Mathematical and Computational Applications

19 pages, 1033 KB

Open AccessArticle

Spectral Bounds and Exit Times for a Stochastic Model of Corruption

by José Villa-Morales

Math. Comput. Appl. 2025, 30(5), 111; https://doi.org/10.3390/mca30050111 - 8 Oct 2025

We study a stochastic differential model for the dynamics of institutional corruption, extending a deterministic three-variable system—corruption perception, proportion of sanctioned acts, and policy laxity—by incorporating Gaussian perturbations into key parameters. We prove global existence and uniqueness of solutions in the physically relevant [...] Read more.

We study a stochastic differential model for the dynamics of institutional corruption, extending a deterministic three-variable system—corruption perception, proportion of sanctioned acts, and policy laxity—by incorporating Gaussian perturbations into key parameters. We prove global existence and uniqueness of solutions in the physically relevant domain, and we analyze the linearization around the asymptotically stable equilibrium of the deterministic system. Explicit mean square bounds for the linearized process are derived in terms of the spectral properties of a symmetric matrix, providing insight into the temporal validity of the linear approximation. To investigate global behavior, we relate the first exit time from the domain of interest to backward Kolmogorov equations and numerically solve the associated elliptic and parabolic PDEs with FreeFEM, obtaining estimates of expectations and survival probabilities. An application to the case of Mexico highlights nontrivial effects: while the spectral structure governs local stability, institutional volatility can non-monotonically accelerate global exit, showing that highly reactive interventions without effective sanctions increase uncertainty. Policy implications and possible extensions are discussed. Full article

(This article belongs to the Section Social Sciences)

24 pages, 386 KB

Open AccessArticle

Saddle Points of Partial Augmented Lagrangian Functions

by Longfei Huang, Jingyong Tang, Yutian Wang and Jinchuan Zhou

Math. Comput. Appl. 2025, 30(5), 110; https://doi.org/10.3390/mca30050110 - 8 Oct 2025

Abstract

In this paper, we study a class of optimization problems with separable constraint structures, characterized by a combination of convex and nonconvex constraints. To handle these two distinct types of constraints, we introduce a partial augmented Lagrangian function by retaining nonconvex constraints while [...] Read more.

In this paper, we study a class of optimization problems with separable constraint structures, characterized by a combination of convex and nonconvex constraints. To handle these two distinct types of constraints, we introduce a partial augmented Lagrangian function by retaining nonconvex constraints while relaxing convex constraints into the objective function. Specifically, we employ the Moreau envelope for the convex term and apply second-order variational geometry to analyze the nonconvex term. For this partial augmented Lagrangian function, we study its saddle points and establish their relationship with KKT conditions. Furthermore, second-order optimality conditions are developed by employing tools such as second-order subdifferentials, asymptotic second-order tangent cones, and second-order tangent sets. Full article

21 pages, 599 KB

Open AccessArticle

Quantized Control of Switched Systems with Partly Unstabilizable Subsystems and Actuator Saturation

by Jingjing Yan, Yunhui Gu, Shengyang Shi and Yuqing Zheng

Math. Comput. Appl. 2025, 30(5), 109; https://doi.org/10.3390/mca30050109 - 5 Oct 2025

Abstract

This paper solves the stabilization problem of the continuous-time switched systems with partly unstabilizable subsystems subject to actuator saturation and data quantization. The static quantizer is designed by properly restraining the density of the finite partition. The relationship between an ellipse and a [...] Read more.

This paper solves the stabilization problem of the continuous-time switched systems with partly unstabilizable subsystems subject to actuator saturation and data quantization. The static quantizer is designed by properly restraining the density of the finite partition. The relationship between an ellipse and a polyhedral is established and a suitable expression for the controller suffered by data quantization and actuator saturation is obtained. By defining the attraction domain and the invariant set based on the union or intersection of ellipses, we guarantee the decrement of the Lyapunov function in the optimal case if the state is within a given annular area. On this basis, if average dwell time and activation time of stabilizable subsystems meet some constraints, we derive that every trajectory whose initial state is within the given region will fall into a small ellipsoid and stay in a slightly larger ellipsoid. An illustrative example is given to verify the validity of the theoretical analysis. Full article

(This article belongs to the Section Engineering)

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18 pages, 2863 KB

Open AccessArticle

Using Non-Lipschitz Signum-Based Functions for Distributed Optimization and Machine Learning: Trade-Off Between Convergence Rate and Optimality Gap

by Mohammadreza Doostmohammadian, Amir Ahmad Ghods, Alireza Aghasi, Zulfiya R. Gabidullina and Hamid R. Rabiee

Math. Comput. Appl. 2025, 30(5), 108; https://doi.org/10.3390/mca30050108 - 4 Oct 2025

Abstract

In recent years, the prevalence of large-scale datasets and the demand for sophisticated learning models have necessitated the development of efficient distributed machine learning (ML) solutions. Convergence speed is a critical factor influencing the practicality and effectiveness of these distributed frameworks. Recently, non-Lipschitz [...] Read more.

In recent years, the prevalence of large-scale datasets and the demand for sophisticated learning models have necessitated the development of efficient distributed machine learning (ML) solutions. Convergence speed is a critical factor influencing the practicality and effectiveness of these distributed frameworks. Recently, non-Lipschitz continuous optimization algorithms have been proposed to improve the slow convergence rate of the existing linear solutions. The use of signum-based functions was previously considered in consensus and control literature to reach fast convergence in the prescribed time and also to provide robust algorithms to noisy/outlier data. However, as shown in this work, these algorithms lead to an optimality gap and steady-state residual of the objective function in discrete-time setup. This motivates us to investigate the distributed optimization and ML algorithms in terms of trade-off between convergence rate and optimality gap. In this direction, we specifically consider the distributed regression problem and check its convergence rate by applying both linear and non-Lipschitz signum-based functions. We check our distributed regression approach by extensive simulations. Our results show that although adopting signum-based functions may give faster convergence, it results in large optimality gaps. The findings presented in this paper may contribute to and advance the ongoing discourse of similar distributed algorithms, e.g., for distributed constrained optimization and distributed estimation. Full article

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27 pages, 2748 KB

Open AccessArticle

Energy Optimization of Compressed Air Systems with Screw Compressors Under Variable Load Conditions

by Guillermo José Barroso García, José Pedro Monteagudo Yanes, Luis Angel Iturralde Carrera, Carlos D. Constantino-Robles, Brenda Juárez Santiago, Juan Manuel Olivares Ramírez, Omar Rodriguez Abreo and Juvenal Rodríguez-Reséndiz

Math. Comput. Appl. 2025, 30(5), 107; https://doi.org/10.3390/mca30050107 - 1 Oct 2025

Abstract

This study evaluates the energy performance of a BOGE C 22-2 oil-injected rotary screw compressor under real industrial conditions. Using direct measurements with a power quality analyzer and thermodynamic modeling, key performance indicators such as compression work, mass flow rate, compressor efficiency, and [...] Read more.

This study evaluates the energy performance of a BOGE C 22-2 oil-injected rotary screw compressor under real industrial conditions. Using direct measurements with a power quality analyzer and thermodynamic modeling, key performance indicators such as compression work, mass flow rate, compressor efficiency, and motor efficiency were determined. The results revealed actual efficiencies of 27–48%, significantly lower than the expected 60–70% for this type of equipment, mainly due to partial-load operation and low airflow demand. A low power factor of approximately 0.72 was also observed, caused by a high share of reactive power consumption. To address these inefficiencies, the study recommends the installation of an automatic capacitor bank to improve power quality and the integration of a secondary variable speed compressor to enhance performance under low-demand conditions. These findings underscore the importance of assessing compressor behavior in real-world environments and implementing techno-economic strategies to increase energy efficiency and reduce industrial electricity consumption. Full article

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

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37 pages, 4368 KB

Open AccessArticle

High-Performance Simulation of Generalized Tempered Stable Random Variates: Exact and Numerical Methods for Heavy-Tailed Data

by Aubain Nzokem and Daniel Maposa

Math. Comput. Appl. 2025, 30(5), 106; https://doi.org/10.3390/mca30050106 - 28 Sep 2025

Abstract

The Generalized Tempered Stable (GTS) distribution extends classical stable laws through exponential tempering, preserving the power-law behavior while ensuring finite moments. This makes it especially suitable for modeling heavy-tailed financial data. However, the lack of closed-form densities poses significant challenges for simulation. This [...] Read more.

The Generalized Tempered Stable (GTS) distribution extends classical stable laws through exponential tempering, preserving the power-law behavior while ensuring finite moments. This makes it especially suitable for modeling heavy-tailed financial data. However, the lack of closed-form densities poses significant challenges for simulation. This study provides a comprehensive and systematic comparison of GTS simulation methods, including rejection-based algorithms, series representations, and an enhanced Fast Fractional Fourier Transform (FRFT)-based inversion method. Through extensive numerical experiments on major financial assets (Bitcoin, Ethereum, the S&P 500, and the SPY ETF), this study demonstrates that the FRFT method outperforms others in terms of accuracy and ability to capture tail behavior, as validated by goodness-of-fit tests. Our results provide practitioners with robust and efficient simulation tools for applications in risk management, derivative pricing, and statistical modeling. Full article

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

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19 pages, 1354 KB

Open AccessFeature PaperArticle

Theory of Functional Connections Extended to Continuous Integral Constraints

by Daniele Mortari

Math. Comput. Appl. 2025, 30(5), 105; https://doi.org/10.3390/mca30050105 - 24 Sep 2025

Abstract

This study extends the Theory of Functional Connections, previously applied to constraints specified at discrete points, to encompass continuous integral constraints of the form

\int_{x_{0}}^{x_{f}} f (x, t) d x = I (t)

, [...] Read more.

This study extends the Theory of Functional Connections, previously applied to constraints specified at discrete points, to encompass continuous integral constraints of the form

\int_{x_{0}}^{x_{f}} f (x, t) d x = I (t)

, where

I (t)

can be a constant, a prescribed function, or an unknown function to be estimated through optimization. The framework of continuous integral constraints is developed within the context of initial value problems (IVP) and boundary value problems (BVP). To demonstrate the effectiveness of this analytical approach, examples validate the method and highlight distinctions between satisfying continuous integral constraints via simple interpolation versus functional interpolation. A limitation of the proposed approach is the inability to inherently enforce inequality constraints, such as the positivity constraint

f (x, t) \geq 0

, for modeling probability density functions in classical mechanics. Despite this, numerical experiments on boundary-value problems rarely result in negative values, indicating that the issue occurs infrequently. However, a mitigation strategy based on non-negative least-squares methods combined with Bernstein polynomials is proposed to address these rare cases. This approach is validated through an additional numerical test, demonstrating its efficacy in ensuring nonnegativity when required. Full article

(This article belongs to the Section Engineering)

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18 pages, 4862 KB

Open AccessArticle

Many-Objective Intelligent Scheduling Optimization Algorithm for Complex Integrated System

by Yanwei Sang, Yan Xu, Cai Zhang, Zongming Zhu and Liang Liang

Math. Comput. Appl. 2025, 30(5), 104; https://doi.org/10.3390/mca30050104 - 24 Sep 2025

Abstract

Due to the increasing consumer demand for custom products, aluminum alloy component creep forming manufacturing has shifted towards production modes designed for multiple varieties and small batches, leading to problems such as complex production organization and low production efficiency. In the specific case [...] Read more.

Due to the increasing consumer demand for custom products, aluminum alloy component creep forming manufacturing has shifted towards production modes designed for multiple varieties and small batches, leading to problems such as complex production organization and low production efficiency. In the specific case of modern large-scale aluminum alloy aerospace components, the manufacturing requirements cannot be satisfied. According to the production characteristics and process requirements in this industry, a many-objective, whole-process production scheduling model was established, and a residual rectangle-based many-objective evolutionary algorithm (RTEA) was developed to solve it effectively. The RTEA uses the residual rectangle method in the decoding phase for autoclave filling, which improves the productivity of the autoclave. We further designed a three-stage environmental selection strategy to strengthen the balance of convergence and diversity and increase the selection pressure in the evolutionary process. Computational experiments were performed using industrial datasets relative to aerospace components and engineering production data. The advantages and competitiveness of the comprehensive production scheduling model and the RTEA were verified, as evidenced by an increase in production line efficiency of 20%. In conclusion, the proposed approach offers an effective solution to the many-objective production scheduling problem hindering aluminum alloy creep forming component production. Full article

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12 pages, 2471 KB

Open AccessArticle

A Priori Error Analysis of an Adaptive Splitting Scheme for Non-Autonomous Second-Order Systems

by Christian Budde

Math. Comput. Appl. 2025, 30(5), 103; https://doi.org/10.3390/mca30050103 - 20 Sep 2025

Abstract

We present a fully discrete splitting-Galerkin scheme for second-order, non-autonomous abstract Cauchy problems with time-dependent perturbations. By reformulating the second-order equation as a first-order system in the product space, we apply a Galerkin semi-discretization in space of order

O (h^{k})

[...] Read more.

We present a fully discrete splitting-Galerkin scheme for second-order, non-autonomous abstract Cauchy problems with time-dependent perturbations. By reformulating the second-order equation as a first-order system in the product space, we apply a Galerkin semi-discretization in space of order

O (h^{k})

and a Strang splitting in time of order

O (Δ t^{2})

. An embedded Runge–Kutta controller provides adaptive time-stepping to handle rapid temporal variations in the perturbation operator

B (t)

. Under standard regularity and commutator assumptions on

A (t)

and

B (t)

, we establish a priori error estimates

max_{0 \leq t_{n} \leq T} {∥ u (t_{n}) - u_{n} ∥}_{Z} = O (h^{k} + Δ t^{2}) .

Numerical experiments for a 1D perturbed wave equation confirm the theoretical convergence rates, illustrate stability thresholds in the unstable regime, and demonstrate up to 40% savings in computational cost via adaptivity. Full article

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

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25 pages, 651 KB

Open AccessSystematic Review

Measuring Circular Economy with Data Envelopment Analysis: A Systematic Literature Review

by Svetlana V. Ratner, Andrey V. Lychev, Elisaveta D. Muravleva and Daniil M. Muravlev

Math. Comput. Appl. 2025, 30(5), 102; https://doi.org/10.3390/mca30050102 - 17 Sep 2025

Abstract

This article presents a systematic literature review of data envelopment analysis (DEA) models used to evaluate circular economy (CE) practices. The review is based on 151 peer-reviewed articles published between 2015 and 2024. By analyzing this collection, this review categorizes different DEA models [...] Read more.

This article presents a systematic literature review of data envelopment analysis (DEA) models used to evaluate circular economy (CE) practices. The review is based on 151 peer-reviewed articles published between 2015 and 2024. By analyzing this collection, this review categorizes different DEA models and their levels of application, discusses the data sources utilized, and identifies the prevailing methodologies and evaluation criteria used to measure the CE performance. Despite the extensive literature on measuring the circular economy using DEA, a critical evaluation of existing DEA approaches that highlights their strengths and weaknesses is still missing. Our analysis shows that DEA models provide valuable insights when assessing circular strategies, namely, R2—Reduce, R8—Recycling, and R9—Recovering. Over 40% of the surveyed literature focuses on China, with nearly 20% on the European Union. Other regions are sparsely represented within our sample, highlighting a potential gap in the current research landscape. Full article

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

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20 pages, 4230 KB

Open AccessArticle

HGREncoder: Enhancing Real-Time Hand Gesture Recognition with Transformer Encoder—A Comparative Study

by Luis Gabriel Macías, Jonathan A. Zea, Lorena Isabel Barona, Ángel Leonardo Valdivieso and Marco E. Benalcázar

Math. Comput. Appl. 2025, 30(5), 101; https://doi.org/10.3390/mca30050101 - 16 Sep 2025

Abstract

In the field of Hand Gesture Recognition (HGR), Electromyography (EMG) is used to detect the electrical impulses that muscles emit when a movement is generated. Currently, there are several HGR models that use EMG to predict hand gestures. However, most of these models [...] Read more.

In the field of Hand Gesture Recognition (HGR), Electromyography (EMG) is used to detect the electrical impulses that muscles emit when a movement is generated. Currently, there are several HGR models that use EMG to predict hand gestures. However, most of these models have limited performance in real-time applications, with the highest recognition rate achieved being 65.78 ± 15.15%, without post-processing steps. Other non-generalizable models, i.e., those trained with a small number of users, achieved a window-based classification accuracy of 93.84%, but not in time-real applications. Therefore, this study addresses these issues by employing transformers to create a generalizable model and enhance recognition accuracy in real-time applications. The architecture of our model is composed of a Convolutional Neural Network (CNN), a positional encoding layer, and the transformer encoder. To obtain a generalizable model, the EMG-EPN-612 dataset was used. This dataset contains records of 612 individuals. Several experiments were conducted with different architectures, and our best results were compared with other previous research that used CNN, LSTM, and transformers. The findings of this research reached a classification accuracy of 95.25 ± 4.9% and a recognition accuracy of 89.7 ± 8.77%. This recognition accuracy is a significant contribution because it encompasses the entire sequence without post-processing steps. Full article

(This article belongs to the Special Issue New Trends in Computational Intelligence and Applications 2025)

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22 pages, 5739 KB

Open AccessArticle

Dynamical Analysis and Solitary Wave Solutions of the Zhanbota-IIA Equation with Computational Approach

by Beenish, Maria Samreen and Manuel De la Sen

Math. Comput. Appl. 2025, 30(5), 100; https://doi.org/10.3390/mca30050100 - 15 Sep 2025

Abstract

This study conducts an in-depth analysis of the dynamical characteristics and solitary wave solutions of the integrable Zhanbota-IIA equation through the lens of planar dynamic system theory. This research applies Lie symmetry to convert nonlinear partial differential equations into ordinary differential equations, enabling [...] Read more.

This study conducts an in-depth analysis of the dynamical characteristics and solitary wave solutions of the integrable Zhanbota-IIA equation through the lens of planar dynamic system theory. This research applies Lie symmetry to convert nonlinear partial differential equations into ordinary differential equations, enabling the investigation of bifurcation, phase portraits, and dynamic behaviors within the framework of chaos theory. A variety of analytical instruments, such as chaotic attractors, return maps, recurrence plots, Lyapunov exponents, Poincaré maps, three-dimensional phase portraits, time analysis, and two-dimensional phase portraits, are utilized to scrutinize both perturbed and unperturbed systems. Furthermore, the study examines the power frequency response and the system’s sensitivity to temporal delays. A novel classification framework, predicated on Lyapunov exponents, systematically categorizes the system’s behavior across a spectrum of parameters and initial conditions, thereby elucidating aspects of multistability and sensitivity. The perturbed system exhibits chaotic and quasi-periodic dynamics. The research employs the maximum Lyapunov exponent portrait as a tool for assessing system stability and derives solitary wave solutions accompanied by illustrative visualization diagrams. The methodology presented herein possesses significant implications for applications in optical fibers and various other engineering disciplines. Full article

(This article belongs to the Section Natural Sciences)

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17 pages, 734 KB

Open AccessArticle

Distributed PD Average Consensus of Lipschitz Nonlinear MASs in the Presence of Mixed Delays

by Tuo Zhou

Math. Comput. Appl. 2025, 30(5), 99; https://doi.org/10.3390/mca30050099 - 11 Sep 2025

Abstract

In this work, the distributed average consensus for dynamical networks with Lipschitz nonlinear dynamics is studied, where the network communication switches quickly among a set of directed and balanced switching graphs. Differing from existing research concerning uniform constant delay or time-varying delays, this [...] Read more.

In this work, the distributed average consensus for dynamical networks with Lipschitz nonlinear dynamics is studied, where the network communication switches quickly among a set of directed and balanced switching graphs. Differing from existing research concerning uniform constant delay or time-varying delays, this study focuses on consensus problems with mixed delays, equipped with one class of delays embedded within the nonlinear dynamics and another class of delays present in the control input. In order to solve these problems, a proportional and derivative control strategy with time delays is proposed. In this way, by using Lyapunov theory, the stability is analytically established and the conditions required for solving the consensus problems are rigorously derived over switching digraphs. Finally, the effectiveness of the designed algorithm is tested using the MATLAB R2021a platform. Full article

(This article belongs to the Topic Fractional Calculus, Symmetry Phenomenon and Probability Theory for PDEs, and ODEs)

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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

Abstract

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

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

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

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

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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