Mathematics

10 pages, 270 KiB

Open AccessFeature PaperArticle

Star-Convexity of the Eigenvalue Regions for Stochastic Matrices and Certain Subclasses

by Brando Vagenende, Brecht Verbeken and Marie-Anne Guerry

Mathematics 2025, 13(12), 2038; https://doi.org/10.3390/math13122038 - 19 Jun 2025

Viewed by 271

Star-convexity of the eigenvalue region for the set of

n \times n

stochastic matrices has already been proven, for

n \geq 2

, by Dmitriev and Dynkin. The star-convexity property enables full determination of the eigenvalue region by its boundary. This study offers [...] Read more.

Star-convexity of the eigenvalue region for the set of

n \times n

stochastic matrices has already been proven, for

n \geq 2

, by Dmitriev and Dynkin. The star-convexity property enables full determination of the eigenvalue region by its boundary. This study offers a more straightforward proof that extends to other subclasses of the stochastic matrices. Furthermore, the proof is constructive as it includes the explicit construction of the corresponding realizing matrices. Explicit sufficient conditions for star-convexity of the eigenvalue regions of stochastic subclasses are presented. In particular, star-convexity of the eigenvalue region is proved for the

n \times n

doubly stochastic and the

n \times n

monotone stochastic matrices. Full article

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28 pages, 398 KiB

Open AccessReview

Existence and Related Properties of Solutions for Klein–Gordon–Maxwell Systems

by Xiao-Qi Liu and Chun-Lei Tang

Mathematics 2025, 13(12), 2037; https://doi.org/10.3390/math13122037 - 19 Jun 2025

Viewed by 461

Abstract

This paper aims to present the application of variational methods in studying the existence and related properties of solutions for Klein–Gordon–Maxwell systems through a literature review. First, we give an introduction and variational framework for the Klein–Gordon–Maxwell system. Second, we review the existence [...] Read more.

This paper aims to present the application of variational methods in studying the existence and related properties of solutions for Klein–Gordon–Maxwell systems through a literature review. First, we give an introduction and variational framework for the Klein–Gordon–Maxwell system. Second, we review the existence and nonexistence of solutions for autonomous Klein–Gordon–Maxwell systems under subcritical growth, critical growth and zero-mass conditions. Third, we introduce studies on the existence and properties of solutions for Klein–Gordon–Maxwell systems classified according to potential functions. Finally, we review the existence of solutions for Klein–Gordon–Maxwell systems in two-dimensional space. Full article

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

35 pages, 1453 KiB

Open AccessArticle

Probabilistic Selling with Unsealing Strategy: An Analysis in Markets with Vertical-Differentiated Products

by Pak Hou Che and Yue Chen

Mathematics 2025, 13(12), 2036; https://doi.org/10.3390/math13122036 - 19 Jun 2025

Viewed by 444

Abstract

Probabilistic selling is a retail strategy in which consumers purchase products without knowing their exact identities until after purchase, with various applications like gaming and retail; a real-world practice involves retailers may unsealing and reselling goods to meet consumer demand for transparency. This [...] Read more.

Probabilistic selling is a retail strategy in which consumers purchase products without knowing their exact identities until after purchase, with various applications like gaming and retail; a real-world practice involves retailers may unsealing and reselling goods to meet consumer demand for transparency. This disrupts manufacturers’ strategies designed to adopt the uncertainty for segmentation and pricing. Using a vertically differentiated supply chain model structured as a Stackelberg game framework, this study examines how transparency from retailer unsealing affects profitability, consumer surplus, and market dynamics. Key findings include the following: (1) Unsealing increases retailer profits by aligning pricing with heterogeneous consumer willingness to pay. (2) Introducing a manufacturer’s direct channel reduces unsealing profits via price competition. (3) Unsealing creates conflicts between manufacturers’ design goals and retailers’ profit-driven incentives. By applying a Stackelberg game framework to model unsealing as a downstream transparency decision, this work advances the probabilistic selling literature by offering a structured approach to analyzing how downstream transparency and retailer strategies reshape probabilistic selling and supply chain dynamics. It highlights the need for manufacturers to balance segmentation, pricing, and channel control, offering insights into mitigating conflicts between design intentions and downstream market behaviors. Full article

(This article belongs to the Special Issue Operations and Supply Chain Management with the Application of Mathematical Models)

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18 pages, 5358 KiB

Open AccessArticle

Fault Diagnosis and Identification of Abnormal Variables Based on Center Nearest Neighbor Reconstruction Theory

by Guozhu Wang, Ruizhe Zhou, Fei Li, Xiang Li and Xinmin Zhang

Mathematics 2025, 13(12), 2035; https://doi.org/10.3390/math13122035 - 19 Jun 2025

Viewed by 357

Abstract

Fault diagnosis and identification are important goals in ensuring the safe production of industrial processes. This article proposes a data reconstruction method based on Center Nearest Neighbor (CNN) theory for fault diagnosis and abnormal variable identification. Firstly, the k-nearest neighbor (k [...] Read more.

Fault diagnosis and identification are important goals in ensuring the safe production of industrial processes. This article proposes a data reconstruction method based on Center Nearest Neighbor (CNN) theory for fault diagnosis and abnormal variable identification. Firstly, the k-nearest neighbor (k-NN) method is used to monitor the process and determine whether there is a fault. Secondly, when there is a fault, a high-precision CNN reconstruction algorithm is used to reconstruct each variable and calculate the reconstructed control index. The variable that reduces the control index the most is replaced with the reconstructed variable in sequence, and the iteration is carried out until the control index is within the control range, and all abnormal variables are finally determined. The accuracy of the CNN reconstruction method was verified through a numerical example. Additionally, it was confirmed that the method is not only suitable for fault diagnosis of a single sensor but also can be used sensor faults that occur simultaneously or propagate due to variable correlation. Finally, the effectiveness and applicability of the proposed method were validated through the penicillin fermentation process. Full article

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22 pages, 1590 KiB

Open AccessArticle

Continuous Exchangeable Markov Chains, Idempotent and 1-Dependent Copulas

by Martial Longla

Mathematics 2025, 13(12), 2034; https://doi.org/10.3390/math13122034 - 19 Jun 2025

Viewed by 1234

Abstract

New copula families are constructed based on orthogonality in

L^{2} (0, 1)

. Subclasses of idempotent copulas with square integrable densities are derived. It is shown that these copulas generate exchangeable Markov chains that behave as independent and identically [...] Read more.

New copula families are constructed based on orthogonality in

L^{2} (0, 1)

. Subclasses of idempotent copulas with square integrable densities are derived. It is shown that these copulas generate exchangeable Markov chains that behave as independent and identically distributed random variables conditionally on the initial variable. We prove that the extracted family of copulas is the only set of symmetric idempotent copulas with square integrable densities. We extend these copula families to asymmetric copulas with square integrable densities having special dependence properties. One of our extensions includes the Farlie–Gumbel–Morgenstern (FGM) copula family. The mixing properties of Markov chains generated by these copulas are established. The Spearman’s correlation coefficient

ρ_{S}

is provided for each of these copula families. Some graphs are also provided to illustrate the properties of the copula densities. Full article

(This article belongs to the Special Issue Advances in Statistical Modeling: Copulas, Large Sample Theory and Applications)

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17 pages, 486 KiB

Open AccessFeature PaperArticle

A Surrogate Piecewise Linear Loss Function for Contextual Stochastic Linear Programs in Transport

by Qi Hong, Mo Jia, Xuecheng Tian, Zhiyuan Liu and Shuaian Wang

Mathematics 2025, 13(12), 2033; https://doi.org/10.3390/math13122033 - 19 Jun 2025

Viewed by 420

Abstract

Accurate decision making under uncertainty for transport problems often requires predicting unknown parameters from contextual information. Traditional two-stage frameworks separate prediction and optimization, which can lead to suboptimal decisions, as minimizing prediction error does not necessarily minimize decision loss. To address this limitation, [...] Read more.

Accurate decision making under uncertainty for transport problems often requires predicting unknown parameters from contextual information. Traditional two-stage frameworks separate prediction and optimization, which can lead to suboptimal decisions, as minimizing prediction error does not necessarily minimize decision loss. To address this limitation, inspired by the smart predict-then-optimize framework, we introduce a novel tunable piecewise linear loss function (PLLF). Rather than directly incorporating decision loss into the learning objective based on specific problem, PLLF serves as a general feedback mechanism that guides the prediction model based on the structure and sensitivity of the downstream optimization task. This design enables the training process to prioritize predictions that are more decision-relevant. We further develop a heuristic parameter search strategy that adapts PLLF using validation data, enhancing its generalizability across different data settings. We test our method with a binary route selection task—the simplest setting to isolate and assess the impact of our modeling approach on decision quality. Experiments across multiple machine learning models demonstrate consistent improvements in decision quality, with neural networks showing the most significant gains—improving decision outcomes in 36 out of 45 cases. These results highlight the potential of our framework to enhance decision-making processes that rely on predictive insights in transportation systems, particularly in routing, scheduling, and resource allocation problems where uncertainty plays a critical role. Overall, our approach offers a practical and scalable solution for integrating prediction and optimization in real-world transport applications. Full article

(This article belongs to the Special Issue Optimization in Sustainable Transport and Logistics)

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25 pages, 3109 KiB

Open AccessArticle

Generalized Modified Unstable Nonlinear Schrödinger’s Equation: Optical Solitons and Modulation Instability

by Jamilu Sabi’u, Ibrahim Sani Ibrahim, Khomsan Neamprem, Surattana Sungnul and Sekson Sirisubtawee

Mathematics 2025, 13(12), 2032; https://doi.org/10.3390/math13122032 - 19 Jun 2025

Viewed by 711

Abstract

This paper proposes the generalized modified unstable nonlinear Schrödinger’s equation with applications in modulated wavetrain instabilities. The extended direct algebra and generalized Ricatti equation methods are applied to find innovative soliton solutions to the equation. The solutions are obtained in the form of [...] Read more.

This paper proposes the generalized modified unstable nonlinear Schrödinger’s equation with applications in modulated wavetrain instabilities. The extended direct algebra and generalized Ricatti equation methods are applied to find innovative soliton solutions to the equation. The solutions are obtained in the form of elliptic, hyperbolic, and trigonometric functions. Moreover, a Galilean transformation is used to convert the problem into a dynamical system. We use the theory of planar dynamical systems to derive the equilibrium points of the dynamical system and analyze the Hamiltonian polynomial. We further investigate the bifurcation phase portrait of the system and study its chaotic behaviors when an external force is applied to the system. Graphical 2D and 3D plots are explored to support our mathematical analysis. A sensitivity analysis confirms that the variation in initial conditions has no substantial effect on the stability of the solutions. Furthermore, we give the modulation instability gain spectrum of the considered model and graphically indicate its dynamics using 2D plots. The reported results demonstrate not only the dynamics of the analyzed equation but are also conceptually relevant in establishing the temporal development of modest disturbances in stable or unstable media. These disturbances will be critical for anticipating, planning treatments, and creating novel mechanisms for modulated wavetrain instabilities. Full article

(This article belongs to the Special Issue Exact Solutions and Numerical Solutions of Differential Equations, 2nd Edition)

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25 pages, 2588 KiB

Open AccessArticle

A Fast and Accurate Numerical Approach for Pricing American-Style Power Options

by Tsvetelin S. Zaevski, Hristo Sariev and Mladen Savov

Mathematics 2025, 13(12), 2031; https://doi.org/10.3390/math13122031 - 19 Jun 2025

Viewed by 877

Abstract

In this paper, we present a fast and accurate numerical approach applied to specific American-style derivatives, namely American power call and put options, whose main feature is that the underlying asset is raised to a power. The study is set in the Black–Scholes [...] Read more.

In this paper, we present a fast and accurate numerical approach applied to specific American-style derivatives, namely American power call and put options, whose main feature is that the underlying asset is raised to a power. The study is set in the Black–Scholes framework, and we consider continuously paying dividends assets and arbitrary positive values for the power. It is important to note that although a log-normal process raised to a power is again log-normal, the resulting change in variables may lead to a negative dividend rate, and this case remains largely understudied in the literature. We derive closed-form formulas for the perpetual options’ optimal boundaries and for the fair prices. For finite maturities, we approximate the optimal boundary using some first-hitting properties of the Brownian motion. As a consequence, we obtain the option price quickly and with relatively high accuracy—the error is at the third decimal position. We further provide a comprehensive analysis of the impact of the parameters on the options’ value, and discuss ordinary European and American capped options. Various numerical examples are provided. Full article

(This article belongs to the Special Issue Stochastic Control and Optimization in Mathematical Finance)

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24 pages, 2038 KiB

Open AccessArticle

Modeling Supply Chain Finance Resilience with a Complex Adaptive SEIJR Framework

by Yimeng Ye, Danqin Huang, Ziyue Li, Shujian Ma and Wanwan Xia

Mathematics 2025, 13(12), 2030; https://doi.org/10.3390/math13122030 - 19 Jun 2025

Viewed by 619

Abstract

This study develops a novel framework for supply chain financial resilience (SCFR) by integrating complex adaptive systems theory with supply chain finance and resilience concepts. To explore how disruption risks propagate through the supply chain, we propose an SEIJR epidemic model that categorizes [...] Read more.

This study develops a novel framework for supply chain financial resilience (SCFR) by integrating complex adaptive systems theory with supply chain finance and resilience concepts. To explore how disruption risks propagate through the supply chain, we propose an SEIJR epidemic model that categorizes node enterprises into five distinct states: susceptible (S), exposed (E), infected (I), quarantined (J), and recovered (R). Transitions between these states are captured using differential equations. Through numerical simulations linking this epidemiological approach to financial resilience metrics, we demonstrate several key findings: first, disruption risks temporarily reduce resilience; second, properly managed risk propagation through timely isolation and effective mitigation can transform disruptions into opportunities for systemic improvement; third, isolation measures need to work alongside recovery mechanisms to significantly improve the overall resilience of supply chain finance. Our results show that optimal isolation strategies enable the system to reach a risk-free equilibrium while simultaneously elevating the supply chain’s long-term financial resilience above initial levels. These findings offer theoretical and practical guidance for dynamic, adaptive risk management strategies in supply chain finance. Empirical validation and other research topics will be explored in subsequent studies. Full article

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

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9 pages, 265 KiB

Open AccessArticle

Sufficient and Necessary Conditions for Generalized Distribution Series on Comprehensive Subclass of Analytic Functions

by Tariq Al-Hawary, Basem Frasin and Ibtisam Aldawish

Mathematics 2025, 13(12), 2029; https://doi.org/10.3390/math13122029 - 19 Jun 2025

Viewed by 415

Abstract

In this paper, we demonstrate a relationship between a generalized distribution series and a comprehensive subclass of analytic functions. The primary aim of this study is to determine a necessary and sufficient condition for the generalized distribution series [...] Read more.

In this paper, we demonstrate a relationship between a generalized distribution series and a comprehensive subclass of analytic functions. The primary aim of this study is to determine a necessary and sufficient condition for the generalized distribution series

E_{ϕ}^{*} (ς, z)

to belong to the inclusive subclass

Π_{η} (Q_{3}, Q_{2}, Q_{1}, Q_{0})

. Necessary and sufficient conditions are also given for the generalized distribution series

E_{ϕ}^{*} (ς, z) ℏ

and the integral operator

J_{ς}^{ϕ} (z)

to be in the inclusive subclass

Π_{η} (Q_{3}, Q_{2}, Q_{1}, 0)

. Further, we provide a number of corollaries, which improve the existing ones that are available in some recent studies. The results presented here not only improve the earlier studies, but also give rise to a number of new results for particular choices of

Q_{3}, Q_{2}, Q_{1}

and

Q_{0}

. Full article

(This article belongs to the Special Issue Current Topics in Geometric Function Theory, 2nd Edition)

26 pages, 1906 KiB

Open AccessArticle

Context-Aware Markov Sensors and Finite Mixture Models for Adaptive Stochastic Dynamics Analysis of Tourist Behavior

by Xiaolong Chen, Hongfeng Zhang, Cora Un In Wong and Zhengchun Song

Mathematics 2025, 13(12), 2028; https://doi.org/10.3390/math13122028 - 19 Jun 2025

Viewed by 368

Abstract

We propose a novel framework for adaptive stochastic dynamics analysis of tourist behavior by integrating context-aware Markov models with finite mixture models (FMMs). Conventional Markov models often fail to capture abrupt changes induced by external shocks, such as event announcements or weather disruptions, [...] Read more.

We propose a novel framework for adaptive stochastic dynamics analysis of tourist behavior by integrating context-aware Markov models with finite mixture models (FMMs). Conventional Markov models often fail to capture abrupt changes induced by external shocks, such as event announcements or weather disruptions, leading to inaccurate predictions. The proposed method addresses this limitation by introducing virtual sensors that dynamically detect contextual anomalies and trigger regime switches in real-time. These sensors process streaming data to identify shocks, which are then used to reweight the probabilities of pre-learned behavioral regimes represented by FMMs. The system employs expectation maximization to train distinct Markov sub-models for each regime, enabling seamless transitions between them when contextual thresholds are exceeded. Furthermore, the framework leverages edge computing and probabilistic programming for efficient, low-latency implementation. The key contribution lies in the explicit modeling of contextual shocks and the dynamic adaptation of stochastic processes, which significantly improves robustness in volatile tourism scenarios. Experimental results demonstrate that the proposed approach outperforms traditional Markov models in accuracy and adaptability, particularly under rapidly changing conditions. Quantitative results show a 13.6% improvement in transition accuracy (0.742 vs. 0.653) compared to conventional context-aware Markov models, with an 89.2% true positive rate in shock detection and a median response latency of 47 min for regime switching. This work advances the state-of-the-art in tourist behavior analysis by providing a scalable, real-time solution for capturing complex, context-dependent dynamics. The integration of virtual sensors and FMMs offers a generalizable paradigm for stochastic modeling in other domains where external shocks play a critical role. Full article

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

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21 pages, 13453 KiB

Open AccessArticle

Buoyant Flow and Thermal Analysis in a Nanofluid-Filled Cylindrical Porous Annulus with a Circular Baffle: A Computational and Machine Learning-Based Approach

by Pushpa Gowda, Sankar Mani, Ahmad Salah and Sebastian A. Altmeyer

Mathematics 2025, 13(12), 2027; https://doi.org/10.3390/math13122027 - 19 Jun 2025

Viewed by 1157

Abstract

Control of buoyancy-assisted convective flow and the associated thermal behavior of nanofluids in finite-sized conduits has become a great challenge for the design of many types of thermal equipment, particularly for heat exchangers. This investigation discusses the numerical simulation of the buoyancy-driven convection [...] Read more.

Control of buoyancy-assisted convective flow and the associated thermal behavior of nanofluids in finite-sized conduits has become a great challenge for the design of many types of thermal equipment, particularly for heat exchangers. This investigation discusses the numerical simulation of the buoyancy-driven convection (BDC) of a nanofluid (NF) in a differently heated cylindrical annular domain with an interior cylinder attached with a thin baffle. The annular region is filled with non-Darcy porous material saturated-nanofluid and both NF and the porous structure are in local thermal equilibrium (LTE). Higher thermal conditions are imposed along the interior cylinder as well as the baffle, while the exterior cylinder is maintained with lower or cold thermal conditions. The Darcy–Brinkman–Forchheimer model, which accounts for inertial, viscous, and non-linear drag forces was adopted to model the momentum equations. An implicit finite difference methodology by considering time-splitting methods for transient equations and relaxation-based techniques is chosen for the steady-state model equations. The impacts of various pertinent parameters, such as the Rayleigh and Darcy numbers, baffle dimensions, like length and position, on flow, thermal distributions, as well as thermal dissipation rates are systematically estimated through accurate numerical predictions. It was found that the baffle dimensions are very crucial parameters to effectively control the flow and associated thermal dissipation rates in the domain. In addition, machine learning techniques were adopted for the chosen analysis and an appropriate model developed to predict the outcome accurately among the different models considered. Full article

(This article belongs to the Special Issue Numerical Simulation and Methods in Computational Fluid Dynamics)

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23 pages, 317 KiB

Open AccessArticle

On the Symbols of Strictly m-Null Elementary Operators

by Isabel Marrero

Mathematics 2025, 13(12), 2026; https://doi.org/10.3390/math13122026 - 19 Jun 2025

Cited by 1 | Viewed by 617

Abstract

This paper extends the previous work by the author on m-null pairs of operators in Hilbert space. If an elementary operator L has elementary symbols A and B that are p-null and q-null, respectively, then L is [...] Read more.

This paper extends the previous work by the author on m-null pairs of operators in Hilbert space. If an elementary operator L has elementary symbols A and B that are p-null and q-null, respectively, then L is

(p + q - 1)

-null. Here, we prove the converse under strictness conditions, modulo some nonzero multiplicative constant—if L is strictly

(p + q - 1)

-null, then a scalar

λ \neq 0

exists such that

λ A

is strictly p-null and

λ^{- 1} B

is strictly q-null. Our constructive argument relies essentially on algebraic and combinatorial methods. Thus, the result obtained by Gu on m-isometries is recovered without resorting to spectral analysis. For several operator classes that generalize m-isometries and are subsumed by m-null operators, the result is new. Full article

(This article belongs to the Section C: Mathematical Analysis)

23 pages, 1438 KiB

Open AccessArticle

Research on Collaborative Governance Mechanism of Air Pollutant Emissions in Ports: A Tripartite Evolutionary Game Analysis with Evidence from Ningbo-Zhoushan Port

by Kebiao Yuan, Lina Ma and Renxiang Wang

Mathematics 2025, 13(12), 2025; https://doi.org/10.3390/math13122025 - 19 Jun 2025

Viewed by 768

Abstract

Under the “Dual Carbon” strategy, collaborative governance of port atmospheric pollutants and carbon emissions is critical for low-carbon transformation. Focusing on Ningbo-Zhoushan Port (48% regional ship emissions), this study examines government, port enterprises, and public interactions. A tripartite evolutionary game model with numerical [...] Read more.

Under the “Dual Carbon” strategy, collaborative governance of port atmospheric pollutants and carbon emissions is critical for low-carbon transformation. Focusing on Ningbo-Zhoushan Port (48% regional ship emissions), this study examines government, port enterprises, and public interactions. A tripartite evolutionary game model with numerical simulation reveals dynamic patterns and key factors. The results show the following: (1) A substitution effect exists between government incentive costs and penalty intensity—increased environmental governance budgets reduce the probability of government incentives, whereas higher public reporting rewards accelerate corporate emission reduction convergence. (2) Public supervision exhibits cyclical fluctuations due to conflicts between individual rationality and collective interests, with excessive reporting rewards potentially triggering free-rider behavior. (3) The system exhibits two stable equilibria: a low-efficiency equilibrium (0,0,0) and a high-efficiency equilibrium (1,1,1). The latter requires policy cost compensation, corporate emission reduction gains exceeding investments, and a supervision benefit–cost ratio greater than 1. Accordingly, the study proposes a three-dimensional “Incentive–Constraint–Collaboration” governance strategy, recommending floating penalty mechanisms, green financial instrument innovation, and community supervision network optimization to balance environmental benefits with fiscal sustainability. This research provides a dynamic decision-making framework for multi-agent collaborative emission reduction in ports, offering both methodological innovation and practical guidance value. Full article

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18 pages, 2831 KiB

Open AccessArticle

Self-Supervised Feature Disentanglement for Deepfake Detection

by Bo Yan, Pan Liu, Yumin Yang and Yanming Guo

Mathematics 2025, 13(12), 2024; https://doi.org/10.3390/math13122024 - 19 Jun 2025

Viewed by 1000

Abstract

Existing deepfake detection methods heavily rely on specific training data distributions and struggle to generalize to unknown forgery techniques. To address the challenge, this paper focuses on two critical research gaps: (1) the lack of systematic mining of standard features across multiple forgery [...] Read more.

Existing deepfake detection methods heavily rely on specific training data distributions and struggle to generalize to unknown forgery techniques. To address the challenge, this paper focuses on two critical research gaps: (1) the lack of systematic mining of standard features across multiple forgery methods; (2) the unresolved distribution shift problem in the strong supervised learning paradigm. To tackle these issues, we propose a self-supervised learning framework based on feature disentanglement, which enhances the generalization ability of detection models by uncovering the intrinsic features of forged content. The core method comprises three key components: self-supervised sample construction and training samples for feature disentanglement, which are generated via an image self-mixing mechanism; feature disentanglement network, where the input image is decomposed into two parts—content features irrelevant to forgery and discriminative forgery-related features; and conditional decoder verification, where both types of features are used to reconstruct the image, with forgery-related features serving as conditional vectors to guide the reconstruction process. Orthogonal constraints on features are enforced to mitigate the overfitting problem in traditional methods. Experimental results demonstrate that, compared with state-of-the-art methods, the proposed framework exhibits superior generalization performance in cross-unknown forgery technique detection tasks, effectively breaking through the dependency bottleneck of traditional supervised learning on training data distributions. This study provides a universal solution for deepfake detection that does not rely on specific forgery techniques. The model’s robustness in real-world complex scenarios is significantly improved by mining the common essence of forgery features. Full article

(This article belongs to the Special Issue New Insights in Machine Learning (ML) and Deep Neural Networks)

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19 pages, 2419 KiB

Open AccessArticle

Combining Lexicon Definitions and the Retrieval-Augmented Generation of a Large Language Model for the Automatic Annotation of Ancient Chinese Poetry

by Jiabin Li, Tingxin Wei, Weiguang Qu, Bin Li, Minxuan Feng and Dongbo Wang

Mathematics 2025, 13(12), 2023; https://doi.org/10.3390/math13122023 - 19 Jun 2025

Viewed by 711

Abstract

Existing approaches to the automatic annotation of classical Chinese poetry often fail to generate precise source citations and depend heavily on manual segmentation, limiting their scalability and accuracy. To address these shortcomings, we propose a novel paradigm that integrates dictionary retrieval with retrieval-augmented [...] Read more.

Existing approaches to the automatic annotation of classical Chinese poetry often fail to generate precise source citations and depend heavily on manual segmentation, limiting their scalability and accuracy. To address these shortcomings, we propose a novel paradigm that integrates dictionary retrieval with retrieval-augmented large language model enhancements for automatic poetic annotation. Our method leverages the contextual understanding capabilities of large models to dynamically select appropriate lexical senses and employs an automated segmentation technique to minimize reliance on manual splitting. For poetic segments absent from standard dictionaries, the system retrieves pertinent information from a domain-specific knowledge base and generates definitions grounded in this auxiliary data, thereby substantially improving both annotation accuracy and coverage. The experimental results demonstrate that our approach outperforms general-purpose large language models and pre-trained classical Chinese language models on automatic annotation tasks; notably, it achieves a micro-averaged accuracy of 94.33% on key semantic segments. By delivering more precise and comprehensive annotations, this framework advances the computational analysis of classical Chinese poetry and offers significant potential for intelligent teaching applications and digital humanities research. Full article

(This article belongs to the Special Issue Neuro Cognitive and Knowledge Driven Natural Language Processing (NLP) in the Large Language Model (LLM) Era)

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26 pages, 1398 KiB

Open AccessArticle

Improving the Reliability of Current Collectors in Electric Vehicles

by Boris V. Malozyomov, Nikita V. Martyushev, Anton Y. Demin, Alexander V. Pogrebnoy, Egor A. Efremenkov, Denis V. Valuev and Aleksandr E. Boltrushevich

Mathematics 2025, 13(12), 2022; https://doi.org/10.3390/math13122022 - 19 Jun 2025

Cited by 1 | Viewed by 647

Abstract

This article presents a mathematically grounded approach to increasing the operational reliability of current collectors in electric transport systems by ensuring a constant contact force between the collector shoe and the power rail. The core objective is achieved through the development and analysis [...] Read more.

This article presents a mathematically grounded approach to increasing the operational reliability of current collectors in electric transport systems by ensuring a constant contact force between the collector shoe and the power rail. The core objective is achieved through the development and analysis of a mechanical system incorporating spring and cam elements, which is specifically designed to provide a nearly invariant contact pressure under varying operating conditions. A set of equilibrium equations was derived to determine the stiffness ratios of the springs and the geometric conditions under which the contact force remains constant despite wear or displacement. Additionally, the paper introduces a method for synthesizing the cam profile that compensates for nonlinear spring deformation, ensuring force constancy over a wide range of movement. The analytical results were validated through parametric simulations, which assessed the influence of wear depth, rail inclination, and external vibrations on the system’s force output. These simulations, executed within a numerical framework using scientific computing tools, demonstrated that the deviation of the contact force does not exceed a few percent under typical disturbances. Experimental verification further confirmed the theoretical predictions. The study exemplifies the effective use of mathematical modeling, nonlinear mechanics, and numerical methods in the design of energy transmission components for transport applications, contributing to the development of robust and maintainable systems. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 3rd Edition)

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21 pages, 4596 KiB

Open AccessArticle

Size–Frequency Distribution Characteristic of Fatalities Due to Workplace Accidents and Industry Dependency

by Fang Zhou, Xiling Liu and Fuxiang Wang

Mathematics 2025, 13(12), 2021; https://doi.org/10.3390/math13122021 - 19 Jun 2025

Viewed by 762

Abstract

The exploration of the statistical characteristics and distribution patterns of workplace accidents can help to reveal the intrinsic features and general laws of safety issues, which is essential for forecasting and decision making in safe production. Here, we conduct the detailed analysis of [...] Read more.

The exploration of the statistical characteristics and distribution patterns of workplace accidents can help to reveal the intrinsic features and general laws of safety issues, which is essential for forecasting and decision making in safe production. Here, we conduct the detailed analysis of the distribution characteristics between the fatality number and the frequency of workplace accidents based on the in-depth data mining of various industries. The results show that the distribution between the fatality number and the frequency of workplace accidents follows a power-law distribution. Moreover, the exponents of such power-law distributions in different industries exhibit significant industry dependence, with the characteristic values of the power-law exponents in the coal mining industry, the hazardous chemicals industry, the transportation industry, and the construction industry being 1.55, 2.16, 2.15, and 2.92, respectively. Meanwhile, the temporal variation in the power-law distribution exponent in each industry can be used for the short-term prediction and evaluation of safe production, which will inform the decision making of the safety management department. Last, but not the least, the results of this study provide the theoretical basis for Heinrich’s Law and confirm that a substantial reduction in the number of small-scale accidents can effectively help control the frequency of large-scale fatal accidents. Full article

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15 pages, 2113 KiB

Open AccessArticle

Enhanced Ratio-Type Estimators in Adaptive Cluster Sampling Using Jackknife Method

by Supawadee Wichitchan, Athipakon Nathomthong, Pannarat Guayjarernpanishk and Nipaporn Chutiman

Mathematics 2025, 13(12), 2020; https://doi.org/10.3390/math13122020 - 18 Jun 2025

Viewed by 313

Abstract

Adaptive cluster sampling is a methodology designed for data collection in contexts where the population is rare and spatially clustered. This approach has been effectively applied in various disciplines, including epidemiology and resource management. The present study introduces novel estimators that incorporate auxiliary [...] Read more.

Adaptive cluster sampling is a methodology designed for data collection in contexts where the population is rare and spatially clustered. This approach has been effectively applied in various disciplines, including epidemiology and resource management. The present study introduces novel estimators that incorporate auxiliary variable information to improve estimation efficiency. These estimators were developed using the jackknife resampling technique to improve the performance of ratio-type estimators. Theoretical properties, including bias and mean square error (MSE), were derived, and a simulation study was conducted to validate the theoretical findings. The results demonstrated that the proposed estimators consistently outperformed conventional estimators that do not utilize auxiliary variables across all network sample sizes. Furthermore, in several scenarios, the proposed estimators also exhibited superior efficiency to existing ratio estimators that do incorporate auxiliary information. Full article

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

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18 pages, 974 KiB

Open AccessArticle

Authenticated Multi-Party Quantum Private Set Intersection with Single Particles

by Gong-De Guo, Li-Qin Zheng, Kai Yu and Song Lin

Mathematics 2025, 13(12), 2019; https://doi.org/10.3390/math13122019 - 18 Jun 2025

Viewed by 211

Abstract

As an important branch of secure multi-party computation, privacy set intersection enables multiple parties to input their private sets and jointly compute the intersection of these sets without revealing any information other than the intersection itself. With the increasing demand for privacy protection [...] Read more.

As an important branch of secure multi-party computation, privacy set intersection enables multiple parties to input their private sets and jointly compute the intersection of these sets without revealing any information other than the intersection itself. With the increasing demand for privacy protection of user data, privacy set intersection has been widely used in privacy computing and other fields. In this paper, we utilize the properties of mutually unbiased bases to propose a multi-party quantum private set intersection protocol that incorporates identity authentication mechanisms. A semi-honest third party (TP) is introduced to facilitate the secure execution of this task among the multiple participating parties. The TP establishes a shared master key with each party, which serves as the basis for authenticating the identity of each participant throughout the protocol. Single-particle quantum states, prepared by the TP, act as the information carriers and are sequentially transmitted among the participating parties. Each party performs a local unitary operation on the circulating particle, thereby encoding their private data within the quantum state. At the end of the protocol, the TP announces his measurement result, by which all participants can concurrently ascertain the intersection of their private data sets. Notably, the proposed protocol eliminates the need for long-term storage of single-particle quantum states, thereby rendering it feasible with existing quantum technological capabilities. Furthermore, a comprehensive security analysis demonstrates that the protocol effectively resists some common external and internal attacks, thereby ensuring its theoretical security. Full article

(This article belongs to the Special Issue Quantum Cryptography and Applications)

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20 pages, 625 KiB

Open AccessArticle

Adaptive Fixed-Time NN-Based Tracking Control for a Type of Stochastic Nonlinear Systems Subject to Input Saturation

by Daohong Zhu, Zhenzhen Long and Liandi Fang

Mathematics 2025, 13(12), 2018; https://doi.org/10.3390/math13122018 - 18 Jun 2025

Viewed by 186

Abstract

This paper considers the adaptive fixed-time tracking control problem for stochastic systems subject to input saturation. Firstly, a smooth function approximation method is utilized to eliminate the effect of input saturation. Then, by combining the neural networks (NNs) approximation method with the backstepping-like [...] Read more.

This paper considers the adaptive fixed-time tracking control problem for stochastic systems subject to input saturation. Firstly, a smooth function approximation method is utilized to eliminate the effect of input saturation. Then, by combining the neural networks (NNs) approximation method with the backstepping-like technique, an adaptive fixed-time tracking control scheme is explicitly developed. The proposed scheme can ensure that the state variables are bounded in probability and the tracking error converges to a small region of the equilibrium point in a fixed time. Eventually, two numerical examples are given to indicate the performance and effectiveness of the presented strategy. Full article

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23 pages, 1053 KiB

Open AccessArticle

Inverse Gravimetric Problem Solving via Prolate Ellipsoidal Parameterization and Particle Swarm Optimization

by Ruben Escudero González, Zulima Fernández Muñiz, Antonio Bernardo Sánchez and Juan Luis Fernández Martínez

Mathematics 2025, 13(12), 2017; https://doi.org/10.3390/math13122017 - 18 Jun 2025

Viewed by 230

Abstract

We present a method for 3D gravity inversion using ellipsoidal parametrization and Particle Swarm Optimization (PSO), aimed at estimating the geometry, density contrast, and orientation of subsurface bodies from gravity anomaly data. The subsurface is modeled as a set of prolate ellipsoids whose [...] Read more.

We present a method for 3D gravity inversion using ellipsoidal parametrization and Particle Swarm Optimization (PSO), aimed at estimating the geometry, density contrast, and orientation of subsurface bodies from gravity anomaly data. The subsurface is modeled as a set of prolate ellipsoids whose parameters are optimized to minimize the misfit between observed and predicted anomalies. This approach enables efficient forward modeling with closed-form solutions and allows the incorporation of geometric and physical constraints. The algorithm is first validated on synthetic models with Gaussian noise, successfully recovering complex multi-body configurations with acceptable uncertainty. A statistical analysis based on multiple PSO runs provides interquartile ranges (IQRs) to quantify inversion stability. The method is then applied to a real microgravity dataset from the Nirano Salse mud volcanoes (northern Italy) using a field acquisition strategy previously described in the literature. Unlike earlier studies based on commercial software, our inversion uses the ellipsoidal–PSO framework. The best-fitting model includes four ellipsoids (two low- and two high-density), reproducing the main features of the observed Bouguer anomaly with a prediction error of 20–25%. The inferred geometry suggests that fluid migration is controlled by fault-related damage zones rather than shallow reservoirs. This method is robust, interpretable, and applicable to both synthetic and real cases, with potential uses in geotechnical, volcanic, and hydrogeological studies. Full article

(This article belongs to the Special Issue Inverse Problems in Science and Engineering)

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8 pages, 216 KiB

Open AccessFeature PaperArticle

Investigating Monogenity in a Family of Cyclic Sextic Fields

by István Gaál

Mathematics 2025, 13(12), 2016; https://doi.org/10.3390/math13122016 - 18 Jun 2025

Viewed by 146

Abstract

Jones characterized, among others, monogenity of a family of cyclic sextic polynomials. Our purpose is to study monogenity of the family of corresponding sextic number fields. We show that several of these number fields are monogenic, despite the defining polynomial of their generating [...] Read more.

Jones characterized, among others, monogenity of a family of cyclic sextic polynomials. Our purpose is to study monogenity of the family of corresponding sextic number fields. We show that several of these number fields are monogenic, despite the defining polynomial of their generating element being non-monogenic. In the monogenic fields, there are several inequivalent generators of power integral bases. Our calculation also provides the first non-trivial application of the method described earlier to study monogenity in totally real extensions of imaginary quadratic fields, emphasizing the efficiency of that algorithm. Full article

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

25 pages, 4467 KiB

Open AccessFeature PaperArticle

Asymptotic Stability of a Rumor Spreading Model with Three Time Delays and Two Saturation Functions

by Teng Sheng, Chunlong Fu, Xiaofan Yang, Yang Qin and Luxing Yang

Mathematics 2025, 13(12), 2015; https://doi.org/10.3390/math13122015 - 18 Jun 2025

Viewed by 251

Abstract

Time delays and saturation effects are critical elements describing complex rumor spreading behaviors. In this article, a rumor spreading model with three time delays and two saturation functions is proposed. The basic properties of the model are reported. The structure of the rumor-endemic [...] Read more.

Time delays and saturation effects are critical elements describing complex rumor spreading behaviors. In this article, a rumor spreading model with three time delays and two saturation functions is proposed. The basic properties of the model are reported. The structure of the rumor-endemic equilibria is deduced. A criterion for the global asymptotic stability of the rumor-free equilibrium is derived. In the presence of very small delays, a criterion for the local asymptotic stability of a rumor-endemic equilibrium is provided. The influence of the delays and the saturation effects on the dynamics of the model is made clear through simulation experiments. In particular, it is found that (a) extended time delays lead to slower change in the number of spreaders or stiflers and (b) lifted saturation coefficients lead to slower change in the number of spreaders or stiflers. This work helps to deepen the understanding of complex rumor spreading phenomenon and develop effective rumor-containing schemes. Full article

(This article belongs to the Special Issue Application of Mathematical Method and Models in Dynamic System, 2nd Edition)

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32 pages, 1553 KiB

Open AccessArticle

A Fuzzy Logic Framework for Text-Based Incident Prioritization: Mathematical Modeling and Case Study Evaluation

by Arturo Peralta, José A. Olivas and Pedro Navarro-Illana

Mathematics 2025, 13(12), 2014; https://doi.org/10.3390/math13122014 - 18 Jun 2025

Viewed by 220

Abstract

Incident prioritization is a critical task in enterprise environments, where textual descriptions of service disruptions often contain vague or ambiguous language. Traditional machine learning models, while effective in rigid classification, struggle to interpret the linguistic uncertainty inherent in natural language reports. This paper [...] Read more.

Incident prioritization is a critical task in enterprise environments, where textual descriptions of service disruptions often contain vague or ambiguous language. Traditional machine learning models, while effective in rigid classification, struggle to interpret the linguistic uncertainty inherent in natural language reports. This paper proposes a fuzzy logic-based framework for incident categorization and prioritization, integrating natural language processing (NLP) with a formal system of fuzzy inference. The framework transforms semantic embeddings from incident reports into fuzzy sets, allowing incident severity and urgency to be represented as degrees of membership in multiple categories. A mathematical model based on Mamdani-type inference and triangular membership functions is developed to capture and process imprecise inputs. The proposed system is evaluated on a real-world dataset comprising 10,000 incident descriptions from a mid-sized technology enterprise. A comparative evaluation is conducted against two baseline models: a fine-tuned BERT classifier and a traditional support vector machine (SVM). Results show that the fuzzy logic approach achieves a 7.4% improvement in F1-score over BERT (92.1% vs. 85.7%) and a 12.5% improvement over SVM (92.1% vs. 79.6%) for medium-severity incidents, where linguistic ambiguity is most prevalent. Qualitative analysis from domain experts confirmed that the fuzzy model provided more interpretable and context-aware classifications, improving operator trust and alignment with human judgment. These findings suggest that fuzzy modeling offers a mathematically sound and operationally effective solution for managing uncertainty in text-based incident management, contributing to the broader understanding of mathematical modeling in enterprise-scale social phenomena. Full article

(This article belongs to the Special Issue Social Phenomena: Mathematical Modeling and Data Analysis)

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24 pages, 349 KiB

Open AccessArticle

Subinjectivity Relative to Cotorsion Pairs

by Yusuf Alagöz, Rafail Alizade, Engin Büyükaşık, Juan Ramón García Rozas and Luis Oyonarte

Mathematics 2025, 13(12), 2013; https://doi.org/10.3390/math13122013 - 18 Jun 2025

Viewed by 174

Abstract

In this paper, we define and study the

X

-subinjectivity domain of a module M where

X = (A, B)

is a complete cotorsion pair, which consists of those modules N such that, for every extension K of N with [...] Read more.

In this paper, we define and study the

X

-subinjectivity domain of a module M where

X = (A, B)

is a complete cotorsion pair, which consists of those modules N such that, for every extension K of N with

K / N

in

A

, any homomorphism

f : N \to M

can be extended to a homomorphism

g : K \to M

. This approach allows us to characterize some classical rings in terms of these domains and generalize some known results. In particular, we classify the rings with

X

-indigent modules—that is, the modules whose

X

-subinjectivity domains are as small as possible—for the cotorsion pair

X = (FC, FI)

, where

FI

is the class of FP-injective modules. Additionally, we determine the rings for which all (simple) right modules are either

X

-indigent or FP-injective. We further investigate

X

-indigent Abelian groups in the category of torsion Abelian groups for the well-known example of the flat cotorsion pair

X = (FL, EC)

, where

FL

is the class of flat modules. Full article

(This article belongs to the Special Issue Algebra, Ring Theory, and Homological Algebra with Analysis and Applications)

24 pages, 3869 KiB

Open AccessArticle

Recursive Bayesian Decoding in State Observation Models: Theory and Application in Quantum-Based Inference

by Branislav Rudić, Markus Pichler-Scheder and Dmitry Efrosinin

Mathematics 2025, 13(12), 2012; https://doi.org/10.3390/math13122012 - 18 Jun 2025

Viewed by 227

Abstract

Accurately estimating a sequence of latent variables in state observation models remains a challenging problem, particularly when maintaining coherence among consecutive estimates. While forward filtering and smoothing methods provide coherent marginal distributions, they often fail to maintain coherence in marginal MAP estimates. Existing [...] Read more.

Accurately estimating a sequence of latent variables in state observation models remains a challenging problem, particularly when maintaining coherence among consecutive estimates. While forward filtering and smoothing methods provide coherent marginal distributions, they often fail to maintain coherence in marginal MAP estimates. Existing methods efficiently handle discrete-state or Gaussian models. However, general models remain challenging. Recently, a recursive Bayesian decoder has been discussed, which effectively infers coherent state estimates in a wide range of models, including Gaussian and Gaussian mixture models. In this work, we analyze the theoretical properties and implications of this method, drawing connections to classical inference frameworks. The versatile applicability of mixture models and the prevailing advantage of the recursive Bayesian decoding method are demonstrated using the double-slit experiment. Rather than inferring the state of a quantum particle itself, we utilize interference patterns from the slit experiments to decode the movement of a non-stationary particle detector. Our findings indicate that, by appropriate modeling and inference, the fundamental uncertainty associated with quantum objects can be leveraged to decrease the induced uncertainty of states associated with classical objects. We thoroughly discuss the interpretability of the simulation results from multiple perspectives. Full article

(This article belongs to the Special Issue Mathematics Methods of Robotics and Intelligent Systems)

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18 pages, 1227 KiB

Open AccessArticle

Approximated Optimal Solution for Economic Manufacturing Quantity Model

by Jinyuan Liu, Pengfei Jiang, Shr-Shiung Hu and Gino K. Yang

Mathematics 2025, 13(12), 2011; https://doi.org/10.3390/math13122011 - 18 Jun 2025

Viewed by 160

Abstract

This study investigates the use of the bisection algorithm in inventory models to obtain an approximated optimal solution for the economic manufacturing quantity (EMQ) problem under imperfect production conditions. The objectives are threefold. First, we utilize refined estimations of exponential functions to provide [...] Read more.

This study investigates the use of the bisection algorithm in inventory models to obtain an approximated optimal solution for the economic manufacturing quantity (EMQ) problem under imperfect production conditions. The objectives are threefold. First, we utilize refined estimations of exponential functions to provide tighter lower and upper bounds for the bisection algorithm. Second, we propose three analytical improvements that simplify the solution process, each supported by rigorous proofs. Third, we incorporate recent results from the literature to further enhance the accuracy of exponential function approximations within the EMQ model. Our improved bounding approach significantly reduces the search interval needed by the bisection method and yields an approximate solution that attains a total cost very close to the true optimum. In a numerical example, the proposed method shrinks the initial search range by over 99% compared to prior methods and achieves a production run length that produces a near-minimal average total cost. These findings demonstrate the effectiveness of the enhanced bounds and provide practical insights for inventory models with imperfect processes. Full article

(This article belongs to the Special Issue Improved Mathematical Methods in Decision Making Models)

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34 pages, 18712 KiB

Open AccessArticle

Statistical Computation of Hjorth Competing Risks Using Binomial Removals in Adaptive Progressive Type II Censoring

by Refah Alotaibi, Mazen Nassar and Ahmed Elshahhat

Mathematics 2025, 13(12), 2010; https://doi.org/10.3390/math13122010 - 18 Jun 2025

Viewed by 215

Abstract

In complex reliability applications, it is common for the failure of an individual or an item to be attributed to multiple causes known as competing risks. This paper explores the estimation of the Hjorth competing risks model based on an adaptive progressive Type [...] Read more.

In complex reliability applications, it is common for the failure of an individual or an item to be attributed to multiple causes known as competing risks. This paper explores the estimation of the Hjorth competing risks model based on an adaptive progressive Type II censoring scheme via a binomial removal mechanism. For parameter and reliability metric estimation, both frequentist and Bayesian methodologies are developed. Maximum likelihood estimates for the Hjorth parameters are computed numerically due to their intricate form, while the binomial removal parameter is derived explicitly. Confidence intervals are constructed using asymptotic approximations. Within the Bayesian paradigm, gamma priors are assigned to the Hjorth parameters and a beta prior for the binomial parameter, facilitating posterior analysis. Markov Chain Monte Carlo techniques yield Bayesian estimates and credible intervals for parameters and reliability measures. The performance of the proposed methods is compared using Monte Carlo simulations. Finally, to illustrate the practical applicability of the proposed methodology, two real-world competing risk data sets are analyzed: one representing the breaking strength of jute fibers and the other representing the failure modes of electrical appliances. Full article

(This article belongs to the Special Issue Statistical Simulation and Computation: 3rd Edition)

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20 pages, 2346 KiB

Open AccessArticle

A Novel Approach to Pine Nut Classification: Combining Near-Infrared Spectroscopy and Image Shape Features with Soft Voting-Based Ensemble Learning

by Yueyun Yu, Xin Huang, Danjv Lv, Benjamin K. Ng and Chan-Tong Lam

Mathematics 2025, 13(12), 2009; https://doi.org/10.3390/math13122009 - 18 Jun 2025

Viewed by 188

Abstract

Pine nuts hold significant economic value due to their rich plant protein and healthy fats, yet precise variety classification has long been hindered by limitations of traditional techniques such as chemical analysis and machine vision. This study proposes a novel near-infrared (NIR) spectral [...] Read more.

Pine nuts hold significant economic value due to their rich plant protein and healthy fats, yet precise variety classification has long been hindered by limitations of traditional techniques such as chemical analysis and machine vision. This study proposes a novel near-infrared (NIR) spectral feature selection algorithm, termed the improved binary equilibrium optimizer with selection probability (IBiEO-SP), which incorporates a dynamic probability adjustment mechanism to achieve efficient feature dimensionality reduction. Experimental validation on a dataset comprising seven pine nut varieties demonstrated that, compared to particle swarm optimization (PSO) and the genetic algorithm (GA), the IBiEO-SP algorithm improved average classification accuracy by 5.7% (p < 0.01, Student’s t-test) under four spectral preprocessing methods (MSC, SNV, SG1, and SG2). Remarkably, only 2–3 features were required to achieve optimal performance (MSC + random forest: 99.05% accuracy, 100% F1/precision; SNV + KNN: 97.14% accuracy, 100% F1/precision). Furthermore, a multimodal data synergy strategy integrating NIR spectroscopy with morphological features was proposed, and a classification model was constructed using a soft voting ensemble. The final classification accuracy reached 99.95%, representing a 2.9% improvement over single-spectral-mode analysis. The results indicate that the IBiEO-SP algorithm effectively balances feature discriminative power and model generalization needs, overcoming the contradiction between high-dimensional data redundancy and low-dimensional information loss. This work provides a high-precision, low-complexity solution for rapid quality detection of pine nuts, with broad implications for agricultural product inspection and food safety. Full article

(This article belongs to the Special Issue Mathematical Modelling in Agriculture)

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Mathematics, Volume 13, Issue 12 (June-2 2025) – 137 articles

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