Mathematical and Computational Applications

13 pages, 3928 KiB

Open AccessArticle

Computational Modeling of Sodium-Ion-Channel-Based Glucose Sensing Biophysics to Study Cardiac Pacemaker Action Potential

by Chitaranjan Mahapatra, Kirubanandan Shanmugam and Maher Ali Rusho

Math. Comput. Appl. 2024, 29(5), 84; https://doi.org/10.3390/mca29050084 - 21 Sep 2024

Abstract

Elevated blood glucose levels, known as hyperglycemia, play a significant role in sudden cardiac arrest, often resulting in sudden cardiac death, particularly among those with diabetes. Understanding the internal mechanisms has been a challenge for healthcare professionals, leading many research groups to investigate [...] Read more.

Elevated blood glucose levels, known as hyperglycemia, play a significant role in sudden cardiac arrest, often resulting in sudden cardiac death, particularly among those with diabetes. Understanding the internal mechanisms has been a challenge for healthcare professionals, leading many research groups to investigate the relationship between blood glucose levels and cardiac electrical activity. Our hypothesis suggests that glucose-sensing biophysics mechanisms in cardiac tissue could clarify this connection. To explore this, we adapted a single-compartment computational model of the human pacemaker action potential. We incorporated glucose-sensing mechanisms with voltage-gated sodium ion channels using ordinary differential equations. Parameters for the model were based on existing experimental studies to mimic the impact of glucose levels on pacemaker action potential firing. Simulations using voltage clamp and current clamp techniques showed that elevated glucose levels decreased sodium ion channel currents, leading to a reduction in the pacemaker action potential frequency. In summary, our mathematical model provides a cellular-level understanding of how high glucose levels can lead to bradycardia and sudden cardiac death. Full article

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14 pages, 552 KiB

Open AccessArticle

Design and Implementation of a Discrete-PDC Controller for Stabilization of an Inverted Pendulum on a Self-Balancing Car Using a Convex Approach

by Yasmani González-Cárdenas, Francisco-Ronay López-Estrada, Víctor Estrada-Manzo, Joaquin Dominguez-Zenteno and Manuel López-Pérez

Math. Comput. Appl. 2024, 29(5), 83; https://doi.org/10.3390/mca29050083 - 18 Sep 2024

Abstract

This paper presents a trajectory-tracking controller of an inverted pendulum system on a self-balancing differential drive platform. First, the system modeling is described by considering approximations of the swing angles. Subsequently, a discrete convex representation of the system via the nonlinear sector technique [...] Read more.

This paper presents a trajectory-tracking controller of an inverted pendulum system on a self-balancing differential drive platform. First, the system modeling is described by considering approximations of the swing angles. Subsequently, a discrete convex representation of the system via the nonlinear sector technique is obtained, which considers the nonlinearities associated with the nonholonomic constraint. The design of a discrete parallel distributed compensation controller is achieved through an alternative method due to the presence of uncontrollable points that avoid finding a solution for the entire polytope. Finally, simulations and experimental results using a prototype illustrate the effectiveness of the proposal. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2024)

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4 pages, 144 KiB

Open AccessEditorial

Significance of Mathematical Modeling and Control in Real-World Problems: New Developments and Applications

by Mehmet Yavuz and Ioannis Dassios

Math. Comput. Appl. 2024, 29(5), 82; https://doi.org/10.3390/mca29050082 - 18 Sep 2024

Abstract

Mathematical modeling and system control are employed in many research problems, ranging from physical and chemical processes to biomathematics and life sciences [...] Full article

(This article belongs to the Special Issue Significance of Mathematical Modelling and Control in Real-World Problems: New Developments and Applications)

13 pages, 508 KiB

Open AccessArticle

A Corruption Impunity Model Considering Anticorruption Policies

by Sandra E. Delgadillo-Alemán, Roberto A. Kú-Carrillo and Alejandra Torres-Nájera

Math. Comput. Appl. 2024, 29(5), 81; https://doi.org/10.3390/mca29050081 - 14 Sep 2024

Abstract

Corruption is a global problem that affects the fair distribution of wealth of every country to different degrees and represents a problem to be solved to prevent the diversion and waste of resources. Among the different efforts to first measure it and later [...] Read more.

Corruption is a global problem that affects the fair distribution of wealth of every country to different degrees and represents a problem to be solved to prevent the diversion and waste of resources. Among the different efforts to first measure it and later reduce it by proposing strategies, there exist a variety of indices, such as the corruption perception index, and other related issues, such as the global impunity index, the laxness of anticorruption policies, etc., which are computed for different countries worldwide. Based on these indices, we propose a model for corruption using a system of ordinary differential equations, considering anticorruption policies. Those three factors were identified after analyzing the phenomenon and available data, particularly for Mexico. Also, we fit it to the reported data of this country and perform simulations expecting to predict the short term, and performed a sensitivity analysis. The model is capable of reproducing the observed oscillatory behavior of the phenomenon. The model fit can still be improved by including the data for the anticorruption policies, which were only studied for different scenarios. Moreover, the model is susceptible to application in other countries, as long as data are available, and then provides a computational tool to predict and visualize the effect of appropriate public policies to fight corruption. Full article

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20 pages, 3041 KiB

Open AccessArticle

Human Activity Recognition from Accelerometry, Based on a Radius of Curvature Feature

by Elizabeth Cavita-Huerta, Juan Reyes-Reyes, Héctor M. Romero-Ugalde, Gloria L. Osorio-Gordillo, Ricardo F. Escobar-Jiménez and Victor M. Alvarado-Martínez

Math. Comput. Appl. 2024, 29(5), 80; https://doi.org/10.3390/mca29050080 - 13 Sep 2024

Abstract

Physical activity recognition using accelerometry is a rapidly advancing field with significant implications for healthcare, sports science, and wearable technology. This research presents an interesting approach for classifying physical activities using solely accelerometry data, signals that were taken from the available “MHEALTH dataset” [...] Read more.

Physical activity recognition using accelerometry is a rapidly advancing field with significant implications for healthcare, sports science, and wearable technology. This research presents an interesting approach for classifying physical activities using solely accelerometry data, signals that were taken from the available “MHEALTH dataset” and processed through artificial neural networks (ANNs). The methodology involves data acquisition, preprocessing, feature extraction, and the application of deep learning algorithms to accurately identify activity patterns. A major innovation in this study is the incorporation of a new feature derived from the radius of curvature. This time-domain feature is computed by segmenting accelerometry signals into windows, conducting double integration to derive positional data, and subsequently estimating a circumference based on the positional data obtained within each window. This characteristic is computed across the three movement planes, providing a robust and comprehensive feature for activity classification. The integration of the radius of curvature into the ANN models significantly enhances their accuracy, achieving over 95%. In comparison with other methodologies, our proposed approach, which utilizes a feedforward neural network (FFNN), demonstrates superior performance. This outperforms previous methods such as logistic regression, which achieved 93%, KNN models with 90%, and the InceptTime model with 88%. The findings demonstrate the potential of this model to improve the precision and reliability of physical activity recognition in wearable health monitoring systems. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2024)

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29 pages, 42369 KiB

Open AccessArticle

Analysis and Design for a Wearable Single-Finger-Assistive Soft Robotic Device Allowing Flexion and Extension for Different Finger Sizes

by Sung bok Chung and Martin Philip Venter

Math. Comput. Appl. 2024, 29(5), 79; https://doi.org/10.3390/mca29050079 - 12 Sep 2024

Abstract

This paper proposes a design framework to create individualised finger actuators that can be expanded to a generic hand. An actuator design is evaluated to help a finger achieve tendon-gliding exercises (TGEs). We consider musculoskeletal analysis for different finger sizes to determine joint [...] Read more.

This paper proposes a design framework to create individualised finger actuators that can be expanded to a generic hand. An actuator design is evaluated to help a finger achieve tendon-gliding exercises (TGEs). We consider musculoskeletal analysis for different finger sizes to determine joint forces while considering safety. The simulated Finite Element Analysis (FEA) response of a bi-directional Pneumatic Network Actuator (PNA) is mapped to a reduced-order model, creating a robust design tool to determine the bending angle and moment generated for actuator units. A reduced-order model is considered for both the 2D plane-strain formulation of the actuator and a full 3D model, providing a means to map between the results for a more accurate 3D model and the less computationally expensive 2D model. A setup considering a cascade of reduced-order actuator units interacting with a finger model determined to be able to achieve TGE was validated, and three exercises were successfully achieved. The FEA simulations were validated using the bending response of a manufactured actuator interacting with a dummy finger. The quality of the results shows that the simulated models can be used to predict the behaviour of the physical actuator in achieving TGE. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics (AfriComp6))

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Graphical abstract

27 pages, 1003 KiB

Open AccessFeature PaperArticle

Surrogate-Assisted Symbolic Time-Series Discretization Using Multi-Breakpoints and a Multi-Objective Evolutionary Algorithm

by Aldo Márquez-Grajales, Efrén Mezura-Montes, Héctor-Gabriel Acosta-Mesa and Fernando Salas-Martínez

Math. Comput. Appl. 2024, 29(5), 78; https://doi.org/10.3390/mca29050078 - 11 Sep 2024

Abstract

The enhanced multi-objective symbolic discretization for time series (eMODiTS) method employs a flexible discretization scheme using different value cuts for each non-equal time interval, which incurs a high computational cost for evaluating each objective function. It is essential to mention that each solution [...] Read more.

The enhanced multi-objective symbolic discretization for time series (eMODiTS) method employs a flexible discretization scheme using different value cuts for each non-equal time interval, which incurs a high computational cost for evaluating each objective function. It is essential to mention that each solution found by eMODiTS is a different-sized vector. Previous work was performed where surrogate models were implemented to reduce the computational cost to solve this problem. However, low-fidelity approximations were obtained concerning the original model. Consequently, our main objective is to propose an improvement to this work, modifying the updating process of the surrogate models to minimize their disadvantages. This improvement was evaluated based on classification, predictive power, and computational cost, comparing it against the original model and ten discretization methods reported in the literature. The results suggest that the proposal achieves a higher fidelity to the original model than previous work. It also achieved a computational cost reduction rate between 15% and 80% concerning the original model. Finally, the classification error of our proposal is similar to eMODiTS and maintains its behavior compared to the other discretization methods. Full article

(This article belongs to the Collection Feature Papers in Mathematical and Computational Applications 2024)

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Graphical abstract

15 pages, 3843 KiB

Open AccessArticle

A Study of Tennis Tournaments by Means of an Agent-Based Model Calibrated with a Genetic Algorithm

by Salvatore Prestipino and Andrea Rapisarda

Math. Comput. Appl. 2024, 29(5), 77; https://doi.org/10.3390/mca29050077 - 11 Sep 2024

Abstract

In this work, we study the sport of tennis, with the aim of understanding competitions and the associated quantities that determine their outcome. We construct an agent-based model that is able to produce data analogous to real data taken from Association of Tennis [...] Read more.

In this work, we study the sport of tennis, with the aim of understanding competitions and the associated quantities that determine their outcome. We construct an agent-based model that is able to produce data analogous to real data taken from Association of Tennis Professionals (ATP) tournaments. This model depends on three parameters: the talent weight, the talent distribution width, and the chance distribution width. Unlike other similar works, we do not fix the values of these parameters and we calibrate the model results with the help of a genetic algorithm, thus exploring all possible combinations of parameters in the parameter space that are able to reproduce real system data. We show that the model fits the real data well only for limited regions of the parameter space. Limiting the region of interest in the parameter space allows us to perform further calibrations of the model that give us more information about the competition under study. Finally, we are able to provide useful information about tennis competitions, obtaining quantitative information about all of the important parameters and quantities related to these competitions with very limited a priori constraints. Through our approach, differing from those of other works, we confirm the importance of chance in the studied competitions, which has a weight of around 80% in determining the outcome of tennis competitions. Full article

(This article belongs to the Topic Mathematical Modeling)

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13 pages, 2327 KiB

Open AccessFeature PaperArticle

An Alternative Analysis of Computational Learning within Behavioral Neuropharmacology in an Experimental Anxiety Model Investigation

by Isidro Vargas-Moreno, Héctor Gabriel Acosta-Mesa, Juan Francisco Rodríguez-Landa, Martha Lorena Avendaño-Garrido, Rafael Fernández-Demeneghi and Socorro Herrera-Meza

Math. Comput. Appl. 2024, 29(5), 76; https://doi.org/10.3390/mca29050076 - 9 Sep 2024

Abstract

Behavioral neuropharmacology, a branch of neuroscience, uses behavioral analysis to demonstrate treatment effects on animal models, which is fundamental for pre-clinical evaluation. Typically, this determination is univariate, neglecting the relevant associations for understanding treatment effects in animals and humans. This study implements regression [...] Read more.

Behavioral neuropharmacology, a branch of neuroscience, uses behavioral analysis to demonstrate treatment effects on animal models, which is fundamental for pre-clinical evaluation. Typically, this determination is univariate, neglecting the relevant associations for understanding treatment effects in animals and humans. This study implements regression trees and Bayesian networks from a multivariate perspective by using variables obtained from behavioral tests to predict the time spent in the open arms of the elevated arm maze, a key variable to assess anxiety. Three doses of allopregnanolone were analyzed and compared to a vehicle group and a diazepam-positive control. Regression trees identified cut-off points between the anxiolytic and anxiogenic effects, with the anxiety index standing out as a robust predictor, combined with the percentage of open-arm entries and the number of entries. Bayesian networks facilitated the visualization and understanding of the interactions between multiple behavioral and biological variables, demonstrating that treatment with allopregnanolone (2 mg) emulates the effects of diazepam, validating the multivariate approach. The results highlight the relevance of integrating advanced methods, such as Bayesian networks, into preclinical research to enrich the interpretation of complex behavioral data in animal models, which can hardly be observed with univariate statistics. Full article

(This article belongs to the Special Issue New Trends in Computational Intelligence and Applications 2023)

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Graphical abstract

13 pages, 2526 KiB

Open AccessArticle

Innovative Solutions to the Fractional Diffusion Equation Using the Elzaki Transform

by Saima Noor, Albandari W. Alrowaily, Mohammad Alqudah, Rasool Shah and Samir A. El-Tantawy

Math. Comput. Appl. 2024, 29(5), 75; https://doi.org/10.3390/mca29050075 - 2 Sep 2024

Abstract

This study explores the application of advanced mathematical techniques to solve fractional differential equations, focusing particularly on the fractional diffusion equation. The fractional diffusion equation, used to simulate a range of physical and engineering phenomena, poses considerable difficulties when applied to fractional orders. [...] Read more.

This study explores the application of advanced mathematical techniques to solve fractional differential equations, focusing particularly on the fractional diffusion equation. The fractional diffusion equation, used to simulate a range of physical and engineering phenomena, poses considerable difficulties when applied to fractional orders. Thus, by utilizing the mighty powers of fractional calculus, we employ the variational iteration method (VIM) with the Elzaki transform to produce highly accurate approximations for these specific differential equations. The VIM provides an iterative framework for refining solutions progressively, while the Elzaki transform simplifies the complex integral transforms involved. By integrating these methodologies, we achieve accurate and efficient solutions to the fractional diffusion equation. Our findings demonstrate the robustness and effectiveness of combining the VIM and the Elzaki transform in handling fractional differential equations, offering explicit functional expressions that are beneficial for theoretical analysis and practical applications. This research contributes to the expanding field of fractional calculus, providing valuable insights and useful tools for solving complex, nonlinear fractional differential equations across various scientific and engineering disciplines. Full article

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15 pages, 1676 KiB

Open AccessArticle

Using Kan Extensions to Motivate the Design of a Surprisingly Effective Unsupervised Linear SVM on the Occupancy Dataset

by Matthew Pugh, Jo Grundy, Corina Cirstea and Nick Harris

Math. Comput. Appl. 2024, 29(5), 74; https://doi.org/10.3390/mca29050074 - 2 Sep 2024

Abstract

Recent research has suggested that category theory can provide useful insights into the field of machine learning (ML). One example is improving the connection between an ML problem and the design of a corresponding ML algorithm. A tool from category theory called a [...] Read more.

Recent research has suggested that category theory can provide useful insights into the field of machine learning (ML). One example is improving the connection between an ML problem and the design of a corresponding ML algorithm. A tool from category theory called a Kan extension is used to derive the design of an unsupervised anomaly detection algorithm for a commonly used benchmark, the Occupancy dataset. Achieving an accuracy of 93.5% and an ROCAUC of 0.98, the performance of this algorithm is compared to state-of-the-art anomaly detection algorithms tested on the Occupancy dataset. These initial results demonstrate that category theory can offer new perspectives with which to attack problems, particularly in making more direct connections between the solutions and the problem’s structure. Full article

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20 pages, 748 KiB

Open AccessArticle

Causal Analysis to Explain the Performance of Algorithms: A Case Study for the Bin Packing Problem

by Jenny Betsabé Vázquez-Aguirre, Guadalupe Carmona-Arroyo, Marcela Quiroz-Castellanos and Nicandro Cruz-Ramírez

Math. Comput. Appl. 2024, 29(5), 73; https://doi.org/10.3390/mca29050073 - 28 Aug 2024

Abstract

This work presents a knowledge discovery approach through Causal Bayesian Networks for understanding the conditions under which the performance of an optimization algorithm can be affected by the characteristics of the instances of a combinatorial optimization problem (COP). We introduce a case study [...] Read more.

This work presents a knowledge discovery approach through Causal Bayesian Networks for understanding the conditions under which the performance of an optimization algorithm can be affected by the characteristics of the instances of a combinatorial optimization problem (COP). We introduce a case study for the causal analysis of the performance of two state-of-the-art algorithms for the one-dimensional Bin Packing Problem (BPP). We meticulously selected the set of features associated with the parameters that define the instances of the problem. Subsequently, we evaluated the algorithmic performance on instances with distinct features. Our analysis scrutinizes both instance features and algorithm performance, aiming to identify causes influencing the performance of the algorithms. The proposed study successfully identifies specific values affecting algorithmic effectiveness and efficiency, revealing shared causes within some value ranges across both algorithms. The knowledge generated establishes a robust foundation for future research, enabling predictions of algorithmic performance, as well as the selection and design of heuristic strategies for improving the performance in the most difficult instances. The causal analysis employed in this study did not require specific configurations, making it an invaluable tool for analyzing the performance of different algorithms in other COPs. Full article

(This article belongs to the Special Issue New Trends in Computational Intelligence and Applications 2023)

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10 pages, 669 KiB

Open AccessArticle

Analysis of a First-Order Delay Model under a History Function with Discontinuity

by Weam G. Alharbi

Math. Comput. Appl. 2024, 29(5), 72; https://doi.org/10.3390/mca29050072 - 24 Aug 2024

Abstract

This paper analyzes the first-order delay equation

y^{'} (t) = α y (t) + β y (t - τ)

subject to a history function in addition to an initial condition that assumes discontinuity at [...] Read more.

This paper analyzes the first-order delay equation

y^{'} (t) = α y (t) + β y (t - τ)

subject to a history function in addition to an initial condition that assumes discontinuity at

t = 0

. The method of steps is successfully applied to derive the exact solution in an explicit form. In addition, a unified formula is provided to describe the solution in any finite sub-interval of the problem’s domain. The characteristics and properties of the solution are theoretically investigated and then confirmed through several plots. The behavior of the solution and its derivative are examined and interpreted. The results show that the method of steps is an effective method of solution to treat the current delay model. The present successful analysis can be used to investigate other delay models with complex initial conditions. Furthermore, the present approach can be generalized to include the inhomogeneous version of the current model without using numerical methods. Full article

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17 pages, 4513 KiB

Open AccessArticle

Machine Learning Based Extraction of Boundary Conditions from Doppler Echo Images for Patient Specific Coarctation of the Aorta: Computational Fluid Dynamics Study

by Vincent Milimo Masilokwa Punabantu, Malebogo Ngoepe, Amit Kumar Mishra, Thomas Aldersley, John Lawrenson and Liesl Zühlke

Math. Comput. Appl. 2024, 29(5), 71; https://doi.org/10.3390/mca29050071 - 23 Aug 2024

Abstract

Patient-specific computational fluid dynamics (CFD) studies on coarctation of the aorta (CoA) in resource-constrained settings are limited by the available imaging modalities for geometry and velocity data acquisition. Doppler echocardiography is considered a suitable velocity acquisition modality due to its low cost and [...] Read more.

Patient-specific computational fluid dynamics (CFD) studies on coarctation of the aorta (CoA) in resource-constrained settings are limited by the available imaging modalities for geometry and velocity data acquisition. Doppler echocardiography is considered a suitable velocity acquisition modality due to its low cost and safety. This study aims to investigate the application of classical machine learning (ML) methods to create an adequate and robust approach to obtain boundary conditions (BCs) from Doppler echocardiography images for haemodynamic modelling using CFD. Our proposed approach combines ML and CFD to model haemodynamic flow within the region of interest. The key feature of the approach is the use of ML models to calibrate the inlet and outlet BCs of the CFD model. In the ML model, patient heart rate served as the crucial input variable due to its temporal variation across the measured vessels. ANSYS Fluent was used for the CFD component of the study, whilst the Scikit-learn Python library was used for the ML component. We validated our approach against a real clinical case of severe CoA before intervention. The maximum coarctation velocity of our simulations was compared to the measured maximum coarctation velocity obtained from the patient whose geometry was used within the study. Of the 5 mL models used to obtain BCs, the top model was within 5% of the maximum measured coarctation velocity. The framework demonstrated that it was capable of taking into account variations in the patient’s heart rate between measurements. Therefore, it allowed for the calculation of BCs that were physiologically realistic when the measurements across each vessel were scaled to the same heart rate while providing a reasonably accurate solution. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics (AfriComp6))

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28 pages, 73507 KiB

Open AccessArticle

Numerical Modelling of Corrugated Paperboard Boxes

by Rhoda Ngira Aduke, Martin P. Venter and Corné J. Coetzee

Math. Comput. Appl. 2024, 29(4), 70; https://doi.org/10.3390/mca29040070 - 22 Aug 2024

Abstract

Numerical modelling of corrugated paperboard is quite challenging due to its waved geometry and material non-linearity which is affected by the material properties of the individual paper sheets. Because of the complex geometry and material behaviour of the board, there is still scope [...] Read more.

Numerical modelling of corrugated paperboard is quite challenging due to its waved geometry and material non-linearity which is affected by the material properties of the individual paper sheets. Because of the complex geometry and material behaviour of the board, there is still scope to enhance the accuracy of current modelling techniques as well as gain a better understanding of the structural performance of corrugated paperboard packaging for improved packaging design. In this study, four-point bending tests were carried out to determine the bending stiffness of un-creased samples in the machine direction (MD) and cross direction (CD). Bending tests were also carried out on creased samples with the fluting oriented in the CD with the crease at the centre. Inverse analysis was applied using the results from the bending tests to determine the material properties that accurately predict the bending stiffness of the horizontal creases, vertical creases, and panels of a box under compression loading. The finite element model of the box was divided into three sections, the horizontal creases, vertical creases, and the box panels. Each of these sections is described using different material properties. The box edges/corners are described using the optimal material properties from bending and compression tests conducted on creased samples, while the box panels are described using the optimal material properties obtained from four-point bending tests conducted on samples without creases. A homogenised finite element (FE) model of a box was simulated using the obtained material properties and validated using experimental results. The developed FE model accurately predicted the failure load of a corrugated paperboard box under compression with a variation of 0.1% when compared to the experimental results. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics (AfriComp6))

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22 pages, 1834 KiB

Open AccessArticle

Analyzing Bifurcations and Optimal Control Strategies in SIRS Epidemic Models: Insights from Theory and COVID-19 Data

by Mohamed Cherif Belili, Mohamed Lamine Sahari, Omar Kebiri and Halim Zeghdoudi

Math. Comput. Appl. 2024, 29(4), 69; https://doi.org/10.3390/mca29040069 - 21 Aug 2024

Abstract

This study investigates the dynamic behavior of an SIRS epidemic model in discrete time, focusing primarily on mathematical analysis. We identify two equilibrium points, disease-free and endemic, with our main focus on the stability of the endemic state. Using data from the US [...] Read more.

This study investigates the dynamic behavior of an SIRS epidemic model in discrete time, focusing primarily on mathematical analysis. We identify two equilibrium points, disease-free and endemic, with our main focus on the stability of the endemic state. Using data from the US Department of Health and optimizing the SIRS model, we estimate model parameters and analyze two types of bifurcations: Flip and Transcritical. Bifurcation diagrams and curves are presented, employing the Carcasses method. for the Flip bifurcation and an implicit function approach for the Transcritical bifurcation. Finally, we apply constrained optimal control to the infection and recruitment rates in the discrete SIRS model. Pontryagin’s maximum principle is employed to determine the optimal controls. Utilizing COVID-19 data from the USA, we showcase the effectiveness of the proposed control strategy in mitigating the pandemic’s spread. Full article

(This article belongs to the Collection Mathematical Modelling of COVID-19)

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15 pages, 4012 KiB

Open AccessArticle

Estimation of Anthocyanins in Heterogeneous and Homogeneous Bean Landraces Using Probabilistic Colorimetric Representation with a Neuroevolutionary Approach

by José-Luis Morales-Reyes, Elia-Nora Aquino-Bolaños, Héctor-Gabriel Acosta-Mesa and Aldo Márquez-Grajales

Math. Comput. Appl. 2024, 29(4), 68; https://doi.org/10.3390/mca29040068 - 19 Aug 2024

Abstract

The concentration of anthocyanins in common beans indicates their nutritional value. Understanding this concentration makes it possible to identify the functional compounds present. Previous studies have presented color characterization as two-dimensional histograms, based on the probability mass function. In this work, we proposed [...] Read more.

The concentration of anthocyanins in common beans indicates their nutritional value. Understanding this concentration makes it possible to identify the functional compounds present. Previous studies have presented color characterization as two-dimensional histograms, based on the probability mass function. In this work, we proposed a new type of color characterization represented by three two-dimensional histograms that consider chromaticity and luminosity channels in order to verify the robustness of the information. Using a neuroevolutionary approach, we also found a convolutional neural network (CNN) for the regression task. The results demonstrate that using three two-dimensional histograms increases the accuracy compared to the color characterization represented by one two-dimensional histogram. As a result, the precision was 93.00 ± 5.26 for the HSI color space and 94.30 ± 8.61 for CIE L*a*b*. Our procedure is suitable for estimating anthocyanins in homogeneous and heterogeneous colored bean landraces. Full article

(This article belongs to the Special Issue New Trends in Computational Intelligence and Applications 2023)

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20 pages, 2538 KiB

Open AccessArticle

Comparison of Interval Type-3 Mamdani and Sugeno Models for Fuzzy Aggregation Applied to Ensemble Neural Networks for Mexican Stock Exchange Time Series Prediction

by Martha Pulido, Patricia Melin, Oscar Castillo and Juan R. Castro

Math. Comput. Appl. 2024, 29(4), 67; https://doi.org/10.3390/mca29040067 - 19 Aug 2024

Abstract

In this work, interval type-2 and type-3 fuzzy systems were designed, of Mamdani and Sugeno types, for time series prediction. The aggregation performed by the type-2 and type-3 fuzzy systems was carried out by using the results of an optimized ensemble neural network [...] Read more.

In this work, interval type-2 and type-3 fuzzy systems were designed, of Mamdani and Sugeno types, for time series prediction. The aggregation performed by the type-2 and type-3 fuzzy systems was carried out by using the results of an optimized ensemble neural network (ENN) obtained with the particle swarm optimization algorithm. The time series data that were used were of the Mexican stock exchange. The method finds the best prediction error. This method consists of the aggregation of the responses of the ENN with type-2 and type-3 fuzzy systems. In this case, the systems consist of five inputs and one output. Each input is made up of two membership functions and there are 32 possible fuzzy if-then rules. The simulation results show that the approach with type-2 and type-3 fuzzy systems provides a good prediction of the Mexican stock exchange. Statistical tests of the comparison of type-1, type-2, and type-3 fuzzy systems are also presented. Full article

(This article belongs to the Section Engineering)

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19 pages, 2402 KiB

Open AccessArticle

Dynamical Properties of Perturbed Hill’s System

by Mohammed K. Ibrahim, Taha Rabeh and Elbaz I. Abouelmagd

Math. Comput. Appl. 2024, 29(4), 66; https://doi.org/10.3390/mca29040066 - 19 Aug 2024

Abstract

In this work, some dynamical properties of Hill’s system are studied under the effect of continued fraction perturbation. The locations and kinds of equilibrium points are identified, and it is demonstrated that these points are saddle points and the general motion in their [...] Read more.

In this work, some dynamical properties of Hill’s system are studied under the effect of continued fraction perturbation. The locations and kinds of equilibrium points are identified, and it is demonstrated that these points are saddle points and the general motion in their proximity is unstable. Furthermore, the curves of zero velocity and the regions of possible motion are defined at different Jacobian constant values. It is shown that the regions of forbidden motion increase with increasing Jacobian constant values and there is a noticeable decrease in the permissible regions of motion, leading to the possibility that the body takes a path far away from the primary body and escapes to take an unknown trajectory. Furthermore, the stability of perturbed motion is analyzed from the perspective of a linear sense, and it is observed that the linear motion is also unstable. Full article

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