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Editor’s Choice Articles

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to readers, or important in the respective research area. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.

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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 2343
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)
28 pages, 3310 KiB  
Article
Multiple Scenarios of Quality of Life Index Using Fuzzy Linguistic Quantifiers: The Case of 85 Countries in Numbeo
by Ziwei Shu, Ramón Alberto Carrasco, Javier Portela García-Miguel and Manuel Sánchez-Montañés
Mathematics 2022, 10(12), 2091; https://doi.org/10.3390/math10122091 - 16 Jun 2022
Cited by 13 | Viewed by 4050
Abstract
In economic development, in addition to comparing the gross domestic product (GDP) between nations, it is critical to assess the quality of life to gain a holistic perspective of their different aspects. However, the quality of life index (QOLI) is a subjective term [...] Read more.
In economic development, in addition to comparing the gross domestic product (GDP) between nations, it is critical to assess the quality of life to gain a holistic perspective of their different aspects. However, the quality of life index (QOLI) is a subjective term that can be difficult to quantify. Although this composite index is typically calculated using universal weights proposed by experts to aggregate indicators, such as safety indexes, healthcare indexes, pollution indexes, and housing indicators, it is complicated to balance multiple dimensions whose weights are adjusted to account for different countries’ circumstances. Therefore, this paper aims to construct various scenarios of the QOLI, using linguistic quantifiers of the ordered weighted averaging (OWA) operator, and the 2-tuple linguistic model. Numbeo, one of the largest quality of life information databases, was used in this paper to estimate the QOLI in 85 countries. Uncertainty and sensitivity analyses were employed to assess the robustness of the QOLI. The results of the proposed model are compared with those obtained using the Numbeo formulation. The results show that the proposed model increases the linguistic interpretability of the QOLI, and obtains different QOLIs, based on diverse country contexts. Full article
(This article belongs to the Topic Multi-Criteria Decision Making)
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16 pages, 586 KiB  
Article
Benchmarking Cost-Effective Opinion Injection Strategies in Complex Networks
by Alexandru Topîrceanu
Mathematics 2022, 10(12), 2067; https://doi.org/10.3390/math10122067 - 15 Jun 2022
Cited by 3 | Viewed by 2095
Abstract
Inferring the diffusion mechanisms in complex networks is of outstanding interest since it enables better prediction and control over information dissemination, rumors, innovation, and even infectious outbreaks. Designing strategies for influence maximization in real-world networks is an ongoing scientific challenge. Current approaches commonly [...] Read more.
Inferring the diffusion mechanisms in complex networks is of outstanding interest since it enables better prediction and control over information dissemination, rumors, innovation, and even infectious outbreaks. Designing strategies for influence maximization in real-world networks is an ongoing scientific challenge. Current approaches commonly imply an optimal selection of spreaders used to diffuse and indoctrinate neighboring peers, often overlooking realistic limitations of time, space, and budget. Thus, finding trade-offs between a minimal number of influential nodes and maximizing opinion coverage is a relevant scientific problem. Therefore, we study the relationship between specific parameters that influence the effectiveness of opinion diffusion, such as the underlying topology, the number of active spreaders, the periodicity of spreader activity, and the injection strategy. We introduce an original benchmarking methodology by integrating time and cost into an augmented linear threshold model and measure indoctrination expense as a trade-off between the cost of maintaining spreaders’ active and real-time opinion coverage. Simulations show that indoctrination expense increases polynomially with the number of spreaders and linearly with the activity periodicity. In addition, keeping spreaders continuously active instead of periodically activating them can increase expenses by 69–84% in our simulation scenarios. Lastly, we outline a set of general rules for cost-effective opinion injection strategies. Full article
(This article belongs to the Special Issue Complex Network Modeling: Theory and Applications)
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15 pages, 325 KiB  
Article
Free Resolutions and Generalized Hamming Weights of Binary Linear Codes
by Ignacio García-Marco, Irene Márquez-Corbella, Edgar Martínez-Moro and Yuriko Pitones
Mathematics 2022, 10(12), 2079; https://doi.org/10.3390/math10122079 - 15 Jun 2022
Cited by 1 | Viewed by 2556
Abstract
In this work, we explore the relationship between the graded free resolution of some monomial ideals and the Generalized Hamming Weights (GHWs) of binary codes. More precisely, we look for a structure that is smaller than the set of codewords of minimal support [...] Read more.
In this work, we explore the relationship between the graded free resolution of some monomial ideals and the Generalized Hamming Weights (GHWs) of binary codes. More precisely, we look for a structure that is smaller than the set of codewords of minimal support that provides us with some information about the GHWs. We prove that the first and second generalized Hamming weights of a binary linear code can be computed (by means of a graded free resolution) from a set of monomials associated with a binomial ideal related with the code. Moreover, the remaining weights are bounded above by the degrees of the syzygies in the resolution. Full article
(This article belongs to the Special Issue Combinatorics and Computation in Commutative Algebra)
17 pages, 752 KiB  
Article
Kernel Matrix-Based Heuristic Multiple Kernel Learning
by Stanton R. Price, Derek T. Anderson, Timothy C. Havens and Steven R. Price
Mathematics 2022, 10(12), 2026; https://doi.org/10.3390/math10122026 - 11 Jun 2022
Cited by 4 | Viewed by 2270
Abstract
Kernel theory is a demonstrated tool that has made its way into nearly all areas of machine learning. However, a serious limitation of kernel methods is knowing which kernel is needed in practice. Multiple kernel learning (MKL) is an attempt to learn a [...] Read more.
Kernel theory is a demonstrated tool that has made its way into nearly all areas of machine learning. However, a serious limitation of kernel methods is knowing which kernel is needed in practice. Multiple kernel learning (MKL) is an attempt to learn a new tailored kernel through the aggregation of a set of valid known kernels. There are generally three approaches to MKL: fixed rules, heuristics, and optimization. Optimization is the most popular; however, a shortcoming of most optimization approaches is that they are tightly coupled with the underlying objective function and overfitting occurs. Herein, we take a different approach to MKL. Specifically, we explore different divergence measures on the values in the kernel matrices and in the reproducing kernel Hilbert space (RKHS). Experiments on benchmark datasets and a computer vision feature learning task in explosive hazard detection demonstrate the effectiveness and generalizability of our proposed methods. Full article
(This article belongs to the Special Issue Mathematical Methods for Pattern Recognition)
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15 pages, 29218 KiB  
Article
Coexisting Attractor in a Gyrostat Chaotic System via Basin of Attraction and Synchronization of Two Nonidentical Mechanical Systems
by Muhammad Marwan, Vagner Dos Santos, Muhammad Zainul Abidin and Anda Xiong
Mathematics 2022, 10(11), 1914; https://doi.org/10.3390/math10111914 - 2 Jun 2022
Cited by 9 | Viewed by 2755
Abstract
This paper is divided into two main portions. First, we look at basins of attraction as a tool with a unique set of characteristics for discussing multistability and coexisting attractors in a gyrostat chaotic system. For the validation of coexisting attractors in different [...] Read more.
This paper is divided into two main portions. First, we look at basins of attraction as a tool with a unique set of characteristics for discussing multistability and coexisting attractors in a gyrostat chaotic system. For the validation of coexisting attractors in different basins, several approaches such as bifurcation diagrams, Lyapunov exponents, and the Poincaré section are applied. The second half of the study synchronizes two mechanical chaotic systems using a novel controller, with gyrostat and quadrotor unmanned aerial vehicle (QUAV) chaotic systems acting as master and slave systems, respectively. The error dynamical system and the parameter updated law are built using Lyapunov’s theory, and it is discovered that under certain parametric conditions, the trajectories of the QUAV chaotic system overlap and begin to match the features of the gyrostat chaotic system. Full article
(This article belongs to the Special Issue Applied Mathematical Modelling and Dynamical Systems)
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74 pages, 751 KiB  
Review
Centrally Essential Rings and Semirings
by Askar Tuganbaev
Mathematics 2022, 10(11), 1867; https://doi.org/10.3390/math10111867 - 30 May 2022
Viewed by 1861
Abstract
This paper is a survey of results on centrally essential rings and semirings. A ring (respectively, semiring) is said to be centrally essential if it is either commutative or satisfies the property that for any non-central element a, there exist non-zero central [...] Read more.
This paper is a survey of results on centrally essential rings and semirings. A ring (respectively, semiring) is said to be centrally essential if it is either commutative or satisfies the property that for any non-central element a, there exist non-zero central elements x and y with ax = y. The class of centrally essential rings is very large; many corresponding examples are given in the work. Full article
(This article belongs to the Special Issue Modules over Noncommutative Rings, Homological Algebra and Noncommutative Geometry)
15 pages, 1612 KiB  
Article
A Preventive Replacement Policy for a System Subject to Bivariate Generalized Polya Failure Process
by Hyunju Lee, Ji Hwan Cha and Maxim Finkelstein
Mathematics 2022, 10(11), 1833; https://doi.org/10.3390/math10111833 - 26 May 2022
Cited by 2 | Viewed by 1717
Abstract
Numerous studies on preventive maintenance of minimally repaired systems with statistically independent components have been reported in reliability literature. However, in practice, the repair can be worse-than-minimal and the components of a system can be statistically dependent. The existing literature does not cover [...] Read more.
Numerous studies on preventive maintenance of minimally repaired systems with statistically independent components have been reported in reliability literature. However, in practice, the repair can be worse-than-minimal and the components of a system can be statistically dependent. The existing literature does not cover this important in-practice setting. Therefore, our paper is the first to deal with these issues by modeling dependence in the bivariate set up when a system consists of two dependent parts. We employ the bivariate generalized Polya process to model the corresponding failure and repair process. Relevant stochastic properties of this process have been obtained in order to propose and further discuss the new optimal bivariate preventive maintenance policy with two decision parameters: age and operational history. Moreover, introducing these two parameters in the considered context is also a new feature of the study. Under the proposed policy, the long-run average cost rate is derived and the optimal replacement policies are investigated. Detailed numerical examples illustrate our findings and show the potential efficiency of the obtained results in practice. Full article
(This article belongs to the Special Issue Probability Theory and Stochastic Modeling with Applications)
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14 pages, 3760 KiB  
Article
An Efficient Computational Technique for the Electromagnetic Scattering by Prolate Spheroids
by Ludovica Tognolatti, Cristina Ponti, Massimo Santarsiero and Giuseppe Schettini
Mathematics 2022, 10(10), 1761; https://doi.org/10.3390/math10101761 - 21 May 2022
Cited by 3 | Viewed by 2397
Abstract
In this paper we present an efficient Matlab computation of a 3-D electromagnetic scattering problem, in which a plane wave impinges with a generic inclination onto a conducting ellipsoid of revolution. This solid is obtained by the rotation of an ellipse around one [...] Read more.
In this paper we present an efficient Matlab computation of a 3-D electromagnetic scattering problem, in which a plane wave impinges with a generic inclination onto a conducting ellipsoid of revolution. This solid is obtained by the rotation of an ellipse around one of its axes, which is also known as a spheroid. We have developed a fast and ad hoc code to solve the electromagnetic scattering problem, using spheroidal vector wave functions, which are special functions used to describe physical problems in which a prolate or oblate spheroidal reference system is considered. Numerical results are presented, both for TE and TM polarization of the incident wave, and are validated by a comparison with results obtained by a commercial electromagnetic simulator. Full article
(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction)
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14 pages, 1158 KiB  
Article
State Estimation for Complex-Valued Inertial Neural Networks with Multiple Time Delays
by Yaning Yu and Ziye Zhang
Mathematics 2022, 10(10), 1725; https://doi.org/10.3390/math10101725 - 18 May 2022
Cited by 10 | Viewed by 2172
Abstract
In this paper, the problem of state estimation for complex-valued inertial neural networks with leakage, additive and distributed delays is considered. By means of the Lyapunov–Krasovskii functional method, the Jensen inequality, and the reciprocally convex approach, a delay-dependent criterion based on linear matrix [...] Read more.
In this paper, the problem of state estimation for complex-valued inertial neural networks with leakage, additive and distributed delays is considered. By means of the Lyapunov–Krasovskii functional method, the Jensen inequality, and the reciprocally convex approach, a delay-dependent criterion based on linear matrix inequalities (LMIs) is derived. At the same time, the network state is estimated by observing the output measurements to ensure the global asymptotic stability of the error system. Finally, two examples are given to verify the effectiveness of the proposed method. Full article
(This article belongs to the Topic Analysis and Controls of Time-Delay Systems with Perturbations: Theory and Application)
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25 pages, 414 KiB  
Article
Heterogeneous Overdispersed Count Data Regressions via Double-Penalized Estimations
by Shaomin Li, Haoyu Wei and Xiaoyu Lei
Mathematics 2022, 10(10), 1700; https://doi.org/10.3390/math10101700 - 16 May 2022
Cited by 3 | Viewed by 2387
Abstract
Recently, the high-dimensional negative binomial regression (NBR) for count data has been widely used in many scientific fields. However, most studies assumed the dispersion parameter as a constant, which may not be satisfied in practice. This paper studies the variable selection and dispersion [...] Read more.
Recently, the high-dimensional negative binomial regression (NBR) for count data has been widely used in many scientific fields. However, most studies assumed the dispersion parameter as a constant, which may not be satisfied in practice. This paper studies the variable selection and dispersion estimation for the heterogeneous NBR models, which model the dispersion parameter as a function. Specifically, we proposed a double regression and applied a double ℓ1-penalty to both regressions. Under the restricted eigenvalue conditions, we prove the oracle inequalities for the lasso estimators of two partial regression coefficients for the first time, using concentration inequalities of empirical processes. Furthermore, derived from the oracle inequalities, the consistency and convergence rate for the estimators are the theoretical guarantees for further statistical inference. Finally, both simulations and a real data analysis demonstrate that the new methods are effective. Full article
(This article belongs to the Special Issue New Advances in High-Dimensional and Non-asymptotic Statistics)
22 pages, 1091 KiB  
Article
Operator Calculus Approach to Comparison of Elasticity Models for Modelling of Masonry Structures
by Klaus Gürlebeck, Dmitrii Legatiuk and Kemmar Webber
Mathematics 2022, 10(10), 1670; https://doi.org/10.3390/math10101670 - 13 May 2022
Viewed by 1851
Abstract
The solution of any engineering problem starts with a modelling process aimed at formulating a mathematical model, which must describe the problem under consideration with sufficient precision. Because of heterogeneity of modern engineering applications, mathematical modelling scatters nowadays from incredibly precise micro- and [...] Read more.
The solution of any engineering problem starts with a modelling process aimed at formulating a mathematical model, which must describe the problem under consideration with sufficient precision. Because of heterogeneity of modern engineering applications, mathematical modelling scatters nowadays from incredibly precise micro- and even nano-modelling of materials to macro-modelling, which is more appropriate for practical engineering computations. In the field of masonry structures, a macro-model of the material can be constructed based on various elasticity theories, such as classical elasticity, micropolar elasticity and Cosserat elasticity. Evidently, a different macro-behaviour is expected depending on the specific theory used in the background. Although there have been several theoretical studies of different elasticity theories in recent years, there is still a lack of understanding of how modelling assumptions of different elasticity theories influence the modelling results of masonry structures. Therefore, a rigorous approach to comparison of different three-dimensional elasticity models based on quaternionic operator calculus is proposed in this paper. In this way, three elasticity models are described and spatial boundary value problems for these models are discussed. In particular, explicit representation formulae for their solutions are constructed. After that, by using these representation formulae, explicit estimates for the solutions obtained by different elasticity theories are obtained. Finally, several numerical examples are presented, which indicate a practical difference in the solutions. Full article
(This article belongs to the Special Issue Numerical Analysis and Scientific Computing II)
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16 pages, 359 KiB  
Article
Fisher, Bayes, and Predictive Inference
by Sandy Zabell
Mathematics 2022, 10(10), 1634; https://doi.org/10.3390/math10101634 - 11 May 2022
Cited by 2 | Viewed by 2491
Abstract
We review historically the position of Sir R.A. Fisher towards Bayesian inference and, particularly, the classical Bayes–Laplace paradigm. We focus on his Fiducial Argument. Full article
(This article belongs to the Special Issue Bayesian Predictive Inference and Related Asymptotics—Festschrift for Eugenio Regazzini's 75th Birthday)
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10 pages, 431 KiB  
Article
Andness Directedness for t-Norms and t-Conorms
by Vicenç Torra
Mathematics 2022, 10(9), 1598; https://doi.org/10.3390/math10091598 - 8 May 2022
Cited by 2 | Viewed by 2148
Abstract
Tools for decision making need to be simple to use. In previous papers, we advocated that decision engineering needs to provide these tools, as well as a list of necessary properties that aggregation functions need to satisfy. When we model decisions using aggregation [...] Read more.
Tools for decision making need to be simple to use. In previous papers, we advocated that decision engineering needs to provide these tools, as well as a list of necessary properties that aggregation functions need to satisfy. When we model decisions using aggregation functions, andness-directedness is one of them. A crucial aspect in any decision is the degree of compromise between criteria. Given an aggregation function, andness establishes to what degree the function behaves in a conjunctive manner. That is, to what degree some criteria are mandatory. Nevertheless, from an engineering perspective, what we know is that some criteria are strongly required and we cannot ignore a bad evaluation even when other criteria are correctly evaluated. That is, given our requirements of andness, what are the aggregation functions we need to select. Andness is not only for mean-like functions, but it also applies to t-norms and t-conorms. In this paper, we study this problem and show how to select t-norms and t-conorms based on the andness level. Full article
(This article belongs to the Special Issue Fuzzy Sets and Artificial Intelligence)
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24 pages, 3902 KiB  
Article
A Safe and Efficient Lane Change Decision-Making Strategy of Autonomous Driving Based on Deep Reinforcement Learning
by Kexuan Lv, Xiaofei Pei, Ci Chen and Jie Xu
Mathematics 2022, 10(9), 1551; https://doi.org/10.3390/math10091551 - 5 May 2022
Cited by 22 | Viewed by 4719
Abstract
As an indispensable branch of machine learning (ML), reinforcement learning (RL) plays a prominent role in the decision-making process of autonomous driving (AD), which enables autonomous vehicles (AVs) to learn an optimal driving strategy through continuous interaction with the environment. This paper proposes [...] Read more.
As an indispensable branch of machine learning (ML), reinforcement learning (RL) plays a prominent role in the decision-making process of autonomous driving (AD), which enables autonomous vehicles (AVs) to learn an optimal driving strategy through continuous interaction with the environment. This paper proposes a deep reinforcement learning (DRL)-based motion planning strategy for AD tasks in the highway scenarios where an AV merges into two-lane road traffic flow and realizes the lane changing (LC) maneuvers. We integrate the DRL model into the AD system relying on the end-to-end learning method. An improved DRL algorithm based on deep deterministic policy gradient (DDPG) is developed with well-defined reward functions. In particular, safety rules (SR), safety prediction (SP) module and trauma memory (TM) as well as the dynamic potential-based reward shaping (DPBRS) function are adopted to further enhance safety and accelerate learning of the LC behavior. For validation, the proposed DSSTD algorithm is trained and tested on the dual-computer co-simulation platform. The comparative experimental results show that our proposal outperforms other benchmark algorithms in both driving safety and efficiency. Full article
(This article belongs to the Special Issue Advances in Mathematical Methods, Machine Learning and Deep Learning Based Applications)
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16 pages, 697 KiB  
Article
Fixed-Time Synchronization for Fuzzy-Based Impulsive Complex Networks
by Lu Pang, Cheng Hu, Juan Yu and Haijun Jiang
Mathematics 2022, 10(9), 1533; https://doi.org/10.3390/math10091533 - 3 May 2022
Cited by 7 | Viewed by 1997
Abstract
This paper mainly deals with the issue of fixed-time synchronization of fuzzy-based impulsive complex networks. By developing fixed-time stability of impulsive systems and proposing a T-S fuzzy control strategy with pure power-law form, some simple criteria are acquired to achieve fixed-time synchronization of [...] Read more.
This paper mainly deals with the issue of fixed-time synchronization of fuzzy-based impulsive complex networks. By developing fixed-time stability of impulsive systems and proposing a T-S fuzzy control strategy with pure power-law form, some simple criteria are acquired to achieve fixed-time synchronization of fuzzy-based impulsive complex networks and the estimation of the synchronized time is given. Ultimately, the presented control scheme and synchronization criteria are verified by numerical simulation. Full article
(This article belongs to the Special Issue Well-Posedness, Dynamics, and Control of Nonlinear Differential System with Initial-Boundary Value)
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16 pages, 310 KiB  
Article
Stability of Solutions to Systems of Nonlinear Differential Equations with Discontinuous Right-Hand Sides: Applications to Hopfield Artificial Neural Networks
by Ilya Boykov, Vladimir Roudnev and Alla Boykova
Mathematics 2022, 10(9), 1524; https://doi.org/10.3390/math10091524 - 2 May 2022
Cited by 7 | Viewed by 2716
Abstract
In this paper, we study the stability of solutions to systems of differential equations with discontinuous right-hand sides. We have investigated nonlinear and linear equations. Stability sufficient conditions for linear equations are expressed as a logarithmic norm for coefficients of systems of equations. [...] Read more.
In this paper, we study the stability of solutions to systems of differential equations with discontinuous right-hand sides. We have investigated nonlinear and linear equations. Stability sufficient conditions for linear equations are expressed as a logarithmic norm for coefficients of systems of equations. Stability sufficient conditions for nonlinear equations are expressed as the logarithmic norm of the Jacobian of the right-hand side of the system of equations. Sufficient conditions for the stability of solutions of systems of differential equations expressed in terms of logarithmic norms of the right-hand sides of equations (for systems of linear equations) and the Jacobian of right-hand sides (for nonlinear equations) have the following advantages: (1) in investigating stability in different metrics from the same standpoints, we have obtained a set of sufficient conditions; (2) sufficient conditions are easily expressed; (3) robustness areas of systems are easily determined with respect to the variation of their parameters; (4) in case of impulse action, information on moments of impact distribution is not required; (5) a method to obtain sufficient conditions of stability is extended to other definitions of stability (in particular, to p-moment stability). The obtained sufficient conditions are used to study Hopfield neural networks with discontinuous synapses and discontinuous activation functions. Full article
(This article belongs to the Special Issue Mathematical Modeling with Differential Equations in Physics, Chemistry, Biology, and Economics)
43 pages, 606 KiB  
Article
General Non-Local Continuum Mechanics: Derivation of Balance Equations
by Vasily E. Tarasov
Mathematics 2022, 10(9), 1427; https://doi.org/10.3390/math10091427 - 23 Apr 2022
Cited by 24 | Viewed by 2152
Abstract
In this paper, mechanics of continuum with general form of nonlocality in space and time is considered. Some basic concepts of nonlocal continuum mechanics are discussed. General fractional calculus (GFC) and general fractional vector calculus (GFVC) are used as mathematical tools for constructing [...] Read more.
In this paper, mechanics of continuum with general form of nonlocality in space and time is considered. Some basic concepts of nonlocal continuum mechanics are discussed. General fractional calculus (GFC) and general fractional vector calculus (GFVC) are used as mathematical tools for constructing mechanics of media with general form of nonlocality in space and time. Balance equations for mass, momentum, and energy, which describe conservation laws for nonlocal continuum, are derived by using the fundamental theorems of the GFC. The general balance equation in the integral form are derived by using the second fundamental theorems of the GFC. The first fundamental theorems of GFC and the proposed fractional analogue of the Titchmarsh theorem are used to derive the differential form of general balance equations from the integral form of balance equations. Using the general fractional vector calculus, the equations of conservation of mass, momentum, and energy are also suggested for a wide class of regions and surfaces. Full article
(This article belongs to the Section Mathematical Physics)
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10 pages, 1798 KiB  
Article
Confidence-Interval-Based Fuzzy Testing for the Lifetime Performance Index of Electronic Product
by Chun-Min Yu, Kuen-Suan Chen and Ting-Hsin Hsu
Mathematics 2022, 10(9), 1405; https://doi.org/10.3390/math10091405 - 22 Apr 2022
Cited by 6 | Viewed by 1620
Abstract
When the lifetime of an electronic component does not reach the required level, it can be enhanced by means of the paralleling current sharing backup system or the redundant backup system. The lifetime of the redundant backup system is the sum of lifetimes [...] Read more.
When the lifetime of an electronic component does not reach the required level, it can be enhanced by means of the paralleling current sharing backup system or the redundant backup system. The lifetime of the redundant backup system is the sum of lifetimes of all electronic components, which is the maximum of all the electronic components’ lifetimes, compared with the lifetime of the parallel current sharing backup system. For the purpose of enhancing products’ reliability, electronic goods are usually designed with spare electronic components. If it is assumed that there are m−1 redundant backup components for each electronic product, then the lifetime of the electronic product will be distributed as a Gamma distribution with two parameters—m and λ, where λ is the mean for each lifetime of each electronic component. According to numerous studies, the sample size is not large, as it takes a long time to test the lifetime of an electronic product, and enterprises consider cost and timeliness. This paper concerns the performance index of the lifetime of the electronic product. Therefore, based on the confidence interval, this paper aims to develop a fuzzy testing model. As this model can integrate past data and expert experience, the testing accuracy can be retained despite small-sized samples. In fact, through adopting the testing model proposed by this paper, companies can make precise and intelligent decisions instantly with the use of small-sized samples to grasp the opportunities for improvement. Full article
(This article belongs to the Special Issue Fuzzy Applications in Industrial Engineering)
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28 pages, 2417 KiB  
Article
Using Markov-Switching Models in US Stocks Optimal Portfolio Selection in a Black–Litterman Context (Part 1)
by Oscar V. De la Torre-Torres, Evaristo Galeana-Figueroa, María de la Cruz Del Río-Rama and José Álvarez-García
Mathematics 2022, 10(8), 1296; https://doi.org/10.3390/math10081296 - 13 Apr 2022
Cited by 5 | Viewed by 2544
Abstract
In this study, we tested the benefit of using Markov-Switching (M-S) models to forecast the views of the 26 most traded stocks in the US in a Black–Litterman (B–L) optimal selection context. With weekly historical data of these stocks from 1 January 1980, [...] Read more.
In this study, we tested the benefit of using Markov-Switching (M-S) models to forecast the views of the 26 most traded stocks in the US in a Black–Litterman (B–L) optimal selection context. With weekly historical data of these stocks from 1 January 1980, we estimated and simulated (from 7 January 2000, to 7 February 2022) three portfolios that used M-S views in each stock and blended them with the market equilibrium views in a B–L context. Our position was that the B–L optimal portfolios could generate alpha (extra return) against a buy-and-hold and an actively managed portfolio with sample portfolio parameters (à la Markowitz, SampP). Our results suggest that the outperformance of the B–L managed portfolios holds only in the short term. In the long-term, the performance of the B–L portfolios, the SampP, and the market portfolio are statistically equal in terms of returns or their mean–variance efficiency in an ex-ante or ex-post analysis. Full article
(This article belongs to the Special Issue Markov-Chain Modelling and Applications)
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11 pages, 2485 KiB  
Article
Edge of Chaos in Memristor Cellular Nonlinear Networks
by Angela Slavova and Ventsislav Ignatov
Mathematics 2022, 10(8), 1288; https://doi.org/10.3390/math10081288 - 12 Apr 2022
Cited by 3 | Viewed by 2198
Abstract
Information processing in the brain takes place in a dense network of neurons connected through synapses. The collaborative work between these two components (Synapses and Neurons) allows for basic brain functions such as learning and memorization. The so-called von Neumann bottleneck, which limits [...] Read more.
Information processing in the brain takes place in a dense network of neurons connected through synapses. The collaborative work between these two components (Synapses and Neurons) allows for basic brain functions such as learning and memorization. The so-called von Neumann bottleneck, which limits the information processing capability of conventional systems, can be overcome by the efficient emulation of these computational concepts. To this end, mimicking the neuronal architectures with silicon-based circuits, on which neuromorphic engineering is based, is accompanied by the development of new devices with neuromorphic functionalities. We shall study different memristor cellular nonlinear networks models. The rigorous mathematical analysis will be presented based on local activity theory, and the edge of chaos domain will be determined in the models under consideration. Simulations of these models working on the edge of chaos will show the generation of static and dynamic patterns. Full article
(This article belongs to the Special Issue Memristor Cellular Nonlinear Networks: Theory and Applications)
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16 pages, 304 KiB  
Article
Limiting Distributions of a Non-Homogeneous Markov System in a Stochastic Environment in Continuous Time
by P. -C. G. Vassiliou
Mathematics 2022, 10(8), 1214; https://doi.org/10.3390/math10081214 - 7 Apr 2022
Cited by 2 | Viewed by 2171
Abstract
The stochastic process non-homogeneous Markov system in a stochastic environment in continuous time (S-NHMSC) is introduced in the present paper. The ordinary non-homogeneous Markov process is a very special case of an S-NHMSC. I studied the expected population structure of the S-NHMSC, the [...] Read more.
The stochastic process non-homogeneous Markov system in a stochastic environment in continuous time (S-NHMSC) is introduced in the present paper. The ordinary non-homogeneous Markov process is a very special case of an S-NHMSC. I studied the expected population structure of the S-NHMSC, the first central classical problem of finding the conditions under which the asymptotic behavior of the expected population structure exists and the second central problem of finding which expected relative population structures are possible limiting ones, provided that the limiting vector of input probabilities into the population is controlled. Finally, the rate of convergence was studied. Full article
(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks)
28 pages, 396 KiB  
Article
On Numerical Approximations of the Koopman Operator
by Igor Mezić
Mathematics 2022, 10(7), 1180; https://doi.org/10.3390/math10071180 - 5 Apr 2022
Cited by 20 | Viewed by 4333
Abstract
We study numerical approaches to computation of spectral properties of composition operators. We provide a characterization of Koopman Modes in Banach spaces using Generalized Laplace Analysis. We cast the Dynamic Mode Decomposition-type methods in the context of Finite Section theory of infinite dimensional [...] Read more.
We study numerical approaches to computation of spectral properties of composition operators. We provide a characterization of Koopman Modes in Banach spaces using Generalized Laplace Analysis. We cast the Dynamic Mode Decomposition-type methods in the context of Finite Section theory of infinite dimensional operators, and provide an example of a mixing map for which the finite section method fails. Under assumptions on the underlying dynamics, we provide the first result on the convergence rate under sample size increase in the finite-section approximation. We study the error in the Krylov subspace version of the finite section method and prove convergence in pseudospectral sense for operators with pure point spectrum. Since Krylov sequence-based approximations can mitigate the curse of dimensionality, this result indicates that they may also have low spectral error without an exponential-in-dimension increase in the number of functions needed. Full article
(This article belongs to the Special Issue Dynamical Systems and Operator Theory)
21 pages, 4051 KiB  
Article
MHD Mixed Convection Hybrid Nanofluids Flow over a Permeable Moving Inclined Flat Plate in the Presence of Thermophoretic and Radiative Heat Flux Effects
by Umair Khan, Iskandar Waini, Aurang Zaib, Anuar Ishak and Ioan Pop
Mathematics 2022, 10(7), 1164; https://doi.org/10.3390/math10071164 - 3 Apr 2022
Cited by 20 | Viewed by 2613
Abstract
Recent nanotech advancements have created a tremendous platform for the development of a superior ultrahigh performance coolant referred to as nanofluid for several industrial and engineering technologies. In this research, the impact of thermophoretic and viscous dissipation on the radiative mixed convective flow [...] Read more.
Recent nanotech advancements have created a tremendous platform for the development of a superior ultrahigh performance coolant referred to as nanofluid for several industrial and engineering technologies. In this research, the impact of thermophoretic and viscous dissipation on the radiative mixed convective flow comprising hybrid nanofluid through an inclined permeable moving flat plate with a magnetic field is examined numerically. A model of non-linear differential equations is derived based on some realistic assumptions and tackled numerically using the bvp4c technique. The impact of the specific set of distinguished parameters on the velocity profiles, shear stress, temperature distribution profiles, heat transfer, concentration distribution profile, and mass transfer for the two dissimilar branch solutions are discussed in detail. In addition, it has been discovered that double solutions exist in the case of an opposing flow, while a single solution is observed in the case of an assisting flow. The temperature distribution profile escalates with the radiation parameter, while decelerating the velocity and concentration profiles. Full article
(This article belongs to the Topic Engineering Mathematics)
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25 pages, 402 KiB  
Article
Bounds on the Number of Maximal Subgroups of Finite Groups: Applications
by Adolfo Ballester-Bolinches, Ramón Esteban-Romero and Paz Jiménez-Seral
Mathematics 2022, 10(7), 1153; https://doi.org/10.3390/math10071153 - 2 Apr 2022
Cited by 3 | Viewed by 2774
Abstract
The determination of bounds for the number of maximal subgroups of a given index in a finite group is relevant to estimate the number of random elements needed to generate a group with a given probability. In this paper, we obtain new bounds [...] Read more.
The determination of bounds for the number of maximal subgroups of a given index in a finite group is relevant to estimate the number of random elements needed to generate a group with a given probability. In this paper, we obtain new bounds for the number of maximal subgroups of a given index in a finite group and we pin-point the universal constants that appear in some results in the literature related to the number of maximal subgroups of a finite group with a given index. This allows us to compare properly our bounds with some of the known bounds. Full article
(This article belongs to the Special Issue Group Theory and Related Topics)
20 pages, 6612 KiB  
Article
Proving Feasibility of a Docking Mission: A Contractor Programming Approach
by Auguste Bourgois, Simon Rohou, Luc Jaulin and Andreas Rauh
Mathematics 2022, 10(7), 1130; https://doi.org/10.3390/math10071130 - 1 Apr 2022
Cited by 1 | Viewed by 2272
Abstract
Recent advances in computational power, algorithms, and sensors allow robots to perform complex and dangerous tasks, such as autonomous missions in space or underwater. Given the high operational costs, simulations are run beforehand to predict the possible outcomes of a mission. However, this [...] Read more.
Recent advances in computational power, algorithms, and sensors allow robots to perform complex and dangerous tasks, such as autonomous missions in space or underwater. Given the high operational costs, simulations are run beforehand to predict the possible outcomes of a mission. However, this approach is limited as it is based on parameter space discretization and therefore cannot be considered a proof of feasibility. To overcome this limitation, set-membership methods based on interval analysis, guaranteed integration, and contractor programming have proven their efficiency. Guaranteed integration algorithms can predict the possible trajectories of a system initialized in a given set in the form of tubes of trajectories. The contractor programming consists in removing the trajectories violating predefined constraints from a system’s tube of possible trajectories. Our contribution consists in merging both approaches to allow for the usage of differential constraints in a contractor programming framework. We illustrate our method through examples related to robotics. We also released an open-source implementation of our algorithm in a unified library for tubes, allowing one to combine it with other constraints and increase the number of possible applications. Full article
(This article belongs to the Special Issue Set-Based Methods for Differential Equations and Applications)
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12 pages, 3181 KiB  
Article
A Dynamic Mechanistic Model of Perceptual Binding
by Pavel Kraikivski
Mathematics 2022, 10(7), 1135; https://doi.org/10.3390/math10071135 - 1 Apr 2022
Cited by 5 | Viewed by 2566
Abstract
The brain’s ability to create a unified conscious representation of an object by integrating information from multiple perception pathways is called perceptual binding. Binding is crucial for normal cognitive function. Some perceptual binding errors and disorders have been linked to certain neurological conditions, [...] Read more.
The brain’s ability to create a unified conscious representation of an object by integrating information from multiple perception pathways is called perceptual binding. Binding is crucial for normal cognitive function. Some perceptual binding errors and disorders have been linked to certain neurological conditions, brain lesions, and conditions that give rise to illusory conjunctions. However, the mechanism of perceptual binding remains elusive. Here, I present a computational model of binding using two sets of coupled oscillatory processes that are assumed to occur in response to two different percepts. I use the model to study the dynamic behavior of coupled processes to characterize how these processes can modulate each other and reach a temporal synchrony. I identify different oscillatory dynamic regimes that depend on coupling mechanisms and parameter values. The model can also discriminate different combinations of initial inputs that are set by initial states of coupled processes. Decoding brain signals that are formed through perceptual binding is a challenging task, but my modeling results demonstrate how crosstalk between two systems of processes can possibly modulate their outputs. Therefore, my mechanistic model can help one gain a better understanding of how crosstalk between perception pathways can affect the dynamic behavior of the systems that involve perceptual binding. Full article
(This article belongs to the Special Issue Dynamics and Bifurcations in Mathematical Neuroscience: Analysis, Modeling and Applications)
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11 pages, 1223 KiB  
Article
Mathematical Modeling and Analytical Solution of Thermoelastic Stability Problem of Functionally Graded Nanocomposite Cylinders within Different Theories
by Mahmure Avey, Nicholas Fantuzzi and Abdullah Sofiyev
Mathematics 2022, 10(7), 1081; https://doi.org/10.3390/math10071081 - 28 Mar 2022
Cited by 31 | Viewed by 2434
Abstract
Revolutionary advances in technology have led to the use of functionally graded nanocomposite structural elements that operate at high temperatures and whose properties depend on position, such as cylindrical shells designed as load-bearing elements. These advances in technology require new mathematical modeling and [...] Read more.
Revolutionary advances in technology have led to the use of functionally graded nanocomposite structural elements that operate at high temperatures and whose properties depend on position, such as cylindrical shells designed as load-bearing elements. These advances in technology require new mathematical modeling and updated numerical calculations to be performed using improved theories at design time to reliably apply such elements. The main goal of this study is to model, mathematically and within an analytical solution, the thermoelastic stability problem of composite cylinders reinforced by carbon nanotubes (CNTs) under a uniform thermal loading within the shear deformation theory (ST). The influence of transverse shear deformations is considered when forming the fundamental relations of CNT-patterned cylindrical shells and the basic partial differential equations (PDEs) are derived within the modified Donnell-type shell theory. The PDEs are solved by the Galerkin method, and the formula is found for the eigenvalue (critical temperature) of the functionally graded nanocomposite cylindrical shells. The influences of CNT patterns, volume fraction, and geometric parameters on the critical temperature within the ST are estimated by comparing the results within classical theory (CT). Full article
(This article belongs to the Special Issue Analytical and Numerical Methods for Linear and Nonlinear Analysis of Structures at Macro, Micro and Nano Scale)
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18 pages, 4281 KiB  
Article
Adaptive Fuzzy Neural Network Harmonic Control with a Super-Twisting Sliding Mode Approach
by Qi Pan, Xiangguo Li and Juntao Fei
Mathematics 2022, 10(7), 1063; https://doi.org/10.3390/math10071063 - 25 Mar 2022
Cited by 5 | Viewed by 2250
Abstract
This paper designed an adaptive super-twisting sliding mode control (STSMC) scheme based on an output feedback fuzzy neural network (OFFNN) for an active power filter (APF), aiming at tracking compensation current quickly and precisely, and solving the harmonic current problem in the electrical [...] Read more.
This paper designed an adaptive super-twisting sliding mode control (STSMC) scheme based on an output feedback fuzzy neural network (OFFNN) for an active power filter (APF), aiming at tracking compensation current quickly and precisely, and solving the harmonic current problem in the electrical grid. With the use of OFFNN approximator, the proposed controller has the characteristic of full regulation and high approximation accuracy, where the parameters of OFFNN can be adjusted to the optimal values adaptively, thereby increasing the versatility of the control method. Moreover, due to an added signal feedback loop, the controller can obtain more information to track the state variable faster and more correctly. Simulations studies are given to demonstrate the performance of the proposed controller in the harmonic suppression, and verify its better steady-state and dynamic performance. Full article
(This article belongs to the Special Issue Advances in Intelligent Control)
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42 pages, 78475 KiB  
Article
Modified Remora Optimization Algorithm for Global Optimization and Multilevel Thresholding Image Segmentation
by Qingxin Liu, Ni Li, Heming Jia, Qi Qi and Laith Abualigah
Mathematics 2022, 10(7), 1014; https://doi.org/10.3390/math10071014 - 22 Mar 2022
Cited by 63 | Viewed by 4244
Abstract
Image segmentation is a key stage in image processing because it simplifies the representation of the image and facilitates subsequent analysis. The multi-level thresholding image segmentation technique is considered one of the most popular methods because it is efficient and straightforward. Many relative [...] Read more.
Image segmentation is a key stage in image processing because it simplifies the representation of the image and facilitates subsequent analysis. The multi-level thresholding image segmentation technique is considered one of the most popular methods because it is efficient and straightforward. Many relative works use meta-heuristic algorithms (MAs) to determine threshold values, but they have issues such as poor convergence accuracy and stagnation into local optimal solutions. Therefore, to alleviate these shortcomings, in this paper, we present a modified remora optimization algorithm (MROA) for global optimization and image segmentation tasks. We used Brownian motion to promote the exploration ability of ROA and provide a greater opportunity to find the optimal solution. Second, lens opposition-based learning is introduced to enhance the ability of search agents to jump out of the local optimal solution. To substantiate the performance of MROA, we first used 23 benchmark functions to evaluate the performance. We compared it with seven well-known algorithms regarding optimization accuracy, convergence speed, and significant difference. Subsequently, we tested the segmentation quality of MORA on eight grayscale images with cross-entropy as the objective function. The experimental metrics include peak signal-to-noise ratio (PSNR), structure similarity (SSIM), and feature similarity (FSIM). A series of experimental results have proved that the MROA has significant advantages among the compared algorithms. Consequently, the proposed MROA is a promising method for global optimization problems and image segmentation. Full article
(This article belongs to the Special Issue Bioinspired Intelligent Algorithms for Optimization, Modeling and Control: Theory and Applications)
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16 pages, 490 KiB  
Article
A Modified Grey Wolf Optimization Algorithm for an Intrusion Detection System
by Abdullah Alzaqebah, Ibrahim Aljarah, Omar Al-Kadi and Robertas Damaševičius
Mathematics 2022, 10(6), 999; https://doi.org/10.3390/math10060999 - 21 Mar 2022
Cited by 88 | Viewed by 6198
Abstract
Cyber-attacks and unauthorized application usage have increased due to the extensive use of Internet services and applications over computer networks, posing a threat to the service’s availability and consumers’ privacy. A network Intrusion Detection System (IDS) aims to detect aberrant traffic behavior that [...] Read more.
Cyber-attacks and unauthorized application usage have increased due to the extensive use of Internet services and applications over computer networks, posing a threat to the service’s availability and consumers’ privacy. A network Intrusion Detection System (IDS) aims to detect aberrant traffic behavior that firewalls cannot detect. In IDSs, dimension reduction using the feature selection strategy has been shown to be more efficient. By reducing the data dimension and eliminating irrelevant and noisy data, several bio-inspired algorithms have been employed to improve the performance of an IDS. This paper discusses a modified bio-inspired algorithm, which is the Grey Wolf Optimization algorithm (GWO), that enhances the efficacy of the IDS in detecting both normal and anomalous traffic in the network. The main improvements cover the smart initialization phase that combines the filter and wrapper approaches to ensure that the informative features will be included in early iterations. In addition, we adopted a high-speed classification method, the Extreme Learning Machine (ELM), and used the modified GWO to tune the ELM’s parameters. The proposed technique was tested against various meta-heuristic algorithms using the UNSWNB-15 dataset. Because the generic attack is the most common attack type in the dataset, the primary goal of this paper was to detect generic attacks in network traffic. The proposed model outperformed other methods in minimizing the crossover error rate and false positive rate to less than 30%. Furthermore, it obtained the best results with 81%, 78%, and 84% for the accuracy, F1-score, and G-mean measures, respectively. Full article
(This article belongs to the Section Mathematics and Computer Science)
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11 pages, 1242 KiB  
Article
Highly Dispersive Optical Soliton Perturbation, with Maximum Intensity, for the Complex Ginzburg–Landau Equation by Semi-Inverse Variation
by Anjan Biswas, Trevor Berkemeyer, Salam Khan, Luminita Moraru, Yakup Yıldırım and Hashim M. Alshehri
Mathematics 2022, 10(6), 987; https://doi.org/10.3390/math10060987 - 18 Mar 2022
Cited by 9 | Viewed by 2855
Abstract
This work analytically recovers the highly dispersive bright 1–soliton solution using for the perturbed complex Ginzburg–Landau equation, which is studied with three forms of nonlinear refractive index structures. They are Kerr law, parabolic law, and polynomial law. The perturbation terms appear with maximum [...] Read more.
This work analytically recovers the highly dispersive bright 1–soliton solution using for the perturbed complex Ginzburg–Landau equation, which is studied with three forms of nonlinear refractive index structures. They are Kerr law, parabolic law, and polynomial law. The perturbation terms appear with maximum allowable intensity, also known as full nonlinearity. The semi-inverse variational principle makes this retrieval possible. The amplitude–width relation is obtained by solving a cubic polynomial equation using Cardano’s approach. The parameter constraints for the existence of such solitons are also enumerated. Full article
(This article belongs to the Special Issue Nonlinear Partial Differential Equations: Exact Solutions, Symmetries, Methods, and Applications)
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21 pages, 4688 KiB  
Article
Evaluation of sEMG Signal Features and Segmentation Parameters for Limb Movement Prediction Using a Feedforward Neural Network
by David Leserri, Nils Grimmelsmann, Malte Mechtenberg, Hanno Gerd Meyer and Axel Schneider
Mathematics 2022, 10(6), 932; https://doi.org/10.3390/math10060932 - 15 Mar 2022
Cited by 3 | Viewed by 2891
Abstract
Limb movement prediction based on surface electromyography (sEMG) for the control of wearable robots, such as active orthoses and exoskeletons, is a promising approach since it provides an intuitive control interface for the user. Further, sEMG signals contain early information about the onset [...] Read more.
Limb movement prediction based on surface electromyography (sEMG) for the control of wearable robots, such as active orthoses and exoskeletons, is a promising approach since it provides an intuitive control interface for the user. Further, sEMG signals contain early information about the onset and course of limb movements for feedback control. Recent studies have proposed machine learning-based modeling approaches for limb movement prediction using sEMG signals, which do not necessarily require domain knowledge of the underlying physiological system and its parameters. However, there is limited information on which features of the measured sEMG signals provide the best prediction accuracy of machine learning models trained with these data. In this work, the accuracy of elbow joint movement prediction based on sEMG data using a simple feedforward neural network after training with different single- and multi-feature sets and data segmentation parameters was compared. It was shown that certain combinations of time-domain and frequency-domain features, as well as segmentation parameters of sEMG data, improve the prediction accuracy of the neural network as compared to the use of a standard feature set from the literature. Full article
(This article belongs to the Special Issue Machine Learning for Technical Systems)
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21 pages, 365 KiB  
Article
Riemann–Hilbert Problems and Soliton Solutions of Type (λ∗, −λ∗) Reduced Nonlocal Integrable mKdV Hierarchies
by Wen-Xiu Ma
Mathematics 2022, 10(6), 870; https://doi.org/10.3390/math10060870 - 9 Mar 2022
Cited by 53 | Viewed by 3043
Abstract
Reduced nonlocal matrix integrable modified Korteweg–de Vries (mKdV) hierarchies are presented via taking two transpose-type group reductions in the matrix Ablowitz–Kaup–Newell–Segur (AKNS) spectral problems. One reduction is local, which replaces the spectral parameter λ with its complex conjugate λ∗, and the [...] Read more.
Reduced nonlocal matrix integrable modified Korteweg–de Vries (mKdV) hierarchies are presented via taking two transpose-type group reductions in the matrix Ablowitz–Kaup–Newell–Segur (AKNS) spectral problems. One reduction is local, which replaces the spectral parameter λ with its complex conjugate λ∗, and the other one is nonlocal, which replaces the spectral parameter λ with its negative complex conjugate −λ∗. Riemann–Hilbert problems and thus inverse scattering transforms are formulated from the reduced matrix spectral problems. In view of the specific distribution of eigenvalues and adjoint eigenvalues, soliton solutions are constructed from the reflectionless Riemann–Hilbert problems. Full article
13 pages, 1455 KiB  
Article
A System with Two Spare Units, Two Repair Facilities, and Two Types of Repairers
by Vahid Andalib and Jyotirmoy Sarkar
Mathematics 2022, 10(6), 852; https://doi.org/10.3390/math10060852 - 8 Mar 2022
Cited by 19 | Viewed by 3081
Abstract
Assuming exponential lifetime and repair time distributions, we study the limiting availability A∞ as well as the per unit time-limiting profit ω of a one-unit system having two identical, cold standby spare units using semi-Markov processes. The failed unit is repaired either [...] Read more.
Assuming exponential lifetime and repair time distributions, we study the limiting availability A∞ as well as the per unit time-limiting profit ω of a one-unit system having two identical, cold standby spare units using semi-Markov processes. The failed unit is repaired either by an in-house repairer within an exponential patience time T or by an external expert who works faster but charges more. When there are two repair facilities, we allow the regular repairer to begin repair or to continue repair beyond T if the expert is busy. Two models arise accordingly as the expert repairs one or all failed units during each visit. We show that (1) adding a second spare to a one-unit system already backed by a spare raises A∞ as well as ω; (2) thereafter, adding a second repair facility improves both criteria further. Finally, we determine whether the expert must repair one or all failed units to maximize these criteria and fulfill the maintenance management objectives better than previously studied models. Full article
(This article belongs to the Special Issue Statistical Simulation and Computation II)
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14 pages, 268 KiB  
Article
Intermediate-Task Transfer Learning with BERT for Sarcasm Detection
by Edoardo Savini and Cornelia Caragea
Mathematics 2022, 10(5), 844; https://doi.org/10.3390/math10050844 - 7 Mar 2022
Cited by 47 | Viewed by 6246
Abstract
Sarcasm detection plays an important role in natural language processing as it can impact the performance of many applications, including sentiment analysis, opinion mining, and stance detection. Despite substantial progress on sarcasm detection, the research results are scattered across datasets and studies. In [...] Read more.
Sarcasm detection plays an important role in natural language processing as it can impact the performance of many applications, including sentiment analysis, opinion mining, and stance detection. Despite substantial progress on sarcasm detection, the research results are scattered across datasets and studies. In this paper, we survey the current state-of-the-art and present strong baselines for sarcasm detection based on BERT pre-trained language models. We further improve our BERT models by fine-tuning them on related intermediate tasks before fine-tuning them on our target task. Specifically, relying on the correlation between sarcasm and (implied negative) sentiment and emotions, we explore a transfer learning framework that uses sentiment classification and emotion detection as individual intermediate tasks to infuse knowledge into the target task of sarcasm detection. Experimental results on three datasets that have different characteristics show that the BERT-based models outperform many previous models. Full article
(This article belongs to the Special Issue Natural Language Processing (NLP) and Machine Learning (ML)—Theory and Applications)
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19 pages, 4041 KiB  
Article
SVseg: Stacked Sparse Autoencoder-Based Patch Classification Modeling for Vertebrae Segmentation
by Syed Furqan Qadri, Linlin Shen, Mubashir Ahmad, Salman Qadri, Syeda Shamaila Zareen and Muhammad Azeem Akbar
Mathematics 2022, 10(5), 796; https://doi.org/10.3390/math10050796 - 2 Mar 2022
Cited by 41 | Viewed by 5197
Abstract
Precise vertebrae segmentation is essential for the image-related analysis of spine pathologies such as vertebral compression fractures and other abnormalities, as well as for clinical diagnostic treatment and surgical planning. An automatic and objective system for vertebra segmentation is required, but its development [...] Read more.
Precise vertebrae segmentation is essential for the image-related analysis of spine pathologies such as vertebral compression fractures and other abnormalities, as well as for clinical diagnostic treatment and surgical planning. An automatic and objective system for vertebra segmentation is required, but its development is likely to run into difficulties such as low segmentation accuracy and the requirement of prior knowledge or human intervention. Recently, vertebral segmentation methods have focused on deep learning-based techniques. To mitigate the challenges involved, we propose deep learning primitives and stacked Sparse autoencoder-based patch classification modeling for Vertebrae segmentation (SVseg) from Computed Tomography (CT) images. After data preprocessing, we extract overlapping patches from CT images as input to train the model. The stacked sparse autoencoder learns high-level features from unlabeled image patches in an unsupervised way. Furthermore, we employ supervised learning to refine the feature representation to improve the discriminability of learned features. These high-level features are fed into a logistic regression classifier to fine-tune the model. A sigmoid classifier is added to the network to discriminate the vertebrae patches from non-vertebrae patches by selecting the class with the highest probabilities. We validated our proposed SVseg model on the publicly available MICCAI Computational Spine Imaging (CSI) dataset. After configuration optimization, our proposed SVseg model achieved impressive performance, with 87.39% in Dice Similarity Coefficient (DSC), 77.60% in Jaccard Similarity Coefficient (JSC), 91.53% in precision (PRE), and 90.88% in sensitivity (SEN). The experimental results demonstrated the method’s efficiency and significant potential for diagnosing and treating clinical spinal diseases. Full article
(This article belongs to the Special Issue Mathematical Methods and Applications for Artificial Intelligence and Computer Vision)
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18 pages, 786 KiB  
Article
How Many Fractional Derivatives Are There?
by Duarte Valério, Manuel D. Ortigueira and António M. Lopes
Mathematics 2022, 10(5), 737; https://doi.org/10.3390/math10050737 - 25 Feb 2022
Cited by 33 | Viewed by 4505
Abstract
In this paper, we introduce a unified fractional derivative, defined by two parameters (order and asymmetry). From this, all the interesting derivatives can be obtained. We study the one-sided derivatives and show that most known derivatives are particular cases. We consider also [...] Read more.
In this paper, we introduce a unified fractional derivative, defined by two parameters (order and asymmetry). From this, all the interesting derivatives can be obtained. We study the one-sided derivatives and show that most known derivatives are particular cases. We consider also some myths of Fractional Calculus and false fractional derivatives. The results are expected to contribute to limit the appearance of derivatives that differ from existing ones just because they are defined on distinct domains, and to prevent the ambiguous use of the concept of fractional derivative. Full article
(This article belongs to the Special Issue Dynamical Systems and Their Applications (DSTA) — In Memory of Prof. Dr. José A. Tenreiro Machado)
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17 pages, 3315 KiB  
Article
PFVAE: A Planar Flow-Based Variational Auto-Encoder Prediction Model for Time Series Data
by Xue-Bo Jin, Wen-Tao Gong, Jian-Lei Kong, Yu-Ting Bai and Ting-Li Su
Mathematics 2022, 10(4), 610; https://doi.org/10.3390/math10040610 - 16 Feb 2022
Cited by 101 | Viewed by 12365
Abstract
Prediction based on time series has a wide range of applications. Due to the complex nonlinear and random distribution of time series data, the performance of learning prediction models can be reduced by the modeling bias or overfitting. This paper proposes a novel [...] Read more.
Prediction based on time series has a wide range of applications. Due to the complex nonlinear and random distribution of time series data, the performance of learning prediction models can be reduced by the modeling bias or overfitting. This paper proposes a novel planar flow-based variational auto-encoder prediction model (PFVAE), which uses the long- and short-term memory network (LSTM) as the auto-encoder and designs the variational auto-encoder (VAE) as a time series data predictor to overcome the noise effects. In addition, the internal structure of VAE is transformed using planar flow, which enables it to learn and fit the nonlinearity of time series data and improve the dynamic adaptability of the network. The prediction experiments verify that the proposed model is superior to other models regarding prediction accuracy and proves it is effective for predicting time series data. Full article
(This article belongs to the Special Issue Mathematical Method and Application of Machine Learning)
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24 pages, 3136 KiB  
Article
Free Vibration of FG-CNTRCs Nano-Plates/Shells with Temperature-Dependent Properties
by Ammar Melaibari, Ahmed Amine Daikh, Muhammad Basha, Ahmed W. Abdalla, Ramzi Othman, Khalid H. Almitani, Mostafa A. Hamed, Alaa Abdelrahman and Mohamed A. Eltaher
Mathematics 2022, 10(4), 583; https://doi.org/10.3390/math10040583 - 13 Feb 2022
Cited by 50 | Viewed by 2747
Abstract
This article presents a mathematical continuum model to analyze the free vibration response of cross-ply carbon-nanotube-reinforced composite laminated nanoplates and nanoshells, including microstructure and length scale effects. Different shell geometries, such as plate (infinite radii), spherical, cylindrical, hyperbolic-paraboloid and elliptical-paraboloid are considered in [...] Read more.
This article presents a mathematical continuum model to analyze the free vibration response of cross-ply carbon-nanotube-reinforced composite laminated nanoplates and nanoshells, including microstructure and length scale effects. Different shell geometries, such as plate (infinite radii), spherical, cylindrical, hyperbolic-paraboloid and elliptical-paraboloid are considered in the analysis. By employing Hamilton’s variational principle, the equations of motion are derived based on hyperbolic sine function shear deformation theory. Then, the derived equations are solved analytically using the Galerkin approach. Two types of material distribution are proposed. Higher-order nonlocal strain gradient theory is employed to capture influences of shear deformation, length scale parameter (nonlocal) and material/microstructurescale parameter (gradient). Temperature-dependent material properties are considered. The validation of the proposed mathematical model is presented. Detailed parametric analyses are carried out to highlight the effects of the carbon nanotubes (CNT) distribution pattern, the thickness stretching, the geometry of the plate/shell, the boundary conditions, the total number of layers, the length scale and the material scale parameters, on the vibrational frequencies of CNTRC laminated nanoplates and nanoshells. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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20 pages, 4930 KiB  
Article
Forecasting of Electrical Energy Consumption in Slovakia
by Michal Pavlicko, Mária Vojteková and Oľga Blažeková
Mathematics 2022, 10(4), 577; https://doi.org/10.3390/math10040577 - 12 Feb 2022
Cited by 24 | Viewed by 4047
Abstract
Prediction of electricity energy consumption plays a crucial role in the electric power industry. Accurate forecasting is essential for electricity supply policies. A characteristic feature of electrical energy is the need to ensure a constant balance between consumption and electricity production, whereas electricity [...] Read more.
Prediction of electricity energy consumption plays a crucial role in the electric power industry. Accurate forecasting is essential for electricity supply policies. A characteristic feature of electrical energy is the need to ensure a constant balance between consumption and electricity production, whereas electricity cannot be stored in significant quantities, nor is it easy to transport. Electricity consumption generally has a stochastic behavior that makes it hard to predict. The main goal of this study is to propose the forecasting models to predict the maximum hourly electricity consumption per day that is more accurate than the official load prediction of the Slovak Distribution Company. Different models are proposed and compared. The first model group is based on the transverse set of Grey models and Nonlinear Grey Bernoulli models and the second approach is based on a multi-layer feed-forward back-propagation network. Moreover, a new potential hybrid model combining these different approaches is used to forecast the maximum hourly electricity consumption per day. Various performance metrics are adopted to evaluate the performance and effectiveness of models. All the proposed models achieved more accurate predictions than the official load prediction, while the hybrid model offered the best results according to performance metrics and supported the legitimacy of this research. Full article
(This article belongs to the Special Issue Statistical Data Modeling and Machine Learning with Applications II)
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18 pages, 1418 KiB  
Article
Data-Driven Maintenance Priority and Resilience Evaluation of Performance Loss in a Main Coolant System
by Hongyan Dui, Zhe Xu, Liwei Chen, Liudong Xing and Bin Liu
Mathematics 2022, 10(4), 563; https://doi.org/10.3390/math10040563 - 11 Feb 2022
Cited by 28 | Viewed by 2298
Abstract
The main coolant system (MCS) plays a vital role in the stability and reliability of a nuclear power plant. However, human errors and natural disasters may cause some reactor coolant system components to fail, resulting in severe consequences such as nuclear leakage. Therefore, [...] Read more.
The main coolant system (MCS) plays a vital role in the stability and reliability of a nuclear power plant. However, human errors and natural disasters may cause some reactor coolant system components to fail, resulting in severe consequences such as nuclear leakage. Therefore, it is crucial to perform a resilience analysis of the MCS, to effectively reduce and prevent losses. In this paper, a resilience importance measure (RIM) for performance loss is proposed to evaluate the performance of the MCS. Specifically, a loss importance measure (LIM) is first proposed to indicate the component maintenance priority of the MCS under different failure conditions. Based on the LIM, RIMs for single component failure and multiple component failures were developed to measure the recovery efficiency of the system performance. Finally, a case study was conducted to demonstrate the proposed resilience measure for system reliability. Results provide a valuable reference for increasing the system security of the MCS and choosing the appropriate total maintenance cost. Full article
(This article belongs to the Special Issue Data-Driven Methods and Artificial Intelligence in Reliability and Maintenance)
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26 pages, 422 KiB  
Article
Some New Concepts Related to Integral Operators and Inequalities on Coordinates in Fuzzy Fractional Calculus
by Muhammad Bilal Khan, Gustavo Santos-García, Hatim Ghazi Zaini, Savin Treanță and Mohamed S. Soliman
Mathematics 2022, 10(4), 534; https://doi.org/10.3390/math10040534 - 9 Feb 2022
Cited by 11 | Viewed by 2720
Abstract
In interval analysis, the fuzzy inclusion relation and the fuzzy order relation are two different concepts. Under the inclusion connection, convexity and non-convexity form a substantial link with various types of inequalities. Moreover, convex fuzzy-interval-valued functions are well known in convex theory because [...] Read more.
In interval analysis, the fuzzy inclusion relation and the fuzzy order relation are two different concepts. Under the inclusion connection, convexity and non-convexity form a substantial link with various types of inequalities. Moreover, convex fuzzy-interval-valued functions are well known in convex theory because they allow us to infer more exact inequalities than convex functions. Most likely, integral operators play significant roles to define different types of inequalities. In this paper, we have successfully introduced the Riemann–Liouville fractional integrals on coordinates via fuzzy-interval-valued functions (FIVFs). Then, with the help of these integrals, some fuzzy fractional Hermite–Hadamard-type integral inequalities are also derived for the introduced coordinated convex FIVFs via a fuzzy order relation (FOR). This FOR is defined by φ-cuts or level-wise by using the Kulish–Miranker order relation. Moreover, some related fuzzy fractional Hermite–Hadamard-type integral inequalities are also obtained for the product of two coordinated convex fuzzy-interval-valued functions. The main results of this paper are the generalization of several known results. Full article
(This article belongs to the Special Issue Fuzzy Sets and Soft Computing)
19 pages, 869 KiB  
Article
Variational Bayesian Inference in High-Dimensional Linear Mixed Models
by Jieyi Yi and Niansheng Tang
Mathematics 2022, 10(3), 463; https://doi.org/10.3390/math10030463 - 31 Jan 2022
Cited by 7 | Viewed by 3896
Abstract
In high-dimensional regression models, the Bayesian lasso with the Gaussian spike and slab priors is widely adopted to select variables and estimate unknown parameters. However, it involves large matrix computations in a standard Gibbs sampler. To solve this issue, the Skinny Gibbs sampler [...] Read more.
In high-dimensional regression models, the Bayesian lasso with the Gaussian spike and slab priors is widely adopted to select variables and estimate unknown parameters. However, it involves large matrix computations in a standard Gibbs sampler. To solve this issue, the Skinny Gibbs sampler is employed to draw observations required for Bayesian variable selection. However, when the sample size is much smaller than the number of variables, the computation is rather time-consuming. As an alternative to the Skinny Gibbs sampler, we develop a variational Bayesian approach to simultaneously select variables and estimate parameters in high-dimensional linear mixed models under the Gaussian spike and slab priors of population-specific fixed-effects regression coefficients, which are reformulated as a mixture of a normal distribution and an exponential distribution. The coordinate ascent algorithm, which can be implemented efficiently, is proposed to optimize the evidence lower bound. The Bayes factor, which can be computed with the path sampling technique, is presented to compare two competing models in the variational Bayesian framework. Simulation studies are conducted to assess the performance of the proposed variational Bayesian method. An empirical example is analyzed by the proposed methodologies. Full article
(This article belongs to the Special Issue Bayesian Inference and Modeling with Applications)
32 pages, 3431 KiB  
Article
An Enhanced Grey Wolf Optimizer with a Velocity-Aided Global Search Mechanism
by Farshad Rezaei, Hamid Reza Safavi, Mohamed Abd Elaziz, Shaker H. Ali El-Sappagh, Mohammed Azmi Al-Betar and Tamer Abuhmed
Mathematics 2022, 10(3), 351; https://doi.org/10.3390/math10030351 - 24 Jan 2022
Cited by 29 | Viewed by 6330
Abstract
This paper proposes a novel variant of the Grey Wolf Optimization (GWO) algorithm, named Velocity-Aided Grey Wolf Optimizer (VAGWO). The original GWO lacks a velocity term in its position-updating procedure, and this is the main factor weakening the exploration capability of this algorithm. [...] Read more.
This paper proposes a novel variant of the Grey Wolf Optimization (GWO) algorithm, named Velocity-Aided Grey Wolf Optimizer (VAGWO). The original GWO lacks a velocity term in its position-updating procedure, and this is the main factor weakening the exploration capability of this algorithm. In VAGWO, this term is carefully set and incorporated into the updating formula of the GWO. Furthermore, both the exploration and exploitation capabilities of the GWO are enhanced in VAGWO via stressing the enlargement of steps that each leading wolf takes towards the others in the early iterations while stressing the reduction in these steps when approaching the later iterations. The VAGWO is compared with a set of popular and newly proposed meta-heuristic optimization algorithms through its implementation on a set of 13 high-dimensional shifted standard benchmark functions as well as 10 complex composition functions derived from the CEC2017 test suite and three engineering problems. The complexity of the proposed algorithm is also evaluated against the original GWO. The results indicate that the VAGWO is a computationally efficient algorithm, generating highly accurate results when employed to optimize high-dimensional and complex problems. Full article
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12 pages, 274 KiB  
Article
Chen Inequalities for Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms
by Simona Decu and Stefan Haesen
Mathematics 2022, 10(3), 330; https://doi.org/10.3390/math10030330 - 21 Jan 2022
Cited by 7 | Viewed by 2915
Abstract
In this paper, we prove some inequalities between intrinsic and extrinsic curvature invariants, namely involving the Chen first invariant and the mean curvature of totally real and holomorphic spacelike submanifolds in statistical manifolds of type para-Kähler space forms. Furthermore, we investigate the equality [...] Read more.
In this paper, we prove some inequalities between intrinsic and extrinsic curvature invariants, namely involving the Chen first invariant and the mean curvature of totally real and holomorphic spacelike submanifolds in statistical manifolds of type para-Kähler space forms. Furthermore, we investigate the equality cases of these inequalities. As illustrations of the applications of the above inequalities, we consider a few examples. Full article
(This article belongs to the Special Issue Analytic and Geometric Inequalities: Theory and Applications)
15 pages, 731 KiB  
Article
Comparison of the Selected Methods Used for Solving the Ordinary Differential Equations and Their Systems
by Edyta Hetmaniok and Mariusz Pleszczyński
Mathematics 2022, 10(3), 306; https://doi.org/10.3390/math10030306 - 19 Jan 2022
Cited by 9 | Viewed by 2865
Abstract
Ordinary differential equations (ODEs), and the systems of such equations, are used for describing many essential physical phenomena. Therefore, the ability to efficiently solve such tasks is important and desired. The goal of this paper is to compare three methods devoted to solving [...] Read more.
Ordinary differential equations (ODEs), and the systems of such equations, are used for describing many essential physical phenomena. Therefore, the ability to efficiently solve such tasks is important and desired. The goal of this paper is to compare three methods devoted to solving ODEs and their systems, with respect to the quality of obtained solutions, as well as the speed and reliability of working. These approaches are the classical and often applied Runge–Kutta method of order 4 (RK4), the method developed on the ground of the Taylor series, the differential transformation method (DTM), and the routine available in the Mathematica software (Mat). Full article
(This article belongs to the Special Issue Applications of Symbolic and Soft Computations in Applied Sciences)
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19 pages, 329 KiB  
Article
Applications of Solvable Lie Algebras to a Class of Third Order Equations
by María S. Bruzón, Rafael de la Rosa, María L. Gandarias and Rita Tracinà
Mathematics 2022, 10(2), 254; https://doi.org/10.3390/math10020254 - 14 Jan 2022
Cited by 3 | Viewed by 1952
Abstract
A family of third-order partial differential equations (PDEs) is analyzed. This family broadens out well-known PDEs such as the Korteweg-de Vries equation, the Gardner equation, and the Burgers equation, which model many real-world phenomena. Furthermore, several macroscopic models for semiconductors considering quantum effects—for [...] Read more.
A family of third-order partial differential equations (PDEs) is analyzed. This family broadens out well-known PDEs such as the Korteweg-de Vries equation, the Gardner equation, and the Burgers equation, which model many real-world phenomena. Furthermore, several macroscopic models for semiconductors considering quantum effects—for example, models for the transmission of electrical lines and quantum hydrodynamic models—are governed by third-order PDEs of this family. For this family, all point symmetries have been derived. These symmetries are used to determine group-invariant solutions from three-dimensional solvable subgroups of the complete symmetry group, which allow us to reduce the given PDE to a first-order nonlinear ordinary differential equation (ODE). Finally, exact solutions are obtained by solving the first-order nonlinear ODEs or by taking into account the Type-II hidden symmetries that appear in the reduced second-order ODEs. Full article
(This article belongs to the Special Issue Symmetry Methods and Applications for Nonlinear Partial Differential Equations)
28 pages, 3306 KiB  
Article
Parameter Identification of Photovoltaic Models by Hybrid Adaptive JAYA Algorithm
by Xiaobing Yu, Xuejing Wu and Wenguan Luo
Mathematics 2022, 10(2), 183; https://doi.org/10.3390/math10020183 - 7 Jan 2022
Cited by 15 | Viewed by 2016
Abstract
As one of the most promising forms of renewable energy, solar energy is increasingly deployed. The simulation and control of photovoltaic (PV) systems requires identification of their parameters. A Hybrid Adaptive algorithm based on JAYA and Differential Evolution (HAJAYADE) is developed to identify [...] Read more.
As one of the most promising forms of renewable energy, solar energy is increasingly deployed. The simulation and control of photovoltaic (PV) systems requires identification of their parameters. A Hybrid Adaptive algorithm based on JAYA and Differential Evolution (HAJAYADE) is developed to identify these parameters accurately and reliably. The HAJAYADE algorithm consists of adaptive JAYA, adaptive DE, and the chaotic perturbation method. Two adaptive coefficients are introduced in adaptive JAYA to balance the local and global search. In adaptive DE, the Rank/Best/1 mutation operator is put forward to boost the exploration and maintain the exploitation. The chaotic perturbation method is applied to reinforce the local search further. The HAJAYADE algorithm is employed to address the parameter identification of PV systems through five test cases, and the eight latest meta-heuristic algorithms are its opponents. The mean RMSE values of the HAJAYADE algorithm from five test cases are 9.8602 × 10−4, 9.8294 × 10−4, 2.4251 × 10−3, 1.7298 × 10−3, and 1.6601 × 10−2. Consequently, HAJAYADE is proven to be an efficient and reliable algorithm and could be an alternative algorithm to identify the parameters of PV systems. Full article
(This article belongs to the Special Issue Applied Computing and Artificial Intelligence)
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18 pages, 2363 KiB  
Article
Fractional-Order Discrete-Time SIR Epidemic Model with Vaccination: Chaos and Complexity
by Zai-Yin He, Abderrahmane Abbes, Hadi Jahanshahi, Naif D. Alotaibi and Ye Wang
Mathematics 2022, 10(2), 165; https://doi.org/10.3390/math10020165 - 6 Jan 2022
Cited by 156 | Viewed by 8398
Abstract
This research presents a new fractional-order discrete-time susceptible-infected-recovered (SIR) epidemic model with vaccination. The dynamical behavior of the suggested model is examined analytically and numerically. Through using phase attractors, bifurcation diagrams, maximum Lyapunov exponent and the 0−1 test, it is verified that the [...] Read more.
This research presents a new fractional-order discrete-time susceptible-infected-recovered (SIR) epidemic model with vaccination. The dynamical behavior of the suggested model is examined analytically and numerically. Through using phase attractors, bifurcation diagrams, maximum Lyapunov exponent and the 0−1 test, it is verified that the newly introduced fractional discrete SIR epidemic model vaccination with both commensurate and incommensurate fractional orders has chaotic behavior. The discrete fractional model gives more complex dynamics for incommensurate fractional orders compared to commensurate fractional orders. The reasonable range of commensurate fractional orders is between γ = 0.8712 and γ = 1, while the reasonable range of incommensurate fractional orders is between γ2 = 0.77 and γ2 = 1. Furthermore, the complexity analysis is performed using approximate entropy (ApEn) and C0 complexity to confirm the existence of chaos. Finally, simulations were carried out on MATLAB to verify the efficacy of the given findings. Full article
(This article belongs to the Special Issue Dynamical Systems and Their Applications (DSTA) — In Memory of Prof. Dr. José A. Tenreiro Machado)
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