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Mathematics
Volume 13
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Mathematics, Volume 13, Issue 13 (July-1 2025) – 179 articles

Cover Story (view full-size image): Randomized response models aim to protect respondent privacy in sensitive surveys but consequently compromise estimator efficiency. This cover illustrates the joint scrambling framework, a new sampling method and family of estimators as proposed in our paper. Joint scrambling preserves all true responses while protecting privacy by asking each respondent to jointly speak both their true response and multiple random responses in an arbitrary order. Notably, we provide a kernel density estimator for the density function with asymptotically equivalent mean squared error for the optimal bandwidth, yet greater generality than existing techniques for randomized response models. We also derive consistent, unbiased estimators for a general class of estimands and present simulations to verify all claimed results. View this paper
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26 pages, 5672 KiB  
Review
Development Status and Trend of Mine Intelligent Mining Technology
by Zhuo Wang, Lin Bi, Jinbo Li, Zhaohao Wu and Ziyu Zhao
Mathematics 2025, 13(13), 2217; https://doi.org/10.3390/math13132217 - 7 Jul 2025
Viewed by 580
Abstract
Intelligent mining technology, as the core driving force for the digital transformation of the mining industry, integrates cyber-physical systems, artificial intelligence, and industrial internet technologies to establish a “cloud–edge–end” collaborative system. In this paper, the development trajectory of intelligent mining technology has been [...] Read more.
Intelligent mining technology, as the core driving force for the digital transformation of the mining industry, integrates cyber-physical systems, artificial intelligence, and industrial internet technologies to establish a “cloud–edge–end” collaborative system. In this paper, the development trajectory of intelligent mining technology has been systematically reviewed, which has gone through four stages: stand-alone automation, integrated automation and informatization, digital and intelligent initial, and comprehensive intelligence. And the current development status of “cloud–edge–end” technologies has been reviewed: (i) The end layer achieves environmental state monitoring and precise control through a multi-source sensing network and intelligent equipment. (ii) The edge layer leverages 5G and edge computing to accomplish real-time data processing, 3D dynamic modeling, and safety early warning. (iii) The cloud layer realizes digital planning and intelligent decision-making, based on the industrial Internet platform. The three-layer collaboration forms a “perception–analysis–decision–execution” closed loop. Currently, there are still many challenges in the development of the technology, including the lack of a standardization system, the bottleneck of multi-source heterogeneous data fusion, the lack of a cross-process coordination of the equipment, and the shortage of interdisciplinary talents. Accordingly, this paper focuses on future development trends from four aspects, providing systematic solutions for a safe, efficient, and sustainable mining operation. Technological evolution will accelerate the formation of an intelligent ecosystem characterized by “standard-driven, data-empowered, equipment-autonomous, and human–machine collaboration”. Full article
(This article belongs to the Special Issue Mathematical Modeling and Analysis in Mining Engineering)
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38 pages, 855 KiB  
Review
Failure Mode and Effects Analysis Integrated with Multi-Attribute Decision-Making Methods Under Uncertainty: A Systematic Literature Review
by Aleksandar Aleksić, Danijela Tadić, Nikola Komatina and Snežana Nestić
Mathematics 2025, 13(13), 2216; https://doi.org/10.3390/math13132216 - 7 Jul 2025
Viewed by 444
Abstract
Failure Mode and Effects Analysis (FMEA) is a proactive management technique widely used to improve the reliability of products and processes across various business sectors. Due to rapid changes stemming from uncertain environments, numerous studies have proposed different approaches to enhance the effectiveness [...] Read more.
Failure Mode and Effects Analysis (FMEA) is a proactive management technique widely used to improve the reliability of products and processes across various business sectors. Due to rapid changes stemming from uncertain environments, numerous studies have proposed different approaches to enhance the effectiveness of the FMEA method. However, there is a lack of systematic literature reviews and classification of research on this topic. The purpose of this paper is to systematically review the literature on the integration of FMEA with Multi-Attribute Decision-Making (MADM) theories and various mathematical models. This study analyses a total of 68 papers published between 2015 and 2024, selected from 51 peer-reviewed journals indexed in Scopus and/or Web of Science. Furthermore, a bibliometric analysis was conducted based on the frequency of different mathematical theories used to model existing uncertainties, methods for determining the weighting vectors of risk factors (RFs), the use of MADM theories extended with uncertain numbers for weighting RFs and prioritizing identified failure modes, publication years, journals, and application domains. This research aims to support both researchers and practitioners in effectively adopting uncertain MADM methods to address the limitations of traditional FMEA and provide insight into the current state of the art in this field. Full article
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Numbers, Fuzzy Modeling, and Their Applications in Management and Engineering, 2nd Edition)
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21 pages, 997 KiB  
Article
Explainable AI and Fuzzy Linguistic Interpretation for Enhanced Transparency in Public Procurement: Analyzing EU Tender Awards
by Cosmin Cernăzanu-Glăvan and Andrei-Ștefan Bulzan
Mathematics 2025, 13(13), 2215; https://doi.org/10.3390/math13132215 - 7 Jul 2025
Viewed by 220
Abstract
Despite the ideal of a unified Single Market, a powerful “home bias” pervades EU public procurement, hinting at unseen barriers that conventional analysis fails to capture. This study introduces an interpretable AI framework to investigate these dynamics, pairing a LightGBM model with SHapley [...] Read more.
Despite the ideal of a unified Single Market, a powerful “home bias” pervades EU public procurement, hinting at unseen barriers that conventional analysis fails to capture. This study introduces an interpretable AI framework to investigate these dynamics, pairing a LightGBM model with SHapley Additive exPlanations (SHAP) to examine the vast Tenders Electronic Daily (TED) database (2018–2023). Concretely, we propose a fuzzy linguistic layer that translates SHAP’s complex quantitative outputs into intuitive, human-readable terms. Our model effectively distinguishes local from non-local awards (AUC ≈ 0.855), revealing that while high-value contracts expectedly attract broader competition, the most potent predictors are a country’s own history of local awards and structural factors like the buyer’s type and location. This points not to isolated incidents, but, rather, to deep-seated patterns shaping market fairness. Our combined XAI-Fuzzy approach offers a new instrument for transparent governance, enabling policymakers to diagnose market realities and forge a more genuinely open and equitable European public square. Full article
(This article belongs to the Special Issue Multi-attribute Decision Making and Intelligent Computing in Smart Governance)
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17 pages, 760 KiB  
Article
Max–Min Share-Based Mechanism for Multi-Resource Fair Allocation with Bounded Number of Tasks in Cloud Computing System
by Jie Li, Haoyu Wang, Jianzhou Wang and Yue Zhang
Mathematics 2025, 13(13), 2214; https://doi.org/10.3390/math13132214 - 7 Jul 2025
Viewed by 203
Abstract
Finding a fair and efficient multi-resource allocation is a fundamental goal in cloud computing systems. In this paper, we consider the problem of multi-resource allocation with a bounded number of tasks. We propose a lexicographic max–min maximin share (LMM-MMS) fair allocation mechanism and [...] Read more.
Finding a fair and efficient multi-resource allocation is a fundamental goal in cloud computing systems. In this paper, we consider the problem of multi-resource allocation with a bounded number of tasks. We propose a lexicographic max–min maximin share (LMM-MMS) fair allocation mechanism and design a non-trivial polynomial-time algorithm to find an LMM-MMS solution. In addition, we prove that LMM-MMS satisfies Pareto efficiency, sharing incentive, envy-freeness, and group strategy-proofness properties. The experimental results showed that LMM-MMS could produce a fair allocation with a higher resource utilization and completion ratio of user jobs than previous known fair mechanisms; LMM-MMS also performed well in resource sharing. Full article
(This article belongs to the Special Issue Data-Driven or AI-Driven Optimization Algorithms and Their Applications)
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15 pages, 467 KiB  
Article
Practical Fixed-Time Tracking Control for Strict-Feedback Nonlinear Systems with Flexible Prescribed Performance
by Xing Wang, Yongzhi Wang, Yulong Ji, Ben Niu and Jianing Hu
Mathematics 2025, 13(13), 2213; https://doi.org/10.3390/math13132213 - 7 Jul 2025
Viewed by 199
Abstract
This paper addresses the issue of practical fixed-time tracking control for a class of strict-feedback nonlinear systems subject to external disturbances, while ensuring flexible prescribed performance. First, a fixed-time disturbance observer is designed to estimate the unknown external disturbances. The primary advantage of [...] Read more.
This paper addresses the issue of practical fixed-time tracking control for a class of strict-feedback nonlinear systems subject to external disturbances, while ensuring flexible prescribed performance. First, a fixed-time disturbance observer is designed to estimate the unknown external disturbances. The primary advantage of the proposed fixed-time disturbance observer lies in its capability to estimate both the disturbance itself and its higher-order derivatives in fixed time. In addition, various prescribed performance behaviors can be realized via a set of function transformations, merely by modifying certain critical parameters, without the need to redesign the controller. It is shown that, under the proposed control strategy, the system output can track the reference signal in fixed time, and the tracking error always remains within the prescribed performance boundaries. Finally, the simulation results are provided to demonstrate the feasibility and effectiveness of the proposed control scheme. Full article
(This article belongs to the Special Issue Advances in Switched Systems and Control Theory: Theory and Application)
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1 pages, 123 KiB  
Correction
Correction: Ullah et al. Enhancing Brain Tumor Segmentation Accuracy through Scalable Federated Learning with Advanced Data Privacy and Security Measures. Mathematics 2023, 11, 4189
by Faizan Ullah, Muhammad Nadeem, Mohammad Abrar, Farhan Amin, Abdu Salam and Salabat Khan
Mathematics 2025, 13(13), 2212; https://doi.org/10.3390/math13132212 - 7 Jul 2025
Viewed by 154
Abstract
The author’s contribution is incomplete in the original publication [...] Full article
20 pages, 1082 KiB  
Article
Influence of Magnetic Field and Porous Medium on Taylor–Couette Flows of Second Grade Fluids Due to Time-Dependent Couples on a Circular Cylinder
by Dumitru Vieru and Constantin Fetecau
Mathematics 2025, 13(13), 2211; https://doi.org/10.3390/math13132211 - 7 Jul 2025
Viewed by 151
Abstract
Axially symmetric Taylor–Couette flows of incompressible second grade fluids induced by time-dependent couples inside an infinite circular cylinder are studied under the action of an external magnetic field. The influence of the medium porosity is taken into account in the mathematical modeling. Analytical [...] Read more.
Axially symmetric Taylor–Couette flows of incompressible second grade fluids induced by time-dependent couples inside an infinite circular cylinder are studied under the action of an external magnetic field. The influence of the medium porosity is taken into account in the mathematical modeling. Analytical expressions for the dimensionless non-trivial shear stress and the corresponding fluid velocity were determined using the finite Hankel and Laplace transforms. The solutions obtained are new in the specialized literature and can be customized for various problems of interest in engineering practice. For illustration, the cases of oscillating and constant couples have been considered, and the steady state components of the shear stresses were presented in equivalent forms. Numerical schemes based on finite differences have been formulated for determining the numerical solutions of the proposed problem. It was shown that the numerical results based on analytical solutions and those obtained with the numerical methods have close values with very good accuracy. It was also proved that the fluid flows more slowly and the steady state is reached earlier in the presence of a magnetic field or porous medium. Full article
(This article belongs to the Special Issue Computational Fluid Dynamics, 3rd Edition)
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29 pages, 647 KiB  
Review
Recent Advances in Optimization Methods for Machine Learning: A Systematic Review
by Xiaodong Liu, Huaizhou Qi, Suisui Jia, Yongjing Guo and Yang Liu
Mathematics 2025, 13(13), 2210; https://doi.org/10.3390/math13132210 - 7 Jul 2025
Viewed by 640
Abstract
This systematic review explores modern optimization methods for machine learning, distinguishing between gradient-based techniques using derivative information and population-based approaches employing stochastic search. Key innovations focus on enhanced regularization, adaptive control mechanisms, and biologically inspired strategies to address challenges like scaling to large [...] Read more.
This systematic review explores modern optimization methods for machine learning, distinguishing between gradient-based techniques using derivative information and population-based approaches employing stochastic search. Key innovations focus on enhanced regularization, adaptive control mechanisms, and biologically inspired strategies to address challenges like scaling to large models, navigating complex non-convex landscapes, and adapting to dynamic constraints. These methods underpin core ML tasks including model training, hyperparameter tuning, and feature selection. While significant progress is evident, limitations in scalability and theoretical guarantees persist, directing future work toward more robust and adaptive frameworks to advance AI applications in areas like autonomous systems and scientific discovery. Full article
(This article belongs to the Special Issue Recent Advances of Neural Network Optimization and Algorithms in Deep Learning)
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22 pages, 3066 KiB  
Article
Optimal Strategies in Green Supply Chains When Considering Consumers’ Green Preferences and Government Subsidies
by Lei Wang, Tao Xu and Tingqiang Chen
Mathematics 2025, 13(13), 2209; https://doi.org/10.3390/math13132209 - 7 Jul 2025
Viewed by 205
Abstract
Green and low-carbon development of supply chains represents a practical approach to addressing climate change and enhancing corporate competitiveness. From the perspective of the relationship between policy subsidies and channel power structures, this paper constructs Stackelberg game models under four different scenarios to [...] Read more.
Green and low-carbon development of supply chains represents a practical approach to addressing climate change and enhancing corporate competitiveness. From the perspective of the relationship between policy subsidies and channel power structures, this paper constructs Stackelberg game models under four different scenarios to conduct theoretical analyses of the optimal strategies, supported by numerical simulations. The research findings reveal the following. (1) Under the product subsidy policy, the enhancement of consumers’ green preference will lead to a green premium, and in the case of the technology subsidy policy, consumers’ green preference will inhibit wholesale prices and retail prices. However, there is a threshold in the manufacturer-led case, and a “green premium” is also claimed when this threshold is exceeded. (2) The effects of the product subsidy policy and the green technology level subsidy policy on prices are opposite, where an increase in the product subsidy will increase the wholesale price and retail price, while an increase in the green technology level subsidy will reduce the wholesale price. The technology subsidy policy has a more significant effect on the promotion of green technology. (3) The power of supply chain channels will directly affect corporate profits, and the leader of the supply chain often has higher profits. Compared with product subsidies, technology subsidies can inhibit the channel power of retailers. Full article
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23 pages, 1794 KiB  
Article
Dynamic Rescheduling Strategy for Passenger Congestion Balancing in Airport Passenger Terminals
by Yohan Lee, Seung Chan Choi, Keyju Lee and Sung Won Cho
Mathematics 2025, 13(13), 2208; https://doi.org/10.3390/math13132208 - 7 Jul 2025
Viewed by 340
Abstract
Airports are facing significant challenges due to the increasing number of air travel passengers. After a significant downturn during the COVID-19 pandemic, airports are implementing measures to enhance security and improve their level of service in response to rising demand. However, the rising [...] Read more.
Airports are facing significant challenges due to the increasing number of air travel passengers. After a significant downturn during the COVID-19 pandemic, airports are implementing measures to enhance security and improve their level of service in response to rising demand. However, the rising passenger volume has led to increased congestion and longer waiting times, undermining operational efficiency and passenger satisfaction. While most previous studies have focused on static modeling or infrastructure improvements, few have addressed the problem of dynamically allocating passengers in real-time. To tackle this issue, this study proposes a mathematical model with a dynamic rescheduling framework to balance the workload across multiple departure areas where security screening takes place, while minimizing the negative impact on passenger satisfaction resulting from increased walking distances. The proposed model strategically allocates departure areas for passengers in advance, utilizing data-based predictions. A mixed integer linear programming (MILP) model was developed and evaluated through discrete event simulation (DES). Real operational data provided by Incheon International Airport Corporation (IIAC) were used to validate the model. Comparative simulations against four baseline strategies demonstrated superior performance in balancing workload, reducing waiting passengers, and minimizing walking distances. In conclusion, the proposed model has the potential to enhance the efficiency of the security screening stage in the passenger departure process. Full article
(This article belongs to the Special Issue Advanced Mathematical Programming and Applications in Operations Research)
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19 pages, 2744 KiB  
Article
Chaotic Behaviour, Sensitivity Assessment, and New Analytical Investigation to Find Novel Optical Soliton Solutions of M-Fractional Kuralay-II Equation
by J. R. M. Borhan, E. I. Hassan, Arafa Dawood, Khaled Aldwoah, Amani Idris A. Sayed, Ahmad Albaity and M. Mamun Miah
Mathematics 2025, 13(13), 2207; https://doi.org/10.3390/math13132207 - 6 Jul 2025
Viewed by 316
Abstract
The implementation of chaotic behavior and a sensitivity assessment of the newly developed M-fractional Kuralay-II equation are the foremost objectives of the present study. This equation has significant possibilities in control systems, electrical circuits, seismic wave propagation, economic dynamics, groundwater flow, image and [...] Read more.
The implementation of chaotic behavior and a sensitivity assessment of the newly developed M-fractional Kuralay-II equation are the foremost objectives of the present study. This equation has significant possibilities in control systems, electrical circuits, seismic wave propagation, economic dynamics, groundwater flow, image and signal denoising, complex biological systems, optical fibers, plasma physics, population dynamics, and modern technology. These applications demonstrate the versatility and advantageousness of the stated model for complex systems in various scientific and engineering disciplines. One more essential objective of the present research is to find closed-form wave solutions of the assumed equation based on the (G′G′+G+A)-expansion approach. The results achieved are in exponential, rational, and trigonometric function forms. Our findings are more novel and also have an exclusive feature in comparison with the existing results. These discoveries substantially expand our understanding of nonlinear wave dynamics in various physical contexts in industry. By simply selecting suitable values of the parameters, three-dimensional (3D), contour, and two-dimensional (2D) illustrations are produced displaying the diagrammatic propagation of the constructed wave solutions that yield the singular periodic, anti-kink, kink, and singular kink-shape solitons. Future improvements to the model may also benefit from what has been obtained as well. The various assortments of solutions are provided by the described procedure. Finally, the framework proposed in this investigation addresses additional fractional nonlinear partial differential equations in mathematical physics and engineering with excellent reliability, quality of effectiveness, and ease of application. Full article
(This article belongs to the Special Issue Applications of Partial Differential Equations in Mathematical Physics, 2nd Edition)
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29 pages, 1997 KiB  
Article
An Efficient Sparse Twin Parametric Insensitive Support Vector Regression Model
by Shuanghong Qu, Yushan Guo, Renato De Leone, Min Huang and Pu Li
Mathematics 2025, 13(13), 2206; https://doi.org/10.3390/math13132206 - 6 Jul 2025
Viewed by 246
Abstract
This paper proposes a novel sparse twin parametric insensitive support vector regression (STPISVR) model, designed to enhance sparsity and improve generalization performance. Similar to twin parametric insensitive support vector regression (TPISVR), STPISVR constructs a pair of nonparallel parametric insensitive bound functions to indirectly [...] Read more.
This paper proposes a novel sparse twin parametric insensitive support vector regression (STPISVR) model, designed to enhance sparsity and improve generalization performance. Similar to twin parametric insensitive support vector regression (TPISVR), STPISVR constructs a pair of nonparallel parametric insensitive bound functions to indirectly determine the regression function. The optimization problems are reformulated as two sparse linear programming problems (LPPs), rather than traditional quadratic programming problems (QPPs). The two LPPs are originally derived from initial L1-norm regularization terms imposed on their respective dual variables, which are simplified to constants via the Karush–Kuhn–Tucker (KKT) conditions and consequently disappear. This simplification reduces model complexity, while the constraints constructed through the KKT conditions— particularly their geometric properties—effectively ensure sparsity. Moreover, a two-stage hybrid tuning strategy—combining grid search for coarse parameter space exploration and Bayesian optimization for fine-grained convergence—is proposed to precisely select the optimal parameters, reducing tuning time and improving accuracy compared to a singlemethod strategy. Experimental results on synthetic and benchmark datasets demonstrate that STPISVR significantly reduces the number of support vectors (SVs), thereby improving prediction speed and achieving a favorable trade-off among prediction accuracy, sparsity, and computational efficiency. Overall, STPISVR enhances generalization ability, promotes sparsity, and improves prediction efficiency, making it a competitive tool for regression tasks, especially in handling complex data structures. Full article
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18 pages, 487 KiB  
Article
Variational Bayesian Variable Selection in Logistic Regression Based on Spike-and-Slab Lasso
by Juanjuan Zhang, Weixian Wang, Mingming Yang and Maozai Tian
Mathematics 2025, 13(13), 2205; https://doi.org/10.3390/math13132205 - 6 Jul 2025
Viewed by 286
Abstract
Logistic regression is often used to solve classification problems. This article combines the advantages of Bayesian methods and spike-and-slab Lasso to select variables in high-dimensional logistic regression. The method of introducing a new hidden variable or approximating the lower bound is used to [...] Read more.
Logistic regression is often used to solve classification problems. This article combines the advantages of Bayesian methods and spike-and-slab Lasso to select variables in high-dimensional logistic regression. The method of introducing a new hidden variable or approximating the lower bound is used to solve the problem of logistic functions without conjugate priors. The Laplace distribution in spike-and-slab Lasso is expressed as a hierarchical form of normal distribution and exponential distribution, so that all parameters in the model are posterior distributions that are easy to deal with. Considering the high time cost of parameter estimation and variable selection in high-dimensional models, we use the variational Bayesian algorithm to perform posterior inference on the parameters in the model. From the simulation results, it can be seen that it is an adaptive prior that can perform parameter estimation and variable selection well in high-dimensional logistic regression. From the perspective of algorithm running time, the method proposed in this article also has high computational efficiency in many cases. Full article
(This article belongs to the Section D: Statistics and Operational Research)
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22 pages, 397 KiB  
Review
Compliant Force Control for Robots: A Survey
by Minglei Zhu, Dawei Gong, Yuyang Zhao, Jiaoyuan Chen, Jun Qi and Shijie Song
Mathematics 2025, 13(13), 2204; https://doi.org/10.3390/math13132204 - 6 Jul 2025
Viewed by 528
Abstract
Compliant force control is a fundamental capability for enabling robots to interact safely and effectively with dynamic and uncertain environments. This paper presents a comprehensive survey of compliant force control strategies, intending to enhance safety, adaptability, and precision in applications such as physical [...] Read more.
Compliant force control is a fundamental capability for enabling robots to interact safely and effectively with dynamic and uncertain environments. This paper presents a comprehensive survey of compliant force control strategies, intending to enhance safety, adaptability, and precision in applications such as physical human–robot interaction, robotic manipulation, and collaborative tasks. The review begins with a classification of compliant control methods into passive and active approaches, followed by a detailed examination of direct force control techniques—including hybrid and parallel force/position control—and indirect methods such as impedance and admittance control. Special emphasis is placed on advanced compliant control strategies applied to structurally complex robotic systems, including aerial, mobile, cable-driven, and bionic robots. In addition, intelligent compliant control approaches are systematically analyzed, encompassing neural networks, fuzzy logic, sliding mode control, and reinforcement learning. Sensorless compliance techniques are also discussed, along with emerging trends in hardware design and intelligent control methodologies. This survey provides a holistic view of the current landscape, identifies key technical challenges, and outlines future research directions for achieving more robust, intelligent, and adaptive compliant force control in robotic systems. Full article
(This article belongs to the Special Issue Intelligent Control and Applications of Nonlinear Dynamic System)
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27 pages, 12221 KiB  
Article
Retinal Vessel Segmentation Based on a Lightweight U-Net and Reverse Attention
by Fernando Daniel Hernandez-Gutierrez, Eli Gabriel Avina-Bravo, Mario Alberto Ibarra-Manzano, Jose Ruiz-Pinales, Emmanuel Ovalle-Magallanes and Juan Gabriel Avina-Cervantes
Mathematics 2025, 13(13), 2203; https://doi.org/10.3390/math13132203 - 5 Jul 2025
Viewed by 845
Abstract
U-shaped architectures have achieved exceptional performance in medical image segmentation. Their aim is to extract features by two symmetrical paths: an encoder and a decoder. We propose a lightweight U-Net incorporating reverse attention and a preprocessing framework for accurate retinal vessel segmentation. This [...] Read more.
U-shaped architectures have achieved exceptional performance in medical image segmentation. Their aim is to extract features by two symmetrical paths: an encoder and a decoder. We propose a lightweight U-Net incorporating reverse attention and a preprocessing framework for accurate retinal vessel segmentation. This concept could be of benefit to portable or embedded recognition systems with limited resources for real-time operation. Compared to the baseline model (7.7 M parameters), the proposed U-Net model has only 1.9 M parameters and was tested on the DRIVE (Digital Retinal Images for Vesselness Extraction), CHASE (Child Heart and Health Study in England), and HRF (High-Resolution Fundus) datasets for vesselness analysis. The proposed model achieved Dice coefficients and IoU scores of 0.7871 and 0.6318 on the DRIVE dataset, 0.8036 and 0.6910 on the CHASE-DB1 Retinal Vessel Reference dataset, as well as 0.6902 and 0.5270 on the HRF dataset, respectively. Notably, the integration of the reverse attention mechanism contributed to a more accurate delineation of thin and peripheral vessels, which are often undetected by conventional models. The model comprised 1.94 million parameters and 12.21 GFLOPs. Furthermore, during inference, the model achieved a frame rate average of 208 FPS and a latency of 4.81 ms. These findings support the applicability of the proposed model in real-world clinical and mobile healthcare environments where efficiency and Accuracy are essential. Full article
(This article belongs to the Special Issue Advanced Research in Image Processing and Optimization Methods)
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21 pages, 6010 KiB  
Article
Reference Modulation-Based H∞ Control for the Hybrid Energy Storage System in DC Microgrids
by Khac Huan Su, Young Seop Son and Youngwoo Lee
Mathematics 2025, 13(13), 2202; https://doi.org/10.3390/math13132202 - 5 Jul 2025
Viewed by 349
Abstract
In DC microgrids, optimizing the hybrid energy storage system (HESS) current control to meet the power requirements of the load is generally a difficult and challenging task. This is because the HESS always operates under various load conditions, which are influenced by measurement [...] Read more.
In DC microgrids, optimizing the hybrid energy storage system (HESS) current control to meet the power requirements of the load is generally a difficult and challenging task. This is because the HESS always operates under various load conditions, which are influenced by measurement disturbances and parameter uncertainties. Therefore, in this paper, we propose the H∞ state feedback control based on the reference modulation to improve the current tracking errors of the battery (Bat) and supercapacitor (SC) in the HESS for power tracking performance. Without altering the system control signal, the reference modulation technique combines the feedforward channel and output feedback signal directly to modulate the required currents of the Bat and SC derived from the required load power. The H∞ state feedback control based on the required Bat and SC currents modulated by the reference modulation technique is proposed to improve the current tracking errors under the influence of measurement disturbances and parameter uncertainties without a disturbance observer. The ability of the reference modulation technique to attenuate the disturbance without the use of a disturbance observer is one advantage for improving transient performance. The improvement of the HESS’s power tracking performance in DC microgrids is confirmed by study results presented under the influence of measurement disturbances for nominal parameters and parameter uncertainties. Full article
(This article belongs to the Section C2: Dynamical Systems)
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31 pages, 49059 KiB  
Article
On the Mechanics of a Fiber Network-Reinforced Elastic Sheet Subjected to Uniaxial Extension and Bilateral Flexure
by Wenhao Yao, Heung Soo Kim and Chun Il Kim
Mathematics 2025, 13(13), 2201; https://doi.org/10.3390/math13132201 - 5 Jul 2025
Viewed by 187
Abstract
The mechanics of an elastic sheet reinforced with fiber mesh is investigated when undergoing bilateral in-plane bending and stretching. The strain energy of FRC is formulated by accounting for the matrix strain energy contribution and the fiber network deformations of extension, flexure, and [...] Read more.
The mechanics of an elastic sheet reinforced with fiber mesh is investigated when undergoing bilateral in-plane bending and stretching. The strain energy of FRC is formulated by accounting for the matrix strain energy contribution and the fiber network deformations of extension, flexure, and torsion, where the strain energy potential of the matrix material is characterized via the Mooney–Rivlin strain energy model and the fiber kinematics is computed via the first and second gradient of deformations. By applying the variational principle on the strain energy of FRC, the Euler–Lagrange equilibrium equations are derived and then solved numerically. The theoretical results highlight the matrix and meshwork deformations of FRC subjected to bilateral bending and stretching simultaneously, and it is found that the interaction between bilateral extension and bending manipulates the matrix and network deformation. It is theoretically observed that the transverse Lagrange strain peaks near the bilateral boundary while the longitudinal strain is intensified inside the FRC domain. The continuum model further demonstrates the bidirectional mesh network deformations in the case of plain woven, from which the extension and flexure kinematics of fiber units are illustrated to examine the effects of fiber unit deformations on the overall deformations of the fiber network. To reduce the observed matrix-network dislocation in the case of plain network reinforcement, the pantographic network reinforcement is investigated, suggesting that the bilateral stretch results in the reduced intersection angle at the mesh joints in the FRC domain. For validation of the continuum model, the obtained results are cross-examined with the existing experimental results depicting the failure mode of conventional fiber-reinforced composites to demonstrate the practical utility of the proposed model. Full article
(This article belongs to the Special Issue Progress in Computational and Applied Mechanics)
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22 pages, 488 KiB  
Article
Dynamics of a Model of Tumor–Immune Cell Interactions Under Chemotherapy
by Rubayyi T. Alqahtani, Abdelhamid Ajbar and Eman Hamed Aljebli
Mathematics 2025, 13(13), 2200; https://doi.org/10.3390/math13132200 - 5 Jul 2025
Viewed by 258
Abstract
This paper analyzes a mathematical model to investigate the complex interactions between tumor cells, immune cells (natural killer (NK) cells and CD8+ cytotoxic T lymphocytes (CTLs)) and chemotherapy. The primary objectives are to analyze tumor–immune interactions without and under treatment, identify critical thresholds [...] Read more.
This paper analyzes a mathematical model to investigate the complex interactions between tumor cells, immune cells (natural killer (NK) cells and CD8+ cytotoxic T lymphocytes (CTLs)) and chemotherapy. The primary objectives are to analyze tumor–immune interactions without and under treatment, identify critical thresholds for tumor eradication, and evaluate how chemotherapy parameters influence therapeutic outcomes. The model integrates NK cells and CTLs as effector cells, combining their dynamics linearly for simplicity. Tumor growth follows a logistic function, while immune–tumor interactions are modeled using a Hill function for fractional cell death. Stability and bifurcation analysis are employed to identify equilibria (tumor-free, high-tumor, and a novel middle steady state), bistability regimes, and critical parameter thresholds. Numerical simulations use experimentally validated parameter values from the literature. This mathematical analysis provides a framework for assessing the efficacy of chemotherapy by examining the dynamic interplay between tumor biology and treatment parameters. Our findings reveal that treatment outcomes are sensitive to the balance between the immune system’s biological parameters and chemotherapy-specific factors. The model highlights scenarios where chemotherapy may fail due to bistability and identifies critical thresholds for successful tumor eradication. These insights can guide clinical decision making in dosing strategies and suggest combination therapies such as immunotherapy–chemotherapy synergies to shift the system toward favorable equilibria. Full article
(This article belongs to the Special Issue Applied Mathematical Modeling in Oncology)
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27 pages, 1630 KiB  
Article
NNG-Based Secure Approximate k-Nearest Neighbor Query for Large Language Models
by Heng Zhou, Yuchao Wang, Yi Qiao and Jin Huang
Mathematics 2025, 13(13), 2199; https://doi.org/10.3390/math13132199 - 5 Jul 2025
Viewed by 239
Abstract
Large language models (LLMs) have driven transformative progress in artificial intelligence, yet critical challenges persist in data management and privacy protection during model deployment and training. The approximate nearest neighbor (ANN) search, a core operation in LLMs, faces inherent trade-offs between efficiency and [...] Read more.
Large language models (LLMs) have driven transformative progress in artificial intelligence, yet critical challenges persist in data management and privacy protection during model deployment and training. The approximate nearest neighbor (ANN) search, a core operation in LLMs, faces inherent trade-offs between efficiency and security when implemented through conventional locality-sensitive hashing (LSH)-based secure ANN (SANN) methods, which often compromise either query accuracy due to false positives. To address these limitations, this paper proposes a novel secure ANN scheme based on nearest neighbor graph (NNG-SANN), which is designed to ensure the security of approximate k-nearest neighbor queries for vector data commonly used in LLMs. Specifically, a secure indexing structure and subset partitioning method are proposed based on LSH and NNG. The approach utilizes neighborhood information stored in the NNG to supplement subset data, significantly reducing the impact of false positive points generated by LSH on query results, thereby effectively improving query accuracy. To ensure data privacy, we incorporate a symmetric encryption algorithm that encrypts the data subsets obtained through greedy partitioning before storing them on the server, providing robust security guarantees. Furthermore, we construct a secure index table that enables complete candidate set retrieval through a single query, ensuring our solution completes the search process in one interaction while minimizing communication costs. Comprehensive experiments conducted on two datasets of different scales demonstrate that our proposed method outperforms existing state-of-the-art algorithms in terms of both query accuracy and security, effectively meeting the precision and security requirements for nearest neighbor queries in LLMs. Full article
(This article belongs to the Special Issue Privacy-Preserving Machine Learning in Large Language Models (LLMs))
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46 pages, 1709 KiB  
Article
Federated Learning-Driven IoT Request Scheduling for Fault Tolerance in Cloud Data Centers
by Sheeja Rani S and Raafat Aburukba
Mathematics 2025, 13(13), 2198; https://doi.org/10.3390/math13132198 - 5 Jul 2025
Viewed by 351
Abstract
Cloud computing is a virtualized and distributed computing model that provides resources and services based on demand and self-service. Resource failure is one of the major challenges in cloud computing, and there is a need for fault tolerance mechanisms. This paper addresses the [...] Read more.
Cloud computing is a virtualized and distributed computing model that provides resources and services based on demand and self-service. Resource failure is one of the major challenges in cloud computing, and there is a need for fault tolerance mechanisms. This paper addresses the issue by proposing a multi-objective radial kernelized federated learning-based fault-tolerant scheduling (MRKFL-FTS) technique for allocating multiple IoT requests or user tasks to virtual machines in cloud IoT-based environments. The MRKFL-FTS technique includes Cloud RAN (C-RAN) and Virtual RAN (V-RAN). The proposed MRKFL-FTS technique comprises four entities, namely, IoT devices, cloud servers, task assigners, and virtual machines. Each IoT device generates several service requests and sends them to the control server. At first, radial kernelized support vector regression is applied in the local training model to identify resource-efficient virtual machines. After that, locally trained models are combined, and the resulting model is fed into the global aggregation model. Finally, using a weighted round-robin method, the task assigner allocates incoming IoT service requests to virtual machines. This approach improves resource awareness and fault tolerance in scheduling. The quantitatively analyzed results show that the MRKFL-FTS technique achieved an 8% improvement in task scheduling efficiency and fault prediction accuracy, a 36% improvement in throughput, and a 14% reduction in makespan and time complexity. In addition, the MRKFL-FTS technique resulted in a 13% reduction in response time. The energy consumption of the MRKFL-FTS technique is reduced by 17% and increases the scalability by 8% compared to conventional scheduling techniques. Full article
(This article belongs to the Special Issue Advanced Information and Signal Processing: Models and Algorithms)
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22 pages, 6463 KiB  
Article
State of Charge Prediction for Electric Vehicles Based on Integrated Model Architecture
by Min Wei, Yuhang Liu, Haojie Wang, Siquan Yuan and Jie Hu
Mathematics 2025, 13(13), 2197; https://doi.org/10.3390/math13132197 - 4 Jul 2025
Viewed by 213
Abstract
To enhance the accuracy of SOC prediction in EVs, which often suffers from significant discrepancies between displayed and actual driving ranges, this study proposes a data-driven model guided by an energy consumption framework. The approach addresses the problem of inaccurate remaining range prediction, [...] Read more.
To enhance the accuracy of SOC prediction in EVs, which often suffers from significant discrepancies between displayed and actual driving ranges, this study proposes a data-driven model guided by an energy consumption framework. The approach addresses the problem of inaccurate remaining range prediction, improving drivers’ travel planning and vehicle efficiency. A PCA-GA-K-Means-based driving cycle clustering method is introduced, followed by driving style feature extraction using a GMM to capture behavioral differences. A coupled library of twelve typical driving cycle style combinations is constructed to handle complex correlations among driving style, operating conditions, and range. To mitigate multicollinearity and nonlinear feature redundancies, a Pearson-DII-based feature extraction method is proposed. A stacking ensemble model, integrating Random Forest, CatBoost, XGBoost, and SVR as base models with ElasticNet as the meta model, is developed for robust prediction. Validated with real-world vehicle data across −21 °C to 39 °C and four driving cycles, the model significantly improves SOC prediction accuracy, offering a reliable solution for EV range estimation and enhancing user trust in EV technology. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
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15 pages, 1239 KiB  
Article
Extremum Seeking for the First Derivative of Nonlinear Maps with Constant Delays via a Time-Delay Approach
by Jianzhong Li, Hongye Su and Yang Zhu
Mathematics 2025, 13(13), 2196; https://doi.org/10.3390/math13132196 - 4 Jul 2025
Viewed by 164
Abstract
This paper introduces an extremum seeking (ES) scheme for the unknown map’s first derivative by tailoring a demodulation signal in which the closed-loop system is subject to constant transmission delays. Unlike most publications that manage delays using predictor-based methods, we are concerned with [...] Read more.
This paper introduces an extremum seeking (ES) scheme for the unknown map’s first derivative by tailoring a demodulation signal in which the closed-loop system is subject to constant transmission delays. Unlike most publications that manage delays using predictor-based methods, we are concerned with the delay-robustness of the introduced ES system via the newly developed time-delay approach. The original ES system is transformed to a nonlinear retarded-type plant with disturbances and the stability condition in the form of linear matrix inequalities is achieved. When the related bounds of the nonlinear map are not known, a rigorous practical stability proof is provided. Second, and more importantly, under the availability of prior knowledge about the nonlinear map, we are able to provide a quantitative calculation on the maximum allowable delay, the upper bound of the dither period, and the ultimate seeking error. Numerical examples are offered to exemplify the effectiveness of the proposed method. Full article
(This article belongs to the Section E2: Control Theory and Mechanics)
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30 pages, 3032 KiB  
Article
A Bayesian Additive Regression Trees Framework for Individualized Causal Effect Estimation
by Lulu He, Lixia Cao, Tonghui Wang, Zhenqi Cao and Xin Shi
Mathematics 2025, 13(13), 2195; https://doi.org/10.3390/math13132195 - 4 Jul 2025
Viewed by 303
Abstract
In causal inference research, accurate estimation of individualized treatment effects (ITEs) is at the core of effective intervention. This paper proposes a dual-structure ITE-estimation model based on Bayesian Additive Regression Trees (BART), which constructs independent BART sub-models for the treatment and control groups, [...] Read more.
In causal inference research, accurate estimation of individualized treatment effects (ITEs) is at the core of effective intervention. This paper proposes a dual-structure ITE-estimation model based on Bayesian Additive Regression Trees (BART), which constructs independent BART sub-models for the treatment and control groups, estimates ITEs using the potential outcome framework and enhances posterior stability and estimation reliability through Markov Chain Monte Carlo (MCMC) sampling. Based on psychological stress questionnaire data from graduate students, the study first integrates BART with the Shapley value method to identify employment pressure as a key driving factor and reveals substantial heterogeneity in ITEs across subgroups. Furthermore, the study constructs an ITE model using a dual-structured BART framework (BART-ITE), where employment pressure is defined as the treatment variable. Experimental results show that the model performs well in terms of credible interval width and ranking ability, demonstrating superior heterogeneity detection and individual-level sorting. External validation using both the Bootstrap method and matching-based pseudo-ITE estimation confirms the robustness of the proposed model. Compared with mainstream meta-learning methods such as S-Learner, X-Learner and Bayesian Causal Forest, the dual-structure BART-ITE model achieves a favorable balance between root mean square error and bias. In summary, it offers clear advantages in capturing ITE heterogeneity and enhancing estimation reliability and individualized decision-making. Full article
(This article belongs to the Special Issue Bayesian Learning and Its Advanced Applications)
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26 pages, 4907 KiB  
Article
A Novel Approach Utilizing Bagging, Histogram Gradient Boosting, and Advanced Feature Selection for Predicting the Onset of Cardiovascular Diseases
by Norma Latif Fitriyani, Muhammad Syafrudin, Nur Chamidah, Marisa Rifada, Hendri Susilo, Dursun Aydin, Syifa Latif Qolbiyani and Seung Won Lee
Mathematics 2025, 13(13), 2194; https://doi.org/10.3390/math13132194 - 4 Jul 2025
Viewed by 245
Abstract
Cardiovascular diseases (CVDs) rank among the leading global causes of mortality, underscoring the necessity for early detection and effective management. This research presents a novel prediction model for CVDs utilizing a bagging algorithm that incorporates histogram gradient boosting as the estimator. This study [...] Read more.
Cardiovascular diseases (CVDs) rank among the leading global causes of mortality, underscoring the necessity for early detection and effective management. This research presents a novel prediction model for CVDs utilizing a bagging algorithm that incorporates histogram gradient boosting as the estimator. This study leverages three preprocessed cardiovascular datasets, employing the Local Outlier Factor technique for outlier removal and the information gain method for feature selection. Through rigorous experimentation, the proposed model demonstrates superior performance compared to conventional machine learning approaches, such as Logistic Regression, Support Vector Classification, Gaussian Naïve Bayes, Multi-Layer Perceptron, k-nearest neighbors, Random Forest, AdaBoost, gradient boosting, and histogram gradient boosting. Evaluation metrics, including precision, recall, F1 score, accuracy, and AUC, yielded impressive results: 93.90%, 98.83%, 96.30%, 96.25%, and 0.9916 for dataset I; 94.17%, 99.05%, 96.54%, 96.48%, and 0.9931 for dataset II; and 89.81%, 82.40%, 85.91%, 86.66%, and 0.9274 for dataset III. The findings indicate that the proposed prediction model has the potential to facilitate early CVD detection, thereby enhancing preventive strategies and improving patient outcomes. Full article
(This article belongs to the Special Issue Application of Artificial Intelligence in Decision Making)
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16 pages, 1929 KiB  
Article
Dynamical Behavior of Solitary Waves for the Space-Fractional Stochastic Regularized Long Wave Equation via Two Distinct Approaches
by Muneerah Al Nuwairan, Bashayr Almutairi and Anwar Aldhafeeri
Mathematics 2025, 13(13), 2193; https://doi.org/10.3390/math13132193 - 4 Jul 2025
Viewed by 173
Abstract
This study investigates the influence of multiplicative noise—modeled by a Wiener process—and spatial-fractional derivatives on the dynamics of the space-fractional stochastic Regularized Long Wave equation. By employing a complete discriminant polynomial system, we derive novel classes of fractional stochastic solutions that capture the [...] Read more.
This study investigates the influence of multiplicative noise—modeled by a Wiener process—and spatial-fractional derivatives on the dynamics of the space-fractional stochastic Regularized Long Wave equation. By employing a complete discriminant polynomial system, we derive novel classes of fractional stochastic solutions that capture the complex interplay between stochasticity and nonlocality. Additionally, the variational principle, derived by He’s semi-inverse method, is utilized, yielding additional exact solutions that are bright solitons, bright-like solitons, kinky bright solitons, and periodic structures. Graphical analyses are presented to clarify how variations in the fractional order and noise intensity affect essential solution features, such as amplitude, width, and smoothness, offering deeper insight into the behavior of such nonlinear stochastic systems. Full article
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37 pages, 3228 KiB  
Article
Queuing Pricing with Time-Varying and Step Tolls: A Mathematical Framework for User Classification and Behavioral Analysis
by Chen-Hsiu Laih
Mathematics 2025, 13(13), 2192; https://doi.org/10.3390/math13132192 - 4 Jul 2025
Viewed by 169
Abstract
This study investigates user behavior at a bottleneck under two queuing pricing schemes: the optimal time-varying toll and the optimal multi-step toll. A mathematical model is developed to classify users based on toll status and arrival timing, further distinguishing between normal compliance and [...] Read more.
This study investigates user behavior at a bottleneck under two queuing pricing schemes: the optimal time-varying toll and the optimal multi-step toll. A mathematical model is developed to classify users based on toll status and arrival timing, further distinguishing between normal compliance and deliberate avoidance behaviors. Under the optimal time-varying toll, queuing is fully eliminated, no avoidance behavior occurs, and the user distribution remains consistent with the non-toll equilibrium. In contrast, the optimal n-step toll induces regular avoidance intervals before each toll change, with each interval exhibiting a uniform duration. The analysis reveals a structured classification of users into 3n + 2 behavioral groups, with predictable proportions in each category. These findings illustrate how step tolling affects user decision-making and temporal arrival patterns, offering valuable insights for the design of congestion pricing and traffic demand management strategies. Overall, the study highlights the practical applicability of queuing theory to transportation systems and contributes to the optimization of dynamic tolling mechanisms. Full article
(This article belongs to the Special Issue Recent Research in Queuing Theory and Stochastic Models, 2nd Edition)
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12 pages, 1293 KiB  
Article
Cross-Domain Approach for Automated Thyroid Classification Using Diff-Quick Images
by Thanh-Ha Do, Huy Le, Minh-Huong Hoang Dang, Van-De Nguyen and Phuc Do
Mathematics 2025, 13(13), 2191; https://doi.org/10.3390/math13132191 - 4 Jul 2025
Viewed by 207
Abstract
Classification of thyroid images based on the Bethesda category using Diff-Quick stained images can assist in diagnosing thyroid cancer. This paper proposes a cross-domain approach that modifies the original deep learning network designed to classify X-ray images to classify stained thyroid images. Since [...] Read more.
Classification of thyroid images based on the Bethesda category using Diff-Quick stained images can assist in diagnosing thyroid cancer. This paper proposes a cross-domain approach that modifies the original deep learning network designed to classify X-ray images to classify stained thyroid images. Since the Diff-Quick stained images have large and high-quality sizes with tiny cells with essential characteristics that can help a doctor diagnose, resizing images is required to maintain this characteristic, which is significant. Thus, in this paper, we also research and evaluate the performance of different interpolation methods, including linear and cubic interpolation. The experiment results evaluated on a private dataset present promising results in the thyroid image classification of the proposed approach. Full article
(This article belongs to the Special Issue AI-Driven Innovations in Healthcare: Advances in Machine Learning and Computer Vision)
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13 pages, 2098 KiB  
Article
A Prescribed-Time Consensus Algorithm for Distributed Time-Varying Optimization Based on Multiagent Systems
by Yanling Zheng, Siyu Liu and Jie Zhong
Mathematics 2025, 13(13), 2190; https://doi.org/10.3390/math13132190 - 4 Jul 2025
Viewed by 254
Abstract
This paper presents a distributed optimization algorithm for time-varying objective functions utilizing a prescribed-time convergent multi-agent system within undirected communication networks. Departing from conventional time-invariant optimization paradigms with static optimal solutions, our approach specifically addresses the challenge of tracking dynamic optimal trajectories in [...] Read more.
This paper presents a distributed optimization algorithm for time-varying objective functions utilizing a prescribed-time convergent multi-agent system within undirected communication networks. Departing from conventional time-invariant optimization paradigms with static optimal solutions, our approach specifically addresses the challenge of tracking dynamic optimal trajectories in evolving environments. A novel continuous-time distributed optimization algorithm is developed based on prescribed-time consensus, guaranteeing the consensus attainment among agents within a user-defined timeframe while asymptotically converging to the time-dependent optimal solution. The proposed methodology enables explicit predetermination of convergence duration, representing a significant advancement over existing asymptotic convergence methods. Moreover, two simulation examples on the rendezvous problem and multi-robots control are presented to validate the theoretical results, exhibiting precise time-controlled convergence characteristics and effective tracking performance for time-varying optimization targets. Full article
(This article belongs to the Special Issue Advances in Switched Systems and Control Theory: Theory and Application)
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26 pages, 21316 KiB  
Article
MultS-ORB: Multistage Oriented FAST and Rotated BRIEF
by Shaojie Zhang, Yinghui Wang, Jiaxing Ma, Jinlong Yang, Liangyi Huang and Xiaojuan Ning
Mathematics 2025, 13(13), 2189; https://doi.org/10.3390/math13132189 - 4 Jul 2025
Viewed by 176
Abstract
Feature matching is crucial in image recognition. However, blurring caused by illumination changes often leads to deviations in local appearance-based similarity, resulting in ambiguous or false matches—an enduring challenge in computer vision. To address this issue, this paper proposes a method named MultS-ORB [...] Read more.
Feature matching is crucial in image recognition. However, blurring caused by illumination changes often leads to deviations in local appearance-based similarity, resulting in ambiguous or false matches—an enduring challenge in computer vision. To address this issue, this paper proposes a method named MultS-ORB (Multistage Oriented FAST and Rotated BRIEF). The proposed method preserves all the advantages of the traditional ORB algorithm while significantly improving feature matching accuracy under illumination-induced blurring. Specifically, it first generates initial feature matching pairs using KNN (K-Nearest Neighbors) based on descriptor similarity in the Hamming space. Then, by introducing a local motion smoothness constraint, GMS (Grid-Based Motion Statistics) is applied to filter and optimize the matches, effectively reducing the interference caused by blurring. Afterward, the PROSAC (Progressive Sampling Consensus) algorithm is employed to further eliminate false correspondences resulting from illumination changes. This multistage strategy yields more accurate and reliable feature matches. Experimental results demonstrate that for blurred images affected by illumination changes, the proposed method improves matching accuracy by an average of 75%, reduces average error by 33.06%, and decreases RMSE (Root Mean Square Error) by 35.86% compared to the traditional ORB algorithm. Full article
(This article belongs to the Topic Intelligent Image Processing Technology)
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19 pages, 4711 KiB  
Article
Dynamical Analysis and Optimization of Combined Vibration Isolator with Time Delay
by Yaowei Wang and Xiangyu Li
Mathematics 2025, 13(13), 2188; https://doi.org/10.3390/math13132188 - 4 Jul 2025
Viewed by 203
Abstract
Vibration control has long been a key concern in engineering, with low-frequency vibration isolation remaining particularly challenging. Traditional linear isolators are limited in their ability to provide high load-bearing capacity and effective low-frequency isolation simultaneously. In contrast, quasi-zero stiffness (QZS) isolators offer low [...] Read more.
Vibration control has long been a key concern in engineering, with low-frequency vibration isolation remaining particularly challenging. Traditional linear isolators are limited in their ability to provide high load-bearing capacity and effective low-frequency isolation simultaneously. In contrast, quasi-zero stiffness (QZS) isolators offer low dynamic stiffness near equilibrium while maintaining high static stiffness, thereby enabling superior isolation performance in the low and ultra-low frequency range. This paper proposes a novel vibration isolation system that combines a grounded dynamic absorber with a QZS isolator, incorporating time-delay feedback control to enhance performance. The dynamic equations of the system are derived using Newton’s second law. The harmonic balance method combined with the arc-length continuation technique is employed to obtain steady-state responses under harmonic force excitation. The influence of feedback gain and time delay on vibration isolation effectiveness and dynamic behavior is analyzed, demonstrating the ability of time-delay feedback to modulate system responses and suppress primary resonance peaks. To further enhance performance, a genetic algorithm is used to optimize the control parameters under harmonic force excitation. The force transmissibility is defined as fitness functions, and the effects of control parameters on these metrics are examined. The results show that the optimized time-delay feedback parameters significantly reduce the transmitted force, improving the overall isolation efficiency. The proposed system provides a promising approach for achieving high-performance vibration isolation in low-frequency environments. Full article
(This article belongs to the Special Issue Advances in Switched Systems and Control Theory: Theory and Application)
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