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Mathematics
Volume 13
Issue 10
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Mathematics, Volume 13, Issue 10 (May-2 2025) – 153 articles

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22 pages, 2702 KiB  
Article
A Novel Forecasting System with Data Preprocessing and Machine Learning for Containerized Freight Market
by Yonghui Duan, Xiaotong Zhang, Xiang Wang, Yingying Fan and Kaige Liu
Mathematics 2025, 13(10), 1695; https://doi.org/10.3390/math13101695 - 21 May 2025
Viewed by 139
Abstract
The Shanghai Containerized Freight Index (SCFI) and Ningbo Containerized Freight Index (NCFI) serve as crucial indicators for management and decision-making in China’s shipping industry. This study proposes a novel real-time rolling decomposition forecasting system integrating multiple influencing factors. The framework consists of two [...] Read more.
The Shanghai Containerized Freight Index (SCFI) and Ningbo Containerized Freight Index (NCFI) serve as crucial indicators for management and decision-making in China’s shipping industry. This study proposes a novel real-time rolling decomposition forecasting system integrating multiple influencing factors. The framework consists of two core modules: data preprocessing and prediction. In the data preprocessing stage, the Hampel filter is utilized to filter and revise each raw containerized freight index dataset, eliminating the adverse effects of outliers. Additionally, variational mode decomposition (VMD) technique is employed to decompose the time series in a rolling manner, effectively avoiding data leakage while extracting significant features. In the forecasting stage, the cheetah optimization algorithm (COA) optimizes the key parameters of the extreme gradient boosting (XGBoost) model, enhancing forecasting accuracy. The empirical analysis based on SCFI and NCFI data reveals that historical pricing serves as a critical determinant, with our integrated model demonstrating superior performance compared to existing methodologies. These findings substantiate the model’s robust generalization capability and operational efficiency across diverse shipping markets, highlighting its potential value for managerial decision-making in maritime industry practices. Full article
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15 pages, 444 KiB  
Article
Exploring the Crossing Numbers of Three Join Products of 6-Vertex Graphs with Discrete Graphs
by Michal Staš and Mária Švecová
Mathematics 2025, 13(10), 1694; https://doi.org/10.3390/math13101694 - 21 May 2025
Viewed by 61
Abstract
The significance of searching for edge crossings in graph theory lies inter alia in enhancing the clarity and readability of graph representations, which is essential for various applications such as network visualization, circuit design, and data representation. This paper focuses on exploring the [...] Read more.
The significance of searching for edge crossings in graph theory lies inter alia in enhancing the clarity and readability of graph representations, which is essential for various applications such as network visualization, circuit design, and data representation. This paper focuses on exploring the crossing number of the join product G*+Dn, where G* is a graph isomorphic to the path on four vertices P4 with an additional two vertices adjacent to two inner vertices of P4, and Dn is a discrete graph composed of n isolated vertices. The proof is based on exact crossing-number values for join products involving particular subgraphs Hk of G* with discrete graphs Dn combined with the symmetrical properties of graphs. This approach could also be adapted to determine the unknown crossing numbers of two other 6-vertices graphs obtained by adding one or two additional edges to the graph G*. Full article
(This article belongs to the Special Issue Advances in Mathematics: Equations, Algebra, and Discrete Mathematics)
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10 pages, 214 KiB  
Article
Mean–Variance–Entropy Framework for Cryptocurrency Portfolio Optimization
by Florentin Șerban and Bogdan-Petru Vrînceanu
Mathematics 2025, 13(10), 1693; https://doi.org/10.3390/math13101693 - 21 May 2025
Viewed by 89
Abstract
Portfolio optimization is a fundamental problem in financial theory, aiming to balance risk and return in asset allocation. Traditional models, such as Mean–Variance optimization, are effective, but often fail to account for diversification adequately. This study introduces the Mean–Variance–Entropy (MVE) model, which integrates [...] Read more.
Portfolio optimization is a fundamental problem in financial theory, aiming to balance risk and return in asset allocation. Traditional models, such as Mean–Variance optimization, are effective, but often fail to account for diversification adequately. This study introduces the Mean–Variance–Entropy (MVE) model, which integrates Tsallis entropy into the classic Mean–Variance framework to enhance portfolio diversification and risk management. Entropy, specifically second-order entropy, penalizes excessive concentration in the portfolio, encouraging a more balanced and diversified allocation of assets. The model is applied to a portfolio of five major cryptocurrencies: Bitcoin (BTC), Ethereum (ETH), Solana (SOL), Cardano (ADA), and Binance Coin (BNB). The performance of the MVE model is compared with that of the traditional Mean–Variance model, and results demonstrate that the entropy-enhanced model provides better diversification, although with a slightly lower Sharpe ratio. The findings suggest that while the entropy-adjusted model results in a slightly lower Sharpe ratio, it offers better diversification and a more resilient portfolio, especially in volatile markets. This study demonstrates the potential of incorporating entropy into portfolio optimization as a means to mitigate concentration risk and improve portfolio performance. The approach is particularly beneficial for markets such as cryptocurrency, where volatility and asset correlations fluctuate rapidly. This paper contributes to the growing body of literature on portfolio optimization by offering a more diversified, robust, and risk-adjusted approach to asset allocation Full article
(This article belongs to the Section E5: Financial Mathematics)
28 pages, 6981 KiB  
Article
Parameter Estimation and Forecasting Strategies for Cholera Dynamics: Insights from the 1991–1997 Peruvian Epidemic
by Hamed Karami, Gerardo Chowell, Oscar J. Mujica and Alexandra Smirnova
Mathematics 2025, 13(10), 1692; https://doi.org/10.3390/math13101692 - 21 May 2025
Viewed by 74
Abstract
Environmental transmission is a critical driver of cholera dynamics and a key factor influencing model-based inference and forecasting. This study focuses on stable parameter estimation and forecasting of cholera outbreaks using a compartmental SIRB model informed by three formulations of the environmental transmission [...] Read more.
Environmental transmission is a critical driver of cholera dynamics and a key factor influencing model-based inference and forecasting. This study focuses on stable parameter estimation and forecasting of cholera outbreaks using a compartmental SIRB model informed by three formulations of the environmental transmission rate: (1) a pre-parameterized periodic function, (2) a temperature-driven function, and (3) a flexible, data-driven time-dependent function. We apply these methods to the 1991–1997 cholera epidemic in Peru, estimating key parameters; these include the case reporting rate and human-to-human transmission rate. We assess practical identifiability via parametric bootstrapping and compare the performance of each transmission formulation in fitting epidemic data and forecasting short-term incidence. Our results demonstrate that while the data-driven approach achieves superior in-sample fit, the temperature-dependent model offers better forecasting performance due to its ability to incorporate seasonal trends. The study highlights trade-offs between model flexibility and parameter identifiability and provides a framework for evaluating cholera transmission models under data limitations. These insights can inform public health strategies for outbreak preparedness and response. Full article
(This article belongs to the Special Issue Advanced Intelligent Algorithms for Decision Making under Uncertainty)
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22 pages, 1296 KiB  
Article
Interpretable Process Monitoring Using Data-Driven Fuzzy-Based Models for Wastewater Treatment Plants
by Rodrigo Salles, Miguel Proença, Rui Araújo, Jorge S. S. Júnior and Jérôme Mendes
Mathematics 2025, 13(10), 1691; https://doi.org/10.3390/math13101691 - 21 May 2025
Viewed by 69
Abstract
Digital transformation of industry has gained emphasis in recent years in academia and industry. Organizations need to be more competitive and efficient and improve their processes and performance to cope with changes in environmental legislation, efficient management of resources and energy, and the [...] Read more.
Digital transformation of industry has gained emphasis in recent years in academia and industry. Organizations need to be more competitive and efficient and improve their processes and performance to cope with changes in environmental legislation, efficient management of resources and energy, and the trend toward zero waste. These factors have led to the emergence of a new concept. This paper studies data-driven fuzzy-based models for process monitoring focused on Wastewater Treatment Plants (WWTPs). This work aims to study interpretable industrial process monitoring models, which must be easily interpretable by expert process operators. For this purpose, different fuzzy-based models were studied. Exhaustive validations are performed. The studied models employ 16 key variables at 14 different points throughout the waterline of a treatment plant. The learning and testing of each model for every key variable at each involved point use distinct sets of input variables and varied learning model parameters. The impact of the selected input variables and the learning parameters on the model accuracy, and the accuracy versus interpretability tradeoff are analyzed. The best model for each key variable is developed based on the accuracy versus interpretability tradeoff. Full article
(This article belongs to the Special Issue Advanced Research in Fuzzy System and Neural Networks)
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15 pages, 588 KiB  
Article
Safest-Value of the Number of Primes in RSA Modulus and an Improvised Generalized Multi-Moduli RSA
by Jay Mehta and Hitarth Rana
Mathematics 2025, 13(10), 1690; https://doi.org/10.3390/math13101690 - 21 May 2025
Viewed by 79
Abstract
Several attacks on the well-known RSA cryptosystem that can be extended to a multi-prime version of RSA reveal that it is preferable to use the modulus having more prime factors. On the contrary, the larger the number of prime factors of the modulus, [...] Read more.
Several attacks on the well-known RSA cryptosystem that can be extended to a multi-prime version of RSA reveal that it is preferable to use the modulus having more prime factors. On the contrary, the larger the number of prime factors of the modulus, the greater the risk of its factorization, due to the reduced size of its prime factors. In this paper, we derive an optimal value of the number of prime factors in a multi-prime RSA modulus and introduce the notion of the “safest-value” and determine such safest-values for moduli of different sizes. By utilizing this concept, we propose an enhanced version of our Generalized Multi-Moduli RSA (GMMRSA), which is now secure against even more attacks than its previous version. Full article
(This article belongs to the Special Issue Analytic Methods in Number Theory and Allied Fields)
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10 pages, 244 KiB  
Article
Revisiting Some Relationships Between the Weighted Spectral Mean and the Wasserstein Mean
by Minh Thanh Duong, Anh Vu Le, Cong Trinh Le and Trung Hoa Dinh
Mathematics 2025, 13(10), 1689; https://doi.org/10.3390/math13101689 - 21 May 2025
Viewed by 68
Abstract
In this paper, we introduce the 2-geometric mean and explore its connections with the spectral geometric mean and the Wasserstein mean for positive definite matrices. Additionally, we revisit and establish several inequalities involving these means in the context of the near order relation. [...] Read more.
In this paper, we introduce the 2-geometric mean and explore its connections with the spectral geometric mean and the Wasserstein mean for positive definite matrices. Additionally, we revisit and establish several inequalities involving these means in the context of the near order relation. Full article
(This article belongs to the Special Issue Matrix Equations and Their Algorithms Analysis)
11 pages, 230 KiB  
Article
Symmetrized, Perturbed Hyperbolic Tangent-Based Complex-Valued Trigonometric and Hyperbolic Neural Network Accelerated Approximation
by George A. Anastassiou
Mathematics 2025, 13(10), 1688; https://doi.org/10.3390/math13101688 - 21 May 2025
Viewed by 175
Abstract
In this study, we research the univariate quantitative symmetrized approximation of complex-valued continuous functions on a compact interval by complex-valued symmetrized and perturbed neural network operators. These approximations are derived by establishing Jackson-type inequalities involving the modulus of continuity of the used function’s [...] Read more.
In this study, we research the univariate quantitative symmetrized approximation of complex-valued continuous functions on a compact interval by complex-valued symmetrized and perturbed neural network operators. These approximations are derived by establishing Jackson-type inequalities involving the modulus of continuity of the used function’s high order derivatives. The kinds of our approximations are trigonometric and hyperbolic. Our symmetrized operators are defined by using a density function generated by a q-deformed and λ-parametrized hyperbolic tangent function, which is a sigmoid function. These accelerated approximations are pointwise and of the uniform norm. The related complex-valued feed-forward neural networks have one hidden layer. Full article
(This article belongs to the Special Issue Current Topics in Optimization, Inequalities and Convex Function Theory)
44 pages, 2144 KiB  
Article
Stochastic Variance Reduced Primal–Dual Hybrid Gradient Methods for Saddle-Point Problems
by Weixin An, Yuanyuan Liu, Fanhua Shang and Hongying Liu
Mathematics 2025, 13(10), 1687; https://doi.org/10.3390/math13101687 - 21 May 2025
Viewed by 71
Abstract
Recently, many stochastic Alternating Direction Methods of Multipliers (ADMMs) have been proposed to solve large-scale machine learning problems. However, for large-scale saddle-point problems, the state-of-the-art (SOTA) stochastic ADMMs still have high per-iteration costs. On the other hand, the stochastic primal–dual hybrid gradient (SPDHG) [...] Read more.
Recently, many stochastic Alternating Direction Methods of Multipliers (ADMMs) have been proposed to solve large-scale machine learning problems. However, for large-scale saddle-point problems, the state-of-the-art (SOTA) stochastic ADMMs still have high per-iteration costs. On the other hand, the stochastic primal–dual hybrid gradient (SPDHG) has a low per-iteration cost but only a suboptimal convergence rate of 𝒪(1/S). Thus, there still remains a gap in the convergence rates between SPDHG and SOTA ADMMs. Motivated by the two matters, we propose (accelerated) stochastic variance reduced primal–dual hybrid gradient ((A)SVR-PDHG) methods. We design a linear extrapolation step to improve the convergence rate and a new adaptive epoch length strategy to remove the extra boundedness assumption. Our algorithms have a simpler structure and lower per-iteration complexity than SOTA ADMMs. As a by-product, we present the asynchronous parallel variants of our algorithms. In theory, we rigorously prove that our methods converge linearly for strongly convex problems and improve the convergence rate to 𝒪(1/S2) for non-strongly convex problems as opposed to the existing 𝒪(1/S) convergence rate. Compared with SOTA algorithms, various experimental results demonstrate that ASVR-PDHG can achieve an average speedup of 2×∼5×. Full article
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19 pages, 6834 KiB  
Article
SCS-Net: Stratified Compressive Sensing Network for Large-Scale Crowd Flow Prediction
by Xiaoyong Tan, Kaiqi Chen, Min Deng, Baoju Liu, Zhiyuan Zhao, Youjun Tu and Sheng Wu
Mathematics 2025, 13(10), 1686; https://doi.org/10.3390/math13101686 - 21 May 2025
Viewed by 51
Abstract
Large-scale crowd flow prediction is a critical task in urban management and public safety. However, achieving accurate and efficient prediction remains challenging. Most existing models overlook spatial heterogeneity, employing unified parameters to fit diverse crowd flow patterns across different spatial units, which limits [...] Read more.
Large-scale crowd flow prediction is a critical task in urban management and public safety. However, achieving accurate and efficient prediction remains challenging. Most existing models overlook spatial heterogeneity, employing unified parameters to fit diverse crowd flow patterns across different spatial units, which limits their accuracy. Meanwhile, the massive spatial units significantly increase the computational cost, limiting model efficiency. To address these limitations, we propose a novel model for large-scale crowd flow prediction, namely the Stratified Compressive Sensing Network (SCS-Net). First, we develop a spatially stratified module that posterior adaptively extracts the underlying spatially stratified structure, effectively modeling spatial heterogeneity. Then, we develop compressive sensing modules to compress redundant information from massive spatial units and learn shared crowd flow patterns, enabling efficient prediction. Finally, we conduct experiments on a large-scale real-world dataset. The results demonstrate that SCS-Net outperforms deep learning baseline models by 35.25–139.2% in MAE and 26.3–112.4% in RMSE while reducing GFLOPs by 53–1067 times and shortening training time by 3.1–83.2 times compared to prevalent spatio-temporal prediction models. Moreover, the spatially stratified structure extracted by SCS-Net offers valuable interpretability for spatial heterogeneity in crowd flow patterns, providing deeper insights into urban functional layouts. Full article
(This article belongs to the Special Issue Big Data Mining and Analytics with Applications)
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28 pages, 2752 KiB  
Article
Incentive Mechanism for Cloud Service Offloading in Edge–Cloud Computing Environment
by Chendie Yao, Junjie Xie and Zhong Liu
Mathematics 2025, 13(10), 1685; https://doi.org/10.3390/math13101685 - 21 May 2025
Viewed by 83
Abstract
Edge computing refers to provision storage and computation resources at the network edge, closer to end users than the remote cloud. In such edge–cloud computing environments, many cloud providers intend to offload cloud services to the edge nodes to offer high-quality services for [...] Read more.
Edge computing refers to provision storage and computation resources at the network edge, closer to end users than the remote cloud. In such edge–cloud computing environments, many cloud providers intend to offload cloud services to the edge nodes to offer high-quality services for data-intensive and latency-sensitive applications. The major obstacle is that edge nodes are rarely willing to offer resources voluntarily without any rewards. To this end, this paper proposes an efficient incentive mechanism for edge–cloud computing environments using Stackelberg game theory to motivate more edge nodes to host offloaded cloud services. We analyze the properties of the game model and present a solution to compute the unique Stackelberg Equilibrium (SE) of the nonlinear model. On this basis, we propose an efficient polynomial-time algorithm to find the SE. Moreover, we discuss the adaptation of our incentive mechanism to dynamic node joining or departing. Performance evaluations compare our incentive mechanism with three benchmarks and a state-of-the-art mechanism. The results indicate that our incentive mechanism can effectively motivate both the edge nodes and the remote cloud to participate in the edge–cloud environment, achieving maximum resource utilization with minimal rewards while remaining robust in dynamic situations. Full article
(This article belongs to the Section E: Applied Mathematics)
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30 pages, 1040 KiB  
Article
The Problem of Assigning Patients to Appropriate Health Institutions Using Multi-Criteria Decision Making and Goal Programming in Health Tourism
by Murat Suat Arsav, Nur Ayvaz-Çavdaroğlu and Ercan Şenyiğit
Mathematics 2025, 13(10), 1684; https://doi.org/10.3390/math13101684 - 21 May 2025
Viewed by 76
Abstract
Health tourism is an increasingly vital sector for both Kayseri and Türkiye, contributing significantly to exports and foreign currency inflows. Recent investments in health tourism infrastructure have positioned Kayseri as one of the leading cities in the country, particularly due to its strong [...] Read more.
Health tourism is an increasingly vital sector for both Kayseri and Türkiye, contributing significantly to exports and foreign currency inflows. Recent investments in health tourism infrastructure have positioned Kayseri as one of the leading cities in the country, particularly due to its strong healthcare facilities. This study explores Kayseri’s potential in health tourism, with a focus on bariatric surgery, by employing Multi-Criteria Decision Making (MCDM) and optimization methods. The study first provides an extensive literature review to identify the key factors influencing patients’ selection of health institutions for bariatric surgery. Subsequently, the Group Best-Worst Method (G-BWM) is applied using expert input from managers of bariatric surgery centers to determine the relative importance of these factors. Based on the G-BWM findings, nine health institutions in Kayseri offering obesity surgery services are evaluated and ranked using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), which generates institutional performance scores. Building on these results, a Goal Programming model is developed to assign patients to suitable health institutions while simultaneously considering the health institution’s revenue and patient satisfaction. This study offers several novel contributions. It integrates MCDM techniques with goal programming in the context of health tourism—a combination not widely explored in the literature. Additionally, it provides a comparative assessment of the factors influencing health tourists’ decision-making processes, offering policymakers a strategic framework for resource allocation. Lastly, by presenting a mathematical model for patient-institution assignment, the study offers practical guidance for health tourism organizations aiming to enhance both health institution revenue and patient satisfaction in the health tourism sector. Full article
(This article belongs to the Special Issue Multi-criteria Decision Making and Data Mining, 2nd Edition)
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14 pages, 292 KiB  
Article
Second-Order Gradient Estimates for the Porous Medium Equation on Riemannian Manifolds
by Jingjing Yang and Guangwen Zhao
Mathematics 2025, 13(10), 1683; https://doi.org/10.3390/math13101683 - 21 May 2025
Viewed by 36
Abstract
In this paper, we derive second-order gradient estimates for positive solutions of the porous medium equation ∂∂tu(x,t)=Δu(x,t)p,p∈1,1+1n−1 on an n-dimensional Riemannian manifold under certain curvature conditions. Full article
12 pages, 253 KiB  
Article
Pinching Results on Totally Real Submanifolds of a Locally Conformal Kähler Manifolds
by Noura M. Alhouiti, Ali H. Alkhaldi, Akram Ali and Piscoran Laurian-Ioan
Mathematics 2025, 13(10), 1682; https://doi.org/10.3390/math13101682 - 21 May 2025
Viewed by 33
Abstract
This paper investigates the relationship between pseudo-umbilical and minimal totally real submanifolds in locally conformal Kähler space forms. Some rigidity theorems and an integral inequality are obtained using the moving-frame method and the DDVV inequality. Our results extend this line of previous research. [...] Read more.
This paper investigates the relationship between pseudo-umbilical and minimal totally real submanifolds in locally conformal Kähler space forms. Some rigidity theorems and an integral inequality are obtained using the moving-frame method and the DDVV inequality. Our results extend this line of previous research. Full article
(This article belongs to the Special Issue Analysis on Differentiable Manifolds)
51 pages, 1639 KiB  
Article
High-Performance Deployment Operational Data Analytics of Pre-Trained Multi-Label Classification Architectures with Differential-Evolution-Based Hyperparameter Optimization (AutoDEHypO)
by Teo Prica and Aleš Zamuda
Mathematics 2025, 13(10), 1681; https://doi.org/10.3390/math13101681 - 20 May 2025
Viewed by 124
Abstract
This article presents a high-performance-computing differential-evolution-based hyperparameter optimization automated workflow (AutoDEHypO), which is deployed on a petascale supercomputer and utilizes multiple GPUs to execute a specialized fitness function for machine learning (ML). The workflow is designed for operational analytics of energy efficiency. In [...] Read more.
This article presents a high-performance-computing differential-evolution-based hyperparameter optimization automated workflow (AutoDEHypO), which is deployed on a petascale supercomputer and utilizes multiple GPUs to execute a specialized fitness function for machine learning (ML). The workflow is designed for operational analytics of energy efficiency. In this differential evolution (DE) optimization use case, we analyze how energy efficiently the DE algorithm performs with different DE strategies and ML models. The workflow analysis considers key factors such as DE strategies and automated use case configurations, such as an ML model architecture and dataset, while monitoring both the achieved accuracy and the utilization of computing resources, such as the elapsed time and consumed energy. While the efficiency of a chosen DE strategy is assessed based on a multi-label supervised ML accuracy, operational data about the consumption of resources of individual completed jobs obtained from a Slurm database are reported. To demonstrate the impact on energy efficiency, using our analysis workflow, we visualize the obtained operational data and aggregate them with statistical tests that compare and group the energy efficiency of the DE strategies applied in the ML models. Full article
(This article belongs to the Special Issue Innovations in High-Performance Computing)
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9 pages, 202 KiB  
Article
The Fourth Hybrid Power Mean Involving the Character Sums and Exponential Sums
by Guohui Chen and Tingting Du
Mathematics 2025, 13(10), 1680; https://doi.org/10.3390/math13101680 - 20 May 2025
Viewed by 94
Abstract
In this paper, we consider the fourth hybrid power mean involving two-term exponential sums and third-order character sum modulo p, a topic of significant importance in analytic number theory. These results generalize prior research, and provide new insights for studying the relationship [...] Read more.
In this paper, we consider the fourth hybrid power mean involving two-term exponential sums and third-order character sum modulo p, a topic of significant importance in analytic number theory. These results generalize prior research, and provide new insights for studying the relationship between character sums and exponential sums. Full article
(This article belongs to the Special Issue Analytic Methods in Number Theory and Allied Fields)
15 pages, 671 KiB  
Article
A Simultaneous Decomposition for a Quaternion Tensor Quaternity with Applications
by Jia-Wei Huo, Yun-Ze Xu and Zhuo-Heng He
Mathematics 2025, 13(10), 1679; https://doi.org/10.3390/math13101679 - 20 May 2025
Viewed by 105
Abstract
Quaternion tensor decompositions have recently been the center of focus due to their wide potential applications in color data processing. In this paper, we establish a simultaneous decomposition for a quaternion tensor quaternity under Einstein product. The decomposition brings the quaternity of four [...] Read more.
Quaternion tensor decompositions have recently been the center of focus due to their wide potential applications in color data processing. In this paper, we establish a simultaneous decomposition for a quaternion tensor quaternity under Einstein product. The decomposition brings the quaternity of four quaternion tensors into a canonical form, which only has 0 and 1 entries. The structure of the canonical form is discussed in detail. Moreover, the proposed decomposition is applied to a new framework of color video encryption and decryption based on discrete wavelet transform. This new approach can realize simultaneous encryption and compression with high security. Full article
(This article belongs to the Special Issue Advanced Numerical Linear Algebra)
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22 pages, 344 KiB  
Article
Inverse Source Problem for a Singular Parabolic Equation with Variable Coefficients
by Xue Qin and Shumin Li
Mathematics 2025, 13(10), 1678; https://doi.org/10.3390/math13101678 - 20 May 2025
Viewed by 99
Abstract
We consider a parabolic equation with a singular potential in a bounded domain Ω⊂Rn. The main result is a Lipschitz stability estimate for an inverse source problem of determining a spatial varying factor f(x) of the [...] Read more.
We consider a parabolic equation with a singular potential in a bounded domain Ω⊂Rn. The main result is a Lipschitz stability estimate for an inverse source problem of determining a spatial varying factor f(x) of the source term R(x,t)f(x). We obtain a consistent stability result for any μ≤p1μ*, where p1>0 is the lower bound of p(x) and μ*=(n−2)2/4, and this condition for μ is also almost a consistently optimal condition for the existence of solutions. The main method we used is the Carleman estimate, and the proof for the inverse source problem relies on the Bukhgeim–Klibanov method. Full article
45 pages, 3653 KiB  
Review
Certified Neural Network Control Architectures: Methodological Advances in Stability, Robustness, and Cross-Domain Applications
by Rui Liu, Jianhua Huang, Biao Lu and Weili Ding
Mathematics 2025, 13(10), 1677; https://doi.org/10.3390/math13101677 - 20 May 2025
Viewed by 118
Abstract
Neural network (NN)-based controllers have emerged as a paradigm-shifting approach in modern control systems, demonstrating unparalleled capabilities in governing nonlinear dynamical systems with inherent uncertainties. This comprehensive review systematically investigates the theoretical foundations and practical implementations of NN controllers through the prism of [...] Read more.
Neural network (NN)-based controllers have emerged as a paradigm-shifting approach in modern control systems, demonstrating unparalleled capabilities in governing nonlinear dynamical systems with inherent uncertainties. This comprehensive review systematically investigates the theoretical foundations and practical implementations of NN controllers through the prism of Lyapunov stability theory, NN controller frameworks, and robustness analysis. The review establishes that recurrent neural architectures inherently address time-delayed state compensation and disturbance rejection, achieving superior trajectory tracking performance compared to classical control strategies. By integrating imitation learning with barrier certificate constraints, the proposed methodology ensures provable closed-loop stability while maintaining safety-critical operation bounds. Experimental evaluations using chaotic system benchmarks confirm the exceptional modeling capacity of NN controllers in capturing complex dynamical behaviors, complemented by formal verification advances through reachability analysis techniques. Practical demonstrations in aerial robotics and intelligent transportation systems highlight the efficacy of controllers in real-world scenarios involving environmental uncertainties and multi-agent interactions. The theoretical framework synergizes data-driven learning with nonlinear control principles, introducing hybrid automata formulations for transient response analysis and adjoint sensitivity methods for network optimization. These innovations position NN controllers as a transformative technology in control engineering, offering fundamental advances in stability-guaranteed learning and topology optimization. Future research directions will emphasize the integration of physics-informed neural operators for distributed control systems and event-triggered implementations for resource-constrained applications, paving the way for next-generation intelligent control architectures. Full article
(This article belongs to the Special Issue Artificial Intelligence and Mathematical Models in Robotics and Automation)
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22 pages, 9551 KiB  
Article
Parametric Analysis of Auxetic Honeycombs
by Stefan Tabacu, Ana-Gabriela Badea, Alina-Ionela Aparaschivei and Daniel-Constantin Anghel
Mathematics 2025, 13(10), 1676; https://doi.org/10.3390/math13101676 - 20 May 2025
Viewed by 119
Abstract
The auxetic honeycomb can change mechanical behavior from positive to negative Poisson’s ratio by slightly adjusting the geometrical feature. As a first step, the paper investigates existing analytical solutions to the problem to provide the theoretical background. The present study discusses the methodology [...] Read more.
The auxetic honeycomb can change mechanical behavior from positive to negative Poisson’s ratio by slightly adjusting the geometrical feature. As a first step, the paper investigates existing analytical solutions to the problem to provide the theoretical background. The present study discusses the methodology used to examine these structures using the finite element method and how to adapt simple numerical models to capture structural behavior. Subsequently, the numerical model is used to run parametric analyses to determine the performance and provide the background for discussing the influence of the dimensional set on the response. Following this set of observations, an empirical solution connecting the unit cell to the global structure was formulated. A large dataset is generated to train and check machine-learning applications to develop a helpful tool for predicting the response without numerical and theoretical evaluation models and methods. The machine-learning section investigates the influence of several parameters on the response and the effect of complete versus incomplete datasets. Full article
(This article belongs to the Special Issue Numerical Analysis and Finite Element Method with Applications)
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17 pages, 6407 KiB  
Article
Robust Closed–Open Loop Iterative Learning Control for MIMO Discrete-Time Linear Systems with Dual-Varying Dynamics and Nonrepetitive Uncertainties
by Yawen Zhang, Yunshan Wei, Zuxin Ye, Shilin Liu, Hao Chen, Yuangao Yan and Junhong Chen
Mathematics 2025, 13(10), 1675; https://doi.org/10.3390/math13101675 - 20 May 2025
Viewed by 92
Abstract
Iterative learning control (ILC) typically requires strict repeatability in initial states, trajectory length, external disturbances, and system dynamics. However, these assumptions are often difficult to fully satisfy in practical applications. While most existing studies have achieved limited progress in relaxing either one or [...] Read more.
Iterative learning control (ILC) typically requires strict repeatability in initial states, trajectory length, external disturbances, and system dynamics. However, these assumptions are often difficult to fully satisfy in practical applications. While most existing studies have achieved limited progress in relaxing either one or two of these constraints simultaneously, this work aims to eliminate the restrictions imposed by all four strict repeatability conditions in ILC. For general finite-duration multi-input multi-output (MIMO) linear discrete-time systems subject to multiple non-repetitive uncertainties—including variations in initial states, external disturbances, trajectory lengths, and system dynamics—an innovative open-closed loop robust iterative learning control law is proposed. The feedforward component is used to make sure the tracking error converges as expected mathematically, while the feedback control part compensates for missing tracking data from previous iterations by utilizing real-time tracking information from the current iteration. The convergence analysis employs an input-to-state stability (ISS) theory for discrete parameterized systems. Detailed explanations are provided on adjusting key parameters to satisfy the derived convergence conditions, thereby ensuring that the anticipated tracking error will eventually settle into a compact neighborhood that meets the required standards for robustness and convergence speed. To thoroughly assess the viability of the proposed ILC framework, computer simulations effectively illustrate the strategy’s effectiveness. Further simulation on a real system, a piezoelectric motor system, verifies that the ILC tracking error converges to a small neighborhood in the sense of mathematical expectation. Extending the ILC to complex real-world applications provides new insights and approaches. Full article
(This article belongs to the Special Issue Analysis and Applications of Control Systems Theory)
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19 pages, 2169 KiB  
Article
Economic Model Predictive Control for Wastewater Treatment Processes Based on Global Maximum Error POD-TPWL
by Zhiyu Wang, Jing Zeng and Jinfeng Liu
Mathematics 2025, 13(10), 1674; https://doi.org/10.3390/math13101674 - 20 May 2025
Viewed by 112
Abstract
To address the challenge of low computational efficiency in nonlinear Economic Model Predictive Control (EMPC) for large-scale systems such as wastewater treatment plants (WWTPs), this paper proposes a Trajectory Piecewise Linearization (TPWL)-based EMPC framework integrated with global maximum error control (GMEC) and Proper [...] Read more.
To address the challenge of low computational efficiency in nonlinear Economic Model Predictive Control (EMPC) for large-scale systems such as wastewater treatment plants (WWTPs), this paper proposes a Trajectory Piecewise Linearization (TPWL)-based EMPC framework integrated with global maximum error control (GMEC) and Proper Orthogonal Decomposition (POD). The TPWL method constructs a reduced-order model framework, while GMEC iteratively refines the linearization point selection process. A two-stage strategy is employed: first, coarse selection of candidate linearization points along the original nonlinear model’s state trajectory based on Euclidean distance, followed by refinement to determine optimal points that minimize global approximation errors. Simulation results demonstrate that the proposed method reduces computational time by at least 65% under identical weather conditions while maintaining effluent quality and total cost indices within acceptable thresholds. Compared with conventional TPWL-POD approaches, this framework achieves higher model accuracy and superior EMPC control performance. These advancements underscore the method’s potential for real-time implementation in complex industrial systems, balancing computational efficiency with control precision. Additionally, the framework’s modular design enables integration with existing optimization techniques to further reduce computational complexity without compromising effluent quality compliance. Full article
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28 pages, 5387 KiB  
Article
A Deep Learning Framework of Super Resolution for License Plate Recognition in Surveillance System
by Pei-Fen Tsai, Jia-Yin Shiu and Shyan-Ming Yuan
Mathematics 2025, 13(10), 1673; https://doi.org/10.3390/math13101673 - 20 May 2025
Viewed by 224
Abstract
Recognizing low-resolution license plates from real-world scenes remains a challenging task. While deep learning-based super-resolution methods have been widely applied, most existing datasets rely on artificially degraded images, and common quality metrics poorly correlate with OCR accuracy. We construct a new paired low- [...] Read more.
Recognizing low-resolution license plates from real-world scenes remains a challenging task. While deep learning-based super-resolution methods have been widely applied, most existing datasets rely on artificially degraded images, and common quality metrics poorly correlate with OCR accuracy. We construct a new paired low- and high-resolution license plate dataset from dashcam videos and propose a specialized super-resolution framework for license plate recognition. Only low-resolution images with OCR accuracy ≥5 are used to ensure sufficient feature information for effective perceptual learning. We analyze existing loss functions and introduce two novel perceptual losses—one CNN-based and one Transformer-based. Our approach improves recognition performance, achieving an average OCR accuracy of 85.14%. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
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15 pages, 280 KiB  
Article
Integral Formulae and Applications for Compact Riemannian Hypersurfaces in Riemannian and Lorentzian Manifolds Admitting Concircular Vector Fields
by Mona Bin-Asfour, Kholoud Saad Albalawi and Mohammed Guediri
Mathematics 2025, 13(10), 1672; https://doi.org/10.3390/math13101672 - 20 May 2025
Viewed by 180
Abstract
This paper investigates compact Riemannian hypersurfaces immersed in (n+1)-dimensional Riemannian or Lorentzian manifolds that admit concircular vector fields, also known as closed conformal vector fields (CCVFs). We focus on the support function of the hypersurface, which is defined [...] Read more.
This paper investigates compact Riemannian hypersurfaces immersed in (n+1)-dimensional Riemannian or Lorentzian manifolds that admit concircular vector fields, also known as closed conformal vector fields (CCVFs). We focus on the support function of the hypersurface, which is defined as the component of the conformal vector field along the unit-normal vector field, and derive an expression for its Laplacian. Using this, we establish integral formulae for hypersurfaces admitting CCVFs. These results are then extended to compact Riemannian hypersurfaces isometrically immersed in Riemannian or Lorentzian manifolds with constant sectional curvatures, highlighting the crucial role of CCVFs in the study of hypersurfaces. We apply these results to provide characterizations of compact Riemannian hypersurfaces in Euclidean space Rn+1, Euclidean sphere Sn+1, and de Sitter space S1n+1. Full article
(This article belongs to the Special Issue Analysis on Differentiable Manifolds)
43 pages, 14479 KiB  
Article
Finite Volume Incompressible Lattice Boltzmann Framework for Non-Newtonian Flow Simulations in Complex Geometries
by Akshay Dongre, John Ryan Murdock and Song-Lin Yang
Mathematics 2025, 13(10), 1671; https://doi.org/10.3390/math13101671 - 20 May 2025
Viewed by 242
Abstract
Arterial diseases are a leading cause of morbidity worldwide, necessitating the development of robust simulation tools to understand their progression mechanisms. In this study, we present a finite volume solver based on the incompressible lattice Boltzmann method (iLBM) to model complex cardiovascular flows. [...] Read more.
Arterial diseases are a leading cause of morbidity worldwide, necessitating the development of robust simulation tools to understand their progression mechanisms. In this study, we present a finite volume solver based on the incompressible lattice Boltzmann method (iLBM) to model complex cardiovascular flows. Standard LBM suffers from compressibility errors and is constrained to uniform Cartesian meshes, limiting its applicability to realistic vascular geometries. To address these issues, we developed an incompressible LBM scheme that recovers the incompressible Navier–Stokes equations (NSEs) and integrated it into a finite volume (FV) framework to handle unstructured meshes while retaining the simplicity of the LBM algorithm. The FV-iLBM model with linear reconstruction (LR) scheme was then validated against benchmark cases, including Taylor–Green vortex flow, shear wave attenuation, Womersley flow, and lid-driven cavity flow, demonstrating improved accuracy in reducing compressibility errors. In simulating flow over National Advisory Committee for Aeronautics (NACA) 0012 airfoil, the FV-iLBM model accurately captured vortex shedding and aerodynamic forces. After validating the FV-iLBM solver for simulating non-Newtonian flows, pulsatile blood flow through an artery afflicted with multiple stenoses was simulated, accurately predicting wall shear stress and flow separation. The results establish FV-iLBM as an efficient and accurate method for modeling cardiovascular flows. Full article
(This article belongs to the Section E2: Control Theory and Mechanics)
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27 pages, 4374 KiB  
Article
Quantifying Temporal Dynamics in Global Cyber Threats: A GPT-Driven Framework for Risk Forecasting and Strategic Intelligence
by Fahim Sufi and Musleh Alsulami
Mathematics 2025, 13(10), 1670; https://doi.org/10.3390/math13101670 - 20 May 2025
Viewed by 198
Abstract
Despite the exponential rise in cybersecurity incidents worldwide, existing analytical approaches often fail to detect subtle temporal dynamics in cyber threats, particularly on a quarterly scale. This paper addresses a critical research gap in the domain of temporal cyber risk analysis by introducing [...] Read more.
Despite the exponential rise in cybersecurity incidents worldwide, existing analytical approaches often fail to detect subtle temporal dynamics in cyber threats, particularly on a quarterly scale. This paper addresses a critical research gap in the domain of temporal cyber risk analysis by introducing a mathematically rigorous and AI-augmented framework capable of identifying, validating, and forecasting quarterly shifts in global cyber-attack patterns. The methodology integrates a hybrid data acquisition pipeline with GPT-based AI classification to construct a structured, high-dimensional dataset comprising 11,497 cybersecurity incidents spanning from October 2023 to March 2025. These incidents cover 106 attack types, 29 industries, and 257 countries. The framework decomposes the dataset into quarterly intervals and applies mathematical formulations to compute frequency shifts across categorical variables (attack types, industries, countries) and numerical variables (attack significance), followed by robust statistical validations (Chi-square and ANOVA tests), time-series forecasting via ARIMA, and the computation of a Quarterly Composite Index (QCI). Key results reveal dominant attack types—Social Engineering (ing1733) and Zero-Day Exploits (1657)—and highlight sectoral vulnerabilities in IT (5959) and Government (2508). Statistically significant quarterly variations were confirmed (χ2=2319.13, F=3.78, p<0.001). ARIMA forecasts predict 1782–2080 incidents per quarter for 2025–2026, while QCI trends average around 0.75, signifying sustained volatility. The research delivers both theoretical and practical advancements by combining generative AI, temporal segmentation, and statistical modeling to create an operationalizable intelligence system. This contribution enhances strategic cybersecurity preparedness and policymaking in a complex, evolving threat landscape. Full article
(This article belongs to the Topic Soft Computing and Machine Learning)
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22 pages, 1130 KiB  
Article
Two-Mode Hereditary Model of Solar Dynamo
by Evgeny Kazakov, Gleb Vodinchar and Dmitrii Tverdyi
Mathematics 2025, 13(10), 1669; https://doi.org/10.3390/math13101669 - 20 May 2025
Viewed by 114
Abstract
The magnetic field of the Sun is formed by the mechanism of hydromagnetic dynamo. In this mechanism, the flow of the conducting medium (plasma) of the convective zone generates a magnetic field, and this field corrects the flow using the Lorentz force, creating [...] Read more.
The magnetic field of the Sun is formed by the mechanism of hydromagnetic dynamo. In this mechanism, the flow of the conducting medium (plasma) of the convective zone generates a magnetic field, and this field corrects the flow using the Lorentz force, creating feedback. An important role in dynamo is played by memory (hereditary), when a change in the current state of a physical system depends on its states in the past. Taking these effects into account may provide a more accurate description of the generation of the Sun’s magnetic field. This paper generalizes classical dynamo models by including hereditary feedback effects. The feedback parameters such as the presence or absence of delay, delay duration, and memory duration are additional degrees of freedom. This can provide more diverse dynamic modes compared to classical memoryless models. The proposed model is based on the kinematic dynamo problem, where the large-scale velocity field is predetermined. The field in the model is represented as a linear combination of two stationary predetermined modes with time-dependent amplitudes. For these amplitudes, equations are obtained based on the kinematic dynamo equations. The model includes two generators of a large-scale magnetic field. In the first, the field is generated due to large-scale flow of the medium. The second generator has a turbulent nature; in it, generation occurs due to the nonlinear interaction of small-scale pulsations of the magnetic field and velocity. Memory in the system under study is implemented in the form of feedback distributed over all past states of the system. The feedback is represented by an integral term of the type of convolution of a quadratic form of phase variables with a kernel of a fairly general form. The quadratic form models the influence of the Lorentz force. This integral term describes the turbulent generator quenching. Mathematically, this model is written with a system of integro-differential equations for amplitudes of modes. The model was applied to a real space object, namely, the solar dynamo. The model representation of the Sun’s velocity field was constructed based on helioseismological data. Free field decay modes were chosen as components of the magnetic field. The work considered cases when hereditary feedback with the system arose instantly or with a delay. The simulation results showed that the model under study reproduces dynamic modes characteristic of the solar dynamo, if there is a delay in the feedback. Full article
(This article belongs to the Special Issue Advances in Nonlinear Dynamical Systems of Mathematical Physics)
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22 pages, 793 KiB  
Article
Decision Support System to Solve Single-Container Loading Problem Considering Practical Constraints
by Natalia Romero-Olarte , Santiago Amézquita-Ortiz, John Willmer Escobar and David Álvarez-Martínez
Mathematics 2025, 13(10), 1668; https://doi.org/10.3390/math13101668 - 19 May 2025
Viewed by 286
Abstract
The container loading problem (CLP) has a broad spectrum of applications in industry and has been studied for over 60 years due to its high complexity. This paper addresses a realistic single-container loading scenario with practical constraints, including orientation limitations, maximum stacking weight, [...] Read more.
The container loading problem (CLP) has a broad spectrum of applications in industry and has been studied for over 60 years due to its high complexity. This paper addresses a realistic single-container loading scenario with practical constraints, including orientation limitations, maximum stacking weight, static stability, overall container weight limit, and fractional loading for multiple drop-off points (multidrop). We propose an open-source decision support system (DSS) implemented on a widely used platform (MS Excel®), which employs a heuristic algorithm to find efficient loading solutions under these constraints. The DSS uses a multi-start randomized constructive algorithm based on a maximal residual space representation. The constructive phase builds the loading pattern in vertical layers (columns or walls), while respecting all practical constraints. The performance of the proposed heuristic is validated through extensive computational experiments on classical benchmark instances, comparing its results against the recent state-of-the-art methods. We also analyze the impact of multi-drop constraints on utilization metrics. The DSS features an interactive interface for creating/loading instances, visualizing step-by-step packing patterns, and displaying key statistics, thus providing a user-friendly decision tool for practitioners. Full article
(This article belongs to the Section D2: Operations Research and Fuzzy Decision Making)
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28 pages, 1450 KiB  
Review
N00N State Generation by Floquet Engineering
by Yusef Maleki
Mathematics 2025, 13(10), 1667; https://doi.org/10.3390/math13101667 - 19 May 2025
Viewed by 117
Abstract
We review quantum architectures for engineering the N00N state, a bipartite maximally entangled state essential in quantum metrology. These schemes transform the initial state |N⟩⊗|0⟩ into the N00N state, [...] Read more.
We review quantum architectures for engineering the N00N state, a bipartite maximally entangled state essential in quantum metrology. These schemes transform the initial state |N⟩⊗|0⟩ into the N00N state, 12(|N⟩⊗|0⟩+|0⟩⊗|N⟩), where |N⟩ and |0⟩ are Fock states with N and 0 excitations, respectively. We demonstrate that this state can be generated through superpositions of quantum light modes, hybrid light–matter interactions, or spin ensembles. Our approach also enables the creation of mesoscopic and macroscopic entangled states, including entangled coherent and squeezed states. Furthermore, we show that a broad class of maximally entangled states can be realized within this framework. Extensions to multi-mode state engineering are also explored. Full article
(This article belongs to the Section E: Applied Mathematics)
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20 pages, 766 KiB  
Article
Representation and Abstraction
by Antal Jakovác and András Telcs
Mathematics 2025, 13(10), 1666; https://doi.org/10.3390/math13101666 - 19 May 2025
Viewed by 143
Abstract
In this paper we propose a mathematical model for cognitive phenomena such as abstraction, generalization and extension. The main concept is the coordination of the observable world with relevant features, a concept defined mathematically in the paper. These features represent necessary conditions for [...] Read more.
In this paper we propose a mathematical model for cognitive phenomena such as abstraction, generalization and extension. The main concept is the coordination of the observable world with relevant features, a concept defined mathematically in the paper. These features represent necessary conditions for performing a task. There are different strategies to choose a coordination, and some of them can be associated with the System 1 and System 2 ways of thinking. System 2 uses multiple, context dependent relevant features for coordination, which makes it possible to speak about abstraction and the generalization of concepts. We also discuss the way extension works in these systems. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
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