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Mathematics, Volume 10, Issue 9 (May-1 2022) – 264 articles

Cover Story (view full-size image): Groups provide the language of symmetry in mathematics and in physics. Essential symmetries in quantum physics come after either the indetermination principle or the invariance of the flat space time in special relativity. In relation to the former, the relevant group is the Heisenberg–Weyl group, while the Euclidean group in n+1 dimensions plays a protagonic role in special relativity. Both groups may be immersed into a more general group, which admits a natural representation on topological linear spaces spanned by generalized Hermite functions. All of this work is based on the masterlines designed by Hermann Weyl some decades ago. View this paper
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27 pages, 12341 KiB  
Article
Deep Learning-Based Detection of Fake Multinational Banknotes in a Cross-Dataset Environment Utilizing Smartphone Cameras for Assisting Visually Impaired Individuals
by Tuyen Danh Pham, Young Won Lee, Chanhum Park and Kang Ryoung Park
Mathematics 2022, 10(9), 1616; https://doi.org/10.3390/math10091616 - 9 May 2022
Cited by 7 | Viewed by 4436
Abstract
The automatic handling of banknotes can be conducted not only by specialized facilities, such as vending machines, teller machines, and banknote counters, but also by handheld devices, such as smartphones, with the utilization of built-in cameras and detection algorithms. As smartphones are becoming [...] Read more.
The automatic handling of banknotes can be conducted not only by specialized facilities, such as vending machines, teller machines, and banknote counters, but also by handheld devices, such as smartphones, with the utilization of built-in cameras and detection algorithms. As smartphones are becoming increasingly popular, they can be used to assist visually impaired individuals in daily tasks, including banknote handling. Although previous studies regarding banknote detection by smartphone cameras for visually impaired individuals have been conducted, these studies are limited, even when conducted in a cross-dataset environment. Therefore, we propose a deep learning-based method for detecting fake multinational banknotes using smartphone cameras in a cross-dataset environment. Experimental results of the self-collected genuine and fake multinational datasets for US dollar, Euro, Korean won, and Jordanian dinar banknotes confirm that our method demonstrates a higher detection accuracy than conventional “you only look once, version 3” (YOLOv3) methods and the combined method of YOLOv3 and the state-of-the-art convolutional neural network (CNN). Full article
(This article belongs to the Special Issue Advances in Pattern Recognition and Image Analysis)
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13 pages, 290 KiB  
Article
Chatterjea and C`iriC` -Type Fixed-Point Theorems Using (αψ) Contraction on C*-Algebra-Valued Metric Space
by Ibtisam Masmali and Saleh Omran
Mathematics 2022, 10(9), 1615; https://doi.org/10.3390/math10091615 - 9 May 2022
Cited by 1 | Viewed by 2985
Abstract
In the present paper, we provide and verify several results obtained by using the Chatterjea and C`iric` fixed-point theorems by using (αψ)-contractive mapping in C*-algebra-valued metric space. We provide some examples and [...] Read more.
In the present paper, we provide and verify several results obtained by using the Chatterjea and C`iric` fixed-point theorems by using (αψ)-contractive mapping in C*-algebra-valued metric space. We provide some examples and an application to illustrate our results. Our study extends and generalizes the results of several studies in the literature. Full article
22 pages, 5998 KiB  
Article
Reservoir Characterization and Productivity Forecast Based on Knowledge Interaction Neural Network
by Yunqi Jiang, Huaqing Zhang, Kai Zhang, Jian Wang, Shiti Cui, Jianfa Han, Liming Zhang and Jun Yao
Mathematics 2022, 10(9), 1614; https://doi.org/10.3390/math10091614 - 9 May 2022
Cited by 11 | Viewed by 2230
Abstract
The reservoir characterization aims to provide the analysis and quantification of the injection-production relationship, which is the fundamental work for production management. The connectivity between injectors and producers is dominated by geological properties, especially permeability. However, the permeability parameters are very heterogenous in [...] Read more.
The reservoir characterization aims to provide the analysis and quantification of the injection-production relationship, which is the fundamental work for production management. The connectivity between injectors and producers is dominated by geological properties, especially permeability. However, the permeability parameters are very heterogenous in oil reservoirs, and expensive to collect by well logging. The commercial simulators enable to get accurate simulation but require sufficient geological properties and consume excessive computation resources. In contrast, the data-driven models (physical models and machine learning models) are developed on the observed dynamic data, such as the rate and pressure data of the injectors and producers, constructing the connectivity relationship and forecasting the productivity by a series of nonlinear mappings or the control of specific physical principles. While, due to the “black box” feature of machine learning approaches, and the constraints and assumptions of physical models, the data-driven methods often face the challenges of poor interpretability and generalizability and the limited application scopes. To solve these issues, integrating the physical principle of the waterflooding process (material balance equation) with an artificial neural network (ANN), a knowledge interaction neural network (KINN) is proposed. KINN consists of three transparent modules with explicit physical significance, and different modules are joined together via the material balance equation and work cooperatively to approximate the waterflooding process. In addition, a gate function is proposed to distinguish the dominant flowing channels from weak connecting ones by their sparsity, and thus the inter-well connectivity can be indicated directly by the model parameters. Combining the strong nonlinear mapping ability with the guidance of physical knowledge, the interpretability of KINN is fully enhanced, and the prediction accuracy on the well productivity is improved. The effectiveness of KINN is proved by comparing its performance with the canonical ANN, on the inter-well connectivity analysis and productivity forecast tasks of three synthetic reservoir experiments. Meanwhile, the robustness of KINN is revealed by the sensitivity analysis on measurement noises and wells shut-in cases. Full article
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15 pages, 303 KiB  
Article
The Mathematical Simulation for the Photocatalytic Fatigue of Polymer Nanocomposites Using the Monte Carlo Methods
by Andrey V. Orekhov, Yurii M. Artemev and Galina V. Pavilaynen
Mathematics 2022, 10(9), 1613; https://doi.org/10.3390/math10091613 - 9 May 2022
Cited by 1 | Viewed by 1519
Abstract
We consider an approach to mathematical modeling of photodegradation of polymer nanocomposites with photoactive additives using the Monte Carlo methods. We principally pay attention to the strength decrease of these materials under solar light action. We propose a new term, “photocatalytic fatigue”, which [...] Read more.
We consider an approach to mathematical modeling of photodegradation of polymer nanocomposites with photoactive additives using the Monte Carlo methods. We principally pay attention to the strength decrease of these materials under solar light action. We propose a new term, “photocatalytic fatigue”, which we apply to the particular case when the mechanical strength decreases only owing to the presence of photocatalytically active components in polymeric nanocomposite material. The propriety of the term is based on a relative similarity of photostimulated mechanical destructive processes in nanocomposites with photoactive additives and mechanical destructive processes typical for metal high-cycle fatigue. Formation of the stress concentrations is one of the major causes of fatigue cracks generation in metals. Photocatalytic active nanoparticles of semiconductors initiate a generation of the stress concentrations under sunlight irradiation. The proposed mathematical model is a Wöhler curve analog for the metal high-cycle fatigue. We assume that equations for high-cycle fatigue curves of samples with stress concentrations could be used in mathematical modeling of polymer nanocomposites photodegradation. In this way, we replace the number of loading cycles with the exposition time in the equations. In the case of polypropylene and polyester samples with photoactive titanium dioxide, the experimental parameters of phenomenological equations for “photocatalytic fatigue” are calculated using one of the Monte Carlo methods based on the random search algorithm. The calculating scheme includes a solution of the extreme task of finding of the minimum of nonnegative transcendent multivariable function, which is a relative average quadratic deviation of calculated values of polymeric nanocomposite stress in comparison with corresponding experimental values. The applicability of the “photocatalytic fatigue” model for polymer nanocomposites with photoactive nanoparticles is confirmed by the example of polypropylene and polyester samples. The approximation error of the experimental strength values for them did not exceed 2%. Full article
(This article belongs to the Special Issue Numerical Methods II)
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15 pages, 336 KiB  
Article
Self-Adaptive Method and Inertial Modification for Solving the Split Feasibility Problem and Fixed-Point Problem of Quasi-Nonexpansive Mapping
by Yuanheng Wang, Tiantian Xu, Jen-Chih Yao and Bingnan Jiang
Mathematics 2022, 10(9), 1612; https://doi.org/10.3390/math10091612 - 9 May 2022
Cited by 8 | Viewed by 1306
Abstract
The split feasibility problem (SFP) has many practical applications, which has attracted the attention of many authors. In this paper, we propose a different method to solve the SFP and the fixed-point problem involving quasi-nonexpansive mappings. We relax the conditions of the operator [...] Read more.
The split feasibility problem (SFP) has many practical applications, which has attracted the attention of many authors. In this paper, we propose a different method to solve the SFP and the fixed-point problem involving quasi-nonexpansive mappings. We relax the conditions of the operator as well as consider the inertial iteration and the adaptive step size. For example, the convergence generated by our new method is better than that of other algorithms, and the convergence rate of our algorithm greatly improves that of previous algorithms. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications II)
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25 pages, 764 KiB  
Article
A Comprehensive Comparison of the Performance of Metaheuristic Algorithms in Neural Network Training for Nonlinear System Identification
by Ebubekir Kaya
Mathematics 2022, 10(9), 1611; https://doi.org/10.3390/math10091611 - 9 May 2022
Cited by 8 | Viewed by 2163
Abstract
Many problems in daily life exhibit nonlinear behavior. Therefore, it is important to solve nonlinear problems. These problems are complex and difficult due to their nonlinear nature. It is seen in the literature that different artificial intelligence techniques are used to solve these [...] Read more.
Many problems in daily life exhibit nonlinear behavior. Therefore, it is important to solve nonlinear problems. These problems are complex and difficult due to their nonlinear nature. It is seen in the literature that different artificial intelligence techniques are used to solve these problems. One of the most important of these techniques is artificial neural networks. Obtaining successful results with an artificial neural network depends on its training process. In other words, it should be trained with a good training algorithm. Especially, metaheuristic algorithms are frequently used in artificial neural network training due to their advantages. In this study, for the first time, the performance of sixteen metaheuristic algorithms in artificial neural network training for the identification of nonlinear systems is analyzed. It is aimed to determine the most effective metaheuristic neural network training algorithms. The metaheuristic algorithms are examined in terms of solution quality and convergence speed. In the applications, six nonlinear systems are used. The mean-squared error (MSE) is utilized as the error metric. The best mean training error values obtained for six nonlinear systems were 3.5×104, 4.7×104, 5.6×105, 4.8×104, 5.2×104, and 2.4×103, respectively. In addition, the best mean test error values found for all systems were successful. When the results were examined, it was observed that biogeography-based optimization, moth–flame optimization, the artificial bee colony algorithm, teaching–learning-based optimization, and the multi-verse optimizer were generally more effective than other metaheuristic algorithms in the identification of nonlinear systems. Full article
(This article belongs to the Special Issue Neural Networks and Learning Systems II)
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11 pages, 1780 KiB  
Article
Research on Multicriteria Decision-Making Scheme of High-Speed Railway Express Product Pricing and Slot Allocation under Competitive Conditions
by Yuxuan Fang, Xiaodong Zhang and Yueyi Li
Mathematics 2022, 10(9), 1610; https://doi.org/10.3390/math10091610 - 9 May 2022
Cited by 7 | Viewed by 1503
Abstract
Scientifically and reasonably pricing products and allocating slots are key to improving the profitability and competitiveness of high-speed railway expresses. In this research, we focus on the freight transportation pricing and slot allocation of high-speed railway express companies in a competitive environment. The [...] Read more.
Scientifically and reasonably pricing products and allocating slots are key to improving the profitability and competitiveness of high-speed railway expresses. In this research, we focus on the freight transportation pricing and slot allocation of high-speed railway express companies in a competitive environment. The goals of this research are to make decisions on the pricing and slot allocation schemes of the high-speed railway express between sections through the method of multicriteria decision making, and then to test these changes in reality. This research innovatively takes the high-speed freight Electric Multiple Unit (EMU) train as its research object and innovatively applies the revenue management theory to high-speed railway express research in a competitive environment, proposing a comprehensive decision-making model based on the sharing rate model. The results show that, by adopting the scheme proposed in this research, the income of high-speed railway express companies can be increased by 13.6%. In addition, the method proposed in this research also enriches the current theory on high-speed railway freight transportation, providing strategies for companies to expand their market and increase profit. Full article
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21 pages, 425 KiB  
Article
Statistical Inference and Optimal Design of Accelerated Life Testing for the Chen Distribution under Progressive Type-II Censoring
by Wenjie Zhang and Wenhao Gui
Mathematics 2022, 10(9), 1609; https://doi.org/10.3390/math10091609 - 9 May 2022
Cited by 5 | Viewed by 1820
Abstract
This paper discusses statistical inference and optimal design of constant-stress accelerated life testing for the Chen distribution under progressive Type-II censoring. The scale parameter of the life distribution is assumed to be a logarithmic linear function of the stress level. The maximum likelihood [...] Read more.
This paper discusses statistical inference and optimal design of constant-stress accelerated life testing for the Chen distribution under progressive Type-II censoring. The scale parameter of the life distribution is assumed to be a logarithmic linear function of the stress level. The maximum likelihood estimates of the parameters are obtained. Then, the observed Fisher information matrix is derived and utilized to construct asymptotic confidence intervals. Meanwhile, the parametric bootstrap methods are provided for the interval estimation. In addition, the Bayes estimates under the squared error loss function are obtained by applying the Tierney and Kadane technique and Lindley’s approximation. As for the optimal design, D- and A-optimality criteria are considered to determine the optimal transformed stress level. Finally, the simulation is carried out to demonstrate the proposed estimation techniques and the optimal criteria, and a real data set is discussed. Full article
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21 pages, 443 KiB  
Article
On the Use of Morpho-Syntactic Description Tags in Neural Machine Translation with Small and Large Training Corpora
by Gregor Donaj and Mirjam Sepesy Maučec
Mathematics 2022, 10(9), 1608; https://doi.org/10.3390/math10091608 - 9 May 2022
Cited by 4 | Viewed by 1807
Abstract
With the transition to neural architectures, machine translation achieves very good quality for several resource-rich languages. However, the results are still much worse for languages with complex morphology, especially if they are low-resource languages. This paper reports the results of a systematic analysis [...] Read more.
With the transition to neural architectures, machine translation achieves very good quality for several resource-rich languages. However, the results are still much worse for languages with complex morphology, especially if they are low-resource languages. This paper reports the results of a systematic analysis of adding morphological information into neural machine translation system training. Translation systems presented and compared in this research exploit morphological information from corpora in different formats. Some formats join semantic and grammatical information and others separate these two types of information. Semantic information is modeled using lemmas and grammatical information using Morpho-Syntactic Description (MSD) tags. Experiments were performed on corpora of different sizes for the English–Slovene language pair. The conclusions were drawn for a domain-specific translation system and for a translation system for the general domain. With MSD tags, we improved the performance by up to 1.40 and 1.68 BLEU points in the two translation directions. We found that systems with training corpora in different formats improve the performance differently depending on the translation direction and corpora size. Full article
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2 pages, 188 KiB  
Editorial
Preface to “Mathematical Methods, Modelling and Applications”
by Lucas Jódar and Rafael Company
Mathematics 2022, 10(9), 1607; https://doi.org/10.3390/math10091607 - 9 May 2022
Viewed by 1418
Abstract
The reality is more complex than it seems [...] Full article
(This article belongs to the Special Issue Mathematical Methods, Modelling and Applications)
18 pages, 1674 KiB  
Article
Factors That Limit the Development of the Digital Entrepreneurial System in the Scale-Up Phase of the Enterprise Life Cycle
by Ivana Đaković Radojičić, Jelena Raut, Slavica Mitrović Veljković, Branislav Dudić, Silvia Treľová and Vijoleta Vrhovac
Mathematics 2022, 10(9), 1606; https://doi.org/10.3390/math10091606 - 9 May 2022
Cited by 3 | Viewed by 1903
Abstract
For the interpretation of digital entrepreneurship, the context in which the entrepreneurial process takes place plays an important role. The context emphasizes that to analyze the entrepreneurial process, it is no longer sufficient to analyze only the entrepreneurial actions, but also the environment [...] Read more.
For the interpretation of digital entrepreneurship, the context in which the entrepreneurial process takes place plays an important role. The context emphasizes that to analyze the entrepreneurial process, it is no longer sufficient to analyze only the entrepreneurial actions, but also the environment in which the entrepreneurial process takes place. The aim of this paper is to analyze the part of the context in which the entrepreneurial process takes place in the Republic of Serbia, Montenegro, Bosnia and Herzegovina and Hungary. Following the methodology of The European Index of Digital Entrepreneurship Systems (EIDES), the paper analyzes the system framework conditions, in the scale-up phase of the enterprise life cycle, in the digital dimension. The aim of this paper is a comparative analysis of three countries in transition with one country belonging to the European Union. After identifying the most developed factors, as well as the most underdeveloped factors, the paper discusses the conditions that influenced the results achieved in the four previously listed countries and why their improvement is important. Full article
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7 pages, 281 KiB  
Article
Common Fixed-Point and Fixed-Circle Results for a Class of Discontinuous F-Contractive Mappings
by Pradip Debnath
Mathematics 2022, 10(9), 1605; https://doi.org/10.3390/math10091605 - 9 May 2022
Cited by 1 | Viewed by 1709
Abstract
The exploration of contractive inequalities which do not imply the continuity of the mapping at fixed points was an interesting open problem for quite some time. A significant amount of progress was made in the last two decades towards the solution of this [...] Read more.
The exploration of contractive inequalities which do not imply the continuity of the mapping at fixed points was an interesting open problem for quite some time. A significant amount of progress was made in the last two decades towards the solution of this problem. In the current paper, we attempt to address the question of discontinuity at fixed point with the help of F-contractions in a metric space. We establish a common fixed-point (CFP) result for such contractive mappings and investigate its discontinuity at the CFP. A fixed-circle result is also obtained consequently. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications II)
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20 pages, 2019 KiB  
Article
Playful Probes for Design Interaction with Machine Learning: A Tool for Aircraft Condition-Based Maintenance Planning and Visualisation
by Jorge Ribeiro, Pedro Andrade, Manuel Carvalho, Catarina Silva, Bernardete Ribeiro and Licínio Roque
Mathematics 2022, 10(9), 1604; https://doi.org/10.3390/math10091604 - 9 May 2022
Cited by 5 | Viewed by 2100
Abstract
Aircraft maintenance is a complex domain where designing new systems that include Machine Learning (ML) algorithms can become a challenge. In the context of designing a tool for Condition-Based Maintenance (CBM) in aircraft maintenance planning, this case study addresses (1) the use of [...] Read more.
Aircraft maintenance is a complex domain where designing new systems that include Machine Learning (ML) algorithms can become a challenge. In the context of designing a tool for Condition-Based Maintenance (CBM) in aircraft maintenance planning, this case study addresses (1) the use of Playful Probing approach to obtain insights that allow understanding of how to design for interaction with ML algorithms, (2) the integration of a Reinforcement Learning (RL) agent for Human–AI collaboration in maintenance planning and (3) the visualisation of CBM indicators. Using a design science research approach, we designed a Playful Probe protocol and materials, and evaluated results by running a participatory design workshop. Our main contribution is to show how to elicit ideas for integration of maintenance planning practices with ML estimation tools and the RL agent. Through a participatory design workshop with participants’ observation, in which they played with CBM artefacts, Playful Probes favour the elicitation of user interaction requirements with the RL planning agent to aid the planner to obtain a reliable maintenance plan and turn possible to understand how to represent CBM indicators and visualise them through a trajectory prediction. Full article
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17 pages, 2521 KiB  
Article
Chenciner Bifurcation Presenting a Further Degree of Degeneration
by Sorin Lugojan, Loredana Ciurdariu and Eugenia Grecu
Mathematics 2022, 10(9), 1603; https://doi.org/10.3390/math10091603 - 8 May 2022
Cited by 1 | Viewed by 1583
Abstract
Chenciner bifurcation appears for some two-dimensional systems with discrete time having two independent variables. Investigated here is a special case of degeneration where the implicit function theorem cannot be used around the origin, so a new approach is necessary. In this scenario, there [...] Read more.
Chenciner bifurcation appears for some two-dimensional systems with discrete time having two independent variables. Investigated here is a special case of degeneration where the implicit function theorem cannot be used around the origin, so a new approach is necessary. In this scenario, there are many more bifurcation diagrams than in the two non-degenerated cases. Several numerical simulations are presented. Full article
(This article belongs to the Special Issue Dynamical System and Stochastic Analysis)
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19 pages, 1815 KiB  
Article
Classical and Bayesian Inference of a Progressive-Stress Model for the Nadarajah–Haghighi Distribution with Type II Progressive Censoring and Different Loss Functions
by Refah Alotaibi, Faten S. Alamri, Ehab M. Almetwally, Min Wang and Hoda Rezk
Mathematics 2022, 10(9), 1602; https://doi.org/10.3390/math10091602 - 8 May 2022
Cited by 2 | Viewed by 2875
Abstract
Accelerated life testing (ALT) is a time-saving technology used in a variety of fields to obtain failure time data for test units in a fraction of the time required to test them under normal operating conditions. This study investigated progressive-stress ALT with progressive [...] Read more.
Accelerated life testing (ALT) is a time-saving technology used in a variety of fields to obtain failure time data for test units in a fraction of the time required to test them under normal operating conditions. This study investigated progressive-stress ALT with progressive type II filtering with the lifetime of test units following a Nadarajah–Haghighi (NH) distribution. It is assumed that the scale parameter of the distribution obeys the inverse power law. The maximum likelihood estimates and estimated confidence intervals for the model parameters were obtained first. The Metropolis–Hastings (MH) algorithm was then used to build Bayes estimators for various squared error loss functions. We also computed the highest posterior density (HPD) credible ranges for the model parameters. Monte Carlo simulations were used to compare the outcomes of the various estimation methods proposed. Finally, one data set was analyzed for validation purposes. Full article
(This article belongs to the Special Issue Recent Advances in Computational Statistics)
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23 pages, 3343 KiB  
Article
Roadmap Optimization: Multi-Annual Project Portfolio Selection Method
by Ran Etgar and Yuval Cohen
Mathematics 2022, 10(9), 1601; https://doi.org/10.3390/math10091601 - 8 May 2022
Cited by 2 | Viewed by 1828
Abstract
The process of project portfolio selection is crucial in many organizations, especially R&D organizations. There is a need to make informed decisions on the investment in various projects or lack thereof. As the projects may continue over more than 1 year, and as [...] Read more.
The process of project portfolio selection is crucial in many organizations, especially R&D organizations. There is a need to make informed decisions on the investment in various projects or lack thereof. As the projects may continue over more than 1 year, and as there are connections between various projects, there is a need to not only decide which project to invest in but also when to invest. Since future benefits from projects are to be depreciated in comparison with near-future ones, and due to the interdependency among projects, the question of allocating the limited resources becomes quite complex. This research provides a novel heuristic method for allocating the limited resources over multi-annual planning horizons and examines its results in comparison with an exact branch and bound solution and various heuristic ones. This paper culminates with an efficient tool that can provide both practical and academic benefits. Full article
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14 pages, 317 KiB  
Article
Annual Operating Costs Minimization in Electrical Distribution Networks via the Optimal Selection and Location of Fixed-Step Capacitor Banks Using a Hybrid Mathematical Formulation
by Oscar Danilo Montoya, Francisco David Moya and Arul Rajagopalan
Mathematics 2022, 10(9), 1600; https://doi.org/10.3390/math10091600 - 8 May 2022
Cited by 5 | Viewed by 1674
Abstract
The minimization of annual operating costs in radial distribution networks with the optimal selection and siting of fixed-step capacitor banks is addressed in this research by means of a two-stage optimization approach. The first stage proposes an approximated mixed-integer quadratic model to select [...] Read more.
The minimization of annual operating costs in radial distribution networks with the optimal selection and siting of fixed-step capacitor banks is addressed in this research by means of a two-stage optimization approach. The first stage proposes an approximated mixed-integer quadratic model to select the nodes where the capacitor banks must be installed. In the second stage, a recursive power flow method is employed to make an exhaustive evaluation of the solution space. The main contribution of this research is the use of the expected load curve to estimate the equivalent annual grid operating costs. Numerical simulations in the IEEE 33- and IEEE 69-bus systems demonstrate the effectiveness of the proposed methodology in comparison with the solution of the exact optimization model in the General Algebraic Modeling System software. Reductions of 33.04% and 34.29% with respect to the benchmark case are obtained with the proposed two-stage approach, with minimum investments in capacitor banks. All numerical implementations are performed in the MATLAB software using the convex tool known as CVX and the Gurobi solver. The main advantage of the proposed hybrid optimization method lies in the possibility of dealing with radial and meshed distribution system topologies without any modification on the MIQC model and the recursive power flow approach. Full article
(This article belongs to the Special Issue Optimization Theory and Applications)
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16 pages, 9199 KiB  
Article
STAGCN: Spatial–Temporal Attention Graph Convolution Network for Traffic Forecasting
by Yafeng Gu and Li Deng
Mathematics 2022, 10(9), 1599; https://doi.org/10.3390/math10091599 - 8 May 2022
Cited by 6 | Viewed by 5080
Abstract
Traffic forecasting plays an important role in intelligent transportation systems. However, the prediction task is highly challenging due to the mixture of global and local spatiotemporal dependencies involved in traffic data. Existing graph neural networks (GNNs) typically capture spatial dependencies with the predefined [...] Read more.
Traffic forecasting plays an important role in intelligent transportation systems. However, the prediction task is highly challenging due to the mixture of global and local spatiotemporal dependencies involved in traffic data. Existing graph neural networks (GNNs) typically capture spatial dependencies with the predefined or learnable static graph structure, ignoring the hidden dynamic patterns in traffic networks. Meanwhile, most recurrent neural networks (RNNs) or convolutional neural networks (CNNs) cannot effectively capture temporal correlations, especially for long-term temporal dependencies. In this paper, we propose a spatial–temporal attention graph convolution network (STAGCN), which acquires a static graph and a dynamic graph from data without any prior knowledge. The static graph aims to model global space adaptability, and the dynamic graph is designed to capture local dynamics in the traffic network. A gated temporal attention module is further introduced for long-term temporal dependencies, where a causal-trend attention mechanism is proposed to increase the awareness of causality and local trends in time series. Extensive experiments on four real-world traffic flow datasets demonstrate that STAGCN achieves an outstanding prediction accuracy improvement over existing solutions. Full article
(This article belongs to the Topic Machine and Deep Learning)
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10 pages, 431 KiB  
Article
Andness Directedness for t-Norms and t-Conorms
by Vicenç Torra
Mathematics 2022, 10(9), 1598; https://doi.org/10.3390/math10091598 - 8 May 2022
Cited by 2 | Viewed by 1829
Abstract
Tools for decision making need to be simple to use. In previous papers, we advocated that decision engineering needs to provide these tools, as well as a list of necessary properties that aggregation functions need to satisfy. When we model decisions using aggregation [...] Read more.
Tools for decision making need to be simple to use. In previous papers, we advocated that decision engineering needs to provide these tools, as well as a list of necessary properties that aggregation functions need to satisfy. When we model decisions using aggregation functions, andness-directedness is one of them. A crucial aspect in any decision is the degree of compromise between criteria. Given an aggregation function, andness establishes to what degree the function behaves in a conjunctive manner. That is, to what degree some criteria are mandatory. Nevertheless, from an engineering perspective, what we know is that some criteria are strongly required and we cannot ignore a bad evaluation even when other criteria are correctly evaluated. That is, given our requirements of andness, what are the aggregation functions we need to select. Andness is not only for mean-like functions, but it also applies to t-norms and t-conorms. In this paper, we study this problem and show how to select t-norms and t-conorms based on the andness level. Full article
(This article belongs to the Special Issue Fuzzy Sets and Artificial Intelligence)
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13 pages, 283 KiB  
Article
Exponential Stability for the Equations of Porous Elasticity in One-Dimensional Bounded Domains
by Tijani A. Apalara and Aminat O. Ige
Mathematics 2022, 10(9), 1597; https://doi.org/10.3390/math10091597 - 8 May 2022
Cited by 1 | Viewed by 1292
Abstract
This work establishes an exponential stability result for a porous-elastic system, where the dissipation mechanisms act on the porous and elastic equations. Our result completes some of the results in the literature for unbounded domains. Full article
16 pages, 724 KiB  
Article
Event-Triggered Consensus Control of Nonlinear Strict Feedback Multi-Agent Systems
by Jiaojiao Zhuang, Zhenxing Li, Zongxiang Hou and Chengdong Yang
Mathematics 2022, 10(9), 1596; https://doi.org/10.3390/math10091596 - 8 May 2022
Cited by 3 | Viewed by 1505
Abstract
In this paper, we investigate the event-triggered consensus problems of nonlinear strict feedback MASs under directed graph. Based on the high-gain control technique, we firstly give a state-based event-triggered consensus algorithm and prove that Zeno behavior can be excluded. When the full state [...] Read more.
In this paper, we investigate the event-triggered consensus problems of nonlinear strict feedback MASs under directed graph. Based on the high-gain control technique, we firstly give a state-based event-triggered consensus algorithm and prove that Zeno behavior can be excluded. When the full state information is unavailable, a high-gain observer is given to estimate state information of each agent and an observer-based algorithm is developed. Finally, we give an example to verify the effectiveness of both state-based and observer-based event-triggered consensus algorithms. Full article
(This article belongs to the Topic Complex Systems and Network Science)
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9 pages, 270 KiB  
Article
Multiple Periodic Solutions for Odd Perturbations of the Discrete Relativistic Operator
by Petru Jebelean and Călin Şerban
Mathematics 2022, 10(9), 1595; https://doi.org/10.3390/math10091595 - 8 May 2022
Cited by 1 | Viewed by 1219
Abstract
We obtain the existence of multiple pairs of periodic solutions for difference equations of type [...] Read more.
We obtain the existence of multiple pairs of periodic solutions for difference equations of type Δ(Δu(n  1)1  |Δu(n  1)|2)=λg(u(n))(nZ), where g:RR is a continuous odd function with anticoercive primitive, and λ>0 is a real parameter. The approach is variational and relies on the critical point theory for convex, lower semicontinuous perturbations of C1-functionals. Full article
(This article belongs to the Special Issue Nonlinear Functional Analysis and Its Applications 2021)
12 pages, 455 KiB  
Article
Spatiotemporal Adaptive Fusion Graph Network for Short-Term Traffic Flow Forecasting
by Shumin Yang, Huaying Li, Yu Luo, Junchao Li, Youyi Song and Teng Zhou
Mathematics 2022, 10(9), 1594; https://doi.org/10.3390/math10091594 - 8 May 2022
Cited by 14 | Viewed by 2483
Abstract
Traffic flow forecasting is challenging for us to analyze intricate spatial–temporal dependencies and obtain incomplete information of spatial–temporal connection. Existing frameworks mostly construct spatial and temporal modeling based on a fixed graph structure and given time series. However, a fixed adjacency matrix is [...] Read more.
Traffic flow forecasting is challenging for us to analyze intricate spatial–temporal dependencies and obtain incomplete information of spatial–temporal connection. Existing frameworks mostly construct spatial and temporal modeling based on a fixed graph structure and given time series. However, a fixed adjacency matrix is limited to learn effective spatial–temporal correlations of the network because it represents incomplete information for missing genuine relation. To solve the difficulty, we design a novel spatial–temporal adaptive fusion graph network (STFAGN) for traffic prediction. First, our model combines fusion convolution layers with a novel adaptive dependency matrix by end-to-end training to capture the hidden spatial-temporal dependency on the data to complete incomplete information. Second, STFAGN could, in parallel, acquire hidden spatial–temporal dependencies by a fusion operation and temporal trend by fast-DTW. Meanwhile, we use ReZero connection as a simple change of deep residual networks to facilitate deep signal propagation and faster converge. Lastly, we conduct comparative experiments on two public traffic network datasets, whose results demonstrate the superiority of our algorithm compared to state-of-the-art baseline types. Ablation experiments also prove the rationality of the framework of STFAGN. Full article
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17 pages, 680 KiB  
Article
Multimedia Applications Processing and Computation Resource Allocation in MEC-Assisted SIoT Systems with DVS
by Xianwei Li, Guolong Chen, Liang Zhao and Bo Wei
Mathematics 2022, 10(9), 1593; https://doi.org/10.3390/math10091593 - 7 May 2022
Cited by 1 | Viewed by 1416
Abstract
Due to the advancements of information technologies and the Internet of Things (IoT), the number of distributed sensors and IoT devices in the social IoT (SIoT) systems is proliferating. This has led to various multimedia applications, face recognition and augmented reality (AR). These [...] Read more.
Due to the advancements of information technologies and the Internet of Things (IoT), the number of distributed sensors and IoT devices in the social IoT (SIoT) systems is proliferating. This has led to various multimedia applications, face recognition and augmented reality (AR). These applications are computation-intensive and delay-sensitive and have become popular in our daily life. However, IoT devices are well-known for their constrained computational resources, which hinders the execution of these applications. Mobile edge computing (MEC) has appeared and been deemed a prospective paradigm to solve this issue. Migrating the applications of IoT devices to be executed in the edge cloud can not only provide computational resources to process these applications but also lower the transmission latency between the IoT devices and the edge cloud. In this paper, computation resource allocation and multimedia applications offloading in MEC-assisted SIoT systems are investigated. We aim to optimize the resource allocation and application offloading by jointly minimizing the execution latency of multimedia applications and the consumed energy of IoT devices. The studied problem is a formulation of the total computation overhead minimization problem by optimizing the computational resources in the edge servers. Besides, as the technology of dynamic voltage scaling (DVS) can offer more flexibility for the MEC system design, we incorporate it into the application offloading. Since the studied problem is a mixed-integer nonlinear programming (MINP) problem, an efficient method is proposed to address it. By comparing with the baseline schemes, the theoretic analysis and simulation results demonstrate that the proposed multimedia applications offloading method can improve the performances of MEC-assisted SIoT systems for the most part. Full article
(This article belongs to the Special Issue Computer Vision and Pattern Recognition with Applications)
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9 pages, 704 KiB  
Article
Graph Colorings and Labelings Having Multiple Restrictive Conditions in Topological Coding
by Xiaohui Zhang, Chengfu Ye, Shumin Zhang and Bing Yao
Mathematics 2022, 10(9), 1592; https://doi.org/10.3390/math10091592 - 7 May 2022
Cited by 2 | Viewed by 1580
Abstract
With the fast development of networks, one has to focus on the security of information running in real networks. A technology that might be able to resist attacks equipped with AI techniques and quantum computers is the so-called topological graphic password of topological [...] Read more.
With the fast development of networks, one has to focus on the security of information running in real networks. A technology that might be able to resist attacks equipped with AI techniques and quantum computers is the so-called topological graphic password of topological coding. In order to further study topological coding, we use the multiple constraints of graph colorings and labelings to propose 6C-labeling, 6C-complementary labeling, and its reciprocal-inverse labeling, since they can be applied to build up topological coding. We show some connections between 6C-labeling and other graph labelings/colorings and show graphs admitting twin-type 6C-labelings, as well as the construction of graphs admitting twin-type 6C-labelings. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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25 pages, 1074 KiB  
Article
TPBF: Two-Phase Bloom-Filter-Based End-to-End Data Integrity Verification Framework for Object-Based Big Data Transfer Systems
by Preethika Kasu, Prince Hamandawana and Tae-Sun Chung
Mathematics 2022, 10(9), 1591; https://doi.org/10.3390/math10091591 - 7 May 2022
Cited by 2 | Viewed by 1939
Abstract
Computational science simulations produce huge volumes of data for scientific research organizations. Often, this data is shared by data centers distributed geographically for storage and analysis. Data corruption in the end-to-end route of data transmission is one of the major challenges in distributing [...] Read more.
Computational science simulations produce huge volumes of data for scientific research organizations. Often, this data is shared by data centers distributed geographically for storage and analysis. Data corruption in the end-to-end route of data transmission is one of the major challenges in distributing the data geographically. End-to-end integrity verification is therefore critical for transmitting such data across data centers effectively. Although several data integrity techniques currently exist, most have a significant negative influence on the data transmission rate as well as the storage overhead. Therefore, existing data integrity techniques are not viable solutions in high performance computing environments where it is very common to transfer huge volumes of data across data centers. In this study, we propose a two-phase Bloom-filter-based end-to-end data integrity verification framework for object-based big data transfer systems. The proposed solution effectively handles data integrity errors by reducing the memory and storage overhead and minimizing the impact on the overall data transmission rate. We investigated the memory, storage, and data transfer rate overheads of the proposed data integrity verification framework on the overall data transfer performance. The experimental findings showed that the suggested framework had 5% and 10% overhead on the total data transmission rate and on the total memory usage, respectively. However, we observed significant savings in terms of storage requirements, when compared with state-of-the-art solutions. Full article
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17 pages, 313 KiB  
Article
Operational Calculus for the General Fractional Derivatives of Arbitrary Order
by Maryam Al-Kandari, Latif A-M. Hanna and Yuri Luchko
Mathematics 2022, 10(9), 1590; https://doi.org/10.3390/math10091590 - 7 May 2022
Cited by 13 | Viewed by 2000
Abstract
In this paper, we deal with the general fractional integrals and the general fractional derivatives of arbitrary order with the kernels from a class of functions that have an integrable singularity of power function type at the origin. In particular, we introduce the [...] Read more.
In this paper, we deal with the general fractional integrals and the general fractional derivatives of arbitrary order with the kernels from a class of functions that have an integrable singularity of power function type at the origin. In particular, we introduce the sequential fractional derivatives of this type and derive an explicit formula for their projector operator. The main contribution of this paper is a construction of an operational calculus of Mikusiński type for the general fractional derivatives of arbitrary order. In particular, we present a representation of the m-fold sequential general fractional derivatives of arbitrary order as algebraic operations in the field of convolution quotients and derive some important operational relations. Full article
12 pages, 1201 KiB  
Article
Highly Dispersive Optical Solitons in Birefringent Fibers with Polynomial Law of Nonlinear Refractive Index by Laplace–Adomian Decomposition
by Oswaldo González-Gaxiola, Anjan Biswas, Yakup Yıldırım and Luminita Moraru
Mathematics 2022, 10(9), 1589; https://doi.org/10.3390/math10091589 - 7 May 2022
Cited by 5 | Viewed by 5495
Abstract
This paper is a numerical simulation of highly dispersive optical solitons in birefringent fibers with polynomial nonlinear form, which is achieved for the first time. The algorithmic approach is applied with the usage of the Laplace–Adomian decomposition scheme. Dark and bright soliton simulations [...] Read more.
This paper is a numerical simulation of highly dispersive optical solitons in birefringent fibers with polynomial nonlinear form, which is achieved for the first time. The algorithmic approach is applied with the usage of the Laplace–Adomian decomposition scheme. Dark and bright soliton simulations are presented. The error measure has a very low count, and thus, the simulations are almost an exact replica of such solitons that analytically arise from the governing system. The suggested iterative scheme finds the solution without any discretization, linearization, or restrictive assumptions. Full article
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11 pages, 876 KiB  
Article
A Domain Adaptation-Based Method for Classification of Motor Imagery EEG
by Changsheng Li, Minyou Chen and Li Zhang
Mathematics 2022, 10(9), 1588; https://doi.org/10.3390/math10091588 - 7 May 2022
Cited by 2 | Viewed by 1738
Abstract
Non-stationarity of EEG signals lead to high variability across sessions, which results in low classification accuracy. To reduce the inter-session variability, an unsupervised domain adaptation method is proposed. Arithmetic mean and covariance are exploited to represent the data distribution. First, overall mean alignment [...] Read more.
Non-stationarity of EEG signals lead to high variability across sessions, which results in low classification accuracy. To reduce the inter-session variability, an unsupervised domain adaptation method is proposed. Arithmetic mean and covariance are exploited to represent the data distribution. First, overall mean alignment is conducted between the source and target data. Then, the data in the target domain is labeled by a classifier trained with the source data. The per-class mean and covariance of the target data are estimated based on the predicted labels. Next, an alignment from the source domain to the target domain is performed according to the covariance of each class in the target domain. Finally, per-class mean adaptation is required after covariance alignment to remove the shift of data distribution caused by covariance alignment. Two public BCI competition datasets, namely the BCI competition III dataset IVa and the BCI competition IV dataset IIa were used to evaluate the proposed method. On both datasets, the proposed method effectively improved classification accuracy. Full article
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13 pages, 1616 KiB  
Article
A Quick Search Dynamic Vector-Evaluated Particle Swarm Optimization Algorithm Based on Fitness Distance
by Suyu Wang, Dengcheng Ma and Miao Wu
Mathematics 2022, 10(9), 1587; https://doi.org/10.3390/math10091587 - 7 May 2022
Cited by 1 | Viewed by 1375
Abstract
A quick search dynamic vector-evaluated particle swarm optimization algorithm based on fitness distance (DVEPSO/FD) is proposed according to the fact that some dynamic multi-objective optimization methods, such as the DVEPSO, cannot achieve a very accurate Pareto optimal front (POF) tracked after each objective [...] Read more.
A quick search dynamic vector-evaluated particle swarm optimization algorithm based on fitness distance (DVEPSO/FD) is proposed according to the fact that some dynamic multi-objective optimization methods, such as the DVEPSO, cannot achieve a very accurate Pareto optimal front (POF) tracked after each objective changes, although they exhibit advantages in multi-objective optimization. Featuring a repository update mechanism using the fitness distance together with a quick search mechanism, the DVEPSO/FD is capable of obtaining the optimal values that are closer to the real POF. The fitness distance is used to streamline the repository to improve the distribution of nondominant solutions, and the flight parameters of the particles are adjusted dynamically to improve the search speed. Groups of the standard benchmark experiments are conducted and the results show that, compared with the DVEPSO method, from the figures generated by the test functions, DVEPSO/FD achieves a higher accuracy and clearness with the POF dynamically changing; from the values of performance indexes, the DVEPSO/FD effectively improves the accuracy of the tracked POF without destroying the stability. The proposed DVEPSO/FD method shows a good dynamic change adaptability and solving set ability of the dynamic multi-objective optimization problem. Full article
(This article belongs to the Special Issue Optimization Theory and Applications)
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