Mathematical and Computational Applications

16 pages, 1172 KB

Open AccessArticle

The Extended Goodwin Model and Wage–Labor Paradoxes Metric in South Africa

by Tichaona Chikore, Miglas Tumelo Makobe and Farai Nyabadza

Math. Comput. Appl. 2025, 30(5), 98; https://doi.org/10.3390/mca30050098 - 10 Sep 2025

This study extends the post-Keynesian framework for cyclical economic growth, initially proposed by Goodwin in 1967, by integrating government intervention to stabilize employment amidst wage mismatches. Given the pressing challenges of unemployment and wage disparity in developing economies, particularly South Africa, this extension [...] Read more.

This study extends the post-Keynesian framework for cyclical economic growth, initially proposed by Goodwin in 1967, by integrating government intervention to stabilize employment amidst wage mismatches. Given the pressing challenges of unemployment and wage disparity in developing economies, particularly South Africa, this extension is necessary to better understand how policy interventions can influence labor market dynamics. Central to the study is the endogenous interaction between capital and labor, where class dynamics influence economic growth patterns. The research focuses on the competitive relationship between real wage growth and its effects on employment. Methodologically, the study measures the impact of intervention strategies using a system of coupled ordinary differential equations (Lotka–Volterra type), along with econometric techniques such as quantile regression, moving averages, and mean absolute error to measure wages mismatch. Results demonstrate the inherent contradictions of capitalism under intervention, confirming established theoretical perspectives. This work further contributes to economic optimality discussions, especially regarding the timing and persistence of economic cycles. The model provides a quantifiable approach for formulating intervention strategies to achieve long-term economic equilibrium and sustainable labor–capital coexistence. Full article

(This article belongs to the Section Natural Sciences)

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15 pages, 1836 KB

Open AccessArticle

Public Security Patrol and Alert Recognition for Police Patrol Robots Based on Improved YOLOv8 Algorithm

by Yuehan Shi, Xiaoming Zhang, Qilei Wang and Xiaojun Liu

Math. Comput. Appl. 2025, 30(5), 97; https://doi.org/10.3390/mca30050097 - 10 Sep 2025

Abstract

Addressing the prevalent challenges of inadequate detection accuracy and sluggish detection speed encountered by police patrol robots during security patrols, we propose an innovative algorithm based on the YOLOv8 model. Our method consists of substituting the backbone network of YOLOv8 with FasterNet. As [...] Read more.

Addressing the prevalent challenges of inadequate detection accuracy and sluggish detection speed encountered by police patrol robots during security patrols, we propose an innovative algorithm based on the YOLOv8 model. Our method consists of substituting the backbone network of YOLOv8 with FasterNet. As a result, the model’s ability to identify accurately is enhanced, and its computational performance is improved. Additionally, the extraction of geographical data becomes more efficient. In addition, we introduce the BiFormer attention mechanism, incorporating dynamic sparse attention to significantly improve algorithm performance and computational efficiency. Furthermore, to bolster the regression performance of bounding boxes and enhance detection robustness, we utilize Wise-IoU as the loss function. Through experimentation across three perilous police scenarios—fighting, knife threats, and gun incidents—we demonstrate the efficacy of our proposed algorithm. The results indicate notable improvements over the original model, with enhancements of 2.42% and 5.83% in detection accuracy and speed for behavioral recognition of fighting, 2.87% and 4.67% for knife threat detection, and 3.01% and 4.91% for gun-related situation detection, respectively. Full article

(This article belongs to the Section Engineering)

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29 pages, 1840 KB

Open AccessArticle

Multi-Objective Optimization in Virtual Power Plants for Day-Ahead Market Considering Flexibility

by Mohammad Hosein Salehi, Mohammad Reza Moradian, Ghazanfar Shahgholian and Majid Moazzami

Math. Comput. Appl. 2025, 30(5), 96; https://doi.org/10.3390/mca30050096 - 5 Sep 2025

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Abstract

This research proposes a novel multi-objective optimization framework for virtual power plants (VPPs) operating in day-ahead electricity markets. The VPP integrates diverse distributed energy resources (DERs) such as wind turbines, solar photovoltaics (PV), fuel cells (FCs), combined heat and power (CHP) systems, and [...] Read more.

This research proposes a novel multi-objective optimization framework for virtual power plants (VPPs) operating in day-ahead electricity markets. The VPP integrates diverse distributed energy resources (DERs) such as wind turbines, solar photovoltaics (PV), fuel cells (FCs), combined heat and power (CHP) systems, and microturbines (MTs), along with demand response (DR) programs and energy storage systems (ESSs). The trading model is designed to optimize the VPP’s participation in the day-ahead market by aggregating these resources to function as a single entity, thereby improving market efficiency and resource utilization. The optimization framework simultaneously minimizes operational costs, maximizes system flexibility, and enhances reliability, addressing challenges posed by renewable energy integration and market uncertainties. A new flexibility index is introduced, incorporating both the technical and economic factors of individual units within the VPP, offering a comprehensive measure of system adaptability. The model is validated on IEEE 24-bus and 118-bus systems using evolutionary algorithms, achieving significant improvements in flexibility (20% increase), cost reduction (15%), and reliability (a 30% reduction in unsupplied energy). This study advances the development of efficient and resilient power systems amid growing renewable energy penetration. Full article

(This article belongs to the Section Engineering)

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23 pages, 575 KB

Open AccessArticle

A Comparison of the Robust Zero-Inflated and Hurdle Models with an Application to Maternal Mortality

by Phelo Pitsha, Raymond T. Chiruka and Chioneso S. Marange

Math. Comput. Appl. 2025, 30(5), 95; https://doi.org/10.3390/mca30050095 - 2 Sep 2025

Viewed by 566

Abstract

This study evaluates the performance of count regression models in the presence of zero inflation, outliers, and overdispersion using both simulated and real-world maternal mortality dataset. Traditional Poisson and negative binomial regression models often struggle to account for the complexities introduced by excess [...] Read more.

This study evaluates the performance of count regression models in the presence of zero inflation, outliers, and overdispersion using both simulated and real-world maternal mortality dataset. Traditional Poisson and negative binomial regression models often struggle to account for the complexities introduced by excess zeros and outliers. To address these limitations, this study compares the performance of robust zero-inflated (RZI) and robust hurdle (RH) models against conventional models using the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to determine the best-fitting model. Results indicate that the robust zero-inflated Poisson (RZIP) model performs best overall. The simulation study considers various scenarios, including different levels of zero inflation (50%, 70%, and 80%), outlier proportions (0%, 5%, 10%, and 15%), dispersion values (1, 3, and 5), and sample sizes (50, 200, and 500). Based on AIC comparisons, the robust zero-inflated Poisson (RZIP) and robust hurdle Poisson (RHP) models demonstrate superior performance when outliers are absent or limited to 5%, particularly when dispersion is low (5). However, as outlier levels and dispersion increase, the robust zero-inflated negative binomial (RZINB) and robust hurdle negative binomial (RHNB) models outperform robust zero-inflated Poisson (RZIP) and robust hurdle Poisson (RHP) across all levels of zero inflation and sample sizes considered in the study. Full article

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18 pages, 6285 KB

Open AccessArticle

Physics-Informed Machine Learning for Mechanical Performance Prediction of ECC-Strengthened Reinforced Concrete Beams: An Empirical-Guided Framework

by Jinshan Yu, Yongchao Li, Haifeng Yang and Yongquan Zhang

Math. Comput. Appl. 2025, 30(5), 94; https://doi.org/10.3390/mca30050094 - 1 Sep 2025

Viewed by 380

Abstract

Predicting the mechanical performance of Engineered Cementitious Composite (ECC)-strengthened reinforced concrete (RC) beams is both meaningful and challenging. Although existing methods each have their advantages, traditional numerical simulations struggle to capture the complex micro-mechanical behavior of ECC, experimental approaches are costly, and data-driven [...] Read more.

Predicting the mechanical performance of Engineered Cementitious Composite (ECC)-strengthened reinforced concrete (RC) beams is both meaningful and challenging. Although existing methods each have their advantages, traditional numerical simulations struggle to capture the complex micro-mechanical behavior of ECC, experimental approaches are costly, and data-driven methods heavily depend on large, high-quality datasets. This study proposes a novel physics-informed machine learning framework that integrates domain-specific empirical knowledge and physical laws into a neural network architecture to enhance predictive accuracy and interpretability. The approach leverages outputs from physics-based simulations and experimental insights as weak supervision and incorporates physically consistent loss terms into the training process to guide the model toward scientifically valid solutions, even for unlabeled or sparse data regimes. While the proposed physics-informed model yields slightly lower accuracy than purely data-driven models (mean squared errors of 0.101 VS. 0.091 on the test set), it demonstrates superior physical consistency and significantly better generalization. This trade-off ensures more robust and scientifically reliable predictions, especially under limited data conditions. The results indicate that the empirical-guided framework is a practical and reliable tool for evaluating the structural performance of ECC-strengthened RC beams, supporting their design, retrofitting, and safety assessment. Full article

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21 pages, 654 KB

Open AccessArticle

Regression Modeling for Cure Factors on Uterine Cancer Data Using the Reparametrized Defective Generalized Gompertz Distribution

by Dionisio Silva-Neto, Francisco Louzada-Neto and Vera Lucia Tomazella

Math. Comput. Appl. 2025, 30(5), 93; https://doi.org/10.3390/mca30050093 - 31 Aug 2025

Viewed by 248

Abstract

Recent advances in medical research have improved survival outcomes for patients with life-threatening diseases. As a result, the existence of long-term survivors from these illnesses is becoming common. However, conventional models in survival analysis assume that all individuals remain at risk of death [...] Read more.

Recent advances in medical research have improved survival outcomes for patients with life-threatening diseases. As a result, the existence of long-term survivors from these illnesses is becoming common. However, conventional models in survival analysis assume that all individuals remain at risk of death after the follow-up, disregarding the presence of a cured subpopulation. An important methodological advancement in this context is the use of defective distributions. In the defective models, the survival function converges to a constant value

p \in (0, 1)

as a function of the parameters. Among these models, the defective generalized Gompertz distribution (DGGD) has emerged as a flexible approach. In this work, we introduce a reparametrized version of the DGGD that incorporates the cure parameter and accommodates covariate effects to assess individual-level factors associated with long-term survival. A Bayesian model is presented, with parameter estimation via the Hamiltonian Monte Carlo algorithm. A simulation study demonstrates good asymptotic results of the estimation process under vague prior information. The proposed methodology is applied to a real-world dataset of patients with uterine cancer. Our results reveal statistically significant protective effects of surgical intervention, alongside elevated risk associated with age over 50 years, diagnosis at the metastatic stage, and treatment with chemotherapy. Full article

(This article belongs to the Special Issue Statistical Inference in Linear Models, 2nd Edition)

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21 pages, 4275 KB

Open AccessFeature PaperArticle

Application of the Kurganov–Tadmor Scheme in Curvilinear Coordinates for Supersonic Flow

by Sebastián Bertolo, Sergio Elaskar and Luis Gutiérrez Marcantoni

Math. Comput. Appl. 2025, 30(5), 92; https://doi.org/10.3390/mca30050092 - 23 Aug 2025

Viewed by 273

Abstract

In this current study, we developed a second-order Kurganov–Tadmor scheme in curvilinear coordinates to analyze the external supersonic flow over bodies of various shapes. This scheme is capable of handling interfaces across different regions of the domain. We utilized a fourth-order Runge–Kutta temporal [...] Read more.

In this current study, we developed a second-order Kurganov–Tadmor scheme in curvilinear coordinates to analyze the external supersonic flow over bodies of various shapes. This scheme is capable of handling interfaces across different regions of the domain. We utilized a fourth-order Runge–Kutta temporal integrator and conducted several test cases to validate the performance of the new scheme. The results from the analyzed tests indicate that the new method produces highly accurate outcomes. Full article

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

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Math. Comput. Appl., Volume 30, Issue 5 (October 2025) – 7 articles

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