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Mathematics
Volume 10
Issue 18
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Mathematics, Volume 10, Issue 18 (September-2 2022) – 192 articles

Cover Story (view full-size image): In this paper, we present a mathematical model to investigate the effect of NK cells on oncolytic virotherapy. Particularly, we focused on the minimum condition for NK cells to be activated in terms of parameters and how the activation of NK cells interacts and changes the dynamics among cancer, infected cancer cells and oncolytic virus. Analytic works for the existence and stability conditions of equilibrium points are provided. Numerical results are in good agreement with analytic solutions. Our numerical results show that equilibrium points can be created or destroyed by the activation of NK cells in a dynamical system and suggest that the balance between the bursting rate of the virus and the activation rate of NK cells is a crucial factor for successful OV therapy. View this paper
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30 pages, 8021 KiB  
Article
Artificial Neuron-Based Model for a Hybrid Real-Time System: Induction Motor Case Study
by Manuel I. Capel
Mathematics 2022, 10(18), 3410; https://doi.org/10.3390/math10183410 - 19 Sep 2022
Cited by 1 | Viewed by 1998
Abstract
Automatic Machine Learning (AML) methods are currently considered of great interest for use in the development of cyber-physical systems. However, in practice, they present serious application problems with respect to fitness computation, overfitting, lack of scalability, and the need for an enormous amount [...] Read more.
Automatic Machine Learning (AML) methods are currently considered of great interest for use in the development of cyber-physical systems. However, in practice, they present serious application problems with respect to fitness computation, overfitting, lack of scalability, and the need for an enormous amount of time for the computation of neural network hyperparameters. In this work, we have experimentally investigated the impact of continuous updating and validation of the hyperparameters, on the performance of a cyber-physical model, with four estimators based on feedforward and narx ANNs, all with the gradient descent-based optimization technique. The main objective is to demonstrate that the optimized values of the hyperparameters can be validated by simulation with MATLAB/Simulink following a mixed approach based on interleaving the updates of their values with a classical training of the ANNs without affecting their efficiency and automaticity of the proposed method. For the two relevant variables of an Induction Motor (IM), two sets of estimators have been trained from the input current and voltage data. In contrast, the training data for the speed and output electromagnetic torque of the IM have been established with the help of a new Simulink model developed entirely. The results have demonstrated the effectiveness of ANN estimators obtained with the Deep Learning Toolbox (DLT) that we used to transform the trained ANNs into blocks that can be directly used in cyber-physical models designed with Simulink. Full article
(This article belongs to the Special Issue Applications of Mathematical Modeling and Neural Networks)
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9 pages, 260 KiB  
Article
Optical Solitons of the Generalized Nonlinear Schrödinger Equation with Kerr Nonlinearity and Dispersion of Unrestricted Order
by Nikolay A. Kudryashov
Mathematics 2022, 10(18), 3409; https://doi.org/10.3390/math10183409 - 19 Sep 2022
Cited by 17 | Viewed by 1815
Abstract
The family of the generalized Schrödinger equations with Kerr nonlinearity of unrestricted order is considered. The solutions of equations are looked for using traveling wave reductions. The Painlevé test is applied for finding arbitrary constants in the expansion of the general solution into [...] Read more.
The family of the generalized Schrödinger equations with Kerr nonlinearity of unrestricted order is considered. The solutions of equations are looked for using traveling wave reductions. The Painlevé test is applied for finding arbitrary constants in the expansion of the general solution into the Laurent series. It is shown that the equation does not pass the Painlevé test but has two arbitrary constants in local expansion. This fact allows us to look for solitary wave solutions for equations of unrestricted order. The main result of this paper is the theorem of existence of optical solitons for equations of unrestricted order that is proved by direct calculation. The optical solitons for partial differential equations of the twelfth order are given in detail. Full article
(This article belongs to the Special Issue Nonlinear Partial Differential Equations: Exact Solutions, Symmetries, Methods, and Applications)
13 pages, 344 KiB  
Article
On the Complexity of Stable and Biased Majority
by Pablo Concha-Vega, Eric Goles, Pedro Montealegre and Martín Ríos-Wilson
Mathematics 2022, 10(18), 3408; https://doi.org/10.3390/math10183408 - 19 Sep 2022
Viewed by 1266
Abstract
A majority automata is a two-state cellular automata, where each cell updates its state according to the most represented state in its neighborhood. A question that naturally arises in the study of these dynamical systems asks whether there exists an efficient algorithm that [...] Read more.
A majority automata is a two-state cellular automata, where each cell updates its state according to the most represented state in its neighborhood. A question that naturally arises in the study of these dynamical systems asks whether there exists an efficient algorithm that can be implemented in order to compute the state configuration reached by the system at a given time-step. This problem is called the prediction problem. In this work, we study the prediction problem for a more general setting in which the local functions can be different according to their behavior in tie cases. We define two types of local rules: the stable majority and biased majority. The first one remains invariant in tie cases, and the second one takes the value 1. We call this class the heterogeneous majority cellular automata (HMCA). For this latter class, we show that in one dimension, the prediction problem for HMCA is in NL as a consequence of the dynamics exhibiting a type of bounded change property, while in two or more dimensions, the problem is P-Complete as a consequence of the capability of the system of simulating Boolean circuits. Full article
(This article belongs to the Section Mathematics and Computer Science)
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11 pages, 909 KiB  
Article
SCAFG: Classifying Single Cell Types Based on an Adaptive Threshold Fusion Graph Convolution Network
by Haonan Peng, Yuanyuan Li and Wei Zhang
Mathematics 2022, 10(18), 3407; https://doi.org/10.3390/math10183407 - 19 Sep 2022
Cited by 1 | Viewed by 2415
Abstract
Single-cell RNA sequencing (scRNA-seq) technology has been a significant direction for single-cell research due to its high accuracy and specificity, as it enables unbiased high-throughput studies with minimal sample sizes. The continuous improvement of scRNA-seq technology has promoted parallel research on single-cell multi-omics. [...] Read more.
Single-cell RNA sequencing (scRNA-seq) technology has been a significant direction for single-cell research due to its high accuracy and specificity, as it enables unbiased high-throughput studies with minimal sample sizes. The continuous improvement of scRNA-seq technology has promoted parallel research on single-cell multi-omics. Instead of sequencing bulk cells, analyzing single cells inspires greater discovery power for detecting novel genes without prior knowledge of sequence information and with greater sensitivity when quantifying rare variants and transcripts. However, current analyses of scRNA-seq data are usually carried out with unsupervised methods, which cannot take advantage of the prior distribution and structural features of the data. To solve this problem, we propose the SCAFG (Classifying Single Cell Types Based on an Adaptive Threshold Fusion Graph Convolution Network), a semi-supervised single-cell classification model that adaptively fuses cell-to-cell correlation matrices under various thresholds according to the distribution of cells. We tested the performance of the SCAFG in identifying cell types on diverse real scRNA-seq data; then, we compared the SCAFG with other commonly used semi-supervised algorithms, and it was shown that the SCAFG can classify single-cell data with a higher accuracy. Full article
(This article belongs to the Special Issue Mathematical Modeling and Analysis in Biology and Medicine, 2nd Edition)
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27 pages, 836 KiB  
Article
The Mathematical Model of Cyclic Signals in Dynamic Systems as a Cyclically Correlated Random Process
by Serhii Lupenko
Mathematics 2022, 10(18), 3406; https://doi.org/10.3390/math10183406 - 19 Sep 2022
Cited by 6 | Viewed by 3041
Abstract
This work is devoted to the procedure for constructing of a cyclically correlated random process of a continuous argument as a mathematical model of cyclic signals in dynamic systems, which makes it possible to consistently describe cyclic stochastic signals, both with regular and [...] Read more.
This work is devoted to the procedure for constructing of a cyclically correlated random process of a continuous argument as a mathematical model of cyclic signals in dynamic systems, which makes it possible to consistently describe cyclic stochastic signals, both with regular and irregular rhythms, not separating them, but complementing them within the framework of a single integrated model. The class of cyclically correlated random processes includes the subclass of cyclostationary (periodically) correlated random processes, which enable the use of a set of powerful methods of analysis and the forecasting of cyclic signals with a stable rhythm. Mathematical structures that model the cyclic, phase and rhythmic structures of a cyclically correlated random process are presented. The sufficient and necessary conditions that the structural function and the rhythm function of the cyclically correlated random process must satisfy have been established. The advantages of the cyclically correlated random process in comparison with other mathematical models of cyclic signals with a variable rhythm are given. The obtained results contribute to the emergence of a more complete and rigorous theory of this class of random processes and increase the validity of the methods of their analysis and computer simulation. Full article
(This article belongs to the Special Issue Dynamical Systems and System Analysis)
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39 pages, 8022 KiB  
Article
CLTSA: A Novel Tunicate Swarm Algorithm Based on Chaotic-Lévy Flight Strategy for Solving Optimization Problems
by Yi Cui, Ronghua Shi and Jian Dong
Mathematics 2022, 10(18), 3405; https://doi.org/10.3390/math10183405 - 19 Sep 2022
Cited by 9 | Viewed by 2041
Abstract
In this paper, we proposed a tunicate swarm algorithm based on Tent-Lévy flight (TLTSA) to avoid converging prematurely or failing to escape from a local optimal solution. First, we combined nine chaotic maps with the Lévy flight strategy to obtain nine different TSAs [...] Read more.
In this paper, we proposed a tunicate swarm algorithm based on Tent-Lévy flight (TLTSA) to avoid converging prematurely or failing to escape from a local optimal solution. First, we combined nine chaotic maps with the Lévy flight strategy to obtain nine different TSAs based on a Chaotic-Lévy flight strategy (CLTSA). Experimental results demonstrated that a TSA based on Tent-Lévy flight (TLTSA) performed the best among nine CLTSAs. Afterwards, the TLTSA was selected for comparative research with other well-known meta-heuristic algorithms. The 16 unimodal benchmark functions, 14 multimodal benchmark functions, 6 fixed-dimension functions, and 3 constrained practical problems in engineering were selected to verify the performance of TLTSA. The results of the test functions suggested that the TLTSA was better than the TSA and other algorithms in searching for global optimal solutions because of its excellent exploration and exploitation capabilities. Finally, the engineering experiments also demonstrated that a TLTSA solved constrained practical engineering problems more effectively. Full article
(This article belongs to the Special Issue Recent Advances in Swarm Intelligence Algorithms and Their Applications)
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22 pages, 11226 KiB  
Article
Entropy Analysis in MHD CNTS Flow Due to a Stretching Surface with Thermal Radiation and Heat Source/Sink
by K. N. Sneha, U. S. Mahabaleshwar, Mohsen Sharifpur, Mohammad Hossein Ahmadi and Mohammed Al-Bahrani
Mathematics 2022, 10(18), 3404; https://doi.org/10.3390/math10183404 - 19 Sep 2022
Cited by 13 | Viewed by 1776
Abstract
The consequence of magnetohydrodynamics (MHD) flow on entropy generation analysis and thermal radiation for carbon nanotubes via a stretched surface through a magnetic field has been discovered. The governing partial differential equations are altered into ordinary differential equations with the aid of the [...] Read more.
The consequence of magnetohydrodynamics (MHD) flow on entropy generation analysis and thermal radiation for carbon nanotubes via a stretched surface through a magnetic field has been discovered. The governing partial differential equations are altered into ordinary differential equations with the aid of the similarity variable. Here, water is considered the base fluid with two types of carbon nanotubes, such as single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs). This domain is used in the energy equation, and then it is solved analytically and transferred in terms of hypergeometric function. The existence and nonexistence of solutions for stretching are investigated. Some of the primary findings discussed in this article show that the presence of carbon nanotubes, magnetic field, and Eckert number develop heat transfer in nanofluids and heat sources and that Eckert number reduces entropy formation. Different regulating parameters, such as Casson fluid, mass transpiration, thermal radiation, solid volume fractions, magnetic constraint, and heat source/sink constraint, can be used to analyze the results of velocity and temperature profiles. The novelty of the current study on the influence of magnetic field entropy analysis on CNTs flow with radiation, is that elastic deformation is the subject of this research, and this has not previously been examined. Higher values of heat sources and thermal radiation enhance the heat transfer rate. The study reveals that thermal radiation, Casson fluid; mass transpiration, Darcy number, and Prandtl number increase, and that decrease in the buoyancy ratio, magnetic parameter, and volume fraction decrease the values of the buoyancy ratio, and also control the transfer of heat. Full article
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5 pages, 175 KiB  
Editorial
Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics
by Shaofeng Wang, Xin Cai, Jian Zhou, Zhengyang Song and Xiaofeng Li
Mathematics 2022, 10(18), 3403; https://doi.org/10.3390/math10183403 - 19 Sep 2022
Cited by 2 | Viewed by 1708
Abstract
With the increasing requirements for energy, resources and space, numerous rock engineering projects (e [...] Full article
(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)
7 pages, 223 KiB  
Article
Application of Simplified Homogeneous Balance Method to Multiple Solutions for (2 + l)-Dimensional Burgers’ Equations
by Lingxiao Li, Jinliang Zhang and Mingliang Wang
Mathematics 2022, 10(18), 3402; https://doi.org/10.3390/math10183402 - 19 Sep 2022
Cited by 3 | Viewed by 1243
Abstract
In this paper, three forms of (2 + l)-dimensional Burgers’ equations are investigated. More general multiple solutions of these Burgers’ equations are obtained by dependent variable transformation derived using the simplified homogeneous balance method. Full article
13 pages, 1698 KiB  
Article
Fault-Tolerant Integrated Guidance and Control Design for Hypersonic Vehicle Based on PPO
by Jia Song, Yuxie Luo, Mingfei Zhao, Yunlong Hu and Yanxue Zhang
Mathematics 2022, 10(18), 3401; https://doi.org/10.3390/math10183401 - 19 Sep 2022
Cited by 6 | Viewed by 1654
Abstract
Aiming at the problem of the terminal guidance phase of hypersonic vehicles (HSV) under fault condition, and considering the existence of various uncertain parameters and actuator faults in the control system, a fault-tolerant integrated guidance and control design of a hypersonic vehicle based [...] Read more.
Aiming at the problem of the terminal guidance phase of hypersonic vehicles (HSV) under fault condition, and considering the existence of various uncertain parameters and actuator faults in the control system, a fault-tolerant integrated guidance and control design of a hypersonic vehicle based on the proximal policy optimization algorithm (PPO) is proposed. First, in view of the problem that the separate guidance and control loop design cannot make full use of the coupling relationship between the two, the relationship between the guidance loop and the control loop is considered and an integrated guidance and control system of HSV is established. Then, the integrated guidance and control problem is converted into a reinforcement learning model, the action space, state observation space, and reward function of the PPO agent are designed, and the network is initialized and designed. Simulations verify the feasibility of the proposed PPO-based IGC system. Full article
(This article belongs to the Section Engineering Mathematics)
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21 pages, 5910 KiB  
Article
Closed-Form Solutions in a Magneto-Electro-Elastic Circular Rod via Generalized Exp-Function Method
by Muhammad Shakeel, Attaullah, Mohammed Kbiri Alaoui, Ahmed M. Zidan, Nehad Ali Shah and Wajaree Weera
Mathematics 2022, 10(18), 3400; https://doi.org/10.3390/math10183400 - 19 Sep 2022
Cited by 17 | Viewed by 1832
Abstract
In this study, the dispersal caused by the transverse Poisson’s effect in a magneto-electro-elastic (MEE) circular rod is taken into consideration using the nonlinear longitudinal wave equation (LWE), a mathematical physics problem. Using the generalized exp-function method, we investigate the families of solitary [...] Read more.
In this study, the dispersal caused by the transverse Poisson’s effect in a magneto-electro-elastic (MEE) circular rod is taken into consideration using the nonlinear longitudinal wave equation (LWE), a mathematical physics problem. Using the generalized exp-function method, we investigate the families of solitary wave solutions of one-dimensional nonlinear LWE. Using the computer program Wolfram Mathematica 10, these new exact and solitary wave solutions of the LWE are derived as trigonometric function, periodic solitary wave, rational function, hyperbolic function, bright and dark solitons solutions, sinh, cosh, and sech2 function solutions of the LWE. These solutions represent the electrostatic potential and pressure for LWE as well as the graphical representation of electrostatic potential and pressure. Full article
(This article belongs to the Special Issue Advances in Differential and Difference Equations with Applications 2023)
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12 pages, 3950 KiB  
Article
Processing Large Outliers in Arrays of Observations
by Gurami Tsitsiashvili
Mathematics 2022, 10(18), 3399; https://doi.org/10.3390/math10183399 - 19 Sep 2022
Cited by 2 | Viewed by 1342
Abstract
The interest in large or extreme outliers in arrays of empirical information is caused by the wishes of users (with whom the author worked): specialists in medical and zoo geography, mining, the application of meteorology in fishing tasks, etc. The following motives are [...] Read more.
The interest in large or extreme outliers in arrays of empirical information is caused by the wishes of users (with whom the author worked): specialists in medical and zoo geography, mining, the application of meteorology in fishing tasks, etc. The following motives are important for these specialists: the substantial significance of large emissions, the fear of errors in the study of large emissions by standard and previously used methods, the speed of information processing and the ease of interpretation of the results obtained. To meet these requirements, interval pattern recognition algorithms and the accompanying auxiliary computational procedures have been developed. These algorithms were designed for specific samples provided by the users (short samples, the presence of rare events in them or difficulties in the construction of interpretation scenarios). They have the common property that the original optimization procedures are built for them or well-known optimization procedures are used. This paper presents a series of results on processing observations by allocating large outliers as in a time series in planar and spatial observations. The algorithms presented in this paper differ in speed and sufficient validity in terms of the specially selected indicators. The proposed algorithms were previously tested on specific measurements and were accompanied by meaningful interpretations. According to the author, this paper is more applied than theoretical. However, to work with the proposed material, it is required to use a more diverse mathematical tool kit than the one that is traditionally used in the listed applications. Full article
(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks)
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12 pages, 3689 KiB  
Article
YOLOv4-Driven Appearance Grading Filing Mechanism: Toward a High-Accuracy Tomato Grading Model through a Deep-Learning Framework
by Yu-Huei Cheng, Cheng-Yen Tseng, Duc-Man Nguyen and Yu-Da Lin
Mathematics 2022, 10(18), 3398; https://doi.org/10.3390/math10183398 - 19 Sep 2022
Cited by 5 | Viewed by 1935
Abstract
In traditional agricultural quality control, agricultural products are screened manually and then packaged and transported. However, long-term fruit storage is challenging in tropical climates, especially in the case of cherry tomatoes. Cherry tomatoes that appear rotten must be immediately discarded while grading; otherwise, [...] Read more.
In traditional agricultural quality control, agricultural products are screened manually and then packaged and transported. However, long-term fruit storage is challenging in tropical climates, especially in the case of cherry tomatoes. Cherry tomatoes that appear rotten must be immediately discarded while grading; otherwise, other neighboring cherry tomatoes could rot. An insufficient agricultural workforce is one of the reasons for an increasing number of rotten tomatoes. The development of smart-technology agriculture has become a primary trend. This study proposed a You Only Look Once version 4 (YOLOv4)-driven appearance grading filing mechanism to grade cherry tomatoes. Images of different cherry-tomato appearance grades and different light sources were used as training sets, and the cherry tomatoes were divided into four categories according to appearance (perfect (pedicled head), good (not pedicled head), defective, and discardable). The AI server ran the YOLOv4 deep-learning framework for deep image learning training. Each dataset group was calculated by considering 100 of the four categories as the difference, and the total numbers of images were 400, 800, 1200, 1600, and 2000. Each dataset group was split into an 80% training set, 10% verification set, and 10% test set to overcome the identification complexity of different appearances and light source intensities. The experimental results revealed that models using 400–2000 images were approximately 99.9% accurate. Thus, we propose a new mechanism for rapidly grading agricultural products. Full article
(This article belongs to the Section Mathematics and Computer Science)
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7 pages, 195 KiB  
Correction
Correction: Mothe, J. Analytics Methods to Understand Information Retrieval Effectiveness—A Survey. Mathematics 2022, 10, 2135
by Josiane Mothe
Mathematics 2022, 10(18), 3397; https://doi.org/10.3390/math10183397 - 19 Sep 2022
Viewed by 1082
Abstract
The author wishes to make the following corrections to this paper [1]:In Abstract, (1) “It depicts how data analytics has been used in IR for a better understanding system effectiveness” should be “It depicts how data analytics has been used in IR to [...] Read more.
The author wishes to make the following corrections to this paper [1]:In Abstract, (1) “It depicts how data analytics has been used in IR for a better understanding system effectiveness” should be “It depicts how data analytics has been used in IR to gain a better understanding of system effectiveness”; (2) “This review concludes lack of full understanding of system effectiveness according to the context although it has been possible to adapt the query processing to some contexts successfully” should be changed to “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”; (3) “This review also concludes that, even if it is possible to distinguish effective from non effective system on average on a query set” should be changed to “This review also concludes that, even if it is possible to distinguish effective from non-effective systems for a query set” [...] Full article
(This article belongs to the Special Issue Natural Language Processing (NLP) and Machine Learning (ML)—Theory and Applications)
19 pages, 16231 KiB  
Article
Nonlinear Bending of Sandwich Plates with Graphene Nanoplatelets Reinforced Porous Composite Core under Various Loads and Boundary Conditions
by Xudong Fan, Aiwen Wang, Pengcheng Jiang, Sijin Wu and Ying Sun
Mathematics 2022, 10(18), 3396; https://doi.org/10.3390/math10183396 - 19 Sep 2022
Cited by 4 | Viewed by 1794
Abstract
The nonlinear bending of the sandwich plates with graphene nanoplatelets (GPLs) reinforced porous composite (GNRPC) core and two metal skins subjected to different boundary conditions and various loads, such as the concentrated load at the center, linear loads with different slopes passing through [...] Read more.
The nonlinear bending of the sandwich plates with graphene nanoplatelets (GPLs) reinforced porous composite (GNRPC) core and two metal skins subjected to different boundary conditions and various loads, such as the concentrated load at the center, linear loads with different slopes passing through the center, linear eccentric loads, uniform loads, and trapezoidal loads, has been presented. The popular four-unknown refined theory accounting for the thickness stretching effects has been employed to model the mechanics of the sandwich plates. The governing equations have been derived from the nonlinear Von Karman strain–displacement relationship and principle of virtual work with subsequent solution by employing the classical finite element method in combination with the Newton downhill method. The convergence of the numerical results has been checked. The accuracy and efficiency of the theory have been confirmed by comparing the obtained results with those available in the literature. Furthermore, a parametric study has been carried out to analyze the effects of load type, boundary conditions, porosity coefficient, GPLs weight fraction, GPLs geometry, and concentrated load radius on the nonlinear central bending deflections of the sandwich plates. In addition, the numerical results reveal that the adopted higher order theory can significantly improve the simulation of the transverse deflection in the thickness direction. Full article
(This article belongs to the Special Issue Modeling and Analysis in Dynamical Systems and Bistability)
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18 pages, 3964 KiB  
Article
ECG Signal Features Classification for the Mental Fatigue Recognition
by Eglė Butkevičiūtė, Aleksėjus Michalkovič and Liepa Bikulčienė
Mathematics 2022, 10(18), 3395; https://doi.org/10.3390/math10183395 - 19 Sep 2022
Cited by 13 | Viewed by 3933
Abstract
Mental fatigue is a major public health issue worldwide that is common among both healthy and sick people. In the literature, various modern technologies, together with artificial intelligence techniques, have been proposed. Most techniques consider complex biosignals, such as electroencephalogram, electro-oculogram or classification [...] Read more.
Mental fatigue is a major public health issue worldwide that is common among both healthy and sick people. In the literature, various modern technologies, together with artificial intelligence techniques, have been proposed. Most techniques consider complex biosignals, such as electroencephalogram, electro-oculogram or classification of basic heart rate variability parameters. Additionally, most studies focus on a particular area, such as driving, surgery, etc. In this paper, a novel approach is presented that combines electrocardiogram (ECG) signal feature extraction, principal component analysis (PCA), and classification using machine learning algorithms. With the aim of daily mental fatigue recognition, an experiment was designed wherein ECG signals were recorded twice a day: in the morning, i.e., a state without fatigue, and in the evening, i.e., a fatigued state. PCA analysis results show that ECG signal parameters, such as Q and R wave amplitude values, as well as QT and T intervals, presented with the largest differences between states compared to other ECG signal parameters. Furthermore, the random forest classifier achieved more than 94.5% accuracy. This work demonstrates the feasibility of ECG signal feature extraction for automatic mental fatigue detection. Full article
(This article belongs to the Special Issue Advances in Artificial Intelligence and Statistical Techniques with Applications to Health and Education)
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21 pages, 391 KiB  
Article
Weak Inflationary BL-Algebras and Filters of Inflationary (Pseudo) General Residuated Lattices
by Xiaohong Zhang, Rong Liang and Benjamín Bedregal
Mathematics 2022, 10(18), 3394; https://doi.org/10.3390/math10183394 - 19 Sep 2022
Cited by 10 | Viewed by 1519
Abstract
After the research on naBL-algebras gained by the non-associative t-norms and overlap functions, inflationary BL-algebras were also studied as a recent kind of non-associative generalization of BL-algebras, which can be obtained by general overlap functions. In this paper, we show that not every [...] Read more.
After the research on naBL-algebras gained by the non-associative t-norms and overlap functions, inflationary BL-algebras were also studied as a recent kind of non-associative generalization of BL-algebras, which can be obtained by general overlap functions. In this paper, we show that not every inflationary general overlap function can induce an inflationary BL-algebra by a counterexample and thus propose the new concept of weak inflationary BL-algebras. We prove that each inflationary general overlap function corresponds to a weak inflationary BL-algebra; therefore, two mistaken results in the previous paper are revised. In addition, some properties satisfied by weak inflationary BL-algebras are discussed, and the relationships among some non-classical logic algebras are analyzed. Finally, we establish the theory of filters and quotient algebras of inflationary general residuated lattice (IGRL) and inflationary pseudo-general residuated lattice (IPGRL), and characterize the properties of some kinds of IGRLs and IPGRLs by naBL-filters, (weak) inflationary BL-filters, and weak inflationary pseudo-BL-filters. Full article
(This article belongs to the Special Issue FSTA: Fuzzy Set Theory and Applications)
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25 pages, 384 KiB  
Article
When Is a Graded Free Complex Exact?
by David C. Molano, Javier A. Moreno and Carlos E. Valencia
Mathematics 2022, 10(18), 3393; https://doi.org/10.3390/math10183393 - 19 Sep 2022
Cited by 1 | Viewed by 2043
Abstract
Minimal free resolutions of a finitely generated module over a polynomial ring S=k[x], with variables x={x1,…,xn} and a field k have been extensively studied. Almost all the [...] Read more.
Minimal free resolutions of a finitely generated module over a polynomial ring S=k[x], with variables x={x1,…,xn} and a field k have been extensively studied. Almost all the results in the literature about minimal free resolutions give their Betti numbers, that is, the ranks of the free modules in the resolution at each degree. Several techniques have been developed to compute Betti numbers, making this a manageable problem in many cases. However, a description of the differentials in the resolution is rarely given, as this turns out to be a more difficult problem. The main purpose of this article is to give a criterion to check when a graded free complex of an S-module is exact. Unlike previous similar criteria, this one allows us to give a description of the differentials using the combinatorics of the S-module. The criterion is given in terms of the Betti numbers of the resolutions in each degree and the set of columns of the matrix representation of the differentials. In the last section, and with the aim of illustrating how to use the criterion, we apply it to one of the first better-understood cases, the edge ideal of the complete graph. However, this criterion can be used to give an explicit description of the differentials of a resolution of several monomial ideals such as the duplication of an ideal, the edge ideal of a cograph, etc. Full article
(This article belongs to the Section Algebra, Geometry and Topology)
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15 pages, 1532 KiB  
Article
Deep Learning Model for Global Spatio-Temporal Image Prediction
by Dušan P. Nikezić, Uzahir R. Ramadani, Dušan S. Radivojević, Ivan M. Lazović and Nikola S. Mirkov
Mathematics 2022, 10(18), 3392; https://doi.org/10.3390/math10183392 - 19 Sep 2022
Cited by 7 | Viewed by 2977
Abstract
Mathematical methods are the basis of most models that describe the natural phenomena around us. However, the well-known conventional mathematical models for atmospheric modeling have some limitations. Machine learning with Big Data is also based on mathematics but offers a new approach for [...] Read more.
Mathematical methods are the basis of most models that describe the natural phenomena around us. However, the well-known conventional mathematical models for atmospheric modeling have some limitations. Machine learning with Big Data is also based on mathematics but offers a new approach for modeling. There are two methodologies to develop deep learning models for spatio-temporal image prediction. On these bases, two models were built—ConvLSTM and CNN-LSTM—with two types of predictions, i.e., sequence-to-sequence and sequence-to-one, in order to forecast Aerosol Optical Thickness sequences. The input dataset for training was NASA satellite imagery MODAL2_E_AER_OD from Terra/MODIS satellites, which presents global Aerosol Optical Thickness with an 8 day temporal resolution from 2000 to the present. The obtained results show that the ConvLSTM sequence-to-one model had the lowest RMSE error and the highest Cosine Similarity value. The advantages of the developed DL models are that they can be executed in milliseconds on a PC, can be used for global-scale Earth observations, and can serve as tracers to study how the Earth’s atmosphere moves. The developed models can be used as transfer learning for similar image time-series forecasting models. Full article
(This article belongs to the Special Issue Mathematical Theories and Models in Environmental Science)
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17 pages, 5358 KiB  
Article
Integrated Control of Spray System and Active Suspension Systems Based on Model-Assisted Active Disturbance Rejection Control Algorithm
by Jianxu Zhu, Dingxuan Zhao, Shuang Liu, Zilong Zhang, Guangyu Liu and Jinming Chang
Mathematics 2022, 10(18), 3391; https://doi.org/10.3390/math10183391 - 19 Sep 2022
Cited by 5 | Viewed by 1801
Abstract
Due to the lack of body stability of emergency rescue vehicles, their attitude stability is insufficient and they are unable to realize working while driving, resulting in low rescue efficiency. Aiming at the water tower fire truck, which is equipped with an active [...] Read more.
Due to the lack of body stability of emergency rescue vehicles, their attitude stability is insufficient and they are unable to realize working while driving, resulting in low rescue efficiency. Aiming at the water tower fire truck, which is equipped with an active suspension system, the vehicle attitude stability is studied. First, combined with the active suspension system and spray system, a 13-DOF integrated dynamic model for the water tower fire truck is established. Using the model-assisted active disturbance rejection control method, the controllers are designed for the vertical displacement, pitch angle, and roll angle of the vehicle attitude. Then, the computer simulation is carried out to verify the effectiveness of this control method. Finally, the water spray obstacle crossing experiment is carried out with a JP32G water tower fire truck. The results show that when the vehicle runs over the triangular obstacle on one side and two sides in the integrated spray-active suspension mode, the peak–peak values of body pitch angle and roll angle are reduced by 10.9% and 23.2%, and 23.7% and 16.3%, respectively, compared with the passive hydro pneumatic suspension. Full article
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18 pages, 394 KiB  
Article
Numerical Analysis of Alternating Direction Implicit Orthogonal Spline Collocation Scheme for the Hyperbolic Integrodifferential Equation with a Weakly Singular Kernel
by Qiong Huang, Omid Nikan and Zakieh Avazzadeh
Mathematics 2022, 10(18), 3390; https://doi.org/10.3390/math10183390 - 19 Sep 2022
Cited by 2 | Viewed by 1578
Abstract
This paper studies an alternating direction implicit orthogonal spline collocation (ADIOSC) technique for calculating the numerical solution of the hyperbolic integrodifferential problem with a weakly singular kernel in the two-dimensional domain. The integral term is approximated with the help of the second-order fractional [...] Read more.
This paper studies an alternating direction implicit orthogonal spline collocation (ADIOSC) technique for calculating the numerical solution of the hyperbolic integrodifferential problem with a weakly singular kernel in the two-dimensional domain. The integral term is approximated with the help of the second-order fractional quadrature formula introduced by Lubich. The stability and convergence analysis of the proposed strategy are proven in L2-norm. Numerical results highlight the high accuracy and efficiency of the proposed strategy and clarify the theoretical prediction. Full article
(This article belongs to the Special Issue Mathematical Methods for Nonlinear Dynamics)
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14 pages, 4484 KiB  
Article
Multiple Degradation Skilled Network for Infrared and Visible Image Fusion Based on Multi-Resolution SVD Updation
by Gunnam Suryanarayana, Vijayakumar Varadarajan, Siva Ramakrishna Pillutla, Grande Nagajyothi and Ghamya Kotapati
Mathematics 2022, 10(18), 3389; https://doi.org/10.3390/math10183389 - 19 Sep 2022
Cited by 10 | Viewed by 1922
Abstract
Existing infrared (IR)-visible (VIS) image fusion algorithms demand source images with the same resolution levels. However, IR images are always available with poor resolution due to hardware limitations and environmental conditions. In this correspondence, we develop a novel image fusion model that brings [...] Read more.
Existing infrared (IR)-visible (VIS) image fusion algorithms demand source images with the same resolution levels. However, IR images are always available with poor resolution due to hardware limitations and environmental conditions. In this correspondence, we develop a novel image fusion model that brings resolution consistency between IR-VIS source images and generates an accurate high-resolution fused image. We train a single deep convolutional neural network model by considering true degradations in real time and reconstruct IR images. The trained multiple degradation skilled network (MDSNet) increases the prominence of objects in fused images from the IR source image. In addition, we adopt multi-resolution singular value decomposition (MRSVD) to capture maximum information from source images and update IR image coefficients with that of VIS images at the finest level. This ensures uniform contrast along with clear textural information in our results. Experiments demonstrate the efficiency of the proposed method over nine state-of-the-art methods using five image quality assessment metrics. Full article
(This article belongs to the Special Issue Mathematical Methods in Image Processing and Computer Vision)
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12 pages, 274 KiB  
Article
h-Almost Ricci–Yamabe Solitons in Paracontact Geometry
by Uday Chand De, Mohammad Nazrul Islam Khan and Arpan Sardar
Mathematics 2022, 10(18), 3388; https://doi.org/10.3390/math10183388 - 18 Sep 2022
Cited by 5 | Viewed by 1582
Abstract
In this article, we classify h-almost Ricci–Yamabe solitons in paracontact geometry. In particular, we characterize para-Kenmotsu manifolds satisfying h-almost Ricci–Yamabe solitons and 3-dimensional para-Kenmotsu manifolds obeying h-almost gradient Ricci–Yamabe solitons. Then, we classify para-Sasakian manifolds and para-cosymplectic manifolds admitting h [...] Read more.
In this article, we classify h-almost Ricci–Yamabe solitons in paracontact geometry. In particular, we characterize para-Kenmotsu manifolds satisfying h-almost Ricci–Yamabe solitons and 3-dimensional para-Kenmotsu manifolds obeying h-almost gradient Ricci–Yamabe solitons. Then, we classify para-Sasakian manifolds and para-cosymplectic manifolds admitting h-almost Ricci–Yamabe solitons and h-almost gradient Ricci–Yamabe solitons, respectively. Finally, we construct an example to illustrate our result. Full article
(This article belongs to the Special Issue Geometry of Manifolds and Applications)
27 pages, 1595 KiB  
Article
Analysis of the Public Opinion Evolution on the Normative Policies for the Live Streaming E-Commerce Industry Based on Online Comment Mining under COVID-19 Epidemic in China
by Tinggui Chen, Chenhao Tong, Yuhan Bai, Jianjun Yang, Guodong Cong and Tianluo Cong
Mathematics 2022, 10(18), 3387; https://doi.org/10.3390/math10183387 - 18 Sep 2022
Cited by 11 | Viewed by 6540
Abstract
Recent years have witnessed the intensive development of live streaming E-commerce, an emerging business mode. Although it contributes to economic growth, various forms of chaos show up and disturbs the market order. Therefore, from 1 July 2020, the official release of the first [...] Read more.
Recent years have witnessed the intensive development of live streaming E-commerce, an emerging business mode. Although it contributes to economic growth, various forms of chaos show up and disturbs the market order. Therefore, from 1 July 2020, the official release of the first domestic document on live streaming E-commerce, the Code of Conduct for Online Live Streaming Marketing, to the end of the first half of 2021, China has witnessed so intensive release of relevant policies that are rare over the past years. Introducing these policies will inevitably attract the general public’s attention and discussions. Based on online comments, this paper uses the LDA models to extract topics from online comments related to live streaming E-commerce and identifies sentiment polarity and sentiment intensity by the analysis models of different emotion dictionaries to study policy implementation effects and the main topics of concern before and after the policy implementation. The analysis results show that people between the age of 20 and 40 attach more importance to the implementation of the normative policy for live streaming E-commerce. Women, the main force of live streaming users, are less enthusiastic about the policy implementation than men. Moreover, the analysis results of the LDA models and online HDP (online hierarchical Dirichlet process) models demonstrate that the most discussed topics are the contribution of live streaming E-commerce to traditional economic transformation, public welfare activities, resumption of work and production, and poverty alleviation, as well as fraud, counterfeit goods, supervision, rights protection and other incidents in this industry. Overall, the majority of the public holds a positive attitude towards the policy implementation. After further analysis of comments under the relevant topics, it is found that compared with the first two policies released on 1 July and 5 November in 2020, although the proportion of netizens with positive emotions during the implementation of the follow-up policy has increased, the increment is not significant, indicating that the implementation of the new normative policy in a short term will hardly curb the occurrence of industry chaos. In turn, the governments should transfer their attention to actual regulatory problems, and intensify efforts to implement normative policies. Full article
(This article belongs to the Special Issue Mathematical and Statistical Analysis of COVID-19 Impact on Global Economy, Business, and Management)
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17 pages, 2408 KiB  
Article
On Comprehension of Genetic Programming Solutions: A Controlled Experiment on Semantic Inference
by Boštjan Slivnik, Željko Kovačević, Marjan Mernik and Tomaž Kosar
Mathematics 2022, 10(18), 3386; https://doi.org/10.3390/math10183386 - 18 Sep 2022
Cited by 1 | Viewed by 1736
Abstract
Applied to the problem of automatic program generation, Genetic Programming often produces code bloat, or unexpected solutions that are, according to common belief, difficult to comprehend. To study the comprehensibility of the code produced by Genetic Programming, attribute grammars obtained by Genetic Programming-based [...] Read more.
Applied to the problem of automatic program generation, Genetic Programming often produces code bloat, or unexpected solutions that are, according to common belief, difficult to comprehend. To study the comprehensibility of the code produced by Genetic Programming, attribute grammars obtained by Genetic Programming-based semantic inference were compared to manually written ones. According to the established procedure, the research was carried out as a controlled classroom experiment that involved two groups of students from two universities, and consisted of a background questionnaire, two tests and a feedback questionnaire after each test. The tasks included in the tests required the identification of various properties of attributes and grammars, the identification of the correct attribute grammar from a list of choices, or correcting a semantic rule in an attribute grammar. It was established that solutions automatically generated by Genetic Programming in the field of semantic inference, in this study attribute grammars, are indeed significantly harder to comprehend than manually written ones. This finding holds, regardless of whether comprehension correctness, i.e., how many attribute grammars were correctly comprehended, or comprehension efficiency is considered, i.e., how quickly attribute grammars were correctly comprehended. Full article
(This article belongs to the Section Mathematics and Computer Science)
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13 pages, 1101 KiB  
Article
Fractional-Order Multivariable Adaptive Control Based on a Nonlinear Scalar Update Law
by Fang Yan, Xiaorong Hou and Tingting Tian
Mathematics 2022, 10(18), 3385; https://doi.org/10.3390/math10183385 - 18 Sep 2022
Cited by 4 | Viewed by 1711
Abstract
This paper proposes a new fractional-order model reference adaptive control (FOMRAC) framework for a fractional-order multivariable system with parameter uncertainty. The designed FOMRAC scheme depends on a fractional-order nonlinear scalar update law. Specifically, the scalar update law does not change as the input–output [...] Read more.
This paper proposes a new fractional-order model reference adaptive control (FOMRAC) framework for a fractional-order multivariable system with parameter uncertainty. The designed FOMRAC scheme depends on a fractional-order nonlinear scalar update law. Specifically, the scalar update law does not change as the input–output dimension changes. The main advantage of the proposed adaptive controller is that only one parameter online update is needed such that the computational burden in the existing FOMRAC can be relieved. Furthermore, we show that all signals in this adaptive scheme are bounded and the mean value of the squared norm of the error converges to zero. Two illustrative numerical examples are presented to demonstrate the efficiency of the proposed control scheme. Full article
(This article belongs to the Special Issue Fractional Calculus and Mathematical Applications)
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21 pages, 22172 KiB  
Article
Model Predictive Control for Stabilization of DC Microgrids in Island Mode Operation
by Duberney Murillo-Yarce, Sebastián Riffo, Carlos Restrepo, Catalina González-Castaño and Alejandro Garcés
Mathematics 2022, 10(18), 3384; https://doi.org/10.3390/math10183384 - 18 Sep 2022
Cited by 5 | Viewed by 2119
Abstract
DC microgrid (DCMG) is a promising technology for integrating distributed resources, such as solar generation and energy storage devices, that are intrinsically DC. Recently, model predictive control (MPC) is one of the control techniques that has been widely used in microgrid applications due [...] Read more.
DC microgrid (DCMG) is a promising technology for integrating distributed resources, such as solar generation and energy storage devices, that are intrinsically DC. Recently, model predictive control (MPC) is one of the control techniques that has been widely used in microgrid applications due to its advantages, such as transient response and flexibility to nonlinearity inclusion. MPC applications can be centralized, distributed, or decentralized based on the communication architecture. A major disadvantage of the centralized model predictive control (CMPC) is the high computational effort. This paper proposes a CMPC for DCMG stabilization that uses the admittance matrix of a reduced DCMG in the prediction equation and the one-step prediction horizon to decrease the computational effort. The proposed CMPC also replaces the hierarchical architecture primary and secondary controls, achieving voltage or power regulation. A hardware-in-the-loop (HIL) tool, known as RT-Box 2, has been used to emulate an 8-node DC microgrid with versatile buck–boost converters at the supply and power consumption nodes. The proposed predictive control exhibited better performance in comparison with the averaged voltage control in the HIL experiments. Full article
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15 pages, 4107 KiB  
Article
Force Tracking Impedance Control of Hydraulic Series Elastic Actuators Interacting with Unknown Environment
by Yong Nie, Jiajia Liu, Gang Liu, Litong Lyu, Jie Li and Zheng Chen
Mathematics 2022, 10(18), 3383; https://doi.org/10.3390/math10183383 - 18 Sep 2022
Cited by 4 | Viewed by 1873
Abstract
Force tracking control for hydraulic series elastic actuators (SEAs) is the demand in robots interacting with the surrounding world. However, the inherent nonlinearities and uncertainties of the hydraulic system, as well as the unknown environment, make it difficult to achieve precise contact force [...] Read more.
Force tracking control for hydraulic series elastic actuators (SEAs) is the demand in robots interacting with the surrounding world. However, the inherent nonlinearities and uncertainties of the hydraulic system, as well as the unknown environment, make it difficult to achieve precise contact force control of hydraulic SEAs. Therefore, in this study, force tracking impedance control of hydraulic SEAs is developed considering interaction with an unknown environment in which the force tracking performance can be guaranteed in theory. Based on the typical force tracking impedance frame, the force tracking performance is improved by introducing backstepping control into the inner position controller to deal with the high-order nonlinear dynamics of the hydraulic SEA. In addition, the environment parameters are also estimated online by the adaptive method. Finally, comparative simulation is conducted with different interacting environments, which verifies the advantages of the proposed method. Full article
(This article belongs to the Special Issue Dynamic Modeling and Simulation for Control Systems)
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22 pages, 4784 KiB  
Article
Bagged Ensemble of Gaussian Process Classifiers for Assessing Rockburst Damage Potential with an Imbalanced Dataset
by Ying Chen, Qi Da, Weizhang Liang, Peng Xiao, Bing Dai and Guoyan Zhao
Mathematics 2022, 10(18), 3382; https://doi.org/10.3390/math10183382 - 17 Sep 2022
Cited by 5 | Viewed by 1598
Abstract
The evaluation of rockburst damage potential plays a significant role in managing rockburst risk and guaranteeing the safety of personnel. However, it is still a challenging problem because of its complex mechanisms and numerous influencing factors. In this study, a bagged ensemble of [...] Read more.
The evaluation of rockburst damage potential plays a significant role in managing rockburst risk and guaranteeing the safety of personnel. However, it is still a challenging problem because of its complex mechanisms and numerous influencing factors. In this study, a bagged ensemble of Gaussian process classifiers (GPCs) is proposed to assess rockburst damage potential with an imbalanced dataset. First, a rockburst dataset including seven indicators and four levels is collected. To address classification problems with an imbalanced dataset, a novel model that integrates the under-sampling technique, Gaussian process classifier (GPC) and bagging method is constructed. Afterwards, the comprehensive performance of the proposed model is evaluated using the values of accuracy, precision, recall, and F1. Finally, the methodology is applied to assess rockburst damage potential in the Perseverance nickel mine. Results show that the performance of the proposed bagged ensemble of GPCs is acceptable, and the integration of data preprocessing, under-sampling technique, GPC, and bagging method can improve the model performance. The proposed methodology can provide an effective reference for the risk management of rockburst. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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20 pages, 1731 KiB  
Article
Comparative Study of Markov Chain Filtering Schemas for Stabilization of Stochastic Systems under Incomplete Information
by Alexey Bosov and Andrey Borisov
Mathematics 2022, 10(18), 3381; https://doi.org/10.3390/math10183381 - 17 Sep 2022
Viewed by 1377
Abstract
The object under investigation is a controllable linear stochastic differential system affected by some external statistically uncertain piecewise continuous disturbances. They are directly unobservable but assumed to be a continuous-time Markov chain. The problem is to stabilize the system output concerning a quadratic [...] Read more.
The object under investigation is a controllable linear stochastic differential system affected by some external statistically uncertain piecewise continuous disturbances. They are directly unobservable but assumed to be a continuous-time Markov chain. The problem is to stabilize the system output concerning a quadratic optimality criterion. As is known, the separation theorem holds for the system. The goal of the paper is performance analysis of various numerical schemes applied to the filtering of the external Markov input for system stabilization purposes. The paper briefly presents the theoretical solution to the considered problem of optimal stabilization for systems with the Markov jump external disturbances: the conditions providing the separation theorem, the equations of optimal control, and the ones defining the Wonham filter. It also contains a complex of the stable numerical approximations of the filter, designed for the time-discretized observations, along with their accuracy characteristics. The approximations of orders 12, 1, and 2 along with the classical Euler–Maruyama scheme are chosen for the comparison of the Wonham filter numerical realization. The filtering estimates are used in the practical stabilization of the various linear systems of the second order. The numerical experiments confirm the significant influence of the filtering precision on the stabilization performance and superiority of the proposed stable schemes of numerical filtering. Full article
(This article belongs to the Special Issue Mathematical Modeling, Optimization and Machine Learning)
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