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Mathematics, Volume 10, Issue 12 (June-2 2022) – 200 articles

Cover Story (view full-size image): The theory of finitely supported structures is used to manage very large sets with a certain degree of symmetry. This framework generalizes the classical set theory of Zermelo–Fraenkel by infinitely allowing many basic elements with no internal structure (atoms) and by equipping classical sets with group actions of the permutation group over these basic elements. On the other hand, soft sets represent a generalization of the fuzzy sets and deal with uncertainty in a parametric manner. In this paper, we study the soft sets in the new framework of finitely supported structures, and their associations with any crisp set family of atoms describing them. We prove some finiteness properties for infinite soft sets and some order properties and present Tarski-like fixed-point results for mappings between soft sets with atoms. View this paper
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27 pages, 2251 KiB  
Article
An Improved Arithmetic Optimization Algorithm for Numerical Optimization Problems
by Mengnan Chen, Yongquan Zhou and Qifang Luo
Mathematics 2022, 10(12), 2152; https://doi.org/10.3390/math10122152 - 20 Jun 2022
Cited by 12 | Viewed by 2280
Abstract
The arithmetic optimization algorithm is a recently proposed metaheuristic algorithm. In this paper, an improved arithmetic optimization algorithm (IAOA) based on the population control strategy is introduced to solve numerical optimization problems. By classifying the population and adaptively controlling the number of individuals [...] Read more.
The arithmetic optimization algorithm is a recently proposed metaheuristic algorithm. In this paper, an improved arithmetic optimization algorithm (IAOA) based on the population control strategy is introduced to solve numerical optimization problems. By classifying the population and adaptively controlling the number of individuals in the subpopulation, the information of each individual can be used effectively, which speeds up the algorithm to find the optimal value, avoids falling into local optimum, and improves the accuracy of the solution. The performance of the proposed IAOA algorithm is evaluated on six systems of nonlinear equations, ten integrations, and engineering problems. The results show that the proposed algorithm outperforms other algorithms in terms of convergence speed, convergence accuracy, stability, and robustness. Full article
(This article belongs to the Special Issue Optimization Algorithms: Theory and Applications)
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11 pages, 3954 KiB  
Article
WAVECNV: A New Approach for Detecting Copy Number Variation by Wavelet Clustering
by Yang Guo, Shuzhen Wang, A. K. Alvi Haque and Xiguo Yuan
Mathematics 2022, 10(12), 2151; https://doi.org/10.3390/math10122151 - 20 Jun 2022
Cited by 1 | Viewed by 1501
Abstract
Copy number variation (CNV) detection based on second-generation sequencing technology is the basis of much gene research, but the read depth is affected by mapping errors, repeated reads, and GC bias. The existing methods have low sensitivity to variation regions with a short [...] Read more.
Copy number variation (CNV) detection based on second-generation sequencing technology is the basis of much gene research, but the read depth is affected by mapping errors, repeated reads, and GC bias. The existing methods have low sensitivity to variation regions with a short length and small variation range. Therefore, it is necessary to improve the sensitivity of algorithms to short-variation fragments. This study proposes a new CNV-detection method named WAVECNV to solve this issue. The algorithm uses wavelet clustering to process the read depth and determine the normal cluster and abnormal cluster according to the size of the cluster. Then, according to the distance between genome bins and normal clusters, the outlier of each genome bin is evaluated. Finally, a statistical model is established, and the p-value test is used for calling CNVs. Through this method, the information of the short variation region is retained. WAVECNV was tested and compared with peer methods in terms of simulated data and real cancer-sequencing data. The results show that the sensitivity of WAVECNV is better than the existing methods. It also has high precision in data with low purity and coverage. In real data experiments, WAVECNV can detect more cancer genes than existing methods. Therefore, this method can be regarded as a conventional method in the field of genomic mutation analysis of cancer samples. Full article
(This article belongs to the Special Issue Mathematical Modelling in Biology)
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14 pages, 134557 KiB  
Article
Transmission Line Object Detection Method Based on Label Adaptive Allocation
by Lijuan Zhao, Chang’an Liu, Zheng Zhang and Hongquan Qu
Mathematics 2022, 10(12), 2150; https://doi.org/10.3390/math10122150 - 20 Jun 2022
Cited by 2 | Viewed by 1709
Abstract
Inspection of the integrality of components and connecting parts is an important task to maintain safe and stable operation of transmission lines. In view of the fact that the scale difference of the auxiliary component in a connecting part is large and the [...] Read more.
Inspection of the integrality of components and connecting parts is an important task to maintain safe and stable operation of transmission lines. In view of the fact that the scale difference of the auxiliary component in a connecting part is large and the background environment of the object is complex, a one-stage object detection method based on the enhanced real feature information and the label adaptive allocation is proposed in this study. Based on the anchor-free detection algorithm FCOS, this method is optimized by expanding the real feature information of the adjacent feature layer fusion and the semantic information of the deep feature layer, as well as adaptively assigning the label through the idea of pixel-by-pixel detection. In addition, the grading ring image is sliced in original data to improve the proportion of bolts in the dataset, which can clear the appearance features of small objects and reduce the difficulty of detection. Experimental results show that this method can eliminate the background interference in the GT (ground truth) as much as possible in object detection process, and improve the detection accuracy for objects with a narrow shape and small size. The evaluation index AP (average precision) increased by 4.1%. Further improvement of detection accuracy lays a foundation for the realization of efficient real-time patrol inspection. Full article
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14 pages, 3406 KiB  
Article
Study on a Quantitative Indicator for Surface Stability Evaluation of Limestone Strata with a Shallowly Buried Spherical Karst Cave
by Peng Xie, Huchen Duan, Haijia Wen, Chao Yang, Shaokun Ma and Zurun Yue
Mathematics 2022, 10(12), 2149; https://doi.org/10.3390/math10122149 - 20 Jun 2022
Cited by 2 | Viewed by 1086
Abstract
This paper developed a quantitative evaluation necessary to ensure ground stability, so a quantitative indicator (bearing capacity). A homogeneous axisymmetric model was generated, considering China’s stress field and the Karst topography characteristics, simultaneously obtaining stress component expression. We then determined the bearing capacity [...] Read more.
This paper developed a quantitative evaluation necessary to ensure ground stability, so a quantitative indicator (bearing capacity). A homogeneous axisymmetric model was generated, considering China’s stress field and the Karst topography characteristics, simultaneously obtaining stress component expression. We then determined the bearing capacity calculation formula by combining the strength theory of shear failure and the stress component expressions. Finally, the comparison of the bearing capacity calculation results between theoretical analysis and a numerical simulation indicated that the error was less than 5%, and the result verified the rationality of the formula. Full article
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30 pages, 7745 KiB  
Article
Short- and Medium-Term Power Demand Forecasting with Multiple Factors Based on Multi-Model Fusion
by Qingqing Ji, Shiyu Zhang, Qiao Duan, Yuhan Gong, Yaowei Li, Xintong Xie, Jikang Bai, Chunli Huang and Xu Zhao
Mathematics 2022, 10(12), 2148; https://doi.org/10.3390/math10122148 - 20 Jun 2022
Cited by 4 | Viewed by 1780
Abstract
With the continuous development of economy and society, power demand forecasting has become an important task of the power industry. Accurate power demand forecasting can promote the operation and development of the power supply industry. However, since power consumption is affected by a [...] Read more.
With the continuous development of economy and society, power demand forecasting has become an important task of the power industry. Accurate power demand forecasting can promote the operation and development of the power supply industry. However, since power consumption is affected by a number of factors, it is difficult to accurately predict the power demand data. With the accumulation of data in the power industry, machine learning technology has shown great potential in power demand forecasting. In this study, gradient boosting decision tree (GBDT), extreme gradient boosting (XGBoost) and light gradient boosting machine (LightGBM) are integrated by stacking to build an XLG-LR fusion model to predict power demand. Firstly, preprocessing was carried out on 13 months of electricity and meteorological data. Next, the hyperparameters of each model were adjusted and optimized. Secondly, based on the optimal hyperparameter configuration, a prediction model was built using the training set (70% of the data). Finally, the test set (30% of the data) was used to evaluate the performance of each model. Mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and goodness-of-fit coefficient (R^2) were utilized to analyze each model at different lengths of time, including their seasonal, weekly, and monthly forecast effect. Furthermore, the proposed fusion model was compared with other neural network models such as the GRU, LSTM and TCN models. The results showed that the XLG-LR model achieved the best prediction results at different time lengths, and at the same time consumed the least time compared to the neural network model. This method can provide a more reliable reference for the operation and dispatch of power enterprises and future power construction and planning. Full article
(This article belongs to the Special Issue Computational Statistics and Data Analysis)
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15 pages, 355 KiB  
Article
Global Prescribed-Time Stabilization of High-Order Nonlinear Systems with Asymmetric Actuator Dead-Zone
by Xin Guo, Hejun Yao and Fangzheng Gao
Mathematics 2022, 10(12), 2147; https://doi.org/10.3390/math10122147 - 20 Jun 2022
Viewed by 1173
Abstract
This paper is concerned with the global prescribed-time stabilization problem for a class of uncertain high-order nonlinear systems (HONSs) with an asymmetric actuator dead-zone. Firstly, a new state-scaling transformation (SST) is developed for high-order nonlinear systems to change the original prescribed-time stabilization into [...] Read more.
This paper is concerned with the global prescribed-time stabilization problem for a class of uncertain high-order nonlinear systems (HONSs) with an asymmetric actuator dead-zone. Firstly, a new state-scaling transformation (SST) is developed for high-order nonlinear systems to change the original prescribed-time stabilization into the finite-time stabilization of the transformed one. The defects of the conventional one introduced in Song et al. (2017), which is unable to ensure the closed-loop stability behind a prespecified convergence time and a closed-loop system, which is only driven to the neighborhood of destination, is successfully overcome by introducing a switching mechanism in our proposed SST. Then, by using the adding a power integrator (API) technique, a state feedback controller is explicitly constructed to achieve the requirements of the closed-loop prescribed time convergence. Lastly, a liquid-level system is utilized to validate the theoretical results. Full article
(This article belongs to the Special Issue Analysis and Control of Dynamical Systems)
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14 pages, 314 KiB  
Article
Innovative Digital Stochastic Methods for Multidimensional Sensitivity Analysis in Air Pollution Modelling
by Venelin Todorov and Ivan Dimov
Mathematics 2022, 10(12), 2146; https://doi.org/10.3390/math10122146 - 20 Jun 2022
Cited by 17 | Viewed by 1811
Abstract
Nowadays, much of the world has a regional air pollution strategy to limit and decrease the pollution levels across governmental borders and control their impact on human health and ecological systems. Environmental protection is among the leading priorities worldwide. Many challenges in this [...] Read more.
Nowadays, much of the world has a regional air pollution strategy to limit and decrease the pollution levels across governmental borders and control their impact on human health and ecological systems. Environmental protection is among the leading priorities worldwide. Many challenges in this research area exist since it is a painful subject for society and a fundamental topic for the healthcare system. Sensitivity analysis has a fundamental role during the process of validating a large-scale air pollution computational models to ensure their accuracy and reliability. We apply the best available stochastic algorithms for multidimensional sensitivity analysis of the UNI-DEM model, which plays a key role in the management of the many self-governed systems and data that form the basis for forecasting and analyzing the consequences of possible climate change. We develop two new highly convergent digital sequences with special generating matrices, which show significant improvement over the best available existing stochastic methods for measuring the sensitivity indices of the digital ecosystem. The results obtained through sensitivity analysis will play an extremely important multi-sided role. Full article
18 pages, 1610 KiB  
Article
Mining and Evolution Analysis of Network Public Opinion Concerns of Stakeholders in Hot Social Events
by Jianhong Chen, Shuyue Du and Shan Yang
Mathematics 2022, 10(12), 2145; https://doi.org/10.3390/math10122145 - 20 Jun 2022
Cited by 11 | Viewed by 1818
Abstract
(1) Background: Hot social events contain a large amount of public opinion information, and a more detailed analysis of this information will help the relevant parts to formulate more targeted supervision strategies at different stages and for the public opinion publishers involved in [...] Read more.
(1) Background: Hot social events contain a large amount of public opinion information, and a more detailed analysis of this information will help the relevant parts to formulate more targeted supervision strategies at different stages and for the public opinion publishers involved in the event discussions, so as to achieve efficient management of public opinion; (2) Methods:Based on stakeholder theory and life cycle theory, this study constructs stakeholder classification system by using keyword identification method; adopts LDA model to complete topic clustering; analyzes and summarizes topic evolution pattern by calculating topic similarity; (3) Results: The study divided the stakeholders involved in the Jiang Ge case into 10 categories, and the results of topic clustering were divided into two categories according to the content of the topics, which were based on the case itself and on the parties involved in the case; it was found that each stakeholder focused on a different topic with different emphasis, no matter the topic of public opinion or the different life cycle stages of public opinion. Based on the differences in topic similarity between adjacent stages, the topic evolution patterns of different stakeholders were categorized into three types; (4) Conclusions: Example verification shows that the method presented in this paper can dig out the topic focus and evolution path of stakeholders in the field of public opinion, and provide a horizontal and vertical comparative analysis between stakeholders and different life cycle stages. Full article
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9 pages, 251 KiB  
Article
On Some Model Theoretic Properties of Totally Bounded Ultrametric Spaces
by Gábor Sági and Karrar Al-Sabti
Mathematics 2022, 10(12), 2144; https://doi.org/10.3390/math10122144 - 20 Jun 2022
Cited by 1 | Viewed by 1138
Abstract
Continuing investigations initiated by the first author, we associate relational structures for metric spaces and investigate their model theoretic properties. In this paper, we consider ultrametric spaces. Among others, we show that any elementary substructure of the relational structure associated with a totally [...] Read more.
Continuing investigations initiated by the first author, we associate relational structures for metric spaces and investigate their model theoretic properties. In this paper, we consider ultrametric spaces. Among others, we show that any elementary substructure of the relational structure associated with a totally bounded ultrametric space X is dense in X. Further, we provide an explicit upper bound for a splitting chain of atomic types in ultrametric spaces of a finite spectrum. For ultrametric spaces, these results improve previous ones of the present authors and may have further practical applications in designing similarity detecting algorithms. Full article
(This article belongs to the Special Issue Model Theoretic Logics and Their Frontiers)
24 pages, 3595 KiB  
Article
Applying the Random Forest Method to Improve Burner Efficiency
by Vladislav Kovalnogov, Ruslan Fedorov, Vladimir Klyachkin, Dmitry Generalov, Yulia Kuvayskova and Sergey Busygin
Mathematics 2022, 10(12), 2143; https://doi.org/10.3390/math10122143 - 20 Jun 2022
Cited by 7 | Viewed by 1971
Abstract
Fuel power plants are one of the main sources of pollutant emissions, so special attention should be paid to improving the efficiency of the fuel combustion process. The mathematical modeling of processes in the combustion chamber makes it possible to reliably predict and [...] Read more.
Fuel power plants are one of the main sources of pollutant emissions, so special attention should be paid to improving the efficiency of the fuel combustion process. The mathematical modeling of processes in the combustion chamber makes it possible to reliably predict and find the best dynamic characteristics of the operation of a power plant, in order to quantify the emission of harmful substances, as well as the environmental and technical and economic efficiency of various regime control actions and measures, and the use of new types of composite fuels. The main purpose of this article is to illustrate how machine learning methods can play an important role in modeling and predicting the performance and control of the combustion process. The paper proposes a mathematical model of an unsteady turbulent combustion process, presents a model of a combustion chamber with a combined burner, and performs a numerical study using the STAR-CCM+ multidisciplinary platform. The influence of various input indicators on the efficiency of burner devices, which is evaluated by several parameters at the output, is investigated. In this case, three possible states of the burners are assumed: optimal, satisfactory and unsatisfactory. Full article
(This article belongs to the Special Issue Advanced Numerical Analysis and Scientific Computing)
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23 pages, 2987 KiB  
Article
A Study on Early Warnings of Financial Crisis of Chinese Listed Companies Based on DEA–SVM Model
by Zhishuo Zhang, Yao Xiao, Zitian Fu, Kaiyang Zhong and Huayong Niu
Mathematics 2022, 10(12), 2142; https://doi.org/10.3390/math10122142 - 20 Jun 2022
Cited by 12 | Viewed by 1924
Abstract
In the era of big data, investor sentiment will have an impact on personal decision making and asset pricing in the securities market. This paper uses the Easteconomy stock forum and Sina stock forum as the carrier of investor sentiment to measure the [...] Read more.
In the era of big data, investor sentiment will have an impact on personal decision making and asset pricing in the securities market. This paper uses the Easteconomy stock forum and Sina stock forum as the carrier of investor sentiment to measure the positive sentiment index based on stockholders’ comments and to construct an evaluation index system for the public opinion dimension. In addition, the evaluation index system is constructed from four dimensions, which include operation, innovation, finance and financing, to evaluate the overall condition of listed companies from multiple perspectives. In this paper, the SBM model in the data envelopment analysis method is used to measure the efficiency values of each dimension of the multidimensional efficiency evaluation index system, and the efficiency values of each dimension are the multidimensional efficiency indicators. Subsequently, two sets of input feature indicators of the SVM model were established: one set contains traditional financial indicators and multidimensional efficiency indicators, and another set has only traditional financial indicators. The early warning accuracy of the two sets of input feature indicators was empirically analyzed based on the support vector machine early warning model. The results show that the early warning model incorporating multidimensional efficiency indicators has improved the accuracy compared with the early warning model based on traditional financial indicators. Then, the model was optimized by the particle swarm intelligent optimization algorithm, and the robustness of the results was tested. Moreover, six mainstream machine learning methods, including Logistic Regression, GBDT, CatBoost, AdaBoost, Random Forest and Bagging, were used to compare with the early warning effect of the DEA–SVM model, and the empirical results show that DEA–SVM has high early warning accuracy, which proves the superiority of the proposed model. The findings of this study have a positive effect on further preventing and controlling the financial crisis risk of Chinese-listed companies and promoting as well as facilitating the healthy growth of Chinese-listed companies. Full article
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17 pages, 2953 KiB  
Article
Federated Learning-Inspired Technique for Attack Classification in IoT Networks
by Tariq Ahamed Ahanger, Abdulaziz Aldaej, Mohammed Atiquzzaman, Imdad Ullah and Muhammad Yousufudin
Mathematics 2022, 10(12), 2141; https://doi.org/10.3390/math10122141 - 20 Jun 2022
Cited by 6 | Viewed by 1631
Abstract
More than 10-billion physical items are being linked to the internet to conduct activities more independently and with less human involvement owing to the Internet of Things (IoT) technology. IoT networks are considered a source of identifiable data for vicious attackers to carry [...] Read more.
More than 10-billion physical items are being linked to the internet to conduct activities more independently and with less human involvement owing to the Internet of Things (IoT) technology. IoT networks are considered a source of identifiable data for vicious attackers to carry out criminal actions using automated processes. Machine learning (ML)-assisted methods for IoT security have gained much attention in recent years. However, the ML-training procedure incorporates large data which is transferable to the central server since data are created continually by IoT devices at the edge. In other words, conventional ML relies on a single server to store all of its data, which makes it a less desirable option for domains concerned about user privacy. The Federated Learning (FL)-based anomaly detection technique, which utilizes decentralized on-device data to identify IoT network intrusions, represents the proposed solution to the aforementioned problem. By exchanging updated weights with the centralized FL-server, the data are kept on local IoT devices while federating training cycles over GRUs (Gated Recurrent Units) models. The ensemble module of the technique assesses updates from several sources for improving the accuracy of the global ML technique. Experiments have shown that the proposed method surpasses the state-of-the-art techniques in protecting user data by registering enhanced performance measures of Statistical Analysis, Energy Efficiency, Memory Utilization, Attack Classification, and Client Accuracy Analysis for the identification of attacks. Full article
(This article belongs to the Special Issue Mathematical Methods for Computer Science)
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16 pages, 2059 KiB  
Article
Parallel Hybrid Algorithms for a Finite Family of G-Nonexpansive Mappings and Its Application in a Novel Signal Recovery
by Suthep Suantai, Kunrada Kankam, Watcharaporn Cholamjiak and Watcharaporn Yajai
Mathematics 2022, 10(12), 2140; https://doi.org/10.3390/math10122140 - 20 Jun 2022
Cited by 2 | Viewed by 929
Abstract
This article considers a parallel monotone hybrid algorithm for a finite family of G-nonexpansive mapping in Hilbert spaces endowed with graphs and suggests iterative schemes for finding a common fixed point by the two different hybrid projection methods. Moreover, we show the [...] Read more.
This article considers a parallel monotone hybrid algorithm for a finite family of G-nonexpansive mapping in Hilbert spaces endowed with graphs and suggests iterative schemes for finding a common fixed point by the two different hybrid projection methods. Moreover, we show the computational performance of our algorithm in comparison to some methods. Strong convergence theorems are proved under suitable conditions. Finally, we give some numerical experiments of our algorithms to show the efficiency and implementation of the LASSO problems in signal recovery with different types of blurred matrices and noise. Full article
(This article belongs to the Section Mathematics and Computer Science)
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20 pages, 5101 KiB  
Article
Bistability and Robustness for Virus Infection Models with Nonmonotonic Immune Responses in Viral Infection Systems
by Tengfei Wang, Shaoli Wang and Fei Xu
Mathematics 2022, 10(12), 2139; https://doi.org/10.3390/math10122139 - 20 Jun 2022
Viewed by 1022
Abstract
Recently, bistable viral infection systems have attracted increased attention. In this paper, we study bistability and robustness for virus infection models with nonmonotonic immune responses in viral infection systems. The results show that the existing transcritical bifurcation undergoes backward or forward bifurcation in [...] Read more.
Recently, bistable viral infection systems have attracted increased attention. In this paper, we study bistability and robustness for virus infection models with nonmonotonic immune responses in viral infection systems. The results show that the existing transcritical bifurcation undergoes backward or forward bifurcation in viral infection models with nonmonotonic immune responses. Our investigation demonstrates that the backward bifurcation threshold is the elite control threshold. When the immune intensity is greater than the elite control threshold, the virus will be under elite control; when the immune intensity is less than the elite control threshold, the virus may rebound. We also give a new definition of robustness to characterize bistable systems. Full article
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11 pages, 293 KiB  
Article
Linear Diophantine Fuzzy Set Theory Applied to BCK/BCI-Algebras
by Ghulam Muhiuddin, Madeline Al-Tahan, Ahsan Mahboob, Sarka Hoskova-Mayerova and Saba Al-Kaseasbeh
Mathematics 2022, 10(12), 2138; https://doi.org/10.3390/math10122138 - 19 Jun 2022
Cited by 3 | Viewed by 1216
Abstract
In this paper, we apply the concept of linear Diophantine fuzzy sets in BCK/BCI-algebras. In this respect, the notions of linear Diophantine fuzzy subalgebras and linear Diophantine fuzzy (commutative) ideals are introduced and some vital properties [...] Read more.
In this paper, we apply the concept of linear Diophantine fuzzy sets in BCK/BCI-algebras. In this respect, the notions of linear Diophantine fuzzy subalgebras and linear Diophantine fuzzy (commutative) ideals are introduced and some vital properties are discussed. Additionally, characterizations of linear Diophantine fuzzy subalgebras and linear Diophantine fuzzy (commutative) ideals are considered. Moreover, the associated results for linear Diophantine fuzzy subalgebras, linear Diophantine fuzzy ideals and linear Diophantine fuzzy commutative ideals are obtained. Full article
(This article belongs to the Special Issue Fuzzy and Extension of Fuzzy Theories)
18 pages, 2048 KiB  
Article
Classical and Bayesian Inference of the Inverse Nakagami Distribution Based on Progressive Type-II Censored Samples
by Liang Wang, Sanku Dey and Yogesh Mani Tripathi
Mathematics 2022, 10(12), 2137; https://doi.org/10.3390/math10122137 - 19 Jun 2022
Cited by 2 | Viewed by 1172
Abstract
This paper explores statistical inferences when the lifetime of product follows the inverse Nakagami distribution using progressive Type-II censored data. Likelihood-based and maximum product of spacing (MPS)-based methods are considered for estimating the parameters of the model. In addition, approximate confidence intervals are [...] Read more.
This paper explores statistical inferences when the lifetime of product follows the inverse Nakagami distribution using progressive Type-II censored data. Likelihood-based and maximum product of spacing (MPS)-based methods are considered for estimating the parameters of the model. In addition, approximate confidence intervals are constructed via the asymptotic theory using both likelihood and product spacing functions. Based on traditional likelihood and the product of spacing functions, Bayesian estimates are also considered under a squared error loss function using non-informative priors, and Gibbs sampling based on the MCMC algorithm is proposed to approximate the Bayes estimates, where the highest posterior density credible intervals of the parameters are obtained. Numerical studies are presented to compare the proposed estimators using Monte Carlo simulations. To demonstrate the proposed methodology in a real-life scenario, a well-known data set on agricultural machine elevators with high defect rates is also analyzed for illustration. Full article
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13 pages, 896 KiB  
Article
Advances in Parameter Estimation and Learning from Data for Mathematical Models of Hepatitis C Viral Kinetics
by Vladimir Reinharz, Alexander Churkin, Harel Dahari and Danny Barash
Mathematics 2022, 10(12), 2136; https://doi.org/10.3390/math10122136 - 19 Jun 2022
Cited by 2 | Viewed by 1442
Abstract
Mathematical models, some of which incorporate both intracellular and extracellular hepatitis C viral kinetics, have been advanced in recent years for studying HCV–host dynamics, antivirals mode of action, and their efficacy. The standard ordinary differential equation (ODE) hepatitis C virus (HCV) kinetic model [...] Read more.
Mathematical models, some of which incorporate both intracellular and extracellular hepatitis C viral kinetics, have been advanced in recent years for studying HCV–host dynamics, antivirals mode of action, and their efficacy. The standard ordinary differential equation (ODE) hepatitis C virus (HCV) kinetic model keeps track of uninfected cells, infected cells, and free virus. In multiscale models, a fourth partial differential equation (PDE) accounts for the intracellular viral RNA (vRNA) kinetics in an infected cell. The PDE multiscale model is substantially more difficult to solve compared to the standard ODE model, with governing differential equations that are stiff. In previous contributions, we developed and implemented stable and efficient numerical methods for the multiscale model for both the solution of the model equations and parameter estimation. In this contribution, we perform sensitivity analysis on model parameters to gain insight into important properties and to ensure our numerical methods can be safely used for HCV viral dynamic simulations. Furthermore, we generate in-silico patients using the multiscale models to perform machine learning from the data, which enables us to remove HCV measurements on certain days and still be able to estimate meaningful observations with a sufficiently small error. Full article
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25 pages, 3539 KiB  
Article
Analytics Methods to Understand Information Retrieval Effectiveness—A Survey
by Josiane Mothe
Mathematics 2022, 10(12), 2135; https://doi.org/10.3390/math10122135 - 19 Jun 2022
Cited by 6 | Viewed by 2033 | Correction
Abstract
Information retrieval aims to retrieve the documents that answer users’ queries. A typical search process consists of different phases for which a variety of components have been defined in the literature; each one having a set of hyper-parameters to tune. Different studies focused [...] Read more.
Information retrieval aims to retrieve the documents that answer users’ queries. A typical search process consists of different phases for which a variety of components have been defined in the literature; each one having a set of hyper-parameters to tune. Different studies focused on how and how much the components and their hyper-parameters affect the system performance in terms of effectiveness, others on the query factor. The aim of these studies is to better understand information retrieval system effectiveness. This paper reviews the literature of this domain. It depicts how data analytics has been used in IR to gain a better understanding of system effectiveness. This review concludes that we lack a full understanding of system effectiveness related to the context which the system is in, though it has been possible to adapt the query processing to some contexts successfully. This review also concludes that, even if it is possible to distinguish effective from non-effective systems for a query set, neither the system component analysis nor the query features analysis were successful in explaining when and why a particular system fails on a particular query. Full article
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8 pages, 264 KiB  
Article
Branching Solutions of the Cauchy Problem for Nonlinear Loaded Differential Equations with Bifurcation Parameters
by Nikolai Sidorov and Denis Sidorov
Mathematics 2022, 10(12), 2134; https://doi.org/10.3390/math10122134 - 19 Jun 2022
Cited by 1 | Viewed by 982
Abstract
The Cauchy problem for a nonlinear system of differential equations with a Stieltjes integral (loads) of the desired solution is considered. The equation contains bifurcation parameters where the system has a trivial solution for any values. The necessary and sufficient conditions are derived [...] Read more.
The Cauchy problem for a nonlinear system of differential equations with a Stieltjes integral (loads) of the desired solution is considered. The equation contains bifurcation parameters where the system has a trivial solution for any values. The necessary and sufficient conditions are derived for those parameter values (bifurcation points) in the neighborhood of which the Cauchy problem has a non-trivial real solution. The constructive method is proposed for the solution of real solutions in the neighborhood of those points. The method uses successive approximations and builds asymptotics of the solution. The theoretical results are illustrated by example. The Cauchy problem with loads and bifurcation parameters has not been studied before. Full article
26 pages, 1947 KiB  
Article
A Hybrid Intuitionistic Fuzzy Group Decision Framework and Its Application in Urban Rail Transit System Selection
by Bing Yan, Yuan Rong, Liying Yu and Yuting Huang
Mathematics 2022, 10(12), 2133; https://doi.org/10.3390/math10122133 - 19 Jun 2022
Cited by 5 | Viewed by 1299
Abstract
The selection of an urban rail transit system from the perspective of green and low carbon can not only promote the construction of an urban rail transit system but also have a positive impact on urban green development. Considering the uncertainty caused by [...] Read more.
The selection of an urban rail transit system from the perspective of green and low carbon can not only promote the construction of an urban rail transit system but also have a positive impact on urban green development. Considering the uncertainty caused by different conflict criteria and the fuzziness of decision-making experts’ cognition in the selection process of a rail transit system, this paper proposes a hybrid intuitionistic fuzzy MCGDM framework to determine the priority of a rail transit system. To begin with, the weights of experts are determined based on the improved similarity method. Secondly, the subjective weight and objective weight of the criterion are calculated, respectively, according to the DEMATEL and CRITIC methods, and the comprehensive weight is calculated by the linear integration method. Thirdly, considering the regret degree and risk preference of experts, the COPRAS method based on regret theory is propounded to determine the prioritization of urban rail transit system ranking. Finally, urban rail transit system selection of City N is selected for the case study to illustrate the feasibility and effectiveness of the developed method. The results show that a metro system (P1) is the most suitable urban rail transit system for the construction of city N, followed by a municipal railway system (P7). Sensitivity analysis is conducted to illustrate the stability and robustness of the designed decision framework. Comparative analysis is also utilized to validate the efficacy, feasibility and practicability of the propounded methodology. Full article
(This article belongs to the Special Issue Advances in Fuzzy Decision Theory and Applications)
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12 pages, 421 KiB  
Article
End-to-End Training of Deep Neural Networks in the Fourier Domain
by András Fülöp and András Horváth
Mathematics 2022, 10(12), 2132; https://doi.org/10.3390/math10122132 - 19 Jun 2022
Cited by 1 | Viewed by 1856
Abstract
Convolutional networks are commonly used in various machine learning tasks, and they are more and more popularly used in the embedded domain with devices such as smart cameras and mobile phones. The operation of convolution can be substituted by point-wise multiplication in the [...] Read more.
Convolutional networks are commonly used in various machine learning tasks, and they are more and more popularly used in the embedded domain with devices such as smart cameras and mobile phones. The operation of convolution can be substituted by point-wise multiplication in the Fourier domain, which can save operation, but usually, it is applied with a Fourier transform before and an inverse Fourier transform after the multiplication, since other operations in neural networks cannot be implemented efficiently in the Fourier domain. In this paper, we will present a method for implementing neural network completely in the Fourier domain, and by this, saving multiplications and the operations of inverse Fourier transformations. Our method can decrease the number of operations by four times the number of pixels in the convolutional kernel with only a minor decrease in accuracy, for example, 4% on the MNIST and 2% on the HADB datasets. Full article
(This article belongs to the Special Issue Neural Networks and Learning Systems II)
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23 pages, 3237 KiB  
Article
Regional Location Routing Problem for Waste Collection Using Hybrid Genetic Algorithm-Simulated Annealing
by Vincent F. Yu, Grace Aloina, Hadi Susanto, Mohammad Khoirul Effendi and Shih-Wei Lin
Mathematics 2022, 10(12), 2131; https://doi.org/10.3390/math10122131 - 19 Jun 2022
Cited by 9 | Viewed by 2335
Abstract
Municipal waste management has become a challenging issue with the rise in urban populations and changes in people’s habits, particularly in developing countries. Moreover, government policy plays an important role associated with municipal waste management. Thus, this research proposes the regional location routing [...] Read more.
Municipal waste management has become a challenging issue with the rise in urban populations and changes in people’s habits, particularly in developing countries. Moreover, government policy plays an important role associated with municipal waste management. Thus, this research proposes the regional location routing problem (RLRP) model and multi-depot regional location routing problem (MRLRP) model, which are extensions of the location routing problem (LRP), to provide a better municipal waste collection process. The model is constructed to cover the minimum number of depot facilities’ policy requirements for each region due to government policy, i.e., the large-scale social restrictions in each region. The goal is to determine the depot locations in each region and the vehicles’ routes for collecting waste to fulfill inter-regional independent needs at a minimum total cost. This research conducts numerical examples with actual data to illustrate the model and implements a hybrid genetic algorithm and simulated annealing optimization to solve the problem. The results show that the proposed method efficiently solves the RLRP and MRLRP. Full article
(This article belongs to the Section Engineering Mathematics)
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14 pages, 2462 KiB  
Article
The Adaptive Composite Block-Structured Grid Calculation of the Gas-Dynamic Characteristics of an Aircraft Moving in a Gas Environment
by Victor V. Kuzenov, Sergei V. Ryzhkov and Aleksey Yu. Varaksin
Mathematics 2022, 10(12), 2130; https://doi.org/10.3390/math10122130 - 19 Jun 2022
Cited by 15 | Viewed by 1329
Abstract
This paper considers the problem associated with the numerical simulation of the interaction between the cocurrent stream occurring near a monoblock moving in the gas medium and solid fuel combustion products flowing from a solid fuel rocket engine (SFRE). The peculiarity of the [...] Read more.
This paper considers the problem associated with the numerical simulation of the interaction between the cocurrent stream occurring near a monoblock moving in the gas medium and solid fuel combustion products flowing from a solid fuel rocket engine (SFRE). The peculiarity of the approach used is the description of gas-dynamic processes inside the combustion chamber, in the nozzle block, and the down jet based on a single calculation methodology. In the formulated numerical methodology, the calculation of gas-dynamic parameters is based on the solution of unsteady Navier–Stokes equations and the application of a hybrid computational grid. A hybrid block-structured computational grid makes it possible to calculate gas flow near bodies of complex geometric shapes. The simulation of the main phase of interaction, corresponding to the stationary mode of rocket flight in the Earth’s atmosphere, has been carried out. A conjugated simulation of the internal ballistics of SFRE and interaction of combustion products jets is conducted. Full article
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39 pages, 16645 KiB  
Article
Single- and Multi-Objective Modified Aquila Optimizer for Optimal Multiple Renewable Energy Resources in Distribution Network
by Mohammed Hamouda Ali, Ahmed Tijani Salawudeen, Salah Kamel, Habeeb Bello Salau, Monier Habil and Mokhtar Shouran
Mathematics 2022, 10(12), 2129; https://doi.org/10.3390/math10122129 - 19 Jun 2022
Cited by 14 | Viewed by 1562
Abstract
Nowadays, the electrical power system has become a more complex, interconnected network that is expanding every day. Hence, the power system faces many problems such as increasing power losses, voltage deviation, line overloads, etc. The optimization of real and reactive power due to [...] Read more.
Nowadays, the electrical power system has become a more complex, interconnected network that is expanding every day. Hence, the power system faces many problems such as increasing power losses, voltage deviation, line overloads, etc. The optimization of real and reactive power due to the installation of energy resources at appropriate buses can minimize the losses and improve the voltage profile, especially for congested networks. As a result, the optimal distributed generation allocation (ODGA) problem is considered a more proper tool for the processes of planning and operation of power systems due to the power grid changes expeditiously based on the type and penetration level of renewable energy sources (RESs). This paper modifies the AO using a quasi-oppositional-based learning operator to address this problem and reduce the burden on the primary grid, making the grid more resilient. To demonstrate the effectiveness of the MAO, the authors first test the algorithm performance on twenty-three competitions on evolutionary computation benchmark functions, considering different dimensions. In addition, the modified Aquila optimizer (MAO) is applied to tackle the optimal distributed generation allocation (ODGA) problem. The proposed ODGA methodology presented in this paper has a multi-objective function that comprises decreasing power loss and total voltage deviation in a distribution system while keeping the system operating and security restrictions in mind. Many publications investigated the effect of expanding the number of DGs, whereas others found out the influence of DG types. Here, this paper examines the effects of different types and capacities of DG units at the same time. The proposed approach is tested on the IEEE 33-bus in different cases with several multiple DG types, including multi-objectives. The obtained simulation results are compared to the Aquila optimizer, particle swarm optimization algorithm, and trader-inspired algorithm. According to the comparison, the suggested approach provides a superior solution for the ODGA problem with faster convergence in the DNs. Full article
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26 pages, 7400 KiB  
Article
A Stochastic Optimization Algorithm to Enhance Controllers of Photovoltaic Systems
by Samia Charfeddine, Hadeel Alharbi, Houssem Jerbi, Mourad Kchaou, Rabeh Abbassi and Víctor Leiva
Mathematics 2022, 10(12), 2128; https://doi.org/10.3390/math10122128 - 19 Jun 2022
Cited by 7 | Viewed by 1415
Abstract
Increasing energy needs, pollution of nature, and eventual depletion of resources have prompted humanity to obtain new technologies and produce energy using clean sources and renewables. In this paper, we design an advanced method to improve the performance of a sliding mode controller [...] Read more.
Increasing energy needs, pollution of nature, and eventual depletion of resources have prompted humanity to obtain new technologies and produce energy using clean sources and renewables. In this paper, we design an advanced method to improve the performance of a sliding mode controller combined with control theory for a photovoltaic system. Specifically, we decouple the controlled output of the system from any perturbation source and assess the effectiveness of the results in terms of solution quality, closed-loop control stability, and dynamical convergence of the state variables. This study focuses on the climatic conditions that may affect the behavior of a solar energy plant to supply a motor with the highest possible efficiency and nominal operating conditions. The designed method enables us to obtain an optimal performance by means of advanced control techniques and a slime mould stochastic optimization algorithm. The efficiency and performance of this method are examined based on a benchmark model of a photovoltaic system via numerical analysis and simulation. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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17 pages, 1680 KiB  
Article
Amid COVID-19 Pandemic, Entrepreneurial Resilience and Creative Performance with the Mediating Role of Institutional Orientation: A Quantitative Investigation Using Structural Equation Modeling
by Alaa M. S. Azazz and Ibrahim A. Elshaer
Mathematics 2022, 10(12), 2127; https://doi.org/10.3390/math10122127 - 18 Jun 2022
Cited by 10 | Viewed by 2997
Abstract
As a result of the spread of the coronavirus (COVID-19), thousands of small companies around the world have been severely disrupted. Many business professionals, particularly entrepreneurs, suffer from the unprecedented magnitude of the lockdown of social activities, which is combined with limits on [...] Read more.
As a result of the spread of the coronavirus (COVID-19), thousands of small companies around the world have been severely disrupted. Many business professionals, particularly entrepreneurs, suffer from the unprecedented magnitude of the lockdown of social activities, which is combined with limits on individual mobility. This study investigates the resilience of entrepreneurs—which is characterized by hardiness, resourcefulness, and optimism—as well as the relationship between resilience and creative performance. Additionally, the mediating role of institutional orientation is investigated in order to highlight how contextual factors influence this relationship. Using a quantitative study approach and structural equation modeling data analysis technique, 390 entrepreneurs were investigated, and the analyzed data demonstrate that entrepreneurs’ ability to persevere in the face of adversity is strongly related to their ability to innovate, with institutional orientation serving as a partial mediating variable. Implications and future research opportunities are also explored in the paper. Full article
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17 pages, 4282 KiB  
Article
A Compact Parallel Pruning Scheme for Deep Learning Model and Its Mobile Instrument Deployment
by Meng Li, Ming Zhao, Tie Luo, Yimin Yang and Sheng-Lung Peng
Mathematics 2022, 10(12), 2126; https://doi.org/10.3390/math10122126 - 18 Jun 2022
Cited by 2 | Viewed by 1318
Abstract
In the single pruning algorithm, channel pruning or filter pruning is used to compress the deep convolution neural network, and there are still many redundant parameters in the compressed model. Directly pruning the filter will largely cause the loss of key information and [...] Read more.
In the single pruning algorithm, channel pruning or filter pruning is used to compress the deep convolution neural network, and there are still many redundant parameters in the compressed model. Directly pruning the filter will largely cause the loss of key information and affect the accuracy of model classification. To solve these problems, a parallel pruning algorithm combined with image enhancement is proposed. Firstly, in order to improve the generalization ability of the model, a data enhancement method of random erasure is introduced. Secondly, according to the trained batch normalization layer scaling factor, the channels with small contribution are cut off, the model is initially thinned, and then the filters are pruned. By calculating the geometric median of the filters, redundant filters similar to them are found and pruned, and their similarity is measured by calculating the distance between filters. Pruning was done using VGG19 and DenseNet40 on cifar10 and cifar100 data sets. The experimental results show that this algorithm can improve the accuracy of the model, and at the same time, it can compress the calculation and parameters of the model to a certain extent. Finally, this method is applied in practice, and combined with transfer learning, traffic objects are classified and detected on the mobile phone. Full article
(This article belongs to the Special Issue Evolutionary Computation for Deep Learning and Machine Learning)
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31 pages, 1442 KiB  
Article
Structure Preserving Uncertainty Modelling and Robustness Analysis for Spatially Distributed Dissipative Dynamical Systems
by Bruno Dogančić, Marko Jokić, Neven Alujević and Hinko Wolf
Mathematics 2022, 10(12), 2125; https://doi.org/10.3390/math10122125 - 18 Jun 2022
Cited by 1 | Viewed by 1375
Abstract
The paper deals with uncertainty modelling, robust stability and performance analysis of multi-input multi-output (MIMO) reduced order spatially distributed dissipative dynamical systems. While researching the topic of modern robust control of such systems, two key findings were discovered: (i) systematic modelling of the [...] Read more.
The paper deals with uncertainty modelling, robust stability and performance analysis of multi-input multi-output (MIMO) reduced order spatially distributed dissipative dynamical systems. While researching the topic of modern robust control of such systems, two key findings were discovered: (i) systematic modelling of the uncertainty and model order reduction (MOR) at the level of a subsystem gives both modelling freedom and the ability for obtaining less conservative uncertainties on the level of a subsystem; (ii) for a special class of interconnected dissipative dynamical systems, uncertainty conservatism at the subsystem level can be reduced—a novel, structure preserving algorithm employing subsystem partitioning and subsystem MOR by means of balanced truncation method (BTM) is used to obtain low-order robustly stable interconnected systems. Such systems are suitable for practical decentralized and distributed robust controller synthesis. Built upon a powerful framework of integral quadratic constraints (IQCs), this approach gives uncertainty modelling flexibility to perform robustness analysis of real world interconnected systems that are usually affected by multiple types of uncertainties at once. The proposed uncertainty modelling procedure and its practical application are presented on the numerical example. A spatially discretized vibration dynamical system comprised of a series of simply supported Euler beams mutually interconnected by springs and dampers is examined. Spatial discretization of the mathematical model is carried out using the finite element method (FEM). Full article
(This article belongs to the Special Issue Dynamics under Uncertainty: Modeling Simulation and Complexity II)
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11 pages, 361 KiB  
Article
Is Jump Robust Two Times Scaled Estimator Superior among Realized Volatility Competitors?
by Maria Čuljak, Josip Arnerić and Ante Žigman
Mathematics 2022, 10(12), 2124; https://doi.org/10.3390/math10122124 - 18 Jun 2022
Cited by 1 | Viewed by 1533
Abstract
This paper compares the empirical performance of the realized volatility estimators on an extensive high-frequency dataset of stock indices from four developed European markets with thick trading and intensive intraday activity. Even though the proposed estimators have distinctive properties, it is not clear [...] Read more.
This paper compares the empirical performance of the realized volatility estimators on an extensive high-frequency dataset of stock indices from four developed European markets with thick trading and intensive intraday activity. Even though the proposed estimators have distinctive properties, it is not clear which one has a better performance in terms of unbiasedness and consistency. Some of them are robust to microstructure noise only, and others are robust solely to price jumps, whereas a few of them are robust to both. Therefore, the main purpose is finding a benchmark estimator among alternative competitors, as the best proxy of integrated variance, and empirical demonstration of its superiority. The vast majority of the existing studies largely rely on developed US data or simulation data, but inferences obtained on such data might deviate from European developed markets. This study aims to fill in that niche. In particular, the optimal sampling frequency of proposed benchmark estimator is determined with respect to the trade-off between its bias and the variance of each stock index individually. Afterwards, probability integral transformation, Mincer–Zarnowitz regression and upper tail correlation from appropriate copula function are considered as an adequate pairwise comparison methods. Notable contributions of this paper include unambiguously proven superiority of robust two times scaled estimator for selected European developed markets within the range of optimal slow time frequency from 10 to 30 s. Finally, recommendations for research and practitioners regarding the usage of jump robust two times scaled estimator are given. In fact, asset managers, institutional investors as well as market regulators could benefit from proposed realized volatility benchmark in making long-term investment decisions, leading to sustainable finance. Full article
(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Financial Markets)
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24 pages, 357 KiB  
Article
Matrix Power Function Based Block Cipher Operating in CBC Mode
by Lina Dindiene, Aleksejus Mihalkovich, Kestutis Luksys and Eligijus Sakalauskas
Mathematics 2022, 10(12), 2123; https://doi.org/10.3390/math10122123 - 18 Jun 2022
Cited by 2 | Viewed by 1737
Abstract
In our previous study, we proposed a perfectly secure Shannon cipher based on the so-called matrix power function. There we also introduced a concept of single round symmetric encryption, i.e., we used the matrix power function together with some rather simple operations to [...] Read more.
In our previous study, we proposed a perfectly secure Shannon cipher based on the so-called matrix power function. There we also introduced a concept of single round symmetric encryption, i.e., we used the matrix power function together with some rather simple operations to define a three-step encryption algorithm that needs no additional rounds. Interestingly enough, the newly proposed Shannon cipher possesses the option of parallelization—an important property of efficiently performing calculations using several processors. Relying on our previous proposal, in this study we introduce a concept of a one round block cipher, which can be used to encrypt an arbitrary large message by dividing it into several blocks. In other words, we construct a block cipher operating in cipher block chaining mode on the basis of the previously defined Shannon cipher. Moreover, due to the perfect secrecy property of the original algorithm, we show that our proposal is able to withstand the chosen plaintext attack. Full article
(This article belongs to the Special Issue Advances in Algebraic Coding Theory and Cryptography)
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