Mathematics

11 pages, 274 KiB

Open AccessArticle

Defining and Analyzing New Classes Associated with (λ,γ)-Symmetrical Functions and Quantum Calculus

by Hanen Louati, Afrah Y. Al-Rezami, Abdulbasit A. Darem and Fuad Alsarari

Mathematics 2024, 12(16), 2603; https://doi.org/10.3390/math12162603 - 22 Aug 2024

Viewed by 516

In this paper, we introduce new classes of functions defined within the open unit disk by integrating the concepts of

(λ, γ)

-symmetrical functions, generalized Janowski functions, and quantum calculus. We derive a structural formula and a representation theorem for [...] Read more.

In this paper, we introduce new classes of functions defined within the open unit disk by integrating the concepts of

(λ, γ)

-symmetrical functions, generalized Janowski functions, and quantum calculus. We derive a structural formula and a representation theorem for the class

S_{q}^{λ, γ} (x, y, z)

. Utilizing convolution techniques and quantum calculus, we investigate convolution conditions supported by examples and corollary, establishing sufficient conditions. Additionally, we derive properties related to coefficient estimates, which further elucidate the characteristics of the defined function classes. Full article

(This article belongs to the Special Issue Mathematical Modelling in Relativity and Quantum Theory)

18 pages, 4594 KiB

Open AccessArticle

Interdisciplinary Education Promotes Scientific Research Innovation: Take the Composite Control of the Permanent Magnet Synchronous Motor as an Example

by Peng Gao, Liandi Fang and Huihui Pan

Mathematics 2024, 12(16), 2602; https://doi.org/10.3390/math12162602 - 22 Aug 2024

Viewed by 467

Abstract

Intersecting disciplines, as an important trend in the development of modern academic research and education, have exerted a profound and positive influence on scientific research activities. Based on control theory and fractional-order theory, this paper presents a novel approach for the speed regulation [...] Read more.

Intersecting disciplines, as an important trend in the development of modern academic research and education, have exerted a profound and positive influence on scientific research activities. Based on control theory and fractional-order theory, this paper presents a novel approach for the speed regulation of a permanent magnet synchronous motor (PMSM) in the presence of uncertainties and external disturbances. The proposed method is a composite control based on a model-free sliding mode and a fractional-order ultra-local model. The model-free sliding mode is a control strategy that utilizes the sliding mode control methodology without explicitly relying on a mathematical model of the system being controlled. The fractional-order ultra-local model is a mathematical representation of a dynamic system that incorporates the concept of fractional-order derivatives. The core of the controller is a new type of fractional-order fast nonsingular terminal sliding mode surface, which ensures high robustness, quick convergence, while preventing singularity. Moreover, a novel fractional-order nonlinear extended state observer is proposed to estimate both internal and external disturbances of the fractional-order ultra-local model. The stability of the system is analyzed using both the Lyapunov stability theory and the Mittag–Leffler stability theory. The analysis confirms the convergence stability of the closed-loop system under the proposed control scheme. The comparison results indicate that the proposed composite control based on the fractional-order ultra-local model is a promising solution for regulating the speed of PMSMs in the presence of uncertainties and disturbances. Full article

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

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21 pages, 793 KiB

Open AccessArticle

A Path-Conservative ADER Discontinuous Galerkin Method for Non-Conservative Hyperbolic Systems: Applications to Shallow Water Equations

by Xiaoxu Zhao, Baining Wang, Gang Li and Shouguo Qian

Mathematics 2024, 12(16), 2601; https://doi.org/10.3390/math12162601 - 22 Aug 2024

Viewed by 441

Abstract

In this article, we propose a new path-conservative discontinuous Galerkin (DG) method to solve non-conservative hyperbolic partial differential equations (PDEs). In particular, the method here applies the one-stage ADER (Arbitrary DERivatives in space and time) approach to fulfill the temporal discretization. In addition, [...] Read more.

In this article, we propose a new path-conservative discontinuous Galerkin (DG) method to solve non-conservative hyperbolic partial differential equations (PDEs). In particular, the method here applies the one-stage ADER (Arbitrary DERivatives in space and time) approach to fulfill the temporal discretization. In addition, this method uses the differential transformation (DT) procedure rather than the traditional Cauchy–Kowalewski (CK) procedure to achieve the local temporal evolution. Compared with the classical ADER methods, the current method is free of solving generalized Riemann problems at inter-cells. In comparison with the Runge–Kutta DG (RKDG) methods, the proposed method needs less computer storage, thanks to the absence of intermediate stages. In brief, this current method is one-step, one-stage, and fully-discrete. Moreover, this method can easily obtain arbitrary high-order accuracy both in space and in time. Numerical results for one- and two-dimensional shallow water equations (SWEs) show that the method enjoys high-order accuracy and keeps good resolution for discontinuous solutions. Full article

(This article belongs to the Special Issue Computational Methods and Applications for Numerical Analysis, 2nd Edition)

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25 pages, 8978 KiB

Open AccessArticle

Accurate Forecasting of Global Horizontal Irradiance in Saudi Arabia: A Comparative Study of Machine Learning Predictive Models and Feature Selection Techniques

by Amir A. Imam, Abdullah Abusorrah, Mustafa M. A. Seedahmed and Mousa Marzband

Mathematics 2024, 12(16), 2600; https://doi.org/10.3390/math12162600 - 22 Aug 2024

Cited by 1 | Viewed by 824

Abstract

The growing interest in solar energy stems from its potential to reduce greenhouse gas emissions. Global horizontal irradiance (GHI) is a crucial determinant of the productivity of solar photovoltaic (PV) systems. Consequently, accurate GHI forecasting is essential for efficient planning, integration, and optimization [...] Read more.

The growing interest in solar energy stems from its potential to reduce greenhouse gas emissions. Global horizontal irradiance (GHI) is a crucial determinant of the productivity of solar photovoltaic (PV) systems. Consequently, accurate GHI forecasting is essential for efficient planning, integration, and optimization of solar PV energy systems. This study evaluates the performance of six machine learning (ML) regression models—artificial neural network (ANN), decision tree (DT), elastic net (EN), linear regression (LR), Random Forest (RF), and support vector regression (SVR)—in predicting GHI for a site in northern Saudi Arabia known for its high solar energy potential. Using historical data from the NASA POWER database, covering the period from 1984 to 2022, we employed advanced feature selection techniques to enhance the predictive models. The models were evaluated based on metrics such as R-squared (R²), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE), and Mean Absolute Error (MAE). The DT model demonstrated the highest performance, achieving an R² of 1.0, MSE of 0.0, RMSE of 0.0, MAPE of 0.0%, and MAE of 0.0. Conversely, the EN model showed the lowest performance with an R² of 0.8396, MSE of 0.4389, RMSE of 0.6549, MAPE of 9.66%, and MAE of 0.5534. While forward, backward, and exhaustive search feature selection methods generally yielded limited performance improvements for most models, the SVR model experienced significant enhancement. These findings offer valuable insights for selecting optimal forecasting strategies for solar energy projects, contributing to the advancement of renewable energy integration and supporting the global transition towards sustainable energy solutions. Full article

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13 pages, 297 KiB

Open AccessArticle

Optimality and Duality of Semi-Preinvariant Convex Multi-Objective Programming Involving Generalized (F,α,ρ,d)-I-Type Invex Functions

by Rongbo Wang and Qiang Feng

Mathematics 2024, 12(16), 2599; https://doi.org/10.3390/math12162599 - 22 Aug 2024

Viewed by 547

Abstract

Multiobjective programming refers to a mathematical problem that requires the simultaneous optimization of multiple independent yet interrelated objective functions when solving a problem. It is widely used in various fields, such as engineering design, financial investment, environmental planning, and transportation planning. Research on [...] Read more.

Multiobjective programming refers to a mathematical problem that requires the simultaneous optimization of multiple independent yet interrelated objective functions when solving a problem. It is widely used in various fields, such as engineering design, financial investment, environmental planning, and transportation planning. Research on the theory and application of convex functions and their generalized convexity in multiobjective programming helps us understand the essence of optimization problems, and promotes the development of optimization algorithms and theories. In this paper, we firstly introduces new classes of generalized

(F, α, ρ, d) - I

functions for semi-preinvariant convex multiobjective programming. Secondly, based on these generalized functions, we derive several sufficient optimality conditions for a feasible solution to be an efficient or weakly efficient solution. Finally, we prove weak duality theorems for mixed-type duality. Full article

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

26 pages, 1279 KiB

Open AccessArticle

Quantum Automated Tools for Finding Impossible Differentials

by Huiqin Xie, Qiqing Xia, Ke Wang, Yanjun Li and Li Yang

Mathematics 2024, 12(16), 2598; https://doi.org/10.3390/math12162598 - 22 Aug 2024

Viewed by 564

Abstract

Due to the superiority of quantum computing, traditional cryptography is facing a severe threat. This makes the security evaluation of cryptographic systems in quantum attack models both significant and urgent. For symmetric ciphers, the security analysis heavily relies on cryptanalysis tools. Thus, exploring [...] Read more.

Due to the superiority of quantum computing, traditional cryptography is facing a severe threat. This makes the security evaluation of cryptographic systems in quantum attack models both significant and urgent. For symmetric ciphers, the security analysis heavily relies on cryptanalysis tools. Thus, exploring the use of quantum algorithms in traditional cryptanalysis tools has garnered considerable attention. In this study, we utilize quantum algorithms to improve impossible differential attacks and design two quantum automated tools to search for impossible differentials. The proposed quantum algorithms exploit the idea of miss-in-the-middle and the properties of truncated differentials. We rigorously prove their validity and calculate the quantum resources required for their implementation. Compared to the existing classical automated cryptanalysis, the proposed quantum tools have the advantage of accurately characterizing S-boxes while only requiring polynomial complexity, and can take into consideration the impact of the key schedules in a single-key model. Full article

(This article belongs to the Special Issue New Advances in Coding Theory and Cryptography, 2nd Edition)

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10 pages, 875 KiB

Open AccessFeature PaperArticle

Approximation of Bivariate Functions by Generalized Wendland Radial Basis Functions

by Abdelouahed Kouibia, Pedro González, Miguel Pasadas, Bassim Mustafa, Hossain Oulad Yakhlef and Loubna Omri

Mathematics 2024, 12(16), 2597; https://doi.org/10.3390/math12162597 - 22 Aug 2024

Viewed by 593

Abstract

In this work, we deal with two approximation problems in a finite-dimensional generalized Wendland space of compactly supported radial basis functions. Namely, we present an interpolation method and a smoothing variational method in this space. Next, the theory of the presented method is [...] Read more.

In this work, we deal with two approximation problems in a finite-dimensional generalized Wendland space of compactly supported radial basis functions. Namely, we present an interpolation method and a smoothing variational method in this space. Next, the theory of the presented method is justified by proving the corresponding convergence result. Likewise, to illustrate this method, some graphical and numerical examples are presented in

R^{2}

, and a comparison with another work is analyzed. Full article

(This article belongs to the Special Issue Approximation and Computation for Numerical Analysis: Latest Advances and Prospects)

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16 pages, 290 KiB

Open AccessArticle

Fixed-Point Theorems Using α-Series in F-Metric Spaces

by Vildan Ozturk and Duran Turkoglu

Mathematics 2024, 12(16), 2596; https://doi.org/10.3390/math12162596 - 22 Aug 2024

Viewed by 487

Abstract

Fixed-point theory, which has been developing since 1922, is widely used. Various contraction principles have been defined in the literature. In this work, we define rational-type contraction and weak Choudhury type contraction using

α

-series in F-metric spaces and prove common fixed-point [...] Read more.

Fixed-point theory, which has been developing since 1922, is widely used. Various contraction principles have been defined in the literature. In this work, we define rational-type contraction and weak Choudhury type contraction using

α

-series in F-metric spaces and prove common fixed-point theorems for sequences of self-mappings. This method is based on the convergence series of coefficients. Our results are the generalized version of the results in the literature. Finally, we apply our main results to solve an integral equation and a differential equation. Full article

(This article belongs to the Section Algebra, Geometry and Topology)

9 pages, 273 KiB

Open AccessArticle

Superconvergence of Modified Nonconforming Cut Finite Element Method for Elliptic Problems

by Xiaoxiao He and Fei Song

Mathematics 2024, 12(16), 2595; https://doi.org/10.3390/math12162595 - 22 Aug 2024

Viewed by 447

Abstract

In this work, we aim to explore the superconvergence of a modified nonconforming cut finite element method with rectangular meshes for elliptic problems. Boundary conditions are imposed via the Nitsche’s method. The superclose property is proven for rectangular meshes. Moreover, a postprocessing interpolation [...] Read more.

In this work, we aim to explore the superconvergence of a modified nonconforming cut finite element method with rectangular meshes for elliptic problems. Boundary conditions are imposed via the Nitsche’s method. The superclose property is proven for rectangular meshes. Moreover, a postprocessing interpolation operator is introduced, and it is proven that the postprocessed discrete solution converges to the exact solution, with a superconvergence rate

O (h^{3 / 2})

. Finally, numerical examples are provided to support the theoretical analysis. Full article

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10 pages, 20467 KiB

Open AccessArticle

Hirota Bilinear Approach to Multi-Component Nonlocal Nonlinear Schrödinger Equations

by Yu-Shan Bai, Li-Na Zheng, Wen-Xiu Ma and Yin-Shan Yun

Mathematics 2024, 12(16), 2594; https://doi.org/10.3390/math12162594 - 22 Aug 2024

Viewed by 698

Abstract

Nonlocal nonlinear Schrödinger equations are among the important models of nonlocal integrable systems. This paper aims to present a general formula for arbitrary-order breather solutions to multi-component nonlocal nonlinear Schrödinger equations by using the Hirota bilinear method. In particular, abundant wave solutions of [...] Read more.

Nonlocal nonlinear Schrödinger equations are among the important models of nonlocal integrable systems. This paper aims to present a general formula for arbitrary-order breather solutions to multi-component nonlocal nonlinear Schrödinger equations by using the Hirota bilinear method. In particular, abundant wave solutions of two- and three-component nonlocal nonlinear Schrödinger equations, including periodic and mixed-wave solutions, are obtained by taking appropriate values for the involved parameters in the general solution formula. Moreover, diverse wave structures of the resulting breather and periodic wave solutions with different parameters are discussed in detail. Full article

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12 pages, 371 KiB

Open AccessFeature PaperArticle

Generalized Bertrand Curves of Non-Light-like Framed Curves in Lorentz–Minkowski 3-Space

by Linlin Wu, Anjie Zhou, Kaixin Yao and Donghe Pei

Mathematics 2024, 12(16), 2593; https://doi.org/10.3390/math12162593 - 22 Aug 2024

Viewed by 629

Abstract

In this paper, we define the generalized Bertrand curves of non-light-like framed curves in Lorentz–Minkowski 3-space; their study is essential for understanding many classical and modern physics problems. Here, we consider two non-light-like framed curves as generalized Bertrand pairs. Our generalized Bertrand pairs [...] Read more.

In this paper, we define the generalized Bertrand curves of non-light-like framed curves in Lorentz–Minkowski 3-space; their study is essential for understanding many classical and modern physics problems. Here, we consider two non-light-like framed curves as generalized Bertrand pairs. Our generalized Bertrand pairs can include Bertrand pairs with either singularities or not, and also include Mannheim pairs with singularities. In addition, we discuss their properties and prove the necessary and sufficient conditions for two non-light-like framed curves to be generalized Bertrand pairs. Full article

(This article belongs to the Special Issue Advances in Differential Geometry and Its Applications)

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15 pages, 297 KiB

Open AccessArticle

Semi-Discretized Approximation of Stability of Sine-Gordon System with Average-Central Finite Difference Scheme

by Xudong Wang, Sizhe Wang, Xing Qiao and Fu Zheng

Mathematics 2024, 12(16), 2592; https://doi.org/10.3390/math12162592 - 22 Aug 2024

Viewed by 479

Abstract

In this study, the energy control and asymptotic stability of the 1D sine-Gordon equation were investigated from the viewpoint of numerical approximation. An order reduction method was employed to transform the closed-loop system into an equivalent system, and an average-central finite difference scheme [...] Read more.

In this study, the energy control and asymptotic stability of the 1D sine-Gordon equation were investigated from the viewpoint of numerical approximation. An order reduction method was employed to transform the closed-loop system into an equivalent system, and an average-central finite difference scheme was constructed. This scheme is not only energy-preserving but also possesses uniform stability. The discrete multiplier method was utilized to obtain the uniformly asymptotic stability of the discrete systems. Moreover, to cope with the nonlinear term of the model, a discrete Wirtinger inequality suitable for our approximating scheme was established. Finally, several numerical experiments based on the eigenvalue distribution of the linearized approximation systems were conducted to demonstrate the effectiveness of the numerical approximating algorithm. Full article

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18 pages, 3527 KiB

Open AccessArticle

Identification of Patterns in CO₂ Emissions among 208 Countries: K-Means Clustering Combined with PCA and Non-Linear t-SNE Visualization

by Ana Lorena Jiménez-Preciado, Salvador Cruz-Aké and Francisco Venegas-Martínez

Mathematics 2024, 12(16), 2591; https://doi.org/10.3390/math12162591 - 22 Aug 2024

Viewed by 712

Abstract

This paper identifies patterns in total and per capita CO₂ emissions among 208 countries considering different emission sources, such as cement, flaring, gas, oil, and coal. This research uses linear and non-linear dimensional reduction techniques, combining K-means clustering with principal component analysis [...] Read more.

This paper identifies patterns in total and per capita CO₂ emissions among 208 countries considering different emission sources, such as cement, flaring, gas, oil, and coal. This research uses linear and non-linear dimensional reduction techniques, combining K-means clustering with principal component analysis (PCA) and t-distributed stochastic neighbor embedding (t-SNE), which allows the identification of distinct emission profiles among nations. This approach allows effective clustering of heterogeneous countries despite the highly dimensional nature of emissions data. The optimal number of clusters is determined using Calinski–Harabasz and Davies–Bouldin scores, of five and six clusters for total and per capita CO₂ emissions, respectively. The findings reveal that for total emissions, t-SNE brings together the world’s largest economies and emitters, i.e., China, USA, India, and Russia, into a single cluster, while PCA provides clusters with a single country for China, USA, and Russia. Regarding per capita emissions, PCA generates a cluster with only one country, Qatar, due to its significant flaring emissions, as byproduct of the oil industry, and its low population. This study concludes that international collaboration and coherent global policies are crucial for effectively addressing CO₂ emissions and developing targeted climate change mitigation strategies. Full article

(This article belongs to the Special Issue Exploring Statistical Learning: Inference, Optimization, and Real-World Applications)

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16 pages, 990 KiB

Open AccessFeature PaperArticle

A Bellman–Ford Algorithm for the Path-Length-Weighted Distance in Graphs

by Roger Arnau, José M. Calabuig, Luis M. García-Raffi, Enrique A. Sánchez Pérez and Sergi Sanjuan

Mathematics 2024, 12(16), 2590; https://doi.org/10.3390/math12162590 - 22 Aug 2024

Viewed by 795

Abstract

Consider a finite directed graph without cycles in which the arrows are weighted by positive weights. We present an algorithm for the computation of a new distance, called path-length-weighted distance, which has proven useful for graph analysis in the context of fraud detection. [...] Read more.

Consider a finite directed graph without cycles in which the arrows are weighted by positive weights. We present an algorithm for the computation of a new distance, called path-length-weighted distance, which has proven useful for graph analysis in the context of fraud detection. The idea is that the new distance explicitly takes into account the size of the paths in the calculations. It has the distinct characteristic that, when calculated along the same path, it may result in a shorter distance between far-apart vertices than between adjacent ones. This property can be particularly useful for modeling scenarios where the connections between vertices are obscured by numerous intermediate vertices, such as in cases of financial fraud. For example, to hide dirty money from financial authorities, fraudsters often use multiple institutions, banks, and intermediaries between the source of the money and its final recipient. Our distance would serve to make such situations explicit. Thus, although our algorithm is based on arguments similar to those at work for the Bellman–Ford and Dijkstra methods, it is in fact essentially different, since the calculation formula contains a weight that explicitly depends on the number of intermediate vertices. This fact totally conditions the algorithm, because longer paths could provide shorter distances—contrary to the classical algorithms mentioned above. We lay out the appropriate framework for its computation, showing the constraints and requirements for its use, along with some illustrative examples. Full article

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3 pages, 127 KiB

Open AccessEditorial

Preface to the Special Issue on “Advances in Machine Learning, Optimization, and Control Applications”

by Wanquan Liu, Xianchao Xiu and Xuefang Li

Mathematics 2024, 12(16), 2589; https://doi.org/10.3390/math12162589 - 22 Aug 2024

Viewed by 634

Abstract

Over the past few decades, data science and machine learning have demonstrated tremendous success in many areas of science and engineering, such as large-scale pattern recognition, computer vision, multiagent control, industrial engineering, etc [...] Full article

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

24 pages, 1023 KiB

Open AccessFeature PaperArticle

A U-Statistic for Testing the Lack of Dependence in Functional Partially Linear Regression Model

by Fanrong Zhao and Baoxue Zhang

Mathematics 2024, 12(16), 2588; https://doi.org/10.3390/math12162588 - 21 Aug 2024

Viewed by 663

Abstract

The functional partially linear regression model comprises a functional linear part and a non-parametric part. Testing the linear relationship between the response and the functional predictor is of fundamental importance. In cases where functional data cannot be approximated with a few principal components, [...] Read more.

The functional partially linear regression model comprises a functional linear part and a non-parametric part. Testing the linear relationship between the response and the functional predictor is of fundamental importance. In cases where functional data cannot be approximated with a few principal components, we develop a second-order U-statistic using a pseudo-estimate for the unknown non-parametric component. Under some regularity conditions, the asymptotic normality of the proposed test statistic is established using the martingale central limit theorem. The proposed test is evaluated for finite sample properties through simulation studies and its application to real data. Full article

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16 pages, 3374 KiB

Open AccessArticle

P-CA: Privacy-Preserving Convolutional Autoencoder-Based Edge–Cloud Collaborative Computing for Human Behavior Recognition

by Haoda Wang, Chen Qiu, Chen Zhang, Jiantao Xu and Chunhua Su

Mathematics 2024, 12(16), 2587; https://doi.org/10.3390/math12162587 - 21 Aug 2024

Viewed by 754

Abstract

With the development of edge computing and deep learning, intelligent human behavior recognition has spawned extensive applications in smart worlds. However, current edge computing technology faces performance bottlenecks due to limited computing resources at the edge, which prevent deploying advanced deep neural networks. [...] Read more.

With the development of edge computing and deep learning, intelligent human behavior recognition has spawned extensive applications in smart worlds. However, current edge computing technology faces performance bottlenecks due to limited computing resources at the edge, which prevent deploying advanced deep neural networks. In addition, there is a risk of privacy leakage during interactions between the edge and the server. To tackle these problems, we propose an effective, privacy-preserving edge–cloud collaborative interaction scheme based on WiFi, named P-CA, for human behavior sensing. In our scheme, a convolutional autoencoder neural network is split into two parts. The shallow layers are deployed on the edge side for inference and privacy-preserving processing, while the deep layers are deployed on the server side to leverage its computing resources. Experimental results based on datasets collected from real testbeds demonstrate the effectiveness and considerable performance of the P-CA. The recognition accuracy can maintain 88%, although it could achieve about 94.8% without the mixing operation. In addition, the proposed P-CA achieves better recognition accuracy than two state-of-the-art methods, i.e., FedLoc and PPDFL, by 2.7% and 2.1%, respectively, while maintaining privacy. Full article

(This article belongs to the Special Issue Intelligent Perception Computing and Graph Neural Networks: Algorithms, Applications, and New Challenges)

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16 pages, 3087 KiB

Open AccessArticle

Predicting the Performance of Ensemble Classification Using Conditional Joint Probability

by Iqbal Murtza, Jin-Young Kim and Muhammad Adnan

Mathematics 2024, 12(16), 2586; https://doi.org/10.3390/math12162586 - 21 Aug 2024

Cited by 1 | Viewed by 630

Abstract

In many machine learning applications, there are many scenarios when performance is not satisfactory by single classifiers. In this case, an ensemble classification is constructed using several weak base learners to achieve satisfactory performance. Unluckily, the construction of the ensemble classification is empirical, [...] Read more.

In many machine learning applications, there are many scenarios when performance is not satisfactory by single classifiers. In this case, an ensemble classification is constructed using several weak base learners to achieve satisfactory performance. Unluckily, the construction of the ensemble classification is empirical, i.e., to try an ensemble classification and if performance is not satisfactory then discard it. In this paper, a challenging analytical problem of the estimation of ensemble classification using the prediction performance of the base learners is considered. The proposed formulation is aimed at estimating the performance of ensemble classification without physically developing it, and it is derived from the perspective of probability theory by manipulating the decision probabilities of the base learners. For this purpose, the output of a base learner (which is either true positive, true negative, false positive, or false negative) is considered as a random variable. Then, the effects of logical disjunction-based and majority voting-based decision combination strategies are analyzed from the perspective of conditional joint probability. To evaluate the forecasted performance of ensemble classifier by the proposed methodology, publicly available standard datasets have been employed. The results show the effectiveness of the derived formulations to estimate the performance of ensemble classification. In addition to this, the theoretical and experimental results show that the logical disjunction-based decision outperforms majority voting in imbalanced datasets and cost-sensitive scenarios. Full article

(This article belongs to the Special Issue Optimization Algorithms in Data Science: Methods and Theory)

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15 pages, 308 KiB

Open AccessArticle

Evaluating Order Allocation Sustainability Using a Novel Framework Involving Z-Number

by Kuan-Yu Lin, Cheng-Lu Yeng and Yi-Kuei Lin

Mathematics 2024, 12(16), 2585; https://doi.org/10.3390/math12162585 - 21 Aug 2024

Viewed by 575

Abstract

The United Nations’ sustainable development goals have highlighted the significance of improving supply chain sustainability and ensuring the proper distribution of orders. This study proposes a novel framework involving Z-number, game theory, an indifference threshold-based attribute ratio analysis (ITARA), and a combined compromise [...] Read more.

The United Nations’ sustainable development goals have highlighted the significance of improving supply chain sustainability and ensuring the proper distribution of orders. This study proposes a novel framework involving Z-number, game theory, an indifference threshold-based attribute ratio analysis (ITARA), and a combined compromise solution method (CoCoSo) to evaluate the sustainability of suppliers and order allocations. To better reflect the decision makers’ current choices for the sustainability of assessed suppliers and order allocations and enhance the comprehensiveness of decision-making, the importance parameter of the supplier is obtained through game theory objectively for transforming supplier performance into order allocation performance. The Z-numbers are involved in ITARA (so-called ZITARA) and CoCoSo (so-called ZCoCoSo) to overcome the issue of information uncertainty in the process of expert evaluation. ZITARA and ZCoCoSo are used to determine the objective weights of criteria and to rank the evaluated order allocations, respectively. A case study of a China company is then presented to demonstrate the usefulness of the proposed framework and to inform their decision-making process regarding which suppliers the orders should be assigned to. Full article

(This article belongs to the Special Issue Fuzzy Applications in Industrial Engineering, 3rd Edition)

28 pages, 481 KiB

Open AccessArticle

Convergence Analysis for an Online Data-Driven Feedback Control Algorithm

by Siming Liang, Hui Sun, Richard Archibald and Feng Bao

Mathematics 2024, 12(16), 2584; https://doi.org/10.3390/math12162584 - 21 Aug 2024

Viewed by 514

Abstract

This paper presents convergence analysis of a novel data-driven feedback control algorithm designed for generating online controls based on partial noisy observational data. The algorithm comprises a particle filter-enabled state estimation component, estimating the controlled system’s state via indirect observations, alongside an efficient [...] Read more.

This paper presents convergence analysis of a novel data-driven feedback control algorithm designed for generating online controls based on partial noisy observational data. The algorithm comprises a particle filter-enabled state estimation component, estimating the controlled system’s state via indirect observations, alongside an efficient stochastic maximum principle-type optimal control solver. By integrating weak convergence techniques for the particle filter with convergence analysis for the stochastic maximum principle control solver, we derive a weak convergence result for the optimization procedure in search of optimal data-driven feedback control. Numerical experiments are performed to validate the theoretical findings. Full article

(This article belongs to the Special Issue Machine Learning and Statistical Learning with Applications)

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20 pages, 2175 KiB

Open AccessArticle

Validation of a Multi-Strain HIV Within-Host Model with AIDS Clinical Studies

by Necibe Tuncer, Kia Ghods, Vivek Sreejithkumar, Adin Garbowit, Mark Zagha and Maia Martcheva

Mathematics 2024, 12(16), 2583; https://doi.org/10.3390/math12162583 - 21 Aug 2024

Viewed by 731

Abstract

We used a previously introduced HIV within-host model with sensitive and resistant strains and validated it with two data sets. The first data set is from a clinical study that investigated multi-drug treatments and measured the total CD4⁺ cell count and viral [...] Read more.

We used a previously introduced HIV within-host model with sensitive and resistant strains and validated it with two data sets. The first data set is from a clinical study that investigated multi-drug treatments and measured the total CD4⁺ cell count and viral load. All nine patients in this data set experienced virologic failure. The second data set includes a unique patient who was treated with a unique drug and for whom both the sensitive and resistant strains were measured as well as the CD4⁺ cells. We studied the structural identifiability of the model with respect to each data set. With respect to the first data set, the model was structurally identifiable when the viral production rate of the sensitive strain was fixed and distinct from the viral production rate of the resistant strain. With respect to the second data set, the model was always structurally identifiable. We fit the model to the first data set using nonlinear mixed effect modeling in Monolix and estimated the population-level parameters. We inferred that the average time to emergence of a resistant strain is 844 days after treatment starts. We fit the model to the second data set and found out that the all the parameters except the mutation rate were practically identifiable. Full article

(This article belongs to the Special Issue Advances in Mathematical Biology and Applications)

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28 pages, 4455 KiB

Open AccessArticle

Leveraging ChatGPT and Long Short-Term Memory in Recommender Algorithm for Self-Management of Cardiovascular Risk Factors

by Tatiana V. Afanasieva, Pavel V. Platov, Andrey V. Komolov and Andrey V. Kuzlyakin

Mathematics 2024, 12(16), 2582; https://doi.org/10.3390/math12162582 - 21 Aug 2024

Viewed by 967

Abstract

One of the new trends in the development of recommendation algorithms is the dissemination of their capabilities to support the population in managing their health, in particular cardiovascular health. Cardiovascular diseases (CVDs) affect people in their prime years and remain the main cause [...] Read more.

One of the new trends in the development of recommendation algorithms is the dissemination of their capabilities to support the population in managing their health, in particular cardiovascular health. Cardiovascular diseases (CVDs) affect people in their prime years and remain the main cause of morbidity and mortality worldwide, and their clinical treatment is expensive and time consuming. At the same time, about 80% of them can be prevented, according to the World Federation of Cardiology. The aim of this study is to develop and investigate a knowledge-based recommender algorithm for the self-management of CVD risk factors in adults at home. The proposed algorithm is based on the original user profile, which includes a predictive assessment of the presence of CVD. To obtain a predictive score for CVD presence, AutoML and LSTM models were studied on the Kaggle dataset, and it was shown that the LSTM model, with an accuracy of 0.88, outperformed the AutoML model. The algorithm recommendations generated contain items of three types: targeted, informational, and explanatory. For the first time, large language models, namely ChatGPT-3.5, ChatGPT-4, and ChatGPT-4.o, were leveraged and studied in creating explanations of the recommendations. The experiments show the following: (1) In explaining recommendations, ChatGPT-3.5, ChatGPT-4, and ChatGPT-4.o demonstrate a high accuracy of 71% to 91% and coherence with modern official guidelines of 84% to 92%. (2) The safety properties of ChatGPT-generated explanations estimated by doctors received the highest score of almost 100%. (3) On average, the stability and correctness of the GPT-4.o responses were more acceptable than those of other models for creating explanations. (4) The degree of user satisfaction with the recommendations obtained using the proposed algorithm was 88%, and the rating of the usefulness of the recommendations was 92%. Full article

(This article belongs to the Special Issue Advances in Recommender Systems and Intelligent Agents)

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18 pages, 7996 KiB

Open AccessArticle

Forecasting and Multilevel Early Warning of Wind Speed Using an Adaptive Kernel Estimator and Optimized Gated Recurrent Units

by Pengjiao Wang, Qiuliang Long, Hu Zhang, Xu Chen, Ran Yu and Fengqi Guo

Mathematics 2024, 12(16), 2581; https://doi.org/10.3390/math12162581 - 21 Aug 2024

Cited by 1 | Viewed by 581

Abstract

Accurately predicting wind speeds is of great significance in various engineering applications, such as the operation of high-speed trains. Machine learning models are effective in this field. However, existing studies generally provide deterministic predictions and utilize decomposition techniques in advance to enhance predictive [...] Read more.

Accurately predicting wind speeds is of great significance in various engineering applications, such as the operation of high-speed trains. Machine learning models are effective in this field. However, existing studies generally provide deterministic predictions and utilize decomposition techniques in advance to enhance predictive performance, which may encounter data leakage and fail to capture the stochastic nature of wind data. This work proposes an advanced framework for the prediction and early warning of wind speeds by combining the optimized gated recurrent unit (GRU) and adaptive kernel density estimator (AKDE). Firstly, 12 samples (26,280 points each) were collected from an extensive open database. Three representative metaheuristic algorithms were then employed to optimize the parameters of diverse models, including extreme learning machines, a transformer model, and recurrent networks. The results yielded an optimal selection using the GRU and the crested porcupine optimizer. Afterwards, by using the AKDE, the joint probability density and cumulative distribution function of wind predictions and related predicting errors could be obtained. It was then applicable to calculate the conditional probability that actual wind speed exceeds the critical value, thereby providing probabilistic-based predictions in a multilevel manner. A comparison of the predictive performance of various methods and accuracy of subsequent decisions validated the proposed framework. Full article

(This article belongs to the Special Issue Statistical Data Modeling and Machine Learning with Applications, 3rd Edition)

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14 pages, 3993 KiB

Open AccessArticle

The Optimization of Picking in Logistics Warehouses in the Event of Sudden Picking Order Changes and Picking Route Blockages

by Daiki Ueno and Enna Hirata

Mathematics 2024, 12(16), 2580; https://doi.org/10.3390/math12162580 - 21 Aug 2024

Viewed by 802

Abstract

(1) Background: This work focuses on improving the efficiency of warehouse operations with the goal of promoting efficiency in the logistics industry and mitigating logistics-related labor shortages. Many factors are involved in warehouse operations, such as the optimal allocation of manpower, the optimal [...] Read more.

(1) Background: This work focuses on improving the efficiency of warehouse operations with the goal of promoting efficiency in the logistics industry and mitigating logistics-related labor shortages. Many factors are involved in warehouse operations, such as the optimal allocation of manpower, the optimal layout design, and the use of automatic guided vehicles, which together affect operational efficiency. (2) Methods: In this work, we developed an optimal method for operating a limited number of workers or picking robots in a specific area, coping with cases of sudden disruptions such as a change in picking order or the blockage of aisles. For this purpose, the number of pickers, the storage capacity, and other constraints such as sudden changes in picking orders during the picking process, as well as blockages in the aisles of a warehouse site, are considered. The total travel distance is minimized using Gurobi, an optimization solver. (3) Results: The picking routes were optimized in three different scenarios using the shortest route between the starting point and the picking points, resulting in up to a 31% efficiency improvement in terms of the total distance traveled. (4) Conclusions: The main contribution of this work is that it focuses on the day-to-day work situations of sudden changes in the picking order and the presence of route blocks in real-world logistics warehouse sites. It demonstrates the feasibility of responding to sudden disruptions and simultaneously optimizing picking routes in real time. This work contributes to the overall efficiency of logistics by providing a simple, yet practical, data-driven solution for the optimization of warehouse operations. Full article

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

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20 pages, 3823 KiB

Open AccessArticle

From Whence Commeth Data Misreporting? A Survey of Benford’s Law and Digit Analysis in the Time of the COVID-19 Pandemic

by Călin Vâlsan, Andreea-Ionela Puiu and Elena Druică

Mathematics 2024, 12(16), 2579; https://doi.org/10.3390/math12162579 - 21 Aug 2024

Viewed by 602

Abstract

We survey the literature on the use of Benford’s distribution digit analysis applied to COVID-19 case data reporting. We combine a bibliometric analysis of 32 articles with a survey of their content and findings. In spite of combined efforts from teams of researchers [...] Read more.

We survey the literature on the use of Benford’s distribution digit analysis applied to COVID-19 case data reporting. We combine a bibliometric analysis of 32 articles with a survey of their content and findings. In spite of combined efforts from teams of researchers across multiple countries and universities, using large data samples from a multitude of sources, there is no emerging consensus on data misreporting. We believe we are nevertheless able to discern a faint pattern in the segregation of findings. The evidence suggests that studies using very large, aggregate samples and a methodology based on hypothesis testing are marginally more likely to identify significant deviations from Benford’s distribution and to attribute this deviation to data tampering. Our results are far from conclusive and should be taken with a very healthy dose of skepticism. Academics and policymakers alike should remain mindful that the misreporting controversy is still far from being settled. Full article

(This article belongs to the Special Issue Statistics and Data Science)

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16 pages, 2006 KiB

Open AccessArticle

Weakly Supervised Specular Highlight Removal Using Only Highlight Images

by Yuanfeng Zheng, Guangwei Hu, Hao Jiang, Hao Wang and Lihua Wu

Mathematics 2024, 12(16), 2578; https://doi.org/10.3390/math12162578 - 21 Aug 2024

Viewed by 510

Abstract

Specular highlight removal is a challenging task in the field of image enhancement, while it can significantly improve the quality of image in highlight regions. Recently, deep learning-based methods have been widely adopted in this task, demonstrating excellent performance by training on either [...] Read more.

Specular highlight removal is a challenging task in the field of image enhancement, while it can significantly improve the quality of image in highlight regions. Recently, deep learning-based methods have been widely adopted in this task, demonstrating excellent performance by training on either massive paired data, wherein both the highlighted and highlight-free versions of the same image are available, or unpaired datasets where the one-to-one correspondence is inapplicable. However, it is difficult to obtain the corresponding highlight-free version of a highlight image, as the latter has already been produced under specific lighting conditions. In this paper, we propose a method for weakly supervised specular highlight removal that only requires highlight images. This method involves generating highlight-free images from highlight images with the guidance of masks estimated using non-negative matrix factorization (NMF). These highlight-free images are then fed consecutively into a series of modules derived from a Cycle Generative Adversarial Network (Cycle-GAN)-style network, namely the highlight generation, highlight removal, and reconstruction modules in sequential order. These modules are trained jointly, resulting in a highly effective highlight removal module during the verification. On the specular highlight image quadruples (SHIQ) and the LIME datasets, our method achieves an accuracy of 0.90 and a balance error rate (BER) of 8.6 on SHIQ, and an accuracy of 0.89 and a BER of 9.1 on LIME, outperforming existing methods and demonstrating its potential for improving image quality in various applications. Full article

(This article belongs to the Special Issue Advances in Applied Mathematics in Computer Vision)

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11 pages, 252 KiB

Open AccessArticle

The Global Existence and Boundedness of Solutions to a Chemotaxis–Haptotaxis Model with Nonlinear Diffusion and Signal Production

by Beibei Ai and Zhe Jia

Mathematics 2024, 12(16), 2577; https://doi.org/10.3390/math12162577 - 21 Aug 2024

Viewed by 497

Abstract

In this paper, we investigate the following chemotaxis–haptotaxis system (1) with nonlinear diffusion and signal production under homogenous Neumann boundary conditions in a bounded domain with smooth boundary. Under suitable conditions on the data we prove the following: (i) For [...] Read more.

In this paper, we investigate the following chemotaxis–haptotaxis system (1) with nonlinear diffusion and signal production under homogenous Neumann boundary conditions in a bounded domain with smooth boundary. Under suitable conditions on the data we prove the following: (i) For

0 < γ \leq \frac{2}{n}

, if

α > γ - k + 1

and

β > 1 - k

, problem (1) admits a classical solution

(u, v, w)

which is globally bounded. (ii) For

\frac{2}{n} < γ \leq 1

, if

α > γ - k + \frac{1}{e} + 1

and

β > max {\frac{(n γ - 2) (n γ + 2 k - 2)}{2 n} - k + 1, \frac{(n γ - 2) (γ + \frac{1}{e})}{n} - k + 1}

or

α > γ - k + 1

and

β > max {\frac{(n γ - 2) (n γ + 2 k - 2)}{2 n} - k + 1, \frac{(n γ - 2) (α + k - 1)}{n} - k + 1}

, problem (1) admits a classical solution

(u, v, w)

which is globally bounded. Full article

(This article belongs to the Special Issue Recent Advances in Complex Dynamics in Non-Smooth Systems)

41 pages, 7497 KiB

Open AccessReview

Review of Fault-Tolerant Control Methods for Suspension Systems: From Road Vehicles to Maglev Trains

by Fei Ni, Yifan Luo, Junqi Xu, Dachuan Liu, Yougang Sun and Wen Ji

Mathematics 2024, 12(16), 2576; https://doi.org/10.3390/math12162576 - 20 Aug 2024

Viewed by 970

Abstract

Road vehicles and maglev trains have garnered significant attention, with their suspension systems being crucial for safe and stable performance. However, these systems can be compromised by faults such as sensor and actuator failures, posing risks to stability and safety. This review explores [...] Read more.

Road vehicles and maglev trains have garnered significant attention, with their suspension systems being crucial for safe and stable performance. However, these systems can be compromised by faults such as sensor and actuator failures, posing risks to stability and safety. This review explores fault-tolerant controls for suspension systems, driven by the need to enhance fault tolerance in such scenarios. We examine the dynamic similarities between the semi-active/active suspension systems in road vehicles and the suspension systems in maglev trains, offering a comprehensive summary of fault-tolerant control strategies for both. Our analysis covers the histories, technical characteristics, fundamentals, modeling, mathematical derivations, and control objectives of both systems. The review categorizes fault-tolerant control methods into hardware redundancy, passive fault-tolerant control, and active fault-tolerant control. We evaluate the advantages and disadvantages of these strategies and propose future directions for the development of fault-tolerant control in suspension systems. Full article

(This article belongs to the Section Computational and Applied Mathematics)

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30 pages, 12231 KiB

Open AccessArticle

Co-Evolutionary Algorithm for Two-Stage Hybrid Flow Shop Scheduling Problem with Suspension Shifts

by Zhijie Huang, Lin Huang and Debiao Li

Mathematics 2024, 12(16), 2575; https://doi.org/10.3390/math12162575 - 20 Aug 2024

Viewed by 713

Abstract

Demand fluctuates in actual production. When manufacturers face demand under their maximum capacity, suspension shifts are crucial for cost reduction and on-time delivery. In this case, suspension shifts are needed to minimize idle time and prevent inventory buildup. Thus, it is essential to [...] Read more.

Demand fluctuates in actual production. When manufacturers face demand under their maximum capacity, suspension shifts are crucial for cost reduction and on-time delivery. In this case, suspension shifts are needed to minimize idle time and prevent inventory buildup. Thus, it is essential to integrate suspension shifts with scheduling under an uncertain production environment. This paper addresses the two-stage hybrid flow shop scheduling problem (THFSP) with suspension shifts under uncertain processing times, aiming to minimize the weighted sum of earliness and tardiness. We develop a stochastic integer programming model and validate it using the Gurobi solver. Additionally, we propose a dual-space co-evolutionary biased random key genetic algorithm (DCE-BRKGA) with parallel evolution of solutions and scenarios. Considering decision-makers’ risk preferences, we use both average and pessimistic criteria for fitness evaluation, generating two types of solutions and scenario populations. Testing with 28 datasets, we use the value of the stochastic solution (VSS) and the expected value of perfect information (EVPI) to quantify benefits. Compared to the average scenario, the VSS shows that the proposed algorithm achieves additional value gains of 0.9% to 69.9%. Furthermore, the EVPI indicates that after eliminating uncertainty, the algorithm yields potential improvements of 2.4% to 20.3%. These findings indicate that DCE-BRKGA effectively supports varying decision-making risk preferences, providing robust solutions even without known processing time distributions. Full article

(This article belongs to the Section Engineering Mathematics)

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30 pages, 9253 KiB

Open AccessArticle

Bayesian Deep Learning and Bayesian Statistics to Analyze the European Countries’ SARS-CoV-2 Policies

by Hamed Khalili, Maria A. Wimmer and Ulf Lotzmann

Mathematics 2024, 12(16), 2574; https://doi.org/10.3390/math12162574 - 20 Aug 2024

Viewed by 789

Abstract

Even if the SARS-CoV-2 pandemic recedes, research regarding the effectiveness of government policies to contain the spread of the pandemic remains important. In this study, we analyze the impact of a set of epidemiological factors on the spread of SARS-CoV-2 in 30 European [...] Read more.

Even if the SARS-CoV-2 pandemic recedes, research regarding the effectiveness of government policies to contain the spread of the pandemic remains important. In this study, we analyze the impact of a set of epidemiological factors on the spread of SARS-CoV-2 in 30 European countries, which were applied from early 2020 up to mid-2022. We combine four data sets encompassing each country’s non-pharmaceutical interventions (NPIs, including 66 government intervention types), distributions of 31 virus types, and accumulated percentage of vaccinated population (by the first five doses) as well as the reported infections, each on a daily basis. First, a Bayesian deep learning model is trained to predict the reproduction rate of the virus one month ahead of each day. Based on the trained deep learning model, the importance of relevant influencing factors and the magnitude of their effects on the outcome of the neural network model are computed by applying explainable machine learning algorithms. Second, in order to re-examine the results of the deep learning model, a Bayesian statistical analysis is implemented. In the statistical analysis, for each influencing input factor in each country, the distributions of pandemic growth rates are compared for days where the factor was active with days where the same factor was not active. The results of the deep learning model and the results of the statistical inference model coincide to a significant extent. We conclude with reflections with regard to the most influential factors on SARS-CoV-2 spread within European countries. Full article

(This article belongs to the Special Issue Current Research in Biostatistics)

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Mathematics, Volume 12, Issue 16 (August-2 2024) – 170 articles

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