Mathematics

17 pages, 2991 KiB

Open AccessArticle

Fault-Tolerant Terminal Sliding Mode Control with Disturbance Observer for Vibration Suppression in Non-Local Strain Gradient Nano-Beams

by Hajid Alsubaie, Amin Yousefpour, Ahmed Alotaibi, Naif D. Alotaibi and Hadi Jahanshahi

Mathematics 2023, 11(3), 789; https://doi.org/10.3390/math11030789 - 03 Feb 2023

Cited by 4 | Viewed by 1335

Abstract

This research investigates the stabilization and control of an uncertain Euler–Bernoulli nano-beam with fixed ends. The governing partial differential equations of motion for the nano-beam are derived using Hamilton’s principle and the non-local strain gradient theory. The Galerkin method is then applied to [...] Read more.

This research investigates the stabilization and control of an uncertain Euler–Bernoulli nano-beam with fixed ends. The governing partial differential equations of motion for the nano-beam are derived using Hamilton’s principle and the non-local strain gradient theory. The Galerkin method is then applied to transform the resulting dimensionless partial differential equation into a nonlinear ordinary differential equation. A novel fault-tolerant terminal sliding mode control technique is proposed to address the uncertainties inherent in micro/nano-systems and the potential for faults and failures in control actuators. The proposed controller includes a finite time estimator, the stability of which and the convergence of the error dynamics are established using the Lyapunov theorem. The significance of this study lies in its application to the field of micro/nano-mechanics, where the precise control and stabilization of small-scale systems is crucial for the development of advanced technologies such as nano-robotics and micro-electromechanical systems (MEMS). The proposed control technique addresses the inherent uncertainties and potential for faults in these systems, making it a valuable choice for practical applications. The simulation results are presented to demonstrate the effectiveness of the proposed control scheme and the high accuracy of the estimation algorithm. Full article

(This article belongs to the Special Issue Analysis and Mathematical Modeling of Control Engineering and Path Planning)

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16 pages, 5619 KiB

Open AccessArticle

Adaptive Output Feedback Control for Constrained Switched Systems with Input Quantization

by Shuyan Qi, Jun Zhao and Li Tang

Mathematics 2023, 11(3), 788; https://doi.org/10.3390/math11030788 - 03 Feb 2023

Cited by 4 | Viewed by 1069

Abstract

This paper investigates adaptive output feedback control problem for switched uncertain nonlinear systems with input quantization, unmeasured system states and state constraints. Firstly, fuzzy logic systems are introduced to identify system uncertainties, then the fuzzy based observer is constructed to estimate unavailable states. [...] Read more.

This paper investigates adaptive output feedback control problem for switched uncertain nonlinear systems with input quantization, unmeasured system states and state constraints. Firstly, fuzzy logic systems are introduced to identify system uncertainties, then the fuzzy based observer is constructed to estimate unavailable states. Secondly, combing the backstepping technique and the barrier Lyapunov function method, an adaptive fuzzy output feedback control law is designed, which guarantees that all signals in the closed-loop system are bounded, the system output tracks the reference signal, and system states satisfy their corresponding constraint conditions. Finally, simulation results further show the good performances of the proposed control scheme. 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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34 pages, 1942 KiB

Open AccessReview

Student Engagement with Technology-Enhanced Resources in Mathematics in Higher Education: A Review

by Caitríona Ní Shé, Eabhnat Ní Fhloinn and Ciarán Mac an Bhaird

Mathematics 2023, 11(3), 787; https://doi.org/10.3390/math11030787 - 03 Feb 2023

Cited by 4 | Viewed by 6740

Abstract

The effectiveness of technology-enhanced resources in mathematics in higher education is far from clear, nor is student engagement with such resources. In this review article, we investigate the existing literature in three interrelated areas: student engagement with technology in higher education and mathematics; [...] Read more.

The effectiveness of technology-enhanced resources in mathematics in higher education is far from clear, nor is student engagement with such resources. In this review article, we investigate the existing literature in three interrelated areas: student engagement with technology in higher education and mathematics; what works and what does not in technology in education and in mathematics in higher education; evaluating the use of technology in higher education and mathematics; and the use of frameworks and models. Over 300 research articles were identified for this purpose and the results are reported in this review. We found a dearth of studies in undergraduate mathematics education that specifically focus on student engagement with technology. In addition, there is no overarching framework that describes both the pedagogical aspects and the educational context of technology integration in mathematics. Full article

(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering II)

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29 pages, 2673 KiB

Open AccessArticle

Exploring the Predictors of Co-Nationals’ Preference over Immigrants in Accessing Jobs—Evidence from World Values Survey

by Daniel Homocianu

Mathematics 2023, 11(3), 786; https://doi.org/10.3390/math11030786 - 03 Feb 2023

Viewed by 1511

Abstract

This paper presents the results of an exploration of the most resilient influences determining the attitude regarding prioritizing co-nationals over immigrants for access to employment. The source data were from the World Values Survey. After many selection and testing steps, a set of [...] Read more.

This paper presents the results of an exploration of the most resilient influences determining the attitude regarding prioritizing co-nationals over immigrants for access to employment. The source data were from the World Values Survey. After many selection and testing steps, a set of the seven most significant determinants was produced (a fair-to-good model as prediction accuracy). These seven determinants (a hepta-core model) correspond to some features, beliefs, and attitudes regarding emancipative values, gender discrimination, immigrant policy, trust in people of another nationality, inverse devoutness or making parents proud as a life goal, attitude towards work, the post-materialist index, and job preferences as more inclined towards self rather than community benefits. Additional controls revealed the significant influence of some socio-demographic variables. They correspond to gender, the number of children, the highest education level attained, employment status, income scale positioning, settlement size, and the interview year. All selection and testing steps considered many principles, methods, and techniques (e.g., triangulation via adaptive boosting (in the Rattle library of R), and pairwise correlation-based data mining—PCDM, LASSO, OLS, binary and ordered logistic regressions (LOGIT, OLOGIT), prediction nomograms, together with tools for reporting default and custom model evaluation metrics, such as ESTOUT and MEM in Stata). Cross-validations relied on random subsamples (CVLASSO) and well-established ones (mixed-effects). In addition, overfitting removal (RLASSO), reverse causality, and collinearity checks succeeded under full conditions for replicating the results. The prediction nomogram corresponding to the most resistant predictors identified in this paper is also a powerful tool for identifying risks. Therefore, it can provide strong support for decision makers in matters related to immigration and access to employment. The paper’s novelty also results from the many robust supporting techniques that allow randomly, and non-randomly cross-validated and fully reproducible results based on a large amount and variety of source data. The findings also represent a step forward in migration and access-to-job research. Full article

(This article belongs to the Special Issue Probability, Stochastic Processes and Optimization)

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19 pages, 5871 KiB

Open AccessArticle

Multi-Layer Decomposition and Synthesis of HDR Images to Improve High-Saturation Boundaries

by Hyuk-Ju Kwon and Sung-Hak Lee

Mathematics 2023, 11(3), 785; https://doi.org/10.3390/math11030785 - 03 Feb 2023

Cited by 2 | Viewed by 1263

Abstract

Recently, high dynamic range (HDR) imaging has been used in many fields such as display, computer graphics, and digital cameras. Various tone mapping operators (TMOs) are used for effective HDR imaging. TMOs aim to express HDR images without loss of information and natural [...] Read more.

Recently, high dynamic range (HDR) imaging has been used in many fields such as display, computer graphics, and digital cameras. Various tone mapping operators (TMOs) are used for effective HDR imaging. TMOs aim to express HDR images without loss of information and natural images on existing display equipment. In this paper, to improve the color distortion that occurs during tone mapping, multi-layer decomposition-based color compensation and global color enhancement of the boundary region are proposed. Multi-layer decomposition is used to preserve the color information of the input image and to find the area where color distortion occurs. Color compensation and enhancement are especially used to improve the color saturation of the border area, which is degraded due to color distortion and tone processing. Color compensation and enhancement are processed in IPT color space with excellent hue linearity to improve effective performance by reducing interference between luminance and chrominance components. The performance of the proposed method was compared to the existing methods using naturalness, distortion, and tone-mapped image quality metrics. The results show that the proposed method is superior to the existing methods. Full article

(This article belongs to the Special Issue Advances in Mathematical Methods for Image Processing and Pattern Recognition)

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18 pages, 8842 KiB

Open AccessArticle

Numerical Simulation of Heat Transfer and Spread of Virus Particles in the Car Interior

by Ivan Panfilov, Alexey N. Beskopylny and Besarion Meskhi

Mathematics 2023, 11(3), 784; https://doi.org/10.3390/math11030784 - 03 Feb 2023

Cited by 1 | Viewed by 1612

Abstract

The epidemic caused by the coronavirus infection SARS-CoV-2 at the beginning of 2022 affected approximately 500 million people in all countries. The source of infection is the particles of the virus, which, when breathing, talking, and coughing, are released with the respiratory droplets [...] Read more.

The epidemic caused by the coronavirus infection SARS-CoV-2 at the beginning of 2022 affected approximately 500 million people in all countries. The source of infection is the particles of the virus, which, when breathing, talking, and coughing, are released with the respiratory droplets and aerosol dust of an infected person. Actions aimed at combating and minimizing the consequences of coronavirus infection led to taking measures in scientific areas to investigate the processes of the spread of viral particles in the air, in ventilation, and air conditioning systems of premises and transport, filtration through masks, the effect of partitions, face shields, etc. The article presents a mathematical model of the spread of viral particles in technological transport. Air intake diverters and the operator’s respiratory tract are the sources of the virus. The Euler–Lagrange approach was used to simulate liquid droplets in a flow. Here, the liquid phase is considered as a continuous medium using Navier–Stokes equations, the continuity equation, the energy equation, and the diffusion equation. Accounting for diffusion makes it possible to explicitly model air humidity and is necessary to consider the evaporation of droplets (changes in the mass and size of particles containing the virus). Liquid droplets are modeled using the discrete-phase model (DPM), in which each particle is tracked in a Lagrange coordinate system. The DPM method is effective, since the volume fraction of particles is small relative to the total volume of the medium, and the interaction of particles with each other can be neglected. In this case, the discrete and continuous phases are interconnected through the source terms in the equations. The averaged RANS equations are solved numerically using the k-ω turbulence model in the Ansys Fluent package. The task was solved in a static form and in the time domain. For a non-stationary problem, the stabilization time of the variables is found. The simulation results are obtained in the form of fields of pressures, velocities, temperatures and air densities, and the field of propagation of particles containing the virus. Various regimes were studied at various free flow rates and initial velocities of droplets with viral particles. The results of trajectories and velocities of particles, and particle concentrations depending on time, size, and on the evaporability of particles are obtained. Full article

(This article belongs to the Section Difference and Differential Equations)

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16 pages, 1494 KiB

Open AccessArticle

Market Demand Optimization Model Based on Information Perception Control

by Guanghui Yuan, Zhiqiang Liu, Yaqiong Wang and Dongping Pu

Mathematics 2023, 11(3), 783; https://doi.org/10.3390/math11030783 - 03 Feb 2023

Viewed by 1109

Abstract

The development of Internet technology and the rise of social networks have expanded the means of product information dissemination. Nowadays, consumers can obtain not only product quality information through real life contacts, but can also obtain product cognitive information through virtual networks, which [...] Read more.

The development of Internet technology and the rise of social networks have expanded the means of product information dissemination. Nowadays, consumers can obtain not only product quality information through real life contacts, but can also obtain product cognitive information through virtual networks, which constitute consumers’ information perception together. However, information in the market can be controlled, and companies can change the perceptions of their consumer base towards their products by enhancing the dissemination of information on the Internet, thus achieving higher corporate revenue. This article aims to study the evolution process of market demand under the control of consumers’ information perception, and a two-layer network model consisting of a cognitive information layer and a quality information layer were constructed. In order to improve product information dissemination efficiency, the opinion leaders who are more active in responding to mentions of the product across social networks are selected, and these opinion leaders are influenced in a stepwise manner using the maximum influence model, thus investigating the relationship between resources and corporate revenue. Using scale-free networks for simulation analysis, there are three main conclusions. First, the cognitive information and quality information of the product could affect market demand. Second, product demand and company profits would increase significantly if key individuals were added to the cognitive information layer. Third, the incremental marginal effect of key individuals decreases as their number increases. Full article

(This article belongs to the Special Issue Evolutionary Games, Propagation Processes and Control in Complex Systems)

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25 pages, 1492 KiB

Open AccessArticle

Semi-Supervised Multi-Label Dimensionality Reduction Learning by Instance and Label Correlations

by Runxin Li, Jiaxing Du, Jiaman Ding, Lianyin Jia, Yinong Chen and Zhenhong Shang

Mathematics 2023, 11(3), 782; https://doi.org/10.3390/math11030782 - 03 Feb 2023

Cited by 2 | Viewed by 1555

Abstract

The label learning mechanism is challenging to integrate into the training model of the multi-label feature space dimensionality reduction problem, making the current multi-label dimensionality reduction methods primarily supervision modes. Many methods only focus attention on label correlations and ignore the instance interrelations [...] Read more.

The label learning mechanism is challenging to integrate into the training model of the multi-label feature space dimensionality reduction problem, making the current multi-label dimensionality reduction methods primarily supervision modes. Many methods only focus attention on label correlations and ignore the instance interrelations between the original feature space and low dimensional space. Additionally, very few techniques consider how to constrain the projection matrix to identify specific and common features in the feature space. In this paper, we propose a new approach of semi-supervised multi-label dimensionality reduction learning by instance and label correlations (SMDR-IC, in short). Firstly, we reformulate MDDM which incorporates label correlations as a least-squares problem so that the label propagation mechanism can be effectively embedded into the model. Secondly, we investigate instance correlations using the k-nearest neighbor technique, and then present the

l_{1}

-norm and

l_{2, 1}

-norm regularization terms to identify the specific and common features of the feature space. Experiments on the massive public multi-label data sets show that SMDR-IC has better performance than other related multi-label dimensionality reduction methods. Full article

(This article belongs to the Special Issue Mathematical Optimization in Pattern Recognition, Machine Learning and Data Mining)

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3 pages, 172 KiB

Open AccessEditorial

Preface to the Special Issue on “Computational Mechanics in Engineering Mathematics”

by Michael R. Booty

Mathematics 2023, 11(3), 781; https://doi.org/10.3390/math11030781 - 03 Feb 2023

Viewed by 860

Abstract

Increases in computational resources and the constant development of numerical methods have greatly expanded the range and complexity of systems that can be simulated numerically [...] Full article

(This article belongs to the Special Issue Computational Mechanics in Engineering Mathematics)

12 pages, 4850 KiB

Open AccessArticle

Simulating the Effects of Gate Machines on Crowd Traffic Based on the Modified Social Force Model

by Xue Lin, Long Cheng, Shuo Zhang and Qianling Wang

Mathematics 2023, 11(3), 780; https://doi.org/10.3390/math11030780 - 03 Feb 2023

Cited by 1 | Viewed by 1320

Abstract

Gate machines, such as ticket gates in stations and secure gates in office buildings, are very common in people’s daily lives. On the one hand, the passage between the gates is not wide enough for pedestrians to pass through, which may affect the [...] Read more.

Gate machines, such as ticket gates in stations and secure gates in office buildings, are very common in people’s daily lives. On the one hand, the passage between the gates is not wide enough for pedestrians to pass through, which may affect the traffic efficiency of the crowd; on the other hand, the gates make pedestrians move more orderly and smooth and may speed up evacuation. Whether the gates benefit or hinder the movement and evacuation of a crowd is not clear for now. This paper studies the effects of gate machines on crowd traffic based on simulations using the modified social force model. Three simulation scenarios are considered, including the absence of any gate machines, the presence of gate machines without invisible walls, and the presence of gate machines with invisible walls. Normal and evacuation situations are distinguished by whether or not a pedestrian pauses for a while in front of the gates. The influences of factors such as the number of passages, exit width, and the number of pedestrians on crowd traffic are analyzed. Simulation results show that for different exit widths, there is a corresponding optimal number of passages to make the evacuation efficiency of the crowd the highest. The conclusions of this paper can provide some suggestions for the setting of the gate machines and the development of evacuation strategies. Full article

(This article belongs to the Section Mathematics and Computer Science)

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20 pages, 372 KiB

Open AccessArticle

Characteristic, C-Characteristic and Positive Cones in Hyperfields

by Dawid Edmund Kędzierski, Alessandro Linzi and Hanna Stojałowska

Mathematics 2023, 11(3), 779; https://doi.org/10.3390/math11030779 - 03 Feb 2023

Cited by 3 | Viewed by 1199

Abstract

We study the notions of the positive cone, characteristic and C-characteristic in (Krasner) hyperfields. We demonstrate how these interact in order to produce interesting results in the theory of hyperfields. For instance, we provide a criterion for deciding whether certain hyperfields cannot be [...] Read more.

We study the notions of the positive cone, characteristic and C-characteristic in (Krasner) hyperfields. We demonstrate how these interact in order to produce interesting results in the theory of hyperfields. For instance, we provide a criterion for deciding whether certain hyperfields cannot be obtained via Krasner’s quotient construction. We prove that any positive integer (larger than 1) can be realized as the characteristic of some infinite hyperfield and an analogous result for the C-characteristic. Finally, we study the (directed) graph associated with the strict partial order induced by a positive cone in a hyperfield in various examples. Full article

(This article belongs to the Special Issue Algebraic Structures and Graph Theory)

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15 pages, 3774 KiB

Open AccessArticle

Training Multilayer Neural Network Based on Optimal Control Theory for Limited Computational Resources

by Ali Najem Alkawaz, Jeevan Kanesan, Anis Salwa Mohd Khairuddin, Irfan Anjum Badruddin, Sarfaraz Kamangar, Mohamed Hussien, Maughal Ahmed Ali Baig and N. Ameer Ahammad

Mathematics 2023, 11(3), 778; https://doi.org/10.3390/math11030778 - 03 Feb 2023

Cited by 2 | Viewed by 1950

Abstract

Backpropagation (BP)-based gradient descent is the general approach to train a neural network with a multilayer perceptron. However, BP is inherently slow in learning, and it sometimes traps at local minima, mainly due to a constant learning rate. This pre-fixed learning rate regularly [...] Read more.

Backpropagation (BP)-based gradient descent is the general approach to train a neural network with a multilayer perceptron. However, BP is inherently slow in learning, and it sometimes traps at local minima, mainly due to a constant learning rate. This pre-fixed learning rate regularly leads the BP network towards an unsuccessful stochastic steepest descent. Therefore, to overcome the limitation of BP, this work addresses an improved method of training the neural network based on optimal control (OC) theory. State equations in optimal control represent the BP neural network’s weights and biases. Meanwhile, the learning rate is treated as the input control that adapts during the neural training process. The effectiveness of the proposed algorithm is evaluated on several logic gates models such as XOR, AND, and OR, as well as the full adder model. Simulation results demonstrate that the proposed algorithm outperforms the conventional method in terms of improved accuracy in output with a shorter time in training. The training via OC also reduces the local minima trap. The proposed algorithm is almost 40% faster than the steepest descent method, with a marginally improved accuracy of approximately 60%. Consequently, the proposed algorithm is suitable to be applied on devices with limited computation resources, since the proposed algorithm is less complex, thus lowering the circuit’s power consumption. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering, 2nd Edition)

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49 pages, 469 KiB

Open AccessFeature PaperArticle

The Algebraic Classification of Nilpotent Bicommutative Algebras

by Kobiljon Abdurasulov, Ivan Kaygorodov and Abror Khudoyberdiyev

Mathematics 2023, 11(3), 777; https://doi.org/10.3390/math11030777 - 03 Feb 2023

Viewed by 4779

Abstract

This paper is devoted to the complete algebraic classification of complex five-dimensional nilpotent bicommutative algebras. Full article

(This article belongs to the Special Issue Non-associative Structures and Their Applications in Physics and Geometry)

24 pages, 1545 KiB

Open AccessArticle

Efficient Net-XGBoost: An Implementation for Facial Emotion Recognition Using Transfer Learning

by Sudheer Babu Punuri, Sanjay Kumar Kuanar, Manjur Kolhar, Tusar Kanti Mishra, Abdalla Alameen, Hitesh Mohapatra and Soumya Ranjan Mishra

Mathematics 2023, 11(3), 776; https://doi.org/10.3390/math11030776 - 03 Feb 2023

Cited by 11 | Viewed by 3326

Abstract

Researchers are interested in Facial Emotion Recognition (FER) because it could be useful in many ways and has promising applications. The main task of FER is to identify and recognize the original facial expressions of users from digital inputs. Feature extraction and emotion [...] Read more.

Researchers are interested in Facial Emotion Recognition (FER) because it could be useful in many ways and has promising applications. The main task of FER is to identify and recognize the original facial expressions of users from digital inputs. Feature extraction and emotion recognition make up the majority of the traditional FER. Deep Neural Networks, specifically Convolutional Neural Network (CNN), are popular and highly used in FER due to their inherent image feature extraction process. This work presents a novel method dubbed as EfficientNet-XGBoost that is based on Transfer Learning (TL) technique. EfficientNet-XGBoost is basically a cascading of the EfficientNet and the XGBoost techniques along with certain enhancements by experimentation that reflects the novelty of the work. To ensure faster learning of the network and to overcome the vanishing gradient problem, our model incorporates fully connected layers of global average pooling, dropout and dense. EfficientNet is fine-tuned by replacing the upper dense layer(s) and cascading the XGBoost classifier making it suitable for FER. Feature map visualization is carried out that reveals the reduction in the size of feature vectors. The proposed method is well-validated on benchmark datasets such as CK+, KDEF, JAFFE, and FER2013. To overcome the issue of data imbalance, in some of the datasets namely CK+ and FER2013, we augmented data artificially through geometric transformation techniques. The proposed method is implemented individually on these datasets and corresponding results are recorded for performance analysis. The performance is computed with the help of several metrics like precision, recall and F1 measure. Comparative analysis with competent schemes are carried out on the same sample data sets separately. Irrespective of the nature of the datasets, the proposed scheme outperforms the rest with overall rates of accuracy being 100%, 98% and 98% for the first three datasets respectively. However, for the FER2013 datasets, efficiency is less promisingly observed in support of the proposed work. Full article

(This article belongs to the Special Issue Fuzzy Logic and Computational Intelligence)

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16 pages, 415 KiB

Open AccessArticle

Embedding Uncertain Temporal Knowledge Graphs

by Tongxin Li, Weiping Wang, Xiaobo Li, Tao Wang, Xin Zhou and Meigen Huang

Mathematics 2023, 11(3), 775; https://doi.org/10.3390/math11030775 - 03 Feb 2023

Cited by 7 | Viewed by 2085

Abstract

Knowledge graph (KG) embedding for predicting missing relation facts in incomplete knowledge graphs (KGs) has been widely explored. In addition to the benchmark triple structural information such as head entities, tail entities, and the relations between them, there is a large amount of [...] Read more.

Knowledge graph (KG) embedding for predicting missing relation facts in incomplete knowledge graphs (KGs) has been widely explored. In addition to the benchmark triple structural information such as head entities, tail entities, and the relations between them, there is a large amount of uncertain and temporal information, which is difficult to be exploited in KG embeddings, and there are some embedding models specifically for uncertain KGs and temporal KGs. However, these models either only utilize uncertain information or only temporal information, without integrating both kinds of information into the underlying model that utilizes triple structural information. In this paper, we propose an embedding model for uncertain temporal KGs called the confidence score, time, and ranking information embedded jointly model (CTRIEJ), which aims to preserve the uncertainty, temporal and structural information of relation facts in the embedding space. To further enhance the precision of the CTRIEJ model, we also introduce a self-adversarial negative sampling technique to generate negative samples. We use the embedding vectors obtained from our model to complete the missing relation facts and predict their corresponding confidence scores. Experiments are conducted on an uncertain temporal KG extracted from Wikidata via three tasks, i.e., confidence prediction, link prediction, and relation fact classification. The CTRIEJ model shows effectiveness in capturing uncertain and temporal knowledge by achieving promising results, and it consistently outperforms baselines on the three downstream experimental tasks. Full article

(This article belongs to the Special Issue Advancement of Mathematical Methods in Feature Representation Learning for Artificial Intelligence, Data Mining and Robotics)

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25 pages, 1856 KiB

Open AccessArticle

Automated Settings of Overcurrent Relays Considering Transformer Phase Shift and Distributed Generators Using Gorilla Troops Optimizer

by Abdelmonem Draz, Mahmoud M. Elkholy and Attia A. El-Fergany

Mathematics 2023, 11(3), 774; https://doi.org/10.3390/math11030774 - 03 Feb 2023

Cited by 6 | Viewed by 1411

Abstract

The relative protective devices are cascaded in a proper sequence with a proper min/max coordination time margin (CTM) to minimize the outage area of the network in case of fault condition. This manuscript addresses a new methodology based on the gorilla troops optimizer [...] Read more.

The relative protective devices are cascaded in a proper sequence with a proper min/max coordination time margin (CTM) to minimize the outage area of the network in case of fault condition. This manuscript addresses a new methodology based on the gorilla troops optimizer (GTO) to produce the best automated settings for overcurrent relays. In the GTO, the exploration and exploitation phases are realized using five methodologies. Three of them are used in the exploration phase and the other two in the exploitation phase. In the exploration phase, all gorillas are considered as candidate solutions and the best one is considered as the silverback gorilla. Then again, the exploitation phase comprises two steps: (i) the first one is the follow of silverback gorilla, and (ii) the second one is the competition for adult females. The latter mentioned offers an added advantage to the GTO framework to move forward steadily to global minima and to avoid trapping into local minima. Two test cases under numerous scenarios are demonstrated comprising an isolated real distribution network with distributed generations for the Agiba Petroleum company which is in the Western Desert of Egypt. The relay coordination problem is adapted as an optimization problem subject to a set of predefined constraints which is solved using the GTO including fixed and varied inverse IEC curves, in which the practical constraints including transformer phase shift and other scenarios for min/max fault conditions are dealt with. In due course, this current effort aims at proving the best strategy for achieving the smoothest coordination of overcurrent relays (OCRs), with the least obtained value of CTMs for the studied cases being established via the automated relay settings. At last, it can be pointed out that the GTO successfully dealt with this problem and was able to produce competitive answers compared to other competitors. Full article

(This article belongs to the Special Issue Mathematical Analysis on Automated Electric Systems)

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22 pages, 1149 KiB

Open AccessArticle

Modeling Spatial Development of the Economy Based on the Concept of Economic Complexity (on the Example of Aerospace Industry)

by Julia Dubrovskaya, Elena Kozonogova and Maria Rusinova

Mathematics 2023, 11(3), 773; https://doi.org/10.3390/math11030773 - 03 Feb 2023

Cited by 1 | Viewed by 1342

Abstract

Ensuring the rational use of limited space is a key function of government bodies at any level of power. Spatial development of the economy is modeled in the presented paper based on the concept of economic complexity. In addition to the innovative application [...] Read more.

Ensuring the rational use of limited space is a key function of government bodies at any level of power. Spatial development of the economy is modeled in the presented paper based on the concept of economic complexity. In addition to the innovative application of the economic complexity concept to the analysis of territorial systems in the form of macroregions, this study used an improved methodology for calculating the index of economic complexity in relation to the processes of interregional cooperation. The methodology of constructing a model of the spatial organization of the economy included determining the composition of the system of equations and their structure, formulating the prerequisites and limitations of the model, and determining an objective function of the model. The minimum level of heterogeneity of spatial development and the maximum of macroregion economic complexity indexes were chosen as the criterion of optimality. As a result of testing the model on real statistical data of the regions in Russia, a grid of macroregions was formed, providing an increase in the diversification of the types of production activities within the macroregion and a decrease in the differentiation of the development of the territories included in it. A computer program was developed during the course of the study that allows simulation experiments to be carried out in order to find the optimal variant of spatial organization of the economy. In addition, in the example of the aerospace industry, the management algorithm of the regional sectoral branching process was tested. Full article

(This article belongs to the Special Issue Mathematical Modelling of Economics and Regional Development)

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19 pages, 2460 KiB

Open AccessArticle

Research into the Relationship between Personality and Behavior in Video Games, Based on Mining Association Rules

by Mengyang Gao, Jun Wang and Jing Yang

Mathematics 2023, 11(3), 772; https://doi.org/10.3390/math11030772 - 03 Feb 2023

Cited by 1 | Viewed by 4064

Abstract

Nowadays, people have started to spend more and more time using the Internet, which has a crucial impact on people’s lives. Individual personality type is often the main factor dictating the various behaviors that people carry out, and it dominates their activities when [...] Read more.

Nowadays, people have started to spend more and more time using the Internet, which has a crucial impact on people’s lives. Individual personality type is often the main factor dictating the various behaviors that people carry out, and it dominates their activities when socializing, communicating, and making choices in the virtual world. This study is dedicated to uncovering how the six dimensions of personality traits relate to players’ in-game behavior. This research is divided into two studies. Study 1 uses the K-means method to classify players in “Clash of Kings”, an online strategy video game, according to their activities. Using apriori algorithm, this research analyzes the correlation between in-game behavior and personality. In Study 2, the correlations are validated. In conclusion, not all personality traits are related to in-game behaviors. Players with high extraversion demonstrate more killings and attacks in games. Conscientiousness is negatively related to deaths. Emotionality shows strong extremes. The highest or lowest emotionality scores are associated with killings and attacks, while players with moderate emotionality will behave irregularly. Honesty/humility, agreeableness, and openness to experience are not predictive of in-game behaviors. For game manufacturers, players’ personality traits can be inferred through their corresponding in-game behaviors, to use in order to carry out targeted promotions. Full article

(This article belongs to the Special Issue Business Analytics: Mining, Analysis, Optimization and Applications)

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21 pages, 1814 KiB

Open AccessArticle

Mathematical–Statistical Nonlinear Model of Zincing Process and Strategy for Determining the Optimal Process Conditions

by Alena Vagaská

Mathematics 2023, 11(3), 771; https://doi.org/10.3390/math11030771 - 03 Feb 2023

Cited by 2 | Viewed by 1057

Abstract

The article is aimed at the mathematical and optimization modeling of technological processes of surface treatments, specifically the zincing process. In surface engineering, it is necessary to eliminate the risk that the resulting product quality will not be in line with the reliability [...] Read more.

The article is aimed at the mathematical and optimization modeling of technological processes of surface treatments, specifically the zincing process. In surface engineering, it is necessary to eliminate the risk that the resulting product quality will not be in line with the reliability requirements or needs of customers. To date, a number of research studies deal with the applications of mathematical modeling and optimization methods to control technological processes and eliminate uncertainties in the technological response variables. The situation is somewhat different with the acid zinc plating process, and we perceive their lack more. This article reacts to the specific requirements from practice for the prescribed thickness and quality of the zinc layer deposited in the acid electrolyte, which stimulated our interest in creating a statistical nonlinear model predicting the thickness of the resulting zinc coating (ZC). The determination of optimal process conditions for acid galvanizing is a complex problem; therefore, we propose an effective solving strategy based on the (i) experiment performed by using the design of experiments (DOE) approach; (ii) exploratory and confirmatory statistical analysis of experimentally obtained data; (iii) nonlinear regression model development; (iv) implementation of nonlinear programming (NLP) methods by the usage of MATLAB toolboxes. The main goal is achieved—regression model for eight input variables, including their interactions, is developed (the coefficient of determination reaches the value of R² = 0.959403); the optimal values of the factors acting during the zincing process to achieve the maximum thickness of the resulting protective zinc layer (the achieved optimum value t_h* = 12.7036 μm), are determined. Full article

(This article belongs to the Special Issue Mathematical Modelling and Hybrid Strategies for Risk and Uncertainty Management)

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19 pages, 4101 KiB

Open AccessArticle

The Improved Element-Free Galerkin Method for 3D Steady Convection-Diffusion-Reaction Problems with Variable Coefficients

by Heng Cheng, Zebin Xing and Yan Liu

Mathematics 2023, 11(3), 770; https://doi.org/10.3390/math11030770 - 03 Feb 2023

Cited by 5 | Viewed by 1020

Abstract

In order to obtain the numerical results of 3D convection-diffusion-reaction problems with variable coefficients efficiently, we select the improved element-free Galerkin (IEFG) method instead of the traditional element-free Galerkin (EFG) method by using the improved moving least-squares (MLS) approximation to obtain the shape [...] Read more.

In order to obtain the numerical results of 3D convection-diffusion-reaction problems with variable coefficients efficiently, we select the improved element-free Galerkin (IEFG) method instead of the traditional element-free Galerkin (EFG) method by using the improved moving least-squares (MLS) approximation to obtain the shape function. For the governing equation of 3D convection-diffusion-reaction problems, we can derive the corresponding equivalent functional; then, the essential boundary conditions are imposed by applying the penalty method; thus, the equivalent integral weak form is obtained. By introducing the IMLS approximation, we can derive the final solved linear equations of the convection-diffusion-reaction problem. In numerical examples, the scale parameter and the penalty factor of the IEFG method for such problems are discussed, the convergence is proved numerically, and the calculation efficiency of the IEFG method are verified by four numerical examples. Full article

(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 2nd Edition)

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20 pages, 1327 KiB

Open AccessArticle

Improving Intent Classification Using Unlabeled Data from Large Corpora

by Gabriel Bercaru, Ciprian-Octavian Truică, Costin-Gabriel Chiru and Traian Rebedea

Mathematics 2023, 11(3), 769; https://doi.org/10.3390/math11030769 - 03 Feb 2023

Cited by 1 | Viewed by 3230

Abstract

Intent classification is a central component of a Natural Language Understanding (NLU) pipeline for conversational agents. The quality of such a component depends on the quality of the training data, however, for many conversational scenarios, the data might be scarce; in these scenarios, [...] Read more.

Intent classification is a central component of a Natural Language Understanding (NLU) pipeline for conversational agents. The quality of such a component depends on the quality of the training data, however, for many conversational scenarios, the data might be scarce; in these scenarios, data augmentation techniques are used. Having general data augmentation methods that can generalize to many datasets is highly desirable. The work presented in this paper is centered around two main components. First, we explore the influence of various feature vectors on the task of intent classification using RASA’s text classification capabilities. The second part of this work consists of a generic method for efficiently augmenting textual corpora using large datasets of unlabeled data. The proposed method is able to efficiently mine for examples similar to the ones that are already present in standard, natural language corpora. The experimental results show that using our corpus augmentation methods enables an increase in text classification accuracy in few-shot settings. Particularly, the gains in accuracy raise up to 16% when the number of labeled examples is very low (e.g., two examples). We believe that our method is important for any Natural Language Processing (NLP) or NLU task in which labeled training data are scarce or expensive to obtain. Lastly, we give some insights into future work, which aims at combining our proposed method with a semi-supervised learning approach. Full article

(This article belongs to the Special Issue Current Trends in Natural Language Processing (NLP) and Human Language Technology (HLT))

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15 pages, 2708 KiB

Open AccessArticle

An Adaptive Multipath Linear Interpolation Method for Sample Optimization

by Yukun Du, Xiao Jin, Hongxia Wang and Min Lu

Mathematics 2023, 11(3), 768; https://doi.org/10.3390/math11030768 - 03 Feb 2023

Viewed by 1207

Abstract

When using machine learning methods to make predictions, the problem of small sample sizes or highly noisy observation samples is common. Current mainstream sample expansion methods cannot handle the data noise problem well. We propose a multipath sample expansion method (AMLI) based on [...] Read more.

When using machine learning methods to make predictions, the problem of small sample sizes or highly noisy observation samples is common. Current mainstream sample expansion methods cannot handle the data noise problem well. We propose a multipath sample expansion method (AMLI) based on the idea of linear interpolation, which mainly solves the problem of insufficient prediction sample size or large error between the observed sample and the actual distribution. The rationale of the AMLI method is to divide the original feature space into several subspaces with equal samples, randomly extract a sample from each subspace as a class, and then perform linear interpolation on the samples in the same class (i.e., K-path linear interpolation). After the AMLI processing, valid samples are greatly expanded, the sample structure is adjusted, and the average noise of the samples is reduced so that the prediction effect of the machine learning model is improved. The hyperparameters of this method have an intuitive explanation and usually require little calibration. We compared the proposed method with a variety of machine learning prediction methods and demonstrated that the AMLI method can significantly improve the prediction result. We also propose an AMLI plus method based on the linear interpolation between classes by combining the idea of AMLI with the clustering method and present theoretical proofs of the effectiveness of the AMLI and AMLI plus methods. Full article

(This article belongs to the Special Issue Advances in Computational Statistics and Applications)

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18 pages, 2891 KiB

Open AccessArticle

A Chaotic Image Encryption Method Based on the Artificial Fish Swarms Algorithm and the DNA Coding

by Yue Zhu, Chunhua Wang, Jingru Sun and Fei Yu

Mathematics 2023, 11(3), 767; https://doi.org/10.3390/math11030767 - 03 Feb 2023

Cited by 38 | Viewed by 2344

Abstract

Aiming at the problems of small key space and weak resistance to differential attacks in existing encryption algorithms, we proposed a chaotic digital image encryption scheme based on an optimized artificial fish swarm algorithm and DNA coding. First, the key is associated with [...] Read more.

Aiming at the problems of small key space and weak resistance to differential attacks in existing encryption algorithms, we proposed a chaotic digital image encryption scheme based on an optimized artificial fish swarm algorithm and DNA coding. First, the key is associated with the ordinary image pixel through the MD5 hash operation, and the hash value generated by the ordinary image is used as the initial value of the hyper-chaotic system to increase the sensitivity of the key. Next, the artificial fish school algorithm is used to scramble the positions of pixels in the block. In addition, scrambling operation between blocks is proposed to increase the scrambling effect. In the diffusion stage, operations are performed based on DNA encoding, obfuscation, and decoding technologies to obtain encrypted images. The research results show that the optimized artificial fish swarm algorithm has good convergence and can obtain the global optimal solution to the greatest extent. In addition, simulation experiments and security analysis show that compared with other encryption schemes, the scheme proposed in this paper has a larger key space and better resistance to differential attacks, indicating that the proposed algorithm has better encryption performance and higher security. Full article

(This article belongs to the Section Dynamical Systems)

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33 pages, 1052 KiB

Open AccessArticle

Lattice Enumeration with Discrete Pruning: Improvements, Cost Estimation and Optimal Parameters

by Luan Luan, Chunxiang Gu, Yonghui Zheng and Yanan Shi

Mathematics 2023, 11(3), 766; https://doi.org/10.3390/math11030766 - 03 Feb 2023

Viewed by 1279

Abstract

Lattice enumeration is a linear-space algorithm for solving the shortest lattice vector problem (SVP). Extreme pruning is a practical technique for accelerating lattice enumeration, which has a mature theoretical analysis and practical implementation. However, these works have yet to be applied to discrete [...] Read more.

Lattice enumeration is a linear-space algorithm for solving the shortest lattice vector problem (SVP). Extreme pruning is a practical technique for accelerating lattice enumeration, which has a mature theoretical analysis and practical implementation. However, these works have yet to be applied to discrete pruning. In this paper, we improve the discrete pruned enumeration (DP enumeration) and provide a solution to the problem proposed by Léo Ducas and Damien Stehlé regarding the cost estimation of discrete pruning. We first rectify the randomness assumption to more precisely describe the lattice point distribution of DP enumeration. Then, we propose a series of improvements, including a new polynomial-time binary search algorithm for cell enumeration radius, a refined cell-decoding algorithm and a rerandomization and reprocessing strategy, all aiming to lift the efficiency and build a more precise cost-estimation model for DP enumeration. Based on these theoretical and practical improvements, we build a precise cost-estimation model for DP enumeration by simulation, which has good accuracy in experiments. This DP simulator enables us to propose an optimization method of calculating the optimal parameters of DP enumeration to minimize the running time. The experimental results and asymptotic analysis both show that the discrete pruning method could outperform extreme pruning, which means that our optimized DP enumeration might become the most efficient polynomial-space SVP solver to date. An open-source implementation of DP enumeration with its simulator is also provided. Full article

(This article belongs to the Special Issue Frontiers in Network Security and Cryptography)

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20 pages, 367 KiB

Open AccessArticle

Design Efficiency of the Asymmetric Minimum Projection Uniform Designs

by Qiming Bai, Hongyi Li, Shixian Zhang and Jiezhong Tian

Mathematics 2023, 11(3), 765; https://doi.org/10.3390/math11030765 - 03 Feb 2023

Cited by 1 | Viewed by 985

Abstract

Highly efficient designs and uniform designs are widely applied in many fields because of their good properties. The purpose of this paper is to study the issue of design efficiency for asymmetric minimum projection uniform designs. Based on the centered

L_{2}

discrepancy, [...] Read more.

Highly efficient designs and uniform designs are widely applied in many fields because of their good properties. The purpose of this paper is to study the issue of design efficiency for asymmetric minimum projection uniform designs. Based on the centered

L_{2}

discrepancy, the uniformity of the designs with mixed levels is defined, which is used to measure the projection uniformity of the designs. The analytical relationship between the uniformity pattern and the design efficiency is established for mixed-level orthogonal arrays with a strength of two. Moreover, a tight lower bound of the uniformity pattern is presented. The research is relevant in the field of experimental design by providing a theoretical basis for constructing the minimum number of projection uniform designs with a high design efficiency under a certain condition. These conclusions are verified by some numerical examples, which illustrate the theoretical results obtained in this paper. Full article

(This article belongs to the Special Issue Distribution Theory and Application)

25 pages, 358 KiB

Open AccessArticle

Limit Theorem for Spectra of Laplace Matrix of Random Graphs

by Alexander N. Tikhomirov

Mathematics 2023, 11(3), 764; https://doi.org/10.3390/math11030764 - 02 Feb 2023

Cited by 1 | Viewed by 1057

Abstract

We consider the limit of the empirical spectral distribution of Laplace matrices of generalized random graphs. Applying the Stieltjes transform method, we prove under general conditions that the limit spectral distribution of Laplace matrices converges to the free convolution of the semicircular law [...] Read more.

We consider the limit of the empirical spectral distribution of Laplace matrices of generalized random graphs. Applying the Stieltjes transform method, we prove under general conditions that the limit spectral distribution of Laplace matrices converges to the free convolution of the semicircular law and the normal law. Full article

(This article belongs to the Special Issue Limit Theorems of Probability Theory)

19 pages, 335 KiB

Open AccessArticle

Convergence Analysis for Yosida Variational Inclusion Problem with Its Corresponding Yosida Resolvent Equation Problem through Inertial Extrapolation Scheme

by Arvind Kumar Rajpoot, Mohd Ishtyak, Rais Ahmad, Yuanheng Wang and Jen-Chih Yao

Mathematics 2023, 11(3), 763; https://doi.org/10.3390/math11030763 - 02 Feb 2023

Cited by 2 | Viewed by 1091

Abstract

In this paper, we study a Yosida variational inclusion problem with its corresponding Yosida resolvent equation problem. We mention some schemes to solve both the problems, but we focus our study on discussing convergence criteria for the Yosida variational inclusion problem in real [...] Read more.

In this paper, we study a Yosida variational inclusion problem with its corresponding Yosida resolvent equation problem. We mention some schemes to solve both the problems, but we focus our study on discussing convergence criteria for the Yosida variational inclusion problem in real Banach space and for the Yosida resolvent equation problem in q-uniformly smooth Banach space. For faster convergence, we apply an inertial extrapolation scheme for both the problems. An example is provided. Full article

(This article belongs to the Special Issue Applied Functional Analysis and Applications)

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15 pages, 666 KiB

Open AccessArticle

A Conway–Maxwell–Poisson Type Generalization of Hypergeometric Distribution

by Sudip Roy, Ram C. Tripathi and Narayanaswamy Balakrishnan

Mathematics 2023, 11(3), 762; https://doi.org/10.3390/math11030762 - 02 Feb 2023

Viewed by 1352

Abstract

The hypergeometric distribution has gained its importance in practice as it pertains to sampling without replacement from a finite population. It has been used to estimate the population size of rare species in ecology, discrete failure rate in reliability, fraction defective in quality [...] Read more.

The hypergeometric distribution has gained its importance in practice as it pertains to sampling without replacement from a finite population. It has been used to estimate the population size of rare species in ecology, discrete failure rate in reliability, fraction defective in quality control, and the number of initial faults present in software coding. Recently, Borges et al. considered a COM type generalization of the binomial distribution, called COM–Poisson–Binomial (CMPB) and investigated many of its characteristics and some interesting applications. In the same spirit, we develop here a generalization of the hypergeometric distribution, called the COM–hypergeometric distribution. We discuss many of its characteristics such as the limiting forms, the over- and underdispersion, and the behavior of its failure rate. We write its probability-generating function (pgf) in the form of Kemp’s family of distributions when the newly introduced shape parameter is a positive integer. In this form, closed-form expressions are derived for its mean and variance. Finally, we develop statistical inference procedures for the model parameters and illustrate the results by extensive Monte Carlo simulations. Full article

(This article belongs to the Special Issue Distribution Theory and Application)

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25 pages, 14006 KiB

Open AccessArticle

Design of Confidence-Integrated Denoising Auto-Encoder for Personalized Top-N Recommender Systems

by Zeshan Aslam Khan, Naveed Ishtiaq Chaudhary, Waqar Ali Abbasi, Sai Ho Ling and Muhammad Asif Zahoor Raja

Mathematics 2023, 11(3), 761; https://doi.org/10.3390/math11030761 - 02 Feb 2023

Cited by 2 | Viewed by 1375

Abstract

A recommender system not only “gains users’ confidence” but also helps them in other ways, such as reducing their time spent and effort. To gain users’ confidence, one of the main goals of recommender systems in an e-commerce industry is to estimate the [...] Read more.

A recommender system not only “gains users’ confidence” but also helps them in other ways, such as reducing their time spent and effort. To gain users’ confidence, one of the main goals of recommender systems in an e-commerce industry is to estimate the users’ interest by tracking the users’ transactional behavior to provide a fast and highly related set of top recommendations out of thousands of products. The standard ranking-based models, i.e., the denoising auto-encoder (DAE) and collaborative denoising auto-encoder (CDAE), exploit positive-only feedback without utilizing the ratings’ ranks for the full set of observed ratings. To confirm the rank of observed ratings (either low or high), a confidence value for each rating is required. Hence, an improved, confidence-integrated DAE is proposed to enhance the performance of the standard DAE for solving recommender systems problems. The correctness of the proposed method is authenticated using two standard MovieLens datasets such as ML-1M and ML-100K. The proposed study acts as a vital contribution for the design of an efficient, robust, and accurate algorithm by learning prominent latent features used for fast and accurate recommendations. The proposed model outperforms the state-of-the-art methods by achieving improved P@10, R@10, NDCG@10, and MAP scores. Full article

(This article belongs to the Special Issue Mathematical Modeling in Industrial Engineering and Electrical Engineering, 2nd Edition)

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20 pages, 595 KiB

Open AccessArticle

5G Multi-Slices Bi-Level Resource Allocation by Reinforcement Learning

by Zhipeng Yu, Fangqing Gu, Hailin Liu and Yutao Lai

Mathematics 2023, 11(3), 760; https://doi.org/10.3390/math11030760 - 02 Feb 2023

Cited by 1 | Viewed by 1460

Abstract

As the centralized unit (CU)—distributed unit (DU) separation in the fifth generation mobile network (5G), the multi-slice and multi-scenario, can be better applied in wireless communication. The development of the 5G network to vertical industries makes its resource allocation also have an obvious [...] Read more.

As the centralized unit (CU)—distributed unit (DU) separation in the fifth generation mobile network (5G), the multi-slice and multi-scenario, can be better applied in wireless communication. The development of the 5G network to vertical industries makes its resource allocation also have an obvious hierarchical structure. In this paper, we propose a bi-level resource allocation model. The up-level objective in this model refers to the profit of the 5G operator through the base station allocating resources to slices. The lower-level objective in this model refers to the slices allocating the resource to its users fairly. The resource allocation problem is a complex optimization problem with mixed-discrete variables, so whether a resource allocation algorithm can quickly and accurately give the resource allocation scheme is the key to its practical application. According to the characteristics of the problem, we select the multi-agent twin delayed deep deterministic policy gradient (MATD3) to solve the upper slice resource allocation and the discrete and continuous twin delayed deep deterministic policy gradient (DCTD3) to solve the lower user resource allocation. It is crucial to accurately characterize the state, environment, and reward of reinforcement learning for solving practical problems. Thus, we provide an effective definition of the environment, state, action, and reward of MATD3 and DCTD3 for solving the bi-level resource allocation problem. We conduct some simulation experiments and compare it with the multi-agent deep deterministic policy gradient (MADDPG) algorithm and nested bi-level evolutionary algorithm (NBLEA). The experimental results show that the proposed algorithm can quickly provide a better resource allocation scheme. Full article

(This article belongs to the Special Issue Emerging Topics in Machine Learning, Image Processing and Pattern Recognition for AI-Related Applications)

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Mathematics, Volume 11, Issue 3 (February-1 2023) – 297 articles

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