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Mathematics, Volume 10, Issue 21 (November-1 2022) – 245 articles

Cover Story (view full-size image): A diffusion-taking value in probability measures on undirected graphs is studied, and applications are presented. The masses on vertices satisfy the stochastic differential equation dx= ∑jN(i) \({\sqrt{x_{i} x_{j}}}\) dBij, where {Bij}  are independent Brownian motions with skew symmetry and N(i) is the neighbour of the vertex i. A dual Markov chain of the diffusion on ordered non-negative integer partitions is effectively used. A chain at a state a = (a1, ..., a|V|), where ai is the number of particles at i, jumps to aei + ej with rate ai(ai − 1)/2 if i and j are adjacent. For this cycle graph, possible transitions from (0, 2, 0, 1), a partition of 3, are shown in the right. A collision occurs between two particles in vertex 2, and one of them moves to one of the adjacent vertices: 1 or 3. View this paper
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Article
Joint Optimization of Multi-Cycle Timetable Considering Supply-to-Demand Relationship and Energy Consumption for Rail Express
Mathematics 2022, 10(21), 4164; https://doi.org/10.3390/math10214164 - 07 Nov 2022
Viewed by 582
Abstract
Rail expresses play a vital role in intracity and intercity transportations. For accommodating multi-source passenger traffic with different travel demand, while optimizing the energy consumption, we propose a multi-cycle train timetable optimization model and a decomposition algorithm. A periodized spatial-temporal network that can [...] Read more.
Rail expresses play a vital role in intracity and intercity transportations. For accommodating multi-source passenger traffic with different travel demand, while optimizing the energy consumption, we propose a multi-cycle train timetable optimization model and a decomposition algorithm. A periodized spatial-temporal network that can support the integrated optimization of passenger service satisfaction and energy consumption considering multi-cycles is studied as the basis of the modeling. Based on this, an integrated optimization model taking the planning of the train spatial-temporal path, cycle length and active lines as variables is proposed. Then, for solving the issues caused by the complex relationships among the cycle length, line and train spatial-temporal path in large-scale cases, a hybrid heuristic Lagrangian decomposition method is investigated. Numerical experiments under different passenger flow demand scenarios are performed. The results show that the more fluctuating the passenger flow is, the more obvious the advantage of a multi-cycle timetable is. For the scenario with two passenger flow peaks, compared to a single-cycle timetable, the demand satisfaction ratio of the multi-cycle timetable is 4.44% higher and the train vacancy rate is 11.49% lower. A multi-cycle timetable also saves 3.24 h running time and 15,553.6 kwh energy consumption compared to a single-cycle timetable. Large-scale real cases show that this advantage still exists in practice. Full article
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Article
Efficient Nonlinear Model Predictive Control of Automated Vehicles
Mathematics 2022, 10(21), 4163; https://doi.org/10.3390/math10214163 - 07 Nov 2022
Viewed by 797
Abstract
In this paper, an efficient model predictive control (MPC) of velocity tracking of automated vehicles is proposed, in which a reference signal is given a priori. Five degree-of-freedom vehicle dynamics with nonlinear tires is chosen as the prediction model, in which coupling [...] Read more.
In this paper, an efficient model predictive control (MPC) of velocity tracking of automated vehicles is proposed, in which a reference signal is given a priori. Five degree-of-freedom vehicle dynamics with nonlinear tires is chosen as the prediction model, in which coupling characteristics of longitudinal and lateral dynamics are taken into account. In order to balance computational burden and prediction accuracy, Koopman operator theory is adopted to transform the nonlinear model into a global linear model. Then, the global linear model is used in the design of MPC to reduce online computational burden and avoid solving nonconvex/nonlinear optimization problems. Furthermore, the effectiveness of Koopman operator in vehicle dynamics control is verified using a Matlab/Simulink environment. Validation results demonstrate that dynamic mode decomposition with control (DMDc) and extended dynamic mode decomposition (EDMD) algorithms are more accurate in model validation and dynamic prediction than local linearization, and DMDc algorithm has less computational burden on solving optimization problems than the EDMD algorithm. Full article
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Review
Moth Search: Variants, Hybrids, and Applications
Mathematics 2022, 10(21), 4162; https://doi.org/10.3390/math10214162 - 07 Nov 2022
Viewed by 483
Abstract
Moth search (MS) is a nature-inspired metaheuristic optimization algorithm based on the most representative characteristics of moths, Lévy flights and phototaxis. Phototaxis signifies a movement which organism towards or away from a source of light, which is the representative features for moths. The [...] Read more.
Moth search (MS) is a nature-inspired metaheuristic optimization algorithm based on the most representative characteristics of moths, Lévy flights and phototaxis. Phototaxis signifies a movement which organism towards or away from a source of light, which is the representative features for moths. The best moth individual is seen as the light source in Moth search. The moths that have a smaller distance from the best one will fly around the best individual by Lévy flights. For reasons of phototaxis, the moths, far from the fittest one, will fly towards the best one with a big step. These two features, Lévy flights and phototaxis, correspond to the processes of exploitation and exploration for metaheuristic optimization. The superiority of the moth search has been demonstrated in many benchmark problems and various application areas. A comprehensive survey of the moth search was conducted in this paper, which included the three sections: statistical research studies about moth search, different variants of moth search, and engineering optimization/applications. The future insights and development direction in the area of moth search are also discussed. Full article
(This article belongs to the Special Issue Biologically Inspired Computing)
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Article
An Approach Based on Semantic Relationship Embeddings for Text Classification
Mathematics 2022, 10(21), 4161; https://doi.org/10.3390/math10214161 - 07 Nov 2022
Viewed by 577
Abstract
Semantic relationships between words provide relevant information about the whole idea in the texts. Existing embedding representation models characterize each word as a vector of numbers with a fixed length. These models have been used in tasks involving text classification, such as recommendation [...] Read more.
Semantic relationships between words provide relevant information about the whole idea in the texts. Existing embedding representation models characterize each word as a vector of numbers with a fixed length. These models have been used in tasks involving text classification, such as recommendation and question–answer systems. However, the embedded information provided by semantic relationships has been neglected. Therefore, this paper proposes an approach that involves semantic relationships in embedding models for text classification, which is evaluated. Three embedding models based on semantic relations extracted from Wikipedia are presented and compared with existing word-based models. Our approach considers the following relationships: synonymy, hyponymy, and hyperonymy. They were considered since previous experiments have shown that they provide semantic knowledge. The relationships are extracted from Wikipedia using lexical-syntactic patterns identified in the literature. The extracted relationships are embedded as a vector: synonymy, hyponymy–hyperonymy, and a combination of all relationships. A Convolutional Neural Network using semantic relationship embeddings was trained for text classification. An evaluation was carried out for the proposed relationship embedding configurations and existing word-based models to compare them based on two corpora. The results were obtained with the metrics of precision, accuracy, recall, and F1-measure. The best results for the 20-Newsgroup corpus were obtained with the hyponymy–hyperonymy embeddings, achieving an accuracy of 0.79. For the Reuters corpus, F1-measure and recall of 0.87 were obtained using synonymy–hyponymy–hyperonymy. Full article
Article
Deep 3D Volumetric Model Genesis for Efficient Screening of Lung Infection Using Chest CT Scans
Mathematics 2022, 10(21), 4160; https://doi.org/10.3390/math10214160 - 07 Nov 2022
Viewed by 513
Abstract
In the present outbreak of COVID-19, radiographic imaging modalities such as computed tomography (CT) scanners are commonly used for visual assessment of COVID-19 infection. However, personal assessment of CT images is a time-taking process and demands expert radiologists. Recent advancement in artificial intelligence [...] Read more.
In the present outbreak of COVID-19, radiographic imaging modalities such as computed tomography (CT) scanners are commonly used for visual assessment of COVID-19 infection. However, personal assessment of CT images is a time-taking process and demands expert radiologists. Recent advancement in artificial intelligence field has achieved remarkable performance of computer-aided diagnosis (CAD) methods. Therefore, various deep learning-driven CAD solutions have been proposed for the automatic diagnosis of COVID-19 infection. However, most of them consider limited number of data samples to develop and validate their methods. In addition, various existing methods employ image-based models considering only spatial information in making a diagnostic decision in case of 3D volumetric data. To address these limitations, we propose a dilated shuffle sequential network (DSS-Net) that considers both spatial and 3D structural features in case of volumetric CT data and makes an effective diagnostic decision. To calculate the performance of the proposed DSS-Net, we combined three publicly accessible datasets that include large number of positive and negative data samples. Finally, our DSS-Net exhibits the average performance of 96.58%, 96.53%, 97.07%, 96.01%, and 98.54% in terms of accuracy, F1-score, average precision, average recall, and area under the curve, respectively, and outperforms various state-of-the-art methods. Full article
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Article
Local Non-Similar Solutions for Boundary Layer Flow over a Nonlinear Stretching Surface with Uniform Lateral Mass Flux: Utilization of Third Level of Truncation
Mathematics 2022, 10(21), 4159; https://doi.org/10.3390/math10214159 - 07 Nov 2022
Viewed by 453
Abstract
The present study aims to examine the effects of uniform lateral mass flux on the boundary layer flow induced by a non-linearly stretching surface. For uniform mass flux, the boundary layer flow does not conform to a similarity solution. The problem may be [...] Read more.
The present study aims to examine the effects of uniform lateral mass flux on the boundary layer flow induced by a non-linearly stretching surface. For uniform mass flux, the boundary layer flow does not conform to a similarity solution. The problem may be resolved by the similarity solution only when the transverse velocity at the boundary of the porous stretching surface is of the form vwxp12. In other words, the flow becomes non-similar; to date, this has not been reported in the literature. That is why, in the current study, the local-similarity approximation up to the third level of truncation is utilized to solve the problem. The pseudo-similarity variable, stream function and transformed streamwise coordinate are defined such that the continuity equation is identically satisfied, and the momentum equation reduces to a non-similar dimensionless boundary layer equation. We derived the non-similar equations of the first, second and third levels of truncations and compared the numerical results obtained from different levels of truncations. In order to find numerical solutions to these equations, the built-in MATLAB routine, known as bvp4c, is used. Further, all non-similar terms that appear in the momentum equations are retained without any approximations. The approximations are introduced only in the subsidiary equations and relative boundary conditions. For the case of suction, the rate of increase in the numerical values of skin friction coefficient obtained from the first level of truncation with increasing velocity index parameter is found to be underestimated, while overestimation is found in the case of injection. The numerical results that were obtained from the third level of truncations are plotted against the embedding physical parameters and are then discussed. Full article
(This article belongs to the Special Issue Computational Fluid Dynamics II)
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Article
Asymptotic Expansions for Symmetric Statistics with Degenerate Kernels
Mathematics 2022, 10(21), 4158; https://doi.org/10.3390/math10214158 - 07 Nov 2022
Viewed by 478
Abstract
Asymptotic expansions for U-statistics and V-statistics with degenerate kernels are investigated, respectively, and the remainder term O(n1p/2), for some p4, is shown in both cases. From the results, it is obtained [...] Read more.
Asymptotic expansions for U-statistics and V-statistics with degenerate kernels are investigated, respectively, and the remainder term O(n1p/2), for some p4, is shown in both cases. From the results, it is obtained that asymptotic expansions for the Crame´r–von Mises statistics of the uniform distribution U(0,1) hold with the remainder term On1p/2 for any p4. The scheme of the proof is based on three steps. The first one is the almost sure convergence in a Fourier series expansion of the kernel function u(x,y). The key condition for the convergence is the nuclearity of a linear operator Tu defined by the kernel function. The second one is a representation of U-statistics or V-statistics by single sums of Hilbert space valued random variables. The third one is to apply asymptotic expansions for single sums of Hilbert space valued random variables. Full article
(This article belongs to the Special Issue Limit Theorems of Probability Theory)
Article
Framework for Integrated Use of Agent-Based and Ambient-Oriented Modeling
Mathematics 2022, 10(21), 4157; https://doi.org/10.3390/math10214157 - 07 Nov 2022
Viewed by 460
Abstract
Agent-based modeling (ABM) is a flexible and simulation-friendly modeling approach. Ambient-oriented modeling is effective for systems containing ambient and spatial representations. In this paper we propose a framework for the integrated use of agent-based modeling and ambient-oriented modeling. We analyze both agents and [...] Read more.
Agent-based modeling (ABM) is a flexible and simulation-friendly modeling approach. Ambient-oriented modeling is effective for systems containing ambient and spatial representations. In this paper we propose a framework for the integrated use of agent-based modeling and ambient-oriented modeling. We analyze both agents and ambient in detail. We also compare both modeling approaches as well and analyze their similarities and differences. The integrated implementation provides a new link between mathematical modeling and simulations. The model developed using this framework has four parts. The first part constitutes the identification, definition, and relations of agents. In this part, we use agent-based modeling along with the concepts of discrete-event simulations and system dynamics. The second part of the model is the mathematical representation of the relations of agents, i.e., the parent and child relation of agents. The third part of the model is the representation of the messages along with relational symbols where we utilize the concepts and symbols of relations and messages from ambient-oriented modeling. The fourth and final part of the model is the simulation, where we describe the rules that govern the processes represented in first two parts. The framework is helpful in overcoming certain limitations of both approaches. Moreover, we provide a scenario of a bus rapid transit system (BRTS) as a proof of concept, and we examine the generic concept of BRTSs using the proposed framework. Full article
(This article belongs to the Special Issue Modeling and Simulation in Dynamical Systems)
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Article
Kinematic Modes Identification and Its Intelligent Control of Micro-Nano Particle Manipulated by Acoustic Signal
Mathematics 2022, 10(21), 4156; https://doi.org/10.3390/math10214156 - 07 Nov 2022
Viewed by 406
Abstract
In this paper, the dynamics of a micro-nano particle on the micro-thin plate driven by an acoustic signal was investigated, including the particle kinematics mode, kinematics equation, and trajectory control. According to Newton’s kinematic theorem, analyzing the forces acting on the particle, the [...] Read more.
In this paper, the dynamics of a micro-nano particle on the micro-thin plate driven by an acoustic signal was investigated, including the particle kinematics mode, kinematics equation, and trajectory control. According to Newton’s kinematic theorem, analyzing the forces acting on the particle, the kinematic modes of the driven particle are distinguished with specific mathematical conditions, which are classified as slide, bounce, and stable modes strictly planned on a thin plate area. Based on the theory of kinematic modal analysis, the simulation results reveal the distribution rules of particle motion modes against the driving signal or plate geometry. The particle kinematics equation governing the sliding movement on the thin plate was then derived in light of the interaction between the particle and driving signal, based on which, the particle trajectory was drawn and analyzed in detail. For the purpose of controlling the particle trajectory, the control problem was designed in accordance with a linear active disturbance rejection controller (LADRC). Further, a guidance law was proposed, and the corresponding controller was designed to realize the linear trajectory following. Full article
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Article
Community Detection Fusing Graph Attention Network
Mathematics 2022, 10(21), 4155; https://doi.org/10.3390/math10214155 - 07 Nov 2022
Viewed by 484
Abstract
It has become a tendency to use a combination of autoencoders and graph neural networks for attribute graph clustering to solve the community detection problem. However, the existing methods do not consider the influence differences between node neighborhood information and high-order neighborhood information, [...] Read more.
It has become a tendency to use a combination of autoencoders and graph neural networks for attribute graph clustering to solve the community detection problem. However, the existing methods do not consider the influence differences between node neighborhood information and high-order neighborhood information, and the fusion of structural and attribute features is insufficient. In order to make better use of structural information and attribute information, we propose a model named community detection fusing graph attention network (CDFG). Specifically, we firstly use an autoencoder to learn attribute features. Then the graph attention network not only calculates the influence weight of the neighborhood node on the target node but also adds the high-order neighborhood information to learn the structural features. After that, the two features are initially fused by the balance parameter. The feature fusion module extracts the hidden layer representation of the graph attention layer to calculate the self-correlation matrix, which is multiplied by the node representation obtained by the preliminary fusion to achieve secondary fusion. Finally, the self-supervision mechanism makes it face the community detection task. Experiments are conducted on six real datasets. Using four evaluation metrics, the CDFG model performs better on most datasets, especially for the networks with longer average paths and diameters and smaller clustering coefficients. Full article
(This article belongs to the Special Issue Computational Intelligence: Theory and Applications)
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Article
Enhanced Marine Predators Algorithm for Solving Global Optimization and Feature Selection Problems
Mathematics 2022, 10(21), 4154; https://doi.org/10.3390/math10214154 - 07 Nov 2022
Cited by 1 | Viewed by 464
Abstract
Feature selection (FS) is applied to reduce data dimensions while retaining much information. Many optimization methods have been applied to enhance the efficiency of FS algorithms. These approaches reduce the processing time and improve the accuracy of the learning models. In this paper, [...] Read more.
Feature selection (FS) is applied to reduce data dimensions while retaining much information. Many optimization methods have been applied to enhance the efficiency of FS algorithms. These approaches reduce the processing time and improve the accuracy of the learning models. In this paper, a developed method called MPAO based on the marine predators algorithm (MPA) and the “narrowed exploration” strategy of the Aquila optimizer (AO) is proposed to handle FS, global optimization, and engineering problems. This modification enhances the exploration behavior of the MPA to update and explore the search space. Therefore, the narrowed exploration of the AO increases the searchability of the MPA, thereby improving its ability to obtain optimal or near-optimal results, which effectively helps the original MPA overcome the local optima issues in the problem domain. The performance of the proposed MPAO method is evaluated on solving FS and global optimization problems using some evaluation criteria, including the maximum value (Max), minimum value (Min), and standard deviation (Std) of the fitness function. Furthermore, the results are compared to some meta-heuristic methods over four engineering problems. Experimental results confirm the efficiency of the proposed MPAO method in solving FS, global optimization, and engineering problems. Full article
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Article
Interpretable Deep Learning for Discriminating Pneumonia from Lung Ultrasounds
Mathematics 2022, 10(21), 4153; https://doi.org/10.3390/math10214153 - 06 Nov 2022
Viewed by 692
Abstract
Lung ultrasound images have shown great promise to be an operative point-of-care test for the diagnosis of COVID-19 because of the ease of procedure with negligible individual protection equipment, together with relaxed disinfection. Deep learning (DL) is a robust tool for modeling infection [...] Read more.
Lung ultrasound images have shown great promise to be an operative point-of-care test for the diagnosis of COVID-19 because of the ease of procedure with negligible individual protection equipment, together with relaxed disinfection. Deep learning (DL) is a robust tool for modeling infection patterns from medical images; however, the existing COVID-19 detection models are complex and thereby are hard to deploy in frequently used mobile platforms in point-of-care testing. Moreover, most of the COVID-19 detection models in the existing literature on DL are implemented as a black box, hence, they are hard to be interpreted or trusted by the healthcare community. This paper presents a novel interpretable DL framework discriminating COVID-19 infection from other cases of pneumonia and normal cases using ultrasound data of patients. In the proposed framework, novel transformer modules are introduced to model the pathological information from ultrasound frames using an improved window-based multi-head self-attention layer. A convolutional patching module is introduced to transform input frames into latent space rather than partitioning input into patches. A weighted pooling module is presented to score the embeddings of the disease representations obtained from the transformer modules to attend to information that is most valuable for the screening decision. Experimental analysis of the public three-class lung ultrasound dataset (PCUS dataset) demonstrates the discriminative power (Accuracy: 93.4%, F1-score: 93.1%, AUC: 97.5%) of the proposed solution overcoming the competing approaches while maintaining low complexity. The proposed model obtained very promising results in comparison with the rival models. More importantly, it gives explainable outputs therefore, it can serve as a candidate tool for empowering the sustainable diagnosis of COVID-19-like diseases in smart healthcare. Full article
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Article
Framework for Classroom Student Grading with Open-Ended Questions: A Text-Mining Approach
Mathematics 2022, 10(21), 4152; https://doi.org/10.3390/math10214152 - 06 Nov 2022
Viewed by 668
Abstract
The purpose of this paper is to present a framework based on text-mining techniques to support teachers in their tasks of grading texts, compositions, or essays, which form the answers to open-ended questions (OEQ). The approach assumes that OEQ must be used as [...] Read more.
The purpose of this paper is to present a framework based on text-mining techniques to support teachers in their tasks of grading texts, compositions, or essays, which form the answers to open-ended questions (OEQ). The approach assumes that OEQ must be used as a learning and evaluation instrument with increasing frequency. Given the time-consuming grading process for those questions, their large-scale use is only possible when computational tools can help the teacher. This work assumes that the grading decision is entirely a teacher’s task responsibility, not the result of an automatic grading process. In this context, the teacher is the author of questions to be included in the tests, administration and results assessment, the entire cycle for this process being noticeably short: a few days at most. An attempt is made to address this problem. The method is entirely exploratory, descriptive and data-driven, the only data assumed as inputs being the texts of essays and compositions created by the students when answering OEQ for a single test on a specific occasion. Typically, the process involves exceedingly small data volumes measured by the power of current home computers, but big data when compared with human capabilities. The general idea is to use software to extract useful features from texts, perform lengthy and complex statistical analyses and present the results to the teacher, who, it is believed, will combine this information with his or her knowledge and experience to make decisions on mark allocation. A generic path model is formulated to represent that specific context and the kind of decisions and tasks a teacher should perform, the estimated results being synthesised using graphic displays. The method is illustrated by analysing three corpora of 126 texts originating in three different real learning contexts, time periods, educational levels and disciplines. Full article
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Article
Existence, Uniqueness and Stability Analysis with the Multiple Exp Function Method for NPDEs
Mathematics 2022, 10(21), 4151; https://doi.org/10.3390/math10214151 - 06 Nov 2022
Viewed by 437
Abstract
In this study, firstly, through an alternative theorem, we study the existence and uniqueness of solution of some nonlinear PDEs and then investigate the Ulam–Hyers–Rassias stability of solution. Secondly, we apply a relatively novel analytical technique, the multiple exp function method, to obtain [...] Read more.
In this study, firstly, through an alternative theorem, we study the existence and uniqueness of solution of some nonlinear PDEs and then investigate the Ulam–Hyers–Rassias stability of solution. Secondly, we apply a relatively novel analytical technique, the multiple exp function method, to obtain the multiple wave solutions of presented nonlinear equations. Finally, we propose the numerical results on tables and discuss the advantages and disadvantages of the method. Full article
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Article
Multibranch Attention Mechanism Based on Channel and Spatial Attention Fusion
Mathematics 2022, 10(21), 4150; https://doi.org/10.3390/math10214150 - 06 Nov 2022
Cited by 1 | Viewed by 488
Abstract
Recently, it has been demonstrated that the performance of an object detection network can be improved by embedding an attention module into it. In this work, we propose a lightweight and effective attention mechanism named multibranch attention (M3Att). For the input feature map, [...] Read more.
Recently, it has been demonstrated that the performance of an object detection network can be improved by embedding an attention module into it. In this work, we propose a lightweight and effective attention mechanism named multibranch attention (M3Att). For the input feature map, our M3Att first uses the grouped convolutional layer with a pyramid structure for feature extraction, and then calculates channel attention and spatial attention simultaneously and fuses them to obtain more complementary features. It is a “plug and play” module that can be easily added to the object detection network and significantly improves the performance of the object detection network with a small increase in parameters. We demonstrate the effectiveness of M3Att on various challenging object detection tasks, including PASCAL VOC2007, PASCAL VOC2012, KITTI, and Zhanjiang Underwater Robot Competition. The experimental results show that this method dramatically improves the object detection effect, especially for the PASCAL VOC2007, and the mapping index of the original network increased by 4.93% when embedded in the YOLOV4 (You Only Look Once v4) network. Full article
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Article
Progressive Fracture Behavior and Acoustic Emission Release of CJBs Affected by Joint Distance Ratio
Mathematics 2022, 10(21), 4149; https://doi.org/10.3390/math10214149 - 06 Nov 2022
Cited by 3 | Viewed by 590
Abstract
The progressive collapse behavior and energy release of columnar jointed basalts (CJBs) can be greatly influenced by different joint distance ratios. By adopting the digital image correlation, a series of heterogeneous CJB models are established. The continuous fracture process and acoustic emissions (AEs) [...] Read more.
The progressive collapse behavior and energy release of columnar jointed basalts (CJBs) can be greatly influenced by different joint distance ratios. By adopting the digital image correlation, a series of heterogeneous CJB models are established. The continuous fracture process and acoustic emissions (AEs) are captured numerically under varying lateral pressures. The load curves under different joint distance ratios and model boundaries are analyzed. Meanwhile, the strength, deformation modulus and AE rule are discussed. The data indicate that under plane strain, the troughs of compression strength appear at the column dip angle β = 30°, 150°, 210° or 330°; the equivalent deformation modulus changes in an elliptical way with β increasing; the compression strength and equivalent deformation modulus are higher than the case between plane stress and plane strain under different joint distance ratios. When β = 30°, the accumulation of AE energy corresponding to the stress peak under plane strain are higher than the case between plane stress and plane strain but becomes lower when β increases to 60°, which implies the critical transformation of the AE energy-related failure precursor affected by column dip angle. These achievements will contribute to the design, construction and support of slopes and tunnels encountering CJBs. Full article
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Article
Mathematical Correlation Study of Nanofluid Flow Merging Points in Entrance Regions
Mathematics 2022, 10(21), 4148; https://doi.org/10.3390/math10214148 - 06 Nov 2022
Viewed by 404
Abstract
Here, hydrodynamic features of laminar forced nanofluid flow between two parallel plates are numerically investigated, and the results are mathematically discussed. The conventional understanding of developing flow in the entrance region of internal flows is based on the idea that boundary layers start [...] Read more.
Here, hydrodynamic features of laminar forced nanofluid flow between two parallel plates are numerically investigated, and the results are mathematically discussed. The conventional understanding of developing flow in the entrance region of internal flows is based on the idea that boundary layers start forming at the inlet and merge at some point just before the fully developed section. However, because of the consideration of mass and flow conservation, the entire conception is required to be detailed with appropriate criteria according to the numerical simulations. Hence, nanofluid flow between two parallel plates is solved by ANSYS Fluent 19.3 for laminar forced in an isothermal condition. Two major criteria are studied to find the location of the boundary layer merging points: vorticity and velocity gradient in a direction perpendicular to the flow. The former presents the influential area of wall shear stress, and the latter is the direct infusion of the boundary layer induced by the solid walls. Vorticity for an irrotational flow is obtained by calculating the curl of the velocity. It is found that the merging points for the hydrodynamic boundary layers are considered before the fully developed region. For the first time, in this study, the results of various Reynolds numbers are collected, and correlations are proposed to predict the length of the boundary layer merging location by using a regression analysis of the data. Full article
(This article belongs to the Special Issue Mathematical Methods on Mechanical Engineering)
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Article
Employing Quantum Fruit Fly Optimization Algorithm for Solving Three-Dimensional Chaotic Equations
Mathematics 2022, 10(21), 4147; https://doi.org/10.3390/math10214147 - 06 Nov 2022
Cited by 2 | Viewed by 508
Abstract
In a chaotic system, deterministic, nonlinear, irregular, and initial-condition-sensitive features are desired. Due to its chaotic nature, it is difficult to quantify a chaotic system’s parameters. Parameter estimation is a major issue because it depends on the stability analysis of a chaotic system, [...] Read more.
In a chaotic system, deterministic, nonlinear, irregular, and initial-condition-sensitive features are desired. Due to its chaotic nature, it is difficult to quantify a chaotic system’s parameters. Parameter estimation is a major issue because it depends on the stability analysis of a chaotic system, and communication systems that are based on chaos make it difficult to give accurate estimates or a fast rate of convergence. Several nature-inspired metaheuristic algorithms have been used to estimate chaotic system parameters; however, many are unable to balance exploration and exploitation. The fruit fly optimization algorithm (FOA) is not only efficient in solving difficult optimization problems, but also simpler and easier to construct than other currently available population-based algorithms. In this study, the quantum fruit fly optimization algorithm (QFOA) was suggested to find the optimum values for chaotic parameters that would help algorithms converge faster and avoid the local optimum. The recommended technique used quantum theory probability and uncertainty to overcome the classic FA’s premature convergence and local optimum trapping. QFOA modifies the basic Newtonian-based search technique of FA by including a quantum behavior-based searching mechanism used to pinpoint the position of the fruit fly swarm. The suggested model has been assessed using a well-known Lorenz system with a specified set of parameter values and benchmarked signals. The results showed a considerable improvement in the accuracy of parameter estimates and better estimation power than state-of-the art parameter estimation approaches. Full article
(This article belongs to the Special Issue Advanced Artificial Intelligence Models and Its Applications)
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Article
A Genetic Hyper-Heuristic for an Order Scheduling Problem with Two Scenario-Dependent Parameters in a Parallel-Machine Environment
Mathematics 2022, 10(21), 4146; https://doi.org/10.3390/math10214146 - 06 Nov 2022
Viewed by 432
Abstract
Studies on the customer order scheduling problem have been attracting increasing attention. Most current approaches consider that either component processing times for customer orders on each machine are constant or all customer orders are available at the outset of production planning. However, these [...] Read more.
Studies on the customer order scheduling problem have been attracting increasing attention. Most current approaches consider that either component processing times for customer orders on each machine are constant or all customer orders are available at the outset of production planning. However, these assumptions do not hold in real-world applications. Uncertainty may be caused by multiple issues including a machine breakdown, the working environment changing, and workers’ instability. On the basis of these factors, we introduced a parallel-machine customer order scheduling problem with two scenario-dependent component processing times, due dates, and ready times. The objective was to identify an appropriate and robust schedule for minimizing the maximum of the sum of weighted numbers of tardy orders among the considered scenarios. To solve this difficult problem, we derived a few dominant properties and a lower bound for determining an optimal solution. Subsequently, we considered three variants of Moore’s algorithm, a genetic algorithm, and a genetic-algorithm-based hyper-heuristic that incorporated the proposed seven low-level heuristics to solve this problem. Finally, the performances of all proposed algorithms were evaluated. Full article
(This article belongs to the Special Issue Combinatorial Optimization Problems in Planning and Decision Making)
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Article
Generalized Spacelike Normal Curves in Minkowski Three-Space
Mathematics 2022, 10(21), 4145; https://doi.org/10.3390/math10214145 - 06 Nov 2022
Viewed by 422
Abstract
Equiform geometry is considered an extension of other geometries. Furthermore, an equiform frame is a generalization of the Frenet frame. In this study, we begin by defining the term “equiform parameter (EQP)”, “equiform frame”, and “equiform formulas (EQF)” in regard to the Minkowski [...] Read more.
Equiform geometry is considered an extension of other geometries. Furthermore, an equiform frame is a generalization of the Frenet frame. In this study, we begin by defining the term “equiform parameter (EQP)”, “equiform frame”, and “equiform formulas (EQF)” in regard to the Minkowski three-space. Second, we define spacelike normal curves (SPN) in Minkowski three-space and present a variety of descriptions of these curves with equiform spacelike (EQS) or equiform timelike (EQN) principal normals in Minkowski three-space. Third, we discuss the implications of these findings. Finally, an example is given to illustrate our theoretical results. Full article
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Article
Deep Neural Network Memory Performance and Throughput Modeling and Simulation Framework
Mathematics 2022, 10(21), 4144; https://doi.org/10.3390/math10214144 - 06 Nov 2022
Viewed by 602
Abstract
Deep neural networks (DNNs) are widely used in various artificial intelligence applications and platforms, such as sensors in internet of things (IoT) devices, speech and image recognition in mobile systems, and web searching in data centers. While DNNs achieve remarkable prediction accuracy, they [...] Read more.
Deep neural networks (DNNs) are widely used in various artificial intelligence applications and platforms, such as sensors in internet of things (IoT) devices, speech and image recognition in mobile systems, and web searching in data centers. While DNNs achieve remarkable prediction accuracy, they introduce major computational and memory bandwidth challenges due to the increasing model complexity and the growing amount of data used for training and inference. These challenges introduce major difficulties not only due to the constraints of system cost, performance, and energy consumption, but also due to limitations in currently available memory bandwidth. The recent advances in semiconductor technologies have further intensified the gap between computational hardware performance and memory systems bandwidth. Consequently, memory systems are, today, a major performance bottleneck for DNN applications. In this paper, we present DRAMA, a deep neural network memory simulator. DRAMA extends the SCALE-Sim simulator for DNN inference on systolic arrays with a detailed, accurate, and extensive modeling and simulation environment of the memory system. DRAMA can simulate in detail the hierarchical main memory components—such as memory channels, modules, ranks, and banks—and related timing parameters. In addition, DRAMA can explore tradeoffs for memory system performance and identify bottlenecks for different DNNs and memory architectures. We demonstrate DRAMA’s capabilities through a set of experimental simulations based on several use cases. Full article
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Article
New Hille Type and Ohriska Type Criteria for Nonlinear Third-Order Dynamic Equations
Mathematics 2022, 10(21), 4143; https://doi.org/10.3390/math10214143 - 06 Nov 2022
Viewed by 443
Abstract
The objective of this paper is to derive new Hille type and Ohriska type criteria for third-order nonlinear dynamic functional equations in the form of [...] Read more.
The objective of this paper is to derive new Hille type and Ohriska type criteria for third-order nonlinear dynamic functional equations in the form of a2(ζ)φα2a1ζφα1xΔ(ζ)ΔΔ+q(ζ)φαx(g(ζ))=0, on a time scale T, where Δ is the forward operator on T, α1, α2, α>0, and g, q, ai, i = 1, 2, are positive rd-continuous functions on T, and φθ(u):=uθ1u. Our results in this paper are new and substantial for dynamic equations of the third order on arbitrary time scales. An example is included to illustrate the results. Full article
Article
A Weakly Nonlinear Dynamic Problem for a Model of the Thermoelastic Medium Absorbing a Part of the Acoustic Spectrum
Mathematics 2022, 10(21), 4142; https://doi.org/10.3390/math10214142 - 06 Nov 2022
Viewed by 390
Abstract
We consider a dynamic problem with a short laser impact on a semi-opaque insulated layer with free borders, accounting for the selective absorption of the acoustic spectrum regions by the media. The behavior of the material is modeled by the extended coupled thermoelasticity [...] Read more.
We consider a dynamic problem with a short laser impact on a semi-opaque insulated layer with free borders, accounting for the selective absorption of the acoustic spectrum regions by the media. The behavior of the material is modeled by the extended coupled thermoelasticity formulated in the previous work of the series. Following the experimental results, we introduce a weakly nonlinear correction to the thermal expansion coefficient. Thus, we aim to level out the inability of classical thermoelasticity (CTE) to correctly describe the deformation processes in a solid under a high-frequency impact, yet staying within the framework of linear models. The parameters of the system of novel equations can be tuned to fit the experimentally measured data, i.e., the frequency-dependent attenuation coefficient. The series solutions of the extended thermoelasticity problem are compared with those obtained within CTE. In contrast to CTE and in accordance with experiments, the model allows for the simultaneous existence of positive and negative extrema for stress over time. Full article
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Article
An Adapted Discrete Lindley Model Emanating from Negative Binomial Mixtures for Autoregressive Counts
Mathematics 2022, 10(21), 4141; https://doi.org/10.3390/math10214141 - 06 Nov 2022
Viewed by 414
Abstract
Analysing autoregressive counts over time remains a relevant and evolving matter of interest, where oftentimes the assumption of normality is made for the error terms. In the case when data are discrete, the Poisson model may be assumed for the structure of the [...] Read more.
Analysing autoregressive counts over time remains a relevant and evolving matter of interest, where oftentimes the assumption of normality is made for the error terms. In the case when data are discrete, the Poisson model may be assumed for the structure of the error terms. In order to address the equidispersion restriction of the Poisson distribution, various alternative considerations have been investigated in such an integer environment. This paper, inspired by the integer autoregressive process of order 1, incorporates negative binomial shape mixtures via a compound Poisson Lindley model for the error terms. The systematic construction of this model is offered and motivated, and is analysed comparatively against common alternate candidates with a number of simulation and data analyses. This work provides insight into noncentral-type behaviour in both the continuous Lindley model and in the discrete case for meaningful application and consideration in integer autoregressive environments. Full article
(This article belongs to the Special Issue Contemporary Contributions to Statistical Modelling and Data Science)
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Article
An Optimized Open Pit Mine Application for Limestone Quarry Production Scheduling to Maximize Net Present Value
Mathematics 2022, 10(21), 4140; https://doi.org/10.3390/math10214140 - 06 Nov 2022
Cited by 1 | Viewed by 696
Abstract
This study involves a working limestone mine that supplies limestone to the cement factory. The two main goals of this paper are to (a) determine how long an operating mine can continue to provide the cement plant with the quality and quantity of [...] Read more.
This study involves a working limestone mine that supplies limestone to the cement factory. The two main goals of this paper are to (a) determine how long an operating mine can continue to provide the cement plant with the quality and quantity of materials it needs, and (b) explore the viability of combining some limestone from a nearby mine with the study mine limestone to meet the cement plant’s quality and quantity goals. These objectives are accomplished by figuring out the maximum net profit for the ultimate pit limit and production sequencing of the mining blocks. The issues were resolved using a branch-and-cut based sequential integer and mixed integer programming problem. The study mine can exclusively feed the cement plant for up to 15 years, according to the data. However, it was also noted that the addition of the limestone from the neighboring mine substantially increased the mine’s life (85 years). The findings also showed that, when compared with the production planning formulation that the company is now using, the proposed approach creates 10% more profit. The suggested method also aids in determining the desired desirable quality of the limestone that will be transported from the nearby mine throughout each production stage. Full article
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Article
A Combined Approach of Fuzzy Cognitive Maps and Fuzzy Rule-Based Inference Supporting Freeway Traffic Control Strategies
Mathematics 2022, 10(21), 4139; https://doi.org/10.3390/math10214139 - 05 Nov 2022
Viewed by 594
Abstract
Freeway networks, despite being built to handle the transportation needs of large traffic volumes, have suffered in recent years from an increase in demand that is rarely resolvable through infrastructure improvements. Therefore, the implementation of particular control methods constitutes, in many instances, the [...] Read more.
Freeway networks, despite being built to handle the transportation needs of large traffic volumes, have suffered in recent years from an increase in demand that is rarely resolvable through infrastructure improvements. Therefore, the implementation of particular control methods constitutes, in many instances, the only viable solution for enhancing the performance of freeway traffic systems. The topic is fraught with ambiguity, and there is no tool for understanding the entire system mathematically; hence, a fuzzy suggested algorithm seems not just appropriate but essential. In this study, a fuzzy cognitive map-based model and a fuzzy rule-based system are proposed as tools to analyze freeway traffic data with the objective of traffic flow modeling at a macroscopic level in order to address congestion-related issues as the primary goal of the traffic control strategies. In addition to presenting a framework of fuzzy system-based controllers in freeway traffic, the results of this study demonstrated that a fuzzy inference system and fuzzy cognitive maps are capable of congestion level prediction, traffic flow simulation, and scenario analysis, thereby enhancing the performance of the traffic control strategies involving the implementation of ramp management policies, controlling vehicle movement within the freeway by mainstream control, and routing control. Full article
(This article belongs to the Special Issue FSTA: Fuzzy Set Theory and Applications)
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Article
Existence and Approximation of Fixed Points of Enriched φ-Contractions in Banach Spaces
Mathematics 2022, 10(21), 4138; https://doi.org/10.3390/math10214138 - 05 Nov 2022
Viewed by 574
Abstract
We introduce the class of enriched φ-contractions in Banach spaces as a natural generalization of φ-contractions and study the existence and approximation of the fixed points of mappings in this new class, which is shown to be an unsaturated class of [...] Read more.
We introduce the class of enriched φ-contractions in Banach spaces as a natural generalization of φ-contractions and study the existence and approximation of the fixed points of mappings in this new class, which is shown to be an unsaturated class of mappings in the setting of a Banach space. We illustrated the usefulness of our fixed point results by studying the existence and uniqueness of the solutions of some second order (p,q)-difference equations with integral boundary value conditions. Full article
Article
Modeling for the Relationship between Monetary Policy and GDP in the USA Using Statistical Methods
Mathematics 2022, 10(21), 4137; https://doi.org/10.3390/math10214137 - 05 Nov 2022
Viewed by 759
Abstract
The Federal Reserve has played an arguably important role in financial crises in the United States since its creation in 1913 through monetary policy tools. Thus, this paper aims to analyze the impact of monetary policy on the United States’ economic growth in [...] Read more.
The Federal Reserve has played an arguably important role in financial crises in the United States since its creation in 1913 through monetary policy tools. Thus, this paper aims to analyze the impact of monetary policy on the United States’ economic growth in the short and long run, measured by Gross Domestic Product (GDP). The Vector Autoregressive (VAR) method explores the relationship among the variables, and the Granger causality test assesses the predictability of the variables. Moreover, the Impulse Response Function (IRF) examines the behavior of one variable after a change in another, utilizing the time-series dataset from the first quarter of 1959 to the second quarter of 2022. This work demonstrates that expansionary monetary policy does have a positive impact on economic growth in the short term though it does not last long. However, in the long term, inflation, measured by the Consumer Price Index (CPI), is affected by expansionary monetary policy. Therefore, if the Federal Reserve wants to cease the expansionary monetary policy in the short run, this should be done appropriately, with the fiscal surplus, to preserve its credibility and trust in the US dollar as a global store of value asset. Also, the paper’s findings suggest that continuous expansion of the Money Supply will lead to a long-term inflationary problem. The purpose of this research is to bring the spotlight to the side effects of expansionary monetary policy on the US economy, but also allow other researchers to test this model in different economies with different dynamics. Full article
(This article belongs to the Special Issue Probability, Statistics and Their Applications 2021)
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Article
Admissible Classes of Multivalent Meromorphic Functions Defined by a Linear Operator
Mathematics 2022, 10(21), 4136; https://doi.org/10.3390/math10214136 - 05 Nov 2022
Viewed by 391
Abstract
The results from this paper are related to the geometric function theory. In order to obtain them, we use the technique based on differential subordination, one of the newest techniques used in the field, also known as the technique of admissible functions. For [...] Read more.
The results from this paper are related to the geometric function theory. In order to obtain them, we use the technique based on differential subordination, one of the newest techniques used in the field, also known as the technique of admissible functions. For that, the appropriate classes of admissible functions are first defined. Based on these classes, we obtain some differential subordination and superordination results for multivalent meromorphic functions, analytic in the punctured unit disc, related to a linear operator ρ,τp(ν), for τ>0,ν,ρC, such that Re(ρν)0, Re(ν)>τp,(pN). Moreover, taking into account both subordination and superordination results, we derive a sandwich-type theorem. The connection with some other known results and an example are also provided. Full article
(This article belongs to the Special Issue Advances on Complex Analysis)
Article
A Metaheuristic Optimization Approach to Solve Inverse Kinematics of Mobile Dual-Arm Robots
Mathematics 2022, 10(21), 4135; https://doi.org/10.3390/math10214135 - 05 Nov 2022
Viewed by 427
Abstract
This work presents an approach to solving the inverse kinematics of mobile dual-arm robots based on metaheuristic optimization algorithms. First, a kinematic analysis of a mobile dual-arm robot is presented. Second, an objective function is formulated based on the forward kinematics equations. The [...] Read more.
This work presents an approach to solving the inverse kinematics of mobile dual-arm robots based on metaheuristic optimization algorithms. First, a kinematic analysis of a mobile dual-arm robot is presented. Second, an objective function is formulated based on the forward kinematics equations. The kinematic analysis does not require using any Jacobian matrix nor its estimation; for this reason, the proposed approach does not suffer from singularities, which is a common problem with conventional inverse kinematics algorithms. Moreover, the proposed method solves cooperative manipulation tasks, especially in the case of coordinated manipulation. Simulation and real-world experiments were performed to verify the proposal’s effectiveness under coordinated inverse kinematics and trajectory tracking tasks. The experimental setup considered a mobile dual-arm system based on the KUKA® Youbot® robot. The solution of the inverse kinematics showed precise and accurate results. Although the proposed approach focuses on coordinated manipulation, it can be implemented to solve non-coordinated tasks. Full article
(This article belongs to the Topic Applied Metaheuristic Computing: 2nd Volume)
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