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Volume 31
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Math. Comput. Appl., Volume 31, Issue 1 (February 2026) – 32 articles

Cover Story (view full-size image): The performance of convolutional neural networks (CNNs) is influenced by model architecture and the quality of training data. This study presents a framework utilizing synthetic datasets to control visual features, enabling a systematic evaluation of their impact on CNN performance. By applying set theory, Shapley values, and the Apriori algorithm, it formalizes a link between CNN kernel weights and pattern frequency counts. The construction of four synthetic digit datasets, training lightweight CNNs through K-fold validation, and statistical cross-dataset evaluation show that internal object patterns enhance accuracy and F1 scores over non-object backgrounds. A dataset similarity prediction algorithm demonstrates a strong correlation (ρ = 0.97) between predicted and actual performance. View this paper
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12 pages, 756 KB  
Communication
Revised Long-Term Scheduling Model for Multi-Stage Biopharmaceutical Processes
by Vaibhav Kumar and Munawar A. Shaik
Math. Comput. Appl. 2026, 31(1), 32; https://doi.org/10.3390/mca31010032 - 15 Feb 2026
Cited by 1 | Viewed by 531
Abstract
Biopharmaceuticals are therapeutic drugs engineered to target specific sites within the body. Their manufacturing process comprises two primary stages: upstream processing (USP) and downstream processing (DSP). USP primarily involves cell culture and growth, whereas DSP focuses on purifying and packaging the final product. [...] Read more.
Biopharmaceuticals are therapeutic drugs engineered to target specific sites within the body. Their manufacturing process comprises two primary stages: upstream processing (USP) and downstream processing (DSP). USP primarily involves cell culture and growth, whereas DSP focuses on purifying and packaging the final product. The recent literature only reports a few studies addressing production planning and scheduling in biopharmaceutical manufacturing. In this work, we address a long-term scheduling and midterm planning problem incorporating on-time or late delivery of final products with unknown finite delivery rates. Early delivery is prohibited, and late delivery incurs a penalty cost. Published models and evolutionary algorithms exhibit key limitations in areas such as shelf-life modeling, inventory management, and product delivery. To overcome these shortcomings, we propose a revised mixed-integer linear programming (MILP) model implemented using the General Algebraic Modeling System (GAMS). When applied to two illustrative examples, the model reduces optimum event counts by two to three, improving computational efficiency through fewer binary variables, continuous variables, and constraints. Furthermore, it achieves up to 7% improvement over two published benchmarks, underscoring its potential to enhance scheduling strategies for multiproduct biopharmaceutical facilities. Full article
(This article belongs to the Special Issue Applied Optimization in Automatic Control and Systems Engineering)
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17 pages, 1365 KB  
Article
A Transfer-Learning Approach for Detection of Multiclass Synthetic Skin Cancer Images Generated by Deep Generative Models to Prevent Medical Insurance Fraud
by Osama Tariq, Muhammad Asad Arshed, Muhammad Kabir, Khalid Ijaz, Ştefan Cristian Gherghina and Hafiza Bukhtawer Batool
Math. Comput. Appl. 2026, 31(1), 31; https://doi.org/10.3390/mca31010031 - 15 Feb 2026
Viewed by 678
Abstract
Artificial Intelligence is advancing rapidly, raising critical concerns about the integrity of digital content, particularly in sensitive domains such as medical imaging. Recent AI techniques, such as Generative Adversarial Networks (GANs) and diffusion models, can generate highly realistic synthetic medical images, posing risks [...] Read more.
Artificial Intelligence is advancing rapidly, raising critical concerns about the integrity of digital content, particularly in sensitive domains such as medical imaging. Recent AI techniques, such as Generative Adversarial Networks (GANs) and diffusion models, can generate highly realistic synthetic medical images, posing risks of misdiagnosis, inappropriate treatment, and other adverse outcomes. This paper presents a deep learning-based approach to distinguish between authentic and synthetic images of skin malignancies generated by DCGAN, Wasserstein GAN (WGAN), and Stable Diffusion. A comprehensive dataset was constructed using authentic malignant skin images from an open-source Kaggle repository, alongside artificially generated images. Multiple deep learning models were trained and evaluated, with DenseNet169 achieving the highest performance, reaching 99.67% training accuracy, 97.50% validation accuracy, and 98.50% test accuracy—along with substantial precision, recall, and F1 scores across all classes. These results demonstrate the model’s efficacy in identifying both real and fake medical images. This work contributes to the emerging field of medical image forensics, highlighting its potential integration into clinical and insurance workflows to prevent fraud, strengthen trust, and mitigate risks. Furthermore, it lays the groundwork for future studies involving larger datasets, additional Deepfake generation methods, and real-time clinical applications. Full article
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31 pages, 461 KB  
Systematic Review
Techniques Applied to Autonomous Liquid Pouring: A Scoping Review
by Jeeangh Jennessi Reyes-Montiel, Ericka Janet Rechy-Ramirez and Antonio Marin-Hernandez
Math. Comput. Appl. 2026, 31(1), 30; https://doi.org/10.3390/mca31010030 - 14 Feb 2026
Viewed by 595
Abstract
In recent years, autonomous liquid pouring systems have gained more relevance, with applications from daily service tasks to complex industrial operations. While seemingly simple for humans, this task poses major challenges for automated systems, as it requires precise control and adaptation to varying [...] Read more.
In recent years, autonomous liquid pouring systems have gained more relevance, with applications from daily service tasks to complex industrial operations. While seemingly simple for humans, this task poses major challenges for automated systems, as it requires precise control and adaptation to varying container geometries, liquid properties, and environmental conditions. This review examines the state-of-the-art on liquid pouring through five research questions: (1) What are the characteristics of the liquids used in the experiments? (2) What are the characteristics of the containers used in the experiments and how do they affect the performance of the pouring tasks? (3) What techniques are used to control liquid pouring (i.e., to control the robotic arm or device)? (4) What metrics are used to assess the methods for pouring liquid? (5) What devices are used to measure poured volume? This scoping review follows the Arksey and O’Malley framework, and uses the PRISMA-ScR protocol to filter the articles. A total of 285 studies published between 2018 and 2025 were screened from IEEE Xplore, SpringerLink, ScienceDirect, Web of Science, and EBSCOhost, of which 23 met the inclusion criteria. Results showed that the most widely used methods for autonomous liquid pouring were classical control methods—PID, PD (30.4% of the studies). Conversely, the least widely used methods for autonomous liquid pouring were learning, imitation learning, and probabilistic models (15% of the studies). Full article
(This article belongs to the Special Issue New Trends in Computational Intelligence and Applications 2025)
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13 pages, 372 KB  
Article
Unifying Models of Trophic Exploitation: A Mathematical Framework for Understanding the Paradox of Enrichment
by Lindomar Soares dos Santos, Brenno Caetano Troca Cabella and Alexandre Souto Martinez
Math. Comput. Appl. 2026, 31(1), 29; https://doi.org/10.3390/mca31010029 - 14 Feb 2026
Viewed by 435
Abstract
The rapid increase in the world’s human population has largely been attributed to efforts aimed at enhancing primary productivity and enriching food resources. However, an intriguing proposition of M. Rosenzweig, known as the paradox of enrichment, challenged the notion that such enrichment schemes [...] Read more.
The rapid increase in the world’s human population has largely been attributed to efforts aimed at enhancing primary productivity and enriching food resources. However, an intriguing proposition of M. Rosenzweig, known as the paradox of enrichment, challenged the notion that such enrichment schemes always lead to sustained population growth. Instead, they can disrupt the delicate equilibrium of predator–prey systems, potentially driving one or both species to extinction. In this study, we develop a comprehensive mathematical framework that unifies Rosenzweig’s six analytical models of trophic exploitation through the Richards growth model, which can be viewed as a Box–Cox transformation of one species’ abundance relative to carrying capacity. Our analysis not only elucidates the connections and similarities between each model but also presents a generalized framework that unveils the underlying relationships between the proposed functions. Using the generalized logarithm and exponential functions of nonextensive statistical mechanics, we offer a fresh perspective and highlight the importance of a cautious approach when enriching ecosystems. This unification clarifies how the parameters that govern growth dynamics and predator–prey interactions determine system stability in diverse ecological contexts. Through numerical simulations and isoclinic analysis, we demonstrate that our generalized model accurately reproduces the classic paradox of enrichment while providing new insights into the mechanisms driving population fluctuations after environmental enrichment. This mathematical synthesis advances both theoretical ecology and practical conservation efforts by enabling a more accurate assessment of enrichment risks in managed ecosystems. Full article
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40 pages, 4792 KB  
Article
GMD-AD: A Graph Metric Dimension-Based Hybrid Framework for Privacy-Preserving Anomaly Detection in Distributed Databases
by Awad M. Awadelkarim
Math. Comput. Appl. 2026, 31(1), 28; https://doi.org/10.3390/mca31010028 - 14 Feb 2026
Viewed by 486
Abstract
Distributed databases are increasingly used in enterprise and cloud environments, but their distributed architecture introduces significant security challenges, including data leaks and insider threats. In the context of escalating cyber threats targeting large-scale distributed databases and cloud-native microservice architectures, this paper presents Graph [...] Read more.
Distributed databases are increasingly used in enterprise and cloud environments, but their distributed architecture introduces significant security challenges, including data leaks and insider threats. In the context of escalating cyber threats targeting large-scale distributed databases and cloud-native microservice architectures, this paper presents Graph Metric Dimension-based Anomaly Detection (GMD-AD), a novel graph-structure model designed to enhance cybersecurity in distributed databases by leveraging the metric dimension of interaction graphs; further, GMD-AD addresses the critical need for real-time, low-overhead, and privacy-aware anomaly detection mechanisms. The model introduces a compact resolving set as landmarks to detect intrusions through distance vector variations with minimal computational overhead. The proposed framework offers four major contributions, including sequential metric dimension updates to support dynamic topologies; a parallel BFS strategy to enable scalable processing; the incorporation of the k-metric anti-dimension to provide provable privacy against re-identification attacks; and a hybrid pipeline in which resolving-set subgraphs are processed by graph neural networks prior to final classification using gradient boosting. Experiments conducted on the SockShop microservices benchmark and a real MongoDB sharded cluster with injected anomalies reveal 60% reduced localization latency (1200 ms → 480 ms), stable detection accuracy (>0.997), increased noise robustness (F1 0.95 → 0.97) and a drop of re-identification success rate from the baseline by 40 percentage points (68% → 28%) when k = 3, ℓ = 2. We demonstrated up to 60% latency reduction and 40% privacy improvement over baselines, validated on real MongoDB clusters. The findings show that GMD-AD is a scalable, real-time and privacy-preserving HTTP anomaly detection solution for both distributed database systems and microservice architectures. Full article
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38 pages, 3813 KB  
Review
Understanding S-Box Security Assessment: A Practical Guide
by David Carcaño Ventura, Lil María Xibai Rodríguez-Henríquez and Saúl E. Pomares Hernández
Math. Comput. Appl. 2026, 31(1), 27; https://doi.org/10.3390/mca31010027 - 13 Feb 2026
Viewed by 1104
Abstract
S-boxes are the core nonlinear components of ciphers, providing confusion and diffusion. As a result, cryptanalysts focus on analyzing these components to identify distinguishers and ultimately recover the secret key of the cipher. Although many constructions exist, the search for new S-boxes remains [...] Read more.
S-boxes are the core nonlinear components of ciphers, providing confusion and diffusion. As a result, cryptanalysts focus on analyzing these components to identify distinguishers and ultimately recover the secret key of the cipher. Although many constructions exist, the search for new S-boxes remains vital as advances in cryptanalysis expose new weaknesses. Evaluating their security is challenging, and the current literature often prioritizes technical depth over clarity for a broader audience. This raises questions that are not always clear, such as how the S-box and its construction affect a cipher’s resilience, how to assess the security of this nonlinear component, and what factors influence its robustness. In this paper, we address these concerns by providing a friendly introduction to the basic principles of S-box security evaluation, structured around four key aspects. First, the importance of the S-box in ensuring block cipher security is discussed. Second, the advantages and disadvantages of three classical S-box construction approaches are outlined. Third, the evaluation of S-boxes through the formal definition of their properties and their associated security implications is presented. Fourth, four S-box evaluation toolkits proposed in the literature are introduced. Finally, open research challenges in S-box design are highlighted. Full article
(This article belongs to the Section Engineering)
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4 pages, 160 KB  
Editorial
Feature Paper Collection of Mathematical and Computational Applications—2025
by Gianluigi Rozza, Oliver Schütze and Nicholas Fantuzzi
Math. Comput. Appl. 2026, 31(1), 26; https://doi.org/10.3390/mca31010026 - 11 Feb 2026
Viewed by 271
Abstract
This Special Issue comprises the fifth collection of papers submitted by both the Editorial Board Members (EBMs) of the journal Mathematical and Computational Applications (MCA) and the outstanding scholars working in the core research fields of MCA [...] Full article
(This article belongs to the Special Issue Feature Papers in Mathematical and Computational Applications 2025)
26 pages, 1575 KB  
Article
A Rocq-Based Formalization of Hilbert’s Geometry: Building a Reusable Foundation for 3D Perpendicularity Theory and Verification
by Qimeng Zhang and Wensheng Yu
Math. Comput. Appl. 2026, 31(1), 25; https://doi.org/10.3390/mca31010025 - 7 Feb 2026
Viewed by 450
Abstract
Hilbert’s axiom system for geometry is a landmark in formal methods. This paper presents a complete formalization of spatial perpendicularity—a theory not fully developed in Hilbert’s original work—using the Rocq proof assistant. We systematically defined the relations of perpendicularity between lines and planes [...] Read more.
Hilbert’s axiom system for geometry is a landmark in formal methods. This paper presents a complete formalization of spatial perpendicularity—a theory not fully developed in Hilbert’s original work—using the Rocq proof assistant. We systematically defined the relations of perpendicularity between lines and planes based solely on Hilbert’s primitive notions and axioms. Within this framework, we mechanized the proof of a significant spatial congruence theorem that Hilbert stated without proof—a theorem that fundamentally reveals the relationship between congruence and motion. The formal proof of this theorem demonstrates the intrinsic completeness of Hilbert’s system for three-dimensional (3D) space. Crucially, no additional spatial congruence axioms are needed, as all properties are derived rigorously from the original planar axioms. All proofs are mechanically verified by Rocq, ensuring logical correctness. This work completes Hilbert’s geometry system. It also delivers a reusable Rocq library that offers a rigorous foundation for verifying geometric reasoning in safety-critical software systems. Full article
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20 pages, 1878 KB  
Article
Research on Scheduling of Metal Structural Part Blanking Workshop with Feeding Constraints
by Yaping Wang, Xuebing Wei, Xiaofei Zhu, Lili Wan and Zihui Zhao
Math. Comput. Appl. 2026, 31(1), 24; https://doi.org/10.3390/mca31010024 - 6 Feb 2026
Viewed by 381
Abstract
Taking a metal structural part blanking workshop as the application background, this study addresses the challenges of high material variety, long crane feeding travel caused by heterogeneous line-side storage layouts, and frequent machine stoppages due to the limited feeding capacity of a single [...] Read more.
Taking a metal structural part blanking workshop as the application background, this study addresses the challenges of high material variety, long crane feeding travel caused by heterogeneous line-side storage layouts, and frequent machine stoppages due to the limited feeding capacity of a single overhead crane. To this end, an integrated machine–crane dual-resource scheduling model is developed by explicitly considering line-side storage locations. The objective is to minimize the maximum waiting time among all machine tools. Under constraints of material assignment, processing sequence, and the crane’s single-task execution and travel requirements, the storage positions of materials in line-side buffers are jointly optimized. To solve the problem, a genetic algorithm with fitness-value-based crossover is proposed, and a simulated-annealing acceptance criterion is embedded to suppress premature convergence and enhance the ability to escape local optima. Comparative experiments on randomly generated instances show that the proposed algorithm can significantly reduce the maximum waiting time and yield more stable results for medium- and large-scale cases. Furthermore, a simulation based on real production data from an industrial enterprise verifies that, under limited feeding capacity, the proposed method effectively shortens material-waiting time, improves equipment utilization, and enhances production efficiency, demonstrating its effectiveness. Full article
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17 pages, 4263 KB  
Article
The Structure of the Route to the Period-Three Orbit in the Collatz Map
by Weicheng Fu and Yisen Wang
Math. Comput. Appl. 2026, 31(1), 23; https://doi.org/10.3390/mca31010023 - 4 Feb 2026
Viewed by 636
Abstract
The Collatz map is investigated from a nonlinear-dynamics perspective with emphasis on the structure of its iterative orbits. By embedding integers within Sharkovsky’s ordering, odd initial values are shown to be sufficient for a complete characterization of dynamics. A “direction-phase” decomposition is introduced [...] Read more.
The Collatz map is investigated from a nonlinear-dynamics perspective with emphasis on the structure of its iterative orbits. By embedding integers within Sharkovsky’s ordering, odd initial values are shown to be sufficient for a complete characterization of dynamics. A “direction-phase” decomposition is introduced to separate iterative orbits into upward and downward phases, yielding a family of recursive functions parameterized by the number of upward phases. This formulation reveals a logarithmic scaling relation between the total iteration count and the initial value, confirming finite-time convergence to the period-three orbit. The Collatz dynamics is further shown to be dynamically equivalent to a binary shift map, whose ergodicity implies inevitable evolution toward attractors, thereby reinforcing convergence. Numerical analysis indicates that attraction basins follow a power-law distribution and display pronounced self-similarity. Moreover, odd integers grouped by upward-phase counts are found to follow Gamma statistics. Beyond its research implications, the framework provides a concise pedagogical case study illustrating how nonlinear dynamics, symbolic dynamics, and statistical characterization can be integrated to analyze a classical discrete problem. Full article
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20 pages, 1125 KB  
Article
Lie Point and Q-Conditional Symmetries, Exact Solutions, and Conservation Laws for a Reaction–Diffusion System in Mathematical Biology
by Yu-Shan Bai, Jin Wang, Yan-Ting Ren and Yu-Xiang Li
Math. Comput. Appl. 2026, 31(1), 22; https://doi.org/10.3390/mca31010022 - 3 Feb 2026
Viewed by 418
Abstract
This study investigates the Lie point and Q-conditional symmetries of a classical two-component reaction–diffusion system in one spatial dimension. The symmetry classifications for the reaction–diffusion system and corresponding symmetry reductions are provided. Employing Ibragimov’s method, we construct conservation laws for the governing [...] Read more.
This study investigates the Lie point and Q-conditional symmetries of a classical two-component reaction–diffusion system in one spatial dimension. The symmetry classifications for the reaction–diffusion system and corresponding symmetry reductions are provided. Employing Ibragimov’s method, we construct conservation laws for the governing system, offering insights into its invariant properties. Additionally, by applying symmetry reduction techniques, new exact solutions are obtained. These solutions demonstrate the practical utility of our approach and enhance our understanding of the system’s behavior and characteristics. Full article
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27 pages, 15499 KB  
Article
Mathematical Model Analysis for Dynamics and Control of Yellow Fever and Malaria Disease Co-Infections
by Obiora C. Collins and Oludolapo A. Olanrewaju
Math. Comput. Appl. 2026, 31(1), 21; https://doi.org/10.3390/mca31010021 - 3 Feb 2026
Viewed by 531
Abstract
Yellow fever (YF) and malaria co-infections are real public health concerns in Africa, especially in countries such as Nigeria, where mosquitoes carrying both pathogens (Aedes for YF, Anopheles for malaria) coexist. A mathematical model that considers the critical factors influencing the transmission dynamics [...] Read more.
Yellow fever (YF) and malaria co-infections are real public health concerns in Africa, especially in countries such as Nigeria, where mosquitoes carrying both pathogens (Aedes for YF, Anopheles for malaria) coexist. A mathematical model that considers the critical factors influencing the transmission dynamics and control interventions of YF and malaria co-infections is formulated and used to analyse the problem. The essential dynamical features of the model, such as the basic reproduction number and disease-free equilibrium, are determined and analysed. The qualitative analysis of the model illustrates the conditions under which the disease can be eradicated or persists. Further analysis, supported by numerical simulations, reveals the intrinsic dynamics of the model and the impact of control interventions such as yellow fever vaccination, use of insecticide-treated mosquito nets, treatment of malaria-infected humans, and use of insecticides. The results of the analysis demonstrate the impact of interventions; specifically, effective implementations of interventions such as yellow fever vaccination, use of insecticide-treated mosquito nets, and use of insecticides appear to have a significant impact in eradicating YF and malaria co-infections in endemic areas. Effective treatment of malaria-infected humans may lead to a decrease in infections but might not necessarily lead to eradicating infections in endemic areas. These findings are expected to aid in improving the management of YF and malaria co-infections in endemic regions for expeditious disease eradication. Full article
(This article belongs to the Section Natural Sciences)
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28 pages, 572 KB  
Article
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 - 2 Feb 2026
Viewed by 401
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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23 pages, 842 KB  
Article
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
Viewed by 579
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)
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26 pages, 4764 KB  
Article
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 642
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  
Article
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 586
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  
Article
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
Cited by 1 | Viewed by 382
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  
Article
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 643
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  
Article
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 499
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  
Article
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 719
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  
Article
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 403
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  
Article
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
Cited by 1 | Viewed by 836
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 R2=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  
Article
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 345
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  
Article
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 579
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  
Article
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 846
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  
Article
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 556
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  
Article
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 967
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  
Article
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
Cited by 1 | Viewed by 451
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  
Article
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 535
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  
Article
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 370
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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