Mathematical and Computational Applications

32 pages, 5759 KiB

Open AccessReview

by Bálint Molnár, József Szőlősi, Attila Gludovátz and Mátyás Andó

Math. Comput. Appl. 2025, 30(2), 38; https://doi.org/10.3390/mca30020038 - 31 Mar 2025

IT (Information Technology) support plays a major role in CPSs (cyber-physical systems). More and more IT solutions and CIS (complex information system) modules are being developed to help engineering systems to a higher level of efficiency. The different specificities of different technological environments [...] Read more.

IT (Information Technology) support plays a major role in CPSs (cyber-physical systems). More and more IT solutions and CIS (complex information system) modules are being developed to help engineering systems to a higher level of efficiency. The different specificities of different technological environments require a very different IT approach. Increasing the efficiency of different manufacturing processes requires an appropriate architecture. The Zachman framework guidelines were applied to design a suitable framework architecture for the welding process. A literature search was conducted to explore the conditions for component matching to a complex information system, in which advanced data management and data protection are important. In order to effectively manage the standards, a dedicated module needs to be created that can be integrated into the MES-ERP (Manufacturing Execution System-Enterprise Resource Planning) architecture. The result of the study is the creation of business UML (Unified Modeling Language) and BPMN (Business Process Model and Notation) diagrams and a roadmap to start a concrete application development. The paper concludes with an example to illustrate ideas for the way forward. Full article

(This article belongs to the Section Engineering)

► Show Figures

Figure 1

17 pages, 562 KiB

Open AccessArticle

A New Higher-Order Convergence Laplace–Fourier Method for Linear Neutral Delay Differential Equations

by Gilbert Kerr and Gilberto González-Parra

Math. Comput. Appl. 2025, 30(2), 37; https://doi.org/10.3390/mca30020037 - 28 Mar 2025

Abstract

In this article, a new higher-order convergence Laplace–Fourier method is developed to obtain the solutions of linear neutral delay differential equations. The proposed method provides more accurate solutions than the ones provided by the pure Laplace method and the original Laplace–Fourier method. We [...] Read more.

In this article, a new higher-order convergence Laplace–Fourier method is developed to obtain the solutions of linear neutral delay differential equations. The proposed method provides more accurate solutions than the ones provided by the pure Laplace method and the original Laplace–Fourier method. We develop and show the crucial modifications of the Laplace–Fourier method. As with the original Laplace–Fourier method, the new method combines the Laplace transform method with Fourier series theory. All of the beneficial features from the original Laplace–Fourier method are retained. The solution still includes a component that accounts for the terms in the tail of the infinite series, allowing one to obtain more accurate solutions. The Laplace–Fourier method requires us to approximate the formula for the residues with an asymptotic expansion. This is essential to enable us to use the Fourier series results that enable us to account for the tail. The improvement is achieved by deriving a new asymptotic expansion which minimizes the error between the actual residues and those which are obtained from this asymptotic expansion. With both the pure Laplace and improved Laplace–Fourier methods, increasing the number of terms in the truncated series obviously increases the accuracy. However, with the pure Laplace method, this improvement is small. As we shall show, with the improved higher-order convergence Laplace–Fourier method, the improvement is significantly larger. We show that the convergence rate of the new Laplace–Fourier solution has a remarkable order of convergence. The validity of the new technique is corroborated by means of illustrative examples. Comparisons of the solutions of the new method with those generated by the pure Laplace method and the unmodified Laplace–Fourier approach are presented. Full article

► Show Figures

Figure 1

13 pages, 1333 KiB

Open AccessArticle

Internet-of-Things-Based CO₂ Monitoring and Forecasting System for Indoor Air Quality Management

by Marya J. Marquez-Zepeda, Ildeberto Santos-Ruiz, Esvan-Jesús Pérez-Pérez, Adrián Navarro-Díaz and Jorge-Alejandro Delgado-Aguiñaga

Math. Comput. Appl. 2025, 30(2), 36; https://doi.org/10.3390/mca30020036 - 28 Mar 2025

Abstract

This study presents a low-cost and scalable CO₂ monitoring system that leverages NDIR sensors and a Long Short-Term Memory (LSTM) neural network to predict indoor CO₂ concentrations over both short- and long-term horizons. The proposed system aims to anticipate air quality [...] Read more.

This study presents a low-cost and scalable CO₂ monitoring system that leverages NDIR sensors and a Long Short-Term Memory (LSTM) neural network to predict indoor CO₂ concentrations over both short- and long-term horizons. The proposed system aims to anticipate air quality deterioration in shared spaces, enabling proactive ventilation strategies. Various LSTM configurations were evaluated, optimizing the number of layers, neurons per layer, and input delays to enhance forecasting accuracy. The optimal model consisted of two LSTM layers with 128 neurons each and a time window of 10 previous observations. This model achieved an RMSE of approximately 57 ppm for an 8 h forecast in a classroom setting. Experimental results demonstrate the reliability of the proposed approach for CO₂ prediction and its potential impact on indoor air quality management. Full article

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

► Show Figures

Figure 1

55 pages, 998 KiB

Open AccessArticle

Nonlinear Finite Element Model for FGM Porous Circular and Annular Micro-Plates Under Thermal and Mechanical Loads Using Modified Couple Stress-Based Third-Order Plate Theory

by Enrique Nava and Jinseok Kim

Math. Comput. Appl. 2025, 30(2), 35; https://doi.org/10.3390/mca30020035 - 26 Mar 2025

Abstract

A nonlinear finite element model for circular and annular micro-plates under thermal and mechanical loading was developed using a third-order shear deformation theory. In the kinematic assumptions, a change in plate thickness is allowed, and no transverse shear strains are considered on the [...] Read more.

A nonlinear finite element model for circular and annular micro-plates under thermal and mechanical loading was developed using a third-order shear deformation theory. In the kinematic assumptions, a change in plate thickness is allowed, and no transverse shear strains are considered on the top and bottom surfaces. A power-law distribution was utilized to account for variations in two constituents through the thickness of the plate. Three different types of porosity distributions are considered. The strain gradient effect in micro-scale structures is accounted for by using the modified couple stress theory. Hamilton’s principle is used to obtain the equations of motion, and conforming plate elements are used in the development of the finite element model. The developed finite element model was verified against the available literature and analytical solutions. The effects of the material and porosity distribution, microstructure-dependency, geometric nonlinearity, and various boundary conditions on the bending response of functionally graded and porous circular and annular micro-plates were studied using the developed nonlinear finite element model. Full article

(This article belongs to the Special Issue Mathematical and Computational Approaches in Applied Mechanics: A Themed Issue Dedicated to Professor J.N. Reddy)

► Show Figures

Figure 1

23 pages, 3658 KiB

Open AccessArticle

MASIP: A Methodology for Assets Selection in Investment Portfolios

by José Purata-Aldaz, Juan Frausto-Solís, Guadalupe Castilla-Valdez, Javier González-Barbosa and Juan Paulo Sánchez Hernández

Math. Comput. Appl. 2025, 30(2), 34; https://doi.org/10.3390/mca30020034 - 24 Mar 2025

Abstract

This paper proposes a Methodology for Assets Selection in Investment Portfolios (MASIP) focused on creating investment portfolios using heuristic algorithms based on the Markowitz and Sharpe models. MASIP selects and allocates financial assets by applying heuristic methods to accomplish three assignments: (a) Select [...] Read more.

This paper proposes a Methodology for Assets Selection in Investment Portfolios (MASIP) focused on creating investment portfolios using heuristic algorithms based on the Markowitz and Sharpe models. MASIP selects and allocates financial assets by applying heuristic methods to accomplish three assignments: (a) Select the stock candidates in an initial portfolio; (b) Forecast the asset values for the short and medium term; and (c) Optimize the investment portfolio by using the Sharpe metric. Once MASIP creates the initial portfolio and forecasts its assets, an optimization process is started in which a set with the best weights determines the participation of each asset. Moreover, a rebalancing process is carried out to enhance the portfolio value. We show that the improvement achieved by MASIP can reach 147% above the SP500 benchmark. We use a dataset of SP500 to compare MASIP with state-of-the-art methods, obtaining superior performance and an outstanding Sharpe Ratio and returns compared to traditional investment approaches. The heuristic algorithms proved effective in asset selection and allocation, and the forecasting process and rebalancing contributed to further improved results. Full article

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

► Show Figures

Figure 1

30 pages, 8417 KiB

Open AccessArticle

Toward a Blood Sensor for an IoT Monitoring: A New Approach for the Design and Implementation of Blood Light Absorption Systems Based on the Finite Element Method and the Diffusion Equation

by Mouna Dhmiri, Yassine Manai and Tahar Ezzedine

Math. Comput. Appl. 2025, 30(2), 33; https://doi.org/10.3390/mca30020033 - 24 Mar 2025

Abstract

Non-invasive blood analysis has the power to completely change how doctors identify and track illnesses. This study presents a novel approach for the non-invasive monitoring of red blood cell (RBC) mobility and concentration within capillaries, using photon absorption as a key diagnostic tool. [...] Read more.

Non-invasive blood analysis has the power to completely change how doctors identify and track illnesses. This study presents a novel approach for the non-invasive monitoring of red blood cell (RBC) mobility and concentration within capillaries, using photon absorption as a key diagnostic tool. The research combines optical modeling with the diffusion equation for light propagation, leveraging COMSOL simulations to create a comprehensive framework for understanding RBC dynamics. A two-dimensional geometric model of capillaries with RBCs is developed, where blood flow is modeled as a laminar, incompressible fluid. The Arbitrary Lagrangian–Eulerian (ALE) formulation is employed to account for the fluid–structure interactions, while photon attenuation by the RBCs is analyzed to investigate wavelength-dependent absorption characteristics. The methodology is implemented through a workflow developed with MATLAB’s S-Function builder, consisting of three main components: mesh generation, fluence computing, and Software-in-the-Loop (SIL) verification. The mesh generation process adapts to the target architecture using COMSOL Multiphysics for fluid–structure interaction (FSI) modeling. The fluence computing function solves the diffusion equation to model light intensity attenuation due to RBCs, and the SIL function compares computed results with real-time measurements, ensuring accuracy for potential real-time embedded system applications. The results demonstrate significant wavelength-dependent variations in photon absorption by RBCs, providing insights into the optical behavior of blood in microvascular structures. The findings have important implications for medical imaging, photodynamic therapy, and diagnostic tools, emphasizing the potential of integrating computational models with real-time systems for enhanced performance in biomedical applications. Full article

(This article belongs to the Topic Numerical Methods for Partial Differential Equations)

► Show Figures

Figure 1

2 pages, 159 KiB

Open AccessCorrection

Correction: Zambou et al. Optimized Nonlinear PID Control for Maximum Power Point Tracking in PV Systems Using Particle Swarm Optimization. Math. Comput. Appl. 2024, 29, 88

by Maeva Cybelle Zoleko Zambou, Alain Soup Tewa Kammogne, Martin Siewe Siewe, Ahmad Taher Azar, Saim Ahmed and Ibrahim A. Hameed

Math. Comput. Appl. 2025, 30(2), 32; https://doi.org/10.3390/mca30020032 - 21 Mar 2025

Abstract

Because of the uncertain meaning in the original publication [...] Full article

25 pages, 668 KiB

Open AccessArticle

An Experimental Study of Strategies to Control Diversity in Grouping Mutation Operators: An Improvement to the Adaptive Mutation Operator for the GGA-CGT for the Bin Packing Problem

by Stephanie Amador-Larrea, Marcela Quiroz-Castellanos and Octavio Ramos-Figueroa

Math. Comput. Appl. 2025, 30(2), 31; https://doi.org/10.3390/mca30020031 - 18 Mar 2025

Abstract

Grouping Genetic Algorithms (GGAs) are among the most outstanding methods for solving NP-hard combinatorial optimization problems by efficiently grouping sets of items. Their performance depends on problem-specific heuristics and a balance between exploration and exploitation. The mutation operator plays a crucial role in [...] Read more.

Grouping Genetic Algorithms (GGAs) are among the most outstanding methods for solving NP-hard combinatorial optimization problems by efficiently grouping sets of items. Their performance depends on problem-specific heuristics and a balance between exploration and exploitation. The mutation operator plays a crucial role in exploring new solutions, but improper mutation control can lead to premature convergence. This work introduces adaptive mutation strategies for the GGA-CGT applied to the One-Dimensional Bin Packing Problem (1D-BPP). These strategies control the level of change that will be introduced to each solution dynamically by using feedback on population diversity, enabling better exploration. The proposed approach resulted in a 4.08% increase in optimal solutions (2227 across all classes) and a severe reduction in the average of individuals with equal fitness (from over 50% to less than 1%), enhancing diversity and avoiding local optima. The adaptive strategies were particularly effective in problem instances with larger item weights, where improvements were the most significant. Furthermore, statistical analysis confirmed the adaptive mutation approach’s superior performance compared with the original one. These findings demonstrate the potential of adaptive mechanisms to improve genetic algorithms, offering a robust strategy for tackling complex optimization problems. Full article

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

► Show Figures

Figure 1

20 pages, 8271 KiB

Open AccessArticle

Deciding on the Regularity of a Planar Coons Map

by Maharavo Randrianarivony and Guido Brunnett

Math. Comput. Appl. 2025, 30(2), 30; https://doi.org/10.3390/mca30020030 - 17 Mar 2025

Abstract

We consider the construction of a regular map from the unit square to a general four-sided domain, a problem that arises in several applications, e.g., in the numerical solution of integral equations or when dealing with trimmed surfaces in CAD. In our approach, [...] Read more.

We consider the construction of a regular map from the unit square to a general four-sided domain, a problem that arises in several applications, e.g., in the numerical solution of integral equations or when dealing with trimmed surfaces in CAD. In our approach, we consider the problem in as general a form as possible, which means that initially no assumptions are made about the type of mathematical representation of the boundary curves. This approach becomes possible by using planar Coons maps to describe the parameterization. We show that the regularity of a Coons map depends both on the waviness and the similarity of the boundary curves. Constraining these properties allows us to formulate sufficient conditions for regularity and to specify special cases in which the regularity of the Coons map is obvious. For the case of polynomial boundary curves, we present a regularity criterion that is both necessary and sufficient and can thus be used to characterize regular polynomial mappings. Our decision algorithm implements this criterion and provides a powerful tool not only for deciding the regularity of a given Coons map, but also for determining the transition between a regular and a non-regular Coons map depending on the curvature of the boundary curves. Full article

► Show Figures

Figure 1

21 pages, 519 KiB

Open AccessArticle

Learning Deceptive Tactics for Defense and Attack in Bayesian–Markov Stackelberg Security Games

by Julio B. Clempner

Math. Comput. Appl. 2025, 30(2), 29; https://doi.org/10.3390/mca30020029 - 17 Mar 2025

Abstract

In this paper, we address the challenges posed by limited knowledge in security games by proposing a novel system grounded in Bayesian–Markov Stackelberg security games (SSGs). These SSGs involve multiple defenders and attackers and serve as a framework for managing incomplete information effectively. [...] Read more.

In this paper, we address the challenges posed by limited knowledge in security games by proposing a novel system grounded in Bayesian–Markov Stackelberg security games (SSGs). These SSGs involve multiple defenders and attackers and serve as a framework for managing incomplete information effectively. To tackle the complexity inherent in these games, we introduce an iterative proximal-gradient approach to compute the Bayesian Equilibrium, which captures the optimal strategies of both defenders and attackers. This method enables us to navigate the intricacies of the game dynamics, even when the specifics of the Markov games are unknown. Moreover, our research emphasizes the importance of Bayesian approaches in solving the reinforcement learning (RL) algorithm, particularly in addressing the exploration–exploitation trade-off. By leveraging Bayesian techniques, we aim to minimize the expected total discounted costs, thus optimizing decision-making in the security domain. In pursuit of effective security game implementation, we propose a novel random walk approach tailored to fulfill the requirements of the scenario. This innovative methodology enhances the adaptability and responsiveness of defenders and attackers, thereby improving overall security outcomes. To validate the efficacy of our proposed strategy, we provide a numerical example that demonstrates its benefits in practice. Through this example, we showcase how our approach can effectively address the challenges posed by limited knowledge, leading to more robust and efficient security solutions. Overall, our paper contributes to advancing the understanding and implementation of security strategies in scenarios characterized by incomplete information. By combining Bayesian and Markov Stackelberg games, reinforcement learning algorithms, and innovative random walk techniques, we offer a comprehensive framework for enhancing security measures in real-world applications. Full article

(This article belongs to the Special Issue Applied Optimization in Automatic Control and Systems Engineering)

► Show Figures

Figure 1

15 pages, 1443 KiB

Open AccessArticle

Characterization of the Appointment’s Reasons for “P—Psychological” on the ICPC-2 Scale in Primary Health Care Services

by Filipa Rocha, Cristiana J. Silva, Sofia J. Pinheiro, Vera Afreixo, Rui Pedro Leitão and Miguel Felgueiras

Math. Comput. Appl. 2025, 30(2), 28; https://doi.org/10.3390/mca30020028 - 14 Mar 2025

Abstract

(1) Background: Mental health significantly impacts personal relationships and societal integration. Portugal faces a high prevalence of psychiatric illnesses and psychological distress, which the COVID-19 pandemic might have exacerbated. Therefore, this study aims to study risk factors that lead to psychological problems, using [...] Read more.

(1) Background: Mental health significantly impacts personal relationships and societal integration. Portugal faces a high prevalence of psychiatric illnesses and psychological distress, which the COVID-19 pandemic might have exacerbated. Therefore, this study aims to study risk factors that lead to psychological problems, using data available in the primary health care centers of the region of Aveiro. (2) Methods: This observational and retrospective study analyzes data from 2009 to 2022 on psychological consultations in the Aveiro municipalities. Variables considered are municipality, International Classification of Primary Care problem, sex, and comorbidities (cancer, obesity, and diabetes). Summary statistics and graphs were employed for data understanding, with R software used for analysis. Regression models, odds ratios, and association tests were calculated. Also, cluster analysis was performed on municipalities. (3) Results: A new, significant increase in the appointment growth rate was observed in 2021 and 2022. Anxiety and depressive disorders contribute to the identified growth. Women reported more problems than men. Cancer was the most present comorbidity. (4) Conclusions: The study reveals increased mental health problems, with primary health care users in Aveiro experiencing worsened psychosocial health, resulting in more medical consultations for psychological reasons. Risk factors included being female and having chronic conditions such as cancer. The findings provide insights into the burden of mental health issues in the region, highlighting the need for effective mental health interventions and resources to address health inequalities and support at-risk groups. Full article

(This article belongs to the Special Issue Feature Papers in Mathematical and Computational Applications 2025)

► Show Figures

Figure 1

21 pages, 597 KiB

Open AccessArticle

Common Attractor for Hutchinson θ-Contractive Operators in Partial Metric Spaces

by Naila Shabir, Ali Raza, Manuel De la Sen, Mujahid Abbas and Shahbaz Ahmad

Math. Comput. Appl. 2025, 30(2), 27; https://doi.org/10.3390/mca30020027 - 14 Mar 2025

Abstract

This paper investigates the existence of common attractors for generalized

θ

-Hutchinson operators within the framework of partial metric spaces. Utilizing a finite iterated function system composed of

θ

-contractive mappings, we establish theoretical results on common attractors, generalizing numerous existing results in [...] Read more.

This paper investigates the existence of common attractors for generalized

θ

-Hutchinson operators within the framework of partial metric spaces. Utilizing a finite iterated function system composed of

θ

-contractive mappings, we establish theoretical results on common attractors, generalizing numerous existing results in the literature. Additionally, to enhance understanding, we present intuitive and easily comprehensible examples in one-, two-, and three-dimensional Euclidean spaces. These examples are accompanied by graphical representations of attractor images for various iterated function systems. As a practical application, we demonstrate how our findings contribute to solving a functional equation arising in a dynamical system, emphasizing the broader implications of the proposed approach. Full article

► Show Figures

Figure 1

31 pages, 571 KiB

Open AccessArticle

Modeling of Nonlinear Systems: Method of Optimal Injections

by Anatoli Torokhti and Pablo Soto-Quiros

Math. Comput. Appl. 2025, 30(2), 26; https://doi.org/10.3390/mca30020026 - 7 Mar 2025

Abstract

In this paper, a nonlinear system is interpreted as an operator

F

transforming random vectors. It is assumed that the operator is unknown and the random vectors are available. It is required to find a model of the system represented by a best [...] Read more.

In this paper, a nonlinear system is interpreted as an operator

F

transforming random vectors. It is assumed that the operator is unknown and the random vectors are available. It is required to find a model of the system represented by a best constructive operator

F

approximation. While the theory of operator approximation with any given accuracy has been well elaborated, the theory of best constrained constructive operator approximation is not so well developed. Despite increasing demands from various applications, this subject is minimally tractable because of intrinsic difficulties with associated approximation techniques. This paper concerns the best constrained approximation of a nonlinear operator in probability spaces. The main conceptual novelty of the proposed approach is that, unlike the known techniques, it targets a constructive optimal determination of all

3 p + 2

ingredients of the approximating operator where p is a nonnegative integer. The solution to the associated problem is represented by a combination of new best approximation techniques with a special iterative procedure. The proposed approximating model of the system has several degrees of freedom to minimize the associated error. In particular, one of the specific features of the developed approximating technique is special random vectors called injections. It is shown that the desired injection is determined from the solution of a special Fredholm integral equation of the second kind. Its solution is called the optimal injection. The determination of optimal injections in this way allows us to further minimize the associated error. Full article

(This article belongs to the Special Issue Recent Advances and New Challenges in Coupled Systems and Networks: Theory, Modelling, and Applications)

► Show Figures

Figure 1

21 pages, 6361 KiB

Open AccessArticle

Imaging Estimation for Liver Damage Using Automated Approach Based on Genetic Programming

by David Herrera-Sánchez, Héctor-Gabriel Acosta-Mesa, Efrén Mezura-Montes, Socorro Herrera-Meza, Eduardo Rivadeneyra-Domínguez, Isaac Zamora-Bello and María Fernanda Almanza-Domínguez

Math. Comput. Appl. 2025, 30(2), 25; https://doi.org/10.3390/mca30020025 - 28 Feb 2025

Abstract

Computer vision and image processing have become relevant in recent years due to their capabilities to support different tasks in several areas. Image classification, segmentation, and estimation are relevant issues addressed using various techniques. Imaging estimation is very important and helpful in biological [...] Read more.

Computer vision and image processing have become relevant in recent years due to their capabilities to support different tasks in several areas. Image classification, segmentation, and estimation are relevant issues addressed using various techniques. Imaging estimation is very important and helpful in biological applications. This work proposes a new approach for estimating the damages in the livers of the Wistar rats, using high-resolution RGB images. Instead of using invasive methods to determine the level of damage, the proposal allows us to measure the damage in the livers. The proposal is based on Genetic Programming (GP), the paradigm of evolutionary computing, which has become relevant in recent years for image-processing tasks. It provides flexibility, which allows the use of image processing functions to extract meaningful information from raw images. Furthermore, it allows the configuration of the regression model by performing a hyperparameter tuning to improve estimation performance. The approach includes a new set of functions through which the regression model is configured. Additionally, a set of functions is included to change the color spaces of the images to extract meaningful features from them. The results demonstrate the effectiveness of our approach when making the hyperparameter tuning and the efficiency in dealing with different color spaces, thus achieving the promised results when estimating according to the

R^{2}

, Mean Average Error (MAE), Mean Squared Error (MSE) and Root Mean Squared Error (RMSE) indicators. The proposed method achieves values higher than 0.5 of

R^{2}

and lower than 0.51 of MSE, using different regression models. Additionally, the approach demonstrates that image preprocessing is necessary for improving the model’s performance, which is better than only using raw data where the values of RMSE are greater than 1.5. The lowest MSE value of our proposed method was 0.51, outperforming the methods without preprocessing. Full article

(This article belongs to the Special Issue New Trends in Computational Intelligence and Applications 2024)

► Show Figures

Graphical abstract

21 pages, 5602 KiB

Open AccessArticle

Multiclass Evaluation of Vision Transformers for Industrial Welding Defect Detection

by Antonio Contreras Ortiz, Ricardo Rioda Santiago, Daniel E. Hernandez and Miguel Lopez-Montiel

Math. Comput. Appl. 2025, 30(2), 24; https://doi.org/10.3390/mca30020024 - 28 Feb 2025

Abstract

Automating industrial processes, particularly quality inspection, is a key objective in manufacturing. While welding tasks are frequently automated, inspection processes remain largely manual. Advances in computer vision and AI, especially ViTs, now enable more effective defect detection and classification, offering opportunities to automate [...] Read more.

Automating industrial processes, particularly quality inspection, is a key objective in manufacturing. While welding tasks are frequently automated, inspection processes remain largely manual. Advances in computer vision and AI, especially ViTs, now enable more effective defect detection and classification, offering opportunities to automate these workflows. This study evaluates ViTs for identifying defects in aluminum welding using the Aluminum 5083 TIG dataset. The analysis spans binary classification (detecting defects) and multiclass categorization (Good Weld, Burn Through, Contamination, Lack of Fusion, Misalignment, and Lack of Penetration). ViTs achieved 98% to 99% accuracy across both tasks, significantly outperforming prior models such as dense and CNNs, which struggled to surpass 80% accuracy in binary and 70% in multiclass tasks. These results, achieved with datasets of 2400 to 8000 images, highlight ViTs’ efficiency even with limited data. The findings underline the potential of ViTs to enhance manufacturing inspection processes by enabling faster, more reliable, and cost-effective automated solutions, reducing reliance on manual inspection methods. Full article

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

► Show Figures

Graphical abstract

24 pages, 399 KiB

Open AccessArticle

Market Regime Identification and Variable Annuity Pricing: Analysis of COVID-19-Induced Regime Shifts in the Indian Stock Market

by Mohammad Sarfraz, Guglielmo D’Amico and Dharmaraja Selvamuthu

Math. Comput. Appl. 2025, 30(2), 23; https://doi.org/10.3390/mca30020023 - 27 Feb 2025

Abstract

Understanding how crises like the COVID-19 pandemic affect variable annuity pricing is crucial, especially in emerging markets like India. The motivation is that financial stability and risk management in these markets depend heavily on accurate pricing models. While prior research has primarily focused [...] Read more.

Understanding how crises like the COVID-19 pandemic affect variable annuity pricing is crucial, especially in emerging markets like India. The motivation is that financial stability and risk management in these markets depend heavily on accurate pricing models. While prior research has primarily focused on Western markets, there is a significant gap in analyzing the impact of extreme volatility and regime-dependent dynamics on variable annuities in emerging economies. This study investigates how regime shifts during the COVID-19 pandemic influence variable annuity pricing in the Indian stock market, specifically using the Nifty 50 Index data from 7 September 2017 until 7 September 2023. Advanced methodologies, including regime-switching hidden Markov models, artificial neural networks, and Monte Carlo simulations, were applied to analyze pre- and post-COVID-19 market behavior. The regime-switching hidden Markov models effectively capture latent market regimes and their transitions, which traditional models often overlook, while neural networks provide flexible functional approximations that enhance pricing accuracy in highly non-linear environments. The Expectation–Maximization (EM) algorithm was employed to achieve robust calibration and enhance pricing accuracy. The analysis showed significant pricing variations across market regimes, with heightened volatility observed during the pandemic. The findings highlight the effectiveness of regime-switching models in capturing market dynamics, particularly during periods of economic uncertainty and turbulence. This research contributes to the understanding of variable annuity pricing under regime-dependent dynamics in emerging markets and offers practical implications for improved risk management and policy formulation. Full article

(This article belongs to the Special Issue Feature Papers in Mathematical and Computational Applications 2025)

► Show Figures

Figure 1

15 pages, 1815 KiB

Open AccessArticle

Predicting Red Blood Cell Transfusion in Elective Cardiac Surgery: A Machine Learning Approach

by Beatriz Lau, Daniel Ramos, Vera Afreixo, Luís M. Silva, Ana Helena Tavares, Miguel Martins Felgueiras, Diana Castro Paupério and João Firmino-Machado

Math. Comput. Appl. 2025, 30(2), 22; https://doi.org/10.3390/mca30020022 - 24 Feb 2025

Abstract

The benefits of Patient Blood Management can vary depending on a patient’s risk profile for requiring a blood transfusion. The objective of this study is to develop and analyse machine learning models that can identify patients at risk of requiring red blood cell [...] Read more.

The benefits of Patient Blood Management can vary depending on a patient’s risk profile for requiring a blood transfusion. The objective of this study is to develop and analyse machine learning models that can identify patients at risk of requiring red blood cell transfusion. This retrospective cohort study was conducted at a tertiary northern Portuguese hospital between 2018 and 2023. Two machine learning algorithms, extreme gradient boosting and neural networks, were employed due to their efficiency in handling complex feature interactions. Shapley additive explanations values were analysed to assess the contribution of each feature to the predictions generated by the models. The neural network achieved an accuracy of 0.735 and an area under the receiver operating characteristic curve of 0.798 (95% CI 0.747 to 0.849). The extreme gradient boosting model achieved an accuracy of 0.700 and an area under the receiver operating characteristic curve of 0.762 (95% CI 0.707 to 0.817). An analysis of Shapley additive explanations values revealed that the most important variable was preoperative haemoglobin levels, which can be optimised through the Patient Blood Management approach. These machine learning models demonstrate the potential to improve the accuracy of transfusion prediction at hospital admission, despite the absence of key variables such as surgeon identity and anaemia diagnosis. Full article

(This article belongs to the Special Issue Feature Papers in Mathematical and Computational Applications 2025)

► Show Figures

Figure 1

19 pages, 4016 KiB

Open AccessArticle

Impact Loading on a Patient-Specific Head Model: The Significance of Brain Constitutive Models and Loading Location

by Amirhossein Gandomirouzbahani, Hadi Taghizadeh, Iman Z. Oskui and Fábio A. O. Fernandes

Math. Comput. Appl. 2025, 30(2), 21; https://doi.org/10.3390/mca30020021 - 21 Feb 2025

Abstract

Head impacts are common incidents that may cause traumatic brain injury (TBI), which imposes significant economic and social burdens. This study developed a patient-specific head model to address the significance of the brain’s constitutive model and loading location on head impact. Two hyperelastic [...] Read more.

Head impacts are common incidents that may cause traumatic brain injury (TBI), which imposes significant economic and social burdens. This study developed a patient-specific head model to address the significance of the brain’s constitutive model and loading location on head impact. Two hyperelastic (Model I and Model II) constitutive models and one hyper-viscoelastic (Model III) constitutive model for the brain tissue were developed. In Models II and III, white and gray matter heterogeneities were included. Respective volumetric and deviatoric responses were compared for a frontal head impact. Then, the load was applied to the head’s frontal, lateral, and posterior regions to report location-wise outcomes. The findings indicated that Model I, which was based on almost quasi-static experiments, underestimated the deviatoric responses. Although the pressure contours were similar for Models II and III, the latter included viscous effects and provided more accurate deviatoric responses. Lateral loading indicated a significantly higher risk of TBI. Interestingly, the deviatoric responses and strain energy density of the brain did not decay with relaxation of the impact load. Hence, the incidence of TBI should be explored after load relaxation. Full article

(This article belongs to the Special Issue Feature Papers in Mathematical and Computational Applications 2025)

► Show Figures

Figure 1

15 pages, 3748 KiB

Open AccessArticle

Control Strategy of a Rotating Power Flow Controller Based on an Improved Hybrid Particle Swarm Optimization Algorithm

by Ziyang Zhang, Jiaoxin Jia, Waseem Aslam, Abubakar Siddique and Fahad R. Albogamy

Math. Comput. Appl. 2025, 30(1), 20; https://doi.org/10.3390/mca30010020 - 19 Feb 2025

Abstract

As the proportion of renewable energy sources integrated into the power grid increases, it imposes significant volatility on the grid, leading to uneven load distribution across certain transmission lines. Rotating Power Flow Controllers (RPFCs) based on Rotating Phase-Shifting Transformers (RPSTs) offer a viable [...] Read more.

As the proportion of renewable energy sources integrated into the power grid increases, it imposes significant volatility on the grid, leading to uneven load distribution across certain transmission lines. Rotating Power Flow Controllers (RPFCs) based on Rotating Phase-Shifting Transformers (RPSTs) offer a viable solution to such issues in lines rated at 10 kV and below. This paper begins with a brief introduction to RPFCs, followed by the modeling of their topology for a single-circuit line and the derivation of active and reactive power flow formulas. Notably, this paper introduces intelligent optimization algorithms to this field for the first time, employing an improved hybrid particle swarm optimization (HPSO) algorithm to control the active power while keeping the reactive power constant and subsequently adjusting the reactive power while maintaining the active power steady, thereby achieving power regulation. Using Matlab/Simulink simulations, this strategy was compared with adaptive adjustment strategies, verifying that it exhibits reduced power fluctuations and overshoots during the adjustment process, thus confirming the effectiveness of the adjustment scheme. By leveraging this algorithm in conjunction with simulations, a Q-P operating range diagram for transmission lines was plotted, determining the adjustable range of actual power. Full article

► Show Figures

Figure 1

Journal Description

Mathematical and Computational Applications

Latest Articles

Journal Menu

Journal Browser

Highly Accessed Articles

Latest Books

E-Mail Alert

News

Topics

Conferences

Special Issues

Topical Collections

Further Information

Guidelines

MDPI Initiatives

Follow MDPI