Mathematics

Open AccessEditor’s ChoiceArticle

A Reliable Way to Deal with Fractional-Order Equations That Describe the Unsteady Flow of a Polytropic Gas

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Mathematics 2022, 10(13), 2293; https://doi.org/10.3390/math10132293 - 30 Jun 2022

Cited by 15 | Viewed by 948

Abstract

In this paper, fractional-order system gas dynamics equations are solved analytically using an appealing novel method known as the Laplace residual power series technique, which is based on the coupling of the residual power series approach with the Laplace transform operator to develop [...] Read more.

In this paper, fractional-order system gas dynamics equations are solved analytically using an appealing novel method known as the Laplace residual power series technique, which is based on the coupling of the residual power series approach with the Laplace transform operator to develop analytical and approximate solutions in quick convergent series types by utilizing the idea of the limit with less effort and time than the residual power series method. The given model is tested and simulated to confirm the proposed technique’s simplicity, performance, and viability. The results show that the above-mentioned technique is simple, reliable, and appropriate for investigating nonlinear engineering and physical problems. Full article

(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications II)

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Open AccessEditor’s ChoiceArticle

A Variable Neighborhood Search Approach for the Dynamic Single Row Facility Layout Problem

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Gintaras Palubeckis

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Armantas Ostreika

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Jūratė Platužienė

Mathematics 2022, 10(13), 2174; https://doi.org/10.3390/math10132174 - 22 Jun 2022

Cited by 1 | Viewed by 734

Abstract

The dynamic single row facility layout problem (DSRFLP) is defined as the problem of arranging facilities along a straight line during a multi-period planning horizon with the objective of minimizing the sum of the material handling and rearrangement costs. The material handling cost [...] Read more.

The dynamic single row facility layout problem (DSRFLP) is defined as the problem of arranging facilities along a straight line during a multi-period planning horizon with the objective of minimizing the sum of the material handling and rearrangement costs. The material handling cost is the sum of the products of the flow costs and center-to-center distances between facilities. In this paper, we focus on metaheuristic algorithms for this problem. The main contributions of the paper are three-fold. First, a variable neighborhood search (VNS) algorithm for the DSRFLP is proposed. The main version of VNS uses an innovative strategy to start the search from a solution obtained by constructing an instance of the single row facility layout problem (SRFLP) from a given instance of the DSRFLP and applying a heuristic algorithm for the former problem. Second, a fast local search (LS) procedure is developed. The innovations of this procedure are two-fold: (i) the fast insertion and swap neighborhood exploration techniques are adapted for the case of the dynamic version of the SRFLP; and (ii) to reduce the computational time, the swap operation is restricted on pairs of facilities of equal lengths. Provided the number of planning periods is a constant, the neighborhood exploration procedures for n facilities have only

O (n^{2})

time complexity. The superiority of these procedures over traditional LS techniques is also shown by performing numerical tests. Third, computational experiments on DSRFLP instances with up to 200 facilities and three or five planning periods are carried out to validate the effectiveness of the VNS approach. The proposed VNS heuristic is compared with the simulated annealing (SA) method which is the state of the art algorithm for the DSRFLP. Experiments show that VNS outperforms SA by a significant margin. Full article

(This article belongs to the Special Issue Advanced Optimization Methods and Applications)

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Open AccessEditor’s ChoiceArticle

Matrix Power Function Based Block Cipher Operating in CBC Mode

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Lina Dindiene

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Aleksejus Mihalkovich

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Kestutis Luksys

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Eligijus Sakalauskas

Mathematics 2022, 10(12), 2123; https://doi.org/10.3390/math10122123 - 18 Jun 2022

Cited by 1 | Viewed by 1084

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)

Open AccessEditor’s ChoiceArticle

Multiple Scenarios of Quality of Life Index Using Fuzzy Linguistic Quantifiers: The Case of 85 Countries in Numbeo

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Ziwei Shu

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Ramón Alberto Carrasco

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Javier Portela García-Miguel

and

Manuel Sánchez-Montañés

Mathematics 2022, 10(12), 2091; https://doi.org/10.3390/math10122091 - 16 Jun 2022

Cited by 3 | Viewed by 1373

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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Open AccessEditor’s ChoiceArticle

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 2 | Viewed by 991

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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Open AccessEditor’s ChoiceArticle

Free Resolutions and Generalized Hamming Weights of Binary Linear Codes

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Ignacio García-Marco

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Irene Márquez-Corbella

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Edgar Martínez-Moro

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Yuriko Pitones

Mathematics 2022, 10(12), 2079; https://doi.org/10.3390/math10122079 - 15 Jun 2022

Cited by 1 | Viewed by 1253

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)

Open AccessEditor’s ChoiceArticle

Kernel Matrix-Based Heuristic Multiple Kernel Learning

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Mathematics 2022, 10(12), 2026; https://doi.org/10.3390/math10122026 - 11 Jun 2022

Cited by 1 | Viewed by 917

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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Open AccessEditor’s ChoiceArticle

Coexisting Attractor in a Gyrostat Chaotic System via Basin of Attraction and Synchronization of Two Nonidentical Mechanical Systems

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Muhammad Marwan

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Vagner Dos Santos

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Muhammad Zainul Abidin

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Anda Xiong

Mathematics 2022, 10(11), 1914; https://doi.org/10.3390/math10111914 - 02 Jun 2022

Cited by 3 | Viewed by 1152

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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Open AccessFeature PaperEditor’s ChoiceReview

Centrally Essential Rings and Semirings

by

Askar Tuganbaev

Mathematics 2022, 10(11), 1867; https://doi.org/10.3390/math10111867 - 30 May 2022

Viewed by 809

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)

Open AccessEditor’s ChoiceArticle

A Preventive Replacement Policy for a System Subject to Bivariate Generalized Polya Failure Process

by

Hyunju Lee

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Ji Hwan Cha

and

Maxim Finkelstein

Mathematics 2022, 10(11), 1833; https://doi.org/10.3390/math10111833 - 26 May 2022

Cited by 1 | Viewed by 899

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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Open AccessEditor’s ChoiceArticle

An Efficient Computational Technique for the Electromagnetic Scattering by Prolate Spheroids

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Mathematics 2022, 10(10), 1761; https://doi.org/10.3390/math10101761 - 21 May 2022

Cited by 2 | Viewed by 1186

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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Open AccessEditor’s ChoiceArticle

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 7 | Viewed by 1161

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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Open AccessEditor’s ChoiceArticle

Heterogeneous Overdispersed Count Data Regressions via Double-Penalized Estimations

by

Shaomin Li

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Haoyu Wei

and

Xiaoyu Lei

Mathematics 2022, 10(10), 1700; https://doi.org/10.3390/math10101700 - 16 May 2022

Cited by 1 | Viewed by 982

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

ℓ_{1}

-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)

Open AccessEditor’s ChoiceArticle

Operator Calculus Approach to Comparison of Elasticity Models for Modelling of Masonry Structures

by

Klaus Gürlebeck

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Dmitrii Legatiuk

and

Kemmar Webber

Mathematics 2022, 10(10), 1670; https://doi.org/10.3390/math10101670 - 13 May 2022

Viewed by 980

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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Open AccessFeature PaperEditor’s ChoiceArticle

Fisher, Bayes, and Predictive Inference

by

Sandy Zabell

Mathematics 2022, 10(10), 1634; https://doi.org/10.3390/math10101634 - 11 May 2022

Cited by 1 | Viewed by 783

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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Open AccessEditor’s ChoiceArticle

Andness Directedness for t-Norms and t-Conorms

by

Vicenç Torra

Mathematics 2022, 10(9), 1598; https://doi.org/10.3390/math10091598 - 08 May 2022

Cited by 1 | Viewed by 855

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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Open AccessEditor’s ChoiceArticle

A Safe and Efficient Lane Change Decision-Making Strategy of Autonomous Driving Based on Deep Reinforcement Learning

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Mathematics 2022, 10(9), 1551; https://doi.org/10.3390/math10091551 - 05 May 2022

Cited by 5 | Viewed by 1751

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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Open AccessEditor’s ChoiceArticle

Fixed-Time Synchronization for Fuzzy-Based Impulsive Complex Networks

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Mathematics 2022, 10(9), 1533; https://doi.org/10.3390/math10091533 - 03 May 2022

Cited by 3 | Viewed by 965

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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Open AccessEditor’s ChoiceArticle

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 - 02 May 2022

Cited by 4 | Viewed by 969

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)

Open AccessEditor’s ChoiceArticle

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 8 | Viewed by 864

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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Open AccessEditor’s ChoiceArticle

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 5 | Viewed by 734

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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Open AccessEditor’s ChoiceArticle

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

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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 1 | Viewed by 1141

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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Open AccessEditor’s ChoiceArticle

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 2 | Viewed by 1105

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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Open AccessEditor’s ChoiceArticle

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 - 07 Apr 2022

Cited by 2 | Viewed by 985

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)

Open AccessEditor’s ChoiceArticle

On Numerical Approximations of the Koopman Operator

by

Igor Mezić

Mathematics 2022, 10(7), 1180; https://doi.org/10.3390/math10071180 - 05 Apr 2022

Cited by 4 | Viewed by 1728

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)

Open AccessEditor’s ChoiceArticle

MHD Mixed Convection Hybrid Nanofluids Flow over a Permeable Moving Inclined Flat Plate in the Presence of Thermophoretic and Radiative Heat Flux Effects

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and

Mathematics 2022, 10(7), 1164; https://doi.org/10.3390/math10071164 - 03 Apr 2022

Cited by 9 | Viewed by 1394

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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Open AccessFeature PaperEditor’s ChoiceArticle

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 - 02 Apr 2022

Cited by 2 | Viewed by 1220

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)

Open AccessEditor’s ChoiceArticle

A Dynamic Mechanistic Model of Perceptual Binding

by

Pavel Kraikivski

Mathematics 2022, 10(7), 1135; https://doi.org/10.3390/math10071135 - 01 Apr 2022

Cited by 3 | Viewed by 1058

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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Open AccessEditor’s ChoiceArticle

Proving Feasibility of a Docking Mission: A Contractor Programming Approach

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Mathematics 2022, 10(7), 1130; https://doi.org/10.3390/math10071130 - 01 Apr 2022

Viewed by 1065

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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Open AccessEditor’s ChoiceArticle

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 15 | Viewed by 1330

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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Open AccessEditor’s ChoiceArticle

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 4 | Viewed by 1324

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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Open AccessEditor’s ChoiceArticle

Modified Remora Optimization Algorithm for Global Optimization and Multilevel Thresholding Image Segmentation

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Mathematics 2022, 10(7), 1014; https://doi.org/10.3390/math10071014 - 22 Mar 2022

Cited by 23 | Viewed by 2193

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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Open AccessEditor’s ChoiceArticle

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 24 | Viewed by 2755

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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Open AccessEditor’s ChoiceArticle

Highly Dispersive Optical Soliton Perturbation, with Maximum Intensity, for the Complex Ginzburg–Landau Equation by Semi-Inverse Variation

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Mathematics 2022, 10(6), 987; https://doi.org/10.3390/math10060987 - 18 Mar 2022

Cited by 7 | Viewed by 1554

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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Open AccessEditor’s ChoiceArticle

Evaluation of sEMG Signal Features and Segmentation Parameters for Limb Movement Prediction Using a Feedforward Neural Network

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Mathematics 2022, 10(6), 932; https://doi.org/10.3390/math10060932 - 15 Mar 2022

Cited by 2 | Viewed by 1592

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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Open AccessEditor’s ChoiceArticle

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 - 09 Mar 2022

Cited by 38 | Viewed by 1464

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

Open AccessEditor’s ChoiceArticle

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 - 08 Mar 2022

Cited by 15 | Viewed by 1584

Abstract

Assuming exponential lifetime and repair time distributions, we study the limiting availability

A_{\infty}

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_{\infty}

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_{\infty}

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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Open AccessEditor’s ChoiceArticle

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 - 07 Mar 2022

Cited by 13 | Viewed by 2880

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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Open AccessEditor’s ChoiceArticle

The Impact of the Wiener Process on the Analytical Solutions of the Stochastic (2+1)-Dimensional Breaking Soliton Equation by Using Tanh–Coth Method

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Mathematics 2022, 10(5), 817; https://doi.org/10.3390/math10050817 - 04 Mar 2022

Cited by 21 | Viewed by 1491

Abstract

The stochastic (2+1)-dimensional breaking soliton equation (SBSE) is considered in this article, which is forced by the Wiener process. To attain the analytical stochastic solutions such as the polynomials, hyperbolic and trigonometric functions of the SBSE, we use the tanh–coth method. The results [...] Read more.

The stochastic (2+1)-dimensional breaking soliton equation (SBSE) is considered in this article, which is forced by the Wiener process. To attain the analytical stochastic solutions such as the polynomials, hyperbolic and trigonometric functions of the SBSE, we use the tanh–coth method. The results provided here extended earlier results. In addition, we utilize Matlab tools to plot 2D and 3D graphs of analytical stochastic solutions derived here to show the effect of the Wiener process on the solutions of the breaking soliton equation. Full article

(This article belongs to the Special Issue Recent Advances in Differential Equations and Applications)

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Open AccessEditor’s ChoiceArticle

SVseg: Stacked Sparse Autoencoder-Based Patch Classification Modeling for Vertebrae Segmentation

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,

Syeda Shamaila Zareen

and

Muhammad Azeem Akbar

Mathematics 2022, 10(5), 796; https://doi.org/10.3390/math10050796 - 02 Mar 2022

Cited by 18 | Viewed by 2707

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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Open AccessEditor’s ChoiceArticle

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 13 | Viewed by 2143

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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Open AccessEditor’s ChoiceArticle

Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay Kernel

by

Meshari Alesemi

,

Naveed Iqbal

and

Thongchai Botmart

Mathematics 2022, 10(4), 615; https://doi.org/10.3390/math10040615 - 17 Feb 2022

Cited by 21 | Viewed by 1479

Abstract

This article presents a homotopy perturbation transform method and a variational iterative transform method for analyzing the fractional-order non-linear system of the unsteady flow of a polytropic gas. In this method, the Yang transform is combined with the homotopy perturbation transformation method and [...] Read more.

This article presents a homotopy perturbation transform method and a variational iterative transform method for analyzing the fractional-order non-linear system of the unsteady flow of a polytropic gas. In this method, the Yang transform is combined with the homotopy perturbation transformation method and the variational iterative transformation method in the sense of Caputo–Fabrizio. A numerical simulation was carried out to verify that the suggested methodologies are accurate and reliable, and the results are revealed using graphs and tables. Comparing the analytical and actual solutions demonstrates that the proposed approaches are effective and efficient in investigating complicated non-linear models. Furthermore, the proposed methodologies control and manipulate the achieved numerical solutions in a very useful way, and this provides us with a simple process to adjust and control the convergence regions of the series solution. Full article

(This article belongs to the Special Issue Computational, Experimental, and Theoretical Aspect of Fractional Order Operators)

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Open AccessEditor’s ChoiceArticle

PFVAE: A Planar Flow-Based Variational Auto-Encoder Prediction Model for Time Series Data

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Mathematics 2022, 10(4), 610; https://doi.org/10.3390/math10040610 - 16 Feb 2022

Cited by 69 | Viewed by 5731

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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Open AccessEditor’s ChoiceArticle

Free Vibration of FG-CNTRCs Nano-Plates/Shells with Temperature-Dependent Properties

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Mathematics 2022, 10(4), 583; https://doi.org/10.3390/math10040583 - 13 Feb 2022

Cited by 21 | Viewed by 1388

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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Open AccessEditor’s ChoiceArticle

Enhanced Convolutional Neural Network Model for Cassava Leaf Disease Identification and Classification

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Umesh Kumar Lilhore

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Agbotiname Lucky Imoize

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Mathematics 2022, 10(4), 580; https://doi.org/10.3390/math10040580 - 13 Feb 2022

Cited by 12 | Viewed by 2587

Abstract

Cassava is a crucial food and nutrition security crop cultivated by small-scale farmers and it can survive in a brutal environment. It is a significant source of carbohydrates in African countries. Sometimes, Cassava crops can be infected by leaf diseases, affecting the overall [...] Read more.

Cassava is a crucial food and nutrition security crop cultivated by small-scale farmers and it can survive in a brutal environment. It is a significant source of carbohydrates in African countries. Sometimes, Cassava crops can be infected by leaf diseases, affecting the overall production and reducing farmers’ income. The existing Cassava disease research encounters several challenges, such as poor detection rate, higher processing time, and poor accuracy. This research provides a comprehensive learning strategy for real-time Cassava leaf disease identification based on enhanced CNN models (ECNN). The existing Standard CNN model utilizes extensive data processing features, increasing the computational overhead. A depth-wise separable convolution layer is utilized to resolve CNN issues in the proposed ECNN model. This feature minimizes the feature count and computational overhead. The proposed ECNN model utilizes a distinct block processing feature to process the imbalanced images. To resolve the color segregation issue, the proposed ECNN model uses a Gamma correction feature. To decrease the variable selection process and increase the computational efficiency, the proposed ECNN model uses global average election polling with batch normalization. An experimental analysis is performed over an online Cassava image dataset containing 6256 images of Cassava leaves with five disease classes. The dataset classes are as follows: class 0: “Cassava Bacterial Blight (CBB)”; class 1: “Cassava Brown Streak Disease (CBSD)”; class 2: “Cassava Green Mottle (CGM)”; class 3: “Cassava Mosaic Disease (CMD)”; and class 4: “Healthy”. Various performance measuring parameters, i.e., precision, recall, measure, and accuracy, are calculated for existing Standard CNN and the proposed ECNN model. The proposed ECNN classifier significantly outperforms and achieves 99.3% accuracy for the balanced dataset. The test findings prove that applying a balanced database of images improves classification performance. Full article

(This article belongs to the Special Issue Mathematical Methods and Applications for Artificial Intelligence and Computer Vision)

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Open AccessEditor’s ChoiceArticle

Forecasting of Electrical Energy Consumption in Slovakia

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Michal Pavlicko

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Mária Vojteková

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Oľga Blažeková

Mathematics 2022, 10(4), 577; https://doi.org/10.3390/math10040577 - 12 Feb 2022

Cited by 13 | Viewed by 2069

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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Open AccessEditor’s ChoiceArticle

A Theoretical Analysis of a Fractional Multi-Dimensional System of Boundary Value Problems on the Methylpropane Graph via Fixed Point Technique

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Mathematics 2022, 10(4), 568; https://doi.org/10.3390/math10040568 - 12 Feb 2022

Cited by 16 | Viewed by 1111

Abstract

Few studies have investigated the existence and uniqueness of solutions for fractional differential equations on star graphs until now. The published papers on the topic are based on the assumption of existence of one junction node and some boundary nodes as the origin [...] Read more.

Few studies have investigated the existence and uniqueness of solutions for fractional differential equations on star graphs until now. The published papers on the topic are based on the assumption of existence of one junction node and some boundary nodes as the origin on a star graph. These structures are special cases and do not cover more general non-star graph structures. In this paper, we state a labeling method for graph vertices, and then we prove the existence results for solutions to a new family of fractional boundary value problems (FBVPs) on the methylpropane graph. We design the chemical compound of the methylpropane graph with vertices specified by 0 or 1, and on every edge of the graph, we consider fractional differential equations. We prove the existence of solutions for the proposed FBVPs by means of the Krasnoselskii’s and Scheafer’s fixed point theorems, and further, we study the Ulam–Hyers type stability for the given multi-dimensional system. Finally, we provide an illustrative example to examine our results. Full article

(This article belongs to the Special Issue Fractional Calculus and Mathematical Applications)

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Open AccessEditor’s ChoiceArticle

Data-Driven Maintenance Priority and Resilience Evaluation of Performance Loss in a Main Coolant System

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Mathematics 2022, 10(4), 563; https://doi.org/10.3390/math10040563 - 11 Feb 2022

Cited by 19 | Viewed by 1132

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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Open AccessEditor’s ChoiceArticle

Some New Concepts Related to Integral Operators and Inequalities on Coordinates in Fuzzy Fractional Calculus

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Muhammad Bilal Khan

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Gustavo Santos-García

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Hatim Ghazi Zaini

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Savin Treanță

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Mohamed S. Soliman

Mathematics 2022, 10(4), 534; https://doi.org/10.3390/math10040534 - 09 Feb 2022

Cited by 6 | Viewed by 1383

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

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-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)

Open AccessEditor’s ChoiceArticle

Optimal Reinforcement Learning-Based Control Algorithm for a Class of Nonlinear Macroeconomic Systems

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Mathematics 2022, 10(3), 499; https://doi.org/10.3390/math10030499 - 03 Feb 2022

Cited by 4 | Viewed by 1292

Abstract

Due to the vital role of financial systems in today’s sophisticated world, applying intelligent controllers through management strategies is of crucial importance. We propose to formulate the control problem of the macroeconomic system as an optimization problem and find optimal actions using a [...] Read more.

Due to the vital role of financial systems in today’s sophisticated world, applying intelligent controllers through management strategies is of crucial importance. We propose to formulate the control problem of the macroeconomic system as an optimization problem and find optimal actions using a reinforcement learning algorithm. Using the Q-learning algorithm, the best optimal action for the system is obtained, and the behavior of the system is controlled. We illustrate that it is possible to control the nonlinear dynamics of the macroeconomic systems using restricted actuation. The highly effective performance of the proposed controller for uncertain systems is demonstrated. The simulation results evidently confirm that the proposed controller satisfies the expected performance. In addition, the numerical simulations clearly confirm that even when we confined the control actions, the proposed controller effectively finds optimal actions for the nonlinear macroeconomic system. Full article

(This article belongs to the Special Issue Mathematics and Economic Modeling)

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