Mathematics

36 pages, 7187 KiB

Open AccessArticle

Elite Evolutionary Discrete Particle Swarm Optimization for Recommendation Systems

by Shanxian Lin, Yifei Yang, Yuichi Nagata and Haichuan Yang

Mathematics 2025, 13(9), 1398; https://doi.org/10.3390/math13091398 - 24 Apr 2025

Recommendation systems (RSs) play a vital role in e-commerce and content platforms, yet balancing efficiency and recommendation quality remains challenging. Traditional deep models are computationally expensive, while heuristic methods like particle swarm optimization struggle with discrete optimization. To address these limitations, this paper [...] Read more.

Recommendation systems (RSs) play a vital role in e-commerce and content platforms, yet balancing efficiency and recommendation quality remains challenging. Traditional deep models are computationally expensive, while heuristic methods like particle swarm optimization struggle with discrete optimization. To address these limitations, this paper proposes elite-evolution-based discrete particle swarm optimization (EEDPSO), a novel framework specifically designed to optimize high-dimensional combinatorial recommendation tasks. EEDPSO restructures the velocity and position update mechanisms to operate effectively in discrete spaces, integrating neighborhood search, elite evolution strategies, and roulette-wheel selection to balance exploration and exploitation. Experiments on the MovieLens and Amazon datasets show that EEDPSO outperforms five metaheuristic algorithms (GA, DE, SA, SCA, and PSO) in both recommendation quality and computational efficiency. For datasets below the million-level scale, EEDPSO also demonstrates superior performance compared to deep learning models like FairGo. The results establish EEDPSO as a robust optimization strategy for recommendation systems that effectively handles the cold-start problem. Full article

(This article belongs to the Special Issue Machine Learning and Evolutionary Algorithms: Theory and Applications)

30 pages, 1411 KiB

Open AccessArticle

Reinforcement Learning for Mitigating Malware Propagation in Wireless Radar Sensor Networks with Channel Modeling

by Guiyun Liu, Hao Li, Lihao Xiong, Yiduan Chen, Aojing Wang and Dongze Shen

Mathematics 2025, 13(9), 1397; https://doi.org/10.3390/math13091397 - 24 Apr 2025

Abstract

With the rapid development of research on Wireless Radar Sensor Networks (WRSNs), security issues have become a major challenge. Recent studies have highlighted numerous security threats in WRSNs. Given their widespread application value, the operational security of WRSNs needs to be ensured. This [...] Read more.

With the rapid development of research on Wireless Radar Sensor Networks (WRSNs), security issues have become a major challenge. Recent studies have highlighted numerous security threats in WRSNs. Given their widespread application value, the operational security of WRSNs needs to be ensured. This study focuses on the problem of malware propagation in WRSNs. In this study, the complex characteristics of WRSNs are considered to construct the epidemic VCISQ model. The model incorporates necessary factors such as node density, Rayleigh fading channels, and time delay, which were often overlooked in previous studies. This model achieves a breakthrough in accurately describing real-world scenarios of malware propagation in WRSNs. To control malware spread, a hybrid control strategy combining quarantine and patching measures are introduced. In addition, the optimal control method is used to minimize control costs. Considering the robustness and adaptability of the control method, two model-free reinforcement learning (RL) strategies are proposed: Proximal Policy Optimization (PPO) and Multi-Agent Proximal Policy Optimization (MAPPO). These strategies reformulate the original optimal control problem as a Markov decision process. To demonstrate the superiority of our approach, multi-dimensional ablation studies and numerical experiments are conducted. The results show that the hybrid control strategy outperforms single strategies in suppressing malware propagation and reducing costs. Furthermore, the experiments reveal the significant impact of time delays on the dynamics of the VCISQ model and control effectiveness. Finally, the PPO and MAPPO algorithms demonstrate superior performance in control costs and convergence compared to traditional RL algorithms. This highlights their effectiveness in addressing malware propagation in WRSNs. Full article

21 pages, 809 KiB

Open AccessArticle

FinGraphFL: Financial Graph-Based Federated Learning for Enhanced Credit Card Fraud Detection

by Zhenyu Xia and Suvash C. Saha

Mathematics 2025, 13(9), 1396; https://doi.org/10.3390/math13091396 - 24 Apr 2025

Abstract

In the field of credit card fraud detection, traditional methods often struggle due to their reliance on complex manual feature engineering or their inability to adapt to rapidly changing fraud patterns. This paper introduces an innovative approach called FinGraphFL, which merges graph-based learning [...] Read more.

In the field of credit card fraud detection, traditional methods often struggle due to their reliance on complex manual feature engineering or their inability to adapt to rapidly changing fraud patterns. This paper introduces an innovative approach called FinGraphFL, which merges graph-based learning with the principles of federated learning and improves security through differential privacy. FinGraphFL utilizes Graph Attention Networks to analyze dynamic relationships between daily credit card transaction records, enhancing its ability to detect fraudulent activities. With the addition of differential privacy, the model allows multiple financial institutions to collaborate to refine the detection model without sharing sensitive data, thus improving adaptability and accuracy. The results are tested in two public datasets that show that FinGraphFL achieves accuracy rates of

0.9780

and

0.9839

, significantly outperforming traditional methods. Building on these results, FinGraphFL sets the stage for future advances in real-time learning and global financial collaboration, ensuring simultaneous progress in security and privacy protections. Full article

(This article belongs to the Special Issue Econophysics, Financial Markets, and Artificial Intelligence)

25 pages, 921 KiB

Open AccessArticle

Efficient Rollout Algorithms for Resource-Constrained Project Scheduling with a Flexible Project Structure and Uncertain Activity Durations

by Chunlai Yu, Xiaoming Wang and Qingxin Chen

Mathematics 2025, 13(9), 1395; https://doi.org/10.3390/math13091395 - 24 Apr 2025

Abstract

This study addresses the resource-constrained project scheduling problem with flexible structures and uncertain activity durations. The problem is formulated as a Markov decision process, with the optimal policy determined through stochastic dynamic programming. To mitigate the curse of dimensionality in large-scale problems, several [...] Read more.

This study addresses the resource-constrained project scheduling problem with flexible structures and uncertain activity durations. The problem is formulated as a Markov decision process, with the optimal policy determined through stochastic dynamic programming. To mitigate the curse of dimensionality in large-scale problems, several approximate methods are proposed to derive suboptimal policies. In addition to traditional methods based on priority rules and metaheuristic algorithms, we focus on the application of rollout algorithms. To improve the computational efficiency of the rollout algorithms, only the best-performing priority rules are employed for action evaluation, and the common random numbers technique is also incorporated. Experimental results demonstrate that rollout algorithms significantly outperform priority rules and metaheuristics. The common random numbers technique not only enhances computational efficiency but also improves the accuracy of action selection. The post-rollout algorithm reduces computation time by 44.37% compared to the one-step rollout, with only a 0.02% performance gap. In addition, rollout algorithms perform more stably than other methods under different problem characteristics. Full article

(This article belongs to the Section D2: Operations Research and Fuzzy Decision Making)

21 pages, 929 KiB

Open AccessArticle

Power Length-Biased New XLindley Distribution: Properties and Modeling of Real Data

by Suresha Kharvi, Muhammed Rasheed Irshad, Amer Ibrahim Al-Omari and Rehab Alsultan

Mathematics 2025, 13(9), 1394; https://doi.org/10.3390/math13091394 - 24 Apr 2025

Abstract

The increasing complexity of modern lifetime data necessitates the development of more flexible probability models. To address this need, we propose the power length-biased new XLindley (PLNXL) distribution, a novel two-parameter model tailored to model a wide range of lifetime datasets. Characterized by [...] Read more.

The increasing complexity of modern lifetime data necessitates the development of more flexible probability models. To address this need, we propose the power length-biased new XLindley (PLNXL) distribution, a novel two-parameter model tailored to model a wide range of lifetime datasets. Characterized by both shape and scale parameters, the PLNXL distribution effectively captures diverse hazard rate functions, including increasing, decreasing, and inverted bathtub-shaped forms. Additionally, its mean residual life function is capable of exhibiting decreasing, increasing, and bathtub-shaped behaviors, thereby enhancing its practical relevance. We derive key mathematical properties of the distribution, including moments, reliability measures, and entropy. The parameters are estimated using the maximum likelihood method, and simulation studies confirm the consistency and efficiency of the estimators. The applicability of the proposed model is illustrated using real-world datasets, where it consistently outperforms the existing models. These results highlight the robustness and adaptability of the PLNXL distribution for lifetime data analysis across a wide array of applications. Full article

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21 pages, 4349 KiB

Open AccessFeature PaperArticle

Gearbox Fault Diagnosis Based on Compressed Sensing and Multi-Scale Residual Network with Lightweight Attention Mechanism

by Shihua Zhou, Xinhai Yu, Xuan Li, Yue Wang, Kaibo Ji and Zhaohui Ren

Mathematics 2025, 13(9), 1393; https://doi.org/10.3390/math13091393 - 24 Apr 2025

Abstract

As a core component of mechanical transmission systems, gear damage status significantly impacts the safety and efficiency of an overall mechanical system. However, existing fault diagnosis methods often struggle to extract features effectively in complex application scenarios characterized by conditions such as high [...] Read more.

As a core component of mechanical transmission systems, gear damage status significantly impacts the safety and efficiency of an overall mechanical system. However, existing fault diagnosis methods often struggle to extract features effectively in complex application scenarios characterized by conditions such as high temperature, high humidity, and high-level vibrations. Consequently, they exhibit poor adaptability and limited anti-noise capabilities. To address these limitations and enhance the adaptability and precision of gear fault diagnosis (GFD), a novel compressive sensing lightweight attention multi-scale residual network (CS-LAMRNet) method is proposed. Initially, compressive sensing technology was employed to remove noise and redundant information from the vibration signal, and the reconstructed 1D gear vibration signal was then converted into a 2D image. Subsequently, a multi-scale feature extraction (MSFE) module was designed based on multi-scale learning, with the aim of improving the feature extraction ability of the signal in noisy environments. Finally, an improved depth residual attention (IDRA) module was established and connected to the MSFE module, further enhancing the exactitude and generalization ability of the diagnosis method. The performance of the proposed CS-LAMRNet was evaluated using the NEU dataset and the SEU dataset, and it was compared with seven other fault diagnosis methods. The experimental results demonstrate that the accuracies of the CS-LAMRNet reached 99.80% and 100%, respectively, thus proving that the proposed method has a higher fault identification capability for gears under noisy environments. Full article

31 pages, 707 KiB

Open AccessArticle

Quantum Game Theory-Based Cloud Resource Allocation: A Novel Approach

by Anjan Bandyopadhyay, Utkarsh Choudhary, Vaibhav Tiwari, Kaushtab Mukherjee, Sapthak Mohajon Turjya, Naim Ahmad, Abid Haleem and Saurav Mallik

Mathematics 2025, 13(9), 1392; https://doi.org/10.3390/math13091392 - 24 Apr 2025

Abstract

This paper explores the application of quantum game theory to optimize cloud resource allocation. By leveraging the principles of quantum mechanics, the proposed framework aims to enhance efficiency, reduce costs, and improve scalability in cloud computing environments. The study introduces a quantum-based game-theoretic [...] Read more.

This paper explores the application of quantum game theory to optimize cloud resource allocation. By leveraging the principles of quantum mechanics, the proposed framework aims to enhance efficiency, reduce costs, and improve scalability in cloud computing environments. The study introduces a quantum-based game-theoretic model and compares its performance with classical approaches. The results demonstrate significant improvements in resource utilization and decision-making efficiency. While prior works have explored classical game theory and auction-based methods, this study is among the first to implement quantum game theory in a practical cloud computing context, propose a resource allocation mechanism that incorporates both fairness and efficiency while leveraging the computational advantages of quantum systems, and highlight the strategic benefits of quantum entanglement in fostering collaboration between competing entities in cloud environments. This work not only addresses the current limitations of resource allocation but also redefines the possibilities for optimization in complex systems, making a substantial contribution to both quantum computing and cloud resource management domains. Full article

(This article belongs to the Special Issue Advances in Quantum Computing and Applications)

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11 pages, 231 KiB

Open AccessArticle

Resolving an Open Problem on the Exponential Arithmetic–Geometric Index of Unicyclic Graphs

by Kinkar Chandra Das and Jayanta Bera

Mathematics 2025, 13(9), 1391; https://doi.org/10.3390/math13091391 - 24 Apr 2025

Abstract

Recently, the exponential arithmetic–geometric index (

E A G

) was introduced. The exponential arithmetic–geometric index (

E A G

) of a graph G is defined as [...] Read more.

Recently, the exponential arithmetic–geometric index (

E A G

) was introduced. The exponential arithmetic–geometric index (

E A G

) of a graph G is defined as

E A G (G) = \sum_{v_{i} v_{j} \in E (G)} e^{\frac{d_{i} + d_{j}}{2 \sqrt{d_{i} d_{j}}}}

, where

d_{i}

represents the degree of the vertex

v_{i}

in G. The characterization of extreme structures in relation to graph invariants from the class of unicyclic graphs is an important problem in discrete mathematics. Cruz et al., 2022 proposed a unified method for finding extremal unicyclic graphs for exponential degree-based graph invariants. However, in the case of

E A G

, this method is insufficient for generating the maximal unicyclic graph. Consequently, the same article presented an open problem for the investigation of the maximal unicyclic graph with respect to this invariant. This article completely characterizes the maximal unicyclic graph in relation to

E A G

. Full article

(This article belongs to the Special Issue Graph Theory and Applications, 2nd Edition)

30 pages, 777 KiB

Open AccessFeature PaperArticle

More Theory About Infinite Numbers and Important Applications

by Emmanuel Thalassinakis

Mathematics 2025, 13(9), 1390; https://doi.org/10.3390/math13091390 - 24 Apr 2025

Abstract

In the author’s previous studies, new infinite numbers, their properties, and calculations were introduced. These infinite numbers quantify infinity and offer new possibilities for solving complicated problems in mathematics and applied sciences in which infinity appears. The current study presents additional properties and [...] Read more.

In the author’s previous studies, new infinite numbers, their properties, and calculations were introduced. These infinite numbers quantify infinity and offer new possibilities for solving complicated problems in mathematics and applied sciences in which infinity appears. The current study presents additional properties and topics regarding infinite numbers, as well as a comparison between infinite numbers. In this way, complex problems with inequalities involving series of numbers, in addition to limits of functions of x ∈ ℝ and improper integrals, can be addressed and solved easily. Furthermore, this study introduces rotational infinite numbers. These are not single numbers but sets of infinite numbers produced as the vectors of ordinary infinite numbers are rotated in the complex plane. Some properties of rotational infinite numbers and their calculations are presented. The rotational infinity unit, its inverse, and its opposite number, as well as the angular velocity of rotational infinite numbers, are defined and illustrated. Based on the above, the Riemann zeta function is equivalently written as the sum of three rotational infinite numbers, and it is further investigated and analyzed from another point of view. Furthermore, this study reveals and proves interesting formulas relating to the Riemann zeta function that can elegantly and simply calculate complicated ratios of infinite series of numbers. Finally, the above theoretical results were verified by a computational numerical simulation, which confirms the correctness of the analytical results. In summary, rotational infinite numbers can be used to easily analyze and solve problems that are difficult or impossible to solve using other methods. Full article

(This article belongs to the Special Issue Special Functions with Applications)

40 pages, 1365 KiB

Open AccessFeature PaperArticle

A Novel Detection-and-Replacement-Based Order-Operator for Differential Evolution in Solving Complex Bound Constrained Optimization Problems

by Sichen Tao, Sicheng Liu, Shoya Ohta, Ruihan Zhao, Zheng Tang and Yifei Yang

Mathematics 2025, 13(9), 1389; https://doi.org/10.3390/math13091389 - 24 Apr 2025

Abstract

The design of differential evolution (DE) operators has long been a key topic in the research of metaheuristic algorithms. This paper systematically reviews the functional differences between mechanism improvements and operator improvements in terms of exploration and exploitation capabilities, based on the general [...] Read more.

The design of differential evolution (DE) operators has long been a key topic in the research of metaheuristic algorithms. This paper systematically reviews the functional differences between mechanism improvements and operator improvements in terms of exploration and exploitation capabilities, based on the general patterns of algorithm enhancements. It proposes a theoretical hypothesis: operator improvement is more directly associated with the enhancement of an algorithm’s exploitation capability. Accordingly, this paper designs a new differential operator, DE/current-to-pbest/order, based on the classic DE/current-to-pbest/1 operator. This new operator introduces a directional judgment mechanism and a replacement strategy based on individual fitness, ensuring that the differential vector consistently points toward better individuals. This enhancement improves the effectiveness of the search direction and significantly strengthens the algorithm’s ability to delve into high-quality solution regions. To verify the effectiveness and generality of the proposed operator, it is embedded into two mainstream evolutionary algorithm frameworks, JADE and LSHADE, to construct OJADE and OLSHADE. A systematic evaluation is conducted using two authoritative benchmark sets: CEC2017 and CEC2011. The CEC2017 set focuses on assessing the optimization capability of theoretical complex functions, covering problems of various dimensions and types; the CEC2011 set, on the other hand, targets multimodal and hybrid optimization challenges in real engineering contexts, featuring higher structural complexity and generalization requirements. On both benchmark sets, OLSHADE demonstrates outstanding solution quality, convergence efficiency, and result stability, showing particular advantages in high-dimensional complex problems, thus fully validating the effectiveness of the proposed operator in enhancing exploitation capability. In addition, the operator has a lightweight structure and is easy to integrate, with good portability and scalability. It can be embedded as a general-purpose module into more DE variants and EAs in the future, providing flexible support for further performance optimization in solving complex problems. Full article

26 pages, 380 KiB

Open AccessArticle

Identification and Empirical Likelihood Inference in Nonlinear Regression Model with Nonignorable Nonresponse

by Xianwen Ding and Xiaoxia Li

Mathematics 2025, 13(9), 1388; https://doi.org/10.3390/math13091388 - 24 Apr 2025

Abstract

The identification of model parameters is a central challenge in the analysis of nonignorable nonresponse data. In this paper, we propose a novel penalized semiparametric likelihood method to obtain sparse estimators for a parametric nonresponse mechanism model. Based on these sparse estimators, an [...] Read more.

The identification of model parameters is a central challenge in the analysis of nonignorable nonresponse data. In this paper, we propose a novel penalized semiparametric likelihood method to obtain sparse estimators for a parametric nonresponse mechanism model. Based on these sparse estimators, an instrumental variable is introduced, enabling the identification of the observed likelihood. Two classes of estimating equations for the nonlinear regression model are constructed, and the empirical likelihood approach is employed to make inferences about the model parameters. The oracle properties of the sparse estimators in the nonresponse mechanism model are systematically established. Furthermore, the asymptotic normality of the maximum empirical likelihood estimators is derived. It is also shown that the empirical log-likelihood ratio functions are asymptotically weighted chi-squared distributed. Simulation studies are conducted to validate the effectiveness of the proposed estimation procedure. Finally, the practical utility of our approach is demonstrated through the analysis of ACTG 175 data. Full article

(This article belongs to the Special Issue Modeling, Control and Optimization of Biological Systems)

30 pages, 20105 KiB

Open AccessArticle

Computational Investigation of Long Free-Span Submarine Pipelines with Buoyancy Modules Using an Automated Python–Abaqus Framework

by Ty Phuor, Pavel A. Trapper, Alon Urlainis and Avshalom Ganz

Mathematics 2025, 13(9), 1387; https://doi.org/10.3390/math13091387 - 24 Apr 2025

Abstract

This paper introduces an efficient and automated computational framework integrating Python scripting with Abaqus finite element analysis (FEA) to investigate the structural behavior of long free-spanning submarine pipelines equipped with buoyancy modules. A comprehensive parametric study was conducted, involving 1260 free-spanning submarine pipeline [...] Read more.

This paper introduces an efficient and automated computational framework integrating Python scripting with Abaqus finite element analysis (FEA) to investigate the structural behavior of long free-spanning submarine pipelines equipped with buoyancy modules. A comprehensive parametric study was conducted, involving 1260 free-spanning submarine pipeline models, and was successfully performed with a wide range of parameters, including the length (

l_{p} =

100, 200, and 300 m), radius (

r_{p} =

0.3, 0.4, and 0.5 m), thickness, type of fluid, type of support, load ratio (

L R =

0.2, 0.4, 0.6, 0.8, and 1), and number of buoyancy modules (

n =

0, 1, 2, 3, 5, 7, and 9) with its length

(l_{b} = 1 / 10 \cdot l_{p})

. The study included a verification process, providing a verification of the presented framework. The results demonstrate excellent agreement with analytical and numerical solutions, validating the accuracy and robustness of the proposed framework. The analysis indicates that pipeline deformation and natural frequency are highly sensitive to variations in buoyancy arrangements, pipeline geometry, and load conditions, whereas the normalized mode shapes remain largely unaffected. Practical implications include the ability to rapidly optimize buoyancy module placements, reducing resonance risks from vortex-induced vibrations (VIVs), thus enhancing the preliminary design efficiency and pipeline safety. The developed approach advances existing methods by significantly reducing the computational complexity and enabling extensive parametric analyses, making it a valuable tool for designing stable, cost-effective offshore pipeline systems. Full article

(This article belongs to the Special Issue Numerical Modeling and Applications in Mechanical Engineering)

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13 pages, 943 KiB

Open AccessArticle

Attribute-Aware Graph Aggregation for Sequential Recommendation

by Yiming Qu, Yang Fang, Zhen Tan and Weidong Xiao

Mathematics 2025, 13(9), 1386; https://doi.org/10.3390/math13091386 - 24 Apr 2025

Abstract

In this paper, we address the challenge of dynamic evolution of user preferences and propose an attribute-sequence-based recommendation model to improve the accuracy and interpretability of recommendation systems. Traditional approaches usually rely on item sequences to model user behavior, but ignore the potential [...] Read more.

In this paper, we address the challenge of dynamic evolution of user preferences and propose an attribute-sequence-based recommendation model to improve the accuracy and interpretability of recommendation systems. Traditional approaches usually rely on item sequences to model user behavior, but ignore the potential value of attributes shared among different items for preference characterization. To this end, this paper innovatively replaces items in user interaction sequences with attributes, constructs attribute sequences to capture fine-grained preference changes, and reinforces the prioritization of current interests by maintaining the latest state of attributes. Meanwhile, the item–attribute relationship is modeled using LightGCN and a variant of GAT, fusing multi-level features using gated attention mechanism, and introducing rotary encoding to enhance the flexibility of sequence modeling. Experiments on four real datasets (Beauty, Video Games, Men, and Fashion) showed that the model in this paper significantly outperformed the benchmark model in both NDCG@10 and Hit Ratio@10 metrics, with a highest improvement of 6.435% and 3.613%, respectively. The ablation experiments further validated the key role of attribute aggregation and sequence modeling in capturing user preference dynamics. This work provides a new concept for recommender systems that balances fine-grained preference evolution with efficient sequence modeling. Full article

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

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12 pages, 412 KiB

Open AccessArticle

Lightweight Models for Influenza and COVID-19 Prediction in Heterogeneous Populations: A Trade-Off Between Performance and Level of Detail

by Andrey Korzin and Vasiliy Leonenko

Mathematics 2025, 13(9), 1385; https://doi.org/10.3390/math13091385 - 24 Apr 2025

Abstract

In this work, we employ two modeling approaches—a mean-field model and a network model—for the purpose of modeling respiratory infection outbreaks in Russia. The presented approaches and their software implementation combine heterogeneity and structural simplicity and, in this sense, they close the gap [...] Read more.

In this work, we employ two modeling approaches—a mean-field model and a network model—for the purpose of modeling respiratory infection outbreaks in Russia. The presented approaches and their software implementation combine heterogeneity and structural simplicity and, in this sense, they close the gap between the compartmental SEIR models and complex detailed solutions based on agent-based approaches—the two most common modeling techniques for influenza and COVID-19 dynamics. The mathematical description of the approaches is presented, with SEIR compartmental model serving as a baseline for comparison. The experiments demonstrate the similarity of the modeling output of the presented approaches, which allows their interchangeable usage in replicating real outbreak dynamics in Russian cities. The ability of the discussed approaches to mimic data from Russian epidemic surveillance is shown by fitting a mean-field model to data from an influenza outbreak in Saint Petersburg in 2014–2015. The comparison of model complexity and their performance is made using synthetic scenarios. Following the results of numerical experiments, the comparative advantages and drawbacks of the approaches in the application to respiratory infection outbreaks are discussed. The presented modeling techniques, in addition to classical SEIR models and agent-based models as a part of epidemic surveillance, allow one to select the best modeling option for any particular task in outbreak surveillance and control, based on the computational resources at hand, data availability, and data quality. Full article

(This article belongs to the Section E3: Mathematical Biology)

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24 pages, 5383 KiB

Open AccessArticle

Optimized Method for Solving Boltzmann Transport Equations in Subgroup Method of Resonance Treatment

by Song Li, Lei Liu, Yongfa Zhang, Qian Zhang and Qi Cai

Mathematics 2025, 13(9), 1384; https://doi.org/10.3390/math13091384 - 24 Apr 2025

Abstract

This study presents an optimized subgroup transport equation solving method to enhance the computational efficiency of resonance calculations in high-fidelity reactor core simulations. By consolidating all the resonance groups into an equivalent single group and performing fixed-source calculations only for the representative subgroup [...] Read more.

This study presents an optimized subgroup transport equation solving method to enhance the computational efficiency of resonance calculations in high-fidelity reactor core simulations. By consolidating all the resonance groups into an equivalent single group and performing fixed-source calculations only for the representative subgroup cross-sections, this method significantly reduced the computational burden compared to the conventional subgroup method. Validation studies on single-cell, 2D assembly, and 3D assembly problems demonstrated that the proposed method achieves computational accuracy comparable to the conventional approach while requiring fewer fixed-source equations. This advancement offers a promising solution for improving the efficiency of resonance calculations in high-fidelity reactor core simulations, paving the way for more accurate and computationally efficient modeling of complex reactor systems. Full article

(This article belongs to the Section E4: Mathematical Physics)

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18 pages, 651 KiB

Open AccessArticle

Quantum Chosen-Cipher Attack on Camellia

by Yanjun Li, Qi Wang, Dingyun Huang, Jian Liu and Huiqin Xie

Mathematics 2025, 13(9), 1383; https://doi.org/10.3390/math13091383 - 24 Apr 2025

Abstract

The Feistel structure represents a fundamental architectural component within the domain of symmetric cryptographic algorithms, with a substantial body of research conducted within the context of classical computing environments. Nevertheless, research into specific symmetric cryptographic algorithms utilizing the Feistel structure is relatively scarce [...] Read more.

The Feistel structure represents a fundamental architectural component within the domain of symmetric cryptographic algorithms, with a substantial body of research conducted within the context of classical computing environments. Nevertheless, research into specific symmetric cryptographic algorithms utilizing the Feistel structure is relatively scarce in quantum computing environments. This paper, for the first time, proposes a five-round distinguisher for Camellia under the quantum chosen-ciphertext attack (qCCA) setting, with its effectiveness empirically validated. Additionally, by combining Grover’s algorithm and Simon’s algorithm, we construct a nine-round key-recovery attack model against Camellia. Through an in-depth analysis of Camellia’s key expansion algorithm, we significantly reduce the complexity of the key-recovery attack. The proposed attack achieves a time complexity of 2^61.5 for recovering the correct key bits and requires 531 quantum bits. Full article

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16 pages, 1000 KiB

Open AccessArticle

A Noise-Robust Deep-Learning Framework for Weld-Defect Detection in Magnetic Flux Leakage Systems

by Junlin Yang and Senxiang Lu

Mathematics 2025, 13(9), 1382; https://doi.org/10.3390/math13091382 - 24 Apr 2025

Abstract

Magnetic flux leakage (MFL) inspection systems are widely used for detecting pipeline defects in industrial sites. However, the acquired MFL signals are affected by field noise, such as electromagnetic interference and mechanical vibrations, which degrade the performance of the developed models. In addition, [...] Read more.

Magnetic flux leakage (MFL) inspection systems are widely used for detecting pipeline defects in industrial sites. However, the acquired MFL signals are affected by field noise, such as electromagnetic interference and mechanical vibrations, which degrade the performance of the developed models. In addition, the noise type or intensity is unknown or changes dynamically during the test phase in contrast to the training phase. To address the above challenges, this paper introduces a novel noise-robust deep-learning framework to remove the noise component in the original signal and learn its noise-invariant feature representation. This can handle the unseen noise pattern and mitigate the impact of dynamic noises on MFL inspection systems. Specifically, we propose a transformer-based architecture for denoising, which encodes noisy input signals into a latent space and reconstructs them into clean signals. We also devise an up–down sampling denoising block to better filter the noise component and generate a noise-invariant representation for weld-defect detection. Finally, extensive experiments demonstrate that the proposed approach effectively improves detection accuracy under both static and dynamic noise conditions, highlighting its value in real-world industrial applications. Full article

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16 pages, 5416 KiB

Open AccessArticle

Improving the Reliability of Parallel and Series–Parallel Systems by Reverse Engineering of Algebraic Inequalities

by Michael Todinov

Mathematics 2025, 13(9), 1381; https://doi.org/10.3390/math13091381 - 24 Apr 2025

Abstract

This paper presents a novel, domain-independent method for enhancing system reliability based on reverse engineering of algebraic inequalities. Although system reliability has been extensively studied, existing approaches have not addressed the challenge of improving reliability without knowing the reliability of individual components. This [...] Read more.

This paper presents a novel, domain-independent method for enhancing system reliability based on reverse engineering of algebraic inequalities. Although system reliability has been extensively studied, existing approaches have not addressed the challenge of improving reliability without knowing the reliability of individual components. This work fills this gap by demonstrating that the reliability of both parallel and series–parallel systems can be improved without any information about component reliability values. Specifically, this study establishes that in parallel systems, a symmetric arrangement of interchangeable components of the same type across parallel branches consistently yields higher system reliability than an asymmetric arrangement—regardless of the individual component reliabilities. This finding is derived through the reverse engineering of a new general algebraic inequality, proposed and proved for the first time. Furthermore, applying the same approach to series–parallel systems reveals that asymmetric arrangements of interchangeable redundancies offer superior system reliability compared with symmetric configurations. Full article

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25 pages, 809 KiB

Open AccessArticle

A Robust Optimization Approach for E-Bus Charging and Discharging Scheduling with Vehicle-to-Grid Integration

by Mingyu Kang, Bosung Lee and Younsoo Lee

Mathematics 2025, 13(9), 1380; https://doi.org/10.3390/math13091380 - 23 Apr 2025

Abstract

Electric buses (E-buses) are gaining popularity in urban transportation due to their environmental benefits and operational efficiency. However, large-scale integration of E-buses and Vehicle-to-Grid (V2G) technology introduces scheduling complexities for charging and discharging operations arising from uncertainties in energy consumption and load reduction [...] Read more.

Electric buses (E-buses) are gaining popularity in urban transportation due to their environmental benefits and operational efficiency. However, large-scale integration of E-buses and Vehicle-to-Grid (V2G) technology introduces scheduling complexities for charging and discharging operations arising from uncertainties in energy consumption and load reduction requests. While prior studies have explored electric vehicle scheduling, few have considered robust optimization for E-bus fleets under uncertain parameters such as trip energy consumption and load reduction requests. This paper proposes a robust optimization approach for the charging and discharging scheduling problem at E-bus depots equipped with V2G. The problem is formulated as a robust mixed-integer linear program (MILP), incorporating real-world operational constraints including dual-port chargers, emergency charging, and demand response. A budgeted uncertainty set is used to model uncertainty in energy consumptions and discharging requests, providing a balance between robustness and conservatism. To ensure tractability, the robust counterpart is reformulated into a solvable MILP using duality theory. The effectiveness of the proposed model is validated through extensive computational experiments, including simulation-based performance assessments and out-of-sample tests. Experiment results demonstrate superior profitability and reliability compared to deterministic and box-uncertainty models, highlighting the practical effectiveness of the proposed approach. Full article

(This article belongs to the Special Issue Mathematical Programming, Optimization and Operations Research)

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