Mathematics

10 pages, 252 KiB

Open AccessArticle

Generalized Local Charge Conservation in Many-Body Quantum Mechanics

by F. Minotti and G. Modanese

Mathematics 2025, 13(5), 892; https://doi.org/10.3390/math13050892 - 6 Mar 2025

Viewed by 365

In the framework of the quantum theory of many-particle systems, we study the compatibility of approximated non-equilibrium Green’s functions (NEGFs) and of approximated solutions of the Dyson equation with a modified continuity equation of the form [...] Read more.

In the framework of the quantum theory of many-particle systems, we study the compatibility of approximated non-equilibrium Green’s functions (NEGFs) and of approximated solutions of the Dyson equation with a modified continuity equation of the form

\partial_{t} ⟨ ρ ⟩ + (1 - γ) \nabla \cdot ⟨ J ⟩ = 0

. A continuity equation of this kind allows the e.m. coupling of the system in the extended Aharonov–Bohm electrodynamics, but not in Maxwell electrodynamics. Focusing on the case of molecular junctions simulated numerically with the Density Functional Theory (DFT), we further discuss the re-definition of local current density proposed by Wang et al., which also turns out to be compatible with the extended Aharonov–Bohm electrodynamics. Full article

(This article belongs to the Special Issue Mathematics and Applications)

34 pages, 592 KiB

Open AccessArticle

A Fractional Adams Method for Caputo Fractional Differential Equations with Modified Graded Meshes

by Yuhui Yang and Yubin Yan

Mathematics 2025, 13(5), 891; https://doi.org/10.3390/math13050891 - 6 Mar 2025

Viewed by 396

Abstract

In this paper, we introduce an Adams-type predictor–corrector method based on a modified graded mesh for solving Caputo fractional differential equations. This method not only effectively handles the weak singularity near the initial point but also reduces errors associated with large intervals in [...] Read more.

In this paper, we introduce an Adams-type predictor–corrector method based on a modified graded mesh for solving Caputo fractional differential equations. This method not only effectively handles the weak singularity near the initial point but also reduces errors associated with large intervals in traditional graded meshes. We prove the error estimates in detail for both

0 < α < 1

and

1 < α < 2

cases, where

α

is the order of the Caputo fractional derivative. Numerical experiments confirm the convergence of the proposed method and compare its performance with the traditional graded mesh approach. Full article

(This article belongs to the Section E: Applied Mathematics)

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42 pages, 2300 KiB

Open AccessArticle

Pricing and Return Strategies in Omni-Channel Apparel Retail Considering the Impact of Fashion Level

by Yanchun Wan, Zhiping Yan and Shudi Wang

Mathematics 2025, 13(5), 890; https://doi.org/10.3390/math13050890 - 6 Mar 2025

Viewed by 658

Abstract

In the context of new retail, the development of omni-channels is flourishing. The entry threshold for the clothing industry is low, and the popularity of online shopping has, to some extent, reduced consumers’ perception of the authenticity of clothing. As a result, returns [...] Read more.

In the context of new retail, the development of omni-channels is flourishing. The entry threshold for the clothing industry is low, and the popularity of online shopping has, to some extent, reduced consumers’ perception of the authenticity of clothing. As a result, returns are a serious issue in the clothing industry. This article focuses on a clothing retailer while addressing retail and return issues in the clothing industry. It develops and analyzes models for an online single-channel strategy and two omni-channel showroom strategies: “Experience in Store and Buy Online (ESBO)” with an experience store and “Buy Online and Return in Store (BORS)” with a physical store. These models are used to examine the pricing and return decisions of the retailer in the three strategic scenarios. Additionally, this study considers the impact of fashion trends on demand. It explores pricing and return strategies in two showroom models under the influence of the fashion trend decay factor. Moreover, sensitivity analyses and numerical analyses of the important parameters are performed. This research demonstrates the following: (1) In the case of high return transportation costs and online return hassle costs, clothing retailers can attract consumers to increase profits through establishing offline channels; (2) extending the sales time of fashionable clothing has a positive effect on profits, but blindly prolonging the continuation of the sales time will lead to a decrease in profits; (3) the larger the initial fashion level or the smaller the fashion level decay factor, the greater the optimal retailer profits. The impacts of the initial fashion level and fashion level decay factor on profits are more significant in omni-channel operations. This article aims to identify optimal strategies for retailers utilizing omni-channel operations and offer managerial insights for the sale of fashionable apparel. Full article

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12 pages, 251 KiB

Open AccessArticle

On the Complexity of Computing a Maximum Acyclic Matching in Undirected Graphs

by Samer Nofal

Mathematics 2025, 13(5), 889; https://doi.org/10.3390/math13050889 - 6 Mar 2025

Viewed by 468

Abstract

The problem of finding a maximum acyclic matching in a simple undirected graph is known to be NP-complete. In this paper, we present new results; we show that a maximum acyclic matching in a given undirected graph (with n vertices and m edges) [...] Read more.

The problem of finding a maximum acyclic matching in a simple undirected graph is known to be NP-complete. In this paper, we present new results; we show that a maximum acyclic matching in a given undirected graph (with n vertices and m edges) can be computed recursively with a recursion depth

O (ln m)

in expectation. Consequently, employing a recursive computation of a maximum acyclic matching in a given graph, if the recursion depth meets the expectation

O (ln m)

, then a maximum acyclic matching can be computed in time

O (n^{3.4})

and space

O (m ln m)

. However, for the general case, the complexity of the recursive computation of a maximum acyclic matching is in

O (n^{2} 2^{m})

time and in

O (m^{2})

space. Full article

17 pages, 591 KiB

Open AccessFeature PaperArticle

Enhancing Uplink Communication in Wireless Powered Communication Networks Through Rate-Splitting Multiple Access and Joint Resource Optimization

by Iqra Hameed, Mario R. Camana, Mohammad Abrar Shakil Sejan and Hyoung Kyu Song

Mathematics 2025, 13(5), 888; https://doi.org/10.3390/math13050888 - 6 Mar 2025

Viewed by 639

Abstract

Wireless powered communication networks (WPCNs) provide a sustainable solution for energy-constrained IoT devices by enabling wireless energy transfer (WET) in the downlink and wireless information transmission (WIT) in the uplink. However, their performance is often limited by interference in uplink communication and inefficient [...] Read more.

Wireless powered communication networks (WPCNs) provide a sustainable solution for energy-constrained IoT devices by enabling wireless energy transfer (WET) in the downlink and wireless information transmission (WIT) in the uplink. However, their performance is often limited by interference in uplink communication and inefficient resource allocation. To address these challenges, we propose an RSMA-aided WPCN framework, which optimizes rate-splitting factors, power allocation, and time division to enhance spectral efficiency and user fairness. To solve this non-convex joint optimization problem, we employ the simultaneous perturbation stochastic approximation (SPSA) algorithm, a gradient-free method that efficiently estimates optimal parameters with minimal function evaluations. Compared to conventional optimization techniques, SPSA provides a scalable and computationally efficient approach for real-time resource allocation in RSMA-aided WPCNs. Our simulation results demonstrate that the proposed RSMA-aided framework improves sum throughput by 12.5% and enhances fairness by 15–20% compared to conventional multiple-access schemes. These findings establish RSMA as a key enabler for next-generation WPCNs, offering a scalable, interference-resilient, and energy-efficient solution for future wireless networks. Full article

(This article belongs to the Special Issue Advanced Algorithms in Wireless Communication and Internet of Things (IoT))

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30 pages, 1422 KiB

Open AccessFeature PaperArticle

A Comparative Analysis of Compression and Transfer Learning Techniques in DeepFake Detection Models

by Andreas Karathanasis, John Violos and Ioannis Kompatsiaris

Mathematics 2025, 13(5), 887; https://doi.org/10.3390/math13050887 - 6 Mar 2025

Viewed by 667

Abstract

DeepFake detection models play a crucial role in ambient intelligence and smart environments, where systems rely on authentic information for accurate decisions. These environments, integrating interconnected IoT devices and AI-driven systems, face significant threats from DeepFakes, potentially leading to compromised trust, erroneous decisions, [...] Read more.

DeepFake detection models play a crucial role in ambient intelligence and smart environments, where systems rely on authentic information for accurate decisions. These environments, integrating interconnected IoT devices and AI-driven systems, face significant threats from DeepFakes, potentially leading to compromised trust, erroneous decisions, and security breaches. To mitigate these risks, neural-network-based DeepFake detection models have been developed. However, their substantial computational requirements and long training times hinder deployment on resource-constrained edge devices. This paper investigates compression and transfer learning techniques to reduce the computational demands of training and deploying DeepFake detection models, while preserving performance. Pruning, knowledge distillation, quantization, and adapter modules are explored to enable efficient real-time DeepFake detection. An evaluation was conducted on four benchmark datasets: “SynthBuster”, “140k Real and Fake Faces”, “DeepFake and Real Images”, and “ForenSynths”. It compared compressed models with uncompressed baselines using widely recognized metrics such as accuracy, precision, recall, F1-score, model size, and training time. The results showed that a compressed model at 10% of the original size retained only 56% of the baseline accuracy, but fine-tuning in similar scenarios increased this to nearly 98%. In some cases, the accuracy even surpassed the original’s performance by up to 12%. These findings highlight the feasibility of deploying DeepFake detection models in edge computing scenarios. Full article

(This article belongs to the Special Issue Ambient Intelligence Methods and Applications)

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39 pages, 806 KiB

Open AccessArticle

Limit Theorems for Kernel Regression Estimator for Quasi-Associated Functional Censored Time Series Within Single Index Structure

by Said Attaoui, Oum Elkheir Benouda, Salim Bouzebda and Ali Laksaci

Mathematics 2025, 13(5), 886; https://doi.org/10.3390/math13050886 - 6 Mar 2025

Viewed by 377

Abstract

In this paper, we develop kernel-based estimators for regression functions under a functional single-index model, applied to censored time series data. By capitalizing on the single-index structure, we reduce the dimensionality of the covariate-response relationship, thereby preserving the ability to capture intricate dependencies [...] Read more.

In this paper, we develop kernel-based estimators for regression functions under a functional single-index model, applied to censored time series data. By capitalizing on the single-index structure, we reduce the dimensionality of the covariate-response relationship, thereby preserving the ability to capture intricate dependencies while maintaining a relatively parsimonious form. Specifically, our framework utilizes nonparametric kernel estimation within a quasi-association setting to characterize the underlying relationships. Under mild regularity conditions, we demonstrate that these estimators attain both strong uniform consistency and asymptotic normality. Through extensive simulation experiments, we confirm their robust finite-sample performance. Moreover, an empirical examination using intraday Nikkei stock index returns illustrates that the proposed method significantly outperforms traditional nonparametric regression approaches. Full article

(This article belongs to the Special Issue Probability, Stochastic Processes and Machine Learning)

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20 pages, 679 KiB

Open AccessArticle

Center of Trapezoid Graph: Application in Selecting Center Location to Set up a Private Hospital

by Shaoli Nandi, Sukumar Mondal, Sovan Samanta, Sambhu Charan Barman, Leo Mrsic and Antonios Kalampakas

Mathematics 2025, 13(5), 885; https://doi.org/10.3390/math13050885 - 6 Mar 2025

Viewed by 434

Abstract

The central location problem is a key aspect of graph theory, with a significant importance in various applications and studies within the field. The center of a graph is made up of nodes that have the smallest eccentricity, where eccentricity is defined as [...] Read more.

The central location problem is a key aspect of graph theory, with a significant importance in various applications and studies within the field. The center of a graph is made up of nodes that have the smallest eccentricity, where eccentricity is defined as the greatest distance between a given node and any other node in the graph. To determine the graph’s center, it is essential to compute the eccentricity of each node. In this article, we explore various characteristics of the BFS tree of trapezoid graphs. We also present new properties that relate to the radius, diameter, and center of trapezoid graphs. For the trapezoid graph G, We prove that the difference between the

d i a m e t e r (G)

and the height of the BFS trees

T_{t} (1), T_{t} (n), T_{t} (a),

and

T_{t} (b)

is at most one. We also establish relationship between

r a d i u s (G)

and

d i a m e t e r (G)

of trapezoid graphs. We also show that, to find the center of a trapezoid graph, it is not necessary to find the eccentricity of all vertices. Based on our studied results, we design an optimal algorithm for finding the center, radius, and diameter of trapezoid graphs. Also, we prove theoretically that our proposed algorithm compiles within

O (n)

time. We also find an algorithmic solution to real problems (that involves finding a center location in a district to build a private hospital that minimizes the farthest distance from it to all areas of the district) with the help of the trapezoid graph model and BFS trees within

O (n)

time. Full article

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28 pages, 18090 KiB

Open AccessArticle

AFSA-FastICA-CEEMD Rolling Bearing Fault Diagnosis Method Based on Acoustic Signals

by Jin Yan, Fubing Zhou, Xu Zhu and Dapeng Zhang

Mathematics 2025, 13(5), 884; https://doi.org/10.3390/math13050884 - 6 Mar 2025

Viewed by 377

Abstract

As one of the key components in rotating machinery, rolling bearings have a crucial impact on the safety and efficiency of production. Acoustic signal is a commonly used method in the field of mechanical fault diagnosis, but an overlapping phenomenon occurs very easily, [...] Read more.

As one of the key components in rotating machinery, rolling bearings have a crucial impact on the safety and efficiency of production. Acoustic signal is a commonly used method in the field of mechanical fault diagnosis, but an overlapping phenomenon occurs very easily, which affects the diagnostic accuracy. Therefore, effective blind source separation and noise reduction of the acoustic signals generated between different devices is the key to bearing fault diagnosis using acoustic signals. To this end, this paper proposes a blind source separation method based on an AFSA-FastICA (Artificial Fish Swarm Algorithm, AFSA). Firstly, the foraging and clustering characteristics of the AFSA algorithm are utilized to perform global optimization on the aliasing matrix W, and then inverse transformation is performed on the global optimal solution W, to obtain a preliminary estimate of the source signal. Secondly, the estimated source signal is subjected to CEEMD noise reduction, and after obtaining the modal components of each order, the number of interrelationships is used as a constraint on the modal components, and signal reconstruction is performed. Finally, the signal is subjected to frequency domain feature extraction and bearing fault diagnosis. The experimental results indicate that, the new method successfully captures three fault characteristic frequencies (

1 f_{i}

,

2 f_{i}

, and

3 f_{i}

), with their energy distribution concentrated in the range of 78.9 Hz to 228.7 Hz, indicative of inner race faults. Similarly, when comparing the different results with each other, the denoised source signal spectrum successfully captures the frequencies

1 f_{o}

,

2 f_{o}

, and

3 f_{o}

and their sideband components, which are characteristic of outer race faults. The sideband components generated in the above spectra are preliminarily judged to be caused by impacts between the fault location and nearby components, resulting in modulated frequency bands where the modulation frequency corresponds to the rotational frequency and its harmonics. Experiments show that the method can effectively diagnose the bearing faults. Full article

(This article belongs to the Special Issue Numerical Analysis in Computational Mathematics)

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29 pages, 3575 KiB

Open AccessArticle

Linear Model and Gradient Feature Elimination Algorithm Based on Seasonal Decomposition for Time Series Forecasting

by Sheng-Tzong Cheng, Ya-Jin Lyu and Yi-Hong Lin

Mathematics 2025, 13(5), 883; https://doi.org/10.3390/math13050883 - 6 Mar 2025

Viewed by 395

Abstract

In the wave of digital transformation and Industry 4.0, accurate time series forecasting has become critical across industries such as manufacturing, energy, and finance. However, while deep learning models offer high predictive accuracy, their lack of interpretability often undermines decision-makers’ trust. This study [...] Read more.

In the wave of digital transformation and Industry 4.0, accurate time series forecasting has become critical across industries such as manufacturing, energy, and finance. However, while deep learning models offer high predictive accuracy, their lack of interpretability often undermines decision-makers’ trust. This study proposes a linear time series model architecture based on seasonal decomposition. The model effectively captures trends and seasonality using an additive decomposition, chosen based on initial data visualization, indicating stable seasonal variations. An augmented feature generator is introduced to enhance predictive performance by generating features such as differences, rolling statistics, and moving averages. Furthermore, we propose a gradient-based feature importance method to improve interpretability and implement a gradient feature elimination algorithm to reduce noise and enhance model accuracy. The approach is validated on multiple datasets, including order demand, energy load, and solar radiation, demonstrating its applicability to diverse time series forecasting tasks. Full article

(This article belongs to the Special Issue Applications of Cloud Computing, Big Data, and Data Dissemination in Information Engineering)

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19 pages, 4910 KiB

Open AccessArticle

A Novel SHAP-GAN Network for Interpretable Ovarian Cancer Diagnosis

by Jingxun Cai, Zne-Jung Lee, Zhihxian Lin and Ming-Ren Yang

Mathematics 2025, 13(5), 882; https://doi.org/10.3390/math13050882 - 6 Mar 2025

Viewed by 508

Abstract

Ovarian cancer stands out as one of the most formidable adversaries in women’s health, largely due to its typically subtle and nonspecific early symptoms, which pose significant challenges to early detection and diagnosis. Although existing diagnostic methods, such as biomarker testing and imaging, [...] Read more.

Ovarian cancer stands out as one of the most formidable adversaries in women’s health, largely due to its typically subtle and nonspecific early symptoms, which pose significant challenges to early detection and diagnosis. Although existing diagnostic methods, such as biomarker testing and imaging, can help with early diagnosis to some extent, these methods still have limitations in sensitivity and accuracy, often leading to misdiagnosis or missed diagnosis. Ovarian cancer’s high heterogeneity and complexity increase diagnostic challenges, especially in disease progression prediction and patient classification. Machine learning (ML) has outperformed traditional methods in cancer detection by processing large datasets to identify patterns missed by conventional techniques. However, existing AI models still struggle with accuracy in handling imbalanced and high-dimensional data, and their “black-box” nature limits clinical interpretability. To address these issues, this study proposes SHAP-GAN, an innovative diagnostic model for ovarian cancer that integrates Shapley Additive exPlanations (SHAP) with Generative Adversarial Networks (GANs). The SHAP module quantifies each biomarker’s contribution to the diagnosis, while the GAN component optimizes medical data generation. This approach tackles three key challenges in medical diagnosis: data scarcity, model interpretability, and diagnostic accuracy. Results show that SHAP-GAN outperforms traditional methods in sensitivity, accuracy, and interpretability, particularly with high-dimensional and imbalanced ovarian cancer datasets. The top three influential features identified are PRR11, CIAO1, and SMPD3, which exhibit wide SHAP value distributions, highlighting their significant impact on model predictions. The SHAP-GAN network has demonstrated an impressive accuracy rate of 99.34% on the ovarian cancer dataset, significantly outperforming baseline algorithms, including Support Vector Machines (SVM), Logistic Regression (LR), and XGBoost. Specifically, SVM achieved an accuracy of 72.78%, LR achieved 86.09%, and XGBoost achieved 96.69%. These results highlight the superior performance of SHAP-GAN in handling high-dimensional and imbalanced datasets. Furthermore, SHAP-GAN significantly alleviates the challenges associated with intricate genetic data analysis, empowering medical professionals to tailor personalized treatment strategies for individual patients. Full article

(This article belongs to the Special Issue Advances in Artificial Intelligence, Machine Learning and Optimization)

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16 pages, 248 KiB

Open AccessArticle

Conformal Interactions of Osculating Curves on Regular Surfaces in Euclidean 3-Space

by Yingxin Cheng, Yanlin Li, Pushpinder Badyal, Kuljeet Singh and Sandeep Sharma

Mathematics 2025, 13(5), 881; https://doi.org/10.3390/math13050881 - 6 Mar 2025

Cited by 1 | Viewed by 428

Abstract

Conformal maps preserve angles and maintain the local shape of geometric structures. The osculating curve plays an important role in analyzing the variations in curvature, providing a detailed understanding of the local geometric properties and the impact of conformal transformations on curves and [...] Read more.

Conformal maps preserve angles and maintain the local shape of geometric structures. The osculating curve plays an important role in analyzing the variations in curvature, providing a detailed understanding of the local geometric properties and the impact of conformal transformations on curves and surfaces. In this paper, we study osculating curves on regular surfaces under conformal transformations. We obtained the conditions required for osculating curves on regular surfaces R and

\tilde{R}

to remain invariant when subjected to a conformal transformation

ψ : R \to \tilde{R}

. The results presented in this paper reveal the specific conditions under which the transformed curve

\tilde{σ} = ψ \circ σ

preserves its osculating properties, depending on whether

\tilde{σ}

is a geodesic, asymptotic, or neither. Furthermore, we analyze these conditions separately for cases with zero and non-zero normal curvatures. We also explore the behavior of these curves along the tangent vector

T_{σ}

and the unit normal vector

P_{σ}

. Full article

(This article belongs to the Special Issue Geometric Topology and Differential Geometry with Applications)

23 pages, 860 KiB

Open AccessArticle

Hybrid Disassembly Line Balancing of Multi-Factory Remanufacturing Process Considering Workers with Government Benefits

by Xiaoyu Niu, Xiwang Guo, Peisheng Liu, Jiacun Wang, Shujin Qin, Liang Qi, Bin Hu and Yingjun Ji

Mathematics 2025, 13(5), 880; https://doi.org/10.3390/math13050880 - 6 Mar 2025

Viewed by 414

Abstract

Optimizing multi-factory remanufacturing systems with social welfare considerations presents critical challenges in task allocation and process coordination. This study addresses this gap by proposing a hybrid disassembly line balancing and multi-factory remanufacturing process optimization problem, considering workers with government benefits. A mixed-integer programming [...] Read more.

Optimizing multi-factory remanufacturing systems with social welfare considerations presents critical challenges in task allocation and process coordination. This study addresses this gap by proposing a hybrid disassembly line balancing and multi-factory remanufacturing process optimization problem, considering workers with government benefits. A mixed-integer programming model is formulated to maximize profit, and its correctness is verified using the CPLEX solver. Furthermore, a discrete zebra optimization algorithm is proposed to solve the model, integrating a survival-of-the-fittest strategy to improve its optimization capabilities. The effectiveness and convergence of the algorithm are demonstrated through experiments on disassembly cases, with comparisons made to six peer algorithms and CPLEX. The experimental results highlight the importance of this research in improving resource utilization efficiency, reducing environmental impacts, and promoting sustainable development. Full article

(This article belongs to the Special Issue Knowledge- and Learning-Driven Meta-Heuristics for Addressing Complex Optimization and Scheduling Problems)

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15 pages, 1447 KiB

Open AccessArticle

The Waxing and Waning of Fear Influence the Control of Vector-Borne Diseases

by Jing Jiao

Mathematics 2025, 13(5), 879; https://doi.org/10.3390/math13050879 - 6 Mar 2025

Viewed by 453

Abstract

One major challenge in preventing infectious diseases comes from human control behaviors. In the context of vector-borne diseases (VBDs), I explored how the waxing and waning of a human psychological emotion—fear—can generate diverse control actions, which, in turn, influence disease dynamics. Fear may [...] Read more.

One major challenge in preventing infectious diseases comes from human control behaviors. In the context of vector-borne diseases (VBDs), I explored how the waxing and waning of a human psychological emotion—fear—can generate diverse control actions, which, in turn, influence disease dynamics. Fear may diminish over time after being triggered but can also be reinforced when new triggers emerge. By integrating fear dynamics into a generic Ross–MacDonald model tailored for the Zika virus, I found that an increase in initial fear can enhance control efforts, thereby reducing the number of infected individuals and deaths. Once initial fear becomes strong enough to deplete the mosquito population, any further increase in fear no longer impacts disease dynamics. When initial fear is at an intermediate level, the increase in disease caused by greater decay in fear can be counterbalanced by increasing the frequency of fear triggers. Interestingly, when the control period is short and initial fear is at an intermediate level, increasing the frequency of fear reinforcement can lead to a “hydra effect”, which increases disease transmission. These findings help explain variations in human control efforts and provide insights for developing more effective disease control strategies that account for the fear dynamics of local communities. This work also contributes to advancing the theory at the intersection of human behavior, disease ecology, and epidemiology. Full article

(This article belongs to the Special Issue Mathematical Epidemiological Models: Classical and Interdisciplinary Applications)

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18 pages, 265 KiB

Open AccessArticle

Strong Solution for a Nonlinear Non-Newtonian Shear Thickening Fluid

by Yukun Song, Lin Jin and Yang Chen

Mathematics 2025, 13(5), 878; https://doi.org/10.3390/math13050878 - 6 Mar 2025

Viewed by 381

Abstract

This paper consider a nonlinear shear thickening fluid in one dimensional bounded interval. The model illustrates that the movement of the compressible fluid is driven by non-Newtonian gravity, and represents a more realistic phenomenon. The well-posedness of strong solution was proved by considering [...] Read more.

This paper consider a nonlinear shear thickening fluid in one dimensional bounded interval. The model illustrates that the movement of the compressible fluid is driven by non-Newtonian gravity, and represents a more realistic phenomenon. The well-posedness of strong solution was proved by considering the influence of damping term. The essential difficulty lies in the equation’s significant nonlinearity and the initial state may allow for vacuum. Full article

(This article belongs to the Special Issue Mathematical Modeling for Fluid Mechanics)

19 pages, 6211 KiB

Open AccessArticle

An Optimization Problem of Distributed Permutation Flowshop Scheduling with an Order Acceptance Strategy in Heterogeneous Factories

by Seung Jae Lee and Byung Soo Kim

Mathematics 2025, 13(5), 877; https://doi.org/10.3390/math13050877 - 6 Mar 2025

Viewed by 477

Abstract

This paper addresses a distributed permutation flowshop scheduling problem with an order acceptance strategy in heterogeneous factories. Each order has a related revenue and due date, and several flowshop machines are operated in each factory, and they have a distinct sequence-dependent setup time. [...] Read more.

This paper addresses a distributed permutation flowshop scheduling problem with an order acceptance strategy in heterogeneous factories. Each order has a related revenue and due date, and several flowshop machines are operated in each factory, and they have a distinct sequence-dependent setup time. We select/reject production orders, assign the selected orders to the factories, and determine the permutation manufacturing sequence in each factory to maximize the total profit. To optimally solve the scheduling problem, we formulate the scheduling problem as a mixed integer linear programming model to find an optimal solution for small-sized experiments. Then, we propose two population-based algorithms, a genetic algorithm and particle swarm optimization for large-sized experiments. We proved that the proposed genetic algorithm effectively and efficiently solves the problem to guarantee a near optimal solution through computational experiments. Finally, we conduct a sensitivity analysis of the genetic algorithm to observe the relationship between order selection, revenue, and order tardiness cost. Full article

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

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32 pages, 3386 KiB

Open AccessArticle

A Column-Generation-Based Exact Algorithm to Solve the Full-Truckload Vehicle-Routing Problem

by Toygar Emre and Rizvan Erol

Mathematics 2025, 13(5), 876; https://doi.org/10.3390/math13050876 - 6 Mar 2025

Viewed by 539

Abstract

This study addresses a specialized variant of the full-truckload delivery problem inspired by a Turkish logistics firm that operates in the liquid transportation sector. An exact algorithm is proposed for the relevant problem, to which no exact approach has been applied before. Multiple [...] Read more.

This study addresses a specialized variant of the full-truckload delivery problem inspired by a Turkish logistics firm that operates in the liquid transportation sector. An exact algorithm is proposed for the relevant problem, to which no exact approach has been applied before. Multiple customer and trailer types, as well as washing operations, are introduced simultaneously during the exact solution process, bringing new aspects to the exact algorithm approach among full-truckload systems in the literature. The objective is to minimize transportation costs while addressing constraints related to multiple time windows, trailer types, customer types, product types, a heterogeneous fleet with limited capacity, multiple departure points, and various actions such as loading, unloading, and washing. Additionally, the elimination or reduction of waiting times is provided along transportation routes. In order to achieve optimal solutions, an exact algorithm based on the column generation method is proposed. A route-based insertion algorithm is also employed for initial routes/columns. Regarding the acquisition of integral solutions in the exact algorithm, both dynamic and static sets of valid inequalities are incorporated. A label-setting algorithm is used to generate columns within the exact algorithm by being accelerated through bi-directional search, ng-route relaxation, subproblem selection, and heuristic column generation. Due to the problem-dependent structure of the column generation method and acceleration techniques, a tailored version of them is included in the solution process. Performance analysis, which was conducted using artificial input sets based on the real-life operations of the logistics firm, demonstrates that optimality gaps of less than 1% can be attained within reasonable times even for large-scale instances relevant to the industry, such as 120 customers, 8 product and 8 trailer types, 4 daily time windows, and 40 departure points. Full article

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25 pages, 7825 KiB

Open AccessArticle

A New Hjorth Distribution in Its Discrete Version

by Hanan Haj Ahmad and Ahmed Elshahhat

Mathematics 2025, 13(5), 875; https://doi.org/10.3390/math13050875 - 6 Mar 2025

Viewed by 381

Abstract

The Hjorth distribution is more flexible in modeling various hazard rate shapes, including increasing, decreasing, and bathtub shapes. This makes it highly useful in reliability analysis and survival studies, where different failure rate behaviors must be captured effectively. In some practical experiments, the [...] Read more.

The Hjorth distribution is more flexible in modeling various hazard rate shapes, including increasing, decreasing, and bathtub shapes. This makes it highly useful in reliability analysis and survival studies, where different failure rate behaviors must be captured effectively. In some practical experiments, the observed data may appear to be continuous, but their intrinsic discreteness requires the development of specialized techniques for constructing discrete counterparts to continuous distributions. This study extends this methodology by discretizing the Hjorth distribution using the survival function approach. The proposed discrete Hjorth distribution preserves the essential statistical characteristics of its continuous counterpart, such as percentiles and quantiles, making it a valuable tool for modeling lifetime data. The complexity of the transformation requires numerical techniques to ensure accurate estimations and analysis. A key feature of this study is the incorporation of Type-II censored samples. We also derive key statistical properties, including the quantile function and order statistics, and then employ maximum likelihood and Bayesian inference methods. A comparative analysis of these estimation techniques is conducted through simulation studies. Furthermore, the proposed model is validated using two real-world datasets, including electronic device failure times and ball-bearing failure analysis, by applying goodness-of-fit tests against alternative discrete models. The findings emphasize the versatility and applicability of the discrete Hjorth distribution in reliability studies, engineering, and survival analysis, offering a robust framework for modeling discrete data in practical scenarios. To our knowledge, no prior research has explored the use of censored data in analyzing discrete Hjorth-distributed data. This study fills this gap, providing new insights into discrete reliability modeling and broadening the application of the Hjorth distribution in real-world scenarios. Full article

(This article belongs to the Special Issue New Advances in Distribution Theory and Its Applications)

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22 pages, 1775 KiB

Open AccessFeature PaperArticle

Classifications of Several Classes of Armendariz-like Rings Relative to an Abelian Monoid and Its Applications

by Jianwei He and Yajun Ma

Mathematics 2025, 13(5), 874; https://doi.org/10.3390/math13050874 - 5 Mar 2025

Viewed by 462

Abstract

Let M be an Abelian monoid. A necessary and sufficient condition for the class

A r m_{M}

of all Armendariz rings relative to M to coincide with the class

A r m

of all Armendariz rings is given. As a consequence, we [...] Read more.

Let M be an Abelian monoid. A necessary and sufficient condition for the class

A r m_{M}

of all Armendariz rings relative to M to coincide with the class

A r m

of all Armendariz rings is given. As a consequence, we prove that

A r m_{M}

has exactly three cases: the empty set,

A r m

, and the class of all rings. If N is an Abelian monoid, then we prove that

A r m_{M \times N} = A r m_{M} ⋂ A r m_{N}

, which gives a partial affirmative answer to the open question of Liu in 2005 (whether R is

M \times N

-Armendariz if R is M-Armendariz and N-Armendariz). We also show that the other Armendariz-like rings relative to an Abelian monoid, such as M-quasi-Armendariz rings, skew M-Armendariz rings, weak M-Armendariz rings, M-

π

-Armendariz rings, nil M-Armendariz rings, upper nil M-Armendariz rings and lower nil M-Armendariz rings can be handled similarly. Some conclusions on these classes have, therefore, been generalized using these classifications. Full article

(This article belongs to the Section A: Algebra and Logic)

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20 pages, 375 KiB

Open AccessFeature PaperArticle

On Error Estimation and Convergence of the Difference Scheme for a Nonlinear Elliptic Equation with an Integral Boundary Condition

by Regimantas Čiupaila, Mifodijus Sapagovas, Kristina Pupalaigė and Gailė Kamilė Šaltenienė

Mathematics 2025, 13(5), 873; https://doi.org/10.3390/math13050873 - 5 Mar 2025

Viewed by 507

Abstract

In this paper, a two-dimensional nonlinear elliptic equation with an integral boundary condition depending on two parameters is investigated. The problem is solved using the finite difference method. The error in the solution is evaluated based on the properties of M-matrices, and herewith [...] Read more.

In this paper, a two-dimensional nonlinear elliptic equation with an integral boundary condition depending on two parameters is investigated. The problem is solved using the finite difference method. The error in the solution is evaluated based on the properties of M-matrices, and herewith the convergence of the difference scheme is proved. The majorant is constructed to estimate the error of the solution of the system of difference equations. Full article

(This article belongs to the Special Issue New Trends in Nonlinear Analysis)

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17 pages, 581 KiB

Open AccessArticle

Nonlinear Stochastic Modeling with Heterogeneous Covariates for Degradation Analysis Applied to Wax Lubrication Layer

by Shixiang Li, Yubin Tian and Dianpeng Wang

Mathematics 2025, 13(5), 872; https://doi.org/10.3390/math13050872 - 5 Mar 2025

Viewed by 439

Abstract

Wax is a commonly used lubricant in many applications. To ensure its security and dependability, degradation analyses for creep are typically conducted. However, challenges arise due to the poorly understood inherent mechanisms of wax and the complicated experimental environment required, leading to nonlinear [...] Read more.

Wax is a commonly used lubricant in many applications. To ensure its security and dependability, degradation analyses for creep are typically conducted. However, challenges arise due to the poorly understood inherent mechanisms of wax and the complicated experimental environment required, leading to nonlinear trends and heterogeneous covariates. In such cases, traditional methods based on parametric forms or linear assumptions may lack the flexibility to capture the complexities and randomness of the degradation process effectively. To address these challenges, we propose a comprehensive degradation analysis framework that employs a Wiener process with an unspecified mean function. By eliminating parametric forms, this approach offers a more versatile way to model nonlinear degradation trends. Moreover, it treats environmental covariates as random variables to handle random environmental influences. We develop tailored semiparametric estimators for the model and establish theoretical asymptotic results that guarantee the consistency and convergence of the proposed estimators. A series of numerical experiments are conducted to illustrate the performance of the estimators and validate their convergence properties. The method is applied to a wax lubrication layer, demonstrating its efficacy in analyzing nonlinear degradation data in a random working environment. This work advances the understanding of wax degradation mechanisms and provides a flexible tool for degradation analysis in materials with heterogenic environments and poorly understood behaviors. Full article

(This article belongs to the Section D1: Probability and Statistics)

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20 pages, 468 KiB

Open AccessArticle

Toward 6G: Latency-Optimized MEC Systems with UAV and RIS Integration

by Abdullah Alshahrani

Mathematics 2025, 13(5), 871; https://doi.org/10.3390/math13050871 - 5 Mar 2025

Viewed by 612

Abstract

Multi-access edge computing (MEC) has emerged as a cornerstone technology for deploying 6G network services, offering efficient computation and ultra-low-latency communication. The integration of unmanned aerial vehicles (UAVs) and reconfigurable intelligent surfaces (RISs) further enhances wireless propagation, capacity, and coverage, presenting a transformative [...] Read more.

Multi-access edge computing (MEC) has emerged as a cornerstone technology for deploying 6G network services, offering efficient computation and ultra-low-latency communication. The integration of unmanned aerial vehicles (UAVs) and reconfigurable intelligent surfaces (RISs) further enhances wireless propagation, capacity, and coverage, presenting a transformative paradigm for next-generation networks. This paper addresses the critical challenge of task offloading and resource allocation in an MEC-based system, where a massive MIMO base station, serving multiple macro-cells, hosts the MEC server with support from a UAV-equipped RIS. We propose an optimization framework to minimize task execution latency for user equipment (UE) by jointly optimizing task offloading and communication resource allocation within this UAV-assisted, RIS-aided network. By modeling this problem as a Markov decision process (MDP) with a discrete-continuous hybrid action space, we develop a deep reinforcement learning (DRL) algorithm leveraging a hybrid space representation to solve it effectively. Extensive simulations validate the superiority of the proposed method, demonstrating significant latency reductions compared to state-of-the-art approaches, thereby advancing the feasibility of MEC in 6G networks. Full article

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12 pages, 247 KiB

Open AccessArticle

On a Quotient Ring That Satisfies Certain Identities via Generalized Reverse Derivations

by Nawaf L. Alsowait, Mohammed Al-Shomrani, Radwan M. Al-omary and Zakia Z. Al-Amery

Mathematics 2025, 13(5), 870; https://doi.org/10.3390/math13050870 - 5 Mar 2025

Viewed by 375

Abstract

In this article, for a prime ideal

ρ

of an arbitrary ring ℜ, we study the commutativity of the quotient ring

ℜ / ρ

, whenever ℜ admits a generalized reverse derivation

ϑ

associated with a reverse derivation ∂ that satisfies certain identities [...] Read more.

In this article, for a prime ideal

ρ

of an arbitrary ring ℜ, we study the commutativity of the quotient ring

ℜ / ρ

, whenever ℜ admits a generalized reverse derivation

ϑ

associated with a reverse derivation ∂ that satisfies certain identities in

ρ

. Additionally, we show that, for some cases, the range of the generalized reverse derivation

ϑ

lies in the prime ideal

ρ

. Moreover, we explore several consequences and special cases. Throughout, we provide examples to demonstrate that various restrictions in the assumptions of our results are essential. Full article

(This article belongs to the Special Issue Advanced Research in Pure and Applied Algebra)

21 pages, 1125 KiB

Open AccessFeature PaperArticle

A Hybrid Approach for the Container Loading Problem for Enhancing the Dynamic Stability Representation

by Ana María Montes-Franco, Juan Camilo Martinez-Franco, Alejandra Tabares and David Álvarez-Martínez

Mathematics 2025, 13(5), 869; https://doi.org/10.3390/math13050869 - 5 Mar 2025

Viewed by 604

Abstract

In the container loading problem (CLP), the construction of packing patterns is driven by the maximization of the volume occupied, and comprises several constraints such as loading feasibility, weight balance, cargo stability, operational safety, material handling, and the prevention of cargo damage during [...] Read more.

In the container loading problem (CLP), the construction of packing patterns is driven by the maximization of the volume occupied, and comprises several constraints such as loading feasibility, weight balance, cargo stability, operational safety, material handling, and the prevention of cargo damage during container shipping. Previous works introduced dynamic stability indicators using simulation or statistical approaches. However, this firstly exponentially increases the computational burden, and secondly misrepresents the essential kinetic mechanical aspects. This paper presents a hybrid scheme to solve the CLP by embedding a mechanical model into a reactive GRASP algorithm, leading to two main novelties; namely, the substitution of the physics simulation engine to find the dynamic stability of the packing patterns, and a modified structure of the metaheuristic, guaranteeing specified minimum stability while achieving efficient packing patterns. The mechanical model dynamically analyzes the forces and accelerations acting on the cargo to predict loss of support, overturning, or critical velocity deltas that would damage it. At the same time, the reactive GRASP algorithm considers the dynamic stability indicators in the improvement steps. The stability indicators are obtained from the mechanical model, allowing the user to know the percentage of damaged boxes in a packing pattern. The effectiveness of the proposed approach is tested using a set of classical benchmark instances, obtaining adequately accurate solutions within a short computational time. The resulting scheme integrates real-world problem conditions and achieves dynamic stability solutions at an acceptable computational cost; it is programmed in C++ instead of relying on proprietary simulation tools. Full article

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25 pages, 3597 KiB

Open AccessArticle

Research on Abstraction-Based Search Space Partitioning and Solving Satisfiability Problems

by Yuexin Huang, Qinzhou Niu and Yanfang Song

Mathematics 2025, 13(5), 868; https://doi.org/10.3390/math13050868 - 5 Mar 2025

Viewed by 391

Abstract

Solving satisfiability problems is central to many areas of computer science, including artificial intelligence and optimization. Efficiently solving satisfiability problems requires exploring vast search spaces, where search space partitioning plays a key role in improving solving efficiency. This paper defines search spaces and [...] Read more.

Solving satisfiability problems is central to many areas of computer science, including artificial intelligence and optimization. Efficiently solving satisfiability problems requires exploring vast search spaces, where search space partitioning plays a key role in improving solving efficiency. This paper defines search spaces and their partitioning, focusing on the relationship between partitioning strategies and satisfiability problem solving. By introducing an abstraction method for partitioning the search space—distinct from traditional assignment-based approaches—the paper proposes sequential, parallel, and hybrid solving algorithms. Experimental results show that the hybrid approach, combining abstraction and assignment, significantly accelerates solving in most cases. Furthermore, a unified method for search space partitioning is presented, defining independent and complete partitions. This method offers a new direction for enhancing the efficiency of SAT problem solving and provides a foundation for future research in the field. Full article

(This article belongs to the Special Issue Formal Methods in Computer Science: Theory and Applications)

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24 pages, 354 KiB

Open AccessFeature PaperReview

The Heroic Age of Probability: Kolmogorov, Doob, Lévy, Khinchin and Feller

by Andrew J. Heunis

Mathematics 2025, 13(5), 867; https://doi.org/10.3390/math13050867 - 5 Mar 2025

Viewed by 534

Abstract

We survey some of the main developments in probability theory during the so-called “heroic age”; that is, the period from the nineteen twenties to the early nineteen fifties. It was during the heroic age that probability finally attained the status of a mathematical [...] Read more.

We survey some of the main developments in probability theory during the so-called “heroic age”; that is, the period from the nineteen twenties to the early nineteen fifties. It was during the heroic age that probability finally attained the status of a mathematical discipline in the full sense of the term, with a complete axiomatic basis and incontestable standards of intellectual rigor to complement and support the extraordinarily rich intuitive content that has always been part of probability theory from its very inception. The axiomatic basis and mathematical rigor are themselves rooted in the abstract theory of measure and integration, which now comprises the very bedrock of modern probability, and among the central characters in the measure-theoretic “re-invention” of probability during the heroic age one finds, in particular, Kolmogorov, Doob, Lévy, Khinchin and Feller, each of whom fundamentally shaped the structure of modern probability. In this survey, we attempt a brief sketch of some of the main contributions of each of these pioneers. Full article

(This article belongs to the Special Issue Anticipating a Hundred Years of Modern Probability and Stochastic Processes)

23 pages, 10129 KiB

Open AccessArticle

Smoothing Filter and Correction Factor for Two-Dimensional Electrical Resistivity Tomography and Time Domain-Induced Polarization Data Collected in Difficult Terrains to Improve Inversion Models

by Andrés Tejero-Andrade, Aide E. López-González, José M. Tejero-Andrade, René E. Chávez-Segura and Denisse L. Argote

Mathematics 2025, 13(5), 866; https://doi.org/10.3390/math13050866 - 5 Mar 2025

Viewed by 1166

Abstract

When collecting data using ERT2D (2D electrical resistivity tomography) and TDIPT2D (2D time domain-induced polarization), different phenomena can occur, which can cause natural or anthropogenic noise, contaminating the data and making its processing, analysis, and interpretation difficult. Different techniques have been developed to [...] Read more.

When collecting data using ERT2D (2D electrical resistivity tomography) and TDIPT2D (2D time domain-induced polarization), different phenomena can occur, which can cause natural or anthropogenic noise, contaminating the data and making its processing, analysis, and interpretation difficult. Different techniques have been developed to eliminate or reduce these effects on the data, such as noise filtering or the development of new techniques to improve data collection in the field. In the present work, an iterative, weighted, least-squares filter was employed after voltage normalization using current and geometrical factor correction on data collected in rough topographic terrains. The selected filter basis function should be able to represent the natural behavior of the function to be filtered. Stationary or variable voltages in electrical prospecting decay with the inverse of the distance, which can be represented by an expansion in Legendre polynomials. On the other hand, uneven spacing of the electrodes leads to using the incorrect geometric factor, resulting in an error in the calculation of the electrical anomaly. The efficiency of the proposed technique was analyzed and tested with field examples using different filters and by comparing applying and not applying the proposed correction factor. The results indicated low RMS and L2-Norm errors, and better definition of the inverted resistivity image was obtained. For the TDIP data, a better correspondence between the inverted images of resistivity and chargeability was obtained. Full article

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23 pages, 1058 KiB

Open AccessArticle

Private Label Introduction and Sales Format Selection with Regard to e-Commerce Platform Supply Chain

by Zhichao Zhang, Zhi Liu, Juan Tang and Ting Tang

Mathematics 2025, 13(5), 865; https://doi.org/10.3390/math13050865 - 5 Mar 2025

Viewed by 447

Abstract

Largely motivated by the industrial practice in which a platform giant will encroach online retailing by introducing private label (PL) products, this paper aims to investigate the optimal introduction decision for a platform and identify the best sales format, between the reselling format [...] Read more.

Largely motivated by the industrial practice in which a platform giant will encroach online retailing by introducing private label (PL) products, this paper aims to investigate the optimal introduction decision for a platform and identify the best sales format, between the reselling format and the agency format, for a manufacturer in an e-commerce platform supply chain. In response to these two sales formats, this paper characterizes and proposes three different PL product introduction strategies, including No Introduction, Partial Introduction, and Full Introduction. By developing a game-theoretic framework and applying the Karush–Kuhn–Tucker optimality, this paper examines the optimal PL product introduction decision and the best sales format. With analytical studies and numerical experiments, several significant implications are derived in this paper. For example, it is first found that the consumer preference for the platform and the quality of the PL products are two key factors influencing the platform’s PL product introduction, with associated effects differing notably. Secondly, improving the PL products’ quality does not necessarily lead to an increased profit for the platform. It will also not lead to a loss in profit for the manufacturer. Lastly, the best sales formats for the manufacturer are significantly influenced by the PL products’ introduction strategy chosen by the platform. Full article

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14 pages, 2439 KiB

Open AccessArticle

A Context-Preserving Tokenization Mismatch Resolution Method for Korean Word Sense Disambiguation Based on the Sejong Corpus and BERT

by Hanjo Jeong

Mathematics 2025, 13(5), 864; https://doi.org/10.3390/math13050864 - 5 Mar 2025

Viewed by 425

Abstract

The disambiguation of word senses (Word Sense Disambiguation, WSD) plays a crucial role in various natural language processing (NLP) tasks, such as machine translation, sentiment analysis, and information retrieval. Due to the complex morphological structure and polysemy of the Korean language, the meaning [...] Read more.

The disambiguation of word senses (Word Sense Disambiguation, WSD) plays a crucial role in various natural language processing (NLP) tasks, such as machine translation, sentiment analysis, and information retrieval. Due to the complex morphological structure and polysemy of the Korean language, the meaning of words can change depending on the context, making the WSD problem challenging. Since a single word can have multiple meanings, accurately distinguishing between them is essential for improving the performance of NLP models. Recently, large-scale pre-trained models like BERT and GPT, based on transfer learning, have shown promising results in addressing this issue. However, for languages with complex morphological structures, like Korean, the tokenization mismatch between pre-trained models and fine-tuning data prevents the rich contextual and lexical information learned by the pre-trained models from being fully utilized in downstream tasks. This paper proposes a novel method to address the tokenization mismatch issue during the fine-tuning of Korean WSD, leveraging BERT-based pre-trained models and the Sejong corpus, which has been annotated by language experts. Experimental results using various BERT-based pre-trained models and datasets from the Sejong corpus demonstrate that the proposed method improves performance by approximately 3–5% compared to existing approaches. Full article

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

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18 pages, 796 KiB

Open AccessArticle

Comparison Among Modified Continual Reassessment Methods with Different Dose Allocation Methods for Phase I Clinical Trials

by Jiacheng Xiao, Weijia Zhang, Rong Li and Conghua Wen

Mathematics 2025, 13(5), 863; https://doi.org/10.3390/math13050863 - 5 Mar 2025

Viewed by 380

Abstract

The continual reassessment method (CRM) has been an essential Bayesian finding design in phase I clinical trials. It utilizes all the information in observed data which contributes to its essential operational characteristics. However, the CRM has been criticized for its aggressive dose escalation. [...] Read more.

The continual reassessment method (CRM) has been an essential Bayesian finding design in phase I clinical trials. It utilizes all the information in observed data which contributes to its essential operational characteristics. However, the CRM has been criticized for its aggressive dose escalation. Model-assisted methods including BOIN, Keyboard, and mTPI improved the safety while retaining relative efficiency. In this paper, we propose four models combining the structure of the CRM and model-assisted methods. We show that these models could operate with comparable CRM performance through simulations. The results suggest that two of the proposed methods outperformed the traditional methods with a higher percentage of correct selection of true maximum tolerated dose. In addition, the interval-based approaches offered by the new models with greater flexibility regarding target toxicity achieved an improvement in the adaptability of the dose-finding process in clinical trials. Full article

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Mathematics, Volume 13, Issue 5 (March-1 2025) – 208 articles

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