Mathematics

25 pages, 395 KiB

Open AccessArticle

Random Generalized Additive Logistic Forest: A Novel Ensemble Method for Robust Binary Classification

by Oyebayo Ridwan Olaniran, Ali Rashash R. Alzahrani, Nada MohammedSaeed Alharbi and Asma Ahmad Alzahrani

Mathematics 2025, 13(7), 1214; https://doi.org/10.3390/math13071214 - 7 Apr 2025

Viewed by 200

Abstract

Ensemble methods have proven highly effective in enhancing predictive performance by combining multiple models. We introduce a novel ensemble approach, the Random Generalized Additive Logistic Forest (RGALF), which integrates generalized additive models (GAMs) within a random forest framework to improve binary classification tasks. [...] Read more.

Ensemble methods have proven highly effective in enhancing predictive performance by combining multiple models. We introduce a novel ensemble approach, the Random Generalized Additive Logistic Forest (RGALF), which integrates generalized additive models (GAMs) within a random forest framework to improve binary classification tasks. Unlike traditional random forests, which rely on piecewise constant predictions in terminal nodes, RGALF fits GAM logistic regression (LR) models to the data in each terminal node, enabling it to capture complex nonlinear relationships and interactions among predictors. By aggregating these node-specific GAMs, RGALF addresses multicollinearity, enhances interpretability, and achieves superior bias–variance tradeoffs, particularly in nonlinear settings. Theoretical analysis confirms that RGALF achieves Stone’s optimal rates for additive models (

O (n^{- 2 k / (2 k + d)}

) under appropriate conditions, outperforming the slower convergence of traditional random forests (

O (n^{- 2 / 3})

). Furthermore, empirical results demonstrate RGALF’s effectiveness across both simulated and real-world datasets. In simulations, RGALF demonstrates superior performance over random forests (RFs), reducing variance by up to 69% and bias by 19% in nonlinear settings, with significant MSE improvements (0.032 vs. RF’s 0.054 at

n = 1000

), while achieving optimal convergence rates (

O (n^{- 0.48})

vs. RF’s

O (n^{- 0.29})

). On real-world medical datasets, RGALF attains near-perfect accuracy and AUC: 100% accuracy/AUC for Heart Failure and Hepatitis C (HCV) prediction, 99% accuracy/100% AUC for Pima Diabetes, and 98.8% accuracy/100% AUC for Indian Liver Patient (ILPD), outperforming state-of-the-art methods. Notably, RGALF captures complex biomarker interactions (BMI–insulin in diabetes) missed by traditional models. Full article

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29 pages, 9003 KiB

Open AccessArticle

A Decomposition-Based Stochastic Multilevel Binary Optimization Model for Agricultural Land Allocation Under Uncertainty

by Fan Wang, Youxi Luo, Wenkai Zhang and Yanshu Yu

Mathematics 2025, 13(7), 1213; https://doi.org/10.3390/math13071213 - 7 Apr 2025

Viewed by 182

Abstract

Crop cultivation planning is vital for optimizing agricultural productivity and sustainable land use under farming uncertainties. This study developed a decomposition-based stochastic multilevel binary optimization model for agricultural plot management. Using land and crops as the division standard, the complex problem of agricultural [...] Read more.

Crop cultivation planning is vital for optimizing agricultural productivity and sustainable land use under farming uncertainties. This study developed a decomposition-based stochastic multilevel binary optimization model for agricultural plot management. Using land and crops as the division standard, the complex problem of agricultural land management was broken down into manageable sub-modules, which were efficiently solved using a greedy algorithm. In order to verify the actual effectiveness of the model, this study conducted an empirical analysis based on the production practice scenario in the mountainous areas of North China from 2023 to 2026. The performance of the model was verified through dimensions such as agricultural income accounting, the assessment of planting dispersion, and the optimization of legume crop rotation patterns. The stability of the system was also tested using sensitivity tests for multiple variables. To further evaluate the performance of the model, we compared it with two single-factor benchmark models that only considered uncertainty or only considered the land constraints. The results showed that in the multi-year and multi-income scenarios, our comprehensive model was significantly better than the two benchmark models in terms of optimization performance, which proves the necessity of considering land constraints and uncertainty at the same time. Full article

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24 pages, 24154 KiB

Open AccessArticle

Multistage Threshold Segmentation Method Based on Improved Electric Eel Foraging Optimization

by Yunlong Hu, Liangkuan Zhu and Hongyang Zhao

Mathematics 2025, 13(7), 1212; https://doi.org/10.3390/math13071212 - 7 Apr 2025

Viewed by 151

Abstract

Multi-threshold segmentation of color images is a critical component of modern image processing. However, as the number of thresholds increases, traditional multi-threshold image segmentation methods face challenges such as low accuracy and slow convergence speed. To optimize threshold selection in color image segmentation, [...] Read more.

Multi-threshold segmentation of color images is a critical component of modern image processing. However, as the number of thresholds increases, traditional multi-threshold image segmentation methods face challenges such as low accuracy and slow convergence speed. To optimize threshold selection in color image segmentation, this paper proposes a multi-strategy improved Electric Eel Foraging Optimization (MIEEFO). The proposed algorithm integrates Differential Evolution and Quasi-Opposition-Based Learning strategies into the Electric Eel Foraging Optimization, enhancing its search capability, accelerating convergence, and preventing the population from falling into local optima. To further boost the algorithm’s search performance, a Cauchy mutation strategy is applied to mutate the best individual, improving convergence speed. To evaluate the segmentation performance of the proposed MIEEFO, 15 benchmark functions are used, and comparisons are made with seven other algorithms. Experimental results show that the MIEEFO algorithm outperforms other algorithms in at least 75% of cases and exhibits similar performance in up to 25% of cases. To further explore its application potential, a multi-level Kapur entropy-based MIEEFO threshold segmentation method is proposed and applied to different types of benchmark images and forest fire images. Experimental results indicate that the improved MIEEFO achieves higher segmentation quality and more accurate thresholds, providing a more effective method for color image segmentation. Full article

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28 pages, 1625 KiB

Open AccessFeature PaperArticle

A Two-Level Parallel Incremental Tensor Tucker Decomposition Method with Multi-Mode Growth (TPITTD-MG)

by Yajian Zhou, Zongqian Yue and Zhe Chen

Mathematics 2025, 13(7), 1211; https://doi.org/10.3390/math13071211 - 7 Apr 2025

Viewed by 153

Abstract

With the rapid growth of streaming data, traditional tensor decomposition methods can hardly handle real-time, high-dimensional data of massive amounts in this scenario. In this paper, a two-level parallel incremental tensor Tucker decomposition method with multi-mode growth (TPITTD-MG) is proposed to address the [...] Read more.

With the rapid growth of streaming data, traditional tensor decomposition methods can hardly handle real-time, high-dimensional data of massive amounts in this scenario. In this paper, a two-level parallel incremental tensor Tucker decomposition method with multi-mode growth (TPITTD-MG) is proposed to address the low parallelism issue of the existing Tucker decomposition methods on large-scale, high-dimensional, dynamically growing data. TPITTD-MG involves two mechanisms, i.e., a parallel sub-tensor partitioning mechanism based on the dynamic programming (PSTPA-DP) and a two-level parallel update method for projection matrices and core tensors. The former can count the non-zero elements in a parallel manner and use dynamic programming to partition sub-tensors, which ensures more uniform task allocation. The latter updates the projection matrices or the core tensors by implementing the first level of parallel updates based on the parallel MTTKRP calculation strategy, followed by the second level of parallel updates of different projection matrices or tensors independently based on different classification of sub-tensors. The experimental results show that execution efficiency is improved by nearly 400% and the uniformity of partition results is improved by more than 20% when the data scale reaches an order of magnitude of tens of millions with a parallelism degree of 4, compared with existing algorithms. For third-order tensors, compared with the single-layer update algorithm, execution efficiency is improved by nearly 300%. Full article

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18 pages, 1929 KiB

Open AccessArticle

Low-Carbon Transport for Prefabricated Buildings: Optimizing Capacitated Truck–Trailer Routing Problem with Time Windows

by Jiajie Zhou, Qiang Du, Qian Chen, Zhongnan Ye, Libiao Bai and Yi Li

Mathematics 2025, 13(7), 1210; https://doi.org/10.3390/math13071210 - 7 Apr 2025

Viewed by 239

Abstract

The transportation of prefabricated components is challenged by the particularity of large cargo transport and urban road conditions, restrictions on parking, height, and weight. To address these challenges and to promote low-carbon logistics, this paper investigates the transportation of prefabricated components by leveraging [...] Read more.

The transportation of prefabricated components is challenged by the particularity of large cargo transport and urban road conditions, restrictions on parking, height, and weight. To address these challenges and to promote low-carbon logistics, this paper investigates the transportation of prefabricated components by leveraging separable fleets of trucks and trailers. Focusing on real-world constraints, this paper formulates the capacitated truck and trailer routing problem with time windows (CTTRPTW) incorporating carbon emissions, and designs a dynamic adaptive hybrid algorithm combining simulated annealing with tabu search (DASA-TS) to solve this model. The efficiency and robustness of the methodology are validated through two computational experiments. The results indicate that the DASA-TS consistently demonstrates excellent performance across all evaluations, with significant reductions in both transportation costs and carbon emissions costs for prefabricated components, particularly in large-scale computational instances. This study contributes to promoting the optimization of low-carbon transport for prefabricated components, offering guidance for routing design involving complex and large cargo, and supporting the sustainable development of urban logistics. Full article

(This article belongs to the Special Issue Optimization and Mathematical Modelling in Transport and Logistics Network)

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17 pages, 2216 KiB

Open AccessArticle

An Anomaly Detection Method for Multivariate Time Series Data Based on Variational Autoencoders and Association Discrepancy

by Haodong Wang and Huaxiong Zhang

Mathematics 2025, 13(7), 1209; https://doi.org/10.3390/math13071209 - 7 Apr 2025

Viewed by 351

Abstract

Driven by rapid advancements in big data and Internet of Things (IoT) technologies, time series data are now extensively utilized across diverse industrial sectors. The precise identification of anomalies in time series data—especially within intricate and ever-changing environments—has emerged as a key focus [...] Read more.

Driven by rapid advancements in big data and Internet of Things (IoT) technologies, time series data are now extensively utilized across diverse industrial sectors. The precise identification of anomalies in time series data—especially within intricate and ever-changing environments—has emerged as a key focus in contemporary research. This paper proposes a multivariate anomaly detection framework that synergistically combines variational autoencoders with association discrepancy analysis. By incorporating prior knowledge of associations and sequence association mechanisms, the model can capture long-term dependencies in time series and effectively model the association discrepancy between different time points. Through reconstructing time series data, the model enhances the distinction between normal and anomalous points, learning the association discrepancy during reconstruction to strengthen its ability to identify anomalies. By combining reconstruction errors and association discrepancy, the model achieves more accurate anomaly detection. Extensive experimental validation demonstrates that the proposed methodological framework achieves statistically significant improvements over existing benchmarks, attaining superior F1 scores across diverse public datasets. Notably, it exhibits enhanced capability in modeling temporal dependencies and identifying nuanced anomaly patterns. This work establishes a novel paradigm for time series anomaly detection with profound theoretical implications and practical implementations. Full article

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13 pages, 2207 KiB

Open AccessArticle

Irreversibility Analysis of Hydromagnetic Casson Fluid Flow Through an Inclined Channel with Isothermal Boundary Conditions

by Bernard Ejugu Njor, Ramoshweu Solomon Lebelo and Samuel Olumide Adesanya

Mathematics 2025, 13(7), 1208; https://doi.org/10.3390/math13071208 - 7 Apr 2025

Viewed by 199

Abstract

Fluid flow along an inclined channel phenomenon is crucial in several geophysical, environmental, engineering, biological, and industrial processes, and in aerodynamics and hemodynamics. This present study examines the effect of a constant magnetic field on the entropy production rate in a steady flow [...] Read more.

Fluid flow along an inclined channel phenomenon is crucial in several geophysical, environmental, engineering, biological, and industrial processes, and in aerodynamics and hemodynamics. This present study examines the effect of a constant magnetic field on the entropy production rate in a steady flow of Casson fluid along an inclined heated channel. The governing equations for the flow of velocity, temperature, and entropy generation are formulated based on the Casson constitutive relations and thermodynamics’ first and second laws. The exact solutions are constructed for the dimensionless equations and validated with previous results in the literature. The effects of various fluid parameters on the flow, heat transfer, and entropy production rate are conducted and reported graphically with adequate discussion. The impact of the Hartmann number parameter reveals a decrease in both flow velocity and entropy generation rate, meanwhile it also enhances the fluid temperature distribution across the inclined channel. An opposite trend is, however, observed with the Casson fluid parameter. Full article

(This article belongs to the Special Issue Advanced Computational Methods for Fluid Dynamics and Applications)

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3 pages, 151 KiB

Open AccessEditorial

Preface to the Special Issue on “Recent Advances in Business and Industry: Mathematical Analysis, Sustainability Assessment Instruments and Methods”

by Cristina Raluca Gh. Popescu

Mathematics 2025, 13(7), 1207; https://doi.org/10.3390/math13071207 - 7 Apr 2025

Viewed by 151

Abstract

Recently, it has become pivotal to include mathematics in all domains and crucial to offer a better and more in-depth understanding of mathematics in the forms in which it has been associated with all fields [...] Full article

(This article belongs to the Special Issue Recent Advances in Business and Industry: Mathematical Analysis, Sustainability Assessment Instruments and Methods)

1 pages, 124 KiB

Open AccessCorrection

Correction: Alanazi et al. An Improved Fick’s Law Algorithm Based on Dynamic Lens-Imaging Learning Strategy for Planning a Hybrid Wind/Battery Energy System in Distribution Network. Mathematics 2023, 11, 1270

by Mohana Alanazi, Abdulaziz Alanazi, Ahmad Almadhor and Hafiz Tayyab Rauf

Mathematics 2025, 13(7), 1206; https://doi.org/10.3390/math13071206 - 7 Apr 2025

Viewed by 100

Abstract

In the published publication [...] Full article

32 pages, 407 KiB

Open AccessArticle

On the Essential Decreasing of the Summation Order in the Abel-Lidskii Sense

by Maksim V. Kukushkin

Mathematics 2025, 13(7), 1205; https://doi.org/10.3390/math13071205 - 7 Apr 2025

Viewed by 216

Abstract

In this paper, we consider a problem of decreasing the summation order in the Abel-Lidskii sense. The problem has a significant prehistory since 1962 created by such mathematicians as Lidskii V.B., Katsnelson V.E., Matsaev V.I., Agranovich M.S. As a main result, we will [...] Read more.

In this paper, we consider a problem of decreasing the summation order in the Abel-Lidskii sense. The problem has a significant prehistory since 1962 created by such mathematicians as Lidskii V.B., Katsnelson V.E., Matsaev V.I., Agranovich M.S. As a main result, we will show that the summation order can be decreased from the values more than a convergence exponent, in accordance with the Lidskii V.B. results, to an arbitrary small positive number. Additionally, we construct a qualitative theory of summation in the Abel-Lidkii sense and produce a number of fundamental propositions that may represent the interest themselves. Full article

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

1 pages, 122 KiB

Open AccessCorrection

Correction: Aziz et al. Geo-Spatial Mapping of Hate Speech Prediction in Roman Urdu. Mathematics 2023, 11, 969

by Samia Aziz, Muhammad Shahzad Sarfraz, Muhammad Usman, Muhammad Umar Aftab and Hafiz Tayyab Rauf

Mathematics 2025, 13(7), 1204; https://doi.org/10.3390/math13071204 - 7 Apr 2025

Viewed by 105

Abstract

In the published publication [...] Full article

18 pages, 1110 KiB

Open AccessArticle

Differential Quadrature Method for Bending Analysis of Asymmetric Circular Organic Solar Cells Resting on Kerr Foundation in Hygrothermal Environment

by Mohammad A. Abazid, Muneer Alali and Mohammed Sobhy

Mathematics 2025, 13(7), 1203; https://doi.org/10.3390/math13071203 - 6 Apr 2025

Viewed by 202

Abstract

This article presents the first theoretical analysis of the bending behavior of circular organic solar cells (COSCs). The solar cell under investigation is built on a flexible Kerr foundation and has five layers of Al, P3HT:PCBM, PEDOT:PSS, ITO, and Glass. The cell is [...] Read more.

This article presents the first theoretical analysis of the bending behavior of circular organic solar cells (COSCs). The solar cell under investigation is built on a flexible Kerr foundation and has five layers of Al, P3HT:PCBM, PEDOT:PSS, ITO, and Glass. The cell is exposed to hygrothermal conditions. The related Kerr foundation lessens displacements and supports the cell. The principle of virtual work is used to generate the basic partial differential equations, which are then solved using the differential quadrature method (DQM). The results of the present theory are validated by comparing them with published ones. The effects of the temperature, humidity, elastic foundation factors, and geometric configuration characteristics on the deflection and stresses of the COSC are examined. Full article

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51 pages, 2432 KiB

Open AccessArticle

A Hubness Information-Based k-Nearest Neighbor Approach for Multi-Label Learning

by Zeyu Teng, Shanshan Tang, Min Huang and Xingwei Wang

Mathematics 2025, 13(7), 1202; https://doi.org/10.3390/math13071202 - 5 Apr 2025

Viewed by 175

Abstract

Multi-label classification (MLC) plays a crucial role in various real-world scenarios. Prediction with nearest neighbors has achieved competitive performance in MLC. Hubness, a phenomenon in which a few points appear in the k-nearest neighbor (kNN) lists of many points in high-dimensional spaces, may [...] Read more.

Multi-label classification (MLC) plays a crucial role in various real-world scenarios. Prediction with nearest neighbors has achieved competitive performance in MLC. Hubness, a phenomenon in which a few points appear in the k-nearest neighbor (kNN) lists of many points in high-dimensional spaces, may significantly impact machine learning applications and has recently attracted extensive attention. However, it has not been adequately addressed in developing MLC algorithms. To address this issue, we propose a hubness-aware kNN-based MLC algorithm in this paper, named multi-label hubness information-based k-nearest neighbor (MLHiKNN). Specifically, we introduce a fuzzy measure of label relevance and employ a weighted kNN scheme. The hubness information is used to compute each training example’s membership in relevance and irrelevance to each label and calculate weights for the nearest neighbors of a query point. Then, MLHiKNN exploits high-order label correlations by training a logistic regression model for each label using the kNN voting results with respect to all possible labels. Experimental results on 28 benchmark datasets demonstrate that MLHiKNN is competitive among the compared methods, including nine well-established MLC algorithms and three commonly used hubness reduction techniques, in dealing with MLC problems. Full article

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20 pages, 618 KiB

Open AccessArticle

Feedforward Factorial Hidden Markov Model

by Zhongxing Peng, Wei Huang and Yinghui Zhu

Mathematics 2025, 13(7), 1201; https://doi.org/10.3390/math13071201 - 5 Apr 2025

Viewed by 120

Abstract

This paper introduces a novel kind of factorial hidden Markov model (FHMM), specifically the feedforward FHMM (FFHMM). In contrast to traditional FHMMs, the FFHMM is capable of directly utilizing supplementary information from observations through predefined states, which are derived using an automatic feature [...] Read more.

This paper introduces a novel kind of factorial hidden Markov model (FHMM), specifically the feedforward FHMM (FFHMM). In contrast to traditional FHMMs, the FFHMM is capable of directly utilizing supplementary information from observations through predefined states, which are derived using an automatic feature filter (AFF). We investigate two variations of FFHMM models that integrate predefined states with the FHMM: the direct FFHMM and the embedded FFHMM. In the direct FFHMM, alterations to one sub-hidden Markov model (HMM) do not affect the others, enabling individual improvements in HMM estimation. On the other hand, the sub-HMM chains within the embedded FFHMM are interconnected, suggesting that adjustments to one HMM chain may enhance the estimations of other HMM chains. Consequently, we propose two algorithms for these FFHMM models to estimate their respective hidden states. Ultimately, experiments conducted on two real-world datasets validate the efficacy of the proposed models and algorithms. Full article

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8 pages, 239 KiB

Open AccessArticle

Geometric Properties of a General Kohn–Nirenberg Domain in ℂⁿ

by Kejia Hu, Hongyi Li, Di Zhao, Yuan Jiang and Baozhu Li

Mathematics 2025, 13(7), 1200; https://doi.org/10.3390/math13071200 - 5 Apr 2025

Viewed by 158

Abstract

The Kohn–Nirenberg domains are unbounded domains in

C^{n}

. In this article, we modify the Kohn–Nirenberg domain

Ω_{K, L} = \{(z_{1}, \dots, z_{n}) \in C^{n} : R e z_{n} + g ∣ z_{n} ∣^{2} + \sum_{j = 1}^{n - 1} (∣ z_{j} ∣^{p} + K_{j} ∣ z_{j} ∣^{p - q} R e z_{j}^{q} + L_{j} ∣ z_{j} ∣^{p - 2 q} I m z_{j}^{2 q}) < 0}

and discuss the existence of supporting surface and peak functions at the origin. Full article

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

27 pages, 331 KiB

Open AccessArticle

Some Bounds for the Generalized Spherical Numerical Radius of Operator Pairs with Applications

by Najla Altwaijry, Silvestru Sever Dragomir, Kais Feki and Shigeru Furuichi

Mathematics 2025, 13(7), 1199; https://doi.org/10.3390/math13071199 - 5 Apr 2025

Viewed by 139

Abstract

This paper investigates a generalization of the spherical numerical radius for a pair

(B, C)

of bounded linear operators on a complex Hilbert space H. The generalized spherical numerical radius is defined as [...] Read more.

This paper investigates a generalization of the spherical numerical radius for a pair

(B, C)

of bounded linear operators on a complex Hilbert space H. The generalized spherical numerical radius is defined as

w_{p} (B, C) : = \sup_{x \in H, ∥ x ∥ = 1} {({| ⟨ B x, x ⟩ |}^{p} + {| ⟨ C x, x ⟩ |}^{p})}^{\frac{1}{p}}

,

p \geq 1

. We derive lower bounds for

w_{p}^{2} (B, C)

involving combinations of B and C, where

p > 1

. Additionally, we establish upper bounds in terms of operator norms. Applications include the cases where

(B, C) = (A, A^{*})

, with

A^{*}

denoting the adjoint of a bounded linear operator A, and

(B, C) = (R (A), I (A))

, representing the real and imaginary parts of A, respectively. We also explore applications to the so-called Davis–Wielandt p-radius for

p \geq 1

, which serves as a natural generalization of the classical Davis–Wielandt radius for Hilbert-space operators. Full article

(This article belongs to the Special Issue Current Topics in Optimization, Inequalities and Convex Function Theory)

31 pages, 10965 KiB

Open AccessArticle

Joint Event Density and Curvature Within Spatio-Temporal Neighborhoods-Based Event Camera Noise Reduction and Pose Estimation Method for Underground Coal Mine

by Wenjuan Yang, Jie Jiang, Xuhui Zhang, Yang Ji, Le Zhu, Yanbin Xie and Zhiteng Ren

Mathematics 2025, 13(7), 1198; https://doi.org/10.3390/math13071198 - 5 Apr 2025

Viewed by 203

Abstract

Aiming at the problems of poor image quality of traditional cameras and serious noise interference of event cameras under complex lighting conditions in coal mines, an event denoising algorithm fusing spatio-temporal information and a method of denoising event target pose estimation is proposed. [...] Read more.

Aiming at the problems of poor image quality of traditional cameras and serious noise interference of event cameras under complex lighting conditions in coal mines, an event denoising algorithm fusing spatio-temporal information and a method of denoising event target pose estimation is proposed. The denoising algorithm constructs a spherical spatio-temporal neighborhood to enhance the spatio-temporal denseness and continuity of valid events, and combines event density and curvature to achieve event stream denoising. The attitude estimation framework adopts the noise reduction event and global optimal perspective-n-line (OPNL) methods to obtain the initial target attitude, and then establishes the event line correlation model through the robust estimation, and achieves the attitude tracking by minimizing the event line distance. The experimental results show that compared with the existing methods, the noise reduction algorithm proposed in this paper has a noise reduction rate of more than 99.26% on purely noisy data, and the event structure ratio (ESR) is improved by 47% and 5% on DVSNoise20 dataset and coal mine data, respectively. The maximum absolute trajectory error of the localization method is 2.365 cm, and the mean square error is reduced by 2.263% compared with the unfiltered event localization method. Full article

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11 pages, 7861 KiB

Open AccessArticle

Chattering-Free PID-Nested Nonsingular Terminal Sliding Mode Controller Design for Electrical Servo Drives

by Nguyen Minh Trieu, Nguyen Tan No, Truong Nguyen Vu and Nguyen Truong Thinh

Mathematics 2025, 13(7), 1197; https://doi.org/10.3390/math13071197 - 5 Apr 2025

Viewed by 207

Abstract

In this study, a PID-nested nonsingular terminal sliding controller is proposed to minimize the chattering phenomenon. By adding both integral and derivative errors of states into the nonsingular terminal sliding manifolds, a composite sliding manifold was created. Compared to nonsingular terminal sliding mode [...] Read more.

In this study, a PID-nested nonsingular terminal sliding controller is proposed to minimize the chattering phenomenon. By adding both integral and derivative errors of states into the nonsingular terminal sliding manifolds, a composite sliding manifold was created. Compared to nonsingular terminal sliding mode (NTSM) techniques, this sliding manifold can handle higher-order derivatives. The speed of the motor is controlled by a sliding control law determined through a higher-order integral, making the signal continuous, and the sliding manifold is achieved in finite time. A special full-order terminal sliding mode manifold is introduced, which allows the system to converge in finite time while being chattering-free and avoiding the singularity phenomenon of conventional and terminal sliding modes. The controller’s efficiency is demonstrated with faster convergence time and fewer errors than state-of-the-art controllers, which is demonstrated through both simulation and experiment. Full article

(This article belongs to the Topic Intelligent Control in Smart Energy Systems)

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21 pages, 1379 KiB

Open AccessArticle

Generalization of Ramsey Number for Cycle with Pendant Edges

by Jagjeet Jakhar, Monu Moun, Youngsoo Seol, Majeed Ahmad Yousif, Muhammad Amer Latif and Pshtiwan Othman Mohammed

Mathematics 2025, 13(7), 1196; https://doi.org/10.3390/math13071196 - 4 Apr 2025

Viewed by 251

Abstract

This paper explores various Ramsey numbers associated with cycles with pendant edges, including the classical Ramsey number, the star-critical Ramsey number, the Gallai–Ramsey number, and the star-critical Gallai–Ramsey number. These Ramsey numbers play a crucial role in combinatorial mathematics, determining the minimum number [...] Read more.

This paper explores various Ramsey numbers associated with cycles with pendant edges, including the classical Ramsey number, the star-critical Ramsey number, the Gallai–Ramsey number, and the star-critical Gallai–Ramsey number. These Ramsey numbers play a crucial role in combinatorial mathematics, determining the minimum number of vertices required to guarantee specific monochromatic substructures. We establish upper and lower bounds for each of these numbers, providing new insights into their behavior for cycles with pendant edges—graphs formed by attaching additional edges to one or more vertices of a cycle. The results presented contribute to the broader understanding of Ramsey theory and serve as a foundation for future research on generalized Ramsey numbers in complex graph structures. Full article

(This article belongs to the Special Issue Advances in Discrete Applied Mathematics and Graph Theory, 3rd Edition)

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18 pages, 2692 KiB

Open AccessFeature PaperArticle

Unit Size Determination for Exploratory Brain Imaging Analysis: A Quest for a Resolution-Invariant Metric

by Jihnhee Yu, HyunAh Lee and Zohi Sternberg

Mathematics 2025, 13(7), 1195; https://doi.org/10.3390/math13071195 - 4 Apr 2025

Viewed by 214

Abstract

Defining an adequate unit size is often crucial in brain imaging analysis, where datasets are complex, high-dimensional, and computationally demanding. Unit size refers to the spatial resolution at which brain data is aggregated for analysis. Optimizing unit size in data aggregation requires balancing [...] Read more.

Defining an adequate unit size is often crucial in brain imaging analysis, where datasets are complex, high-dimensional, and computationally demanding. Unit size refers to the spatial resolution at which brain data is aggregated for analysis. Optimizing unit size in data aggregation requires balancing computational efficiency in handling large-scale data sets with the preservation of brain activity patterns, minimizing signal dilution. We propose using the Calinski–Harabasz index, demonstrating its invariance to sample size changes due to varying image resolutions when no distributional differences are present, while the index effectively identifies an appropriate unit size for detecting suspected regions in image comparisons. The resolution-independent metric can be used for unit size evaluation, ensuring adaptability across different imaging protocols and modalities. This study enhances the scalability and efficiency of brain imaging research by providing a robust framework for unit size optimization, ultimately strengthening analytical tools for investigating brain function and structure. Full article

(This article belongs to the Special Issue Mathematical Methods for Image Processing and Computer Vision)

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14 pages, 515 KiB

Open AccessFeature PaperArticle

Set-Valued Approximation—Revisited and Improved

by David Levin

Mathematics 2025, 13(7), 1194; https://doi.org/10.3390/math13071194 - 4 Apr 2025

Viewed by 164

Abstract

We address the problem of approximating a set-valued function F, where

F : [a, b] \to K (R^{d})

given its samples

{F (a + i h)}_{i = 0}^{N}

, with [...] Read more.

We address the problem of approximating a set-valued function F, where

F : [a, b] \to K (R^{d})

given its samples

{F (a + i h)}_{i = 0}^{N}

, with

h = (b - a) / N

. We revisit an existing method that approximates set-valued functions by interpolating signed-distance functions. This method provides a high-order approximation for general topologies but loses accuracy near points where F undergoes topological changes. To address this, we introduce new techniques that enhance efficiency and maintain high-order accuracy across

[a, b]

. Building on the foundation of previous publication, we introduce new techniques to improve the method’s efficiency and extend its high-order approximation accuracy throughout the entire interval

[a, b]

. Particular focus is placed on identifying and analyzing the behavior of F near topological transition points. To address this, two algorithms are introduced. The first algorithm employs signed-distance quasi-interpolation, incorporating specialized adjustments to effectively handle singularities at points of topological change. The second algorithm leverages an implicit function representation of

G r a p h (F)

, offering an alternative and robust approach to its approximation. These enhancements improve accuracy and stability in handling set-valued functions with changing topologies. Full article

(This article belongs to the Special Issue Advances in Approximation Theory and Numerical Functional Analysis)

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24 pages, 380 KiB

Open AccessArticle

Pseudorandom Function from Learning Burnside Problem

by Dhiraj K. Pandey and Antonio R. Nicolosi

Mathematics 2025, 13(7), 1193; https://doi.org/10.3390/math13071193 - 4 Apr 2025

Viewed by 168

Abstract

We present three progressively refined pseudorandom function (PRF) constructions based on the learning Burnside homomorphisms with noise (

B_{n}

-LHN) assumption. A key challenge in this approach is error management, which we address by extracting errors from the secret key. Our first [...] Read more.

We present three progressively refined pseudorandom function (PRF) constructions based on the learning Burnside homomorphisms with noise (

B_{n}

-LHN) assumption. A key challenge in this approach is error management, which we address by extracting errors from the secret key. Our first design, a direct pseudorandom generator (PRG), leverages the lower entropy of the error set (E) compared to the Burnside group (

B_{r}

). The second, a parameterized PRG, derives its function description from public parameters and the secret key, aligning with the relaxed PRG requirements in the Goldreich–Goldwasser–Micali (GGM) PRF construction. The final indexed PRG introduces public parameters and an index to refine efficiency. To optimize computations in Burnside groups, we enhance concatenation operations and homomorphisms from

B_{n}

to

B_{r}

for

n ≫ r

. Additionally, we explore algorithmic improvements and parallel computation strategies to improve efficiency. Full article

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

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27 pages, 3729 KiB

Open AccessArticle

How Can Viruses Affect the Growth of Zooplankton on Phytoplankton in a Chemostat?

by Nada A. Almuallem and Miled El Hajji

Mathematics 2025, 13(7), 1192; https://doi.org/10.3390/math13071192 - 4 Apr 2025

Viewed by 140

Abstract

In this work, we investigated a simple mathematical model describing the consumption of virus-infected phytoplankton by zooplankton in a chemostat. The system was studied by calculating the basic reproduction number, the equilibrium points, and their local and global stability. A sensitivity analysis was [...] Read more.

In this work, we investigated a simple mathematical model describing the consumption of virus-infected phytoplankton by zooplankton in a chemostat. The system was studied by calculating the basic reproduction number, the equilibrium points, and their local and global stability. A sensitivity analysis was used to identify key chemostat factors that significantly affected the aquatic system. Additionally, we considered an optimal strategy based on the use of the dilution rate as an operating parameter that helps maintain the ecological balance of the aquatic food web. Full article

(This article belongs to the Section C2: Dynamical Systems)

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23 pages, 2975 KiB

Open AccessArticle

Coevolutionary Algorithm with Bayes Theorem for Constrained Multiobjective Optimization

by Shaoyu Zhao, Heming Jia, Yongchao Li and Qian Shi

Mathematics 2025, 13(7), 1191; https://doi.org/10.3390/math13071191 - 4 Apr 2025

Viewed by 147

Abstract

The effective resolution of constrained multi-objective optimization problems (CMOPs) requires a delicate balance between maximizing objectives and satisfying constraints. Previous studies have demonstrated that multi-swarm optimization models exhibit robust performance in CMOPs; however, their high computational resource demands can hinder convergence efficiency. This [...] Read more.

The effective resolution of constrained multi-objective optimization problems (CMOPs) requires a delicate balance between maximizing objectives and satisfying constraints. Previous studies have demonstrated that multi-swarm optimization models exhibit robust performance in CMOPs; however, their high computational resource demands can hinder convergence efficiency. This article proposes an environment selection model based on Bayes’ theorem, leveraging the advantages of dual populations. The model constructs prior knowledge using objective function values and constraint violation values, and then, it integrates this information to enhance selection processes. By dynamically adjusting the selection of the auxiliary population based on prior knowledge, the algorithm significantly improves its adaptability to various CMOPs. Additionally, a population size adjustment strategy is introduced to mitigate the computational burden of dual populations. By utilizing past prior knowledge to estimate the probability of function value changes, offspring allocation is dynamically adjusted, optimizing resource utilization. This adaptive adjustment prevents unnecessary computational waste during evolution, thereby enhancing both convergence and diversity. To validate the effectiveness of the proposed algorithm, comparative experiments were performed against seven constrained multi-objective optimization algorithms (CMOEAs) across three benchmark test sets and 12 real-world problems. The results show that the proposed algorithm outperforms the others in both convergence and diversity. Full article

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26 pages, 482 KiB

Open AccessArticle

Computational Construction of Sequential Efficient Designs for the Second-Order Model

by Norah Alshammari, Stelios Georgiou and Stella Stylianou

Mathematics 2025, 13(7), 1190; https://doi.org/10.3390/math13071190 - 4 Apr 2025

Viewed by 216

Abstract

Sequential experimental designs enhance data collection efficiency by reducing resource usage and accelerating experimental objectives. This paper presents a model-driven approach to sequential Latin hypercube designs (SLHDs) tailored for second-order models. Unlike traditional model-free SLHDs, our method optimizes a conditional A-criterion to improve [...] Read more.

Sequential experimental designs enhance data collection efficiency by reducing resource usage and accelerating experimental objectives. This paper presents a model-driven approach to sequential Latin hypercube designs (SLHDs) tailored for second-order models. Unlike traditional model-free SLHDs, our method optimizes a conditional A-criterion to improve efficiency, particularly in higher dimensions. By relaxing the restriction of non-replicated points within equally spaced intervals, our approach maintains space-filling properties while allowing greater flexibility for model-specific optimization. Using Sobol sequences, the algorithm iteratively selects good points, enhancing conditional A-efficiency compared to distance minimization methods. Additional criteria, such as D-efficiency, further validate the generated design matrices, ensuring robust performance. The proposed approach demonstrates superior results, with detailed tables and graphs illustrating its advantages across applications in engineering, pharmacology, and manufacturing. Full article

(This article belongs to the Special Issue Advances in Computational Statistics, Design of Experiments, and Its Applications)

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17 pages, 5491 KiB

Open AccessArticle

Dynamics of the Diphtheria Epidemic in Nigeria: Insights from the Kano State Outbreak Data

by Sani Musa, Salisu Usaini, Idris Ahmed, Chanakarn Kiataramkul and Jessada Tariboon

Mathematics 2025, 13(7), 1189; https://doi.org/10.3390/math13071189 - 4 Apr 2025

Viewed by 215

Abstract

Diphtheria is a severely infectious and deadly bacterial disease with Corynebacterium diphtheriae as the causative agent. Since the COVID-19 pandemic, contagious diseases such as diphtheria have re-emerged due to disruptions in routine childhood immunization programs worldwide. Nigeria is witnessing a significant increase in [...] Read more.

Diphtheria is a severely infectious and deadly bacterial disease with Corynebacterium diphtheriae as the causative agent. Since the COVID-19 pandemic, contagious diseases such as diphtheria have re-emerged due to disruptions in routine childhood immunization programs worldwide. Nigeria is witnessing a significant increase in diphtheria outbreaks likely due to an inadequate health care system and insufficient public enlightenment campaign. This paper presents a mathematical epidemic diphtheria model in Nigeria, which includes a public enlightenment campaign to assess its positive impact on the prevalence of the disease. The mathematical analysis of the model reveals two equilibrium points: the diphtheria infection-free equilibrium and the endemic equilibrium. These equilibrium points are shown to be stable globally asymptotically if

R_{c} < 1

and

R_{c} > 1

, respectively. The model was fit using the confirmed diphtheria cases data of Kano State from January to December 2023. Sensitivity analysis indicates that the transmission rate and recovery rate of asymptomatic peopleare crucial parameters to be considered in developing effective strategies for diphtheria control and prevention. This analysis also reveals that the implementation of a high-level public enlightenment campaign and its high efficacy effectively reduce the prevalence of diphtheria. Finally, numerical simulations show that combining the public enlightenment campaign and isolating infected individuals is the best strategy to contain the spread of diphtheria. Full article

(This article belongs to the Special Issue Mathematical Modeling of Disease Dynamics)

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16 pages, 7032 KiB

Open AccessArticle

I-NeRV: A Single-Network Implicit Neural Representation for Efficient Video Inpainting

by Jie Ji, Shuxuan Fu and Jiaju Man

Mathematics 2025, 13(7), 1188; https://doi.org/10.3390/math13071188 - 4 Apr 2025

Viewed by 252

Abstract

Deep learning methods based on implicit neural representations offer an efficient and automated solution for video inpainting by leveraging the inherent characteristics of video data. However, the limited size of the video embedding (e.g.,

16 \times 2 \times 4

) generated by the [...] Read more.

Deep learning methods based on implicit neural representations offer an efficient and automated solution for video inpainting by leveraging the inherent characteristics of video data. However, the limited size of the video embedding (e.g.,

16 \times 2 \times 4

) generated by the encoder restricts the available feature information for the decoder, which, in turn, constrains the model’s representational capacity and degrades inpainting performance. While implicit neural representations have shown promise for video inpainting, most of the existing research still revolves around image inpainting and does not fully account for the spatiotemporal continuity and relationships present in videos. This gap highlights the need for more advanced techniques capable of capturing and exploiting the spatiotemporal dynamics of video data to further improve inpainting results. To address this issue, we introduce I-NeRV, the first implicit neural-representation-based design specifically tailored for video inpainting. By embedding spatial features and modeling the spatiotemporal continuity between frames, I-NeRV significantly enhances inpainting performance, especially for videos with missing regions. To further boost the quality of inpainting, we propose an adaptive embedding size design and a weighted loss function. We also explore strategies for balancing model size and computational efficiency, such as fine-tuning the embedding size and customizing convolution kernels to accommodate various resource constraints. Extensive experiments on benchmark datasets demonstrate that our approach substantially outperforms state-of-the-art methods in video inpainting, achieving an average of 3.47 PSNR improvement in quality metrics. Full article

(This article belongs to the Special Issue New Trends in Computer Vision, Deep Learning and Artificial Intelligence)

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19 pages, 915 KiB

Open AccessFeature PaperArticle

The Inverse Scattering of Three-Dimensional Inhomogeneous Steady-State Sound Field Models

by Zhaoxi Sun, Wenbin Zhang and Meiling Zhao

Mathematics 2025, 13(7), 1187; https://doi.org/10.3390/math13071187 - 3 Apr 2025

Viewed by 178

Abstract

We propose a U-Net regression network model for sliced data to reconstruct a three-dimensional irregular steady-state sound field filling inhomogeneous anisotropic media. Through an innovative sliced data processing strategy, the 3D reconstruction problem is decomposed into a combination of 2D problems, thereby significantly [...] Read more.

We propose a U-Net regression network model for sliced data to reconstruct a three-dimensional irregular steady-state sound field filling inhomogeneous anisotropic media. Through an innovative sliced data processing strategy, the 3D reconstruction problem is decomposed into a combination of 2D problems, thereby significantly reducing the computational cost. The designed multi-channel U-Net fully utilizes the strengths of both the encoder and decoder, exhibiting strong feature extraction and spatial detail recovery capabilities. Numerical experiments show that the model can not only effectively reconstruct the complex sound field structure containing non-convex regions, but it can also synchronously restore the spatial distribution of the media and their parameter matrix, successfully achieving the dual reconstruction of the shape and physical parameters of the steady-state sound field. Full article

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22 pages, 302 KiB

Open AccessFeature PaperArticle

A Novel Group Decision-Making Method with Adjustment Willingness in a Distributed Hesitant Fuzzy Linguistic Environment

by Xiao Liang, Xiaoxia Xu and Francisco Javier Cabrerizo

Mathematics 2025, 13(7), 1186; https://doi.org/10.3390/math13071186 - 3 Apr 2025

Viewed by 147

Abstract

This research aims to construct a group decision-making (GDM) method that considers decision makers’ (DMs’) willingness to adjust in a distributed hesitant fuzzy linguistic (DHFL) environment. First, to address the practical scenario where DMs may express preferences using multiple linguistic values with explicit [...] Read more.

This research aims to construct a group decision-making (GDM) method that considers decision makers’ (DMs’) willingness to adjust in a distributed hesitant fuzzy linguistic (DHFL) environment. First, to address the practical scenario where DMs may express preferences using multiple linguistic values with explicit preference strengths, this paper extends the distributed hesitant fuzzy linguistic preference relation (DHFLPR) and supplements missing probabilities. Second, we integrate multiplicative consistency and consensus within a DHFL environment to construct two preference optimization models, whose objective functions are to minimize the overall adjustment based on DMs’ willingness to adjust, thus making the decision more consistent with actual environments. Finally, the viability and effectiveness of the new method are validated by numerical examples. The results show that our new method allows individual preferences to quickly meet the consistency requirement while maximally preserving their original preferences. Additionally, the DHFLPRs maintain the fuzziness and hesitancy in the new preferences, and effectively address the issue of unequal importance among distinct linguistic preference values. Full article

14 pages, 272 KiB

Open AccessArticle

Weak Solutions to Leray–Lions-Type Degenerate Quasilinear Elliptic Equations with Nonlocal Effects, Double Hardy Terms, and Variable Exponents

by Khaled Kefi and Mohammed M. Al-Shomrani

Mathematics 2025, 13(7), 1185; https://doi.org/10.3390/math13071185 - 3 Apr 2025

Viewed by 154

Abstract

This study investigates the existence and multiplicity of weak solutions for a class of degenerate weighted quasilinear elliptic equations that incorporate nonlocal nonlinearities, a double Hardy term, and variable exponents. The problem encompasses a degenerate nonlinear operator characterized by variable exponent growth, along [...] Read more.

This study investigates the existence and multiplicity of weak solutions for a class of degenerate weighted quasilinear elliptic equations that incorporate nonlocal nonlinearities, a double Hardy term, and variable exponents. The problem encompasses a degenerate nonlinear operator characterized by variable exponent growth, along with a nonlocal interaction term and specific constraints on the nonlinearity. By employing critical point theory, we establish the existence of at least three weak solutions under sufficiently general assumptions. Full article

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Mathematics, Volume 13, Issue 7 (April-1 2025) – 194 articles

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