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Mathematics
Volume 10
Issue 19
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Mathematics, Volume 10, Issue 19 (October-1 2022) – 308 articles

Cover Story (view full-size image): Bulk-service queueing systems have been widely applied in many areas in real life. Compared to well-developed single-server queueing systems, multi-server queueing systems are more complex and harder to deal with, especially when the inter-arrival time distributions are arbitrary. This paper deals with analytic and computational analysis of queue-length distributions for a complex bulk-service, multi-server queueing system GI/Ma,b/c, wherein inter-arrival times follow an arbitrary distribution, a is the quorum, b is the capacity of each server, and c is the number of servers; service times follow exponential distributions. The introduction of quorum increases the complexity of the model. In view of this, a two-dimensional Markov chain has to be involved. Currently, it appears that this system has not been addressed. View this paper
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25 pages, 8252 KiB  
Article
2D Newton Schwarz Legendre Collocation Method for a Convection Problem
by Darío Martínez, Henar Herrero and Francisco Pla
Mathematics 2022, 10(19), 3718; https://doi.org/10.3390/math10193718 - 10 Oct 2022
Cited by 1 | Viewed by 1286
Abstract
In this work, an alternate Schwarz domain decomposition method is proposed to solve a Rayleigh–Bénard problem. The problem is modeled with the incompressible Navier–Stokes equations coupled with a heat equation in a rectangular domain. The Boussinesq approximation is considered. The nonlinearity is solved [...] Read more.
In this work, an alternate Schwarz domain decomposition method is proposed to solve a Rayleigh–Bénard problem. The problem is modeled with the incompressible Navier–Stokes equations coupled with a heat equation in a rectangular domain. The Boussinesq approximation is considered. The nonlinearity is solved with Newton’s method. Each iteration of Newton’s method is discretized with an alternating Schwarz scheme, and each Schwarz problem is solved with a Legendre collocation method. The original domain is divided into several subdomains in both directions of the plane. Legendre collocation meshes are coarse, so the problem in each subdomain is well conditioned, and the size of the total mesh can grow by increasing the number of subdomains. In this way, the ill conditioning of Legendre collocation is overcome. The present work achieves an efficient alternating Schwarz algorithm such that the number of subdomains can be increased indefinitely in both directions of the plane. The method has been validated with a benchmark with numerical solutions obtained with other methods and with real experiments. Thanks to this domain decomposition method, the aspect ratio and Rayleigh number can be increased considerably by adding subdomains. Rayleigh values near to the turbulent regime can be reached. Namely, the great advantage of this method is that we obtain solutions close to turbulence, or in domains with large aspect ratios, by solving systems of linear equations with well-conditioned matrices of maximum size one thousand. This is an advantage over other methods that require solving systems with huge matrices of the order of several million, usually with conditioning problems. The computational cost is comparable to other methods, and the code is parallelizable. Full article
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20 pages, 409 KiB  
Article
Convergence of Uniformity Criteria and the Application in Numerical Integration
by Yang Huang and Yongdao Zhou
Mathematics 2022, 10(19), 3717; https://doi.org/10.3390/math10193717 - 10 Oct 2022
Cited by 2 | Viewed by 1180
Abstract
Quasi-Monte Carlo (QMC) methods have been successfully used for the estimation of numerical integrations arising in many applications. In most QMC methods, low-discrepancy sequences have been used, such as digital nets and lattice rules. In this paper, we derive the convergence rates of [...] Read more.
Quasi-Monte Carlo (QMC) methods have been successfully used for the estimation of numerical integrations arising in many applications. In most QMC methods, low-discrepancy sequences have been used, such as digital nets and lattice rules. In this paper, we derive the convergence rates of order of some improved discrepancies, such as centered L2-discrepancy, wrap-around L2-discrepancy, and mixture discrepancy, and propose a randomized QMC method based on a uniform design constructed by the mixture discrepancy and Baker’s transformation. Moreover, the numerical results show that the proposed method has better approximation than the Monte Carlo method and many other QMC methods, especially when the number of dimensions is less than 10. Full article
(This article belongs to the Special Issue Distribution Theory and Application)
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18 pages, 12947 KiB  
Article
Robustness Learning via Inference-Softmax Cross Entropy in Misaligned Distribution of Image
by Bingbing Song, Ruxin Wang, Wei He and Wei Zhou
Mathematics 2022, 10(19), 3716; https://doi.org/10.3390/math10193716 - 10 Oct 2022
Cited by 2 | Viewed by 1286
Abstract
Adversarial examples easily mislead vision systems based on deep neural networks (DNNs) trained with softmax cross entropy (SCE) loss. The vulnerability of DNN comes from the fact that SCE drives DNNs to fit on the training examples, whereas the resultant feature distributions between [...] Read more.
Adversarial examples easily mislead vision systems based on deep neural networks (DNNs) trained with softmax cross entropy (SCE) loss. The vulnerability of DNN comes from the fact that SCE drives DNNs to fit on the training examples, whereas the resultant feature distributions between the training and adversarial examples are unfortunately misaligned. Several state-of-the-art methods start from improving the inter-class separability of training examples by modifying loss functions, where we argue that the adversarial examples are ignored, thus resulting in a limited robustness to adversarial attacks. In this paper, we exploited the inference region, which inspired us to apply margin-like inference information to SCE, resulting in a novel inference-softmax cross entropy (I-SCE) loss, which is intuitively appealing and interpretable. The inference information guarantees that it is difficult for neural networks to cross the decision boundary under an adversarial attack, and guarantees both the inter-class separability and the improved generalization to adversarial examples, which was further demonstrated and proved under the min-max framework. Extensive experiments show that the DNN models trained with the proposed I-SCE loss achieve a superior performance and robustness over the state-of-the-arts under different prevalent adversarial attacks; for example, the accuracy of I-SCE is 63% higher than SCE under the PGD50un attack on the MNIST dataset. These experiments also show that the inference region can effectively solve the misaligned distribution. Full article
(This article belongs to the Special Issue Advanced Deep Learning and Mathematical Modeling for Reliability, Security and Privacy Problems in Engineering)
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25 pages, 679 KiB  
Article
The Large Arcsine Exponential Dispersion Model—Properties and Applications to Count Data and Insurance Risk
by Shaul K. Bar-Lev and Ad Ridder
Mathematics 2022, 10(19), 3715; https://doi.org/10.3390/math10193715 - 10 Oct 2022
Viewed by 1107
Abstract
The large arcsine exponential dispersion model (LAEDM) is a class of three-parameter distributions on the non-negative integers. These distributions show the specific characteristics of being leptokurtic, zero-inflated, overdispersed, and skewed to the right. Therefore, these distributions are well suited to fit count data [...] Read more.
The large arcsine exponential dispersion model (LAEDM) is a class of three-parameter distributions on the non-negative integers. These distributions show the specific characteristics of being leptokurtic, zero-inflated, overdispersed, and skewed to the right. Therefore, these distributions are well suited to fit count data with these properties. Furthermore, recent studies in actuarial sciences argue for the consideration of such distributions in the computation of risk factors. In this paper, we provide a thorough analysis of the LAEDM by deriving (a) the mean value parameterization of the LAEDM; (b) exact expressions for its probability mass function at n=0,1,…; (c) a simple bound for these probabilities that is sharp for large n; (d) a simulation algorithm for sampling from LAEDM. We have implemented the LAEDM for statistical modeling of various real count data sets. We assess its fitting performance by comparing it with the performances of traditional counting models. We use a simulation algorithm for computing tail probabilities of the aggregated claim size in an insurance risk model. Full article
(This article belongs to the Section Probability and Statistics)
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21 pages, 1827 KiB  
Article
RanKer: An AI-Based Employee-Performance Classification Scheme to Rank and Identify Low Performers
by Keyur Patel, Karan Sheth, Dev Mehta, Sudeep Tanwar, Bogdan Cristian Florea, Dragos Daniel Taralunga, Ahmed Altameem, Torki Altameem and Ravi Sharma
Mathematics 2022, 10(19), 3714; https://doi.org/10.3390/math10193714 - 10 Oct 2022
Cited by 4 | Viewed by 3999
Abstract
An organization’s success depends on its employees, and an employee’s performance decides whether the organization is successful. Employee performance enhances the productivity and output of organizations, i.e., the performance of an employee paves the way for the organization’s success. Hence, analyzing employee performance [...] Read more.
An organization’s success depends on its employees, and an employee’s performance decides whether the organization is successful. Employee performance enhances the productivity and output of organizations, i.e., the performance of an employee paves the way for the organization’s success. Hence, analyzing employee performance and giving performance ratings to employees is essential for companies nowadays. It is evident that different people have different skill sets and behavior, so data should be gathered from all parts of an employee’s life. This paper aims to provide the performance rating of an employee based on various factors. First, we compare various AI-based algorithms, such as random forest, artificial neural network, decision tree, and XGBoost. Then, we propose an ensemble approach, RanKer, combining all the above approaches. The empirical results illustrate that the efficacy of the proposed model compared to traditional models such as random forest, artificial neural network, decision tree, and XGBoost is high in terms of precision, recall, F1-score, and accuracy. Full article
(This article belongs to the Special Issue Application of Advanced Computing and Artificial Intelligence in Engineering and Science)
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27 pages, 1850 KiB  
Article
Potentially Related Commodity Discovery Based on Link Prediction
by Xiaoji Wan, Fen Chen, Hailin Li and Weibin Lin
Mathematics 2022, 10(19), 3713; https://doi.org/10.3390/math10193713 - 10 Oct 2022
Viewed by 1224
Abstract
The traditional method of related commodity discovery mainly focuses on direct co-occurrence association of commodities and ignores their indirect connection. Link prediction can estimate the likelihood of links between nodes and predict the existent yet unknown future links. This paper proposes a potentially [...] Read more.
The traditional method of related commodity discovery mainly focuses on direct co-occurrence association of commodities and ignores their indirect connection. Link prediction can estimate the likelihood of links between nodes and predict the existent yet unknown future links. This paper proposes a potentially related commodities discovery method based on link prediction (PRCD) to predict the undiscovered association. The method first builds a network with the discovered binary association rules among items and uses link prediction approaches to assess possible future links in the network. The experimental results show that the accuracy of the proposed method is better than traditional methods. In addition, it outperforms the link prediction based on graph neural network in some datasets. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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16 pages, 6396 KiB  
Article
Analysis and Performance Evaluation of a Novel Adjustable Speed Drive with a Homopolar-Type Rotor
by Songlin Guo, Zhengkang Yi, Pan Liu, Guoshuai Wang, Houchuan Lai, Kexun Yu and Xianfei Xie
Mathematics 2022, 10(19), 3712; https://doi.org/10.3390/math10193712 - 10 Oct 2022
Cited by 3 | Viewed by 1295
Abstract
The use of a magnetic adjustable speed drive is a popular choice in industrial settings due to its efficient operation, vibration isolation, low maintenance, and overload protection. Most conventional magnetic adjustable speed drives use various forms of the permanent magnets (PMs). Due to [...] Read more.
The use of a magnetic adjustable speed drive is a popular choice in industrial settings due to its efficient operation, vibration isolation, low maintenance, and overload protection. Most conventional magnetic adjustable speed drives use various forms of the permanent magnets (PMs). Due to the PMs, this type of machine has continuous free-wheeling losses in the form of hysteresis and induced eddy currents. In recent years, the homopolar-type rotor has been widely used in high-speed machines, superconducting machines, and in the application of flywheel energy storage. This study proposes a new application of the homopolar-type rotor. A novel adjustable speed drive with a homopolar-type rotor (HTR-ASD), which has obvious advantages (no brush, no permanent magnet, and no mechanical flux regulation device), is designed and analyzed in this study. Its speed and torque can be adjusted only by adjusting the excitation current. Firstly, in this study, the structure, operation principles, and flux-modulated mechanism of the HTR-ASD are studied. The homopolar-type rotor has a special three-dimensional magnetic circuit structure with the same pole. The 3D-FEM is usually used to calculate its parameters, which is time consuming. In this study, an analytical method is developed to solve this issue. To analytically calculate the torque characteristics, the air gap magnetic flux density, and the winding inductance parameter, the equivalent circuit and the air gap permeance are researched to simplify the analysis. Then, the key parameters of the HTR-ASD are calculated. Finally, the performance of the HTR-ASD is comparatively studied using the analytical method and finite element method, and a comparison of the results is carried out. The comparison indicates that the analytical method is in good agreement with simulation results, and that it is very helpful for designing homopolar-type rotor machines. According to the analysis, the proposed adjustable speed drive displays a great performance in relation to the operating characteristics of a flexible mechanical speed drive. Full article
(This article belongs to the Special Issue Modeling and Simulation in Engineering, 2nd Edition)
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15 pages, 5742 KiB  
Article
A Novel RBF Collocation Method Using Fictitious Centre Nodes for Elasticity Problems
by Hui Zheng, Xiaoling Lai, Anyu Hong and Xing Wei
Mathematics 2022, 10(19), 3711; https://doi.org/10.3390/math10193711 - 10 Oct 2022
Cited by 1 | Viewed by 1042
Abstract
The traditional radial basis function collocation method (RBFCM) has poor stability when solving two-dimensional elastic problems, and the numerical results are very sensitive to shape parameters, especially in solving elastic problems. In this paper, a novel radial basis function collocation method (RBFCM) using [...] Read more.
The traditional radial basis function collocation method (RBFCM) has poor stability when solving two-dimensional elastic problems, and the numerical results are very sensitive to shape parameters, especially in solving elastic problems. In this paper, a novel radial basis function collocation method (RBFCM) using fictitious centre nodes is applied to the elastic problem. The proposed RBFCM employs fictitious centre nodes to interpolate the unknown coefficients, and is much less sensitive to the shape parameter compared with the traditional RBFCM. The details of the shape parameters are discussed for the novel RBFCM in elastic problems. Elastic problems with and without analytical solutions are given to show the effectiveness of the improved RBFCM. Full article
(This article belongs to the Special Issue Recent Advances in Numerical Methods for Scientific and Engineering Applications)
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15 pages, 440 KiB  
Article
Entropy-Randomized Clustering
by Yuri S. Popkov, Yuri A. Dubnov and Alexey Yu. Popkov
Mathematics 2022, 10(19), 3710; https://doi.org/10.3390/math10193710 - 10 Oct 2022
Viewed by 839
Abstract
This paper proposes a clustering method based on a randomized representation of an ensemble of possible clusters with a probability distribution. The concept of a cluster indicator is introduced as the average distance between the objects included in the cluster. The indicators averaged [...] Read more.
This paper proposes a clustering method based on a randomized representation of an ensemble of possible clusters with a probability distribution. The concept of a cluster indicator is introduced as the average distance between the objects included in the cluster. The indicators averaged over the entire ensemble are considered the latter’s characteristics. The optimal distribution of clusters is determined using the randomized machine learning approach: an entropy functional is maximized with respect to the probability distribution subject to constraints imposed on the averaged indicator of the cluster ensemble. The resulting entropy-optimal cluster corresponds to the maximum of the optimal probability distribution. This method is developed for binary clustering as a basic procedure. Its extension to t-ary clustering is considered. Some illustrative examples of entropy-randomized clustering are given. Full article
(This article belongs to the Special Issue Mathematical Modeling, Optimization and Machine Learning)
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32 pages, 16329 KiB  
Article
Stability Evaluation of Medium Soft Soil Pile Slope Based on Limit Equilibrium Method and Finite Element Method
by Xiaoyan Du and Jinfei Chai
Mathematics 2022, 10(19), 3709; https://doi.org/10.3390/math10193709 - 10 Oct 2022
Cited by 1 | Viewed by 1262
Abstract
The stability of an open-pit slope is an extremely important factor related to the safe production of an open-pit mine. It is the first safety technical problem encountered and should be solved in the process of mine design and production. By the means [...] Read more.
The stability of an open-pit slope is an extremely important factor related to the safe production of an open-pit mine. It is the first safety technical problem encountered and should be solved in the process of mine design and production. By the means of an engineering geology and hydrogeological investigation of the waste dump area of the Nayuan open-pit coal mine and numerical simulation research, this paper analyzes and studies the slope stability of the stope and waste dump of the Nayuan open-pit coal mine in detail and puts forward measures such as slope prevention and automatic monitoring to achieve the goal of protecting the slope of the stope and waste dump and the surrounding environment. The main research results are as follows: (1) The geotechnical physical and mechanical indexes of stope and waste dump are collected and analyzed, and the geotechnical mechanical indexes in this report were determined, which basically meet the requirements of slope stability analysis. (2) The limit equilibrium method and finite element method were used to analyze and evaluate the current slope stability of the Nayuan open-pit coal mine. It was concluded that the foundation of the waste dump is basically stable, and the potential landslide modes of the slope are arc-shaped sliding surface and arc-shaped straight-line sliding surface. The numerical simulation and checking results showed that the current stope and waste dump slope are stable. (3) According to the analysis and evaluation results of slope stability, feasible slope prevention measures are put forward. The research results are of great significance to the safety of important facilities in open-pit mines and provide a basis for the design and safety implementation of open-pit slope engineering. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering)
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26 pages, 11505 KiB  
Article
Sizing and Design of a PV-Wind-Fuel Cell Storage System Integrated into a Grid Considering the Uncertainty of Load Demand Using the Marine Predators Algorithm
by Fayza S. Mahmoud, Ashraf M. Abdelhamid, Ameena Al Sumaiti, Abou-Hashema M. El-Sayed and Ahmed A. Zaki Diab
Mathematics 2022, 10(19), 3708; https://doi.org/10.3390/math10193708 - 10 Oct 2022
Cited by 8 | Viewed by 1783
Abstract
In this paper, the utility grid is integrated with hybrid photovoltaic (PV)/wind/fuel cells to overcome the unavailability of the grid and the single implementation of renewable energy. The main purpose of this study is smart management of hydrogen storage tanks and power exchange [...] Read more.
In this paper, the utility grid is integrated with hybrid photovoltaic (PV)/wind/fuel cells to overcome the unavailability of the grid and the single implementation of renewable energy. The main purpose of this study is smart management of hydrogen storage tanks and power exchange between the hybrid renewable energy and the grid to minimize the total cost of the hybrid system and load uncertainties. PV and wind act as the main renewable energy sources, whereas fuel cells act as auxiliary sources designed to compensate for power variations and to ensure continuous power flow to the load. The grid is considered a backup system that works when hybrid renewable energy and fuel cells are unavailable. In this study, the optimal size of the components of the hybrid energy system is introduced using two methods: the marine predators’ algorithm (MPA) and the seagull optimization algorithm (SOA). The optimal sizing problem is also run accounting for the uncertainty in load demand. The results obtained from the proposed optimization are given with and without uncertainty in load demand. The simulation results of the hybrid system without uncertainty demonstrate the superiority of the MPA compared with SOA. However, in the case of load uncertainty, the simulation results (the uncertainty) are given using the MPA optimization technique with +5%, +10%, and +15% uncertainty in load, which showed that the net present cost and purchase energy are increased with uncertainty. Full article
(This article belongs to the Special Issue Advanced Mathematical Approaches to Engineering and Computational Problems)
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18 pages, 572 KiB  
Article
Research on the Mathematical Model for Optimal Allocation of Human Resources in the Operation and Maintenance Units of a Heavy Haul Railway
by Linfang Shen, Kuoyu Liu, Jinfei Chai, Weibin Ma, Xiaoxiong Guo, Yao Li, Peng Zhao and Boying Liu
Mathematics 2022, 10(19), 3707; https://doi.org/10.3390/math10193707 - 10 Oct 2022
Cited by 1 | Viewed by 1439
Abstract
According to the existing personnel structure, quantity, development strategy, and market demand of the Shuohuang Railway Company’s operation and maintenance project, the demand quantity of various employees of the company for the past three years is predicted, and a human resource optimization model [...] Read more.
According to the existing personnel structure, quantity, development strategy, and market demand of the Shuohuang Railway Company’s operation and maintenance project, the demand quantity of various employees of the company for the past three years is predicted, and a human resource optimization model based on existing human resources and future plans is established. Then, the optimal solutions of the two mathematical models were calculated and analyzed using LINGO software. Finally, combined with the actual situation, the optimal allocation of human resources for the operation and maintenance project of KY company was obtained. The following conclusions are obtained. (1) For the optimal allocation model of existing human resources, the maximum net profit of the optimal staffing model is CNY 3258000. (2) The human resources allocation cost of the minimum dismissal model is CNY 81000. (3) The human resources allocation cost of the lowest cost model is CNY 15500. The research results can effectively guide the human resource management of the operation and maintenance project of the Shuohuang Railway Company, and have important theoretical and practical significance for further analysis of human resources model and its optimal allocation method. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering)
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12 pages, 309 KiB  
Article
About AutoGraphiX Conjecture on Domination Number and Remoteness of Graphs
by Lidan Pei
Mathematics 2022, 10(19), 3706; https://doi.org/10.3390/math10193706 - 10 Oct 2022
Viewed by 915
Abstract
A set D⊆V(G) is called a dominating set if N[v]∩D≠∅ for every vertex v in graph G. The domination number γ(G) is the minimum cardinality of a [...] Read more.
A set D⊆V(G) is called a dominating set if N[v]∩D≠∅ for every vertex v in graph G. The domination number γ(G) is the minimum cardinality of a dominating set of G. The proximity π(v) of a vertex v is the average distance from it to all other vertices in graph. The remoteness ρ(G) of a connected graph G is the maximum proximity of all the vertices in graph G. AutoGraphiX Conjecture A.565 gives the sharp upper bound on the difference between the domination number and remoteness. In this paper, we characterize the explicit graphs that attain the upper bound in the above conjecture, and prove the improved AutoGraphiX conjecture. Full article
(This article belongs to the Special Issue Research and Applications of Discrete Mathematics)
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19 pages, 5662 KiB  
Article
Effect of Different Tunnel Distribution on Dynamic Behavior and Damage Characteristics of Non-Adjacent Tunnel Triggered by Blasting Disturbance
by Jiadong Qiu and Fan Feng
Mathematics 2022, 10(19), 3705; https://doi.org/10.3390/math10193705 - 10 Oct 2022
Cited by 3 | Viewed by 1178
Abstract
When a blasting is executed near two tunnels, the blasting wave will trigger a dynamic response and damage to the tunnels. Depending on the tunnel distribution, the path of the blasting wave to the remote non-adjacent tunnels will change. The aim of this [...] Read more.
When a blasting is executed near two tunnels, the blasting wave will trigger a dynamic response and damage to the tunnels. Depending on the tunnel distribution, the path of the blasting wave to the remote non-adjacent tunnels will change. The aim of this study is to analyze the effect of the tunnel distribution on the dynamic response characteristics of a remote non-adjacent tunnel. Numerical models of two tunnels were established by PFC2D and three different tunnel distributions were considered. The two tunnels were divided into the adjacent tunnel and the non-adjacent tunnel according to their relative distance to the blasting source. The dynamic stress evolution, damage characteristics and the evolution of strain energy of the non-adjacent tunnel were initially analyzed. The results show that the stress wave amplitude of the non-adjacent tunnel is closely related to the tunnel distribution, but only near the sidewalls of the non-adjacent tunnel is the stress wave waveform sensitive to the tunnel distribution. The larger the tunnel dip, the more severe the damage to the non-adjacent tunnel. In addition, as the tunnel dip increases, the maximum strain energy densities (SEDs) in the roof, floor and sidewalls of the non-adjacent tunnel exhibit different trends. The influence of the wavelength of the blasting wave is further discussed. It is shown that the dynamic stress amplification factor and damage degree around the non-adjacent tunnel is usually positively correlated with the wavelength of the blasting wave. Moreover, the release of strain energy around the non-adjacent tunnel has a positive correlation with the wavelength. The SED variations in different areas around the non-adjacent tunnel also exhibit different trends with the increase of tunnel dip. Full article
(This article belongs to the Special Issue Mathematical Problems in Rock Mechanics and Rock Engineering)
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21 pages, 308 KiB  
Article
On Some Characterizations for Uniform Dichotomy of Evolution Operators in Banach Spaces
by Rovana Boruga (Toma) and Mihail Megan
Mathematics 2022, 10(19), 3704; https://doi.org/10.3390/math10193704 - 10 Oct 2022
Cited by 7 | Viewed by 930
Abstract
The present paper deals with two of the most significant behaviors in the theory of dynamical systems: the uniform exponential dichotomy and the uniform polynomial dichotomy for evolution operators in Banach spaces. Assuming that the evolution operator has uniform exponential growth, respectively uniform [...] Read more.
The present paper deals with two of the most significant behaviors in the theory of dynamical systems: the uniform exponential dichotomy and the uniform polynomial dichotomy for evolution operators in Banach spaces. Assuming that the evolution operator has uniform exponential growth, respectively uniform polynomial growth, we give some characterizations for the uniform exponential dichotomy, respectively for the uniform polynomial dichotomy. The proof techniques that we use for the polynomial case are new. In addition, connections between the concepts approached are established. Full article
(This article belongs to the Special Issue Recent Investigations of Differential and Fractional Equations and Inclusions II)
23 pages, 661 KiB  
Article
The Sufficient Conditions for Orthogonal Matching Pursuit to Exactly Reconstruct Sparse Polynomials
by Aitong Huang, Renzhong Feng and Andong Wang
Mathematics 2022, 10(19), 3703; https://doi.org/10.3390/math10193703 - 10 Oct 2022
Cited by 2 | Viewed by 881
Abstract
Orthogonal matching pursuit (OMP for short) is a classical method for sparse signal recovery in compressed sensing. In this paper, we consider the application of OMP to reconstruct sparse polynomials generated by uniformly bounded orthonormal systems, which is an extension of the work [...] Read more.
Orthogonal matching pursuit (OMP for short) is a classical method for sparse signal recovery in compressed sensing. In this paper, we consider the application of OMP to reconstruct sparse polynomials generated by uniformly bounded orthonormal systems, which is an extension of the work on OMP to reconstruct sparse trigonometric polynomials. Firstly, in both cases of sampled data with and without noise, sufficient conditions for OMP to recover the coefficient vector of a sparse polynomial are given, which are more loose than the existing results. Then, based on a more accurate estimation of the mutual coherence of a structured random matrix, the recovery guarantees and success probabilities for OMP to reconstruct sparse polynomials are obtained with the help of those sufficient conditions. In addition, the error estimation for the recovered coefficient vector is gained when the sampled data contain noise. Finally, the validity and correctness of the theoretical conclusions are verified by numerical experiments. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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13 pages, 494 KiB  
Article
An MM Algorithm for the Frailty-Based Illness Death Model with Semi-Competing Risks Data
by Xifen Huang, Jinfeng Xu, Hao Guo, Jianhua Shi and Wenjie Zhao
Mathematics 2022, 10(19), 3702; https://doi.org/10.3390/math10193702 - 10 Oct 2022
Cited by 2 | Viewed by 1308
Abstract
For analyzing multiple events data, the illness death model is often used to investigate the covariate–response association for its easy and direct interpretation as well as the flexibility to accommodate the within-subject dependence. The resulting estimation and inferential procedures often depend on the [...] Read more.
For analyzing multiple events data, the illness death model is often used to investigate the covariate–response association for its easy and direct interpretation as well as the flexibility to accommodate the within-subject dependence. The resulting estimation and inferential procedures often depend on the subjective specification of the parametric frailty distribution. For certain frailty distributions, the computation can be challenging as the estimation involves both the nonparametric component and the parametric component. In this paper, we develop efficient computational methods for analyzing semi-competing risks data in the illness death model with the general frailty, where the Minorization–Maximization (MM) principle is employed for yielding accurate estimation and inferential procedures. Simulation studies are conducted to assess the finite-sample performance of the proposed method. An application to a real data is also provided for illustration. Full article
(This article belongs to the Special Issue Recent Advances in Computational Statistics)
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14 pages, 487 KiB  
Article
On Strictly Positive Fragments of Modal Logics with Confluence
by Stanislav Kikot and Andrey Kudinov
Mathematics 2022, 10(19), 3701; https://doi.org/10.3390/math10193701 - 10 Oct 2022
Viewed by 1087
Abstract
We axiomatize strictly positive fragments of modal logics with the confluence axiom. We consider unimodal logics such as K.2, D.2, D4.2 and S4.2 with unimodal confluence [...] Read more.
We axiomatize strictly positive fragments of modal logics with the confluence axiom. We consider unimodal logics such as K.2, D.2, D4.2 and S4.2 with unimodal confluence ⋄□p→□⋄p as well as the products of modal logics in the set K,D,T,D4,S4, which contain bimodal confluence ⋄1□2p→□2⋄1p. We show that the impact of the unimodal confluence axiom on the axiomatisation of strictly positive fragments is rather weak. In the presence of ⊤→⋄⊤, it simply disappears and does not contribute to the axiomatisation. Without ⊤→⋄⊤ it gives rise to a weaker formula ⋄⊤→⋄⋄⊤. On the other hand, bimodal confluence gives rise to more complicated formulas such as ⋄1p∧⋄2n⊤→⋄1(p∧⋄2n⊤) (which are superfluous in a product if the corresponding factor contains ⊤→⋄⊤). We also show that bimodal confluence cannot be captured by any finite set of strictly positive implications. Full article
(This article belongs to the Special Issue Combinatorial Algebra, Computation, and Logic)
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16 pages, 10103 KiB  
Article
Printed Texture Guided Color Feature Fusion for Impressionism Style Rendering of Oil Paintings
by Jing Geng, Li’e Ma, Xiaoquan Li, Xin Zhang and Yijun Yan
Mathematics 2022, 10(19), 3700; https://doi.org/10.3390/math10193700 - 09 Oct 2022
Viewed by 1704
Abstract
As a major branch of Non-Photorealistic Rendering (NPR), image stylization mainly uses computer algorithms to render a photo into an artistic painting. Recent work has shown that the ex-traction of style information such as stroke texture and color of the target style image [...] Read more.
As a major branch of Non-Photorealistic Rendering (NPR), image stylization mainly uses computer algorithms to render a photo into an artistic painting. Recent work has shown that the ex-traction of style information such as stroke texture and color of the target style image is the key to image stylization. Given its stroke texture and color characteristics, a new stroke rendering method is proposed. By fully considering the tonal characteristics and the representative color of the original oil painting, it can fit the tone of the original oil painting image into a stylized image whilst keeping the artist’s creative effect. The experiments have validated the efficacy of the proposed model in comparison to three state-of-the-arts. This method would be more suitable for the works of pointillism painters with a relatively uniform style, especially for natural scenes, otherwise, the results can be less satisfactory. Full article
(This article belongs to the Special Issue Advances in Computer Vision and Machine Learning)
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13 pages, 431 KiB  
Article
Bipartite Synchronization of Fractional-Order Memristor-Based Coupled Delayed Neural Networks with Pinning Control
by P. Babu Dhivakaran, A. Vinodkumar, S. Vijay, S. Lakshmanan, J. Alzabut, R. A. El-Nabulsi and W. Anukool
Mathematics 2022, 10(19), 3699; https://doi.org/10.3390/math10193699 - 09 Oct 2022
Cited by 5 | Viewed by 1406
Abstract
This paper investigates the bipartite synchronization of memristor-based fractional-order coupled delayed neural networks with structurally balanced and unbalanced concepts. The main result is established for the proposed model using pinning control, fractional-order Jensen’s inequality, and the linear matrix inequality. Further, new sufficient conditions [...] Read more.
This paper investigates the bipartite synchronization of memristor-based fractional-order coupled delayed neural networks with structurally balanced and unbalanced concepts. The main result is established for the proposed model using pinning control, fractional-order Jensen’s inequality, and the linear matrix inequality. Further, new sufficient conditions are derived using the Lyapunov–Krasovskii functional with delay-dependent criteria. Finally, numerical simulations are provided including two numerical examples to show the effectiveness of the theoretical results. Full article
(This article belongs to the Special Issue Memristor Cellular Nonlinear Networks: Theory and Applications)
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33 pages, 3285 KiB  
Article
Optimization Methods for Redundancy Allocation in Hybrid Structure Large Binary Systems
by Petru Cașcaval and Florin Leon
Mathematics 2022, 10(19), 3698; https://doi.org/10.3390/math10193698 - 09 Oct 2022
Cited by 1 | Viewed by 1384
Abstract
This paper addresses the issue of optimal redundancy allocation in hybrid structure large binary systems. Two aspects of optimization are considered: (1) maximizing the reliability of the system under the cost constraint, and (2) obtaining the necessary reliability at a minimum cost. The [...] Read more.
This paper addresses the issue of optimal redundancy allocation in hybrid structure large binary systems. Two aspects of optimization are considered: (1) maximizing the reliability of the system under the cost constraint, and (2) obtaining the necessary reliability at a minimum cost. The complex binary system considered in this work is composed of many subsystems with redundant structure. To cover most of the cases encountered in practice, the following kinds of redundancy are considered: active redundancy, passive redundancy, hybrid standby redundancy with a hot or warm reserve and possibly other cold ones, triple modular redundancy (TMR) structure with control facilities and cold spare components, static redundancy: triple modular redundancy or 5-modular redundancy (5MR), TMR/Simplex with cold standby redundancy, and TMR/Duplex with cold standby redundancy. A classic evolutionary algorithm highlights the complexity of this optimization problem. To master the complexity of this problem, two fundamentally different optimization methods are proposed: an improved evolutionary algorithm and a zero-one integer programming formulation. To speed up the search process, a lower bound is determined first. The paper highlights the difficulty of these optimization problems for large systems and, based on numerical results, shows the effectiveness of zero-one integer programming. Full article
(This article belongs to the Special Issue Advances in Artificial Intelligence: Models, Optimization, and Machine Learning, 2nd Edition)
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14 pages, 8895 KiB  
Article
Perspective Transformer and MobileNets-Based 3D Lane Detection from Single 2D Image
by Mengyu Li, Phuong Minh Chu and Kyungeun Cho
Mathematics 2022, 10(19), 3697; https://doi.org/10.3390/math10193697 - 09 Oct 2022
Viewed by 1714
Abstract
Three-dimensional (3D) lane detection is widely used in image understanding, image analysis, 3D scene reconstruction, and autonomous driving. Recently, various methods for 3D lane detection from single two-dimensional (2D) images have been proposed to address inaccurate lane layouts in scenarios (e.g., uphill, downhill, [...] Read more.
Three-dimensional (3D) lane detection is widely used in image understanding, image analysis, 3D scene reconstruction, and autonomous driving. Recently, various methods for 3D lane detection from single two-dimensional (2D) images have been proposed to address inaccurate lane layouts in scenarios (e.g., uphill, downhill, and bumps). Many previous studies struggled in solving complex cases involving realistic datasets. In addition, these methods have low accuracy and high computational resource requirements. To solve these problems, we put forward a high-quality method to predict 3D lanes from a single 2D image captured by conventional cameras, which is also cost effective. The proposed method comprises the following three stages. First, a MobileNet model that requires low computational resources was employed to generate multiscale front-view features from a single RGB image. Then, a perspective transformer calculated bird’s eye view (BEV) features from the front-view features. Finally, two convolutional neural networks were used for predicting the 2D and 3D coordinates and respective lane types. The results of the high-reliability experiments verified that our method achieves fast convergence and provides high-quality 3D lanes from single 2D images. Moreover, the proposed method requires no exceptional computational resources, thereby reducing its implementation costs. Full article
(This article belongs to the Special Issue Mathematics and Computer Programming in 2D and 3D Open Source Software)
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19 pages, 13221 KiB  
Article
Machine-Learning-Based Improved Smith Predictive Control for MIMO Processes
by Xinlan Guo, Mohammadamin Shirkhani and Emad M. Ahmed
Mathematics 2022, 10(19), 3696; https://doi.org/10.3390/math10193696 - 09 Oct 2022
Cited by 11 | Viewed by 1577
Abstract
Controlling time-delayed processes is one of the challenges in today’s process industries. If the multi-input/multi-output system is dynamically coupled, the delay problem becomes more critical. In this paper, a new method based on Smith’s predictive method, with the help of a type-2 fuzzy [...] Read more.
Controlling time-delayed processes is one of the challenges in today’s process industries. If the multi-input/multi-output system is dynamically coupled, the delay problem becomes more critical. In this paper, a new method based on Smith’s predictive method, with the help of a type-2 fuzzy system to control the system with the mentioned features, is presented. The variability in the time delay, the existence of disturbances and the existence of structural and parametric uncertainty lead to the poor performance of the traditional Smith predictor. Even if the control system is set up correctly at the beginning of the setup, it will eventually wear out, and the above problems will appear. Therefore, computational intelligence is used here, and by updating the parameters of the control system at the same time as the system changes, the control system adapts itself to achieve the best performance. To evaluate the proposed control system, a complex process system is simulated, the results of which show the good performance of Smith’s prediction method based on a type-2 fuzzy system. Full article
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24 pages, 1756 KiB  
Review
Recent Advances on Penalized Regression Models for Biological Data
by Pei Wang, Shunjie Chen and Sijia Yang
Mathematics 2022, 10(19), 3695; https://doi.org/10.3390/math10193695 - 09 Oct 2022
Cited by 3 | Viewed by 3218
Abstract
Increasingly amounts of biological data promote the development of various penalized regression models. This review discusses the recent advances in both linear and logistic regression models with penalization terms. This review is mainly focused on various penalized regression models, some of the corresponding [...] Read more.
Increasingly amounts of biological data promote the development of various penalized regression models. This review discusses the recent advances in both linear and logistic regression models with penalization terms. This review is mainly focused on various penalized regression models, some of the corresponding optimization algorithms, and their applications in biological data. The pros and cons of different models in terms of response prediction, sample classification, network construction and feature selection are also reviewed. The performances of different models in a real-world RNA-seq dataset for breast cancer are explored. Finally, some future directions are discussed. Full article
(This article belongs to the Section Mathematical Biology)
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17 pages, 2607 KiB  
Article
Application of an Adaptive Adjacency Matrix-Based Graph Convolutional Neural Network in Taxi Demand Forecasting
by Jian-You Xu, Shuo Zhang, Chin-Chia Wu, Win-Chin Lin and Qing-Li Yuan
Mathematics 2022, 10(19), 3694; https://doi.org/10.3390/math10193694 - 09 Oct 2022
Cited by 2 | Viewed by 1631
Abstract
Accurate forecasting of taxi demand has facilitated the rational allocation of urban public transport resources, reduced congestion in urban transport networks, and shortened passenger waiting time. However, virtual station discovery and modelling of the demand when forecasting through graph convolutional neural networks remains [...] Read more.
Accurate forecasting of taxi demand has facilitated the rational allocation of urban public transport resources, reduced congestion in urban transport networks, and shortened passenger waiting time. However, virtual station discovery and modelling of the demand when forecasting through graph convolutional neural networks remains challenging. In this study, the virtual station discovery problem was addressed by using a two-stage clustering approach, which considers the geographical and load characteristics of taxi demand. Furthermore, a fusion model combining non-negative matrix decomposition and a graph convolutional neural network was proposed in order to extract the features of the nodes for dimension reduction and adaptive adjacency matrix computation. By the construction of a local processing structure, further extraction of the local characteristics of the demand was achieved. The experimental results show that the method in this study outperforms state-of-the-art methods in terms of the root mean square error and average absolute value error. Therefore, the model proposed in this study is able to achieve accurate forecasting of taxi demand. Full article
(This article belongs to the Special Issue Theoretical and Computational Research in Various Scheduling Models, 2nd Edition)
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18 pages, 7008 KiB  
Article
Determining Subway Emergency Evacuation Efficiency Using Hybrid System Dynamics and Multiple Agents
by Kai Yu, Nannan Qu, Jifeng Lu and Lujie Zhou
Mathematics 2022, 10(19), 3693; https://doi.org/10.3390/math10193693 - 09 Oct 2022
Cited by 4 | Viewed by 1516
Abstract
With the rapid development of the city, more and more people are choosing the subway as their travel mode. However, the hidden dangers of the subway are becoming increasingly prominent, and emergency evacuation of the subway has become a key factor for its [...] Read more.
With the rapid development of the city, more and more people are choosing the subway as their travel mode. However, the hidden dangers of the subway are becoming increasingly prominent, and emergency evacuation of the subway has become a key factor for its safe operation. Therefore, the research objectives of this paper were to focus on the subway emergency evacuation hybrid model to fill the gap in the field of emergency evacuation simulation methods and countermeasure optimization. The analysis network process (ANP) was used to analyze the influence factors and weights of subway pedestrian evacuation. On this basis, a multiagent model of subway pedestrian evacuation (SD + multiagent) was developed and simulated. The results show that the comprehensive evacuation strategy could improve the evacuation efficiency, shorten the evacuation time, and avoid the waste of resources. This study not only improved the accuracy of the simulation, but also clarified the evacuation process. This approach can effectively prevent the occurrence of subway accidents, reduce casualties, and prevent large-scale casualties such as secondary accidents (induced secondary disasters). Full article
(This article belongs to the Special Issue Application of Advanced Computing and Artificial Intelligence in Engineering and Science)
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15 pages, 457 KiB  
Article
An Efficient Third-Derivative Hybrid Block Method for the Solution of Second-Order BVPs
by Mufutau Ajani Rufai
Mathematics 2022, 10(19), 3692; https://doi.org/10.3390/math10193692 - 09 Oct 2022
Cited by 8 | Viewed by 1235
Abstract
A new one-step hybrid block method with two-point third derivatives is developed to solve the second-order boundary value problems (BVPs). The mathematical derivation of the proposed method is based on the interpolation and collocation methods. The theoretical properties of the proposed method, such [...] Read more.
A new one-step hybrid block method with two-point third derivatives is developed to solve the second-order boundary value problems (BVPs). The mathematical derivation of the proposed method is based on the interpolation and collocation methods. The theoretical properties of the proposed method, such as consistency and convergence, are well analysed. Some BVPs with different boundary conditions are solved to demonstrate the efficiency and feasibility of the suggested method. The numerical results of the proposed method are much closer to the exact solutions and more competitive than other numerical methods in the available literature. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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18 pages, 5061 KiB  
Article
Efficiency and Core Loss Map Estimation with Machine Learning Based Multivariate Polynomial Regression Model
by Oğuz Mısır and Mehmet Akar
Mathematics 2022, 10(19), 3691; https://doi.org/10.3390/math10193691 - 09 Oct 2022
Cited by 4 | Viewed by 2136
Abstract
Efficiency mapping has an important place in examining the maximum efficiency distribution as well as the energy consumption of designed electric motors at maximum torque and speed. Performing analysis at all operating points with FEM analysis in the motor design process requires high [...] Read more.
Efficiency mapping has an important place in examining the maximum efficiency distribution as well as the energy consumption of designed electric motors at maximum torque and speed. Performing analysis at all operating points with FEM analysis in the motor design process requires high processing costs and time. In this article, a machine learning-based multivariate polynomial regression estimation model was developed to overcome these costly processes from FEM analysis. With the proposed method, the operating points of the motors in different conditions during the design process can be predicted in advance with high accuracy. In the study, two different models are developed for efficiency map and core loss estimation of interior permanent magnet synchronous motor design. The developed models use few parameters and predict with high accuracy. Estimation models shorten the design process and offer a less complex model. Obtained results are validated by comparison with FEM analysis. Full article
(This article belongs to the Special Issue Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine and Power Converters)
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17 pages, 4742 KiB  
Article
Signal Identification of Wire Breaking in Bridge Cables Based on Machine Learning
by Guangming Li, Heming Ding, Yaohan Li, Chun-Yin Li and Chi-Chung Lee
Mathematics 2022, 10(19), 3690; https://doi.org/10.3390/math10193690 - 09 Oct 2022
Cited by 1 | Viewed by 1267
Abstract
With the booming development of bridge construction, bridge operation and maintenance have always been major issues to ensure the safety of the community. Affected by the long-term service of bridges and natural factors, the safety and durability of cables can be threatened. Cables [...] Read more.
With the booming development of bridge construction, bridge operation and maintenance have always been major issues to ensure the safety of the community. Affected by the long-term service of bridges and natural factors, the safety and durability of cables can be threatened. Cables are critical stress-bearing elements of large bridges such as cable-stayed bridges. Realizing the health monitoring of bridge cables is the key to ensuring the normal operation of bridges. Acoustic emission (AE) is a dynamic nondestructive testing method that is increasingly used in the local monitoring of bridge cables. In this paper, a testbed is described for generating the acoustic emission signals for signal identification testing with machine learning (ML) models. Owing to the limited number of measured signals being available, an algorithm is proposed to simulate acoustic emission signals for model training. A multi-angle feature extraction method is proposed to extract the acoustic emission signals and construct a comprehensive feature vector to characterize the acoustic emission signals. Seven ML models are trained with the simulated acoustic emission signals. Long short-term memory (LSTM) has been specially applied for deep learning demonstration which requires a large amount of training data. As all machine learning models (including LSTM) provide desired performance, it shows that the proposed approach of simulating acoustic emission signals can be effective. Full article
(This article belongs to the Special Issue Mathematical Methods for Pattern Recognition)
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22 pages, 2952 KiB  
Article
A Boundary Shape Function Method for Computing Eigenvalues and Eigenfunctions of Sturm–Liouville Problems
by Chein-Shan Liu, Jiang-Ren Chang, Jian-Hung Shen and Yung-Wei Chen
Mathematics 2022, 10(19), 3689; https://doi.org/10.3390/math10193689 - 09 Oct 2022
Cited by 3 | Viewed by 1315
Abstract
In the paper, we transform the general Sturm–Liouville problem (SLP) into two canonical forms: one with the homogeneous Dirichlet boundary conditions and another with the homogeneous Neumann boundary conditions. A boundary shape function method (BSFM) was constructed to solve the SLPs of these [...] Read more.
In the paper, we transform the general Sturm–Liouville problem (SLP) into two canonical forms: one with the homogeneous Dirichlet boundary conditions and another with the homogeneous Neumann boundary conditions. A boundary shape function method (BSFM) was constructed to solve the SLPs of these two canonical forms. Owing to the property of the boundary shape function, we could transform the SLPs into an initial value problem for the new variable with initial values that were given definitely. Meanwhile, the terminal value at the right boundary could be entirely determined by using a given normalization condition for the uniqueness of the eigenfunction. In such a manner, we could directly determine the eigenvalues as the intersection points of an eigenvalue curve to the zero line, which was a horizontal line in the plane consisting of the zero values of the target function with respect to the eigen-parameter. We employed a more delicate tuning technique or the fictitious time integration method to solve an implicit algebraic equation for the eigenvalue curve. We could integrate the Sturm–Liouville equation using the given initial values to obtain the associated eigenfunction when the eigenvalue was obtained. Eight numerical examples revealed a great advantage of the BSFM, which easily obtained eigenvalues and eigenfunctions with the desired accuracy. Full article
(This article belongs to the Special Issue Computational Methods in Nonlinear Analysis and Their Applications)
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