to its needs, explore new business, and engage in capital market investments. This is under the assumption that insurance companies’surplus capital adheres to the classical Cramér-Lundberg model. The capital market is made up of risk-free bonds, equities, and derivatives, with pricing dependent on the underlying stock’s basic price and volatility. To obtain the most profitable expressions and functions for the associated investment strategies and time guarantees, we solve a system of expanded Hamilton–Jacobi–Bellman equations. In addition, we delve into scenarios involving optimal investment and reinsurance issues with no derivatives trading. In the end, we present a few numerical instances to display our findings, demonstrating that the efficient frontier in the case of derivative trading surpasses that in scenarios where derivative trading is absent. Full article
(This article belongs to the Special Issue Stochastic Optimal Control in Finance)
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12 pages, 594 KiB  
Article
Edge of Chaos in Integro-Differential Model of Nerve Conduction
by Ravi Agarwal, Alexander Domoshnitsky, Angela Slavova and Ventsislav Ignatov
Mathematics 2024, 12(13), 2046; https://doi.org/10.3390/math12132046 (registering DOI) - 30 Jun 2024
Viewed by 115
Abstract
In this paper, we consider an integro-differential model of nerve conduction which presents the propagation of impulses in the nerve’s membranes. First, we approximate the original problem via cellular nonlinear networks (CNNs). The dynamics of the CNN model is investigated by means of [...] Read more.
In this paper, we consider an integro-differential model of nerve conduction which presents the propagation of impulses in the nerve’s membranes. First, we approximate the original problem via cellular nonlinear networks (CNNs). The dynamics of the CNN model is investigated by means of local activity theory. The edge of chaos domain of the parameter set is determined in the low-dimensional case. Computer simulations show the bifurcation diagram of the model and the dynamic behavior in the edge of chaos region. Moreover, stabilizing control is applied in order to stabilize the chaotic behavior of the model under consideration to the solutions related to the original behavior of the system. Full article
(This article belongs to the Section Difference and Differential Equations)
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14 pages, 886 KiB  
Article
Applying the Laplace Transform Procedure, Testing Exponentiality against the NBRUmgf Class
by Naglaa A. Hassan, Mayar M. Said, Rasha Abd El-Wahab Attwa and Taha Radwan
Mathematics 2024, 12(13), 2045; https://doi.org/10.3390/math12132045 (registering DOI) - 30 Jun 2024
Viewed by 146
Abstract
This paper addresses a hypothesis testing problem for comparing exponentially distributed data against a new class termed “New Better than Renewal Used in Moment Generating Function” (NBRUmgf). A measure of departure from exponentiality is constructed [...] Read more.
This paper addresses a hypothesis testing problem for comparing exponentially distributed data against a new class termed “New Better than Renewal Used in Moment Generating Function” (NBRUmgf). A measure of departure from exponentiality is constructed using the Laplace transform, followed by the development of a U-statistic-based test for the hypothesis. Additionally, a test based on the goodness of fit approach is examined as a special case. The asymptotic normality of the proposed statistic is introduced, and Pitman’s asymptotic efficiency of the two tests is computed and compared with other tests. Percentiles of the test statistics are computed for certain sample sizes in the case of complete data, and the powers of the tests are computed for popular reliability distributions. Finally, practical applications of the proposed tests are demonstrated in multiple cases. Full article
(This article belongs to the Special Issue Parametric and Nonparametric Statistics: From Theory to Applications)
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13 pages, 627 KiB  
Article
Torricelli’s Law in Fractal Space–Time Continuum
by Didier Samayoa, Liliana Alvarez-Romero, José Alfredo Jiménez-Bernal, Lucero Damián Adame, Andriy Kryvko and Claudia del C. Gutiérrez-Torres
Mathematics 2024, 12(13), 2044; https://doi.org/10.3390/math12132044 (registering DOI) - 30 Jun 2024
Viewed by 112
Abstract
A new formulation of Torricelli’s law in a fractal space–time continuum is developed to compute the water discharge in fractal reservoirs. Fractal Torricelli’s law is obtained by applying fractal continuum calculus concepts using local fractional differential operators. The model obtained can be used [...] Read more.
A new formulation of Torricelli’s law in a fractal space–time continuum is developed to compute the water discharge in fractal reservoirs. Fractal Torricelli’s law is obtained by applying fractal continuum calculus concepts using local fractional differential operators. The model obtained can be used to describe the behavior of real flows, considering the losses in non-conventional reservoirs, taking into account two additional fractal parameters α and β in the spatial and temporal fractal continuum derivatives, respectively. This model is applied to the flows in reservoirs with structures of three-dimensional deterministic fractals, such as inverse Menger sponge, Sierpinski cube, and Cantor dust. The results of the level water discharge H(t) are presented as a curve series, showing the impact and influence of fluid flow in naturally fractured reservoirs that posses self-similar properties. Full article
(This article belongs to the Special Issue Advances in Fractional Operators and Their Applications in Physical Sciences)
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11 pages, 311 KiB  
Article
A Matrix Approach to Vertex-Degree-Based Topological Indices
by Roberto Cruz, Carlos Espinal and Juan Rada
Mathematics 2024, 12(13), 2043; https://doi.org/10.3390/math12132043 (registering DOI) - 30 Jun 2024
Viewed by 104
Abstract
A VDB (vertex-degree-based) topological index over a set of digraphs H is a function φ:H→R, defined for each H∈H as [...] Read more.
A VDB (vertex-degree-based) topological index over a set of digraphs H is a function φ:H→R, defined for each H∈H as φH=12∑uv∈Eφdu+dv−, where E is the arc set of H, du+ and dv− denote the out-degree and in-degree of vertices u and v respectively, and φij=f(i,j) for an appropriate real symmetric bivariate function f. It is our goal in this article to introduce a new approach where we base the concept of VDB topological index on the space of real matrices instead of the space of symmetric real functions of two variables. We represent a digraph H by the p×p matrix αH, where αHij is the number of arcs uv such that du+=i and dv−=j, and p is the maximum value of the in-degrees and out-degrees of H. By fixing a p×p matrix φ, a VDB topological index of H is defined as the trace of the matrix φTα(H). We show that this definition coincides with the previous one when φ is a symmetric matrix. This approach allows considering nonsymmetric matrices, which extends the concept of a VDB topological index to nonsymmetric bivariate functions. Full article
(This article belongs to the Special Issue Graph Theory and Applications, 2nd Edition)
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10 pages, 219 KiB  
Article
Additive Results of Group Inverses in Banach Algebras
by Dayong Liu and Huanyin Chen
Mathematics 2024, 12(13), 2042; https://doi.org/10.3390/math12132042 (registering DOI) - 30 Jun 2024
Viewed by 123
Abstract
In this paper, we present new presentations of group inverses for the sum of two group invertible elements in a Banach algebra. We then apply these results to block complex matrices. The group invertibility of certain block complex matrices is thereby obtained. Full article
(This article belongs to the Section Algebra, Geometry and Topology)
22 pages, 2334 KiB  
Article
Private Partner Prioritization for Public–Private Partnership Contracts in a Brazilian Water Company Using a Multi-Criteria Decision Aid Method
by Thaís Lima Corrêa and Danielle Costa Morais
Mathematics 2024, 12(13), 2041; https://doi.org/10.3390/math12132041 (registering DOI) - 30 Jun 2024
Viewed by 141
Abstract
Public–private partnerships (PPPs) are long-term contracts between government entities and private companies, and are increasingly being adopted in developing countries due to the large need for investments in sectors such as water and sewerage and also in order to benefit from the experience [...] Read more.
Public–private partnerships (PPPs) are long-term contracts between government entities and private companies, and are increasingly being adopted in developing countries due to the large need for investments in sectors such as water and sewerage and also in order to benefit from the experience and to have access to the resources and technology of the private sector. Prioritizing the private party of the contract becomes a complex decision due to the characteristics of PPP contracts, and a standard of evaluation has not been adopted yet, the decision usually being made by evaluating the price. Thus, this research aims to propose a set of criteria to be incorporated into the decision problem that involves technical aspects. It then seeks to rank alternatives by using a multi-criteria decision aid method, FITradeoff, which supports the decision-maker (DM) in prioritization and provides transparency and security to the process. Full article
(This article belongs to the Special Issue Multi-criteria Optimization Models and Methods for Smart Cities)
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20 pages, 1678 KiB  
Article
Influencing Factors Analysis in Railway Engineering Technological Innovation under Complex and Difficult Areas: A System Dynamics Approach
by Chaoxun Cai, Shiyu Tian, Yuefeng Shi, Yongjun Chen and Xiaojian Li
Mathematics 2024, 12(13), 2040; https://doi.org/10.3390/math12132040 (registering DOI) - 30 Jun 2024
Viewed by 134
Abstract
The geological complexity, environmental sensitivity, and ecological fragility inherent in complex and difficult areas (CDAs) present new opportunities and challenges for technological innovation in railway engineering development in China. At the current stage in China, the process of technological innovation in railway engineering [...] Read more.
The geological complexity, environmental sensitivity, and ecological fragility inherent in complex and difficult areas (CDAs) present new opportunities and challenges for technological innovation in railway engineering development in China. At the current stage in China, the process of technological innovation in railway engineering within CDAs still faces a series of pressing issues that need addressing. The paper identifies and determines 22 influencing factors for technological innovation in railway engineering within CDAs across five dimensions. Subsequently, a technological innovation model for railway engineering in such areas is constructed based on system dynamics (SD), which is followed by simulation and sensitivity analysis to identify the key influencing factors. The results indicate that key influencing factors for technological innovation in railway engineering within CDAs include technological innovation capability, the adaptability of technology to the environment, R&D funding investment, technological product requirements, technological innovation incentive mechanisms, and the level of technological development. The importance ranking of each dimension is as follows: technological factors > technical factors > management factors > resource factors > environmental factors. The paper provides new insights for promoting technological innovation and management development in complex and challenging railway engineering projects. It offers a fresh perspective to enhance the technological innovation efficiency of railway projects in complex and challenging areas. Full article
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13 pages, 266 KiB  
Article
Maximizing Closeness in Bipartite Networks: A Graph-Theoretic Analysis
by Fazal Hayat and Daniele Ettore Otera
Mathematics 2024, 12(13), 2039; https://doi.org/10.3390/math12132039 (registering DOI) - 30 Jun 2024
Viewed by 130
Abstract
A fundamental aspect of network analysis involves pinpointing nodes that hold significant positions within the network. Graph theory has emerged as a powerful mathematical tool for this purpose, and there exist numerous graph-theoretic parameters for analyzing the stability of the system. Within this [...] Read more.
A fundamental aspect of network analysis involves pinpointing nodes that hold significant positions within the network. Graph theory has emerged as a powerful mathematical tool for this purpose, and there exist numerous graph-theoretic parameters for analyzing the stability of the system. Within this framework, various graph-theoretic parameters contribute to network analysis. One such parameter used in network analysis is the so-called closeness, which serves as a structural measure to assess the efficiency of a node’s ability to interact with other nodes in the network. Mathematically, it measures the reciprocal of the sum of the shortest distances from a node to all other nodes in the network. A bipartite network is a particular type of network in which the nodes can be divided into two disjoint sets such that no two nodes within the same set are adjacent. This paper mainly studies the problem of determining the network that maximize the closeness within bipartite networks. To be more specific, we identify those networks that maximize the closeness over bipartite networks with a fixed number of nodes and one of the fixed parameters: connectivity, dissociation number, cut edges, and diameter. Full article
(This article belongs to the Special Issue Geometry and Topology with Applications)
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15 pages, 2744 KiB  
Article
Symmetric Effects of Renewable Energy Markets on China’s Green Financial Markets: A Perspective of Time and Frequency Dynamic Connectedness
by Juan Meng, Yonghong Jiang, Haiwen Zhao and Ansheng Tanliang
Mathematics 2024, 12(13), 2038; https://doi.org/10.3390/math12132038 (registering DOI) - 30 Jun 2024
Viewed by 144
Abstract
This study investigates dynamic risk spillover effects between renewable energy markets and Chinese green financial markets from a time-frequency perspective by utilizing weekly data from two types of markets with a span from January 2010 to August 2022. The results show that the [...] Read more.
This study investigates dynamic risk spillover effects between renewable energy markets and Chinese green financial markets from a time-frequency perspective by utilizing weekly data from two types of markets with a span from January 2010 to August 2022. The results show that the total spillover and net spillover effects vary widely across time. Short-run spillover is more dominant than long-run spillover. In most cases, green finance markets play the role of risk receivers in the system, while renewable energy markets are the main risk transmitters in the short run and the main risk spillover contributors in the long run. Finally, we determine that the hedging effect of green finance assets in the renewable energy market may decrease after the COVID-19 pandemic. Full article
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14 pages, 3740 KiB  
Article
Towards Human-Interactive Controllable Video Captioning with Efficient Modeling
by Yoonseok Heo, Taehoon Kim, Seunghwan Kim, Jungyun Seo and Juae Kim
Mathematics 2024, 12(13), 2037; https://doi.org/10.3390/math12132037 (registering DOI) - 30 Jun 2024
Viewed by 142
Abstract
Video captioning is a task of describing the visual scene of a given video in natural language. There have been several lines of research focused on developing large-scale models in a transfer learning paradigm, with major challenge being the tradeoff between scalability and [...] Read more.
Video captioning is a task of describing the visual scene of a given video in natural language. There have been several lines of research focused on developing large-scale models in a transfer learning paradigm, with major challenge being the tradeoff between scalability and performance in limited environments. To address this problem, we propose a simple yet effective encoder–decoder-based video captioning model integrating transformers and CLIP, both of which are widely adopted in the vision and language domains, together with appropriate temporal feature embedding modules. Taking this proposal a step further, we also address the challenge of human-interactive video captioning, where the captions are tailored to specific information desired by humans. To design a human-interactive environment, we assume that a human offers an object or action in the video as a short prompt; in turn, the system then provides a detailed explanation regarding the prompt. We embed human prompts within an LSTM-based prompt encoder and leverage soft prompting to tune the model effectively. We extensively evaluated our model on benchmark datasets, demonstrating comparable results, particularly on the MSR-VTT dataset, where we achieve state-of-the-art performance with 4% improvement. In addition, we also show potential for human-interactive video captioning through quantitative and qualitative analysis. Full article
(This article belongs to the Special Issue Advanced Artificial Intelligence Models and Its Applications, 2nd Edition)
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14 pages, 885 KiB  
Article
Speed Control for PMSM with Fast Variable-Speed Sliding Mode Control via High-Gain Disturbance Observer
by Hengqiang Wang, Guangming Zhang and Xiaojun Liu
Mathematics 2024, 12(13), 2036; https://doi.org/10.3390/math12132036 (registering DOI) - 29 Jun 2024
Viewed by 204
Abstract
Since robustness only exists on the sliding mode/surface, sliding mode control is non-globally stable. Therefore, shortening the time to reach the sliding mode is an important method of improving sliding mode robustness. However, there is an inherent contradiction between rapidity and overshoot. Therefore, [...] Read more.
Since robustness only exists on the sliding mode/surface, sliding mode control is non-globally stable. Therefore, shortening the time to reach the sliding mode is an important method of improving sliding mode robustness. However, there is an inherent contradiction between rapidity and overshoot. Therefore, ensuring rapid convergence without overshoot is a worthwhile research problem. Consequently, this paper proposes a design for a fast variable speed reaching law (FVSRL) to improve the quality of sliding mode control. The constructed approach rate is based on a variable speed term, an exponential term, and a fast term, ensuring rapid convergence without overshoot. At the same time, a high-gain disturbance observer is employed for feedforward compensation. Finally, the designed reaching law is validated by comparing it with conventional exponential approach rates and a new sliding mode reaching law, demonstrating its superior performance. Detailed comparative and quantitative analyses of the simulation results using the conventional exponential reaching law, the new sliding mode reaching law, and the FVSRL are performed, utilizing metrics such as integrated square error, integral time square error, integrated absolute error, and integral time absolute error. Full article
8 pages, 243 KiB  
Article
A Counterexample Concerning C0-Semigroups of Holomorphic Carathéodory Isometries
by László L. Stachó
Mathematics 2024, 12(13), 2035; https://doi.org/10.3390/math12132035 (registering DOI) - 29 Jun 2024
Viewed by 211
Abstract
We give an example for a C0-semigroup of non-linear 0-preserving holomorphic Carathéodory isometries of the unit ball. Full article
(This article belongs to the Special Issue Advances on Nonlinear Functional Analysis)
11 pages, 254 KiB  
Article
A (2 + 1)-Dimensional Integrable Breaking Soliton Equation and Its Algebro-Geometric Solutions+
by Xiaohong Chen, Tiecheng Xia and Liancheng Zhu
Mathematics 2024, 12(13), 2034; https://doi.org/10.3390/math12132034 (registering DOI) - 29 Jun 2024
Viewed by 204
Abstract
A new (2 + 1)-dimensional breaking soliton equation with the help of the nonisospectral Lax pair is presented. It is shown that the compatible solutions of the first two nontrivial equations in the (1 + 1)-dimensional Kaup–Newell soliton hierarchy provide solutions of the [...] Read more.
A new (2 + 1)-dimensional breaking soliton equation with the help of the nonisospectral Lax pair is presented. It is shown that the compatible solutions of the first two nontrivial equations in the (1 + 1)-dimensional Kaup–Newell soliton hierarchy provide solutions of the new breaking soliton equation. Then, the new breaking soliton equation is decomposed into the systems of solvable ordinary differential equations. Finally, a hyperelliptic Riemann surface and Abel–Jacobi coordinates are introduced to straighten the associated flow, from which the algebro-geometric solutions of the new (2 + 1)-dimensional integrable equation are constructed by means of the Riemann θ functions. Full article
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