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Mathematics, Volume 12, Issue 11 (June-1 2024) – 166 articles

Cover Story (view full-size image): Topic modeling is a widely used tool in text analysis, aiming to extract meaningful 'topics' from a collection of documents. This paper investigates the optimal statistical guarantees for estimating a topic model. The authors introduce a new normalized word count matrix and provide a sharp entry-wise eigenvector analysis for this matrix. These results are used to enhance an existing spectral algorithm, Topic-SCORE, for topic modeling. The authors demonstrate that the error rate of the enhanced algorithm is minimax optimal across the entire parameter regime of interest. Compared to existing results, the improvement is particularly significant in the challenging regime where all documents are short. View this paper
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13 pages, 450 KiB  
Article
Properties of Convex Lattice Sets under the Discrete Legendre Transform
by Tingting He, Ruifeng Yue and Lin Si
Mathematics 2024, 12(11), 1773; https://doi.org/10.3390/math12111773 - 6 Jun 2024
Viewed by 338
Abstract
The discrete Legendre transform is a powerful tool for analyzing the properties of convex lattice sets. In this paper, for t>0, we study a class of convex lattice sets and establish a relationship between vertices of the polar of convex [...] Read more.
The discrete Legendre transform is a powerful tool for analyzing the properties of convex lattice sets. In this paper, for t>0, we study a class of convex lattice sets and establish a relationship between vertices of the polar of convex lattice sets and vertices of the polar of its tdilation. Subsequently, we show that there exists a class of convex lattice sets such that its polar is itself. In addition, we calculate upper and lower bounds for the discrete Mahler product of a class of convex lattice sets. Full article
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12 pages, 629 KiB  
Article
An Efficient Iterative Approach for Hermitian Matrices Having a Fourth-Order Convergence Rate to Find the Geometric Mean
by Tao Liu, Ting Li, Malik Zaka Ullah, Abdullah Khamis Alzahrani and Stanford Shateyi
Mathematics 2024, 12(11), 1772; https://doi.org/10.3390/math12111772 - 6 Jun 2024
Viewed by 332
Abstract
The target of this work is to present a multiplication-based iterative method for two Hermitian positive definite matrices to find the geometric mean. The method is constructed via the application of the matrix sign function. It is theoretically investigated that it has fourth [...] Read more.
The target of this work is to present a multiplication-based iterative method for two Hermitian positive definite matrices to find the geometric mean. The method is constructed via the application of the matrix sign function. It is theoretically investigated that it has fourth order of convergence. The type of convergence is also discussed, which is global under an appropriate choice of the initial matrix. Numerical experiments are reported based on input matrices of different sizes as well as various stopping termination levels with comparisons to methods of the same nature and same number of matrix–matrix multiplications. The simulation results confirm the efficiency of the proposed scheme in contrast to its competitors of the same nature. Full article
(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)
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20 pages, 3610 KiB  
Article
An Analytical Study of the Effects of Kinematic Parameters on the Motion Stability of a 3-RPR Parallel Manipulator in Singular Configurations
by Yu-Tong Li and Yu-Xin Wang
Mathematics 2024, 12(11), 1771; https://doi.org/10.3390/math12111771 - 6 Jun 2024
Viewed by 310
Abstract
Due to the Jacobian matrix rank reduction near singularities, applying numerical methods to study PMs’ motion stability at singularities is quite difficult. As a result, there is a scarcity of literature on the investigation of PMs’ dynamic behaviors near singularities and the influence [...] Read more.
Due to the Jacobian matrix rank reduction near singularities, applying numerical methods to study PMs’ motion stability at singularities is quite difficult. As a result, there is a scarcity of literature on the investigation of PMs’ dynamic behaviors near singularities and the influence of kinematic parameters on the motion stability of PMs. To address the research gap related to the above issues, based on the Gerschgorin perturbation method, Hurwitz exact approach, and the Lyapunov dynamic stability theory, the influence of kinematic parameters and external loads on a PM’s motion stability at singularities is studied for the first time. The theoretical analysis results reported in this paper reveal many previously undiscovered features beyond those derived from previous numerical methods, and indicate the limitations of some widely accepted statements. For example, increasing the angular speed of the movable platform can expand the range of the external loads that meet the motion stability at singular configurations. The prevailing notion in prior research that PMs are unable to support external loads in the direction of the gained DoF at singular configurations is only partially accurate. This pioneering research establishes a theoretical foundation for exploring a new real-time approach to avoid dynamic singularities by fully exploiting the influence mechanisms of kinematic parameters on PMs’ dynamic stability at singularities. Full article
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20 pages, 286 KiB  
Article
Fixed Point Theory in Bicomplex Metric Spaces: A New Framework with Applications
by Badriah Alamri
Mathematics 2024, 12(11), 1770; https://doi.org/10.3390/math12111770 - 6 Jun 2024
Viewed by 292
Abstract
This paper investigates the existence of common fixed points for mappings satisfying generalized rational type contractive conditions in the framework of bicomplex valued metric spaces. Our findings extend well-established results in the existing literature. As an application of our leading result, we explore [...] Read more.
This paper investigates the existence of common fixed points for mappings satisfying generalized rational type contractive conditions in the framework of bicomplex valued metric spaces. Our findings extend well-established results in the existing literature. As an application of our leading result, we explore the existence and uniqueness of solutions of the Volttera integral equation of the second kind. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications II)
14 pages, 335 KiB  
Article
Flexible and Compact MLWE-Based KEM
by Wenqi Liang, Zhaoman Liu, Xuyang Zhao, Yafang Yang and Zhichuang Liang
Mathematics 2024, 12(11), 1769; https://doi.org/10.3390/math12111769 - 6 Jun 2024
Viewed by 413
Abstract
In order to resist the security risks caused by quantum computing, post-quantum cryptography (PQC) has been a research focus. Constructing a key encapsulation mechanism (KEM) based on lattices is one of the promising PQC routines. The algebraically structured learning with errors (LWE) problem [...] Read more.
In order to resist the security risks caused by quantum computing, post-quantum cryptography (PQC) has been a research focus. Constructing a key encapsulation mechanism (KEM) based on lattices is one of the promising PQC routines. The algebraically structured learning with errors (LWE) problem over power-of-two cyclotomics has been one of the most widely used hardness assumptions for lattice-based cryptographic schemes. However, power-of-two cyclotomic rings may be exploited in the inflexibility of selecting parameters. Recently, trinomial cyclotomic rings of the form Zq[x]/(xnxn/2+1), where n=2k3l, k1,l0, have received widespread attention due to their flexible parameter selection. In this paper, we propose Tyber, a variant scheme of the NIST-standardized KEM candidate Kyber over trinomial cyclotomic rings. We provide three parameter sets, aiming at the quantum security of 128, 192, and 256 bits (actually achieving 129, 197, and 276 bits) with matching and negligible error probabilities. When compared to Kyber, our Tyber exhibits stronger quantum security, by 22, 31, and 44 bits, than Kyber for three security levels. Full article
(This article belongs to the Special Issue New Advances in Cryptographic Theory and Application)
25 pages, 7997 KiB  
Article
Typology and Design of Parametric Cat-in-a-Box and Cat-in-a-Grid Triggers for Tropical Cyclone Risk Transfer
by Guillermo Franco, Laura Lemke-Verderame, Roberto Guidotti, Ye Yuan, Gianbattista Bussi, Dag Lohmann and Paolo Bazzurro
Mathematics 2024, 12(11), 1768; https://doi.org/10.3390/math12111768 - 6 Jun 2024
Viewed by 836
Abstract
The insurance industry has used parametric solutions to transfer catastrophe risks since the 1990s. Instead of relying on a lengthy process to assess a claim, these products pay the insured a pre-agreed amount if the physical characteristics of the event fulfill pre-defined conditions. [...] Read more.
The insurance industry has used parametric solutions to transfer catastrophe risks since the 1990s. Instead of relying on a lengthy process to assess a claim, these products pay the insured a pre-agreed amount if the physical characteristics of the event fulfill pre-defined conditions. Cat-in-a-box or cat-in-a-circle triggers, commonly used tools for tropical cyclone risk transfer, provide a payout to the insured if the track of a hurricane crosses the perimeter of a geographic area defined by a polygon or a circle with a certain intensity. Cat-in-a-grid solutions are novel and more sophisticated. They rely on a set of multiple cat-in-a-box triggers arranged on an orthogonal grid. The consideration of multiple geographic domains instead of a single box or circle is helpful to reduce basis risk, i.e., the difference between the parametric loss estimate and the target loss. In the case study for Miami presented here, for instance, a cat-in-a-grid solution showed 18.5% less basis risk than a typical cat-in-a-box alternative. To organize the different types of triggers within a common framework, we classify the existing alternatives based on whether they use a single geographic domain (like a box or a circle) or multiple domains (like a grid). We discuss their advantages and disadvantages and describe the process required to calibrate any one solution with the help of a catastrophe-risk model. We focus, in particular, on the analysis and construction of cat-in-a-grid triggers, the alternative that we believe offers the greatest potential for global standardization and adoption. Full article
(This article belongs to the Special Issue New Advances in Quantitative Environmental Finance)
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16 pages, 775 KiB  
Article
Robust Adaptive Fault-Tolerant Control of Quadrotor Unmanned Aerial Vehicles
by Imil Hamda Imran, Nezar M. Alyazidi, Ahmed Eltayeb and Gamil Ahmed
Mathematics 2024, 12(11), 1767; https://doi.org/10.3390/math12111767 - 6 Jun 2024
Viewed by 340
Abstract
The paper introduces a robust adaptive fault-tolerant control system for the six-degree-of-freedom (six-DOF) dynamics of quadrotor unmanned aerial vehicles (UAVs), incorporating disturbances and abrupt actuator faults to represent real-world conditions. The proposed control scheme employs robust control terms to manage unknown disturbances. However, [...] Read more.
The paper introduces a robust adaptive fault-tolerant control system for the six-degree-of-freedom (six-DOF) dynamics of quadrotor unmanned aerial vehicles (UAVs), incorporating disturbances and abrupt actuator faults to represent real-world conditions. The proposed control scheme employs robust control terms to manage unknown disturbances. However, robust control performance may degrade due to sudden fault impacts. To handle this issue, we introduce adaptive laws to ensure continuous adaptation. The control architecture ensures the tracking system’s stability by combining robust control using sliding-mode control (SMC) with adaptive control developed using the certainty equivalence principle. The sliding-surface error limits the adaptive laws, in which the convergence of estimated parameters to the actual unknown variables is not required as they fully rely on the convergence of the tracking error. We provide rigorous mathematics to validate the proposed control design. Furthermore, we conduct numerical simulations for a quadrotor UAV to showcase the effectiveness of the proposed scheme. The results demonstrate the efficacy of the proposed design in handling external disturbances and abrupt actuator faults. Full article
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11 pages, 272 KiB  
Article
Systems of Hemivariational Inclusions with Competing Operators
by Dumitru Motreanu
Mathematics 2024, 12(11), 1766; https://doi.org/10.3390/math12111766 - 6 Jun 2024
Viewed by 247
Abstract
This paper focuses on a system of differential inclusions expressing hemivariational inequalities driven by competing operators constructed with p-Laplacians that involve two real parameters. The existence of a generalized solution is shown by means of an approximation process through approximate solutions in [...] Read more.
This paper focuses on a system of differential inclusions expressing hemivariational inequalities driven by competing operators constructed with p-Laplacians that involve two real parameters. The existence of a generalized solution is shown by means of an approximation process through approximate solutions in finite dimensional spaces. When the parameters are negative, the generalized solutions become weak solutions. The main novelty of this work is the solvability of systems of differential inclusions for which the ellipticity condition may fail. Full article
(This article belongs to the Special Issue Problems and Methods in Nonlinear Analysis)
15 pages, 6840 KiB  
Article
Dynamic Binary-Medium Model for Jointed Rock Subjected to Cyclic Loading
by Mingxing Liu, Enlong Liu, Xingyan Liu and Qingsong Zheng
Mathematics 2024, 12(11), 1765; https://doi.org/10.3390/math12111765 - 6 Jun 2024
Viewed by 310
Abstract
Revealing the damage mechanism of jointed rocks under a cyclic loading and formulating the corresponding dynamic constitutive model to meet the requirements for the evaluation of anti-vibration safety for critical engineering construction and operation is an essential, urgent and basic subject. Based on [...] Read more.
Revealing the damage mechanism of jointed rocks under a cyclic loading and formulating the corresponding dynamic constitutive model to meet the requirements for the evaluation of anti-vibration safety for critical engineering construction and operation is an essential, urgent and basic subject. Based on the breakage mechanics for geological material, jointed rock is considered as a binary-medium material composed of the bonded elements and frictional elements. The bonded elements are regarded as elastic-brittle elements, and the frictional elements are regarded as elastic-plastic elements. Firstly, the static binary-medium model for jointed rock is established based on the homogenization method and by introducing the breakage ratio and the strain concentration coefficient. Then, the dynamic binary-medium model for jointed rock under cyclic loads is established considering the nonlinear damage effect resulting from cyclic loads. The breakage ratio formula is improved, and the Drucker–Prager criterion is introduced. During the unloading stage, it is supposed that the breakage ratios and strain concentration coefficients remain unchanged and the stress–strain ratios of both bonded elements and frictional elements are constant. The model is verified by static and dynamic triaxial tests of jointed rock samples with an interpenetrated joint. It is found that the model can describe the nonlinear stress–strain characteristics of a jointed rock subjected to cyclic loads relatively well and can reflect the effects of cyclic loading on the deformation and damage, including the lateral deformation characteristics. Meanwhile, the typical three-stage (varying from sparse to dense to sparse) evolution laws of the stress–strain curves are also reflected relatively well. Full article
(This article belongs to the Special Issue Numerical Modeling and Simulation in Geomechanics)
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16 pages, 398 KiB  
Article
Stability Analysis of the Credit Market in Supply Chain Finance Based on Stochastic Evolutionary Game Theory
by Chunsheng Wang, Jiatong Weng, Jingshi He, Xiaopin Wang, Hong Ding and Quanxin Zhu
Mathematics 2024, 12(11), 1764; https://doi.org/10.3390/math12111764 - 6 Jun 2024
Viewed by 287
Abstract
The rapid development of supply chain finance (SCF) has significantly alleviated the financing difficulties of small and medium-sized enterprises (SMEs). However, it is important to recognize that within the accounts receivable financing segment of the SCF credit market, the credit risk associated with [...] Read more.
The rapid development of supply chain finance (SCF) has significantly alleviated the financing difficulties of small and medium-sized enterprises (SMEs). However, it is important to recognize that within the accounts receivable financing segment of the SCF credit market, the credit risk associated with SMEs poses a serious challenge and potential threat to the stability, health, and sustainable development of the SCF system. This paper pays special attention to the stability of the two-party evolutionary game between SMEs and financial institutions (FIs) within the context of the Chinese SCF credit market. To identify a pathway to reduce credit risks for SMEs while simultaneously enhancing system stability, this paper adopts the stochastic evolutionary game (SEG) model and combines the fixed-point method to determine the conditions that satisfy the stability of the system’s index p mean square of the system. This study has made attempts in various aspects, such as the innovative construction and investigation of a nonlinear SEG model, the endeavor to study the stability of SEG systems using fixed-point methods, and the innovative construction of a more realistic two-player SEG system. The data and simulation results generated from hypothetical scenarios show that the conclusions of the article are credible and feasible. Through the study, we conclude that the higher credit ratio from FI and the higher penalty intensity from core enterprises (CEs) will accelerate the stability of the system. Based on solid data and modeling analysis, insights into the regulation of FI are provided. Full article
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21 pages, 898 KiB  
Article
The Role of Risk Factors in System Performance: A Comprehensive Study with Adaptive Progressive Type-II Censoring
by Hanan Haj Ahmad, Mohamed Aboshady and Mahmoud Mansour
Mathematics 2024, 12(11), 1763; https://doi.org/10.3390/math12111763 - 5 Jun 2024
Viewed by 362
Abstract
The quality performance of many vital systems depends on how long the units are performing; hence, research works started focusing on increasing the reliability of systems while taking into consideration that many factors may cause the failures of operating systems. In this study, [...] Read more.
The quality performance of many vital systems depends on how long the units are performing; hence, research works started focusing on increasing the reliability of systems while taking into consideration that many factors may cause the failures of operating systems. In this study, the combination of a parametric generalized linear failure rate distribution model and an adaptive progressive Type-II censoring scheme for practical purposes is explored. A comprehensive investigation is performed on the risk factors that cause failure and determines which of the factors has a more harmful effect on the units. A lifetime experiment is performed under the condition of an adaptive progressive Type-II censoring scheme to obtain observations as a result of the competing factors of failures. The obtained observations are assumed to follow a three-parameter generalized linear failure rate distribution and are assumed to be competing to cause failure. Two statistical inference methods are employed for estimating this model’s parameters: the frequentist maximum likelihood method and the Bayesian approach. Our model’s validity is demonstrated through extensive simulations and real data applications in the medical and electrical engineering fields. Full article
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20 pages, 3079 KiB  
Article
A New Generalization of the Truncated Gumbel Distribution with Quantile Regression and Applications
by Héctor J. Gómez, Karol I. Santoro, Diego Ayma, Isaac E. Cortés, Diego I. Gallardo and Tiago M. Magalhães
Mathematics 2024, 12(11), 1762; https://doi.org/10.3390/math12111762 - 5 Jun 2024
Viewed by 342
Abstract
In this article, we introduce a new model with positive support. This model is an extension of the truncated Gumbel distribution, where a shape parameter is incorporated that provides greater flexibility to the new model. The model is parameterized in terms of the [...] Read more.
In this article, we introduce a new model with positive support. This model is an extension of the truncated Gumbel distribution, where a shape parameter is incorporated that provides greater flexibility to the new model. The model is parameterized in terms of the p-th quantile of the distribution to perform quantile regression in this model. An extensive simulation study demonstrates the good performance of the maximum likelihood estimators in finite samples. Finally, two applications to real datasets related to the level of beta-carotene and body mass index are presented. Full article
(This article belongs to the Special Issue Mathematical and Computational Statistics and Applications)
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31 pages, 724 KiB  
Article
Matrix Pencil Optimal Iterative Algorithms and Restarted Versions for Linear Matrix Equation and Pseudoinverse
by Chein-Shan Liu, Chung-Lun Kuo and Chih-Wen Chang
Mathematics 2024, 12(11), 1761; https://doi.org/10.3390/math12111761 - 5 Jun 2024
Viewed by 371
Abstract
We derive a double-optimal iterative algorithm (DOIA) in an m-degree matrix pencil Krylov subspace to solve a rectangular linear matrix equation. Expressing the iterative solution in a matrix pencil and using two optimization techniques, we determine the expansion coefficients explicitly, by inverting [...] Read more.
We derive a double-optimal iterative algorithm (DOIA) in an m-degree matrix pencil Krylov subspace to solve a rectangular linear matrix equation. Expressing the iterative solution in a matrix pencil and using two optimization techniques, we determine the expansion coefficients explicitly, by inverting an m×m positive definite matrix. The DOIA is a fast, convergent, iterative algorithm. Some properties and the estimation of residual error of the DOIA are given to prove the absolute convergence. Numerical tests demonstrate the usefulness of the double-optimal solution (DOS) and DOIA in solving square or nonsquare linear matrix equations and in inverting nonsingular square matrices. To speed up the convergence, a restarted technique with frequency m is proposed, namely, DOIA(m); it outperforms the DOIA. The pseudoinverse of a rectangular matrix can be sought using the DOIA and DOIA(m). The Moore–Penrose iterative algorithm (MPIA) and MPIA(m) based on the polynomial-type matrix pencil and the optimized hyperpower iterative algorithm OHPIA(m) are developed. They are efficient and accurate iterative methods for finding the pseudoinverse, especially the MPIA(m) and OHPIA(m). Full article
(This article belongs to the Special Issue Nonlinear Functional Analysis: Theory, Methods, and Applications)
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20 pages, 359 KiB  
Article
Change Point Test for Length-Biased Lognormal Distribution under Random Right Censoring
by Mei Li, Wei Ning and Yubin Tian
Mathematics 2024, 12(11), 1760; https://doi.org/10.3390/math12111760 - 5 Jun 2024
Viewed by 306
Abstract
The length-biased lognormal distribution is a length-biased version of lognormal distribution, which is developed to model the length-biased lifetime data from, for example, biological investigation, medical research, and engineering fields. Owing to the existence of censoring phenomena in lifetime data, we study the [...] Read more.
The length-biased lognormal distribution is a length-biased version of lognormal distribution, which is developed to model the length-biased lifetime data from, for example, biological investigation, medical research, and engineering fields. Owing to the existence of censoring phenomena in lifetime data, we study the change-point-testing problem of length-biased lognormal distribution under random censoring in this paper. A procedure based on the modified information criterion is developed to detect changes in parameters of this distribution. Under the sufficient condition of the Fisher information matrix being positive definite, it is proven that the null asymptotic distribution of the test statistic follows a chi-square distribution. In order to evaluate the uncertainty of change point location estimation, a way of calculating the coverage probabilities and average lengths of confidence sets of change point location based on the profile likelihood and deviation function is proposed. The simulations are conducted, under the scenarios of uniform censoring and exponential censoring, to investigate the validity of the proposed method. And the results indicate that the proposed approach performs better in terms of test power, coverage probabilities, and average lengths of confidence sets compared to the method based on the likelihood ratio test. Subsequently, the proposed approach is applied to the analysis of survival data from heart transplant patients, and the results show that there are differences in the median survival time post-heart transplantation among patients of different ages. Full article
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15 pages, 2104 KiB  
Article
An Improved Reacceleration Optimization Algorithm Based on the Momentum Method for Image Recognition
by Haijing Sun, Ying Cai, Ran Tao, Yichuan Shao, Lei Xing, Can Zhang and Qian Zhao
Mathematics 2024, 12(11), 1759; https://doi.org/10.3390/math12111759 - 5 Jun 2024
Viewed by 279
Abstract
The optimization algorithm plays a crucial role in image recognition by neural networks. However, it is challenging to accelerate the model’s convergence and maintain high precision. As a commonly used stochastic gradient descent optimization algorithm, the momentum method requires many epochs to find [...] Read more.
The optimization algorithm plays a crucial role in image recognition by neural networks. However, it is challenging to accelerate the model’s convergence and maintain high precision. As a commonly used stochastic gradient descent optimization algorithm, the momentum method requires many epochs to find the optimal parameters during model training. The velocity of its gradient descent depends solely on the historical gradients and is not subject to random fluctuations. To address this issue, an optimization algorithm to enhance the gradient descent velocity, i.e., the momentum reacceleration gradient descent (MRGD), is proposed. The algorithm utilizes the point division of the current momentum and the gradient relationship, multiplying it with the gradient. It can adjust the update rate and step size of the parameters based on the gradient descent state, so as to achieve faster convergence and higher precision in training the deep learning model. The effectiveness of this method is further proven by applying the reacceleration mechanism to the Adam optimizer, resulting in the MRGDAdam algorithm. We verify both algorithms using multiple image classification datasets, and the experimental results show that the proposed optimization algorithm enables the model to achieve higher recognition accuracy over a small number of training epochs, as well as speeding up model implementation. This study provides new ideas and expansions for future optimizer research. Full article
(This article belongs to the Special Issue Computational Methods in Materials Design)
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19 pages, 665 KiB  
Article
A Learnheuristic Algorithm Based on Thompson Sampling for the Heterogeneous and Dynamic Team Orienteering Problem
by Antonio R. Uguina, Juan F. Gomez, Javier Panadero, Anna Martínez-Gavara and Angel A. Juan
Mathematics 2024, 12(11), 1758; https://doi.org/10.3390/math12111758 - 5 Jun 2024
Viewed by 292
Abstract
The team orienteering problem (TOP) is a well-studied optimization challenge in the field of Operations Research, where multiple vehicles aim to maximize the total collected rewards within a given time limit by visiting a subset of nodes in a network. With the goal [...] Read more.
The team orienteering problem (TOP) is a well-studied optimization challenge in the field of Operations Research, where multiple vehicles aim to maximize the total collected rewards within a given time limit by visiting a subset of nodes in a network. With the goal of including dynamic and uncertain conditions inherent in real-world transportation scenarios, we introduce a novel dynamic variant of the TOP that considers real-time changes in environmental conditions affecting reward acquisition at each node. Specifically, we model the dynamic nature of environmental factors—such as traffic congestion, weather conditions, and battery level of each vehicle—to reflect their impact on the probability of obtaining the reward when visiting each type of node in a heterogeneous network. To address this problem, a learnheuristic optimization framework is proposed. It combines a metaheuristic algorithm with Thompson sampling to make informed decisions in dynamic environments. Furthermore, we conduct empirical experiments to assess the impact of varying reward probabilities on resource allocation and route planning within the context of this dynamic TOP, where nodes might offer a different reward behavior depending upon the environmental conditions. Our numerical results indicate that the proposed learnheuristic algorithm outperforms static approaches, achieving up to 25% better performance in highly dynamic scenarios. Our findings highlight the effectiveness of our approach in adapting to dynamic conditions and optimizing decision-making processes in transportation systems. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)
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17 pages, 760 KiB  
Article
Parameter Estimation of Birnbaum-Saunders Distribution under Competing Risks Using the Quantile Variant of the Expectation-Maximization Algorithm
by Chanseok Park and Min Wang
Mathematics 2024, 12(11), 1757; https://doi.org/10.3390/math12111757 - 5 Jun 2024
Viewed by 340
Abstract
Competing risks models, also known as weakest-link models, are utilized to analyze diverse strength distributions exhibiting multi-modality, often attributed to various types of defects within the material. The weakest-link theory posits that a material’s fracture is dictated by its most severe defect. However, [...] Read more.
Competing risks models, also known as weakest-link models, are utilized to analyze diverse strength distributions exhibiting multi-modality, often attributed to various types of defects within the material. The weakest-link theory posits that a material’s fracture is dictated by its most severe defect. However, multimodal problems can become intricate due to potential censoring, a common constraint stemming from time and cost limitations during experiments. Additionally, determining the mode of failure can be challenging due to factors like the absence of suitable diagnostic tools, costly autopsy procedures, and other obstacles, collectively referred to as the masking problem. In this paper, we investigate the distribution of strength for multimodal failures with censored data. We consider both full and partial maskings and present an EM-type parameter estimate for the Birnbaum-Saunders distribution under competing risks. We compare the results with those obtained from other distributions, such as lognormal, Weibull, and Wald (inverse-Gaussian) distributions. The effectiveness of the proposed method is demonstrated through two illustrative examples, as well as an analysis of the sensitivity of parameter estimates to variations in starting values. Full article
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14 pages, 3722 KiB  
Article
Dynamic Properties of Coupled Nonlinear Split-Ring Resonators
by Xiao Lin and Mi Wang
Mathematics 2024, 12(11), 1756; https://doi.org/10.3390/math12111756 - 5 Jun 2024
Viewed by 250
Abstract
In this paper, we delve into the dynamics of two and three coupled SRRs models, exploring their nonlinear properties such as stability, periodicity, or chaos. Additionally, we examine the energy function Hamilton within the context of these models. Numerical examples are provided to [...] Read more.
In this paper, we delve into the dynamics of two and three coupled SRRs models, exploring their nonlinear properties such as stability, periodicity, or chaos. Additionally, we examine the energy function Hamilton within the context of these models. Numerical examples are provided to illustrate the obtained results and demonstrate the applicability of our findings. Full article
(This article belongs to the Section Dynamical Systems)
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17 pages, 15356 KiB  
Article
Interference Management for a Wireless Communication Network Using a Recurrent Neural Network Approach
by Mohammad Abrar Shakil Sejan, Md Habibur Rahman, Md Abdul Aziz, Rana Tabassum, Young-Hwan You, Duck-Dong Hwang and Hyoung-Kyu Song
Mathematics 2024, 12(11), 1755; https://doi.org/10.3390/math12111755 - 5 Jun 2024
Viewed by 357
Abstract
Wireless communication technologies have profoundly impacted the interconnectivity of mobile users and terminals. Nevertheless, the exponential increase in the number of users poses significant challenges, particularly in interference management, which is a major concern in wireless communication. Machine learning (ML) approaches have emerged [...] Read more.
Wireless communication technologies have profoundly impacted the interconnectivity of mobile users and terminals. Nevertheless, the exponential increase in the number of users poses significant challenges, particularly in interference management, which is a major concern in wireless communication. Machine learning (ML) approaches have emerged as powerful tools for solving various problems in this domain. However, existing studies have not fully addressed the problem of interference management for wireless communication using ML techniques. In this paper, we explore the application of recurrent neural network (RNN) approaches to address co-channel interference in wireless communication. Specifically, we investigate the effectiveness of long short-term memory (LSTM), bidirectional LSTM (Bi-LSTM), and gated recurrent unit (GRU) network architectures in two different network settings. The first network comprises 10 connected devices, while the second network involves 20 devices. Our experimental results demonstrate that Bi-LSTM outperforms LSTM and GRU in terms of mean squared error, normalized mean squared error, and sum rate. While LSTM and GRU produce similar results, LSTM exhibits a marginal advantage over GRU. In addition, a combined RNN approach is also studied, and it can provide better results in dense networks. Full article
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21 pages, 1776 KiB  
Systematic Review
Multicriteria Decision-Making in Public Security: A Systematic Review
by Jefferson Costa and Maisa Silva
Mathematics 2024, 12(11), 1754; https://doi.org/10.3390/math12111754 - 5 Jun 2024
Viewed by 435
Abstract
The Multiple Criteria Decision-Making/Analysis (MCDM/A) methods have been widely used in several management contexts. In public security, their use enhances managerial decision-making by considering the decision-maker’s preference structure and providing a multidimensional view of problems. However, methodological support for their applications in this [...] Read more.
The Multiple Criteria Decision-Making/Analysis (MCDM/A) methods have been widely used in several management contexts. In public security, their use enhances managerial decision-making by considering the decision-maker’s preference structure and providing a multidimensional view of problems. However, methodological support for their applications in this field lacks clarity, including selecting appropriate methods, addressing pertinent problematics, and identifying alternatives and criteria. To address this gap, this article conducts a Systematic Literature Review (SLR) to diagnose the state of the art and identify the main directions of the research in multicriteria models applied to public security management. The research methodology involves five main research questions, and the extraction and analysis of data from 51 articles selected through a structured filtering process. The analysis includes identifying the number of publications and citations, as well as listing the MCDM/A approaches and issues employed. Furthermore, the criteria used and the number of criteria considered are discussed, as well as the method employed. Finally, the identification of the main research directions in MCDM/A models applied to public security is presented. The findings suggest that prioritization and classification are common problematics, social criteria are frequently considered, and the AHP method is widely used, often employing fuzzy sets and hybrid models. Full article
(This article belongs to the Special Issue Advances in Behavioral Decision Analytics and Informatics)
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20 pages, 5974 KiB  
Article
Adaptive Slicing Method for Hermite Non-Planar Tessellated Surfaces Models
by Yang Chen, Ruichao Lian, Shikai Jing and Jiangxin Fan
Mathematics 2024, 12(11), 1753; https://doi.org/10.3390/math12111753 - 5 Jun 2024
Viewed by 277
Abstract
This paper presents an adaptive slicing method for Hermite non-planar tessellated surfaces models to improve the geometric accuracy of Rapid Prototyping (RP). Based on the bending characteristics of Hermite curved triangles, a slicing method for a complete Hermite surface model, including the grouping, [...] Read more.
This paper presents an adaptive slicing method for Hermite non-planar tessellated surfaces models to improve the geometric accuracy of Rapid Prototyping (RP). Based on the bending characteristics of Hermite curved triangles, a slicing method for a complete Hermite surface model, including the grouping, the construction of the topological relationships, and the calculation of the intersection contours, was employed. The adaptive layering method considering the normal vector at the vertexes of the Hermite curved triangles was employed to grain the variable thickness of all layers of the Hermite surface model. The classical Stanford bunny model illustrates the significant improvement in the accuracy of the proposed method compared to the traditional method. Full article
(This article belongs to the Special Issue Advances in Applied Mathematics, Mechanics and Engineering)
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5 pages, 152 KiB  
Editorial
New Trends in Complex Analysis Research
by Georgia Irina Oros
Mathematics 2024, 12(11), 1752; https://doi.org/10.3390/math12111752 - 5 Jun 2024
Viewed by 315
Abstract
This Special Issue aims to present some of the newest results obtained from the study of complex-valued functions of one or several complex variables [...] Full article
23 pages, 1893 KiB  
Article
Optimizing Inventory and Pricing for Substitute Products with Soft Supply Constraints
by Armando Meza, Paolo Latorre, Milena Bonacic, Héctor López-Ospina and Juan Pérez
Mathematics 2024, 12(11), 1751; https://doi.org/10.3390/math12111751 - 4 Jun 2024
Viewed by 379
Abstract
This paper presents a profit optimization model for substitute products in a competitive, time-sensitive market with scarcity and shifting user preferences. The model maximizes profit, considering production costs and inventory maintenance. It uses a discrete choice model to represent demand, sensitivity to price, [...] Read more.
This paper presents a profit optimization model for substitute products in a competitive, time-sensitive market with scarcity and shifting user preferences. The model maximizes profit, considering production costs and inventory maintenance. It uses a discrete choice model to represent demand, sensitivity to price, availability, and changing preferences. A two-phase PSO-type metaheuristic solution tackles the nonlinear, recursive model, efficiently managing inventories and evolving consumer preferences. The model integrates production decisions, inventories, and sales prices, considering scarcity conditions and user preferences. It uses a multinomial logit for the consumers’ demand function with soft exogenous constraints, which influence utility and change consumption preferences and choices. This research offers a tool for companies to manage stock, production, and pricing in a context where goods are substitutes, providing a new perspective on business strategy. Full article
(This article belongs to the Section Fuzzy Sets, Systems and Decision Making)
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19 pages, 5733 KiB  
Article
A Numerical Analysis of the Non-Uniform Layered Ground Vibration Caused by a Moving Railway Load Using an Efficient Frequency–Wave-Number Method
by Shaofeng Yao, Wei Xie, Jianlong Geng, Xiaolu Xu and Sen Zheng
Mathematics 2024, 12(11), 1750; https://doi.org/10.3390/math12111750 - 4 Jun 2024
Viewed by 343
Abstract
The ground vibration caused by the operation of high-speed trains has become a key challenge in the development of high-speed railways. In order to study the train-induced ground vibration affected by geotechnical heterogeneity, an efficient frequency–wave-number method coupled with the random variable theory [...] Read more.
The ground vibration caused by the operation of high-speed trains has become a key challenge in the development of high-speed railways. In order to study the train-induced ground vibration affected by geotechnical heterogeneity, an efficient frequency–wave-number method coupled with the random variable theory model is proposed to quickly obtain the numerical results without losing accuracy. The track is regarded as a composite Euler–Bernoulli beam resting on the layered ground, and the spatial heterogeneity of the ground soil is considered. The ground dynamic characteristics of an elastic, layered, non-uniform foundation are investigated, and numerical results at three typical train speeds are reported based on the developed Fortran computer programs. The results show that as the soil homogeneity coefficient increases, the peak acceleration continuously decreases in the transonic case, while it gradually increases in the supersonic case, and the ground acceleration spectrum at a far distance obviously decreases; the maximum acceleration occurs at the track edge, and a local rebound in vibration attenuation occurs in the supersonic case. Full article
(This article belongs to the Special Issue Numerical Modeling and Simulation in Geomechanics)
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30 pages, 1038 KiB  
Article
Mathematical Modeling and Transmission Dynamics Analysis of the African Swine Fever Virus in Benin
by Sèna Yannick Ayihou, Têlé Jonas Doumatè, Cedric Hameni Nkwayep, Samuel Bowong Tsakou and Romain Glèlè Kakai
Mathematics 2024, 12(11), 1749; https://doi.org/10.3390/math12111749 - 4 Jun 2024
Viewed by 347
Abstract
African swine fever (ASF) is endemic in many African countries, and its control is challenging because no vaccine or treatment is available to date. Nowadays, mathematical modeling is a key tool in infectious disease studies, complementing traditional biological investigations. In this study, we [...] Read more.
African swine fever (ASF) is endemic in many African countries, and its control is challenging because no vaccine or treatment is available to date. Nowadays, mathematical modeling is a key tool in infectious disease studies, complementing traditional biological investigations. In this study, we propose and analyze a mathematical model for the transmission dynamics of African swine fever (ASF) in Benin that considers the free-living virus in the environment. We provide the theoretical results of the model. The study of the model is conducted by first proving that the model is well posed by showing the positivity and the boundedness of solutions as well as the existence and uniqueness of the solution. We compute the control reproduction number Rc as well as the basic reproduction number R0, which helps to analyze the extinction or the persistence of the disease in the pig population. We provide the global attractivity of the disease-free equilibrium and the endemic equilibrium and study their stabilities. After, we estimate some unknown parameters from the proposed model, and the sensitivity analysis is carried out to determine the parameters that influence the control reproduction number. Finally, through numerical simulations, in the current situation, we find that R0=2.78, which implies that the disease will not die out without any control measures and Rc=1.55 showing that the eradication of the disease highly depends on the control measures taken to reduce disease transmission. Full article
(This article belongs to the Special Issue Mathematical Modeling of Disease Dynamics)
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20 pages, 1772 KiB  
Article
Numerical Recovering of Space-Dependent Sources in Hyperbolic Transmission Problems
by Miglena N. Koleva and Lubin G. Vulkov
Mathematics 2024, 12(11), 1748; https://doi.org/10.3390/math12111748 - 4 Jun 2024
Viewed by 256
Abstract
A body may have a structural, thermal, electromagnetic or optical role. In wave propagation, many models are described for transmission problems, whose solutions are defined in two or more domains. In this paper, we consider an inverse source hyperbolic problem on disconnected intervals, [...] Read more.
A body may have a structural, thermal, electromagnetic or optical role. In wave propagation, many models are described for transmission problems, whose solutions are defined in two or more domains. In this paper, we consider an inverse source hyperbolic problem on disconnected intervals, using solution point constraints. Applying a transform method, we reduce the inverse problems to direct ones, which are studied for well-posedness in special weighted Sobolev spaces. This means that the inverse problem is said to be well posed in the sense of Tikhonov (or conditionally well posed). The main aim of this study is to develop a finite difference method for solution of the transformed hyperbolic problems with a non-local differential operator and initial conditions. Numerical test examples are also analyzed. Full article
(This article belongs to the Special Issue Advanced Approaches to Mathematical Physics Problems)
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17 pages, 5378 KiB  
Article
An Innovative Method for Wind Load Estimation in High-Rise Buildings Based on Green’s Function
by Lin Song, Yang Yu, Jianxing Yu, Shibo Wu, Jiandong Ma and Zihang Jin
Mathematics 2024, 12(11), 1747; https://doi.org/10.3390/math12111747 - 4 Jun 2024
Viewed by 228
Abstract
High-rise buildings are inherently vulnerable to substantial wind-induced forces. The increasing complexity of building designs has posed challenges in calculating wind loads, while traditional methods involving physical models have proven to be intricate and time-consuming. In order to overcome these obstacles, this paper [...] Read more.
High-rise buildings are inherently vulnerable to substantial wind-induced forces. The increasing complexity of building designs has posed challenges in calculating wind loads, while traditional methods involving physical models have proven to be intricate and time-consuming. In order to overcome these obstacles, this paper investigates a theoretical methodology aimed at streamlining the computation of wind loads. In the initial theoretical exploration, a simplified mathematical model based on Green’s function is introduced to take into account the interaction between wind loads and building geometry, while the model is not user-friendly and difficult to solve for complex polygonal buildings. To overcome this challenge, the study incorporates numerical simulations to extend the ideas and refine the methodology. To simplify the problem from a three-dimensional to a two-dimensional context, a bold tangential field assumption is made, assuming the wind pressure distribution remains similar across horizontal sections at different heights. The Schwarz–Christoffel formulation is then employed to facilitate the transformation. By integrating Green’s functions and conformal mapping to solve potential flow problems beyond the boundary layer, a comprehensive mathematical derivation is established. The above broadens the applicability of the mathematical theory and provides a new direction for estimations of high-speed wind load on buildings. Full article
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28 pages, 8142 KiB  
Article
Integrating Uncertainties in a Multi-Criteria Decision Analysis with the Entscheidungsnavi
by Sven Peters, Mendy Tönsfeuerborn and Rüdiger von Nitzsch
Mathematics 2024, 12(11), 1746; https://doi.org/10.3390/math12111746 - 4 Jun 2024
Viewed by 287
Abstract
The Entscheidungsnavi is an open-source decision support system based on multi-attribute utility theory, that offers various methods for dealing with uncertainties. To model decisions with uncertainties, decision-makers can use two categories: Forecast and Parameter Uncertainties. Forecast Uncertainty is modeled with (combined) influence factors [...] Read more.
The Entscheidungsnavi is an open-source decision support system based on multi-attribute utility theory, that offers various methods for dealing with uncertainties. To model decisions with uncertainties, decision-makers can use two categories: Forecast and Parameter Uncertainties. Forecast Uncertainty is modeled with (combined) influence factors using discrete, user-defined probability distributions or predefined ‘worst-median-best’ distributions. Parameter Uncertainty allows imprecision for utilities, objective weights, and probability distributions. To analyze these uncertainties, the Entscheidungsnavi offers several methods and tools, like a robustness check, based on (Monte Carlo) simulations and a sensitivity analysis. The objective weight analysis provides insights into the effects of different objective weight combinations. Indicator impacts, tornado diagrams, and risk profiles visualize the impact of uncertainties in a decision under risk. Risk profiles also enable a check for stochastic and simulation dominance. This article presents the complete range of methods for dealing with uncertainties in the Entscheidungsnavi using a hypothetical case study. Full article
(This article belongs to the Special Issue Mathematical Modelling in Decision Making Analysis)
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19 pages, 4308 KiB  
Article
A Comprehensive Decision-Making Approach for Strategic Product Module Planning in Mass Customization
by Shuo-Fang Liu, Shi-Yu Wang and Hsueh-Hung Tung
Mathematics 2024, 12(11), 1745; https://doi.org/10.3390/math12111745 - 3 Jun 2024
Viewed by 148
Abstract
This paper explores the integrated optimization of complex coupled industrial manufacturing systems and production strategies based on user customization needs. Two optimization metrics are considered: one is whether the production process of engineering manufacturing is simplified, and the other is whether it is [...] Read more.
This paper explores the integrated optimization of complex coupled industrial manufacturing systems and production strategies based on user customization needs. Two optimization metrics are considered: one is whether the production process of engineering manufacturing is simplified, and the other is whether it is based on the customization requirements of the customer. These two metrics are interrelated, and cases may even be conflicting. Considering the interdependence between engineering manufacturing and user requirements, this paper develops an integrated customized modular engineering manufacturing process to minimize production and maintenance costs and improve efficiency while meeting user customization requirements. This paper takes expert evaluation as an important decision indicator and optimizes the production process strategy on this basis. Finally, a case study is given to illustrate the applicability of the proposed process model. Full article
(This article belongs to the Section Fuzzy Sets, Systems and Decision Making)
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15 pages, 351 KiB  
Article
Linear Combination of Order Statistics Moments from Log-Extended Exponential Geometric Distribution with Applications to Entropy
by Fatimah E. Almuhayfith, Mahfooz Alam, Hassan S. Bakouch, Sudeep R. Bapat and Olayan Albalawi
Mathematics 2024, 12(11), 1744; https://doi.org/10.3390/math12111744 - 3 Jun 2024
Viewed by 217
Abstract
Moments of order statistics (OSs) characterize the Weibull–geometric and half-logistic families of distributions, of which the extended exponential–geometric (EEG) distribution is a particular case. The EEG distribution is used to create the log-extended exponential–geometric (LEEG) distribution, which is bounded in the unit interval [...] Read more.
Moments of order statistics (OSs) characterize the Weibull–geometric and half-logistic families of distributions, of which the extended exponential–geometric (EEG) distribution is a particular case. The EEG distribution is used to create the log-extended exponential–geometric (LEEG) distribution, which is bounded in the unit interval (0, 1). In addition to the generalized Stirling numbers of the first kind, a few years ago, the polylogarithm function and the Lerch transcendent function were used to determine the moments of order statistics of the LEEG distributions. As an application based on the L-moments, we expand the features of the LEEG distribution in this work. In terms of the Gauss hypergeometric function, this work presents the precise equations and recurrence relations for the single moments of OSs from the LEEG distribution. Along with recurrence relations between the expectations of function of two OSs from the LEEG distribution, it also displays the truncated and conditional distribution of the OSs. Additionally, we use the L-moments to estimate the parameters of the LEEG distribution. We further fit the LEEG distribution on three practical data sets from medical and environmental sciences areas. It is seen that the estimated parameters through L-moments of the OSs give a superior fit. We finally determine the correspondence between the entropies and the OSs. Full article
(This article belongs to the Special Issue Advances in Applied Probability and Statistical Inference)
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