Mathematics

29 pages, 3855 KiB

Open AccessArticle

Inferring Complementary and Substitutable Products Based on Knowledge Graph Reasoning

by Yan Fang, Jiayin Yu, Yumei Ding and Xiaohua Lin

Mathematics 2023, 11(22), 4709; https://doi.org/10.3390/math11224709 - 20 Nov 2023

Viewed by 1361

Complementarity and substitutability between products are essential concepts in retail and marketing. To achieve this, existing approaches take advantage of knowledge graphs to learn more evidence for inference. However, they often omit the knowledge that lies in the unstructured data. In this research, [...] Read more.

Complementarity and substitutability between products are essential concepts in retail and marketing. To achieve this, existing approaches take advantage of knowledge graphs to learn more evidence for inference. However, they often omit the knowledge that lies in the unstructured data. In this research, we concentrate on inferring complementary and substitutable products in e-commerce from mass structured and unstructured data. An improved knowledge-graph-based reasoning model has been proposed which cannot only derive related products but also provide interpretable paths to explain the relationship. The methodology employed in our study unfolds through several stages. First, a knowledge graph refining entities and relationships from data was constructed. Second, we developed a two-stage knowledge representation learning method to better represent the structured and unstructured knowledge based on TransE and SBERT. Then, the relationship inferring problem was converted into a path reasoning problem under the Markov decision process environment by learning a dynamic policy network. We also applied a soft pruning strategy and a modified reward function to improve the effectiveness of the policy network training. We demonstrate the effectiveness of the proposed method on standard Amazon datasets, and it gives about 5–15% relative improvement over the state-of-the-art models in terms of NDCG@10, Recall@10, Precision @10, and HR@10. Full article

(This article belongs to the Special Issue Advances in Business Intelligence: Theoretical and Empirical Issues)

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27 pages, 2341 KiB

Open AccessArticle

An Algorithm That Adjusts the Stepsize to Be Self-Adaptive with an Inertial Term Aimed for Solving Split Variational Inclusion and Common Fixed Point Problems

by Matlhatsi Dorah Ngwepe, Lateef Olakunle Jolaoso, Maggie Aphane and Ibrahim Oyeyemi Adenekan

Mathematics 2023, 11(22), 4708; https://doi.org/10.3390/math11224708 - 20 Nov 2023

Cited by 1 | Viewed by 944

Abstract

In this research paper, we present a new inertial method with a self-adaptive technique for solving the split variational inclusion and fixed point problems in real Hilbert spaces. The algorithm is designed to choose the optimal choice of the inertial term at every [...] Read more.

In this research paper, we present a new inertial method with a self-adaptive technique for solving the split variational inclusion and fixed point problems in real Hilbert spaces. The algorithm is designed to choose the optimal choice of the inertial term at every iteration, and the stepsize is defined self-adaptively without a prior estimate of the Lipschitz constant. A convergence theorem is demonstrated to be strong even under lenient conditions and to showcase the suggested method’s efficiency and precision. Some numerical tests are given. Moreover, the significance of the proposed method is demonstrated through its application to an image reconstruction issue. Full article

(This article belongs to the Special Issue Advances in Fixed Point Theory and Its Applications)

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18 pages, 332 KiB

Open AccessArticle

Noisy Tree Data Structures and Quantum Applications

by Kamil Khadiev, Nikita Savelyev, Mansur Ziatdinov and Denis Melnikov

Mathematics 2023, 11(22), 4707; https://doi.org/10.3390/math11224707 - 20 Nov 2023

Cited by 2 | Viewed by 1194

Abstract

We suggest a new technique for developing noisy tree data structures. We call it a “walking tree”. As applications of the technique we present a noisy Self-Balanced Binary Search Tree (we use a Red–Black tree as an implementation) and a noisy segment tree. [...] Read more.

We suggest a new technique for developing noisy tree data structures. We call it a “walking tree”. As applications of the technique we present a noisy Self-Balanced Binary Search Tree (we use a Red–Black tree as an implementation) and a noisy segment tree. The asymptotic complexity of the main operations for the tree data structures does not change compared to the case without noise. We apply the data structures in quantum algorithms for several problems on strings like the string-sorting problem and auto-complete problem. For both problems, we obtain quantum speed-up. Moreover, for the string-sorting problem, we show a quantum lower bound. Full article

(This article belongs to the Special Issue Quantum Algorithms and Quantum Computing)

24 pages, 930 KiB

Open AccessArticle

Analysis of Fluctuating Antenna Beamwidth in UAV-Assisted Cellular Networks

by Mohammad Arif and Wooseong Kim

Mathematics 2023, 11(22), 4706; https://doi.org/10.3390/math11224706 - 20 Nov 2023

Cited by 3 | Viewed by 1046

Abstract

This paper investigates a cellular network assisted by unmanned aerial vehicles (UAVs) in the presence of a fluctuating 3-dimensional (3D) antenna beamwidth. The primary objective is to perform an analysis of typical user equipment (T-UE) performance with a specific focus on coverage probability [...] Read more.

This paper investigates a cellular network assisted by unmanned aerial vehicles (UAVs) in the presence of a fluctuating 3-dimensional (3D) antenna beamwidth. The primary objective is to perform an analysis of typical user equipment (T-UE) performance with a specific focus on coverage probability and spectral efficiency (SE) in the presence of fluctuations of 3D antenna beamwidth. Within this analytical framework, the macro base stations (MBSs) are meticulously characterized through the application of an independent 2D homogeneous Poisson point process (PPP), while the low-altitude platforms (LAPs) are described using an independent 3D PPP. The study entails the derivation of association probabilities, determining the likelihood of the T-UE associating with MBSs, line-of-sight LAPs, and non-line-of-sight LAPs. Through rigorous mathematical analysis, the paper formulates precise analytical expressions that encapsulate the association and coverage probabilities, taking into account the inherent variability in the UAV antenna beamwidth. This research focuses on a thorough performance evaluation of the T-UE across diverse network configurations, encompassing LAP density, the transmission power of LAPs, and the critical signal-to-interference ratio threshold. The outcomes of this study distinctly underscore the substantial disruptive impact resulting from fluctuating beamwidth on the performance of the T-UE within the UAV-assisted cellular network. Additionally, this performance is further impacted by larger densities and transmission power of the LAP. Hence, it is imperative to take into account the influence of these fluctuations on network association, coverage, and SE whenever contemplating a UAV-assisted cellular network. Full article

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

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17 pages, 327 KiB

Open AccessArticle

Scheduling of Software Test to Minimize the Total Completion Time

by Man-Ting Chao and Bertrand M. T. Lin

Mathematics 2023, 11(22), 4705; https://doi.org/10.3390/math11224705 - 20 Nov 2023

Cited by 1 | Viewed by 1119

Abstract

This paper investigates a single-machine scheduling problem of a software test with shared common setup operations. Each job has a corresponding set of setup operations, and the job cannot be executed unless its setups are completed. If two jobs have the same supporting [...] Read more.

This paper investigates a single-machine scheduling problem of a software test with shared common setup operations. Each job has a corresponding set of setup operations, and the job cannot be executed unless its setups are completed. If two jobs have the same supporting setups, the common setups are performed only once. No preemption of any processing is allowed. This problem is known to be computationally intractable. In this study, we propose sequence-based and position-based integer programming models and a branch-and-bound algorithm for finding optimal solutions. We also propose an ant colony optimization algorithm for finding approximate solutions, which will be used as the initial upper bound of the branch-and-bound algorithm. The computational experiments are designed and conducted to numerically appraise all of the proposed methods. Full article

(This article belongs to the Special Issue Recent Advances of Disсrete Optimization and Scheduling)

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16 pages, 659 KiB

Open AccessArticle

Improving the Performance of Optimization Algorithms Using the Adaptive Fixed-Time Scheme and Reset Scheme

by Yuquan Chen, Yunkang Sun and Bing Wang

Mathematics 2023, 11(22), 4704; https://doi.org/10.3390/math11224704 - 20 Nov 2023

Cited by 1 | Viewed by 1008

Abstract

Optimization algorithms have now played an important role in many fields, and the issue of how to design high-efficiency algorithms has gained increasing attention, for which it has been shown that advanced control theories could be helpful. In this paper, the fixed-time scheme [...] Read more.

Optimization algorithms have now played an important role in many fields, and the issue of how to design high-efficiency algorithms has gained increasing attention, for which it has been shown that advanced control theories could be helpful. In this paper, the fixed-time scheme and reset scheme are introduced to design high-efficiency gradient descent methods for unconstrained convex optimization problems. At first, a general reset framework for existing accelerated gradient descent methods is given based on the systematic representation, with which both convergence speed and stability are significantly improved. Then, the design of a novel adaptive fixed-time gradient descent, which has fewer tuning parameters and maintains better robustness to initial conditions, is presented. However, its discrete form introduces undesirable overshoot and easily leads to instability, and the reset scheme is then applied to overcome the drawbacks. The linear convergence and better stability of the proposed algorithms are theoretically proven, and several dedicated simulation examples are finally given to validate the effectiveness. Full article

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21 pages, 14317 KiB

Open AccessReview

Exploring the Contributions to Mathematical Economics: A Bibliometric Analysis Using Bibliometrix and VOSviewer

by Kyriaki Tsilika

Mathematics 2023, 11(22), 4703; https://doi.org/10.3390/math11224703 - 20 Nov 2023

Cited by 5 | Viewed by 2257

Abstract

From Cournot, Walras, and Pareto’s research to what followed in the form of marginalist economics, chaos theory, agent-based modeling, game theory, and econophysics, the interpretation and analysis of economic systems have been carried out using a broad range of higher mathematics methods. The [...] Read more.

From Cournot, Walras, and Pareto’s research to what followed in the form of marginalist economics, chaos theory, agent-based modeling, game theory, and econophysics, the interpretation and analysis of economic systems have been carried out using a broad range of higher mathematics methods. The evolution of mathematical economics is associated with the most productive and influential authors, sources, and countries, as well as the identification of interactions between the authors and research topics. Bibliometric analysis provides journal-, author-, document-, and country-level metrics. In the present study, a bibliometric overview of mathematical economics came from a screening performed in September 2023, covering the timespan 1898–2023. About 6477 documents on mathematical economics were retrieved and extracted from the Scopus academic database for analysis. The Bibliometrix package in the statistical programming language R was employed to perform a bibliometric analysis of scientific literature and citation data indexed in the Scopus database. VOSviewer (version 1.6.19) was used for the visualization of similarities using several bibliometric techniques, including bibliographic coupling, co-citation, and co-occurrence of keywords. The analysis traced the most influential papers, keywords, countries, and journals among high-quality studies in mathematical economics. Full article

(This article belongs to the Special Issue Latest Advances in Mathematical Economics)

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14 pages, 337 KiB

Open AccessFeature PaperArticle

Terracini Loci: Dimension and Description of Its Components

by Edoardo Ballico

Mathematics 2023, 11(22), 4702; https://doi.org/10.3390/math11224702 - 20 Nov 2023

Cited by 2 | Viewed by 804

Abstract

We study the Terracini loci of an irreducible variety X embedded in a projective space: non-emptiness, dimensions and the geometry of their maximal dimension’s irreducible components. These loci were studied because they describe where the differential of an important geometric map drops rank. [...] Read more.

We study the Terracini loci of an irreducible variety X embedded in a projective space: non-emptiness, dimensions and the geometry of their maximal dimension’s irreducible components. These loci were studied because they describe where the differential of an important geometric map drops rank. Our best results are if X is either a Veronese embedding of a projective space of arbitrary dimension (the set-up for the additive decomposition of homogeneous polynomials) or a Segre–Veronese embedding of a multiprojective space (the set-up for partially symmetric tensors). For an arbitrary X, we give several examples in which all Terracini loci are empty, several criteria for non-emptiness and examples with the maximal defect possible a priori of an element of a minimal Terracini locus. We raise a few open questions. Full article

14 pages, 300 KiB

Open AccessArticle

A New Class of Leonardo Hybrid Numbers and Some Remarks on Leonardo Quaternions over Finite Fields

by Elif Tan, Diana Savin and Semih Yılmaz

Mathematics 2023, 11(22), 4701; https://doi.org/10.3390/math11224701 - 20 Nov 2023

Cited by 7 | Viewed by 1153

Abstract

In this paper, we present a new class of Leonardo hybrid numbers that incorporate quantum integers into their components. This advancement presents a broader generalization of the q-Leonardo hybrid numbers. We explore some fundamental properties associated with these numbers. Moreover, we study [...] Read more.

In this paper, we present a new class of Leonardo hybrid numbers that incorporate quantum integers into their components. This advancement presents a broader generalization of the q-Leonardo hybrid numbers. We explore some fundamental properties associated with these numbers. Moreover, we study special Leonardo quaternions over finite fields. In particular, we determine the Leonardo quaternions that are zero divisors or invertible elements in the quaternion algebra over the finite field

Z_{p}

for special values of prime integer p. Full article

(This article belongs to the Special Issue Algebraic, Analytic, and Computational Number Theory and Its Applications)

17 pages, 2094 KiB

Open AccessArticle

Improved Self-Learning Genetic Algorithm for Solving Flexible Job Shop Scheduling

by Ming Jiang, Haihan Yu and Jiaqing Chen

Mathematics 2023, 11(22), 4700; https://doi.org/10.3390/math11224700 - 20 Nov 2023

Cited by 1 | Viewed by 2091

Abstract

The flexible job shop scheduling problem (FJSP), one of the core problems in the field of generative manufacturing process planning, has become a hotspot and a challenge in manufacturing production research. In this study, an improved self-learning genetic algorithm is proposed. The single [...] Read more.

The flexible job shop scheduling problem (FJSP), one of the core problems in the field of generative manufacturing process planning, has become a hotspot and a challenge in manufacturing production research. In this study, an improved self-learning genetic algorithm is proposed. The single mutation approach of the genetic algorithm was improved, while four mutation operators were designed on the basis of process coding and machine coding; their weights were updated and their selection mutation operators were adjusted according to the performance in the iterative process. Combined with the improved population initialization method and the optimized crossover strategy, the local search capability was enhanced, and the convergence speed was accelerated. The effectiveness and feasibility of the algorithm were verified by testing the benchmark arithmetic examples and numerical experiments. Full article

(This article belongs to the Special Issue Advances and Applications on Fuzzy Logic for Decision Making Processes)

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13 pages, 1465 KiB

Open AccessArticle

A Reduced-Dimension Extrapolating Method of Finite Element Solution Coefficient Vectors for Fractional Tricomi-Type Equation

by Yuejie Li and Zhendong Luo

Mathematics 2023, 11(22), 4699; https://doi.org/10.3390/math11224699 - 20 Nov 2023

Viewed by 825

Abstract

We here employ a proper orthogonal decomposition (POD) to reduce the dimensionality of unknown coefficient vectors of finite element (FE) solutions for the fractional Tricomi-type equation and develop a reduced-dimension extrapolating FE (RDEFE) method for the fractional Tricomi-type equation. For this purpose, we [...] Read more.

We here employ a proper orthogonal decomposition (POD) to reduce the dimensionality of unknown coefficient vectors of finite element (FE) solutions for the fractional Tricomi-type equation and develop a reduced-dimension extrapolating FE (RDEFE) method for the fractional Tricomi-type equation. For this purpose, we first develop an FE method for the fractional Tricomi-type equation and provide the existence, unconditional stability, and error analysis for the FE solutions. We then develop the RDEFE method for the fractional Tricomi-type equation by means of the POD technique and analyze the existence, unconditional stability, and errors for the RDEFE solutions by using the matrix analysis. Lastly, we provide two numerical examples to verify our theoretical results and to explain the advantages of the RDEFE method. Full article

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

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31 pages, 7299 KiB

Open AccessArticle

Developing System-Based Artificial Intelligence Models for Detecting the Attention Deficit Hyperactivity Disorder

by Hasan Alkahtani, Theyazn H. H. Aldhyani, Zeyad A. T. Ahmed and Ahmed Abdullah Alqarni

Mathematics 2023, 11(22), 4698; https://doi.org/10.3390/math11224698 - 20 Nov 2023

Cited by 2 | Viewed by 2679

Abstract

This study presents a novel methodology for automating the classification of pediatric ADHD using electroencephalogram (EEG) biomarkers through machine learning and deep learning techniques. The primary objective is to develop accurate EEG-based screening tools to aid clinical diagnosis and enable early intervention for [...] Read more.

This study presents a novel methodology for automating the classification of pediatric ADHD using electroencephalogram (EEG) biomarkers through machine learning and deep learning techniques. The primary objective is to develop accurate EEG-based screening tools to aid clinical diagnosis and enable early intervention for ADHD. The proposed system utilizes a publicly available dataset consisting of raw EEG recordings from 61 individuals with ADHD and 60 control subjects during a visual attention task. The methodology involves meticulous preprocessing of raw EEG recordings to isolate brain signals and extract informative features, including time, frequency, and entropy signal characteristics. The feature selection techniques, including least absolute shrinkage and selection operator (LASSO) regularization and recursive elimination, were applied to identify relevant variables and enhance generalization. The obtained features are processed by employing various machine learning and deep learning algorithms, namely CatBoost, Random Forest Decision Trees, Convolutional Neural Networks (CNNs), and Long Short-Term Memory Networks (LSTMs). The empirical results of the proposed algorithms highlight the effectiveness of feature selection approaches in matching informative biomarkers with optimal model classes. The convolutional neural network model achieves superior testing accuracy of 97.75% using LASSO-regularized biomarkers, underscoring the strengths of deep learning and customized feature optimization. The proposed framework advances EEG analysis to uncover discriminative patterns, significantly contributing to the field of ADHD screening and diagnosis. The suggested methodology achieved high performance compared with different existing systems based on AI approaches for diagnosing ADHD. Full article

(This article belongs to the Special Issue Advanced Artificial Intelligence Models and Its Applications, 2nd Edition)

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10 pages, 278 KiB

Open AccessArticle

Hyperconnectedness and Resolvability of Soft Ideal Topological Spaces

by Ahmad Al-Omari and Wafa Alqurashi

Mathematics 2023, 11(22), 4697; https://doi.org/10.3390/math11224697 - 19 Nov 2023

Cited by 2 | Viewed by 1252

Abstract

This paper introduces and explores the concept of soft ideal dense sets, utilizing soft open sets and soft local functions, to examine their fundamental characteristics under some conditions for the following notions: soft ideal hyperconnectedness, soft ideal resolvability, soft ideal irresolvability, and soft [...] Read more.

This paper introduces and explores the concept of soft ideal dense sets, utilizing soft open sets and soft local functions, to examine their fundamental characteristics under some conditions for the following notions: soft ideal hyperconnectedness, soft ideal resolvability, soft ideal irresolvability, and soft ideal semi-irresolvability in soft ideal topological spaces. Moreover, it explores the relationship between these notions if

τ ⊓ \bar{I} = ϕ_{E}

is obtained in the soft set environment. Full article

(This article belongs to the Special Issue Advances and Applications of Soft Computing)

19 pages, 3109 KiB

Open AccessArticle

On the State-Feedback Controller Design for Polynomial Linear Parameter-Varying Systems with Pole Placement within Linear Matrix Inequality Regions

by Jorge A. Brizuela-Mendoza, Juan Carlos Mixteco-Sánchez, Maria A. López-Osorio, Gerardo Ortiz-Torres, Felipe D. J. Sorcia-Vázquez, Ricardo Eliú Lozoya-Ponce, Moises B. Ramos-Martínez, Alan F. Pérez-Vidal, Jesse Y. Rumbo Morales, Cesar H. Guzmán-Valdivia, Mayra G. Mena-Enriquez and Carlos Alberto Torres-Cantero

Mathematics 2023, 11(22), 4696; https://doi.org/10.3390/math11224696 - 19 Nov 2023

Viewed by 1160

Abstract

The present paper addresses linear parameter-varying systems with high-order time-varying parameter dependency known as polynomial LPV systems and their controller design. Throughout this work, a procedure ensuring a state-feedback controller from a parameterized linear matrix inequality (PLMI) solution is presented. As the main [...] Read more.

The present paper addresses linear parameter-varying systems with high-order time-varying parameter dependency known as polynomial LPV systems and their controller design. Throughout this work, a procedure ensuring a state-feedback controller from a parameterized linear matrix inequality (PLMI) solution is presented. As the main contribution of this paper, the controller is designed by considering the time-varying parameter rate as a tuning parameter with a continuous control gain in such a way that the closed-loop eigenvalues lie in a complex plane subset, with high-order time-varying parameters defining the system dynamics. Simulation results are presented, aiming to show the effectiveness of the proposed controller design. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Automatic Control)

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18 pages, 10242 KiB

Open AccessArticle

Gaussian Process-Based Transfer Kernel Learning for Unsupervised Domain Adaptation

by Pengfei Ge and Yesen Sun

Mathematics 2023, 11(22), 4695; https://doi.org/10.3390/math11224695 - 19 Nov 2023

Cited by 3 | Viewed by 1399

Abstract

The discriminability and transferability of models are two important factors for the success of domain adaptation methods. Recently, some domain adaptation methods have improved models by adding a discriminant information extraction module. However, these methods need to carefully balance the discriminability and transferability [...] Read more.

The discriminability and transferability of models are two important factors for the success of domain adaptation methods. Recently, some domain adaptation methods have improved models by adding a discriminant information extraction module. However, these methods need to carefully balance the discriminability and transferability of a model. To address this problem, we propose a new deep domain adaptation method, Gaussian Process-based Transfer Kernel Learning (GPTKL), which can perform domain knowledge transfer and improve the discrimination ability of the model simultaneously. GPTKL uses the kernel similarity between all samples in the source and target domains as a priori information to establish a cross-domain Gaussian process. By maximizing its likelihood function, GPTKL reduces the domain discrepancy between the source and target domains, thereby enhancing generalization across domains. At the same time, GPTKL introduces the deep kernel learning strategy into the cross-domain Gaussian process to learn a transfer kernel function based on deep features. Through transfer kernel learning, GPTKL learns a deep feature space with both discriminability and transferability. In addition, GPTKL uses cross-entropy and mutual information to learn a classification model shared by the source and target domains. Experiments on four benchmarks show that GPTKL achieves superior classification performance over state-of-the-art methods. Full article

(This article belongs to the Special Issue Application of Machine Learning in Image Processing and Computer Vision)

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11 pages, 287 KiB

Open AccessArticle

Applications to Solving Variational Inequality Problems via MR-Kannan Type Interpolative Contractions

by Rizwan Anjum, Andreea Fulga and Muhammad Waqar Akram

Mathematics 2023, 11(22), 4694; https://doi.org/10.3390/math11224694 - 19 Nov 2023

Viewed by 964

Abstract

The aim of this paper is manifold. We first define the new class of operators called MR-Kannan interpolative type contractions, which includes the Kannan, enriched Kannan, interpolative Kannan type, and enriched interpolative Kannan type operators. Secondly, we prove the existence of a unique [...] Read more.

The aim of this paper is manifold. We first define the new class of operators called MR-Kannan interpolative type contractions, which includes the Kannan, enriched Kannan, interpolative Kannan type, and enriched interpolative Kannan type operators. Secondly, we prove the existence of a unique fixed point for this class of operators. Thirdly, we study Ulam-Hyers stability, well-posedness, and periodic point properties. Finally, an application of the main results to the variational inequality problem is given. Full article

(This article belongs to the Special Issue New Advances in Fuzzy Metric Spaces, Soft Metric Spaces, and Other Related Structures, 2nd Edition)

33 pages, 6791 KiB

Open AccessArticle

Power Transformer Fault Diagnosis Using Neural Network Optimization Techniques

by Vasiliki Rokani, Stavros D. Kaminaris, Petros Karaisas and Dimitrios Kaminaris

Mathematics 2023, 11(22), 4693; https://doi.org/10.3390/math11224693 - 19 Nov 2023

Cited by 9 | Viewed by 2724

Abstract

Artificial Intelligence (AI) techniques are considered the most advanced approaches for diagnosing faults in power transformers. Dissolved Gas Analysis (DGA) is the conventional approach widely adopted for diagnosing incipient faults in power transformers. The IEC-599 standard Ratio Method is an accurate method that [...] Read more.

Artificial Intelligence (AI) techniques are considered the most advanced approaches for diagnosing faults in power transformers. Dissolved Gas Analysis (DGA) is the conventional approach widely adopted for diagnosing incipient faults in power transformers. The IEC-599 standard Ratio Method is an accurate method that evaluates the DGA. All the classical approaches have limitations because they cannot diagnose all faults accurately. Precisely diagnosing defects in power transformers is a significant challenge due to their extensive quantity and dispersed placement within the power network. To deal with this concern and to improve the reliability and precision of fault diagnosis, different Artificial Intelligence techniques are presented. In this manuscript, an artificial neural network (ANN) is implemented to enhance the accuracy of the Rogers Ratio Method. On the other hand, it should be noted that the complexity of an ANN demands a large amount of storage and computing power. In order to address this issue, an optimization technique is implemented with the objective of maximizing the accuracy and minimizing the architectural complexity of an ANN. All the procedures are simulated using the MATLAB R2023a software. Firstly, the authors choose the most effective classification model by automatically training five classifiers in the Classification Learner app (CLA). After selecting the artificial neural network (ANN) as the sufficient classification model, we trained 30 ANNs with different parameters and determined the 5 models with the best accuracy. We then tested these five ANNs using the Experiment Manager app and ultimately selected the ANN with the best performance. The network structure is determined to consist of three layers, taking into consideration both diagnostic accuracy and computing efficiency. Ultimately, a (100-50-5) layered ANN was selected to optimize its hyperparameters. As a result, following the implementation of the optimization techniques, the suggested ANN exhibited a high level of accuracy, up to 90.7%. The conclusion of the proposed model indicates that the optimization of hyperparameters and the increase in the number of data samples enhance the accuracy while minimizing the complexity of the ANN. The optimized ANN is simulated and tested in MATLAB R2023a—Deep Network Designer, resulting in an accuracy of almost 90%. Moreover, compared to the Rogers Ratio Method, which exhibits an accuracy rate of just 63.3%, this approach successfully addresses the constraints associated with the conventional Rogers Ratio Method. So, the ANN has evolved a supremacy diagnostic method in the realm of power transformer fault diagnosis. Full article

(This article belongs to the Special Issue Artificial Intelligence Techniques Applications on Power Systems)

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25 pages, 316 KiB

Open AccessArticle

A Two-Server Queue with Interdependence between Arrival and Service Processes

by Sindhu S, Achyutha Krishnamoorthy and Dmitry Kozyrev

Mathematics 2023, 11(22), 4692; https://doi.org/10.3390/math11224692 - 18 Nov 2023

Cited by 2 | Viewed by 2330

Abstract

In this paper, we analyse a queueing system with two servers where the arrival and service processes are interdependent. The evolution of these processes is governed by transitions on the product space of three Markov chains, which are descriptors of the arrival and [...] Read more.

In this paper, we analyse a queueing system with two servers where the arrival and service processes are interdependent. The evolution of these processes is governed by transitions on the product space of three Markov chains, which are descriptors of the arrival and service processes. The transitions in this Markov chain follow a semi-Markov rule and the exponential distribution governs the sojourn times in the states. The stability condition of the system is derived and the stationary distribution is calculated for the system in equilibrium. Several important performance measures are provided, and numerical illustrations of the model are presented. Full article

(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks, 2nd Edition)

23 pages, 675 KiB

Open AccessArticle

Fourier Transform of the Lippmann-Schwinger Equation: Solving Vectorial Electromagnetic Scattering by Arbitrary Shapes

by Frederic Gruy, Victor Rabiet and Mathias Perrin

Mathematics 2023, 11(22), 4691; https://doi.org/10.3390/math11224691 - 18 Nov 2023

Viewed by 1316

Abstract

In Electromagnetics, the field scattered by an ensemble of particles—of arbitrary size, shape, and material—can be obtained by solving the Lippmann–Schwinger equation. This singular vectorial integral equation is generally formulated in the direct space

R^{n}

(typically

n = 2

or [...] Read more.

In Electromagnetics, the field scattered by an ensemble of particles—of arbitrary size, shape, and material—can be obtained by solving the Lippmann–Schwinger equation. This singular vectorial integral equation is generally formulated in the direct space

R^{n}

(typically

n = 2

or

n = 3

). In the article, we rigorously computed the Fourier transform of the vectorial Lippmann–Schwinger equation in the space of tempered distributions,

S^{'} (R^{3})

, splitting it in a singular and a regular contribution. One eventually obtains a simple equation for the scattered field in the Fourier space. This permits to draw an explicit link between the shape of the scatterer and the field through the Fourier Transform of the body indicator function. We compare our results with accurate calculations based on the T-matrix method and find a good agreement. Full article

(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction, 2nd Edition)

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15 pages, 2176 KiB

Open AccessArticle

Improving Numerical Accuracy of the Localized Oscillatory Radial Basis Functions Collocation Method for Solving Elliptic Partial Differential Equations in 2D

by Anup Lamichhane, Balaram Khatri Ghimire and Thir Dangal

Mathematics 2023, 11(22), 4690; https://doi.org/10.3390/math11224690 - 18 Nov 2023

Viewed by 1020

Abstract

Recently, the localized oscillatory radial basis functions collocation method (L-ORBFs) has been introduced to solve elliptic partial differential equations in 2D with a large number of computational nodes. The research clearly shows that the L-ORBFs is very convenient and useful for solving large-scale [...] Read more.

Recently, the localized oscillatory radial basis functions collocation method (L-ORBFs) has been introduced to solve elliptic partial differential equations in 2D with a large number of computational nodes. The research clearly shows that the L-ORBFs is very convenient and useful for solving large-scale problems, but this method is numerically less accurate. In this paper, we propose a numerical scheme to improve the accuracy of the L-ORBFs by adding low-degree polynomials in the localized collocation process. The numerical results validate that the proposed numerical scheme is highly accurate and clearly outperforms the results of the L-ORBFs. Full article

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

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13 pages, 4333 KiB

Open AccessArticle

Projection and Contraction Method for Pricing American Bond Options

by Qi Zhang, Qi Wang, Ping Zuo, Hongbo Du and Fangfang Wu

Mathematics 2023, 11(22), 4689; https://doi.org/10.3390/math11224689 - 18 Nov 2023

Cited by 2 | Viewed by 1075

Abstract

In this paper, an effective numerical method is proposed for a linear complementarity problem (LCP) arising in the valuation of American bond options under the Cox–Ingersoll–Ross (CIR) model. Firstly, a variable substitution is used to simplify the linear complementary model. Secondly, the finite [...] Read more.

In this paper, an effective numerical method is proposed for a linear complementarity problem (LCP) arising in the valuation of American bond options under the Cox–Ingersoll–Ross (CIR) model. Firstly, a variable substitution is used to simplify the linear complementary model. Secondly, the finite difference method is adopted to discretize the simplified model, and an equivalent variational form is obtained. Based on the positive definiteness of the discretized matrix, a projection and contraction method (PCM) is adopted for the resulting discretized variational problem. Finally, numerical experiments highlight the effectiveness and performance of the proposed algorithm. Full article

(This article belongs to the Special Issue Recent Advances on Nonlinear Models in Mathematical Finance, 2nd Edition)

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18 pages, 410 KiB

Open AccessArticle

Updating Utility Functions on Preordered Sets

by Pavel Chebotarev

Mathematics 2023, 11(22), 4688; https://doi.org/10.3390/math11224688 - 17 Nov 2023

Viewed by 1015

Abstract

We consider the problem of extending a function

f_{P}^{}

defined on a subset P of an arbitrary set X to X strictly monotonically with respect to a preorder ≽ defined on X , without imposing continuity constraints. We show that whenever ≽ [...] Read more.

We consider the problem of extending a function

f_{P}^{}

defined on a subset P of an arbitrary set X to X strictly monotonically with respect to a preorder ≽ defined on X , without imposing continuity constraints. We show that whenever ≽ has a utility representation,

f_{P}^{}

is extendable if and only if it is gap-safe increasing. This property means that whenever x

^{'} ≻

x, the infimum of

f_{P}^{}

on the upper contour of x

^{'}

exceeds the supremum of

f_{P}^{}

on the lower contour of x, where x, x

^{'} \in \tilde{X}

and

\tilde{X}

is X completed with two absolute ≽-extrema and, moreover,

f_{P}^{}

is weakly increasing. The completion of X makes the condition sufficient. The proposed method of extension is flexible in the sense that for any bounded utility representation u of ≽, it provides an extension of

f_{P}^{}

that coincides with u on a region of X that includes the set of P-neutral elements of X . An analysis of related topological theorems shows that the results obtained are not their consequences. The necessary and sufficient condition of extendability and the form of the extension are simplified when P is a Pareto set. Full article

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20 pages, 4473 KiB

Open AccessArticle

Determination of Reservoir Oxidation Zone Formation in Uranium Wells Using Ensemble Machine Learning Methods

by Ravil I. Mukhamediev, Yan Kuchin, Yelena Popova, Nadiya Yunicheva, Elena Muhamedijeva, Adilkhan Symagulov, Kirill Abramov, Viktors Gopejenko, Vitaly Levashenko, Elena Zaitseva, Natalya Litvishko and Sergey Stankevich

Mathematics 2023, 11(22), 4687; https://doi.org/10.3390/math11224687 - 17 Nov 2023

Cited by 2 | Viewed by 1199

Abstract

Approximately 50% of the world’s uranium is mined in a closed way using underground well leaching. In the process of uranium mining at formation-infiltration deposits, an important role is played by the correct identification of the formation of reservoir oxidation zones (ROZs), within [...] Read more.

Approximately 50% of the world’s uranium is mined in a closed way using underground well leaching. In the process of uranium mining at formation-infiltration deposits, an important role is played by the correct identification of the formation of reservoir oxidation zones (ROZs), within which the uranium content is extremely low and which affect the determination of ore reserves and subsequent mining processes. The currently used methodology for identifying ROZs requires the use of highly skilled labor and resource-intensive studies using neutron fission logging; therefore, it is not always performed. At the same time, the available electrical logging measurements data collected in the process of geophysical well surveys and exploration well data can be effectively used to identify ROZs using machine learning models. This study presents a solution to the problem of detecting ROZs in uranium deposits using ensemble machine learning methods. This method provides an index of weighted harmonic measure (f1_weighted) in the range from 0.72 to 0.93 (XGB classifier), and sufficient stability at different ratios of objects in the input dataset. The obtained results demonstrate the potential for practical use of this method for detecting ROZs in formation-infiltration uranium deposits using ensemble machine learning. Full article

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

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16 pages, 2878 KiB

Open AccessArticle

Optimal Transport and Seismic Rays

by Fabrizio Magrini and Malcolm Sambridge

Mathematics 2023, 11(22), 4686; https://doi.org/10.3390/math11224686 - 17 Nov 2023

Viewed by 1444

Abstract

We present a theoretical framework that links Fermat’s principle of least time to optimal transport theory via a cost function that enforces local transport. The proposed cost function captures the physical constraints inherent in wave propagation; when paired with specific mass distributions, it [...] Read more.

We present a theoretical framework that links Fermat’s principle of least time to optimal transport theory via a cost function that enforces local transport. The proposed cost function captures the physical constraints inherent in wave propagation; when paired with specific mass distributions, it yields shortest paths in the considered media through the optimal transport plans. In the discrete setting, our formulation results in physically significant optimal couplings, whose off-diagonal entries identify shortest paths in both directed and undirected graphs. For undirected graphs with positive edge weights, commonly used to parameterize seismic media, our method provides solutions to the Eikonal equation consistent with those from the Dijkstra algorithm. For directed negative-weight graphs, corresponding to transportation cost matrices with negative entries, our approach aligns with the Bellman–Ford algorithm but offers considerable computational advantages. We also highlight potential research directions. These include the use of sparse cost matrices to reduce the number of unknowns and constraints in the considered transportation problem, and solving specific classes of optimal transport problems through the Dijkstra algorithm to enhance computational efficiency. Full article

(This article belongs to the Special Issue Mathematical Modeling in Geophysics: Concepts and Practices)

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19 pages, 392 KiB

Open AccessArticle

Optimal Non-Asymptotic Bounds for the Sparse β Model

by Xiaowei Yang, Lu Pan, Kun Cheng and Chao Liu

Mathematics 2023, 11(22), 4685; https://doi.org/10.3390/math11224685 - 17 Nov 2023

Viewed by 934

Abstract

This paper investigates the sparse

β

model with

𝓁_{1}

penalty in the field of network data models, which is a hot topic in both statistical and social network research. We present a refined algorithm designed for parameter estimation in the proposed model. [...] Read more.

This paper investigates the sparse

β

model with

𝓁_{1}

penalty in the field of network data models, which is a hot topic in both statistical and social network research. We present a refined algorithm designed for parameter estimation in the proposed model. Its effectiveness is highlighted through its alignment with the proximal gradient descent method, stemming from the convexity of the loss function. We study the estimation consistency and establish an optimal bound for the proposed estimator. Empirical validations facilitated through meticulously designed simulation studies corroborate the efficacy of our methodology. These assessments highlight the prospective contributions of our methodology to the advanced field of network data analysis. Full article

(This article belongs to the Special Issue New Advances in High-Dimensional and Non-asymptotic Statistics)

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14 pages, 339 KiB

Open AccessArticle

Convergence of the Euler Method for Impulsive Neutral Delay Differential Equations

by Yang Sun, Gui-Lai Zhang, Zhi-Wei Wang and Tao Liu

Mathematics 2023, 11(22), 4684; https://doi.org/10.3390/math11224684 - 17 Nov 2023

Cited by 1 | Viewed by 961

Abstract

In this paper, we are concerned with a fixed stepsize Euler method for a class of linear impulsive neutral delay differential equations. By taking the partition nodes for the Euler scheme and employing the linear interpolation, we strictly prove the method is convergent [...] Read more.

In this paper, we are concerned with a fixed stepsize Euler method for a class of linear impulsive neutral delay differential equations. By taking the partition nodes for the Euler scheme and employing the linear interpolation, we strictly prove the method is convergent of order one. Two examples illustrating the efficiency results are also presented. Full article

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

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16 pages, 323 KiB

Open AccessArticle

Metallic Structures for Tangent Bundles over Almost Quadratic ϕ-Manifolds

by Mohammad Nazrul Islam Khan, Sudhakar Kumar Chaubey, Nahid Fatima and Afifah Al Eid

Mathematics 2023, 11(22), 4683; https://doi.org/10.3390/math11224683 - 17 Nov 2023

Cited by 1 | Viewed by 963

Abstract

This paper aims to explore the metallic structure

J^{2} = p J + q I,

where p and q are natural numbers, using complete and horizontal lifts on the tangent bundle

T M

over almost quadratic

ϕ

-structures (briefly, [...] Read more.

This paper aims to explore the metallic structure

J^{2} = p J + q I,

where p and q are natural numbers, using complete and horizontal lifts on the tangent bundle

T M

over almost quadratic

ϕ

-structures (briefly,

(ϕ, ξ, η)

). Tensor fields

\tilde{F}

and

F^{*}

are defined on

T M

, and it is shown that they are metallic structures over

(ϕ, ξ, η)

. Next, the fundamental 2-form

Ω

and its derivative

d Ω

, with the help of complete lift on

T M

over

(ϕ, ξ, η)

, are evaluated. Furthermore, the integrability conditions and expressions of the Lie derivative of metallic structures

\tilde{F}

and

F^{*}

are determined using complete and horizontal lifts on

T M

over

(ϕ, ξ, η)

, respectively. Finally, we prove the existence of almost quadratic

ϕ

-structures on

T M

with non-trivial examples. Full article

(This article belongs to the Special Issue Differential Geometry: Structures on Manifolds and Submanifolds)

12 pages, 1848 KiB

Open AccessArticle

Causality-Driven Efficient Feature Selection for Deep-Learning-Based Surface Roughness Prediction in Milling Machines

by Hyeon-Uk Lee, Chang-Jae Chun and Jae-Mo Kang

Mathematics 2023, 11(22), 4682; https://doi.org/10.3390/math11224682 - 17 Nov 2023

Cited by 3 | Viewed by 1209

Abstract

This paper studies the application of artificial intelligence to milling machines, focusing specifically on identifying the inputs (features) required for predicting surface roughness. Previous studies have extensively reviewed and presented useful features for surface roughness prediction. However, applying research findings to actual operational [...] Read more.

This paper studies the application of artificial intelligence to milling machines, focusing specifically on identifying the inputs (features) required for predicting surface roughness. Previous studies have extensively reviewed and presented useful features for surface roughness prediction. However, applying research findings to actual operational factories can be challenging due to the additional costs of sensor installations and the diverse environments present in each factory setting. To address these issues, in this paper, we introduced effective features for predicting surface roughness in situations where additional sensors are not installed in the existing environment. These features include feed per tooth,

F_{z}

; material removal rate, Q; and the load information. These features are suitable for use in highly constrained environments where separate sensor installation is not required, making it possible to apply the research findings in various factory environments. Additionally, to efficiently select the optimal subset for surface roughness prediction among subsets formed by available features, we apply causality to the feature selection method, proposing an approach called causality-driven efficient feature selection. The experimental results demonstrate that the features introduced in this paper are quite suitable for predicting surface roughness and that the proposed feature selection approach is more effective and efficient compared to existing selection methods. Full article

(This article belongs to the Special Issue Industrial Big Data and Process Modelling for Smart Manufacturing)

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15 pages, 4026 KiB

Open AccessArticle

WT-CNN: A Hybrid Machine Learning Model for Heart Disease Prediction

by Farah Mohammad and Saad Al-Ahmadi

Mathematics 2023, 11(22), 4681; https://doi.org/10.3390/math11224681 - 17 Nov 2023

Cited by 3 | Viewed by 3898

Abstract

Heart disease remains a predominant health challenge, being the leading cause of death worldwide. According to the World Health Organization (WHO), cardiovascular diseases (CVDs) take an estimated 17.9 million lives each year, accounting for 32% of all global deaths. Thus, there is a [...] Read more.

Heart disease remains a predominant health challenge, being the leading cause of death worldwide. According to the World Health Organization (WHO), cardiovascular diseases (CVDs) take an estimated 17.9 million lives each year, accounting for 32% of all global deaths. Thus, there is a global health concern necessitating accurate prediction models for timely intervention. Several data mining techniques are used by researchers to help healthcare professionals to predict heart disease. However, the traditional machine learning models for predicting heart disease often struggle with handling imbalanced datasets. Moreover, when prediction is on the bases of complex data like ECG, feature extraction and selecting the most pertinent features that accurately represent the underlying pathophysiological conditions without succumbing to overfitting is also a challenge. In this paper, a continuous wavelet transformation and convolutional neural network-based hybrid model abbreviated as WT-CNN is proposed. The key phases of WT-CNN are ECG data collection, preprocessing, RUSBoost-based data balancing, CWT-based feature extraction, and CNN-based final prediction. Through extensive experimentation and evaluation, the proposed model achieves an exceptional accuracy of 97.2% in predicting heart disease. The experimental results show that the approach improves classification accuracy compared to other classification approaches and that the presented model can be successfully used by healthcare professionals for predicting heart disease. Furthermore, this work can have a potential impact on improving heart disease prediction and ultimately enhancing patient lifestyle. Full article

(This article belongs to the Section Fuzzy Sets, Systems and Decision Making)

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11 pages, 284 KiB

Open AccessArticle

An Application for Bi-Concave Functions Associated with q-Convolution

by Sheza M. El-Deeb and Adriana Catas

Mathematics 2023, 11(22), 4680; https://doi.org/10.3390/math11224680 - 17 Nov 2023

Viewed by 797

Abstract

The aim of this paper is to introduce and investigate some new subclasses of bi-concave functions using q-convolution and some applications. These special cases are obtaining by making use of a q- derivative linear operator. For the new introduced subclasses, the [...] Read more.

The aim of this paper is to introduce and investigate some new subclasses of bi-concave functions using q-convolution and some applications. These special cases are obtaining by making use of a q- derivative linear operator. For the new introduced subclasses, the authors obtain the first two initial Taylor–Maclaurin coefficients

| c_{2} |

and

| c_{3} |

of bi-concave functions. For certain values of the parameters, the authors deduce interesting corollaries for coefficient bounds which imply special cases of the new introduced operator. Also, we develop two examples for coefficients

| c_{2} |

and

| c_{3} |

for certain functions. Full article

(This article belongs to the Special Issue Current Topics in Geometric Function Theory)

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Mathematics, Volume 11, Issue 22 (November-2 2023) – 146 articles

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