Mathematical and Computational Applications

28 pages, 572 KB

Open AccessArticle

New Adaptive Echolocation Radar Technique Incorporated into the Bat Algorithm Applied to Benchmark Functions (Radar-Bat)

by Miguel A. García-Morales, Rubén Salas-Cabrera, Bárbara María-Esther García-Morales, Juan Frausto-Solís and Joel Rodríguez-Guillén

Math. Comput. Appl. 2026, 31(1), 20; https://doi.org/10.3390/mca31010020 (registering DOI) - 2 Feb 2026

Abstract

This article proposes a bat algorithm that incorporates novel techniques inspired by maritime radars, referred to as the Radar-Bat algorithm. This proposed method allows each virtual bat to identify the position of the best solution at a given distance within the search space. [...] Read more.

This article proposes a bat algorithm that incorporates novel techniques inspired by maritime radars, referred to as the Radar-Bat algorithm. This proposed method allows each virtual bat to identify the position of the best solution at a given distance within the search space. It incorporates an adaptive threshold to maintain a constant false alarm rate (CFAR), enabling the acceptance of solutions based on the best value found, thus improving the exploitation of the search space. Furthermore, a systematic directional sweep balances exploration and exploitation effectively. This algorithm is used to solve complex optimization problems, essentially those with multimodal functions, demonstrating that the proposed algorithm achieves better convergence and robustness compared to the basic bat algorithm, highlighting its potential as a novel contribution to the field of metaheuristics. To evaluate the performance of the proposed algorithm against the basic bat algorithm, the Wilcoxon and Friedman non-parametric tests are applied, with a significance level of 5%. Computational experiments show that the proposed algorithm outperforms the state-of-the-art algorithm. In terms of quality, the proposed algorithm shows clear superiority over the basic bat algorithm across most benchmark functions. Regarding efficiency, although Radar Bat incorporates additional mechanisms, the experimental results do not indicate a consistent disadvantage in execution time, with both algorithms exhibiting comparable performance depending on the problem and dimensionality. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2025)

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24 pages, 847 KB

Open AccessArticle

Vine Copula Modelling of Extreme Temperature, Wind Speed, and Relative Humidity Towards Enhancement of Renewable Energy Production

by Maashele Kholofelo Metwane, Daniel Maposa and Caston Sigauke

Math. Comput. Appl. 2026, 31(1), 19; https://doi.org/10.3390/mca31010019 - 1 Feb 2026

Abstract

The increasing global reliance on wind and solar energy underscores the critical vulnerability of renewable systems to extreme weather, which can severely disrupt power generation. Accurately modelling the complex, multivariate dependencies of weather extremes is essential for building grid resilience, yet conventional statistical [...] Read more.

The increasing global reliance on wind and solar energy underscores the critical vulnerability of renewable systems to extreme weather, which can severely disrupt power generation. Accurately modelling the complex, multivariate dependencies of weather extremes is essential for building grid resilience, yet conventional statistical models often fail to capture critical tail dependencies. This study aims to develop a robust framework using vine copulas to model the tail dependencies among key meteorological variables, extreme temperature, wind speed, and relative humidity, across the Eastern Cape province, South Africa, in order to identify optimal seasons for renewable energy production. We first clustered weather stations across the province into five distinct groups using Partitioning Around Medoids (PAM), based on geographical features (elevation, longitude, and latitude). This study explored an automatic selection of the optimal vine copula structure that adequately describes the dependence structure of the meteorological variables employed. The analysis demonstrated that R-vine copulas successfully captured the multivariate tail behaviour of temperature and relative humidity, while D-vine copulas were highly effective for wind speed. The models revealed significant tail dependencies, indicating a high potential for concurrent extreme weather events that impact energy generation. Our findings confirm that vine copulas offer a superior framework for assessing the risks associated with extreme weather to renewable energy systems. The results provide critical insights for regional energy policy and grid resilience planning, highlighting the importance of advanced risk assessment to safeguard renewable energy production against climate extremes. Full article

(This article belongs to the Section Natural Sciences)

26 pages, 4764 KB

Open AccessArticle

Hybrid ConvLSTM U-Net Deep Neural Network for Land Use and Land Cover Classification from Multi-Temporal Sentinel-2 Images: Application to Yaoundé, Cameroon

by Ange Gabriel Belinga, Stéphane Cédric Tékouabou Koumetio and Mohammed El Haziti

Math. Comput. Appl. 2026, 31(1), 18; https://doi.org/10.3390/mca31010018 - 26 Jan 2026

Viewed by 110

Abstract

Accurate mapping of land use and land cover (LULC) is crucial for various applications such as urban planning, environmental management, and sustainable development, particularly in rapidly growing urban areas. African cities such as Yaoundé, Cameroon, are particularly affected by this rapid and often [...] Read more.

Accurate mapping of land use and land cover (LULC) is crucial for various applications such as urban planning, environmental management, and sustainable development, particularly in rapidly growing urban areas. African cities such as Yaoundé, Cameroon, are particularly affected by this rapid and often uncontrolled urban growth with complex spatio-temporal dynamics. Effective modeling of LULC indicators in such areas requires robust algorithms for high-resolution images segmentation and classification, as well as reliable data with great spatio-temporal distributions. Among the most suitable data sources for these types of studies, Sentinel-2 image time series, thanks to their high spatial (10 m) and temporal (5 days) resolution, are a valuable source of data for this task. However, for an effective LULC modeling purpose in such dynamic areas, many challenges remain, including spectral confusion between certain classes, seasonal variability, and spatial heterogeneity. This study proposes a hybrid deep learning architecture combining U-Net and Convolutional Long Short-Term Memory (ConvLSTM) layers, allowing the spatial structures and temporal dynamics of the Sentinel-2 series to be exploited jointly. Applied to the Yaoundé region (Cameroon) over the period 2018–2025, the hybrid model significantly outperforms the U-Net and ConvLSTM models alone. It achieves a macro-average F1 score of 0.893, an accuracy of 0.912, and an average IoU of 0.811 on the test set. These segmentation performances reached up to 0.948, 0.953, and 0.910 for precision, F1-score, and IoU, respectively, on the built-up areas class. Moreover, despite its better performance, in terms of complexity, the figures confirm that the hybrid does not significantly penalize evaluation speed. These results demonstrate the relevance of jointly integrating space and time for robust LULC classification from multi-temporal satellite images. Full article

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21 pages, 1463 KB

Open AccessArticle

A Mathematical Framework for E-Commerce Sales Prediction Using Attention-Enhanced BiLSTM and Bayesian Optimization

by Hao Hu, Jinshun Cai and Chenke Xu

Math. Comput. Appl. 2026, 31(1), 17; https://doi.org/10.3390/mca31010017 - 22 Jan 2026

Viewed by 79

Abstract

Accurate sales prediction is crucial for inventory and marketing in e-commerce. Cross-border sales involve complex patterns that traditional models cannot capture. To address this, we propose an improved Bidirectional Long Short-Term Memory (BiLSTM) model, enhanced with an attention mechanism and Bayesian hyperparameter optimization. [...] Read more.

Accurate sales prediction is crucial for inventory and marketing in e-commerce. Cross-border sales involve complex patterns that traditional models cannot capture. To address this, we propose an improved Bidirectional Long Short-Term Memory (BiLSTM) model, enhanced with an attention mechanism and Bayesian hyperparameter optimization. The attention mechanism focuses on key temporal features, improving trend identification. The BiLSTM captures both forward and backward dependencies, offering deeper insights into sales patterns. Bayesian optimization fine-tunes hyperparameters such as learning rate, hidden-layer size, and dropout rate to achieve optimal performance. These innovations together improve forecasting accuracy, making the model more adaptable and efficient for cross-border e-commerce sales. Experimental results show that the model achieves an Root Mean Square Error (RMSE) of 13.2, Mean Absolute Error (MAE) of 10.2, Mean Absolute Percentage Error (MAPE) of 8.7 percent, and a Coefficient of Determination (R²) of 0.92. It outperforms baseline models, including BiLSTM (RMSE 16.5, MAPE 10.9 percent), BiLSTM with Attention (RMSE 15.2, MAPE 10.1 percent), Temporal Convolutional Network (RMSE 15.0, MAPE 9.8 percent), and Transformer for Time Series (RMSE 14.8, MAPE 9.5 percent). These results highlight the model’s superior performance in forecasting cross-border e-commerce sales, making it a valuable tool for inventory management and demand planning. Full article

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

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13 pages, 717 KB

Open AccessArticle

Gaining Understanding of Neural Networks with Programmatically Generated Data

by Eric O’Sullivan, Ken Kennedy and Jean Mohammadi-Aragh

Math. Comput. Appl. 2026, 31(1), 16; https://doi.org/10.3390/mca31010016 - 22 Jan 2026

Viewed by 106

Abstract

The performance of convolutional neural networks (CNNs) depends not only on model architecture but also on the structure and quality of the training data. While most artificial network interpretability methods focus on explaining trained models, less attention has been given to understanding how [...] Read more.

The performance of convolutional neural networks (CNNs) depends not only on model architecture but also on the structure and quality of the training data. While most artificial network interpretability methods focus on explaining trained models, less attention has been given to understanding how dataset composition itself shapes learning outcomes. This work introduces a novel framework that uses programmatically generated synthetic datasets to isolate and control visual features, enabling systematic evaluation of their contribution to CNN performance. Guided by principles from set theory, Shapley values, and the Apriori algorithm, we formalize an equivalence between CNN kernel weights and pattern frequency counts, showing that feature overlap across datasets predicts model generalization. Methods include the construction of four synthetic digit datasets with controlled object and background features, training lightweight CNNs under K-fold validation, and statistical evaluation of cross-dataset performance. The results show that internal object patterns significantly improve accuracy and F1 scores compared to non-object background features, and that a dataset similarity prediction algorithm achieves near-perfect correlation (

ρ = 0.97

) between the predicted and observed performance. The conclusions highlight that dataset feature composition can be treated as a measurable proxy for model behavior, offering a new path for dataset evaluation, pruning, and design optimization. This approach provides a principled framework for predicting CNN performance without requiring full-scale model training. Full article

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

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25 pages, 1643 KB

Open AccessArticle

Advanced Mathematical Optimization of PMSM Speed Control Using Enhanced Adaptive Particle Swarm Optimization Algorithm

by Huajun Ran, Xian Huang, Jiahao Dong and Jiefei Yang

Math. Comput. Appl. 2026, 31(1), 15; https://doi.org/10.3390/mca31010015 - 20 Jan 2026

Viewed by 245

Abstract

To address the challenges of low precision, slow convergence, and poor anti-interference in traditional Particle Swarm Optimization (PSO) for Permanent Magnet Synchronous Motor (PMSM) speed control, a new Adaptive Hybrid Particle Swarm Optimization (AM-PSO) algorithm is proposed. This algorithm integrates adaptive dynamic inertia [...] Read more.

To address the challenges of low precision, slow convergence, and poor anti-interference in traditional Particle Swarm Optimization (PSO) for Permanent Magnet Synchronous Motor (PMSM) speed control, a new Adaptive Hybrid Particle Swarm Optimization (AM-PSO) algorithm is proposed. This algorithm integrates adaptive dynamic inertia weight, hybrid local search mechanisms, neural network-based adjustments, multi-stage optimization, and multi-objective optimization. The adaptive dynamic inertia weight improves the balance, boosting both convergence speed and accuracy. The inclusion of Simulated Annealing (SA) and Differential Evolution (DE) strengthens local search and avoids local optima. Neural network adjustments improve search flexibility by intelligently modifying search direction and step size. Additionally, the multi-stage strategy allows broad exploration initially and refines local searches as the solution approaches, speeding up convergence. The multi-objective optimization further ensures the simultaneous improvement of key performance metrics like precision, response time, and robustness. Experimental results demonstrate that AM-PSO outperforms traditional PSO in PMSM speed control, achieving a 40% reduction in speed error, 25% faster convergence, and enhanced robustness. Notably, the speed error increased only marginally from 0.03 RPM to 0.05 RPM, showcasing the algorithm’s superior ability to reject disturbances. Full article

(This article belongs to the Section Engineering)

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18 pages, 944 KB

Open AccessArticle

An Improved Approach Based on a New Laplace Model Using Classical and Risk Measures

by Morad Alizadeh, Gauss M. Cordeiro, Jondeep Das, Partha Jyoti Hazarika, Javier E. Contreras-Reyes, Mohamed S. Hamed and Haitham M. Yousof

Math. Comput. Appl. 2026, 31(1), 14; https://doi.org/10.3390/mca31010014 - 17 Jan 2026

Viewed by 268

Abstract

In this paper, we propose a generalized odd log-logistic standard Laplace model and study some of its main properties. The novelty of this model is based on classical and risk-based measures to effectively analyze the body mass index (BMI) data. The analysis underscores [...] Read more.

In this paper, we propose a generalized odd log-logistic standard Laplace model and study some of its main properties. The novelty of this model is based on classical and risk-based measures to effectively analyze the body mass index (BMI) data. The analysis underscores the importance of a multidisciplinary approach in addressing challenges related to health, performance, and risk management. The proposed methodology not only is helpful to understand the variability of BMI measurements, but also prove how common statistical models considered in financial field can be effectively adapted to other ones, offering insights that drive informed decision-making and strategic planning. Full article

(This article belongs to the Section Natural Sciences)

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27 pages, 2521 KB

Open AccessArticle

IoTToe: Monitoring Foot Angle Variability for Health Management and Safety

by Ata Jahangir Moshayedi, Zeashan Khan, Zhonghua Wang and Mehran Emadi Andani

Math. Comput. Appl. 2026, 31(1), 13; https://doi.org/10.3390/mca31010013 - 16 Jan 2026

Viewed by 230

Abstract

Toe-in (inward) and toe-out (outward) foot alignments significantly affect gait, posture, and joint stress, causing issues like abnormal gait, joint strain, and foot conditions such as plantar fasciitis and high arches. Addressing these alignments is crucial for improving mobility and comfort. This study [...] Read more.

Toe-in (inward) and toe-out (outward) foot alignments significantly affect gait, posture, and joint stress, causing issues like abnormal gait, joint strain, and foot conditions such as plantar fasciitis and high arches. Addressing these alignments is crucial for improving mobility and comfort. This study introduces IoTToe, a wearable IoT device designed to detect and monitor gait patterns by using six ADXL345 sensors positioned on the foot, allowing healthcare providers to remotely monitor alignment via a webpage, reducing the need for physical tests. Tested on 45 participants aged 20–25 years with diverse BMIs, IoTToe proved suitable for both children and adults, supporting therapy and diagnostics. Statistical tests, including ICC, DFA, and ANOVA, confirmed the device’s effectiveness in detecting gait and postural control differences between legs. Gait variability results indicated that left leg showed more adaptability (DFA close to 0.5), compared to the right leg which was found more consistent (DFA close to 1). Postural control showed stable and agile standing with values between 0.5 and 1. Sensor combinations revealed that removing sensor B (on the gastrocnemius muscle) did not affect data quality. Moreover, taller individuals displayed smaller ankle angle changes, highlighting challenges in balance and upper body stability. IoTToe offers accurate data collection, reliability, portability, and significant potential for gait monitoring and injury prevention. Future studies would expand participation, especially among women and those with alignment issues, to enhance the system’s applicability for foot health management, safety and rehabilitation, further supporting telemetric applications in healthcare. Full article

(This article belongs to the Special Issue Advances in Computational and Applied Mechanics (SACAM))

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24 pages, 2901 KB

Open AccessArticle

Performance Defect Identification in Switching Power Supplies Based on Multi-Strategy-Enhanced Dung Beetle Optimizer

by Zibo Yang, Jiale Guo, Rui Li, Guoqing An, Kai Zhang, Jiawei Liu and Long Zhang

Math. Comput. Appl. 2026, 31(1), 12; https://doi.org/10.3390/mca31010012 - 12 Jan 2026

Viewed by 136

Abstract

To address the limited defect-detection capability of existing performance testing methods for switching power supplies under varying operating conditions, this paper proposes a defect identification approach based on an enhanced Dung Beetle Optimizer. The algorithm integrates multi-strategy improvements—including piecewise chaotic mapping, Lévy flight [...] Read more.

To address the limited defect-detection capability of existing performance testing methods for switching power supplies under varying operating conditions, this paper proposes a defect identification approach based on an enhanced Dung Beetle Optimizer. The algorithm integrates multi-strategy improvements—including piecewise chaotic mapping, Lévy flight perturbation, hybrid sine–cosine updating, and an alert sparrow mechanism—to refine the initial population generation, position update rules, and late-stage exploration. These enhancements strengthen its spatial search ability and computational performance. The experimental results show that the method accurately identifies the predefined defect intervals with a precision of 94.79%, covering 91.3% of the operating conditions. Comparisons with existing mainstream methods confirm the superior performance, effectiveness, and feasibility of the proposed method. Full article

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22 pages, 616 KB

Open AccessArticle

A Graph-Theoretical Approach to Bond Length Prediction in Flavonoids Using a Molecular Graph Model

by Moster Zhangazha, Alex Somto Arinze Alochukwu, Elizabeth Jonck, Ronald John Maartens, Eunice Mphako-Banda, Simon Mukwembi and Farai Nyabadza

Math. Comput. Appl. 2026, 31(1), 9; https://doi.org/10.3390/mca31010009 - 9 Jan 2026

Viewed by 366

Abstract

The accurate determination of bond lengths is fundamental to understanding molecular geometry and the physicochemical behavior of chemical compounds. However, obtaining these measurements is often challenging, as both experimental techniques and advanced quantum-chemical methods are complex, computationally demanding, and costly to apply across [...] Read more.

The accurate determination of bond lengths is fundamental to understanding molecular geometry and the physicochemical behavior of chemical compounds. However, obtaining these measurements is often challenging, as both experimental techniques and advanced quantum-chemical methods are complex, computationally demanding, and costly to apply across diverse molecular systems. In this work, we present a novel graph-theoretical model for predicting bond lengths in flavonoid molecules based on molecular descriptors derived from atomic and topological parameters. By integrating atomic electronegativity with graph-based descriptors, such as the weighted second-order neighborhood, the proposed model predicts the bond lengths of luteolin with a coefficient of determination of

R^{2} = 0.990

. This approach offers a computationally efficient and highly accurate alternative to conventional experimental and theoretical methods, providing a practical framework for bond length estimation when experimental data are unavailable. Full article

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16 pages, 968 KB

Open AccessArticle

Equilibrium Drift Restriction: A Control Strategy for Reducing Steady-State Error Under System Inconsistency

by Fangyuan Li

Math. Comput. Appl. 2026, 31(1), 11; https://doi.org/10.3390/mca31010011 - 9 Jan 2026

Viewed by 168

Abstract

The inconsistency of system parameters inevitably emerges due to reasons such as modeling imprecision, manufacturing error, and aging process. Due to the inconsistency between nominal models and real-world conditions, controllers designed accordingly frequently fail to maintain performance guarantees during physical deployment. This phenomenon [...] Read more.

The inconsistency of system parameters inevitably emerges due to reasons such as modeling imprecision, manufacturing error, and aging process. Due to the inconsistency between nominal models and real-world conditions, controllers designed accordingly frequently fail to maintain performance guarantees during physical deployment. This phenomenon exemplifies the open sim-to-real gap problem. To address this limitation, we develop an equilibrium drift restriction strategy (EDR) to reduce the steady-state error due to the system inconsistency. We first present an example to show the reason why some existing controllers cannot counteract the system inconsistency when the equilibrium is not at the origin. Then, a control strategy is proposed by using the EDR method to reduce the induced steady-state error. Both intuitive interpretation and theoretical analysis demonstrate how EDR reduces steady-state deviations. Simulation results of a common pendulum system are provided to demonstrate that the restriction mitigates the impact of parameter inconsistency. A comparison with the popular Q-learning method is also presented. The results show that the EDR method can serve as a simple but effective tool to improve the steady-state performance of existing controllers. This paper offers a fresh perspective for exploring the control functions with specific properties in the realm of related controller research. Full article

(This article belongs to the Section Engineering)

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16 pages, 3759 KB

Open AccessArticle

Clinical Prediction and Spatial Statistical Analysis of Ascending Thoracic Aortic Aneurysm Structure

by Katalina Oviedo Rodríguez, Alda Carvalho, Rodrigo Valente, José Xavier and António Cruz Tomás

Math. Comput. Appl. 2026, 31(1), 10; https://doi.org/10.3390/mca31010010 - 9 Jan 2026

Viewed by 250

Abstract

This study presents an analysis of data from patients with ascending thoracic aortic aneurysms (ATAAs). Two databases of 87 patients were available: one containing clinical variables and the other consisting of measurements of the maximum diameter taken along the ascending aorta. For the [...] Read more.

This study presents an analysis of data from patients with ascending thoracic aortic aneurysms (ATAAs). Two databases of 87 patients were available: one containing clinical variables and the other consisting of measurements of the maximum diameter taken along the ascending aorta. For the clinical database, both a supervised and an unsupervised learning method were applied to explore patterns within the data. On the other hand, for the ascending aorta dataset, experimental variograms were calculated, from which key parameters of interest were extracted. These parameters were then analyzed over time to assess temporal patterns. This analysis aimed to assess the emergence of similar patterns or behaviour in patients with aneurysms of comparable sizes. Based on the analyses conducted, the clinical variables with the greatest importance in surgical decision-making were identified, while the spatial statistical analysis revealed patterns that may be related to elasticity, stiffness, or deformations of the aorta. Full article

(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications 2025)

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21 pages, 988 KB

Open AccessArticle

Study of Performance from Hierarchical Decision Modeling in IVAs Within a Greedy Context

by Francisco Federico Meza-Barrón, Nelson Rangel-Valdez, María Lucila Morales-Rodríguez, Claudia Guadalupe Gómez-Santillán, Juan Javier González-Barbosa, Guadalupe Castilla-Valdez, Nohra Violeta Gallardo-Rivas and Ana Guadalupe Vélez-Chong

Math. Comput. Appl. 2026, 31(1), 8; https://doi.org/10.3390/mca31010008 - 7 Jan 2026

Viewed by 361

Abstract

This study examines decision-making in intelligent virtual agents (IVAs) and formalizes the distinction between tactical decisions (individual actions) and strategic decisions (composed of sequences of tactical actions) using a mathematical model based on set theory and the Bellman equation. Although the equation itself [...] Read more.

This study examines decision-making in intelligent virtual agents (IVAs) and formalizes the distinction between tactical decisions (individual actions) and strategic decisions (composed of sequences of tactical actions) using a mathematical model based on set theory and the Bellman equation. Although the equation itself is not modified, the analysis reveals that the discount factor (γ) influences the type of decision: low values favor tactical decisions, while high values favor strategic ones. The model was implemented and validated in a proof-of-concept simulated environment, namely the Snake Coin Change Problem (SCCP), using a Deep Q-Network (DQN) architecture, showing significant differences between agents with different decision profiles. These findings suggest that adjusting γ can serve as a useful mechanism to regulate both tactical and strategic decision-making processes in IVAs, thus offering a conceptual basis that could facilitate the design of more intelligent and adaptive agents in domains such as video games, and potentially in robotics and artificial intelligence as future research directions. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2025)

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14 pages, 3500 KB

Open AccessArticle

Generalization of Log-Logistic Family with Quantile Regression Model

by Fazlollah Lak, Emrah Altun, Morad Alizadeh, Javier E. Contreras-Reyes and Hamid Esmaeili

Math. Comput. Appl. 2026, 31(1), 7; https://doi.org/10.3390/mca31010007 - 5 Jan 2026

Viewed by 288

Abstract

A new general class of distributions is proposed by applying the transformation to the random variable that follows the generalized odd-logistic family. Using the proposed family, we introduce a flexible Weibull distribution. The importance of the proposed distribution is demonstrated and compared with [...] Read more.

A new general class of distributions is proposed by applying the transformation to the random variable that follows the generalized odd-logistic family. Using the proposed family, we introduce a flexible Weibull distribution. The importance of the proposed distribution is demonstrated and compared with different generalizations of the Weibull distribution via three real data applications. A quantile regression model is obtained using the newly developed Weibull model and compared with the standard Weibull quantile regression model through a real data application. Full article

(This article belongs to the Section Engineering)

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25 pages, 520 KB

Open AccessArticle

Modelling Extreme Rainfall in KwaZulu-Natal Province of South Africa Using Extreme Value Theory

by Hulisani Lutombo, Daniel Maposa and Simon Setsweke Nkoane

Math. Comput. Appl. 2026, 31(1), 6; https://doi.org/10.3390/mca31010006 - 4 Jan 2026

Viewed by 413

Abstract

This study reviews advanced extreme value theory techniques and applies them to extreme rainfall events recorded at two meteorological stations, Port Edward and Virginia, in the KwaZulu-Natal province of South Africa. The study aims to provide a comparative analysis of the performance of [...] Read more.

This study reviews advanced extreme value theory techniques and applies them to extreme rainfall events recorded at two meteorological stations, Port Edward and Virginia, in the KwaZulu-Natal province of South Africa. The study aims to provide a comparative analysis of the performance of three extreme value theory models—the generalised extreme value distribution (GEVD), the generalised extreme value distribution for r-largest order statistics (GEVDr), and the blended generalised extreme value distribution (bGEVD)—in modelling extreme rainfall events. The monthly maximum rainfall data used in the study was obtained from the South African Weather Service. The Shapiro–Wilk test demonstrated the non-normality of the rainfall datasets. Parameter estimation was performed using maximum likelihood estimation and Bayesian estimation methods, both yielding positive shape parameters consistent with the Fréchet class of distributions. The goodness-of-fit tests confirmed the suitability of the GEVD model for the data. The results of both the standard GEVD and GEVDr models provided consistent return level estimates, suggesting strong model performance. The bGEVD model produced lower return level estimates compared to the GEVD and GEVDr models. Overall, the findings of the study offer valuable insights into the behaviour of extreme rainfall in KwaZulu-Natal province, with significant implications for risk management, infrastructure planning, and disaster preparedness. This study will add value to the literature and knowledge of statistics. Full article

(This article belongs to the Section Natural Sciences)

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15 pages, 2563 KB

Open AccessArticle

Eigenstructure-Oriented Optimization Design of Active Suspension Controllers

by Yulong Du and Huping Mao

Math. Comput. Appl. 2026, 31(1), 5; https://doi.org/10.3390/mca31010005 - 1 Jan 2026

Viewed by 256

Abstract

Active suspension systems can significantly enhance vehicle ride comfort and attitude stability, but often at the cost of increased energy consumption. To achieve both high dynamic performance and reduced energy usage, this study proposes an eigenstructure-oriented optimization method for active suspensions. Controller design [...] Read more.

Active suspension systems can significantly enhance vehicle ride comfort and attitude stability, but often at the cost of increased energy consumption. To achieve both high dynamic performance and reduced energy usage, this study proposes an eigenstructure-oriented optimization method for active suspensions. Controller design is reformulated as a synergistic process of modal regulation and dynamic response optimization, in which partial eigenstructure assignment redistributes the dominant modes and system responses are computed using fourth-order Runge–Kutta integration. An energy-minimization optimization problem with performance constraints is then solved via the sequential quadratic programming (SQP) algorithm. Simulation results show that the proposed method markedly improves vibration performance: peak body acceleration is reduced from 3.48 m/s² to 1.70 m/s² (a 51.1% reduction), and the root mean square (RMS) acceleration decreases from 0.74 to 0.40 (a 45.6% reduction), while body displacement is also significantly suppressed. Compared with passive suspension and proportional–integral–derivative (PID) active suspension, the proposed system achieves superior performance in key indices such as body acceleration and displacement, leading to noticeably improved ride comfort and attitude stability. Furthermore, robustness analysis indicates that the method remains effective under variations in the receptance matrix, with only minor influence on system performance, demonstrating the practical applicability of the proposed control strategy. Full article

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

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19 pages, 614 KB

Open AccessArticle

Modeling Diverse Hazard Shapes with the Power Length-Biased XLindley Distribution

by Suresha Kharvi, Muhammed Rasheed Irshad, Christophe Chesneau and Jabir Kakkottakath Valappil Thekkepurayil

Math. Comput. Appl. 2026, 31(1), 4; https://doi.org/10.3390/mca31010004 - 24 Dec 2025

Viewed by 295

Abstract

In many fields, including engineering, biology and economics, modeling and analyzing lifetime data is crucial for understanding the reliability and survival characteristics of systems and components. To address the limitations of existing lifetime distributions in capturing complex hazard rate behaviors, this article introduces [...] Read more.

In many fields, including engineering, biology and economics, modeling and analyzing lifetime data is crucial for understanding the reliability and survival characteristics of systems and components. To address the limitations of existing lifetime distributions in capturing complex hazard rate behaviors, this article introduces a new and flexible two-parameter distribution, the power length-biased XLindley (PLXL) distribution. This distribution extends the XLindley distribution family by incorporating a power transformation applied to a length-biased variant, thereby enriching its structural flexibility. It can model a variety of hazard rate shapes, including increasing, decreasing, decreasing–increasing–decreasing and inverted bathtub forms, making it suitable for a range of real-world applications. We derive the statistical properties of the PLXL distribution and develop parameter estimation methods based on the maximum likelihood and the least squares approach. We conduct a comprehensive simulation study to evaluate the performance of the proposed estimators in terms of bias and mean squared error. The practical utility and superior adaptability of the PLXL distribution are demonstrated by applying it to real lifetime data sets. Full article

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

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27 pages, 2187 KB

Open AccessArticle

Fixed/Preassigned-Time Synchronization of Quaternion-Valued Stochastic BAM Neural Networks with Discontinuous Activations Using Impulsive Control Technique

by Abuduwali Abudukeremu and Mairemunisa Abudusaimaiti

Math. Comput. Appl. 2026, 31(1), 3; https://doi.org/10.3390/mca31010003 - 23 Dec 2025

Viewed by 225

Abstract

In this study, a comprehensive analysis of the fixed/preassigned-time synchronization of a class of quaternion-valued BAM (QBAM) neural networks with stochastic and impulsive effects is conducted. Unlike previous analysis methods, our method features a direct analysis approach. First, to clarify the combined impact [...] Read more.

In this study, a comprehensive analysis of the fixed/preassigned-time synchronization of a class of quaternion-valued BAM (QBAM) neural networks with stochastic and impulsive effects is conducted. Unlike previous analysis methods, our method features a direct analysis approach. First, to clarify the combined impact of impulsive and stochastic phenomena on synchronization behavior, we establish a QBAM neural network system incorporating stochastic and impulsive effects. Notably, differing from prior relevant studies, we assume that the activation function is discontinuous, thereby enhancing the practical relevance of this research. Second, leveraging the quaternion-valued sign function and its properties, we implement impulsive control via the direct analysis method to achieve Fixed/Predefined-Time synchronization of the considered system. Finally, numerical simulations are performed to verify the ability of the theoretical analysis and the proposed control protocol to realize synchronization under impulsive and stochastic effects. Full article

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17 pages, 1766 KB

Open AccessArticle

Detection of Nonstationarity in Peak Flow, Volume, and Duration in an Urbanizing Catchment

by Aure Flo Oraya, Eugene Herrera and Guillermo Tabios III

Math. Comput. Appl. 2026, 31(1), 2; https://doi.org/10.3390/mca31010002 - 23 Dec 2025

Viewed by 355

Abstract

Urban catchments are increasingly vulnerable to hydrologic extremes driven by land-use change and climate variability, challenging the traditional assumption of stationarity. This study develops a computational framework to assess the nonstationary behavior of peak flow, volume, and duration in an urban catchment in [...] Read more.

Urban catchments are increasingly vulnerable to hydrologic extremes driven by land-use change and climate variability, challenging the traditional assumption of stationarity. This study develops a computational framework to assess the nonstationary behavior of peak flow, volume, and duration in an urban catchment in the Philippines using 39 years of daily flow records (June 1984–November 2022). Missing observations (~8% of the series) were reconstructed using multiple linear regression (MLR) and artificial neural networks (ANNs) with four predictors: daily rainfall, antecedent rainfall, antecedent flow, and built-up area index. MLR with all predictors yielded the most accurate reconstructions. Nonstationarity was detected using the Mann–Kendall test, Sen slope estimator, Pettitt test, and variance change test. Flood events were extracted using block maxima (BM) and peak-over-threshold (POT) methods. BM-based results showed stationary peak flow and volume, while duration increased by 1.78 h/year. POT analyses revealed nonstationarity across all variables, without significant shifts in variance. These findings demonstrate that methodological choices strongly influence nonstationary detection. The framework underscores the importance of reliable data reconstruction and robust statistical testing for nonstationary analysis of flood events. POT-based approaches more effectively capture evolving trends in peak flow, volume, and duration. These can be used in designing resilient infrastructure and flood risk management in urbanizing catchments. Full article

(This article belongs to the Section Engineering)

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Open AccessArticle

A Hybrid Numerical Framework Based on Radial Basis Functions and Finite Difference Method for Solving Advection–Diffusion–Reaction-Type Interface Models

by Muhammad Asif, Javairia Gul, Mehnaz Shakeel and Ioan-Lucian Popa

Math. Comput. Appl. 2026, 31(1), 1; https://doi.org/10.3390/mca31010001 - 19 Dec 2025

Viewed by 336

Abstract

Advection–diffusion–reaction-type interface models have wide-ranging applications in environmental science, chemical engineering, and biological systems, particularly in modeling pollutant transport in groundwater, reactive flows, and drug diffusion across biological membranes. This paper presents a novel numerical method for the solution of these models. The [...] Read more.

Advection–diffusion–reaction-type interface models have wide-ranging applications in environmental science, chemical engineering, and biological systems, particularly in modeling pollutant transport in groundwater, reactive flows, and drug diffusion across biological membranes. This paper presents a novel numerical method for the solution of these models. The proposed method integrates the meshless collocation technique with the finite difference method. The temporal derivative is approximated using a finite difference scheme, while spatial derivatives are approximated using radial basis functions. The interface across the fixed boundary is treated with discontinuous diffusion, advection, and reaction coefficients. The proposed numerical scheme is applied to both linear and non-linear models. The Gauss elimination method is used for the linear models, while the quasi-Newton linearization method is employed to address the non-linearity in non-linear cases. The

L_{\infty}

error is computed for varying numbers of collocation points to assess the method’s accuracy. Furthermore, the performance of the method is compared with the Haar wavelet collocation method and the immersed interface method. Numerical results demonstrate that the proposed approach is more efficient, accurate, and easier to implement than existing methods. The technique is implemented in MATLAB R2024b software. Full article

(This article belongs to the Special Issue Radial Basis Functions)

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Math. Comput. Appl., Volume 31, Issue 1 (February 2026) – 20 articles

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