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On the Self-Similarity of Remainder Processes and the Relationship Between Stable and Dickman Distributions
Vanishing Cycles and Analysis of Singularities of Feynman Diagrams
Computationally Efficient Design of 16-Poles and 24-Slots IPMSM for EV Traction Considering PWM-Induced Iron Loss Using Active Transfer Learning
Traveling-Wave Solutions of Several Nonlinear Mathematical Physics Equations
Generalized Closeness and Decay Stability of Some Graphs

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 18.3 days after submission; acceptance to publication is undertaken in 1.9 days (median values for papers published in this journal in the second half of 2024).
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: 2.3 (2023); 5-Year Impact Factor: 2.2 (2023)

Imprint Information Journal Flyer Open Access ISSN: 2227-7390

Latest Articles

16 pages, 691 KiB

Open AccessArticle

A Hybrid Vector Autoregressive Model for Accurate Macroeconomic Forecasting: An Application to the U.S. Economy

by Faridoon Khan, Hasnain Iftikhar, Imran Khan, Paulo Canas Rodrigues, Abdulmajeed Atiah Alharbi and Jeza Allohibi

Mathematics 2025, 13(11), 1706; https://doi.org/10.3390/math13111706 - 22 May 2025

Forecasting macroeconomic variables is essential to macroeconomics, financial economics, and monetary policy analysis. Due to the high dimensionality of the macroeconomic dataset, it is challenging to forecast efficiently and accurately. Thus, this study provides a comprehensive analysis of predicting macroeconomic variables by comparing [...] Read more.

Forecasting macroeconomic variables is essential to macroeconomics, financial economics, and monetary policy analysis. Due to the high dimensionality of the macroeconomic dataset, it is challenging to forecast efficiently and accurately. Thus, this study provides a comprehensive analysis of predicting macroeconomic variables by comparing various vector autoregressive models followed by different estimation techniques. To address this, this paper proposes a novel hybrid model based on a smoothly clipped absolute deviation estimation method and a vector autoregression model that combats the curse of dimensionality and simultaneously produces reliable forecasts. The proposed hybrid model is applied to the U.S. quarterly macroeconomic data from the first quarter of 1959 to the fourth quarter of 2023, yielding multi-step-ahead forecasts (one-, three-, and six-step ahead). The multi-step-ahead out-of-sample forecast results (root mean square error and mean absolute error) for the considered data suggest that the proposed hybrid model yields a highly accurate and efficient gain. Additionally, it is demonstrated that the proposed models outperform the baseline models. Finally, the authors believe the proposed hybrid model may be expanded to other countries to assess its efficacy and accuracy. Full article

(This article belongs to the Special Issue Recent Advances in Time Series Analysis: Methods, Theory, and Applications)

15 pages, 602 KiB

Open AccessArticle

Mixed-Order Fuzzy Time Series Forecast

by Hao Wu, Haiming Long and Jiancheng Jiang

Mathematics 2025, 13(11), 1705; https://doi.org/10.3390/math13111705 - 22 May 2025

Fuzzy time series forecasting has gained significant attention for its accuracy, robustness, and interpretability, making it widely applicable in practical prediction tasks. In classical fuzzy time series models, the lag order plays a crucial role, with variations in order often leading to markedly [...] Read more.

Fuzzy time series forecasting has gained significant attention for its accuracy, robustness, and interpretability, making it widely applicable in practical prediction tasks. In classical fuzzy time series models, the lag order plays a crucial role, with variations in order often leading to markedly different forecasting results. To obtain the best performance, we propose a mixed-order fuzzy time series model, which incorporates fuzzy logical relationships (FLRs) of different orders into its rule system. This approach mitigates the uncertainty in fuzzy forecasting caused by empty FLRs and FLR groups while fully exploiting the fitting advantages of different-order FLRs. Theoretical analysis is provided to establish the mathematical foundation of the mixed-order model, and its superiority over fixed-order models is demonstrated. Simulation studies reveal that the proposed model outperforms several classical time series models in specific scenarios. Furthermore, applications to real-world datasets, including a COVID-19 case study and a TAIEX financial dataset, validate the effectiveness and applicability of the proposed methodology. Full article

(This article belongs to the Special Issue Statistics: Theories and Applications)

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37 pages, 6596 KiB

Open AccessArticle

Optimizing Route Planning via the Weighted Sum Method and Multi-Criteria Decision-Making

by Guanquan Zhu, Minyi Ye, Xinqi Yu, Junhao Liu, Mingju Wang, Zihang Luo, Haomin Liang and Yubin Zhong

Mathematics 2025, 13(11), 1704; https://doi.org/10.3390/math13111704 - 22 May 2025

Choosing the optimal path in planning is a complex task due to the numerous options and constraints; this is known as the trip design problem (TTDP). This study aims to achieve path optimization through the weighted sum method and multi-criteria decision analysis. Firstly, [...] Read more.

Choosing the optimal path in planning is a complex task due to the numerous options and constraints; this is known as the trip design problem (TTDP). This study aims to achieve path optimization through the weighted sum method and multi-criteria decision analysis. Firstly, this paper proposes a weighted sum optimization method using a comprehensive evaluation model to address TTDP, a complex multi-objective optimization problem. The goal of the research is to balance experience, cost, and efficiency by using the Analytic Hierarchy Process (AHP) and Entropy Weight Method (EWM) to assign subjective and objective weights to indicators such as ratings, duration, and costs. These weights are optimized using the Lagrange multiplier method and integrated into the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) model. Additionally, a weighted sum optimization method within the Traveling Salesman Problem (TSP) framework is used to maximize ratings while minimizing costs and distances. Secondly, this study compares seven heuristic algorithms—the genetic algorithm (GA), particle swarm optimization (PSO), the tabu search (TS), genetic-particle swarm optimization (GA-PSO), the gray wolf optimizer (GWO), and ant colony optimization (ACO)—to solve the TOPSIS model, with GA-PSO performing the best. The study then introduces the Lagrange multiplier method to the algorithms, improving the solution quality of all seven heuristic algorithms, with an average solution quality improvement of 112.5% (from 0.16 to 0.34). The PSO algorithm achieves the best solution quality. Based on this, the study introduces a new variant of PSO, namely PSO with Laplace disturbance (PSO-LD), which incorporates a dynamic adaptive Laplace perturbation term to enhance global search capabilities, improving stability and convergence speed. The experimental results show that PSO-LD outperforms the baseline PSO and other algorithms, achieving higher solution quality and faster convergence speed. The Wilcoxon signed-rank test confirms significant statistical differences among the algorithms. This study provides an effective method for experience-oriented path optimization and offers insights into algorithm selection for complex TTDP problems. Full article

(This article belongs to the Special Issue Mathematical Modeling and Intelligent Algorithms in Operations Research)

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26 pages, 3357 KiB

Open AccessArticle

Two-Dimensional Fluid Flow Due to Blade-Shaped Waving of Cilia in Human Lungs

by Nisachon Kumankat and Nachayadar Kamolmitisom

Mathematics 2025, 13(11), 1703; https://doi.org/10.3390/math13111703 - 22 May 2025

The mucociliary clearance system is an innate defense mechanism in the human respiratory tract, which plays a crucial role in protecting the airways from infections. The clearance system secretes mucus from the goblet cells, which scatters in the respiratory epithelium to trap foreign [...] Read more.

The mucociliary clearance system is an innate defense mechanism in the human respiratory tract, which plays a crucial role in protecting the airways from infections. The clearance system secretes mucus from the goblet cells, which scatters in the respiratory epithelium to trap foreign particles entering the airway, and then the mucus is removed from the body via the movement of cilia residing under the mucus and above the epithelium cells. The layer containing cilia is called the periciliary layer (PCL). This layer also contains an incompressible Newtonian fluid called PCL fluid. This study aims to determine the velocity of the PCL fluid driven by the cilia movement instead of a pressure gradient. We consider bundles of cilia, rather than an individual cilium. So, the generalized Brinkman equation in a macroscopic scale is used to predict the fluid velocity in the PCL. We apply a mixed finite element method to the governing equation and calculate the numerical solutions in a two-dimensional domain. The numerical domain is set up to be the shape of a fan blade, which is similar to the motion of the cilia. This problem can be applied to problems of fluid flow propelled via moving solid phases. Full article

18 pages, 355 KiB

Open AccessArticle

A Hybrid Algorithm with a Data Augmentation Method to Enhance the Performance of the Zero-Inflated Bernoulli Model

by Chih-Jen Su, I-Fei Chen, Tzong-Ru Tsai and Yuhlong Lio

Mathematics 2025, 13(11), 1702; https://doi.org/10.3390/math13111702 - 22 May 2025

The zero-inflated Bernoulli model, enhanced with elastic net regularization, effectively handles binary classification for zero-inflated datasets. This zero-inflated structure significantly contributes to data imbalance. To improve the ZIBer model’s ability to accurately identify minority classes, we explore the use of momentum and Nesterov’s [...] Read more.

The zero-inflated Bernoulli model, enhanced with elastic net regularization, effectively handles binary classification for zero-inflated datasets. This zero-inflated structure significantly contributes to data imbalance. To improve the ZIBer model’s ability to accurately identify minority classes, we explore the use of momentum and Nesterov’s gradient descent methods, particle swarm optimization, and a novel hybrid algorithm combining particle swarm optimization with Nesterov’s accelerated gradient techniques. Additionally, the synthesized minority oversampling technique is employed for data augmentation and training the model. Extensive simulations using holdout cross-validation reveal that the proposed hybrid algorithm with data augmentation excels in identifying true positive cases. Conversely, the hybrid algorithm without data augmentation is preferable when aiming for a balance between the metrics of recall and precision. Two case studies about diabetes and biopsy are provided to demonstrate the model’s effectiveness, with performance assessed through K-fold cross-validation. Full article

(This article belongs to the Special Issue Significant Applications in Economics, Business, Management and Industrial Statistics)

29 pages, 2538 KiB

Open AccessArticle

A Finite Element–Finite Volume Code Coupling for Optimal Control Problems in Fluid Heat Transfer for Incompressible Navier–Stokes Equations

by Samuele Baldini, Giacomo Barbi, Giorgio Bornia, Antonio Cervone, Federico Giangolini, Sandro Manservisi and Lucia Sirotti

Mathematics 2025, 13(11), 1701; https://doi.org/10.3390/math13111701 - 22 May 2025

In this work, we present a numerical approach for solving optimal control problems for fluid heat transfer applications with a mixed optimality system: an FEM code to solve the adjoint solution over a precise restricted admissible solution set and an open-source well-known code [...] Read more.

In this work, we present a numerical approach for solving optimal control problems for fluid heat transfer applications with a mixed optimality system: an FEM code to solve the adjoint solution over a precise restricted admissible solution set and an open-source well-known code for solving the state problem defined over a different one. In this way, we are able to decouple the optimality system and use well-established and validated numerical tools for the physical modeling. Specifically, two different CFD codes, OpenFOAM (finite volume-based) and FEMuS (finite element-based), have been used to solve the optimality system, while the data transfer between them is managed by the external library MEDCOUPLING. The state equations are solved in the finite volume code, while the adjoint and the control are solved in the finite element code. Two examples taken from the literature are implemented in order to validate the numerical algorithm: the first one considers a natural convection cavity resulting from a Rayleigh–Bénard configuration, and the second one is a conjugate heat transfer problem between a fluid and a solid region. Full article

(This article belongs to the Special Issue Mathematical Modelling, Analysis, and Optimization for Engineering and Mechanics)

20 pages, 1016 KiB

Open AccessArticle

Efficient AI-Driven Query Optimization in Large-Scale Databases: A Reinforcement Learning and Graph-Based Approach

by Najla Sassi and Wassim Jaziri

Mathematics 2025, 13(11), 1700; https://doi.org/10.3390/math13111700 - 22 May 2025

As data-centric applications become increasingly complex, understanding effective query optimization in large-scale relational databases is crucial for managing this complexity. Yet, traditional cost-based and heuristic approaches simply do not scale, adapt, or remain accurate in highly dynamic multi-join queries. This research work proposes [...] Read more.

As data-centric applications become increasingly complex, understanding effective query optimization in large-scale relational databases is crucial for managing this complexity. Yet, traditional cost-based and heuristic approaches simply do not scale, adapt, or remain accurate in highly dynamic multi-join queries. This research work proposes the reinforcement learning and graph-based hybrid query optimizer (GRQO), the first ever to apply reinforcement learning and graph theory for optimizing query execution plans, specifically in join order selection and cardinality estimation. By employing proximal policy optimization for adaptive policy learning and using graph-based schema representations for relational modeling, GRQO effectively traverses the combinatorial optimization space. Based on TPC-H (1 TB) and IMDB (500 GB) workloads, GRQO runs 25% faster in query execution time, scales 30% better, reduces CPU and memory use by 20–25%, and reduces the cardinality estimation error by 47% compared to traditional cost-based optimizers and machine learning-based optimizers. These findings highlight the ability of GRQO to optimize performance and resource efficiency in database management in cloud computing, data warehousing, and real-time analytics. Full article

(This article belongs to the Section E1: Mathematics and Computer Science)

20 pages, 2251 KiB

Open AccessArticle

A Cloud-Based Approach to Modeling ERP Information Flows Using a Bivariate Pólya–Aeppli Process

by Fatima Sapundzhi, Vesna Dimitrova, Meglena Lazarova, Slavi Georgiev, Michail Todorov and Venelin Todorov

Mathematics 2025, 13(11), 1699; https://doi.org/10.3390/math13111699 - 22 May 2025

Fast-growing technology and the development of IT services give the idea of founding a new application of stochastic processes and their properties. We give a new connection between electronic process management and a stochastic process named the bivariate Pólya–Aeppli counting process. This process [...] Read more.

Fast-growing technology and the development of IT services give the idea of founding a new application of stochastic processes and their properties. We give a new connection between electronic process management and a stochastic process named the bivariate Pólya–Aeppli counting process. This process is applied as a counting process in the mathematical construction of the given model and it has been introduced as a counting process in electronic process management. In our current study, we assume a company that has two locations in two countries—Bulgaria and Romania. For seamless communication and data sharing, the integrated factories leverage the System Applications and Products in Data Processing (SAP) system. By combining these functions into one structure, we optimize coordination, streamline operations, and improve the company’s productivity and profitability. The automated tools within the system facilitate uninterrupted production and secure supply chains and thus the decision making is improved. A key benefit of these tools is to boost production and procurement activities for success in today’s competitive market which results in cost savings, will increase visibility, and also will improve rapid decision making. Full article

(This article belongs to the Special Issue Data-Driven Algorithms for Optimal Decision Making in Logistics and Supply Chain Management)

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27 pages, 1898 KiB

Open AccessArticle

Advanced Vehicle Routing for Electric Fleets Using DPCGA: Addressing Charging and Traffic Constraints

by Yuehan Zheng, Hao Chang, Peng Yu, Taofeng Ye and Ying Wang

Mathematics 2025, 13(11), 1698; https://doi.org/10.3390/math13111698 - 22 May 2025

With the rapid proliferation of electric vehicles (EVs), urban logistics faces increasing challenges in optimizing vehicle routing. This paper presents a new modeling framework for the Electric Vehicle Routing Problem (EVRP), where multiple electric trucks serve a set of customers within their capacity [...] Read more.

With the rapid proliferation of electric vehicles (EVs), urban logistics faces increasing challenges in optimizing vehicle routing. This paper presents a new modeling framework for the Electric Vehicle Routing Problem (EVRP), where multiple electric trucks serve a set of customers within their capacity limits. The model incorporates critical EV-specific constraints, including limited battery range, charging demand, and dynamic urban traffic conditions, with the objective of minimizing total delivery cost. To efficiently solve this problem, a Dual Population Cooperative Genetic Algorithm (DPCGA) is proposed. The algorithm employs a dual-population mechanism for global exploration, effectively expanding the search space and accelerating convergence. It then introduces local refinement operators to improve solution quality and enhance population diversity. A large number of experimental results demonstrate that DPCGA significantly outperforms traditional algorithms in terms of performance, achieving an average 3% improvement in customer satisfaction and a 15% reduction in computation time. Furthermore, this algorithm shows superior solution quality and robustness compared to the AVNS and ESA-VRPO algorithms, particularly in complex scenarios such as adjustments in charging station layouts and fluctuations in vehicle range. Sensitivity analysis further verifies the stability and practicality of DPCGA in real-world urban delivery environments. Full article

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10 pages, 223 KiB

Open AccessArticle

Local Well-Posedness of Classical Solutions to the Time-Dependent Ginzburg–Landau Model for Superconductivity in

R^{n}

by Jishan Fan and Yong Zhou

Mathematics 2025, 13(11), 1697; https://doi.org/10.3390/math13111697 - 22 May 2025

In this paper, we prove the local well-posedness of classical solutions

(ψ, A, ϕ)

to the

n D (n \geq 3)

time-dependent Ginzburg–Landau model in superconductivity with the choice of Coulomb gauge and the main assumptions [...] Read more.

In this paper, we prove the local well-posedness of classical solutions

(ψ, A, ϕ)

to the

n D (n \geq 3)

time-dependent Ginzburg–Landau model in superconductivity with the choice of Coulomb gauge and the main assumptions

ψ_{0}, A_{0} \in H^{s} (R^{n})

with

div A_{0} = 0

in

R^{n}

and

s > \frac{n}{2}

. This result can be used in the proof of regularity criterion and global-in-time well-posedness of the strong solution. Full article

(This article belongs to the Section C1: Difference and Differential Equations)

15 pages, 5838 KiB

Open AccessArticle

Design and Performance Verification of Deep Learning-Based River Flood Prediction System Design and Digital Twin-Based Its Application

by Heesang Eom, Younghun Kim and Jongho Paik

Mathematics 2025, 13(11), 1696; https://doi.org/10.3390/math13111696 - 22 May 2025

This paper presents a digital twin-based river management and flood prediction system designed for hydrological environments, including volcanic geology. To address the problems of rapid runoff and complex terrain, a deep learning-based hybrid model is proposed that integrates a Convolutional Neural Network (CNN) [...] Read more.

This paper presents a digital twin-based river management and flood prediction system designed for hydrological environments, including volcanic geology. To address the problems of rapid runoff and complex terrain, a deep learning-based hybrid model is proposed that integrates a Convolutional Neural Network (CNN) for spatial feature extraction and a Recurrent Neural Network (RNN) with Long Short-Term Memory (LSTM) units for temporal sequence modeling. The performance evaluation results show that the proposed CNN-RNN hybrid model outperforms individual CNN and RNN baselines. The hybrid model achieves a macro-average precision of 0.97, a recall of 0.99, and an F1 score of 0.98, significantly outperforming existing methods. The system is also integrated with a 3D digital twin visualization platform to enable real-time monitoring and data-driven decision-making. Full article

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22 pages, 2702 KiB

Open AccessArticle

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

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, 470 KiB

Open AccessFeature PaperArticle

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

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^{*} + D_{n}

, where

G^{*}

is a graph isomorphic to the path on four vertices

P_{4}

with an additional two vertices adjacent to two inner vertices of

P_{4}

, and

D_{n}

is a discrete graph composed of n isolated vertices. The proof is based on exact crossing-number values for join products involving particular subgraphs

H_{k}

of

G^{*}

with discrete graphs

D_{n}

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)

10 pages, 214 KiB

Open AccessArticle

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

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

Open AccessArticle

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

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

Open AccessArticle

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

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

Open AccessArticle

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

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

Open AccessArticle

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

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

Open AccessFeature PaperArticle

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

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, 2138 KiB

Open AccessArticle

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

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 / \sqrt{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 / S^{2})

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 \times \sim 5 \times

. Full article

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