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Journal Description

Mathematics

Mathematics is a peer-reviewed, open access journal which provides an advanced forum for studies related to mathematics, and is published semimonthly online by MDPI. The European Society for Fuzzy Logic and Technology (EUSFLAT) and International Society for the Study of Information (IS4SI) are affiliated with Mathematics and their members receive a discount on article processing charges.

Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
High Visibility: indexed within Scopus, SCIE (Web of Science), RePEc, and other databases.
Journal Rank: JCR - Q1 (Mathematics) / CiteScore - Q1 (General Mathematics )
Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 18.4 days after submission; acceptance to publication is undertaken in 2.4 days (median values for papers published in this journal in the first half of 2025).
Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
Sections: published in 17 topical sections.
Companion journals for Mathematics include: Foundations, Analytics, International Journal of Topology, Geometry and Logics.

Impact Factor: 2.2 (2024); 5-Year Impact Factor: 2.0 (2024)

Imprint Information Journal Flyer Open Access ISSN: 2227-7390

Latest Articles

27 pages, 12221 KiB

Open AccessArticle

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 (registering DOI) - 5 Jul 2025

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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22 pages, 2107 KiB

Open AccessArticle

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 (registering DOI) - 5 Jul 2025

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)

31 pages, 49075 KiB

Open AccessFeature PaperArticle

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 (registering DOI) - 5 Jul 2025

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)

22 pages, 478 KiB

Open AccessArticle

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 (registering DOI) - 5 Jul 2025

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)

27 pages, 1628 KiB

Open AccessArticle

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 (registering DOI) - 5 Jul 2025

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))

46 pages, 1709 KiB

Open AccessArticle

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 (registering DOI) - 5 Jul 2025

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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24 pages, 3730 KiB

Open AccessArticle

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 (registering DOI) - 4 Jul 2025

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)

15 pages, 1233 KiB

Open AccessArticle

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 (registering DOI) - 4 Jul 2025

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)

30 pages, 3032 KiB

Open AccessArticle

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 (registering DOI) - 4 Jul 2025

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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27 pages, 2328 KiB

Open AccessArticle

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

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)

16 pages, 1927 KiB

Open AccessArticle

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

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

36 pages, 1506 KiB

Open AccessArticle

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

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)

12 pages, 1293 KiB

Open AccessArticle

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

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, 2087 KiB

Open AccessArticle

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

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)

26 pages, 21316 KiB

Open AccessArticle

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

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

Open AccessFeature PaperArticle

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

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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16 pages, 817 KiB

Open AccessArticle

Rat Locomotion Analysis Based on Straight Line Detection in Hough Space

by José Trinidad Guillen Bonilla, Héctor Guillen Bonilla, Nancy Elizabeth Franco Rodríguez, Mario Alberto García Ramírez, Alex Guillen Bonilla, Maricela Jiménez Rodríguez and María Eugenia Sánchez Morales

Mathematics 2025, 13(13), 2187; https://doi.org/10.3390/math13132187 - 4 Jul 2025

This paper demonstrates a method to perform movement analysis on rats named Movement Measurement in Hough Transform Space (MMHTS). The MMHTS method consists of representing locomotion of movement based on a system of linear equations and subsequently detecting the straight lines in the [...] Read more.

This paper demonstrates a method to perform movement analysis on rats named Movement Measurement in Hough Transform Space (MMHTS). The MMHTS method consists of representing locomotion of movement based on a system of linear equations and subsequently detecting the straight lines in the Hough transform space. Four straight lines

L_{0}

,

L_{1}

,

L_{2}

and

L_{3}

are detected, and with their information the angles between the beelines

α_{0}

,

α_{1}

,

α_{3}

, intersection points

p_{1} (x_{1}, y_{1})

,

p_{2} (x_{2}, y_{2})

,

p_{3} (x_{3}, y_{3})

and their lengths

d_{L_{0}}

,

d_{L_{1}}

,

d_{L_{3}}

,

d_{L_{4}}

are measured, corresponding to the locomotion geometry of the rats’ limps. Experimentally, the MMHTS method was employed for locomotion movement and the obtained results were compared with professional design software, detecting the following miscalculations: 0.144° for the angle measurements, 0.131 for the length measurement and 0.139 for the point detection. Based in the measurements results and the calculated errors, the MMHTS method is efficient and exhibits a high application potential in motion analysis. Full article

(This article belongs to the Special Issue Advanced Image Processing and Computational Intelligence: Methodologies and Applications)

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21 pages, 3918 KiB

Open AccessArticle

Comparative Analysis of Resampling Techniques for Class Imbalance in Financial Distress Prediction Using XGBoost

by Guodong Hou, Dong Ling Tong, Soung Yue Liew and Peng Yin Choo

Mathematics 2025, 13(13), 2186; https://doi.org/10.3390/math13132186 - 4 Jul 2025

One of the key challenges in financial distress data is class imbalance, where the data are characterized by a highly imbalanced ratio between the number of distressed and non-distressed samples. This study examines eight resampling techniques for improving distress prediction using the XGBoost [...] Read more.

One of the key challenges in financial distress data is class imbalance, where the data are characterized by a highly imbalanced ratio between the number of distressed and non-distressed samples. This study examines eight resampling techniques for improving distress prediction using the XGBoost algorithm. The study was performed on a dataset acquired from the CSMAR database, containing 26,383 firm-quarter samples from 639 Chinese A-share listed companies (2007–2024), with only 12.1% of the cases being distressed. Results show that standard Synthetic Minority Oversampling Technique (SMOTE) enhanced F1-score (up to 0.73) and Matthews Correlation Coefficient (MCC, up to 0.70), while SMOTE-Tomek and Borderline-SMOTE further boosted recall, slightly sacrificing precision. These oversampling and hybrid methods also maintained reasonable computational efficiency. However, Random Undersampling (RUS), though yielding high recall (0.85), suffered from low precision (0.46) and weaker generalization, but was the fastest method. Among all techniques, Bagging-SMOTE achieved balanced performance (AUC 0.96, F1 0.72, PR-AUC 0.80, MCC 0.68) using a minority-to-majority ratio of 0.15, demonstrating that ensemble-based resampling can improve robustness with minimal impact on the original class distribution, albeit with higher computational cost. The compared findings highlight that no single approach fits all use cases, and technique selection should align with specific goals. Techniques favoring recall (e.g., Bagging-SMOTE, SMOTE-Tomek) are suited for early warning, while conservative techniques (e.g., Tomek Links) help reduce false positives in risk-sensitive applications, and efficient methods such as RUS are preferable when computational speed is a priority. Full article

(This article belongs to the Special Issue New Advances in Computational Finance and Computational Intelligence in Finance)

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16 pages, 662 KiB

Open AccessArticle

Augmenting Naïve Bayes Classifiers with k-Tree Topology

by Fereshteh R. Dastjerdi and Liming Cai

Mathematics 2025, 13(13), 2185; https://doi.org/10.3390/math13132185 - 4 Jul 2025

The Bayesian network is a directed, acyclic graphical model that can offer a structured description for probabilistic dependencies among random variables. As powerful tools for classification tasks, Bayesian classifiers often require computing joint probability distributions, which can be computationally intractable due to potential [...] Read more.

The Bayesian network is a directed, acyclic graphical model that can offer a structured description for probabilistic dependencies among random variables. As powerful tools for classification tasks, Bayesian classifiers often require computing joint probability distributions, which can be computationally intractable due to potential full dependencies among feature variables. On the other hand, Naïve Bayes, which presumes zero dependencies among features, trades accuracy for efficiency and often comes with underperformance. As a result, non-zero dependency structures, such as trees, are often used as more feasible probabilistic graph approximations; in particular, Tree Augmented Naïve Bayes (TAN) has been demonstrated to outperform Naïve Bayes and has become a popular choice. For applications where a variable is strongly influenced by multiple other features, TAN has been further extended to the k-dependency Bayesian classifier (KDB), where one feature can depend on up to k other features (for a given

k \geq 2

). In such cases, however, the selection of the k parent features for each variable is often made through heuristic search methods (such as sorting), which do not guarantee an optimal approximation of network topology. In this paper, the novel notion of k-tree Augmented Naïve Bayes (k-TAN) is introduced to augment Naïve Bayesian classifiers with k-tree topology as an approximation of Bayesian networks. It is proved that, under the Kullback–Leibler divergence measurement, k-tree topology approximation of Bayesian classifiers loses the minimum information with the topology of a maximum spanning k-tree, where the edge weights of the graph are mutual information between random variables conditional upon the class label. In addition, while in general finding a maximum spanning k-tree is NP-hard for fixed

k \geq 2

, this work shows that the approximation problem can be solved in time

O (n^{k + 1})

if the spanning k-tree also desires to retain a given Hamiltonian path in the graph. Therefore, this algorithm can be employed to ensure efficient approximation of Bayesian networks with k-tree augmented Naïve Bayesian classifiers of the guaranteed minimum loss of information. Full article

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23 pages, 1708 KiB

Open AccessArticle

Sales Mode Selection and Blockchain Adoption for Platform Supply Chain Under Risk Aversion

by Yu Jing and Fengzhi Liu

Mathematics 2025, 13(13), 2184; https://doi.org/10.3390/math13132184 - 4 Jul 2025

Uncertainty in consumer purchasing behavior within online markets propels manufacturers to adopt blockchain for risk mitigation, reshaping supply chain operational dynamics. This study investigates the sales mode selection and blockchain adoption strategies of a risk-averse manufacturer in platform supply chain under uncertain market [...] Read more.

Uncertainty in consumer purchasing behavior within online markets propels manufacturers to adopt blockchain for risk mitigation, reshaping supply chain operational dynamics. This study investigates the sales mode selection and blockchain adoption strategies of a risk-averse manufacturer in platform supply chain under uncertain market demand. By integrating Stackelberg game theory with mean-variance analysis, we analyze supply chain equilibrium across four scenarios: RN, RB, AN, and AB. Our findings highlight the significance of a critical commission rate threshold in the manufacturer’s sales mode choice, emphasizing that blockchain adoption enhances the preference for the agency mode. Importantly, highly risk-averse manufacturers are inclined to absorb higher costs associated with blockchain adoption, while those with lower risk aversion only consider it when costs are minimal. Notably, the “agency mode with blockchain adoption” (AB) creates mutual benefits under low adoption costs and risk aversion. When both parties exhibit risk aversion, the platform’s risk aversion significantly influences resale-mode decisions, leading to a transition from the scenario AN to the RB, thereby optimizing synchronized profits. Full article

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