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Math. Comput. Appl., Volume 29, Issue 6 (December 2024) – 23 articles

Cover Story (view full-size image): Due to the extreme complexity of Alzheimer’s disease, mathematical models, if deemed reliable, can be used to test medical hypotheses. In this context, it is important to understand how and τ proteins interact and spread. Here, we are interested in studying the spreading of misfolded τ and we present four different mathematical models on networks. The models differ in both the choice of network and diffusion operator. Through comparison with clinical data on τ concentration, obtained with careful multimodal analysis techniques, we show that some models are more adequate than others to simulate the dynamics of the protein. This type of study may suggest that, when it comes to modeling certain pathologies, the choice of the mathematical setting must be made with great care if comparison with clinical data are considered decisive. View this paper
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28 pages, 907 KiB  
Article
Design of Dual-Channel Supply Chain Network Based on the Internet of Things Under Uncertainty
by Hamed Nozari, Hossein Abdi, Agnieszka Szmelter-Jarosz and Seyyed Hesamoddin Motevalli
Math. Comput. Appl. 2024, 29(6), 118; https://doi.org/10.3390/mca29060118 - 12 Dec 2024
Abstract
In this paper, a mathematical model of a dual-channel supply chain network (DCSCN) based on the Internet of Things (IoT) under uncertainty is presented, and its solution using algorithms based on artificial intelligence such as genetic algorithm (GA), particle swarm optimization (PSO), imperialist [...] Read more.
In this paper, a mathematical model of a dual-channel supply chain network (DCSCN) based on the Internet of Things (IoT) under uncertainty is presented, and its solution using algorithms based on artificial intelligence such as genetic algorithm (GA), particle swarm optimization (PSO), imperialist competitive algorithm (ICA), and gray wolf optimizer (GWO). The main goal of this model is to maximize the total DCSCN profit to determine the amount of demand accurately, price in direct and indirect channels, locate distribution centers, and equip/not equip these centers with IoT devices. The results show that with the increase in the uncertainty rate, the amount of demand and corresponding transportation costs have increased. This issue has led to a decrease in the total DCSCN profit. By analyzing the mathematical model, it was also observed that deploying IoT equipment in distribution centers has increased fixed costs. Examining this issue shows that by increasing the savings factor by 0.2, the total DCSCN profit has increased by 6.5%. By ranking the algorithms with the TOPSIS method, the GA was ranked as the most efficient algorithm, followed by PSO, ICA, and GWO. This IoT-enhanced dual-channel supply chain model not only aims to optimize traditional supply chain metrics but also introduces advanced, data-driven strategies for improving demand management, pricing, and infrastructure allocation, ultimately driving profitability in uncertain environments. Full article
29 pages, 6603 KiB  
Article
A Mathematical Study of Effects of Alzheimer’s Drug Donepezil Hydrochloride on Neuronal Viscoelasticity and Action Potentials
by Corina S. Drapaca
Math. Comput. Appl. 2024, 29(6), 117; https://doi.org/10.3390/mca29060117 - 12 Dec 2024
Abstract
Alzheimer’s disease (AD) is a degenerative disorder characterized by progressive cognitive decline and memory loss. The few contemporary therapies may ease symptoms and/or slow down AD progression but cannot cure the disease. The orally administered AD drug donepezil hydrochloride enhances the availability of [...] Read more.
Alzheimer’s disease (AD) is a degenerative disorder characterized by progressive cognitive decline and memory loss. The few contemporary therapies may ease symptoms and/or slow down AD progression but cannot cure the disease. The orally administered AD drug donepezil hydrochloride enhances the availability of acetylcholine that supports cholinergic neurotransmission. In this paper, a generalized Hodgkin-Huxley model is proposed that uses Caputo fractional order temporal derivatives to link action potentials and viscoelasticity of cholinergic receptors. The model provides not only structurally dependent action potentials for health and AD but also a possible mechanism of donepezil effect on action potentials: the binding between the acetylcholine and the receptors preserves the structural fitness of these receptors. In addition, a generalized pharmacokinetic model of donepezil transport to the brain is proposed that incorporates controlled release modalities. Caputo fractional order temporal derivatives are used again to model anomalous drug release. Numerical simulations show how controlled release donepezil recovers the structural integrity of the receptors which further brings the abnormal action potentials due to AD to their healthy state. The results suggest that combining various drug release modalities and dosages may improve treatment effectiveness with donepezil. Full article
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23 pages, 3275 KiB  
Article
A PDE-ODE Coupled Model for Biofilm Growth in Porous Media That Accounts for Longitudinal Diffusion and Its Effect on Substrate Degradation
by Emma Bottomley and Hermann J. Eberl
Math. Comput. Appl. 2024, 29(6), 116; https://doi.org/10.3390/mca29060116 - 11 Dec 2024
Viewed by 285
Abstract
We derive a one-dimensional macroscopic model for biofilm formation in a porous medium reactor to investigate the role of longitudinal diffusion of substrate and suspended bacteria on reactor performance. By comparing an existing base model—one without longitudinal diffusion, which was the point of [...] Read more.
We derive a one-dimensional macroscopic model for biofilm formation in a porous medium reactor to investigate the role of longitudinal diffusion of substrate and suspended bacteria on reactor performance. By comparing an existing base model—one without longitudinal diffusion, which was the point of departure for our work, to the new model—we noticed significant changes in system dynamics. Our results suggest that neglecting it can lead to underestimation of quenching length and biofilm accumulation downstream, even in the advection-dominated regime. The effects of attachment and detachment of suspended bacteria on biofilm formation and substrate degradation were also examined. In the one-dimensional model, it was found that attachment has a stronger influence on substrate depletion, which becomes more pronounced as diffusion in the pore space increases. Full article
(This article belongs to the Special Issue New Trends in Biomathematics)
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12 pages, 3814 KiB  
Article
Compressive Sensing of Multichannel Electroencephalogram Signals Based on Nonlocal Low-Rank and Cosparse Priors
by Jun Zhu, Lei Feng and Chunmeng Wang
Math. Comput. Appl. 2024, 29(6), 115; https://doi.org/10.3390/mca29060115 - 6 Dec 2024
Viewed by 316
Abstract
Recent studies have shown that by using channel-correlation and cosparsity in a centralized framework, the accuracy of reconstructing multichannel EEG signals can be improved. A single-channel electroencephalogram (EEG) signal is intrinsically non-sparse in both the converted and raw time domains, which presents a [...] Read more.
Recent studies have shown that by using channel-correlation and cosparsity in a centralized framework, the accuracy of reconstructing multichannel EEG signals can be improved. A single-channel electroencephalogram (EEG) signal is intrinsically non-sparse in both the converted and raw time domains, which presents a number of important issues. However, this is ignored by contemporary compressive sensing (CS) algorithms, resulting in less recovery quality than is ideal. To address these constraints, we provide a novel CS method that takes advantage of Nonlocal Low-Rank and Cosparse priors (NLRC). By utilizing low-rank approximations and block operations, our method aims to improve the CS recovery process and take advantage of channel correlations. The Alternating Direction Method of Multipliers (ADMM) are also used to efficiently solve the resulting non-convex optimization problem. The outcomes of the experiments unequivocally demonstrate that by using NLRC, the quality of signal reconstruction is significantly enhanced. Full article
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22 pages, 2331 KiB  
Article
A Novel Hybrid Computational Technique to Study Conformable Burgers’ Equation
by Abdul-Majeed Ayebire, Atul Pasrija, Mukhdeep Singh Manshahia and Shelly Arora
Math. Comput. Appl. 2024, 29(6), 114; https://doi.org/10.3390/mca29060114 - 5 Dec 2024
Viewed by 390
Abstract
A fully discrete computational technique involving the implicit finite difference technique and cubic Hermite splines is proposed to solve the non-linear conformable damped Burgers’ equation with variable coefficients numerically. The proposed scheme is capable of solving the equation having singularity at [...] Read more.
A fully discrete computational technique involving the implicit finite difference technique and cubic Hermite splines is proposed to solve the non-linear conformable damped Burgers’ equation with variable coefficients numerically. The proposed scheme is capable of solving the equation having singularity at t=0. The space direction is discretized using cubic Hermite splines, whereas the time direction is discretized using an implicit finite difference scheme. The convergence, stability and error estimates of the proposed scheme are discussed in detail to prove the efficiency of the technique. The convergence of the proposed scheme is found to be of order h2 in space and order (Δt)α in the time direction. The efficiency of the proposed scheme is verified by calculating error norms in the Eucledian and supremum sense. The proposed technique is applied on conformable damped Burgers’ equation with different initial and boundary conditions and the results are presented as tables and graphs. Comparison with results already in the literature also validates the application of the proposed technique. Full article
(This article belongs to the Topic Numerical Methods for Partial Differential Equations)
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18 pages, 1079 KiB  
Article
A Network-Based Study of the Dynamics of and τ Proteins in Alzheimer’s Disease
by Stefano Bianchi, Germana Landi, Camilla Marella, Maria Carla Tesi, Claudia Testa and on behalf of the Alzheimer’s Disease Neuroimaging Initiative
Math. Comput. Appl. 2024, 29(6), 113; https://doi.org/10.3390/mca29060113 - 4 Dec 2024
Viewed by 544
Abstract
Due to the extreme complexity of Alzheimer’s disease (AD), the etiology of which is not yet known, and for which there are no known effective treatments, mathematical modeling can be very useful. Indeed, mathematical models, if deemed reliable, can be used to test [...] Read more.
Due to the extreme complexity of Alzheimer’s disease (AD), the etiology of which is not yet known, and for which there are no known effective treatments, mathematical modeling can be very useful. Indeed, mathematical models, if deemed reliable, can be used to test medical hypotheses that could be difficult to verify directly. In this context, it is important to understand how Aβ and τ proteins, which, in abnormal aggregate conformations, are hallmarks of the disease, interact and spread. We are particularly interested, in this paper, in studying the spreading of misfolded τ. To this end, we present four different mathematical models, all on networks on which the protein evolves. The models differ in both the choice of network and diffusion operator. Through comparison with clinical data on τ concentration, which we carefully obtained with multimodal analysis techniques, we show that some models are more adequate than others to simulate the dynamics of the protein. This type of study may suggest that, when it comes to modeling certain pathologies, the choice of the mathematical setting must be made with great care if comparison with clinical data is considered decisive. Full article
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28 pages, 995 KiB  
Article
A Conservative and Compact Finite Difference Scheme for the Sixth-Order Boussinesq Equation with Surface Tension
by Xiaofeng Wang, Weizhong Dai and Anjan Biswas
Math. Comput. Appl. 2024, 29(6), 112; https://doi.org/10.3390/mca29060112 - 29 Nov 2024
Viewed by 358
Abstract
In this study, we propose a conservative and compact finite difference scheme designed to preserve both the mass change rate and energy for solving the sixth-order Boussinesq equation with surface tension. Theoretical analysis confirms that the proposed scheme achieves second-order accuracy in temporal [...] Read more.
In this study, we propose a conservative and compact finite difference scheme designed to preserve both the mass change rate and energy for solving the sixth-order Boussinesq equation with surface tension. Theoretical analysis confirms that the proposed scheme achieves second-order accuracy in temporal discretization and fourth-order accuracy in spatial discretization. The solvability, convergence, and stability of the difference scheme are rigorously established through the application of the discrete energy method. Additionally, a series of numerical experiments are conducted to illustrate the effectiveness and reliability of the conservative scheme for long-time simulations. Full article
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13 pages, 2920 KiB  
Article
Dynamic Time Warping as Elementary Effects Metric for Morris-Based Global Sensitivity Analysis of High-Dimension Dynamical Models
by Dhan Lord B. Fortela, Ashley P. Mikolajczyk, Rafael Hernandez, Emmanuel Revellame, Wayne Sharp, William Holmes, Daniel Gang and Mark E. Zappi
Math. Comput. Appl. 2024, 29(6), 111; https://doi.org/10.3390/mca29060111 - 27 Nov 2024
Viewed by 363
Abstract
This work focused on demonstrating the use of dynamic time warping (DTW) as a metric for the elementary effects computation in Morris-based global sensitivity analysis (GSA) of model parameters in multivariate dynamical systems. One of the challenges of GSA on multivariate time-dependent dynamics [...] Read more.
This work focused on demonstrating the use of dynamic time warping (DTW) as a metric for the elementary effects computation in Morris-based global sensitivity analysis (GSA) of model parameters in multivariate dynamical systems. One of the challenges of GSA on multivariate time-dependent dynamics is the modeling of parameter perturbation effects propagated to all model outputs while capturing time-dependent patterns. The study establishes and demonstrates the use of DTW as a metric of elementary effects across the time domain and the multivariate output domain, which are all aggregated together via the DTW cost function into a single metric value. Unlike the commonly studied coefficient-based functional approximation and covariance decomposition methods, this new DTW-based Morris GSA algorithm implements curve alignment via dynamic programing for cost computation in every parameter perturbation trajectory, which captures the essence of “elementary effect” in the original Morris formulation. This new algorithm eliminates approximations and assumptions about the model outputs while achieving the objective of capturing perturbations across time and the array of model outputs. The technique was demonstrated using an ordinary differential equation (ODE) system of mixed-order adsorption kinetics, Monod-type microbial kinetics, and the Lorenz attractor for chaotic solutions. DTW as a Morris-based GSA metric enables the modeling of parameter sensitivity effects on the entire array of model output variables evolving in the time domain, resulting in parameter rankings attributed to the entire model dynamics. Full article
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21 pages, 5633 KiB  
Article
Polynomial Approximation over Arbitrary Shape Domains
by Mohammad J. Mahtabi, Arash Ghasemi, Amirehsan Ghasemi and James C. Newman III
Math. Comput. Appl. 2024, 29(6), 110; https://doi.org/10.3390/mca29060110 - 25 Nov 2024
Viewed by 453
Abstract
In spectral/finite element methods, a robust and stable high-order polynomial approximation method for the solution can significantly reduce the required number of degrees of freedom (DOFs) to achieve a certain level of accuracy. In this work, a closed-form relation is proposed to approximate [...] Read more.
In spectral/finite element methods, a robust and stable high-order polynomial approximation method for the solution can significantly reduce the required number of degrees of freedom (DOFs) to achieve a certain level of accuracy. In this work, a closed-form relation is proposed to approximate the Fekete points (AFPs) on arbitrary shape domains based on the singular value decomposition (SVD) of the Vandermonde matrix. In addition, a novel method is derived to compute the moments on highly complex domains, which may include discontinuities. Then, AFPs are used to generate compatible basis functions using SVD. Equations are derived and presented to determine orthogonal/orthonormal modal basis functions, as well as the Lagrange basis. Furthermore, theorems are proved to show the convergence and accuracy of the proposed method, together with an explicit form of the Weierstrass theorem for polynomial approximation. The method was implemented and some classical cases were analyzed. The results show the superior performance of the proposed method in terms of convergence and accuracy using many fewer DOFs and, thus, a much lower computational cost. It was shown that the orthogonal modal basis is the best choice to decrease the DOFs while maintaining a small Lebesgue constant when very high degree of polynomial is employed. Full article
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3 pages, 194 KiB  
Editorial
Mathematical and Computational Modelling in Mechanics of Materials and Structures
by Nicholas Fantuzzi, Francesco Fabbrocino, Marco Montemurro, Francesca Nanni, Qun Huang, José António Correia, Leonardo Dassatti and Michele Bacciocchi
Math. Comput. Appl. 2024, 29(6), 109; https://doi.org/10.3390/mca29060109 - 25 Nov 2024
Viewed by 500
Abstract
The intersection of mathematics and computational modeling with the mechanics of materials and structural engineering continues to yield substantial advancements in both theoretical and applied domains [...] Full article
25 pages, 1607 KiB  
Review
Optimizing Power Flow and Stability in Hybrid AC/DC Microgrids: AC, DC, and Combined Analysis
by Ghanshyam Meena, Veerpratap Meena, Akhilesh Mathur, Vinay Pratap Singh, Ahmad Taher Azar and Ibrahim A. Hameed
Math. Comput. Appl. 2024, 29(6), 108; https://doi.org/10.3390/mca29060108 - 24 Nov 2024
Viewed by 462
Abstract
A microgrid (MG) is a unique area of a power distribution network that combines distributed generators (conventional as well as renewable power sources) and energy storage systems. Due to the integration of renewable generation sources, microgrids have become more unpredictable. MGs can operate [...] Read more.
A microgrid (MG) is a unique area of a power distribution network that combines distributed generators (conventional as well as renewable power sources) and energy storage systems. Due to the integration of renewable generation sources, microgrids have become more unpredictable. MGs can operate in two different modes, namely, grid-connected and islanded modes. MGs face various challenges of voltage variations, frequency deviations, harmonics, unbalances, etc., due to the uncertain behavior of renewable sources. To study the impact of these issues, it is necessary to analyze the behavior of the MG system under normal and abnormal operating conditions. Two different tools are used for the analysis of microgrids under normal and abnormal conditions, namely, power flow and short-circuit analysis, respectively. Power flow analysis is used to determine the voltages, currents, and real and reactive power flow in the MG system under normal operating conditions. Short-circuit analysis is carried out to analyze the behavior of MGs under faulty conditions. In this paper, a review of power flow and short-circuit analysis algorithms for MG systems under two different modes of operation, grid-connected and islanded, is presented. This paper also presents a comparison of various power flow as well as short-circuit analysis techniques for MGs in tabular form. The modeling of different components of MGs is also discussed in this paper. Full article
(This article belongs to the Special Issue Applied Optimization in Automatic Control and Systems Engineering)
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18 pages, 2638 KiB  
Article
Radical Petrov–Galerkin Approach for the Time-Fractional KdV–Burgers’ Equation
by Youssri Hassan Youssri and Ahmed Gamal Atta
Math. Comput. Appl. 2024, 29(6), 107; https://doi.org/10.3390/mca29060107 - 21 Nov 2024
Viewed by 566
Abstract
This paper presents a novel numerical spectral scheme to handle the time-fractional KdV–Burgers’ equation, which is very important in both physics and engineering. The scheme basically uses the tau approach combined with Gegenbauer polynomials to provide accurate and stable numerical solutions. Instead of [...] Read more.
This paper presents a novel numerical spectral scheme to handle the time-fractional KdV–Burgers’ equation, which is very important in both physics and engineering. The scheme basically uses the tau approach combined with Gegenbauer polynomials to provide accurate and stable numerical solutions. Instead of solving the differential problem together with the conditions, we solve a system of algebraic equations. The method can handle complex boundary conditions. Some numerical experiments are exhibited to demonstrate that this approach is highly efficient and produces results that are better than some existing numerical methods in the literature. This technique offers more advanced solutions for time-fractional problems in various fields. Full article
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23 pages, 463 KiB  
Article
Semantic Categories: Uncertainty and Similarity
by Ares Fabregat-Hernández, Javier Palanca and Vicent Botti
Math. Comput. Appl. 2024, 29(6), 106; https://doi.org/10.3390/mca29060106 - 16 Nov 2024
Viewed by 347
Abstract
This paper addresses understanding and categorizing language by using Markov categories to establish a mathematical framework for semantic concepts. This framework enables us to measure the semantic similarity between linguistic expressions within a given text. Furthermore, this approach enables the measurement and control [...] Read more.
This paper addresses understanding and categorizing language by using Markov categories to establish a mathematical framework for semantic concepts. This framework enables us to measure the semantic similarity between linguistic expressions within a given text. Furthermore, this approach enables the measurement and control of uncertainty in language categorization and the creation of metrics for evaluating semantic similarity. We provide use cases to demonstrate how the proposed methods can be applied and computed, focusing on their interpretability and the universality of categorical constructions. This work contributes to the field by offering a novel perspective on semantic similarity and uncertainty metrics in language processing, generating criteria to automate their computation. Full article
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13 pages, 436 KiB  
Article
Structural Stability of Pseudo-Parabolic Equations for Basic Data
by Yanping Wang and Yuanfei Li
Math. Comput. Appl. 2024, 29(6), 105; https://doi.org/10.3390/mca29060105 - 15 Nov 2024
Viewed by 339
Abstract
This article investigates the spatial decay properties and continuous dependence on the basic geometric structure. Assuming that the total potential energy is bounded and the homogeneous Dirichlet condition is satisfied on the side of the solution within the cylindrical domain, we establish an [...] Read more.
This article investigates the spatial decay properties and continuous dependence on the basic geometric structure. Assuming that the total potential energy is bounded and the homogeneous Dirichlet condition is satisfied on the side of the solution within the cylindrical domain, we establish an auxiliary function related to the solution. By extending the data at the finite end forward, we can establish the continuous dependence on the perturbation of base data. Full article
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22 pages, 56577 KiB  
Article
Resolving Contrast and Detail Trade-Offs in Image Processing with Multi-Objective Optimization
by Daniel Molina-Pérez and Alam Gabriel Rojas-López
Math. Comput. Appl. 2024, 29(6), 104; https://doi.org/10.3390/mca29060104 - 11 Nov 2024
Viewed by 594
Abstract
This article addresses the complex challenge of simultaneously enhancing contrast and detail in an image, where improving one property often compromises the other. This trade-off is tackled using a multi-objective optimization approach. Specifically, the proposal’s model integrates the sigmoid transformation function and unsharp [...] Read more.
This article addresses the complex challenge of simultaneously enhancing contrast and detail in an image, where improving one property often compromises the other. This trade-off is tackled using a multi-objective optimization approach. Specifically, the proposal’s model integrates the sigmoid transformation function and unsharp masking highboost filtering with the NSGA-II algorithm. Additionally, a posterior preference articulation is introduced to select three key solutions from the Pareto front: the maximum contrast solution, the maximum detail solution, and the knee point solution. The proposed technique is evaluated on a range of image types, including medical and natural scenes. The final solutions demonstrated significant superiority in terms of contrast and detail compared to the original images. The three selected solutions, although all are optimal, captured distinct characteristics within the images, offering different solutions according to field preferences. This highlights the method’s effectiveness across different types and enhancement requirements and emphasizes the importance of the proposed preferences in different contexts. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2024)
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16 pages, 504 KiB  
Article
An Experimental Comparison of Self-Adaptive Differential Evolution Algorithms to Induce Oblique Decision Trees
by Rafael Rivera-López, Efrén Mezura-Montes, Juana Canul-Reich and Marco-Antonio Cruz-Chávez
Math. Comput. Appl. 2024, 29(6), 103; https://doi.org/10.3390/mca29060103 - 9 Nov 2024
Viewed by 474
Abstract
This study addresses the challenge of generating accurate and compact oblique decision trees using self-adaptive differential evolution algorithms. Although traditional decision tree induction methods create explainable models, they often fail to achieve optimal classification accuracy. To overcome these limitations, other strategies, such as [...] Read more.
This study addresses the challenge of generating accurate and compact oblique decision trees using self-adaptive differential evolution algorithms. Although traditional decision tree induction methods create explainable models, they often fail to achieve optimal classification accuracy. To overcome these limitations, other strategies, such as those based on evolutionary computation, have been proposed in the literature. In particular, we evaluate the use of self-adaptive differential evolution variants to evolve a population of oblique decision trees encoded as real-valued vectors. Our proposal includes (1) an alternative initialization strategy that reduces redundant nodes and (2) a fitness function that penalizes excessive leaf nodes, promoting smaller and more accurate decision trees. We perform a comparative performance analysis of these differential evolution variants, showing that while they exhibit similar statistical behavior, the Single-Objective real-parameter optimization (jSO) method produces the most accurate oblique decision trees and is second best in compactness. The findings highlight the potential of self-adaptive differential evolution algorithms to improve the effectiveness of oblique decision trees in machine learning applications. Full article
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21 pages, 3240 KiB  
Article
A Mathematical Lens on the Zoonotic Transmission of Lassa Virus Infections Leading to Disabilities in Severe Cases
by Yasir Ramzan, Hanadi Alzubadi, Aziz Ullah Awan, Kamel Guedri, Mohammed Alharthi and Bandar M. Fadhl
Math. Comput. Appl. 2024, 29(6), 102; https://doi.org/10.3390/mca29060102 - 7 Nov 2024
Viewed by 504
Abstract
This study aims to analyze the dynamics of Lassa fever transmission and its impact on the brain and spinal cord then devise and analyze preventive actions. The stability of the infection-free equilibrium point is evaluated; the model’s precision is examined using empirical data; [...] Read more.
This study aims to analyze the dynamics of Lassa fever transmission and its impact on the brain and spinal cord then devise and analyze preventive actions. The stability of the infection-free equilibrium point is evaluated; the model’s precision is examined using empirical data; and all parameters are estimated and fitted. Subsequently, the basic reproductive number is determined, and subpopulation trends are observed over time. Sensitivity analysis is conducted to identify critical drivers influencing transmission dynamics. Two-dimensional plots visualize the impact of crucial parameters on the reproductive number. Through a comprehensive literature review and case analysis, an association between Lassa fever and various disabilities is established, including conditions such as encephalitis, hearing loss, ataxia, neuropsychiatric manifestations, meningitis, seizures, and coma. Solutions are devised and analyzed to enhance early detection, treatment, and mitigation of disease. Full article
(This article belongs to the Special Issue New Trends in Biomathematics)
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19 pages, 5947 KiB  
Article
Analytical Solutions of PBTK Models for Evaluating the Impact of Surface Diffusion Characteristics on the Leaching Profile of Implant Byproducts
by Matheos Giakoumi, Konstantinos Kapnisis, Andreas Anayiotos and Pavlos S. Stephanou
Math. Comput. Appl. 2024, 29(6), 101; https://doi.org/10.3390/mca29060101 - 4 Nov 2024
Viewed by 702
Abstract
Toxicokinetic or pharmacokinetic models, physiologically based or not, offer a unique avenue to understand the transport of toxins or pharmaceuticals in living organisms. The availability of analytical solutions to such models offers the means to engage in a plethora of applications. In the [...] Read more.
Toxicokinetic or pharmacokinetic models, physiologically based or not, offer a unique avenue to understand the transport of toxins or pharmaceuticals in living organisms. The availability of analytical solutions to such models offers the means to engage in a plethora of applications. In the present work, we provide the framework to solve analytically such models using the matrix exponential, and we then apply this method to derive an explicit solution to four-to-five-compartment physiologically based toxicokinetic (PBTK) models considering a single- and an infinite-exponential expression for the amount of mass released from an implantable device. We also offer the conditions that need to be met for analytical solutions to be obtained when the kinetic rates are time-dependent functions. Our analysis compares the computation time between analytical and numerical solutions and characterizes the dependency of the maximum substance mass value and the time it occurs in the various tissue compartments from the material surface diffusion characteristics. Our analytical solutions, which have several advantages over the solutions obtained using numerical solvers, can be incorporated into in silico tools and provide valuable information for human health risk assessment. Full article
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17 pages, 532 KiB  
Article
Numerical Study of Multi-Term Time-Fractional Sub-Diffusion Equation Using Hybrid L1 Scheme with Quintic Hermite Splines
by Priyanka Priyanka, Shelly Arora, Saroj Sahani and Sharandeep Singh
Math. Comput. Appl. 2024, 29(6), 100; https://doi.org/10.3390/mca29060100 - 2 Nov 2024
Viewed by 568
Abstract
Anomalous diffusion of particles has been described by the time-fractional reaction–diffusion equation. A hybrid formulation of numerical technique is proposed to solve the time-fractional-order reaction–diffusion (FRD) equation numerically. The technique comprises the semi-discretization of the time variable using an L1 finite-difference scheme and [...] Read more.
Anomalous diffusion of particles has been described by the time-fractional reaction–diffusion equation. A hybrid formulation of numerical technique is proposed to solve the time-fractional-order reaction–diffusion (FRD) equation numerically. The technique comprises the semi-discretization of the time variable using an L1 finite-difference scheme and space discretization using the quintic Hermite spline collocation method. The hybrid technique reduces the problem to an iterative scheme of an algebraic system of equations. The stability analysis of the proposed numerical scheme and the optimal error bounds for the approximate solution are also studied. A comparative study of the obtained results and an error analysis of approximation show the efficiency, accuracy, and effectiveness of the technique. Full article
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3 pages, 154 KiB  
Editorial
Feature Paper Collection of Mathematical and Computational Applications—2023
by Gianluigi Rozza, Oliver Schütze and Nicholas Fantuzzi
Math. Comput. Appl. 2024, 29(6), 99; https://doi.org/10.3390/mca29060099 - 1 Nov 2024
Viewed by 404
Abstract
This Special Issue comprises the second collection of papers submitted by both the Editorial Board Members (EBMs) of the journal Mathematical and Computational Applications (MCA) and the outstanding scholars working in the core research fields of MCA [...] Full article
24 pages, 6455 KiB  
Article
Using Artificial Neural Network Analysis to Study Jeffrey Nanofluid Flow in Cone–Disk Systems
by Nasser Nammas Albaqami
Math. Comput. Appl. 2024, 29(6), 98; https://doi.org/10.3390/mca29060098 - 31 Oct 2024
Viewed by 518
Abstract
Artificial intelligence (AI) is employed in fluid flow models to enhance the simulation’s accuracy, to more effectively optimize the fluid flow models, and to realize reliable fluid flow systems with improved performance. Jeffery fluid flow through the interstice of a cone-and-disk system is [...] Read more.
Artificial intelligence (AI) is employed in fluid flow models to enhance the simulation’s accuracy, to more effectively optimize the fluid flow models, and to realize reliable fluid flow systems with improved performance. Jeffery fluid flow through the interstice of a cone-and-disk system is considered in this study. The mathematical description of this flow involves converting a partial differential system into a nonlinear ordinary differential system and solving it using a neurocomputational technique. The fluid streaming through the disk–cone gap is investigated under four contrasting frameworks, i.e., (i) passive cone and spinning disk, (ii) spinning cone and passive disk, (iii) cone and disk rotating in the same direction, and (iv) cone and disk rotating in opposite directions. Employing the recently developed technique of artificial neural networks (ANNs) can be effective for handling and optimizing fluid flow exploits. The proposed approach integrates training, testing and analysis, and authentication based on a locus dataset to address various aspects of fluid problems. The mean square error, regression plots, curve-fitting graphs, and error histograms are used to evaluate the performance of the least mean square neural network algorithm (LMS-NNA). The results show that these equations are consistently aligned, and agreement is, on average, in the order of 10−8. While the resting parameters were kept static, the transverse velocity distribution, in all four cases, exhibited an incremental decreasing behavior in the estimates of magnetic and Jeffery fluid factors. Furthermore, the results obtained were compared with those in the literature, and the close agreement confirms our results. To train the model, 80% of the data were used for LMS-NNA, with 10% used for testing and the remaining 10% for validation. The quantitative and qualitative outputs obtained from the neural network strategy and parameter variation were thoroughly examined and discussed. Full article
(This article belongs to the Special Issue Symmetry Methods for Solving Differential Equations)
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13 pages, 7092 KiB  
Article
Design and Optimization of Microfluidic Vortex Diode
by Krzysztof Tadyszak, Alessandro Jäger, Jiří Pánek and Martin Hrubý
Math. Comput. Appl. 2024, 29(6), 97; https://doi.org/10.3390/mca29060097 - 30 Oct 2024
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Abstract
The performed research presents modeling results for designing microfluidic vortex diodes. These devices rectify fluid flow and can be used in many applications on micro and macro scales. The modeling, utilizing computational fluid dynamics (CFD) with the turbulence model RANS k-ε in COMSOL [...] Read more.
The performed research presents modeling results for designing microfluidic vortex diodes. These devices rectify fluid flow and can be used in many applications on micro and macro scales. The modeling, utilizing computational fluid dynamics (CFD) with the turbulence model RANS k-ε in COMSOL Multiphysics, has led to optimizing diodicity—the reversed-to-forward flow pressure drop ratio. The goal was to find the best flow-rectifying geometry within the 2D vortex-type design by changing the wall geometry, diode shape, and inflow velocities, identifying significant parameters and dependencies. Improving diodicity can be achieved by increasing the radius r1 of the central channel, increasing the entire diode radius r2, decreasing the width w of the rectangular channel, and reducing its length L. Additionally, changing the circular shape of the diode to an elliptical one can improve diodicity. The significance of this research is evident in the potential applications of these devices in microfluidic setups where fixed-geometry unidirectional flow is required, e.g., mixing, filtration, cell separation, and drug delivery, or on industrial scales, e.g., energy harvesting, wastewater treatment, and water sterilization. Full article
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30 pages, 858 KiB  
Article
Sliding Mode Fault-Tolerant Control for Nonlinear LPV Systems with Variable Time-Delay
by Omayma Mansouri, Ali Ben Brahim, Fayçal Ben Hmida and Anis Sellami
Math. Comput. Appl. 2024, 29(6), 96; https://doi.org/10.3390/mca29060096 - 26 Oct 2024
Viewed by 681
Abstract
This paper presents a robust sliding mode fault-tolerant control (FTC) strategy for a class of linear parameter variant (LPV) systems with variable time-delays and uncertainties. First fault estimation (FE) is conducted using a robust sliding mode observer, synthesized to simultaneously estimate the states [...] Read more.
This paper presents a robust sliding mode fault-tolerant control (FTC) strategy for a class of linear parameter variant (LPV) systems with variable time-delays and uncertainties. First fault estimation (FE) is conducted using a robust sliding mode observer, synthesized to simultaneously estimate the states and actuator faults of LPV polytopic delayed systems. Second, a sliding mode FTC is developed, ensuring all states of the closed-loop system converge to the origin. This paper presents an integrated sliding mode FTC strategy to achieve optimal robustness between the observer and controller models. The integrated design approach offers several advantages over traditional separated FTC methods. Our novel approach is based on incorporating adaptive law into the design of the Lyapunov–Krasovskii functional to improve both robustness and performance. This is achieved by combining the concept of sliding mode control (SMC) with the Lyapunov–Krasovskii function under the H criteria, which plays a key role in guaranteeing the stability of this class of system. The effectiveness of the proposed method is demonstrated through a diesel engine example, which highlights the validity and benefits of the integrated and separated FTC strategy for uncertain nonlinear systems with time delays and the sliding mode control. Full article
(This article belongs to the Special Issue Applied Optimization in Automatic Control and Systems Engineering)
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