Mathematics

18 pages, 1518 KiB

Open AccessArticle

Classification of Motor Imagery Using Trial Extension in Spatial Domain with Rhythmic Components of EEG

by Md. Khademul Islam Molla, Sakir Ahamed, Ahmed M. M. Almassri and Hiroaki Wagatsuma

Mathematics 2023, 11(17), 3801; https://doi.org/10.3390/math11173801 - 4 Sep 2023

Cited by 1 | Viewed by 2503

Electrical activities of the human brain can be recorded with electroencephalography (EEG). To characterize motor imagery (MI) tasks for brain–computer interface (BCI) implementation is an easy and cost-effective tool. The MI task is represented by a short-time trial of multichannel EEG. In this [...] Read more.

Electrical activities of the human brain can be recorded with electroencephalography (EEG). To characterize motor imagery (MI) tasks for brain–computer interface (BCI) implementation is an easy and cost-effective tool. The MI task is represented by a short-time trial of multichannel EEG. In this paper, the signal of each channel of raw EEG is decomposed into a finite set of narrowband signals using a Fourier-transformation-based bandpass filter. Rhythmic components of EEG are represented by each of the narrowband signals that characterize the brain activities related to MI tasks. The subband signals are arranged to extend the dimension of the EEG trial in the spatial domain. The spatial features are extracted from the set of extended trials using a common spatial pattern (CSP). An optimum number of features are employed to classify the motor imagery tasks using an artificial neural network. An integrated approach with full-band and narrowband signals is implemented to derive discriminative features for MI classification. In addition, the subject-dependent parameter optimization scheme enhances the performance of the proposed method. The performance evaluation of the proposed method is obtained using two publicly available benchmark datasets (Dataset I and Dataset II). The experimental results in terms of classification accuracy (93.88% with Dataset I and 91.55% with Dataset II) show that it performs better than the recently developed algorithms. The enhanced MI classification accuracy is very much applicable in BCI implementation. Full article

(This article belongs to the Special Issue Machine Learning in Bioinformatics and Biostatistics)

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17 pages, 412 KiB

Open AccessArticle

Modeling the Production Process of Fuel Gas, LPG, Propylene, and Polypropylene in a Petroleum Refinery Using Generalized Nets

by Danail D. Stratiev, Angel Dimitriev, Dicho Stratiev and Krassimir Atanassov

Mathematics 2023, 11(17), 3800; https://doi.org/10.3390/math11173800 - 4 Sep 2023

Cited by 5 | Viewed by 1887

Abstract

The parallel processes involved in the production of refinery fuel gas, liquid petroleum gas (LPG), propylene, and polypropylene, occurring in thirteen refinery units, are modeled by the use of a Generalized Net (GN) apparatus. The modeling of the production of these products is [...] Read more.

The parallel processes involved in the production of refinery fuel gas, liquid petroleum gas (LPG), propylene, and polypropylene, occurring in thirteen refinery units, are modeled by the use of a Generalized Net (GN) apparatus. The modeling of the production of these products is important because they affect the energy balance of petroleum refinery and the associated emissions of greenhouse gases. For the first time, such a model is proposed and it is a continuation of the investigations of refinery process modelling by GNs. The model contains 17 transitions, 55 places, and 47 types of tokens, and considers the orders of fuel gas for the refinery power station, refinery process furnaces, LPG, liquid propylene, and 6 grades of polypropylene. This model is intended to be used as a more detailed lower-level GN model in a higher-level GN model that facilitates and optimizes the process of decision making in the petroleum refining industry. Full article

(This article belongs to the Special Issue Intuitionistic Fuzziness and Parallelism: Theory and Applications)

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18 pages, 5470 KiB

Open AccessArticle

A Hybrid Non-Polynomial Spline Method and Conformable Fractional Continuity Equation

by Majeed A. Yousif and Faraidun K. Hamasalh

Mathematics 2023, 11(17), 3799; https://doi.org/10.3390/math11173799 - 4 Sep 2023

Cited by 3 | Viewed by 1542

Abstract

This paper presents a groundbreaking numerical technique for solving nonlinear time fractional differential equations, combining the conformable continuity equation (CCE) with the Non-Polynomial Spline (NPS) interpolation to address complex mathematical challenges. By employing conformable descriptions of fractional derivatives within the CCE framework, our [...] Read more.

This paper presents a groundbreaking numerical technique for solving nonlinear time fractional differential equations, combining the conformable continuity equation (CCE) with the Non-Polynomial Spline (NPS) interpolation to address complex mathematical challenges. By employing conformable descriptions of fractional derivatives within the CCE framework, our method ensures enhanced accuracy and robustness when dealing with fractional order equations. To validate our approach’s applicability and effectiveness, we conduct a comprehensive set of numerical examples and assess stability using the Fourier method. The proposed technique demonstrates unconditional stability within specific parameter ranges, ensuring reliable performance across diverse scenarios. The convergence order analysis reveals its efficiency in handling complex mathematical models. Graphical comparisons with analytical solutions substantiate the accuracy and efficacy of our approach, establishing it as a powerful tool for solving nonlinear time-fractional differential equations. We further demonstrate its broad applicability by testing it on the Burgers–Fisher equations and comparing it with existing approaches, highlighting its superiority in biology, ecology, physics, and other fields. Moreover, meticulous evaluations of accuracy and efficiency using (

L_{2}

and

L_{\infty}

) norm errors reinforce its robustness and suitability for real-world applications. In conclusion, this paper presents a novel numerical technique for nonlinear time fractional differential equations, with the CCE and NPS methods’ unique combination driving its effectiveness and broad applicability in computational mathematics, scientific research, and engineering endeavors. Full article

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15 pages, 337 KiB

Open AccessArticle

Stable Matching Assisted Resource Allocation in Fog Computing Based IoT Networks

by Ahmed S. Alfakeeh and Muhammad Awais Javed

Mathematics 2023, 11(17), 3798; https://doi.org/10.3390/math11173798 - 4 Sep 2023

Cited by 1 | Viewed by 1170

Abstract

Future Internet of Things (IoT) will be a connected network of sensors enabling applications such as industrial automation and autonomous driving. To manage such a large number of applications, efficient computing techniques using fog nodes will be required. A major challenge in such [...] Read more.

Future Internet of Things (IoT) will be a connected network of sensors enabling applications such as industrial automation and autonomous driving. To manage such a large number of applications, efficient computing techniques using fog nodes will be required. A major challenge in such IoT networks is to manage the resource allocation of fog computing nodes considering security and system efficiency. A secure selection of fog nodes will be needed for forwarding the tasks without interception by the eavesdropper and minimizing the task delay. However, challenges such as the secure selection of fog nodes for forwarding the tasks without interception by the eavesdropper and minimizing the task delay are critical in IoT-based fog computing. In this paper, an efficient technique is proposed that solves the formulated problem of allocation of the tasks to the fog node resources using a stable matching algorithm. The proposed technique develops preference profiles for both IoT and fog nodes based on factors such as delay and secrecy rate. Finally, Gale–Shapley matching is used for task offloading. Detailed simulation results show that the performance of the proposed technique is significantly higher than the recent techniques in the literature. Full article

(This article belongs to the Special Issue Advances in Communication Systems, IoT and Blockchain)

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14 pages, 314 KiB

Open AccessArticle

Quasi-Exponentiated Normal Distributions: Mixture Representations and Asymmetrization

by Victor Korolev and Alexander Zeifman

Mathematics 2023, 11(17), 3797; https://doi.org/10.3390/math11173797 - 4 Sep 2023

Viewed by 1128

Abstract

In the paper, quasi-exponentiated normal distributions are introduced for any real power (exponent) no less than two. With natural exponents, the quasi-exponentiated normal distributions coincide with the distributions of the corresponding powers of normal random variables with zero mean. Their representability as scale [...] Read more.

In the paper, quasi-exponentiated normal distributions are introduced for any real power (exponent) no less than two. With natural exponents, the quasi-exponentiated normal distributions coincide with the distributions of the corresponding powers of normal random variables with zero mean. Their representability as scale mixtures of normal and exponential distributions is proved. The mixing distributions are written out in the closed form. Two approaches to the construction of asymmetric quasi-exponentiated normal distributions are described. A limit theorem is proved for sums of a random number of independent random variables in which the asymmetric quasi-exponentiated normal distribution is the limit law. Full article

(This article belongs to the Section Probability and Statistics)

20 pages, 385 KiB

Open AccessArticle

Homogenization of Smoluchowski Equations in Thin Heterogeneous Porous Domains

by Reine Gladys Noucheun and Jean Louis Woukeng

Mathematics 2023, 11(17), 3796; https://doi.org/10.3390/math11173796 - 4 Sep 2023

Viewed by 828

Abstract

In a thin heterogeneous porous layer, we carry out a multiscale analysis of Smoluchowski’s discrete diffusion–coagulation equations describing the evolution density of diffusing particles that are subject to coagulation in pairs. Assuming that the thin heterogeneous layer is made up of microstructures that [...] Read more.

In a thin heterogeneous porous layer, we carry out a multiscale analysis of Smoluchowski’s discrete diffusion–coagulation equations describing the evolution density of diffusing particles that are subject to coagulation in pairs. Assuming that the thin heterogeneous layer is made up of microstructures that are uniformly distributed inside, we obtain in the limit an upscaled model in the lower space dimension. We also prove a corrector-type result very useful in numerical computations. In view of the thin structure of the domain, we appeal to a concept of two-scale convergence adapted to thin heterogeneous media to achieve our goal. Full article

(This article belongs to the Special Issue Asymptotic Analysis and Homogenization of PDEs)

16 pages, 921 KiB

Open AccessArticle

Generalized Quantification Function of Monogenic Phase Congruency

by Manuel G. Forero, Carlos A. Jacanamejoy, Maximiliano Machado and Karla L. Penagos

Mathematics 2023, 11(17), 3795; https://doi.org/10.3390/math11173795 - 4 Sep 2023

Cited by 1 | Viewed by 1006

Abstract

Edge detection is a technique in digital image processing that detects the contours of objects based on changes in brightness. Edges can be used to determine the size, orientation, and properties of the object of interest within an image. There are different techniques [...] Read more.

Edge detection is a technique in digital image processing that detects the contours of objects based on changes in brightness. Edges can be used to determine the size, orientation, and properties of the object of interest within an image. There are different techniques employed for edge detection, one of them being phase congruency, a recently developed but still relatively unknown technique due to its mathematical and computational complexity compared to more popular methods. Additionally, it requires the adjustment of a greater number of parameters than traditional techniques. Recently, a unique formulation was proposed for the mathematical description of phase congruency, leading to a better understanding of the technique. This formulation consists of three factors, including a quantification function, which, depending on its characteristics, allows for improved edge detection. However, a detailed study of the characteristics had not been conducted. Therefore, this article proposes the development of a generalized function for quantifying phase congruency, based on the family of functions that, according to a previous study, yielded the best results in edge detection. Full article

(This article belongs to the Special Issue Advances of Mathematical Image Processing)

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16 pages, 6995 KiB

Open AccessArticle

Attitude Control of UAVs with Search Optimization and Disturbance Rejection Strategies

by Wensheng Li, Fanke Yang, Liqiang Zhong, Hao Wu, Xiangyuan Jiang and Andrei V. Chukalin

Mathematics 2023, 11(17), 3794; https://doi.org/10.3390/math11173794 - 4 Sep 2023

Cited by 3 | Viewed by 1745 | Correction

Abstract

This study aims to achieve rapid and stable control of quadrotor unmanned aerial vehicles’ (UAVs) attitude by using an Active Disturbance Rejection Control (ADRC) controller. Addressing the challenge of numerous and complex ADRC parameters, optimization algorithms are employed for parameter tuning. This paper [...] Read more.

This study aims to achieve rapid and stable control of quadrotor unmanned aerial vehicles’ (UAVs) attitude by using an Active Disturbance Rejection Control (ADRC) controller. Addressing the challenge of numerous and complex ADRC parameters, optimization algorithms are employed for parameter tuning. This paper draws on the group mechanism of the Ant Colony Optimization (ACO) algorithm and innovatively introduces population search into the Beetle Antennae Search (BAS) algorithm. The refined algorithm is then applied to tune the ADRC parameters, reducing complexity and human intervention while enhancing intelligence and efficiency. The advanced optimization algorithm exhibits an exceptional global optimization capacity, convergence speed, and stability. Ultimately, flight simulation and experimental results suggest that the optimized ADRC controller demonstrates superior control and antidisturbance capabilities. Full article

(This article belongs to the Topic Intelligent Systems and Robotics)

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21 pages, 3994 KiB

Open AccessArticle

Deep Learning-Based Classification of Abrasion and Ischemic Diabetic Foot Sores Using Camera-Captured Images

by Mudassir Khalil, Ahmad Naeem, Rizwan Ali Naqvi, Kiran Zahra, Syed Atif Moqurrab and Seung-Won Lee

Mathematics 2023, 11(17), 3793; https://doi.org/10.3390/math11173793 - 4 Sep 2023

Cited by 1 | Viewed by 2008

Abstract

Diabetic foot sores (DFS) are serious diabetic complications. The patient’s weakened neurological system damages the tissues of the foot’s skin, which results in amputation. This study aims to validate and deploy a deep learning-based system for the automatic classification of abrasion foot sores [...] Read more.

Diabetic foot sores (DFS) are serious diabetic complications. The patient’s weakened neurological system damages the tissues of the foot’s skin, which results in amputation. This study aims to validate and deploy a deep learning-based system for the automatic classification of abrasion foot sores (AFS) and ischemic diabetic foot sores (DFS). We proposed a novel model combining convolutional neural network (CNN) capabilities with Vgg-19. The proposed method utilized two benchmark datasets to classify AFS and DFS from the patient’s foot. A data augmentation technique was used to enhance the accuracy of the training. Moreover, image segmentation was performed using UNet++. We tested and evaluated the proposed model’s classification performance against two well-known pre-trained classifiers, Inceptionv3 and MobileNet. The proposed model classified AFS and ischemia DFS images with an accuracy of 99.05%, precision of 98.99%, recall of 99.01%, MCC of 0.9801, and f1 score of 99.04%. Furthermore, the results of statistical evaluations using ANOVA and Friedman tests revealed that the proposed model exhibited a remarkable performance. The proposed model achieved an excellent performance that assist medical professionals in identifying foot ulcers. Full article

(This article belongs to the Special Issue Machine Learning and Deep Learning for Healthcare Applications and Advances)

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13 pages, 2841 KiB

Open AccessArticle

Designing a Bayesian Regularization Approach to Solve the Fractional Layla and Majnun System

by Zulqurnain Sabir, Atef F. Hashem, Adnène Arbi and Mohamed A. Abdelkawy

Mathematics 2023, 11(17), 3792; https://doi.org/10.3390/math11173792 - 4 Sep 2023

Cited by 8 | Viewed by 1079

Abstract

The present work provides the numerical solutions of the mathematical model based on the fractional-order Layla and Majnun model (MFLMM). A soft computing stochastic-based Bayesian regularization neural network approach (BRNNA) is provided to investigate the numerical accomplishments of the MFLMM. The nonlinear system [...] Read more.

The present work provides the numerical solutions of the mathematical model based on the fractional-order Layla and Majnun model (MFLMM). A soft computing stochastic-based Bayesian regularization neural network approach (BRNNA) is provided to investigate the numerical accomplishments of the MFLMM. The nonlinear system is classified into two dynamics, whereas the correctness of the BRNNA is observed through the comparison of results. Furthermore, the reducible performance of the absolute error improves the exactitude of the computational BRNNA. Twenty neurons have been chosen, along with the data statics of training 74% and 13%, for both authorization and testing. The consistency of the designed BRNNA is demonstrated using the correlation/regression, error histograms, and transition of state values in order to solve the MFLMM. Full article

(This article belongs to the Section Dynamical Systems)

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17 pages, 2128 KiB

Open AccessArticle

Robust Sliding-Mode Control Design of DC-DC Zeta Converter Operating in Buck and Boost Modes

by Humam Al-Baidhani, Fabio Corti, Alberto Reatti and Marian K. Kazimierczuk

Mathematics 2023, 11(17), 3791; https://doi.org/10.3390/math11173791 - 4 Sep 2023

Cited by 4 | Viewed by 1387

Abstract

This paper presents a new nonlinear control scheme for a pulse-width modulated dc-dc Zeta converter operating in buck and boost modes. The averaged model of the dc-dc power converter is derived, based on which a robust control law is developed using a simplified [...] Read more.

This paper presents a new nonlinear control scheme for a pulse-width modulated dc-dc Zeta converter operating in buck and boost modes. The averaged model of the dc-dc power converter is derived, based on which a robust control law is developed using a simplified sliding-mode control technique. The existence and stability conditions are introduced to select proper controller gains that ensure fast output voltage convergence towards reference voltage. A detailed design procedure is provided to realize the control scheme using low-cost discrete components. The proposed control method handles large disturbances, accommodates the non-minimum phase property, and maintains regulated output voltage during step-up and step-down operation modes. The control system also maintains constant switching frequency, improves the transient response, and eliminates the steady-state error at the output voltage. A MATLAB/SIMULINK model is developed to simulate the closed-loop dc-dc Zeta converter in continuous conduction mode and investigate the tracking and regulation performance. The simulation results confirm the robustness and stability of the nonlinear controlled power converter under abrupt line and load variations. Full article

(This article belongs to the Special Issue Dynamics and Control Theory with Applications)

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25 pages, 29463 KiB

Open AccessArticle

Numerical Simulation of Failure Modes in Irregular Columnar Jointed Rock Masses under Dynamic Loading

by Yingjie Xia, Bingchen Liu, Tianjiao Li, Danchen Zhao, Ning Liu, Chun’an Tang and Jun Chen

Mathematics 2023, 11(17), 3790; https://doi.org/10.3390/math11173790 - 4 Sep 2023

Cited by 2 | Viewed by 1270

Abstract

The mechanical properties and failure characteristics of columnar jointed rock mass (CJRM) are significantly influenced by its irregular structure. Current research on CJRMs is mainly under static loading, which cannot meet the actual needs of engineering. This paper adopts the finite element method [...] Read more.

The mechanical properties and failure characteristics of columnar jointed rock mass (CJRM) are significantly influenced by its irregular structure. Current research on CJRMs is mainly under static loading, which cannot meet the actual needs of engineering. This paper adopts the finite element method (FEM) to carry out numerical simulation tests on irregular CJRMs with different dip angles under different dynamic stress wave loadings. The dynamic failure modes of irregular CJRMs and the influence law of related stress wave parameters are obtained. The results show that when the column dip angle α is 0°, the tensile-compressive-shear failure occurs in the CJRMs; when α is 30°, the CJRMs undergo tensile failure and a small amount of compressive shear failure, and an obvious crack-free area appears in the middle of the rock mass; when α is 60°, tensile failure is dominant and compressive shear failure is minimal and no crack area disappears; and when α is 90°, the rock mass undergoes complete tensile failure. In addition, in terms of the change law of stress wave parameters, the increase in peak amplitude will increase the number of cracks, promote the development of cracks, and increase the proportion of compression-shear failure units for low-angle rock mass. The changes in the loading and decay rate only affect the degree of crack development in the CJRMs, but do not increase the number of cracks. Meanwhile, the simulation results show that the crack expansion velocity of the CJRMs increases with the increase in dip angle, and the CJRMs with dip angle α = 60° are the most vulnerable to failure. The influence of the loading and decay rate on the rock mass failure is different with the change in dip angle. The results of the study provide references for related rock engineering. Full article

(This article belongs to the Special Issue Advances in Mathematical, Numerical and Artificial Intelligence Methods in Rock Engineering Applications)

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28 pages, 514 KiB

Open AccessArticle

Homogeneity Test for Multiple Semicontinuous Data with the Density Ratio Model

by Yufan Wang and Xingzhong Xu

Mathematics 2023, 11(17), 3789; https://doi.org/10.3390/math11173789 - 4 Sep 2023

Viewed by 897

Abstract

The density ratio model has been widely used in many research fields. To test the homogeneity of the model, the empirical likelihood ratio test (ELRT) has been shown to be valid. In this paper, we conduct a parametric test procedure. We transform the [...] Read more.

The density ratio model has been widely used in many research fields. To test the homogeneity of the model, the empirical likelihood ratio test (ELRT) has been shown to be valid. In this paper, we conduct a parametric test procedure. We transform the hypothesis of homogeneity to one on the equality of mean parameters of the exponential family of distributions. Then, we propose a modified Wald test and give its asymptotic power. We further apply it to the semicontinuous case when there is an excess of zeros in the sample. The simulation studies show that the new test controls the type-I error better than ELRT while retaining competitive power. Benefiting from the simple closed form of the test statistic, the computational cost is small. We also use a real data example to illustrate the effectiveness of our test. Full article

(This article belongs to the Special Issue Statistical Analysis: Theory, Methods and Applications)

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18 pages, 774 KiB

Open AccessArticle

Stability and Convergence Analysis of Multi-Symplectic Variational Integrator for Nonlinear Schrödinger Equation

by Siqi Lv, Zhihua Nie and Cuicui Liao

Mathematics 2023, 11(17), 3788; https://doi.org/10.3390/math11173788 - 4 Sep 2023

Viewed by 978

Abstract

Stability and convergence analyses of the multi-symplectic variational integrator for the nonlinear Schr

\ddot{o}

dinger equation are discussed in this paper. The variational integrator is proved to be unconditionally linearly stable using the von Neumann method. A priori error bound for the [...] Read more.

Stability and convergence analyses of the multi-symplectic variational integrator for the nonlinear Schr

\ddot{o}

dinger equation are discussed in this paper. The variational integrator is proved to be unconditionally linearly stable using the von Neumann method. A priori error bound for the scheme is given from the Sobolev inequality and the discrete conservation laws. Subsequently, the variational integrator is derived to converge at

O (Δ x^{2} + Δ t^{2})

in the discrete

L^{2}

norm using the energy method. The numerical experimental results match our theoretical derivation. Full article

(This article belongs to the Section Computational and Applied Mathematics)

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7 pages, 244 KiB

Open AccessArticle

Keller–Osserman Phenomena for Kardar–Parisi–Zhang-Type Inequalities

by Andrey B. Muravnik

Mathematics 2023, 11(17), 3787; https://doi.org/10.3390/math11173787 - 4 Sep 2023

Viewed by 786

Abstract

For coercive quasilinear partial differential inequalities containing nonlinearities of the Kardar–Parisi–Zhang type, we find conditions guaranteeing the absence of global positive solutions. These conditions extend both the classical result of Keller and Osserman and its recent Kon’kov–Shishkov generalization. Additionally, they complement the results [...] Read more.

For coercive quasilinear partial differential inequalities containing nonlinearities of the Kardar–Parisi–Zhang type, we find conditions guaranteeing the absence of global positive solutions. These conditions extend both the classical result of Keller and Osserman and its recent Kon’kov–Shishkov generalization. Additionally, they complement the results for the noncoercive case, which had been previously established by the same author. Full article

(This article belongs to the Special Issue Direct and Inverse Spectral Problems for Ordinary Differential and Functional-Differential Operators)

15 pages, 1131 KiB

Open AccessArticle

Fourth-Order Difference Scheme and a Matrix Transform Approach for Solving Fractional PDEs

by Zahrah I. Salman, Majid Tavassoli Kajani, Mohammed Sahib Mechee and Masoud Allame

Mathematics 2023, 11(17), 3786; https://doi.org/10.3390/math11173786 - 3 Sep 2023

Viewed by 1479

Abstract

Proposing a matrix transform method to solve a fractional partial differential equation is the main aim of this paper. The main model can be transferred to a partial-integro differential equation (PIDE) with a weakly singular kernel. The spatial direction is approximated by a [...] Read more.

Proposing a matrix transform method to solve a fractional partial differential equation is the main aim of this paper. The main model can be transferred to a partial-integro differential equation (PIDE) with a weakly singular kernel. The spatial direction is approximated by a fourth-order difference scheme. Also, the temporal derivative is discretized via a second-order numerical procedure. First, the spatial derivatives are approximated by a fourth-order operator to compute the second-order derivatives. This process produces a system of differential equations related to the time variable. Then, the Crank–Nicolson idea is utilized to achieve a full-discrete scheme. The kernel of the integral term is discretized by using the Lagrange polynomials to overcome its singularity. Subsequently, we prove the convergence and stability of the new difference scheme by utilizing the Rayleigh–Ritz theorem. Finally, some numerical examples in one-dimensional and two-dimensional cases are presented to verify the theoretical results. Full article

(This article belongs to the Section Computational and Applied Mathematics)

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15 pages, 3839 KiB

Open AccessArticle

SCM Enables Improved Single-Cell Clustering by Scoring Consensus Matrices

by Yilin Yu and Juntao Liu

Mathematics 2023, 11(17), 3785; https://doi.org/10.3390/math11173785 - 3 Sep 2023

Cited by 2 | Viewed by 1173

Abstract

Single-cell clustering facilitates the identification of different cell types, especially the identification of rare cells. Preprocessing and dimensionality reduction are the two most commonly used data-processing methods and are very important for single-cell clustering. However, we found that different preprocessing and dimensionality reduction [...] Read more.

Single-cell clustering facilitates the identification of different cell types, especially the identification of rare cells. Preprocessing and dimensionality reduction are the two most commonly used data-processing methods and are very important for single-cell clustering. However, we found that different preprocessing and dimensionality reduction methods have very different effects on single-cell clustering. In addition, there seems to be no specific combination of preprocessing and dimensionality reduction methods that is applicable to all datasets. In this study, we developed a new algorithm for improving single-cell clustering results, called SCM. It first automatically searched for an optimal combination that corresponds to the best cell type clustering of a given dataset. It then defined a flexible cell-to-cell distance measure with data specificity for cell-type clustering. Experiments on ten benchmark datasets showed that SCM performed better than almost all the other seven popular clustering algorithms. For example, the average ARI improvement of SCM over the second best method SC3 even reached 29.31% on the ten datasets, which demonstrated its great potential in revealing cellular heterogeneity, identifying cell types, depicting cell functional states, inferring cellular dynamics, and other related research areas. Full article

(This article belongs to the Special Issue Mathematical Models and Computer Science Applied to Biology)

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12 pages, 259 KiB

Open AccessArticle

Inverses and Determinants of n × n Block Matrices

by Müge Saadetoğlu and Şakir Mehmet Dinsev

Mathematics 2023, 11(17), 3784; https://doi.org/10.3390/math11173784 - 3 Sep 2023

Cited by 3 | Viewed by 4737

Abstract

Block matrices play an important role in all branches of pure and applied mathematics. In this paper, we study the two fundamental concepts: inverses and determinants of general

n \times n

block matrices. In the first part, the inverses of

2 \times 2

[...] Read more.

Block matrices play an important role in all branches of pure and applied mathematics. In this paper, we study the two fundamental concepts: inverses and determinants of general

n \times n

block matrices. In the first part, the inverses of

2 \times 2

block matrices are given, where one of the blocks is a non-singular matrix, a result which can be generalised to a block matrix of any size, by splitting it into four blocks. The second part focuses on the determinants, which is covered in two different methods. In the first approach, we revise a formula for the determinant of a block matrix A, with blocks elements of R; a commutative subring of

M_{n \times n} (F)

. The determinants of tensor products of two matrices are also given in this part. In the second method for computing the determinant, we give the general formula, which would work for any block matrix, regardless of the ring or the field under consideration. The individual formulas for determinants of

2 \times 2

and

3 \times 3

block matrices are also produced here. Full article

(This article belongs to the Section Algebra, Geometry and Topology)

21 pages, 666 KiB

Open AccessArticle

The Hybrid Modeling of Spatial Autoregressive Exogenous Using Casetti’s Model Approach for the Prediction of Rainfall

by Annisa Nur Falah, Budi Nurani Ruchjana, Atje Setiawan Abdullah and Juli Rejito

Mathematics 2023, 11(17), 3783; https://doi.org/10.3390/math11173783 - 3 Sep 2023

Cited by 3 | Viewed by 1241

Abstract

Spatial Autoregressive (SAR) models are used to model the relationship between variables within a specific region or location, considering the influence of neighboring variables, and have received considerable attention in recent years. However, when the impact of exogenous variables becomes notably pronounced, an [...] Read more.

Spatial Autoregressive (SAR) models are used to model the relationship between variables within a specific region or location, considering the influence of neighboring variables, and have received considerable attention in recent years. However, when the impact of exogenous variables becomes notably pronounced, an alternative approach is warranted. Spatial Expansion, coupled with the Casetti model approach, serves as an extension of the SAR model, accommodating the influence of these exogenous variables. This modeling technique finds application in the realm of rainfall prediction, where exogenous factors, such as air temperature, humidity, solar irradiation, wind speed, and surface pressure, play pivotal roles. Consequently, this research aimed to combine the SAR and Spatial Expansion models through the Casetti model approach, leading to the creation of the Spatial Autoregressive Exogenous (SAR-X) model. The SAR-X was employed to forecast the rainfall patterns in the West Java region, utilizing data obtained from the National Aeronautics and Space Administration Prediction of Worldwide Energy Resources (NASA POWER) dataset. The practical execution of this research capitalized on the computational capabilities of the RStudio software version 2022.12.0. Within the framework of this investigation, a comprehensive and integrated RStudio script, seamlessly incorporated into the RShiny web application, was developed so that it is easy to use. Full article

(This article belongs to the Special Issue Applied Mathematics and Machine Learning)

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12 pages, 297 KiB

Open AccessArticle

Data Transformation in the Predict-Then-Optimize Framework: Enhancing Decision Making under Uncertainty

by Xuecheng Tian, Yanxia Guan and Shuaian Wang

Mathematics 2023, 11(17), 3782; https://doi.org/10.3390/math11173782 - 3 Sep 2023

Cited by 1 | Viewed by 1851

Abstract

Decision making under uncertainty is pivotal in real-world scenarios, such as selecting the shortest transportation route amidst variable traffic conditions or choosing the best investment portfolio during market fluctuations. In today’s big data age, while the predict-then-optimize framework has become a standard method [...] Read more.

Decision making under uncertainty is pivotal in real-world scenarios, such as selecting the shortest transportation route amidst variable traffic conditions or choosing the best investment portfolio during market fluctuations. In today’s big data age, while the predict-then-optimize framework has become a standard method for tackling uncertain optimization challenges using machine learning tools, many prediction models overlook data intricacies such as outliers and heteroskedasticity. These oversights can degrade decision-making quality. To enhance predictive accuracy and consequent decision-making quality, we introduce a data transformation technique into the predict-then-optimize framework. Our approach transforms target values in linear regression, decision tree, and random forest models using a power function, aiming to boost their predictive prowess and, in turn, drive better decisions. Empirical validation on several datasets reveals marked improvements in decision tree and random forest models. In contrast, the benefits of linear regression are nuanced. Thus, while data transformation can bolster the predict-then-optimize framework, its efficacy is model-dependent. This research underscores the potential of tailoring transformation techniques for specific models to foster reliable and robust decision-making under uncertainty. Full article

(This article belongs to the Special Issue Data-Driven Decision Making: Models, Methods and Applications)

21 pages, 5223 KiB

Open AccessArticle

Analytical Solution of Stability Problem of Nanocomposite Cylindrical Shells under Combined Loadings in Thermal Environments

by Mahmure Avey, Nicholas Fantuzzi and Abdullah H. Sofiyev

Mathematics 2023, 11(17), 3781; https://doi.org/10.3390/math11173781 - 3 Sep 2023

Cited by 4 | Viewed by 954

Abstract

The mathematical modeling of the stability problem of nanocomposite cylindrical shells is one of the applications of partial differential equations (PDEs). In this study, the stability behavior of inhomogeneous nanocomposite cylindrical shells (INH-NCCSs), under combined axial compression and hydrostatic pressure in the thermal [...] Read more.

The mathematical modeling of the stability problem of nanocomposite cylindrical shells is one of the applications of partial differential equations (PDEs). In this study, the stability behavior of inhomogeneous nanocomposite cylindrical shells (INH-NCCSs), under combined axial compression and hydrostatic pressure in the thermal environment, is investigated by means of the first-order shear deformation theory (FSDT). The nanocomposite material is modeled as homogeneous and heterogeneous and is based on a carbon nanotube (CNT)-reinforced polymer with the linear variation of the mechanical properties throughout the thickness. In the heterogeneous case, the mechanical properties are modeled as the linear function of the thickness coordinate. The basic equations are derived as partial differential equations and solved in a closed form, using the Galerkin procedure, to determine the critical combined loads for the selected structure in thermal environments. To test the reliability of the proposed formulation, comparisons with the results obtained by finite element and numerical methods in the literature are accompanied by a systematic study aimed at testing the sensitivity of the design response to the loading parameters, CNT models, and thermal environment. Full article

(This article belongs to the Special Issue Differential and Integro–Differential Equations: Theory and Applications)

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16 pages, 5565 KiB

Open AccessArticle

A Study on Cognitive Error Validation for LED In-Ground Traffic Lights Using a Digital Twin and Virtual Environment

by Bong Gu Kang and Byeong Soo Kim

Mathematics 2023, 11(17), 3780; https://doi.org/10.3390/math11173780 - 3 Sep 2023

Cited by 1 | Viewed by 2193

Abstract

Traffic accident prevention is considered one of the most crucial public safety issues due to the ongoing rise in traffic accidents. The installation of LED in-ground traffic lights is one strategy that has proven to be quite effective in preventing numerous traffic accidents, [...] Read more.

Traffic accident prevention is considered one of the most crucial public safety issues due to the ongoing rise in traffic accidents. The installation of LED in-ground traffic lights is one strategy that has proven to be quite effective in preventing numerous traffic accidents, notably pedestrian accidents. The traffic signal helps reduce accidents for pedestrians, but there is a drawback in that such installations may lead to cognitive errors, such as the driver making a mistaken start or stop. Therefore, it is crucial to validate cognitive errors in advance of the widespread adoption of LED in-ground traffic signals. To this end, in this study, we (i) built an experimental environment that can be employed for various traffic tests using digital twins and virtual simulators; (ii) designed test scenarios and measurement plans for validation to conduct a validation test, and (iii) demonstrated cognitive errors through data from various experiments. As a result, it was proven that there is a possibility that the LED in-ground traffic lights may cause cognitive errors for drivers, and the causes of this were analyzed. In the future, this framework can be used to demonstrate various transportation problems and can contribute to improving the quality of public safety. Full article

(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems)

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28 pages, 2305 KiB

Open AccessArticle

Perception of Facial Impressions Using Explicit Features of the Face (xFoFs)

by Jihyeon Yeom, Jeongin Lee, Heekyung Yang and Kyungha Min

Mathematics 2023, 11(17), 3779; https://doi.org/10.3390/math11173779 - 3 Sep 2023

Viewed by 1483

Abstract

We present a novel approach to perceiving facial impressions by defining the explicit features of the face (xFoFs) based on anthropometric studies. The xFoFs estimate 35 anthropometric features of human faces with normal expressions and frontalized poses. Using these xFoFs, we have developed [...] Read more.

We present a novel approach to perceiving facial impressions by defining the explicit features of the face (xFoFs) based on anthropometric studies. The xFoFs estimate 35 anthropometric features of human faces with normal expressions and frontalized poses. Using these xFoFs, we have developed a method to objectively measure facial impressions, compiling a dataset of approximately 4896 facial images to validate our method. The ranking of xFoFs among the face image dataset guides an objective and quantitative estimation of facial impressions. To further corroborate our study, we conducted two user studies: an examination of the first and strongest impression perception and a validation of the consistency of multiple important impression perceptions. Our work significantly contributes to the field of facial recognition and explainable artificial intelligence (XAI) by providing an effective solution for integrating xFoFs with existing facial recognition models. Full article

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

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11 pages, 6846 KiB

Open AccessArticle

A Network-Level Stochastic Model for Pacemaker GABAergic Neurons in Substantia Nigra Pars Reticulata

by Karine Guimarães and Aline Duarte

Mathematics 2023, 11(17), 3778; https://doi.org/10.3390/math11173778 - 3 Sep 2023

Viewed by 889

Abstract

In this paper we present computational simulations of a mathematical model describing the time evolution of membrane potentials in a GABAergic neural network. This model, with stochastic and evolutionary characteristics, is an application of the version introduced previously where the authors present the [...] Read more.

In this paper we present computational simulations of a mathematical model describing the time evolution of membrane potentials in a GABAergic neural network. This model, with stochastic and evolutionary characteristics, is an application of the version introduced previously where the authors present the continuous time version of a new class of stochastic models for biological neural networks. The goal is to computationally simulate the model (with the interaction conditions of a GABAergic network) and make biological inferences. More specifically, the computational simulations of the model that describe spiking neurons with electrophysiological characteristics of a brain region called substantia nigra pars reticulata, emphasize changes in desynchronized firing activity and how changes in individual activity propagate through the network. Full article

(This article belongs to the Special Issue Mathematical Models and Novel Data-Analyzing Methods in Neuroscience)

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12 pages, 294 KiB

Open AccessArticle

Seismological Problem, Seismic Waves and the Seismic Mainshock

by Bogdan Felix Apostol

Mathematics 2023, 11(17), 3777; https://doi.org/10.3390/math11173777 - 2 Sep 2023

Viewed by 1142

Abstract

The elastic wave equation with seismic tensorial force is solved in a homogeneous and isotropic medium (the Earth). Spherical-shell waves are obtained, which are associated to the primary P and S seismic waves. It is shown that these waves produce secondary waves with [...] Read more.

The elastic wave equation with seismic tensorial force is solved in a homogeneous and isotropic medium (the Earth). Spherical-shell waves are obtained, which are associated to the primary P and S seismic waves. It is shown that these waves produce secondary waves with sources on the plane surface of a half-space, which have the form of abrupt walls with a long tail, propagating in the interior and on the surface of the half-space. These secondary waves are associated to the seismic mainshock. The results, previously reported, are re-derived using Fourier transformations and specific regularization procedures. The relevance of this seismic motion for the ground motion, the seismographs’ recordings and the effect of the inhomogeneities in the medium are discussed. Full article

(This article belongs to the Special Issue Mathematical Modeling in Geophysics: Concepts and Practices)

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20 pages, 746 KiB

Open AccessArticle

Estimating the Capital Asset Pricing Model with Many Instruments: A Bayesian Shrinkage Approach

by Cássio Roberto de Andrade Alves and Márcio Laurini

Mathematics 2023, 11(17), 3776; https://doi.org/10.3390/math11173776 - 2 Sep 2023

Cited by 2 | Viewed by 1641

Abstract

This paper introduces an instrumental variable Bayesian shrinkage approach specifically designed for estimating the capital asset pricing model (CAPM) while utilizing a large number of instruments. Our methodology incorporates horseshoe, Laplace, and factor-based shrinkage priors to construct Bayesian estimators for CAPM, accounting for [...] Read more.

This paper introduces an instrumental variable Bayesian shrinkage approach specifically designed for estimating the capital asset pricing model (CAPM) while utilizing a large number of instruments. Our methodology incorporates horseshoe, Laplace, and factor-based shrinkage priors to construct Bayesian estimators for CAPM, accounting for the presence of measurement errors. Through the use of simulated data, we illustrate the potential of our approach in mitigating the bias arising from errors-in-variables. Importantly, the conventional two-stage least squares estimation of the CAPM beta is shown to experience bias escalation as the number of instruments increases. In contrast, our approach effectively counters this bias, particularly in scenarios with a substantial number of instruments. In an empirical application using real-world data, our proposed methodology generates subtly distinct estimated CAPM beta values compared with both the ordinary least squares and the two-stage least squares approaches. This disparity in estimations carries notable economic implications. Furthermore, when applied to average cross-sectional asset returns, our approach significantly enhances the explanatory power of the CAPM framework. Full article

(This article belongs to the Special Issue Bayesian Statistics and Causal Inference)

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24 pages, 1055 KiB

Open AccessArticle

A Richness Estimator Based on Integrated Data

by Chun-Huo Chiu

Mathematics 2023, 11(17), 3775; https://doi.org/10.3390/math11173775 - 2 Sep 2023

Viewed by 1158

Abstract

Species richness is a widely used measure for assessing the diversity of a particular area. However, observed richness often underestimates the true richness due to resource limitations, particularly in a small-sized sample or highly heterogeneous assemblage. To estimate the number of different species [...] Read more.

Species richness is a widely used measure for assessing the diversity of a particular area. However, observed richness often underestimates the true richness due to resource limitations, particularly in a small-sized sample or highly heterogeneous assemblage. To estimate the number of different species (species richness) present across several different sites (communities), researchers often use a combined collection of data (an integrated dataset). This dataset is created by collecting samples from each site individually and independently. However, the pooled sample of integrated data is no longer a random sample from the entire area, and the use of different sampling schemes results in different collected data formats. Consequently, employing a single sampling distribution to model the pooled sample becomes unfeasible, rendering existing richness estimators inadequate. This study provides a theoretical explanation for the applicability of Chao’s lower bound estimator in assessing species richness across multiple sites based on the pooled sample. Additionally, a new non-parametric estimator is introduced, which adjusts the bias of Chao’s lower bound estimator by leveraging the Good–Turing frequency formula. This proposed estimator only utilizes the richness of singletons, doubletons, and tripletons in the pooled sample to estimate undetected richness. Simulated datasets across various models are employed to demonstrate the statistical performance of the estimator, showcasing its ability to reduce the bias of observed richness and provide accurate 95% confidence intervals. Real datasets are also utilized to illustrate the practical application of the proposed approach. Full article

(This article belongs to the Special Issue Mathematical Modeling and Analysis in Biology and Medicine, 2nd Edition)

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22 pages, 366 KiB

Open AccessArticle

Two-Dimensional Moran Model: Final Altitude and Number of Resets

by Rafik Aguech and Mohamed Abdelkader

Mathematics 2023, 11(17), 3774; https://doi.org/10.3390/math11173774 - 2 Sep 2023

Cited by 2 | Viewed by 883

Abstract

In this paper, we consider a two-dimension symmetric random walk with reset. We give, in the first part, some results about the distribution of every component. In the second part, we give some results about the final altitude

Z_{n}

. Finally, we [...] Read more.

In this paper, we consider a two-dimension symmetric random walk with reset. We give, in the first part, some results about the distribution of every component. In the second part, we give some results about the final altitude

Z_{n}

. Finally, we analyse the statistical properties of

N_{n}^{X}

, the number of resets (the number of returns to state 1 after n steps) of the first component of the random walk. As a principal tool in these studies, we use the probability generating function. Full article

(This article belongs to the Section Probability and Statistics)

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19 pages, 1217 KiB

Open AccessArticle

A Hybrid MCDM Approach Based on Fuzzy MEREC-G and Fuzzy RATMI

by Anas A. Makki and Reda M. S. Abdulaal

Mathematics 2023, 11(17), 3773; https://doi.org/10.3390/math11173773 - 2 Sep 2023

Cited by 8 | Viewed by 1568

Abstract

Multi-criteria decision-making (MCDM) assists in making judgments on complex problems by evaluating several alternatives based on conflicting criteria. Several MCDM methods have been introduced. However, real-world problems often involve uncertain and ambiguous decision-maker inputs. Therefore, fuzzy MCDM methods have emerged to handle this [...] Read more.

Multi-criteria decision-making (MCDM) assists in making judgments on complex problems by evaluating several alternatives based on conflicting criteria. Several MCDM methods have been introduced. However, real-world problems often involve uncertain and ambiguous decision-maker inputs. Therefore, fuzzy MCDM methods have emerged to handle this problem using fuzzy logic. Most recently, the method based on the removal effects of criteria using the geometric mean (MEREC-G) and ranking the alternatives based on the trace to median index (RATMI) were introduced. However, to date, there is no fuzzy extension of the two novel methods. This study introduces a new hybrid fuzzy MCDM approach combining fuzzy MEREC-G and fuzzy RATMI. The fuzzy MEREC-G can accept linguistic input terms from multiple decision-makers and generates consistent fuzzy weights. The fuzzy RATMI can rank alternatives according to their fuzzy performance scores on each criterion. The study provides the algorithms of both fuzzy MEREC-G and fuzzy RATMI and demonstrates their application in adopted real-world problems. Correlation and scenario analyses were performed to check the new approach’s validity and sensitivity. The new approach demonstrates high accuracy and consistency and is sufficiently sensitive to changes in the criteria weights, yet not too sensitive to produce inconsistent rankings. Full article

(This article belongs to the Special Issue Advances in Fuzzy Decision Theory and Applications)

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16 pages, 500 KiB

Open AccessFeature PaperArticle

Cumulative Incidence Functions for Competing Risks Survival Data from Subjects with COVID-19

by Mohammad Anamul Haque and Giuliana Cortese

Mathematics 2023, 11(17), 3772; https://doi.org/10.3390/math11173772 - 2 Sep 2023

Cited by 1 | Viewed by 3184

Abstract

Competing risks survival analysis is used to answer questions about the time to occurrence of events with the extension of multiple causes of failure. Studies that investigate how clinical features and risk factors of COVID-19 are associated with the survival of patients in [...] Read more.

Competing risks survival analysis is used to answer questions about the time to occurrence of events with the extension of multiple causes of failure. Studies that investigate how clinical features and risk factors of COVID-19 are associated with the survival of patients in the presence of competing risks (CRs) are limited. The main objective of this paper is, under a CRs setting, to estimate the Cumulative Incidence Function (CIF) of COVID-19 death, the CIF of other-causes death, and the probability of being cured in subjects with COVID-19, who have been under observation from the date of symptoms to the date of death or exit from the study because they are cured. In particular, we compared the non-parametric estimator of the CIF based on the naive technique of Kaplan–Meier (K–M) with the Aalen–Johansen estimator based on the cause-specific approach. Moreover, we compared two of the most popular regression approaches for CRs data: the cause-specific hazard (CSH) and the sub-distribution hazard (SDH) approaches. A clear overestimation of the CIF function over time was observed under the K–M estimation technique. Moreover, exposure to asthma, diabetes, obesity, older age, male sex, black and indigenous races, absence of flu vaccine, admission to the ICU, and the presence of other risk factors, such as immunosuppression and chronic kidney, neurological, liver, and lung diseases, significantly increased the probability of COVID-19 death. The highest hazard ratio of

2.03

was observed for subjects with an age greater than 70 years compared with subjects aged 50–60 years. The SDH approach showed slightly higher survival probabilities compared with the CSH approach. An important foundation for producing precise individualized predictions was provided by the competing risks regression models discussed in this paper. This foundation allowed us, in general, to more realistically model complex data, such as the COVID-19 data, and can be used, for instance, by many modern statistical learning and personalized medicine techniques to obtain more accurate conclusions. Full article

(This article belongs to the Special Issue New Challenges in Mathematical Modelling and Control of COVID-19 Epidemics: Analysis of Non-pharmaceutical Actions and Vaccination Strategies)

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Mathematics, Volume 11, Issue 17 (September-1 2023) – 181 articles

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