Mathematical and Computational Applications doi: 10.3390/mca31030086

Authors: Qing Liu Yanqiang Di Xianguo Meng Zhiqiang Wang Zhiying Xie Haohao Cui Tao Wang

Diffusion probabilistic models are powerful generative tools but are purely data-driven, limiting their ability to incorporate domain knowledge—such as physical laws, degradation trends, or engineering priors—in scientific and engineering applications. We introduce Prior-Guided Diffusion Processes (PGDPs), a unified mathematical framework that integrates arbitrary differentiable prior knowledge into the reverse diffusion dynamics by augmenting the score function with a guidance term derived from a prior potential V(x,t) and weighted by a time-dependent strength γt. This formulation subsumes existing mechanisms (classifier guidance, model-based diffusion, physics-informed corrections) as special cases. We analyze the guided path measures, providing an upper bound on the Kullback–Leibler divergence between guided and unguided marginals (Theorem 1), quantifying the inherent trade-off between data fidelity and prior satisfaction. Experiments on synthetic data confirm the predicted dependence on γt. On the NASA C-MAPSS turbofan benchmark, we enforce compressor-oriented physical constraints (e.g., speed–pressure consistency, monotonicity) within PGDP; remaining useful life scores are reported only as reference metrics under transparent protocols. A cross-domain study on the NASA IGBT accelerated aging dataset, using the same backbone with a replaced physics module, achieves a 99.98% reduction in monotonicity loss, demonstrating generality across distinct degradation mechanisms. PGDP provides a principled, extensible template for knowledge-informed generative modeling with theoretical guarantees and verifiable physical consistency.

Mathematical and Computational Applications doi: 10.3390/mca31030085

Authors: Seyed Amin Bagherzadeh

Accurate aerodynamic modeling of aircraft during post-stall maneuvers remains challenging due to massive flow separation, vortex breakdown, and unsteady hysteresis. This paper presents a gray-box system identification framework that integrates a Long Short-Term Memory (LSTM) network into the physical equations of aircraft motion. Unlike black-box methods that sacrifice interpretability, the proposed architecture preserves the rigid-body Newton-Euler equations while replacing empirical aerodynamic coefficient models with an LSTM network. The LSTM directly predicts the aerodynamic coefficients, which are transformed into forces and moments via exact physical laws, ensuring hard constraint satisfaction. Validation using real flight test data from a large-scale (3/8) fighter aircraft at angles of attack up to 80° demonstrates that the method achieves regression coefficients exceeding 0.96 for all coefficients on unseen data, with near-zero mean errors. Quantitative comparisons show that the proposed method reduces prediction error by 50–70% compared to black-box LSTM and PINN baselines. The framework offers a practical balance of accuracy, interpretability, and extrapolation reliability for post-stall aerodynamic identification.

Mathematical and Computational Applications doi: 10.3390/mca31030084

Authors: Qin Li Wei Zhang Bingyun Zheng

Unmanned aerial vehicles (UAVs) are widely used for inspection and monitoring tasks, where mission efficiency is strongly influenced by environmental conditions such as wind. In this work, we study a joint route–speed optimization problem for UAV inspection missions under uncertain wind conditions. The objective is to determine both the visiting sequence of inspection targets and the flight speeds along route segments in order to minimize worst-case energy consumption while satisfying mission duration constraints. We formulate the problem using a robust optimization framework that accounts for uncertainty in both wind speed and wind direction. The resulting model involves coupled discrete routing decisions and continuous speed control variables, which makes the problem computationally challenging. To address this difficulty, we propose a robust route–speed decomposition (RRSD) framework that alternates between route improvement and nonlinear speed optimization. Computational experiments on randomly generated instances, evaluated over eight random seeds per setting and compared against five baselines, including a simulated-annealing metaheuristic, demonstrate that RRSD consistently reduces worst-case energy consumption. A sensitivity analysis over the wind-uncertainty half-widths further shows that this advantage widens as the uncertainty set grows, and comparisons with exact enumeration on small instances confirm near-optimal solution quality at reasonable computational cost. These results highlight the importance of jointly optimizing routing decisions and speed control for energy-efficient UAV mission planning under uncertain environmental conditions.

Mathematical and Computational Applications doi: 10.3390/mca31030083

Authors: Amira A. Allam Mohamed A. Tawhid Mahmoud Owais

Numerous engineering problems can be represented as minimax optimization problems, including machine learning, classification, robust optimal control, signal processing, game theory, and more. Typically, minimax problems are considered challenging, especially constrained ones. The recently introduced artificial rabbits optimization (ARO) is inspired by the natural behaviour of rabbits. ARO exhibits robust effectiveness in tackling optimization challenges. Despite its advantages, ARO converges early to local optima, especially in complex or multi-modal optimization problems, and it struggles to balance exploration and exploitation, often leading to premature convergence and reduced accuracy. In this paper, we present a chaotic ARO that employs five maps exhibiting randomization behaviour to refresh candidate solutions. We assess the performance of the suggested CARO by applying it to 46 benchmark functions (25 unconstrained and 21 non-smooth minimax) and 15 constrained test functions with diverse characteristics. We evaluate its performance against six swarm intelligence algorithms. Also, we employ the chaotic maps to ARO and the six compared algorithms, and we perform a non-parametric statistical test, the Friedman test, on all outcomes. The findings show that the proposed algorithm can solve both unconstrained and constrained minimax problems more effectively and efficiently than other swarm intelligence methods.

Mathematical and Computational Applications doi: 10.3390/mca31030082

Authors: Adriana-Laura López-Lobato Héctor-Gabriel Acosta-Mesa Efrén Mezura-Montes Jimena-Esther Alba-Jiménez Amalia-Guadalupe Rodríguez-Gómez Elia-Nora Aquino-Bolaños Rosa-Hayde Alfaro-Rodríguez

Chilacayote (Cucurbita ficifolia Bouché) is recognized as a rich source of nutrients and bioactive compounds, making it a promising ingredient for fortifying staple foods such as corn tortillas. While fortification can improve nutritional properties, it may also alter sensory characteristics that determine consumer acceptance. Therefore, a rigorous and structurally grounded assessment of these sensory modifications is required. In this study, sensory evaluations were conducted with regular tortilla consumers using Check-All-That-Apply (CATA) questionnaires to examine six attributes (color, smell, texture, taste, mouthfeel, and aftertaste) in tortillas made with nixtamalized dough and commercial flour, both with and without chilacayote powder. Then, a structured framework for dimensionality reduction and sensory profile identification of tortillas is proposed. In this framework, three classical feature extraction methods (Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), and a combination of both (PCA+LDA)) were compared with an evolutionary discriminant approach (Differential Evolutionary Linear Discriminant Analysis for Feature Extraction and Visualization (DE-LDAFE)). The projection quality of these methods was evaluated using a multi-scale separability index that integrates global, semi-global, and local metrics, and the experiments were conducted considering global and attribute-based analyses. Beyond quantitative discrimination, the optimized projections enabled a geometric interpretation that allows the identification of sensory profiles for the tortilla variants. The proposed methodology bridges evolutionary optimization, structural separability assessment, and interpretable sensory characterization, offering a robust and adaptable strategy for multivariate food analysis and other complex discrimination problems and insights into the sensory impact of chilacayote fortification for the development of nutritionally enhanced tortillas that preserve consumer appeal.

Mathematical and Computational Applications doi: 10.3390/mca31030081

Authors: Mashael A. Aljohani Mohamed Y. Abouzeid

Significance: This study addresses critical industrial and biomedical applications including glass blowing (thermal management of shrinking sheets), polymer sheet extrusion (controlled cooling), magnetic drug delivery (nanoparticle targeting), and nuclear reactor cooling (enhanced heat transfer). Aim: We present a novel nonlinear analysis of magnetohydrodynamic (MHD) boundary layer flow of a Jeffery Al2O3 nanofluid over a shrinking permeable plate with convective boundary conditions, uniquely integrating mixed convection, Ohmic dissipation, heat generation, Brownian motion, and thermophoresis within a non-Newtonian nanofluid framework. Methodology: The governing partial differential equations are transformed using similarity transformations and solved via the Adomian decomposition method (ADM). Comprehensive validation against RK4, RK45, and bvp4c demonstrates excellent agreement with maximum relative errors below 5×10−4. Key Contribution: (i) Normal velocity decreases by 15–25% as the Biot number increases from Bi=0.4 to 0.6; (ii) tangential velocity decreases by 20–30% as the magnetic parameter increases from M=5 to 15; (iii) temperature increases by 30–40% as the Eckert number increases from Ec=0.5 to 2.5; (iv) ADM converges within 12–15 terms with L2 errors <10−5; (v) skin friction coefficient increases from Cf=3.02713 to 3.90082 as Q0 increases from 1 to 4; (vi) Nusselt number values: Nu/Re=0.4621 at Pr=0.7, 0.8954 at Pr=2, 3.2890 at Pr=20. These quantitative findings provide design guidelines for engineers in thermal management and biomedical applications.

Mathematical and Computational Applications doi: 10.3390/mca31030080

Authors: Jose Luis Purata Aldaz Juan Frausto Solís Juan J. Gonzalez Barbosa Guadalupe Castilla-Valdez Juan Paulo Sánchez Hernández

Accurate price forecasting and portfolio optimization in emerging financial markets remain challenging due to the non-stationary dynamics, structural breaks, and heterogeneous behavior of traded instruments. This paper proposes the Time-series Adaptive Forecast Ensemble (TAFE), a method that combines single popular forecasting methods, such as ARIMA, by using an algorithm derived from both the simulated annealing (SA) and Threshold Accepting algorithms. The TAFE is applied to twenty-four weekly price series of Mexican exchange-traded funds (ETFs) and Real Estate Investment Trusts (FIBRAs) over the period 2020–2025. A top-K pre-selection strategy is used, mitigating the adverse cross-model interaction effect of some assets over others, in other words, reducing the propagation of errors from poorly performing base learners. In addition, the sample results show that the TAFE achieves the lowest mean SMAPE across the panel, with statistical superiority over the equal-weight benchmark and a Hybrid Model, confirmed by Diebold–Mariano and Harvey–Leybourne–Newbold tests. Out-of-sample evaluation over a 26-week horizon reveals a regime-shift-driven performance reversal consistent with the bias–variance tradeoff in adaptive combination schemes. Portfolio optimization using SA-generated forecasts yields with an expected return of 35.77%; thus, the model presents a slight overestimation of the return, with a variance of 2.4%. However, it has an acceptable level of risk.

Mathematical and Computational Applications doi: 10.3390/mca31030079

Authors: Carlos Julio Fierro-Silva Carlos A. Sánchez Jorge S. Sánchez Carolina Del-Valle-Soto Nancy Velasco José Varela-Aldás

This study addresses the growing need for scalable solutions to monitor domestic and stray animals in urban environments. The objective is to develop and evaluate a real-time animal detection system using transfer learning and lightweight object detection models. The methodology includes the adaptation of a custom dataset with annotated images of cats and dogs under real-world conditions, followed by preprocessing, data augmentation, and model fine-tuning. Two architectures, SSD-MobileNet and YOLOv26s, were trained and evaluated using standard metrics such as precision, recall, F1-score, and mAP, as well as operational indicators like inference speed and system responsiveness. The best-performing model was integrated into a web-based platform with real-time detection, mobile access, and automated alerts. Results show that YOLOv26s outperforms SSD-MobileNet, achieving higher precision and recall while significantly reducing false positives and improving background discrimination. The system demonstrates near real-time performance suitable for monitoring applications and effective deployment across different input sources. The discussion findings highlight that integrating detection models with notification and visualization tools enhances practical applicability. Although SSD-MobileNet is suitable for low-resource environments, YOLOv26s provides a better balance between accuracy and reliability, making it more appropriate for real-world intelligent monitoring systems.

Mathematical and Computational Applications doi: 10.3390/mca31030078

Authors: Emmanuel Isaac Juárez Caballero Horacio Tapia-McClung Efrén Mezura-Montes

The selection of the right topology (ansatz) for a Variational Quantum Algorithm (VQA) is a complex task that usually involves deep knowledge of a particular problem. The importance of the selection is greater when we consider the current state of quantum hardware, particularly the noise associated with the complexity of Variational Quantum Circuits (VQCs) that implement VQAs. Here, a comparison is presented between two confronted approaches for solving the MaxCut problem: QAOA, which has a theoretical proof of convergence, and the automatic design proposal (QNAS), which relies on evolutionary algorithms (NSGA-II) to discover efficient circuits. The comparison was made across 490 graph instances from different graph topologies and sizes (n=4 to n=16), accounting for noise models such as depolarizing noise, gate errors, and readout noise. The results show that QAOA achieves an approximation ratio (rA) ≈1 on complete graphs at the cost of being almost 12 times more complex than QNAS in ideal conditions while approaching the random noise floor (rA≈0.5). QNAS was capable of finding circuits less complex while maintaining 69% of the fidelity at a cost of having an rA on the interval 0.7≤rA≤0.8. However, when the comparison is made across sparse graphs, performance is comparable, while QNAS is less complex.

Mathematical and Computational Applications doi: 10.3390/mca31030077

Authors: Alexander Hüls Benjamin Alheit Swantje Bargmann

We study 2D RVEs based on microstructures inspired by limpet teeth with the objective of efficiently identifying auxetic designs and building surrogates for effective elastic response. The starting point is an unbalanced database; thus, we run a weighted random forest classifier and a neural network classifier to balance it. The resulting feature importances provide an interpretable ranking of 18 geometric and material variables and guide importance-biased Monte Carlo sampling. Random forest and FCNN classifiers are used to prioritize candidates. Dataset rebalancing is achieved by adding newly FEM-confirmed auxetic samples and applying clustering-guided downsampling to the non-auxetic majority. On this final set, a multi-output FCNN regressor predicts nine targets: inclusion volume fractions and minima/means/maxima of Young’s modulus and Poisson’s ratio. Overall, the framework supports rapid, interpretable screening and property prediction for auxetic composite designs while reducing the need for repeated FEM evaluations.

Mathematical and Computational Applications doi: 10.3390/mca31030076

Authors: Can Jiang Weicheng Li Ziqian Geng Hongmei Shang Yan Li

Medical big data derived from clinical records, laboratory tests, sequencing outputs, and quality-control indicators provides new opportunities for individualized prenatal risk assessment and optimized screening strategies. This study proposes an interpretable computational framework for prenatal risk assessment and testing-time optimization by integrating ensemble learning, BMI-stratified analysis, and uncertainty evaluation. For male-fetus samples, Y-chromosome-related measurements were used as biologically meaningful proxies for fetal signal. Linear regression, polynomial regression, random forest regression, and least-squares boosting were evaluated using cross-validated root mean squared error and coefficient of determination. BMI-stratified monotonic success-rate functions across gestational age were then estimated using a sliding-window procedure to identify practical sampling windows. Monte Carlo perturbation and bootstrap resampling were further applied to assess robustness against measurement noise and threshold variation. Least-squares boosting achieved the best overall predictive performance. The estimated optimal sampling ages were approximately 10 weeks, 14 weeks + 5 days, and 23 weeks + 3 days for the low-, medium-, and high-BMI strata, respectively, with greater instability observed in the high-BMI stratum. For female-fetus samples, aneuploidy screening was formulated as a binary classification task. Random forest substantially outperformed logistic regression, with an ROC-AUC of 0.884 versus 0.538 and an average precision of 0.668 versus 0.070, and supported a decision threshold of 0.1437. These findings suggest that medical big data-driven methods can improve prenatal risk assessment, testing-time optimization, and uncertainty-aware decision support in prenatal screening.

Mathematical and Computational Applications doi: 10.3390/mca31030075

Authors: Francisco Rivera Vargas Juan Javier González Barbosa Juan Frausto Solís Mirna Ponce Flores José Luis Purata Aldaz Guadalupe Castilla-Valdez Juan Paulo Sánchez Hernández

An investment portfolio consists of a set of financial assets, such as stocks, fixed-income securities, mutual funds, and real estate, held to achieve diversification and to optimize returns. Accurate asset forecasting provides investors with valuable information to support decision-making. Although existing studies have proposed models for forecasting and portfolio optimization, most rely mainly on traditional techniques and metaheuristic approaches. This work introduces ESIPO (Ensemble Strategies for Investment Portfolio Optimization), a methodology that integrates deep learning and metaheuristic algorithms to perform asset forecasting and investment portfolio optimization. The dataset is obtained from the S&P 500 index, one of the main stock markets. To enhance forecasting accuracy, ESIPO combines five methods from the top-performing models of the international M4 competition: (a) ARIMA (AutoRegressive Integrated Moving Average) and ETS (the statistical exponential-smoothing state-space), which represent classical statistical approaches; (b) FFORMA (Feature-based FORecast Model Averaging) and JAGANATHAN, two ensemble-based methods; (c) CNN (Convolutional Neural Network), which is one of the most common deep learning models. ESIPO improves the forecast performance of the portfolio by applying the TAIPO (Threshold Accepting Investment Portfolio Optimization) metaheuristic to select the best assets and optimize portfolio composition. The results obtained 45% of improvement according to the Sharpe Ratio metric.

Mathematical and Computational Applications doi: 10.3390/mca31030074

Authors: Lianbin Zhou Zhifeng Zhou Peiwen Zhang Lidan Li

Amid the rapid growth of the aviation sector, carbon reduction presents a significant challenge for airlines. This study investigates the structural characteristics and dynamic evolution of carbon emission efficiency among 18 global airlines from 2015 to 2021 using a two-stage super-efficient slack-based measure model (SBM) and an SBM-based Hicks–Moorsteen productivity index, incorporating absolute β-convergence tests. Key findings include the following: (1) The overall mean static efficiency of the airlines ranged from 0.225 (American Airlines) to 0.662 (Singapore Airlines), with an industry-wide average of 0.44. (2) Dynamic productivity change also exhibited significant variation: the overall mean superefficient SBM-based Hicks–Moorsteen (HM) productivity index was 0.962, but it dropped sharply to 0.526 in 2019–2020 due to the COVID-19 pandemic. After 2020, several airlines demonstrated significant recovery, with Emirates and Singapore Airlines achieving dynamic productivity change indices above 1.5. (3) In 16 out of 18 airlines, operational efficiency exceeded production efficiency, highlighting the importance of technological improvements in production. (4) Limited technological progress was identified as the main factor behind efficiency declines, while absolute β-convergence indicated that inefficient airlines are gradually catching up with efficient peers. These findings provide insights for airlines and policymakers in designing targeted carbon reduction strategies and promoting sustainable aviation development. The empirical scope of this study is limited to 18 major global airlines over the period 2015–2021. Due to data availability constraints, the sample does not fully cover all regions or low-cost carriers. The Hicks–Moorsteen index and its EC/TC components are used for interpretative and heuristic purposes only and should not be understood as a strict mathematical decomposition within the two-stage network SBM framework.

Mathematical and Computational Applications doi: 10.3390/mca31030073

Authors: Timm Gödde Eisso Hendrik Atzema Bojana Rosić

Data-driven neural networks (NNs) have gained significant attention across engineering disciplines, particularly in design optimization and experimental settings, where they are widely used to construct surrogate models for high-dimensional regression problems. Despite their power as global approximators, neural networks often struggle to accurately capture local features without relying on a large number of trainable parameters and training data points, resulting in increased training time. To address these limitations, in this paper we propose domain decomposition methods (DDMs), which divide the input feature space into multiple local subdomains, each modeled by a simpler NN, trained in parallel. Interface constraints are introduced in the local loss functions to enforce continuity between subdomains. They are enforced with two different approaches: by utilizing Lagrange multipliers or augmented Lagrange multiplier methods. Compared to unconstrained approximations, both methods significantly improve continuity across subdomain interfaces. For a 2D and a 3D problem, computational time and accuracy are investigated across varying numbers of subdomains to identify optimal partitioning strategies. The use of DDMs improves approximation accuracy in local regions with smaller number of parameters when compared to standard global NN training. In terms of convergence, the augmented Lagrange method outperforms the standard Lagrange formulation by converging faster due to lower convergence requirements, albeit with a slightly lower accuracy. Overall, these results highlight the augmented Lagrange method as a promising DDM approach for training efficient and scalable NN surrogate models.

Mathematical and Computational Applications doi: 10.3390/mca31030071

Authors: Yiran Tian Yuanjia Liu

To address node redundancy and coverage holes in Wireless Sensor Network (WSN) deployment, this paper proposes an Improved Northern Goshawk Optimization (INGO) algorithm with multiple enhancements. It integrates a Diverse Chaotic Map Initialization Strategy (DCMIS) into the standard Northern Goshawk Optimization (NGO) for Diverse, uniform initial populations and improved global exploration. A Bidirectional Population Evolution Dynamics (BPED) mechanism follows the pursuit-and-evasion phase, applying asymmetric logic—elite guidance and selective replacement of weak individuals—to escape local optima and accelerate global convergence. Simulations reveal uniform grid topologies and an average coverage ratio of 91.90% with INGO, outperforming Northern Goshawk Optimization (NGO), Artificial Bee Colony (ABC), Improved Wild Horse Optimizer (IWHO), and the Firefly Algorithm (FA). INGO also achieves 100.00% connectivity, eliminating isolated nodes and ensuring reliable full-network communication. These results indicate that INGO achieves higher coverage and full connectivity under the studied simulation setting, demonstrating its effectiveness for WSN deployment optimization.

Mathematical and Computational Applications doi: 10.3390/mca31030072

Authors: Ahmed Raoof Tawfeeq Al-Hasani Ali Broumandnia Hamid Haj Seyyed Javadi

The rapid proliferation of Internet of Things (IoT) devices increases the demand for task offloading mechanisms that satisfy strict latency constraints while limiting security exposure in edge computing environments. This paper proposes a security-aware task offloading framework for IoT edge networks, using Software-Defined Networking (SDN) as a centralized control plane. The SDN controller combines real-time monitoring, threat-aware risk estimation, and a lightweight heuristic decision engine to assign tasks to heterogeneous edge nodes according to latency constraints, resource availability, and task security sensitivity. To avoid optimistic scalability assumptions, the evaluation explicitly models contention through load-dependent queueing delay at edge nodes and reduced effective bandwidth on shared links. Simulation results with realistic IoT task parameters and heterogeneous edge capacities show that the proposed framework achieves an average latency of approximately 125±5 ms, a task completion ratio (TCR) of about 92±2%, and a security success rate (SSR) near 95±1.5%, compared to the considered baselines. These results indicate that incorporating risk assessment into SDN-based offloading decisions can improve security-related outcomes while maintaining practical performance under contention. Limitations include the use of an analytical risk model and a single-controller SDN setting; future work will investigate multi-controller deployments, attack-trace-driven evaluation, and energy-aware extensions.

Mathematical and Computational Applications doi: 10.3390/mca31030070

Authors: Sergio Hernandez-Mendez Carolina Maldonado-Mendez Sergio Fabian Ruiz-Paz Hiram García-Lozano Antonio Marin-Hernandez Oscar Alonso-Ramirez

In recent years, animation-based systems for human-computer interaction have attracted increasing attention. This work proposes a hybrid framework that combines mathematical modeling and bio-inspired optimization algorithms to generate motion sequences from skeletal data. The framework takes as input a complete skeletal sequence corresponding to a given action and optimizes both the number of key poses and the parameters of a homotopy-based formulation to generate transitions between consecutive poses. A homotopy-based approach is used to compute transitions between selected key poses. The homotopy parameter λ serves as an indicator of the completeness of the transition between pairs of key poses. Four nature-inspired optimization algorithms: Genetic Algorithm, Micro Genetic Algorithm, Particle Swarm Optimization, and Ant Colony Optimization were evaluated to determine the number of key poses and homotopy parameters that enable feasible motion generation. Dynamic Time Warping (DTW) is used as an external metric to assess the similarity between generated and reference sequences. It is important to note that Dynamic Time Warping (DTW) should be considered as a sequence similarity measure, as it does not explicitly evaluate perceptual realism or biomechanical plausibility. The framework was evaluated on 18 action sequences, demonstrating its ability to generate feasible motion transitions in 16 of the 18 evaluated actions when using PSO and MicroGA. For each pair of key poses, a fixed number of intermediate frames is generated to provide a uniform temporal discretization of the motion. The results suggest that homotopy-based methods provide a feasible approach for animation-based interaction systems.

Mathematical and Computational Applications doi: 10.3390/mca31030069

Authors: Saad Alqithami

Human–AI systems often involve repeated interaction among users, organizations, and AI components rather than isolated model outputs. In such settings, cooperation can be pursued either by changing agent incentives or by adding an explicit accountability layer. We formalize the Institutional Monitoring and Ledger (IML) framework, which augments a Markov game with monitoring, evidence logging, delayed settlement, and review while leaving the base dynamics unchanged. We derive conservative incentive checks that clarify how detection quality, review accuracy, settlement delay, and sanction size jointly shape deterrence and wrongful-penalty risk. We then provide pilot evidence in two canonical sequential social dilemmas, Harvest and Cleanup, using five agents, PPO training, five training seeds per condition, and comparisons against PPO, inequity aversion, social influence, and IML ablations. In these settings, IML avoided some of the optimization instability observed in the representative internalization baselines tested here, made monitoring error directly visible through ledger records, and showed how false positives can accumulate into a persistent welfare cost. Agent-level analyses in these symmetric environments found nearly uniform measured enforcement burden, while temporal analyses showed that late-stage enforcement is increasingly dominated by residual false positives. These results do not establish legitimacy in human-facing settings or deployment readiness. They instead position IML as a framework with pilot evidence for studying accountability mechanisms in cooperative human–AI systems and highlight measurement error, review design, and due process as central design constraints.

Mathematical and Computational Applications doi: 10.3390/mca31030068

Authors: Feng Zhao Xiaokun Li Juncheng Luo Weidong Lei Hongjun Li

The treatment of logarithmic spatial singular integrals is a key challenge affecting the reliability of results when the time domain boundary element method (TD-BEM) is used to solve elastodynamic problems. To address this problem, this paper derives and establishes a set of analytically rigorous integration formulas for logarithmic spatial singularities based on the fundamental properties of the Heaviside function, which enables the direct spatiotemporal analytical solution of such singular integrals in TD-BEM. The formulas fill the research gap of the absence of direct analytical solutions for logarithmic spatial singular integrals in elastodynamic problems of TD-BEM, and enrich the theoretical system of the treatment of singular integrals for TD-BEM. Three typical elastodynamic engineering problems, including a fixed–fixed beam under a uniform sudden load, an infinite domain with a single cavity under a boundary blasting load, and a double tunnel beneath valley topography subjected to metro vibration load, are selected for numerical verification. The calculation results of the proposed method are compared with the reference solutions. It is shown that the calculation results of the proposed method are in good agreement with the reference solutions, which effectively verifies the correctness and engineering applicability of the analytical integration formulas.

Mathematical and Computational Applications doi: 10.3390/mca31030067

Authors: Zhiji Cui Zimin Liang Miqing Li

Understanding the structure of multi-objective optimisation problems (MOPs) is essential for analysing search difficulty and supporting informed decision-making. In single-objective optimisation, fitness landscapes offer a spatial view of a problem, but extending such visualisations to MOPs is challenging due to the vector-valued nature of objectives. In this work, we introduce Pareto landscape, a fitness landscape visualisation technique for multi-objective optimisation on the basis of the Pareto dominance relation. We illustrate the main characteristics of a Pareto landscape, relate it to the classical fitness landscape, and examine its behaviour across benchmark suites, constrained problems, multimodal problems and real-world cases. We also show how it captures problem landscape structures relevant to optimisation difficulty. A comparison with gradient field heatmaps, PLOT, cost landscape, and constrained cost landscape further demonstrates that Pareto landscape offers complementary insight by highlighting structural patterns not visible with existing visualisation methods. Overall, the results indicate that the Pareto landscape provides a consistent way to observe problem structure across different classes of multi-objective optimisation problems.

Mathematical and Computational Applications doi: 10.3390/mca31030066

Authors: José Luis Llaguno-Roque Adriana Laura López-Lobato Juan Carlos Pérez-Arriaga Héctor Gabriel Acosta-Mesa Ángel J. Sánchez-García Gabriel Gutiérrez-Ospina Antonia Barranca-Enríquez Tania Romo-González

In Mexico, the high prevalence and mortality rates associated with breast cancer (BC) constitute a critical public health challenge that demands context-specific preventive measures. This study proposes an integrative framework for predicting BC risk based on a biopsychosocial model. We hypothesize that emotional suppression and repression act as key neuroendocrine disruptors and predisposing factors within the Mexican female population. To test this, we systematically compared the predictive performance of various machine learning classification models using the clinical, psychological, and combined profiles of 110 women. These models were evaluated with and without the application of a robust evolutionary algorithm: Differential Evolutionary Linear Discriminant Analysis for Feature Extraction (DE−LDAFE). The results demonstrated that integrating clinical and psychological data into a combined latent space significantly improved the performance of the classification algorithms. The Artificial Neural Network achieved the highest metrics (0.9975 Precision; 0.9976 F1-score). However, due to the inherent “black-box” nature of these models (limited clinical interpretability), the Decision Tree emerged as the optimal practical alternative, providing highly competitive (0.8874 Precision; 0.8853 F1-score) and interpretable results. These findings provide empirical evidence that psychological factors, rather than being mere incidental comorbidities, could be associated with the etiology of breast cancer and be used as risk factors in predicting the disease. Ultimately, this AI-driven biopsychosocial screening model offers a scalable, low-cost, and context-adapted risk assessment tool for early BC diagnosis in Mexican women.

Mathematical and Computational Applications doi: 10.3390/mca31020065

Authors: Carlos-Alberto López-Herrera Héctor-Gabriel Acosta-Mesa Efrén Mezura-Montes Jesús-Arnulfo Barradas-Palmeros

Liquid State Machines (LSMs), a reservoir computing model based on recurrent spiking neural networks, provide a powerful framework for solving spatiotemporal classification tasks by leveraging rich temporal dynamics and event-driven processing. Although the traditional LSM formulation assumes a fixed, randomly generated reservoir, recent research has explored optimization strategies to improve liquid dynamics. However, most existing approaches focus primarily on optimizing synaptic connectivity or reservoir structure, while the role of neuron-level parameters remains largely underexplored. This work proposes a neuroevolutionary strategy based on a Genetic Algorithm (GA) that encodes both neuron configurations and their spatial positions, explicitly treating neuron-level parameters as optimization targets. By evolving neuron-specific parameters and spatial positions, the method induces diverse reservoir dynamics. Unlike approaches that directly optimize synaptic weights, the proposed representation maintains an encoding whose dimensionality scales linearly with the number of neurons. The approach was evaluated on four synthetic benchmark tasks, including one Frequency Recognition task and three Pattern Recognition tasks, using compact reservoirs composed of only 20 Leaky Integrate-and-Fire neurons. Despite the small reservoir size, the method achieved state-of-the-art or highly competitive performance, reaching mean accuracies of up to 99.71%. In the most challenging case (PR12), performance improved when the reservoir size was increased to 64 neurons. The method was further evaluated on two real-world datasets, N-MNIST and the Free Spoken Digit Dataset (FSDD), using reservoirs of 300 neurons, achieving 90.65% and 81.47% accuracy, respectively, while using substantially fewer neurons than many existing LSM-based approaches. These results highlight the potential of evolving neuron configurations and spatial organization to produce compact and effective liquid reservoirs.

Mathematical and Computational Applications doi: 10.3390/mca31020064

Authors: José Alejandro Cornejo-Acosta Carlos Segura Jesús García-Díaz Julio César Pérez-Sansalvador

The Hamiltonian p-median problem (HpMP) generalizes the classical traveling salesperson (TSP) and the Hamiltonian cycle problems. The HpMP aims to find a collection of p non-intersecting cycles that span all the vertices of a given edge-weighted graph G=(V,E,w) while minimizing the sum of the costs of the cycles. This paper introduces a memetic algorithm (MA) with explicit diversity management for the upper-bounded HpMP (UB-HpMP), where upper-bounded means that each cycle in the solution cannot exceed a maximum number of vertices. This MA approaches the problem as a set-partitioning problem, where each cluster of the partition contains the vertices of each cycle. Moreover, it uses a novel crossover operator based on the Hungarian algorithm, exploits the Lin–Kernighan heuristic, a state-of-the-art algorithm for the TSP, and uses best-non-penalized (BNP) selection to explicitly manage the population’s diversity. The proposed MA is tested against state-of-the-art algorithms and classical techniques, including those with and without implicit diversity management, as well as an open-source heuristic solver. The computational experimentation results show that explicit diversity management has advantages over other techniques.

Mathematical and Computational Applications doi: 10.3390/mca31020063

Authors: Julio B. Clempner

In this paper, we propose a Newton-inspired black-box optimization algorithm for multiobjective optimization in constrained ergodic Markov chain environments. The method is motivated by challenges in application areas, where decision-making under uncertainty and limited access to structural information is pervasive. A central contribution of the proposed algorithm is the complexity analysis, which yields substantial computational advantages over conventional optimization approaches. Operating in a purely black-box setting, the algorithm relies exclusively on function evaluations and derivative approximations, without requiring explicit knowledge of the objective function’s internal structure. To approximate system dynamics, we employ an Euler-based scheme that enhances the scalability and adaptability of convex optimization problems. While Markov chains are seldom leveraged in black-box optimization, we demonstrate that constrained ergodic Markov chains constitute a powerful and underexplored modeling framework for learning and decision-making under structural constraints. We provide a complexity analysis and illustrate the effectiveness of the proposed method through a numerical example, highlighting its potential to advance applications in multiobjective optimization and decision-making.

Mathematical and Computational Applications doi: 10.3390/mca31020062

Authors: Adrian Kwiecien Waddah Saeed

Distributed denial-of-service (DDoS) attacks, a type of Denial-of-Service (DoS) attack in which the targeted server, service or network is overloaded with malicious traffic originating from various different sources with the aim of making such targets inaccessible for legitimate users, continue to pose a pertinent threat to the availability and integrity of organisational digital assets. While many studies have shown that machine learning models can provide high predictive accuracy in detecting such attacks, they often fail to evaluate the practicality of deploying such models to production. This study aims to address this gap by evaluating a considerable amount of pipelines based on five popular supervised classifiers for detecting DDoS attacks using the CICDDoS2019 dataset. The study employs a comprehensive methodology that combines both manual feature removal with automated encoding, scaling and feature selection integrated within pipelines. A total of 210 pipelines formed of five classifiers, three features selectors, two hyperparameter tuners and seven train–test splits were initially evaluated. Pipeline performance was assessed using both conventional and computational performance metrics. To identify the champion pipeline, a two-step approach was employed: composite scoring for shortlisting and statistical testing using Friedman and post hoc Nemenyi tests. The champion pipeline was shown to be Decision Tree coupled with Recursive Feature Elimination (with 20 features selected) and Grid Search hyperparameter tuning with a 90-10 train–test split. It achieved the most optimal balance of predictive capabilities and computational overheads, achieving an MCC of 0.993±0.024, training time of 0.194±0.001 s, inference time of 0.000998±0.00008 s, CPU time of 0.194±0.008 s and average memory usage of 15,167 ± 322 kilobytes across training and inference. The findings highlight the importance of a holistic and more nuanced approach when selecting a champion pipeline that is not only effective but also feasible for deployment in resource-constrained environments.

Mathematical and Computational Applications doi: 10.3390/mca31020061

Authors: Guillermo Valencia-Palomo

Applied optimization in automatic control and systems engineering involves developing and implementing mathematical methods to improve the performance and efficiency of automated systems [...]

Mathematical and Computational Applications doi: 10.3390/mca31020060

Authors: Pablo García-González Luca A. Bianchini Andrea Fuk Simone Villanova José Antonio González-Jurado Maria Francesca Piacentini

Background: The aim of the present study was to identify the discipline with the greatest predictive value for overall performance in Olympic-distance triathlon. Methods: Data were extracted from the API (Application Programming Interface) service on the World Triathlon website by signing up for the free service. A custom Python code was written to perform different data collection operations. General statistical analyses and machine learning analyses were performed by creating a Jupyter Notebook file. TensorFlow and PyTorch libraries were used for machine learning analysis. Results: Fifty percent of the employed models identified cycling as the most predictive discipline for race success for both sexes, whereas 33% selected running as the determining discipline. To achieve a podium finish, approximately 78% of the models classified running as the most predictive discipline for males, and approximately 56% of the models did so for females. For finishes between fourth and tenth place, approximately 78% of the models proposed running as the most predictive discipline for both sexes. Swimming was never identified as the most predictive discipline by the majority of models for any group or sex. Conclusion: The most predictive discipline in Olympic triathlon depends on the athlete’s sex and competitive level. Nonetheless, running remains the most consistently predictive discipline, whereas swimming rarely acts as a performance differentiator.

Mathematical and Computational Applications doi: 10.3390/mca31020059

Authors: Abeer M. Al-Bugami Rola S. Al-Harbi Amr M. S. Mahdy

This research investigates the numerical analysis of a two-dimensional (2D) delay mixed integral equation (DMIE) of the second kind with a continuous kernel. The existence, uniqueness, stability, and convergence of the solution are rigorously established in the functional space C([a,b]×[0,T]), providing a solid theoretical foundation. A collocation method based on Chebyshev and Legendre polynomials is applied to obtain accurate numerical approximations, leading to a system of algebraic equations applicable to both linear and nonlinear cases. Numerical simulations are performed using MATLAB to evaluate the method’s performance and calculate the results, including error behavior, convergence, and stability. Several illustrative applications are presented to demonstrate the method’s numerical stability and versatility in handling both linear and nonlinear problems. The results underscore the efficiency, accuracy, and robustness of the proposed numerical schemes in solving complex 2D DMIE, highlighting the novelty of the framework and its strong potential for broad applications in contemporary scientific and engineering problems.

Mathematical and Computational Applications doi: 10.3390/mca31020058

Authors: Armando Sánchez-Nungaray Marcelo Pérez-Medel Carlos González-Flores Raquiel R. López-Martínez Martín Solís-Pérez

This article introduces an automaton designed to improve feasible solutions to the Monge–Kantorovich (MK) problem, particularly effective when the cost function is continuous. To enhance its performance, a good initial solution is obtained using the discrete wavelet transform. Specifically, a transportation problem is solved where the cost matrix is composed of the approximation coefficients of the transform, reducing the number of variables to one quarter of the original discrete problem. The solution to this reduced problem is extended using the detail coefficients, yielding a feasible solution to the original problem. This solution serves as the initial state of the tuning automaton, whose final states provide approximations to the optimal solution of the transportation problem.

Mathematical and Computational Applications doi: 10.3390/mca31020057

Authors: Monzur Alam Imteaz ABM Sharif Hossain Hassan Ahmed Rudayni Amimul Ahsan Shahriar Shams

This study develops generalised equations to predict arsenic removal efficiency during adsorption using synthetic sand, based on two key factors: adsorbent dose and temperature. Previous experimental investigations demonstrated that iron oxide coated sand (IOCS), aluminium oxide coated sand (AOCS), and their mixtures are highly effective for arsenic removal. Best-fit equations were first derived for IOCS and AOCS at discrete temperatures as functions of dose concentration, and these were subsequently unified into single predictive equations capable of estimating removal efficiency across a wide range of temperatures and doses. The resulting models closely replicate experimental results, with correlation coefficients exceeding 0.99 for both IOCS and AOCS. Using the same methodology, an additional equation was developed for a 50:50 mixture of IOCS and AOCS, yielding a slightly lower but still strong correlation coefficient of 0.97. In contrast, linear proportioning of the individual IOCS and AOCS equations failed to accurately predict the removal efficiency of the mixed adsorbent, indicating that simple linear scaling is inadequate for representing the combined adsorption behaviour.

Mathematical and Computational Applications doi: 10.3390/mca31020056

Authors: Awad Awadelkarim

Predicting loan defaults is a significant challenge for financial institutions; however, current machine learning techniques often encounter issues in areas such as data privacy, cross-institutional cooperation, and model transparency. The restrictions on the practical implementation of advanced predictive models are centralized training paradigms, which limit the application of advanced models because of regulatory and confidentiality issues, and black-box decision making, which diminishes confidence in automated credit risk tools. This study mitigates these problems by adopting a federated-inspired decentralized ensemble learning model combined with explainable artificial intelligence (XAI) in predicting loan defaults. Various machine learning classifiers are trained on partitioned institutional data without the need to share any data; they include K-Nearest Neighbors, support vector machine, random forest, and XGBoost. They use a prediction-level aggregation strategy to simulate the collaborative decision-making process without losing locality of data. SHAP and LIME are used to promote model interpretability by giving both global and local explanations of the consequences of prediction. The proposed framework was tested on a large public dataset of loans that contains more than 116,000 records, including various financial and borrower-related features. The experimental findings show that XGBoost has high and reliable predictive accuracy in both centralized and decentralized scenarios, achieving 99.7% accuracy under federated-inspired evaluation. The explanation analysis shows interest rate spread and upfront charges as the most significant predictors of loan default risk. The main contributions of this research are as follows: (i) a privacy-preserving decentralized ensemble learning framework that is applicable in multi-institutional financial contexts, (ii) a detailed analysis of centralized and decentralized predictive performances, and (iii) the pipeline of the XAI, which can be used to increase its transparency and regulatory confidence in automated credit risk evaluation. These results prove that decentralized learning combined with explainable AI can provide high-performing, transparent and privacy-sensitive loan default prediction systems in practice in real-world banking systems.

Mathematical and Computational Applications doi: 10.3390/mca31020055

Authors: Longde Yan Aidong Chen Wenwen Chen Jiawang Huang Yanlong Zhang Shuo Wang Jing Zhou

With the rapid development of Internet technology, information security has become increasingly important. Cryptographic analysis techniques, especially side-channel analysis (SCA), pose a significant threat to security systems. The latest SCA technology mainly utilizes the physical leakage signals generated during the operation of encryption devices, such as power consumption, temperature and electromagnetic radiation. These signals themselves carry the physical characteristics of the device, which are related to the encryption algorithm. Among them, the power consumption trace remains the main target of modern SCA research. However, such trajectories often bring about some analytical difficulties, such as the data sequence being too long, the feature points being distributed sparsely, and the internal relationships of the data being complex. These challenges hinder effective analysis. While Transformer architectures are good at capturing long-range dependencies in sequential data, their high computational complexity limits practical deployment. To address this, we propose replacing the self-attention (SA) module in Transformers with a focal modulation module. This modification significantly reduces computational complexity and reduces computational operations during feature extraction, enabling efficient and accurate side-channel attacks. Experimental results on benchmark datasets (ASCAD, AES_RD, AES_HD, DPAv4) demonstrate the superiority of our approach. The proposed method achieves a reduction in training time compared to standard Transformer models, and achieves superior key recovery performance, outperforming existing state-of-the-art models.

Mathematical and Computational Applications doi: 10.3390/mca31020054

Authors: Hailu Wan Zhuo Jin Gengqiang Huang Shuang Li

Glass artworks represent a significant component of cultural heritage, yet their surfaces are highly vulnerable to physicochemical weathering resulting from composition-dependent interactions with environmental factors. Understanding the complex and nonlinear relationships between glass composition and deterioration remains challenging using conventional, often invasive, analytical techniques. To address this issue, this study proposes an interpretable and non-destructive computational framework to analyze weathering patterns in historical glass based on oxide composition data. The framework combines statistical hypothesis testing (Chi-squared analysis), metric-based machine learning (Prototypical Networks), probabilistic modeling (Gaussian Mixture Models), multivariate statistical analysis (orthogonal partial least squares discriminant analysis), and information-theoretic methods (mutual information analysis) to identify key compositional features and inter-elemental relationships associated with surface degradation. The results show that lead-barium glass exhibits a higher susceptibility to weathering compared with high-potassium glass, with PbO, BaO, and SiO2 identified as the most discriminative components. The Prototypical Network achieved 100% accuracy on most specific data partitions within the analyzed dataset, demonstrating its effectiveness in small-sample compositional classification. Meanwhile, mutual information network analysis revealed the complex interrelationships among chemical components involved in surface weathering behavior. These findings indicate that interpretable machine learning and statistical modeling can provide meaningful insights into composition-dependent patterns and support reproducible analysis for the sustainable conservation of cultural heritage glass.

Mathematical and Computational Applications doi: 10.3390/mca31020053

Authors: Takuya Kanazawa

Quantifying predictive uncertainty is essential for safe and trustworthy real-world AI deployment. However, the fully nonparametric estimation of conditional distributions remains challenging for multivariate targets. We propose Tomographic Quantile Forests (TQF), a nonparametric, uncertainty-aware, tree-based regression model for multivariate targets. TQF learns conditional quantiles of directional projections n⊤y as functions of the input x and the direction n. At inference, it aggregates quantiles across many directions and reconstructs the multivariate conditional distribution by minimizing the sliced Wasserstein distance via an efficient alternating scheme with convex subproblems. Unlike classical directional-quantile approaches that typically produce only convex quantile regions and require training separate models for different directions, TQF covers all directions with a single model to reconstruct the full conditional distribution itself, naturally overcoming any convexity restrictions. We evaluate TQF on synthetic and real-world datasets, and release the source code on GitHub.

Mathematical and Computational Applications doi: 10.3390/mca31020052

Authors: Mamoon Aamir Mohamed Omri Aqsa Zafar Abbasi Lioua Kolsi

There is a demand for a structurally sound fire detection and suppression system that can support a large deployable ground or space antenna in a lower Earth orbit (LEO) environment and remains thermally stable across the entire range of the LEO environment. This paper describes a new type of deployable antenna, i.e., triple scissor deployable antenna mechanism (TSDAM), which has a circumferential modular structure and can deploy into position with one degree of freedom; its deployment does not change its geometric precision or structural stability. This research creates a comprehensive design methodology based on a multiphysics approach, which encompasses nonlinear kinematics analysis, fuzzy logic-based material selection, structural and thermal optimization using fuzzy logic geometries, coupled thermo-structural-dynamic analysis, and finally, dynamic analysis of the deployed structure. The material selection process identified the most suitable candidate material to be the T1100G carbon fiber reinforced plastic as its stiffness-to-weight ratio and thermal performance under LEO cycling was the best in the study. The optimal geometric deployment yield for the antenna was 26.8 m with a total structural weight of 128.4 kg and the base case geometric deployment yielded a feasible ratio of 0.91. This work provides a comparison of the mass savings using traditional deployable truss designs; testing of conventional designs showed a much greater mass overhead compared to the smart design’s mass. From a dynamic analysis perspective, the predicted fundamental frequency for the TSDAM as deployed was 0.09912 Hz and compared favorably to the corresponding finite element models (1.91% error), thereby validating the analytical model. The overall test provides a systematic, scalable methodology for designing ultra-lightweight, geometrically precise deployable reflector systems that satisfy the requirements of next-generation space operations.

Mathematical and Computational Applications doi: 10.3390/mca31020051

Authors: Joel Rodríguez-Guillén Rubén Salas-Cabrera Bárbara María-Esther García-Morales Miguel A. García-Morales Juan Frausto-Solís

The Bond Graph (BG) methodology, a multi-domain graphical description formalism, is used to study a horizontal-axis two-mass drive train of a wind turbine. The main contribution of this work is to address the lack of wind energy literature dealing with fully unambiguous, traceable, and dimensionally homogeneous per-unit quantities for two-mass drive train models. Data in real quantities for the drive train are collected from open-access datasheets and their corresponding design information files. Wind turbines that may serve as Reference Wind Turbines (RWTs), with traceable calculations, are carefully selected. A lumped-parameter order-reduction method is employed to convert data from higher-order models into data for a reduced-order two-mass model. The BG methodology is then used to formally derive the per-unit drive train model and its corresponding dimensionally homogeneous per-unit parameters for a set of six representative Reference Wind Turbines, covering a nominal power range from 0.75 MW to 5 MW.

Mathematical and Computational Applications doi: 10.3390/mca31020050

Authors: Mingyuan Liu Lintao Liu Zhujia Yu Futai Liang Guocheng Wang

Emergency facility location and layout are critical to the efficiency of emergency rescue and resource allocation. However, practical emergency scenarios are plagued by two key challenges: the risk of facility failure due to various uncertain factors and the presence of complex polygonal barriers (including convex and concave polygons) that hinder transportation. Existing studies often overlook concave polygonal barriers or fail to prioritize time satisfaction, a core demand in emergency response. To address these gaps, this paper proposes a reliable emergency facility location optimization model with the objective of maximizing time satisfaction, considering constraints such as capacity, cost, and demand. The model integrates three key methods: a convex hull algorithm to convert concave barriers into convex ones for simplified calculation, a path optimization algorithm to find the shortest bypass routes around barriers, and an Artificial Ecosystem Optimization (AEO) algorithm to solve the nonlinear programming model. Through numerical experiments (single-facility, multi-facility, and medium-scale scenarios) and a practical case study in the Meknès region of Morocco for ambulance deployment, the feasibility and effectiveness of the model and algorithms are verified. The results show that the model achieves high time satisfaction (all above 0.8, with most exceeding 0.9) and efficiently optimizes facility locations and resource allocation. Sensitivity analysis indicates that increased failure risk parameters (α and θ) lead to a gradual decrease in average time satisfaction. This research provides a systematic mathematical model and practical method for emergency facility location decision-making, effectively addressing the challenges of complex barriers and facility failure.

Mathematical and Computational Applications doi: 10.3390/mca31020049

Authors: Vishwanath Srikanth Machiraju Vijay Kumar Sahil Sharma

Elastic cloud systems are increasingly employing machine learning (ML) to automate resource scaling in response to variable workloads and stringent service-level objectives. However, current ML-based autoscalers are fragmented across different platforms, objectives, and evaluation frameworks. This survey examines 60 primary studies conducted between 2015 and 2025, categorising them according to a five-dimensional taxonomy that includes goal, decision logic, scaling mode, control scope, and deployment. This study classifies supervised, unsupervised, and reinforcement learning approaches and analyzes their integration into practical frameworks, including Kubernetes-based controllers and cloud provider services. This paper summarizes the application of machine learning to workload prediction, proactive and hybrid horizontal–vertical scaling, and adaptive policy optimization. Additionally, it synthesises common evaluation practices, encompassing workloads, metrics, and benchmarks. The analysis identifies ongoing challenges: actuation delays and telemetry lag, the intricacies of hybrid scaling, coordination across multi-service and edge-cloud deployments, and the constrained joint consideration of cost, SLO, and energy objectives. The identified gaps necessitate additional research on unified machine learning-driven orchestration, multi-agent and federated control, standardised benchmarks, and sustainability-aware autoscaling.

Mathematical and Computational Applications doi: 10.3390/mca31020048

Authors: Xiaohang Wan

Aiming at the poor robustness of maintenance schemes in industrial equipment maintenance projects, which arises from uncertain factors including fault degree, maintenance time, and resource availability, this paper proposes a synergistic cost-risk optimization method that integrates Distributionally Robust Optimization (DRO) and Conditional Value-at-Risk (CVaR). First, the paper analyzes the uncertainty characteristics of such projects and constructs a distribution ambiguity set based on the Wasserstein distance to depict unknown probability distributions. Second, a two-stage DRO-CVaR optimization model is established: the first stage formulates a pre-optimization scheme to minimize maintenance costs, and the second stage introduces CVaR for extreme risk measurement, thus achieving optimal decision-making under the worst-case scenario. Finally, a nested Column-and-Constraint Generation (C&CG) algorithm is designed to solve the proposed model. A numerical example is conducted for verification, and results show that compared with traditional stochastic programming and pure DRO methods, the proposed method reduces the total cost by 10.4%, the worst-case scenario loss by 28.9%, and the CVaR value by 32.0%. It thus exhibits superior economic efficiency and risk resistance in uncertain environments.

Mathematical and Computational Applications doi: 10.3390/mca31020047

Authors: Yang Li He Ren Yacong Li Dong Sui Maozu Guo

Cliff carvings, as significant art forms bearing historical, cultural, and religious connotations, face dual threats from natural weathering and human-induced damage. Their protection and restoration of the artistic style present pressing challenges. In recent years, the rapid advancement of digital technologies has offered new opportunities for preserving and reproducing cultural heritage. Particularly, 3D style transfer techniques are emerging as crucial tools for digital safeguarding. The advantages of three-dimensional style transfer in cultural heritage applications include dynamic stylized rendering, simulation of styles from multiple historical periods, alternative modes of exhibition, and facilitating a paradigm shift in conservation practices from static digital archiving to dynamic revitalization. This study proposes a novel 3D stylization method for cliff carvings by integrating 3D Gaussian Splatting (3DGS) and Nearest Neighbor Feature Matching (NNFM) loss metric. The method represents ancient cliff carvings as a set of optimizable 3D Gaussians representation, enabling efficient capture and processing of complex geometric structures and rich textural details. By integrating the textural and geometric characteristics of the target artistic style, 3DGS facilitates high-quality transfer of diverse artistic styles while effectively preserving the original intricate details of the carvings. Additionally, we employ the NNFM loss function to transfer 2D visual details into 3D representations while maintaining multi-perspective style consistency. Experimental results demonstrate that the proposed method exhibits significant advantages in texture fidelity, style consistency, and rendering efficiency. This research showcases the potential of our model for the digital preservation and presentation of cliff-carved cultural heritage, offering an innovative technological approach with theoretical value and practical significance.

Mathematical and Computational Applications doi: 10.3390/mca31020046

Authors: Dun Ao Yao Xiao Fei Lei

Sequential recommendation systems face challenges in integrating local sequential patterns with global collaborative information. While Transformers capture long-term dependencies through self-attention, they suffer from quadratic complexity. State-space models offer linear efficiency but are constrained by Markovian assumptions that limit their ability to model direct inter-item relationships. This paper addresses the expressiveness limitations of selective state-space models in capturing collaborative signals. We propose MCARec, which integrates selective state spaces with a dedicated collaborative awareness module. The key components include: (1) a lightweight attention mechanism that explicitly models item co-occurrence and transition patterns, enabling direct pairwise relationship modeling beyond the sequential bottleneck; (2) context-aware adaptive gating that dynamically balances sequential and collaborative features based on input context; (3) a lightweight architecture that enhances representational capacity while maintaining computational efficiency. On MovieLens-1M, a dataset characterized by dense user interactions, MCARec achieves improvements of 3.89% in HR@10, 5.52% in NDCG@10, and 6.97% in MRR@10 over Mamba4Rec, and 9.19%, 12.09%, and 8.45% respectively over SASRec (all p<0.001). Performance gains correlate with interaction density: substantial improvements on dense datasets diminish on sparser Amazon datasets (2–6% over SASRec in most metrics), while showing mixed results compared to Mamba4Rec on sparse datasets, suggesting that the collaborative awareness mechanism is most effective when sufficient co-occurrence signals are available. This work provides the first systematic analysis of how Markovian constraints in state-space models limit collaborative information utilization in recommendations. MCARec demonstrates that augmenting state-space models with explicit collaborative modeling significantly improves recommendation accuracy in dense interaction scenarios, offering a complementary approach to pure sequential or pure attention-based methods.

Mathematical and Computational Applications doi: 10.3390/mca31020045

Authors: Mofoka Rebuseditsoe Mathibela Daniel Maposa

This study develops a hybrid framework integrating ensemble learning with explainable artificial intelligence to address the methodological challenge of balancing predictive accuracy and interpretability in credit risk model comparison. Using the German Credit Dataset, we implemented a comprehensive preprocessing pipeline, including feature encoding, scaling, and SMOTE for class imbalance handling. Four base models, logistic regression, Random Forest, XGBoost, and Multilayer Perceptron, were combined through a Stacked Ensemble with a logistic regression meta learner. The ensemble demonstrated strong performance, achieving an AUC of 0.761, precision of 0.783, recall of 0.806, and an F1 score of 0.794, which represented the highest scores among all models tested. Notably, Random Forest (AUC = 0.749) surpassed XGBoost (AUC = 0.733), challenging conventional algorithmic hierarchies. SHAP analysis provided transparent global and local interpretability, identifying Current Account status (SHAP = 0.153), Loan Duration (0.064), and Savings Account (0.063) as dominant predictor variables. Class-imbalance handling and threshold optimisation enhanced practical utility by reducing false positives from 39 to 16, thereby aligning with financial risk priorities. The framework provides a reproducible methodological pipeline for systematically comparing credit scoring approaches, demonstrating how predictive performance can be evaluated alongside interpretability considerations within a benchmark dataset context.

Mathematical and Computational Applications doi: 10.3390/mca31020044

Authors: Faisal Bilal Muhammad Asif Mehnaz Shakeel Ioan-Lucian Popa

Time-fractional interface problems, found in heat transfer with discontinuous conductivities and fluid flows with surface tension forces, are challenging due to irregular interfaces and the history-dependent nature of fractional derivatives. This paper presents two numerical methods for simulating time-fractional double interface problems. The first method uses the Haar wavelet collocation technique, while the second relies on a meshless approach with radial basis functions. The fractional derivatives are replaced with the Caputo sense, the resulting first-order time derivatives are handled using the finite difference method, and the spatial operator is approximated using the two proposed methods. Gauss elimination is used to solve linear problems. Quasi-Newton linearization method is used for nonlinear problems. Both methods accommodate constant and variable coefficients, handling discontinuities and singularities in both solutions and coefficients. To evaluate the effectiveness of the proposed methods, numerical experiments are carried out. The accuracy of each method is quantified using the L∞ error norm, and a comparative analysis highlights the validity and advantages of the approaches. Moreover, the proposed schemes are rigorously analyzed to establish their stability, and the existence and uniqueness of the solutions.

Mathematical and Computational Applications doi: 10.3390/mca31020043

Authors: Stefan Mirchevski Aleksandra Popovska-Mitrovikj Verica Bakeva

We investigate cost optimization in an M/Coxk/1 queueing system with phase-dependent service speeds. A unified parametric framework is introduced to model both homogeneous and heterogeneous service regimes, and closed-form expressions for steady-state performance measures are derived. These results are used to construct an expected total cost function explicitly parameterized by the traffic intensity. We prove that the cost function is strictly convex on the stability region, ensuring the existence and uniqueness of the optimal traffic intensity. For the Coxian-2 case, analytical and numerical sweep analyses are conducted with respect to waiting and service-capacity cost parameters. Polynomial response surfaces and nonparametric statistical tests are employed to validate the robustness of the results. The analysis shows that balanced service speeds across phases consistently yield lower optimal traffic intensity levels and reduced expected total costs, whereas heterogeneous service speeds increase congestion and cost sweep. These findings provide practical guidance for the economic design and control of multi-phase service systems.

Mathematical and Computational Applications doi: 10.3390/mca31020042

Authors: Yadamragchaa Tsogtgerel Sharifu Ura

Human civilization embodies a rich cultural heritage shaped over long historical periods by numerous ethnic groups, each employing distinctive motifs and patterns in religious spaces, architecture, clothing, utensils, and other artifacts. Such motifs commonly originate from elementary geometric primitives that are organized through symmetric or asymmetric compositions to convey symbolic and esthetic meaning. This study focuses on Mongolian patterns derived from the nomadic heritage of Mongolia and still prevalent in contemporary design. These patterns draw inspiration from nature, geometry, animals, plants, and symbolic forms. This article proposes a mathematical modeling-driven digitization framework for the systematic analysis and digitization of Mongolian patterns, with the objective of generating accurate digital representations in the form of computer-aided design (CAD) models. A concise review of related work is first presented, followed by a structured digitization framework and a taxonomy of representative Mongolian motifs. A case study demonstrates that, when combined through distance-preserving and shape-preserving geometric operations such as translation, rotation, and reflection, four fundamental geometric entities, namely the circle, circular arc, spiral, and astroid, are sufficient to retain the intrinsic symmetry and compositional coherence of complex patterns observed in selected artifacts. Furthermore, the proposed analytical modeling approach enables the generation of vector-based line drawings that support precise CAD model construction. Accordingly, this study establishes a computational design workflow that integrates cultural heritage patterns into CAD-based modeling environments, thereby supporting digital preservation and fabrication with high geometric fidelity.

Mathematical and Computational Applications doi: 10.3390/mca31020041

Authors: Haneen Hamam

This work introduces a new mathematical model designed to describe the glucose–insulin dynamics associated with a glucose-responsive smart microneedle patch reported in the literature. The model captures the complete sequence of the patch behavior, from detecting glucose changes to controlled transdermal insulin delivery and gradually restoring blood glucose levels to the normal range. Our simulations show that the patch can effectively manage glucose not only during fasting conditions but also after single and multiple meals, restoring glucose levels to healthy levels within a short period. The model predictions are consistent with experimentally reported trends in previously published studies, which strengthens confidence in the biological realism of the proposed mechanism. Because some parameters in such systems are difficult to measure directly, we also performed a comprehensive sensitivity analysis to understand how variations in key parameters influence system stability. The results highlight the central role of the insulin release rate and the five glucose–regulation parameters examined in the sensitivity analysis, providing clear guidance on the most critical aspects of patch design for reliable performance. Overall, this study provides a simplified yet robust mathematical framework that makes the behavior of a glucose-responsive microneedle patch easy to understand and analyze. It lays the groundwork for future refinement of control strategies and optimization of patch design, improving control strategies, and developing more advanced systems that can maintain healthy glucose levels naturally and intuitively.

Mathematical and Computational Applications doi: 10.3390/mca31020040

Authors: Mudassir Shams Nasreen Kausar Pourya Pourhejazy

The existing methods for solving non-linear equations encounter convergence issues and computing constraints, especially when used in fractional-order or complex non-linear problems. This study develops a higher-order fractional technique for solving non-linear equations based on the Caputo fractional derivative. The proposed method uses a fractional framework to improve local convergence and stability while ensuring high efficiency in every iteration step. Local convergence analysis using generalized Taylor series expansion reveals that the order of the new fractional scheme for solving non-linear equations is 5¢+1, where ¢∈ (0,1] represents the Caputo fractional order, determining the memory depth of the Caputo fractional derivative. The performance of the method is further investigated using a variety of non-linear problems from engineering optimization and applied sciences, such as engineering control systems, computational chemistry, thermodynamics models, and operations research, such as inventory optimization. Analyzing the key performance metrics, such as dynamical analysis, percentage convergence, residual error, and computation time, confirms the advantages of the developed method over the state-of-the-art. This study provides a solid framework for higher-order fractional iterative approaches, paving the way for advanced applications of non-linear problems.

Mathematical and Computational Applications doi: 10.3390/mca31020039

Authors: Milena Nikolić Marina Marjanović Žarko Rađenović

Customer Lifetime Value (CLV) estimation over the observed transactional horizon is a fundamental challenge in hospitality analytics, supporting revenue management, personalization, and long-term customer relationship strategies. However, existing models predominantly rely on structured behavioral data while overlooking the emotional intelligence embedded in guest narratives. This study proposes an interpretable multimodal deep learning (DL) framework that bridges behavioral and emotional intelligence for CLV estimation by integrating structured booking records with unstructured hotel review text. Model interpretability is ensured through SHAP analysis for structured attributes, LIME for local textual explanations, and attention visualization for modality interaction analysis. Experimental evaluation on large-scale hospitality datasets demonstrates that the proposed multimodal framework outperforms traditional machine learning models, unimodal deep learning baselines, and classical ensemble learners, yielding consistent improvements across multiple error metrics and a notable increase in goodness of fit. The results confirm that emotional intelligence extracted from guest reviews significantly enhances CLV estimation and provides actionable insights for hospitality decision-making, supporting the deployment of transparent and explainable artificial intelligence (XAI) systems for strategic customer value management.

Mathematical and Computational Applications doi: 10.3390/mca31020038

Authors: Biao Geng Liping Pu

For few-shot image classification tasks, the recognition accuracy of existing models remains limited due to the inherent complexity of the few-shot learning setting. To address this challenge, this paper proposes a few-shot image classification approach, termed GDFSIC, which integrates a Global–Local Channel Attention Module (GLCAM) with a graph-propagation-based Distance–Direction Similarity Earth Mover’s Distance (DDS-EMD). The GLCAM module is incorporated into the feature extractor to enhance focus on discriminative regions and increase model attention to critical feature areas. Furthermore, a Distance–Direction Similarity (DDS) metric is introduced as a more effective distance criterion for capturing subtle differences in latent spatial representations. The proposed method is evaluated on four widely used few-shot image classification benchmarks: CIFAR-FS, CUB-200-2011, mini-ImageNet, and Tiered-ImageNet. Experimental results demonstrate that our approach achieves a clear competitive advantage in classification accuracy across these datasets. Ablation studies and further analyses confirm the effectiveness of each component of the proposed framework.

Mathematical and Computational Applications doi: 10.3390/mca31020037

Authors: Eduardo David Martínez-Hernández Bárbara María-Esther García-Morales María Lucila Morales-Rodríguez Claudia Guadalupe Gómez-Santillán Nelson Rangel-Valdez

Recent advancements in AI have enabled autonomous agents to interact within complex environments, with deliberative BDI (Belief–Desire–Intention) agents standing out for their human-inspired reasoning capabilities. However, defining the initial beliefs that constitute an agent’s cognitive profile remains a significant challenge. This process often relies on manual approaches that limit scalability and validation. This study proposes the Personality–Role–Belief (P–R–B) Model for BDI agents, introducing a novel architecture for generating cognitive profiles applicable to domains such as social simulation and non-player characters (NPCs). The model translates Five-Factor Model (FFM) scores into specific social roles, assigning base beliefs to each. A key contribution is a weighting mechanism designed to resolve conflicts between beliefs when multiple roles coexist. Inspired by Cohen’s effect size conventions, this mechanism establishes an influence hierarchy that quantifies belief strength based on social roles. Consequently, this approach not only enables agents to exhibit coherent behavior consistent with their personality but also establishes a foundation for modeling ethical decision-making through role–trait alignment, thereby facilitating the creation of agents capable of navigating morally complex social contexts.

Mathematical and Computational Applications doi: 10.3390/mca31020036

Authors: Antonio Labinjan Sandi Baressi Šegota Ivan Lorencin Nikola Tanković

Face recognition is increasingly being adopted in industries such as education, security, and personalized services. This research introduces a face recognition system that leverages the embedding capabilities of the CLIP model. The model is trained on multimodal data, such as images and text and it generates high-dimensional features, which are then stored in a vector index for further queries. The system is designed to facilitate accurate real-time identification, with potential applications in areas such as attendance tracking and security screening. Specific use cases include event check-ins, implementation of advanced security systems, and more. The process involves encoding known faces into high-dimensional vectors, indexing them using a vector index FAISS, and comparing them to unknown images based on L2 (euclidean) distance. Experimental results demonstrate a high accuracy that exceeds 90% and prove efficient scalability and good performance efficiency even in datasets with a high volume of entries. Notably, the system exhibits superior computational efficiency compared to traditional deep convolutional neural networks (CNNs), significantly reducing CPU load and memory consumption while maintaining competitive inference speeds. In the first iteration of experiments, the system achieved over 90% accuracy on live video feeds where each identity had a single reference video for both training and validation; however, when tested on a more challenging dataset with many low-quality classes, accuracy dropped to approximately 73%, highlighting the impact of dataset quality and variability on performance.

Mathematical and Computational Applications doi: 10.3390/mca31020035

Authors: Xiheng Gao Weimin Li Hongxiu Zhu

Anomaly identification and fault localization of wind turbines through Supervisory Control and Data Acquisition (SCADA) data is a popular topic today, but most studies overlook the complex time-space interdependence between wind turbine (WT) SCADA variables, which results in low detection accuracy for anomalies in critical moving components of the wind turbine. To address this problem, this paper proposes a fault detection and identification method based on a dynamic graph model with a causal spatio-temporal attention mechanism and variable-level normalized flow. First, it introduces a spatio-temporal attention mechanism under causality to extract the spatio-temporal attention mechanism under causality to extract spatio-temporal features of the variables and uses a graph convolutional neural network to represent the extracted spatio-temporal features as a dynamic graph. Secondly, a dynamic normalization flow is suggested for calculating the logarithmic density estimation between variables. Finally, the anomaly scores are calculated through logarithmic density estimation. Based on these scores, anomalies are detected and localized. Experimental validation on real SCADA data from wind turbines demonstrates that the method can effectively identify abnormal operating states and provide early warnings, achieving higher accuracy and greater stability.

Mathematical and Computational Applications doi: 10.3390/mca31020034

Authors: Stephanie Amador-Larrea Marcela Quiroz-Castellanos Octavio Ramos-Figueroa Alejandro Guerra-Hernández

The one-dimensional Bin Packing Problem (1D-BPP) is a well-known NP-hard grouping problem characterized by high structural complexity and broad practical relevance. Among the metaheuristic approaches proposed for this problem, the Grouping Genetic Algorithm with Controlled Gene Transmission (GGA-CGT) has shown remarkable performance. In this work, an Adaptive Grouping Genetic Algorithm with Controlled Gene Transmission based on Fullness and Item Strategies (AGGA-CGT-FIS) is presented. This approach extends the original GGA-CGT by integrating domain-guided crossover mechanisms and adaptive parameter control schemes. The proposed algorithm incorporates a novel gene-level crossover operator, termed Fullness–Items Gene-Level Crossover 1 (FI-GLX-1). This operator exploits structural information from the solutions through Fullness- and Item-based ordering and transmission strategies. In addition, adaptive control schemes are introduced for key evolutionary parameters associated with crossover and mutation. These mechanisms allow the algorithm to dynamically adjust its behavior according to feedback extracted from the search process, resulting in a fully adaptive variant of the GGA-CGT. The effectiveness of AGGA-CGT-FIS is evaluated using two benchmark sets for the 1D-BPP: the classic and the BPPvu_c instances. The proposed approach is compared against the baseline GGA-CGT using the original Gene-Level Crossover (GLX) operator. Experimental results show improvements in solution quality and convergence behavior, supported by statistical analyses that confirm the significance of the observed performance differences.

Mathematical and Computational Applications doi: 10.3390/mca31020033

Authors: Cynthia Lopez-Jordan Mohammad Jafari

This paper presents a real-time adaptive Linear Quadratic Regulator (LQR) control strategy for the rotary inverted pendulum. The state weighting matrix of the LQR cost function is continuously adapted online based on real-time tracking error, state dynamics, and sliding-mode-inspired robustness measures. Unlike conventional LQR controllers with fixed weighting matrices or hybrid schemes that apply sliding mode control directly to the control input, the proposed approach modulates the LQR cost function itself, enabling dynamic reshaping of controller behavior while preserving smooth control action. The real-time adaptive controller is implemented using a continuous-time Riccati differential equation solved online, making the method suitable for real-time deployment. Experimental validation is conducted on two Quanser QUBE-Servo 2 rotary inverted pendulum platforms under square, sinusoidal, and sawtooth reference trajectories. Performance is compared against a fixed-gain LQR controller using multiple quantitative metrics, including tracking error and control effort. Experimental results demonstrate substantial improvements in tracking accuracy, with reductions exceeding 70–90% in error metrics, while simultaneously achieving over 94% reduction in control effort. These findings verify that adaptive cost shaping provides an effective and practical mechanism for enhancing LQR performance in underactuated experimental systems.

Mathematical and Computational Applications doi: 10.3390/mca31010031

Authors: Osama Tariq Muhammad Asad Arshed Muhammad Kabir Khalid Ijaz Ştefan Cristian Gherghina Hafiza Bukhtawer Batool

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.

Mathematical and Computational Applications doi: 10.3390/mca31010032

Authors: Vaibhav Kumar Munawar A. Shaik

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.

Mathematical and Computational Applications doi: 10.3390/mca31010030

Authors: Jeeangh Jennessi Reyes-Montiel Ericka Janet Rechy-Ramirez Antonio Marin-Hernandez

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).

Mathematical and Computational Applications doi: 10.3390/mca31010028

Authors: Awad M. Awadelkarim

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.

Mathematical and Computational Applications doi: 10.3390/mca31010029

Authors: Lindomar Soares dos Santos Brenno Caetano Troca Cabella Alexandre Souto Martinez

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.

Mathematical and Computational Applications doi: 10.3390/mca31010027

Authors: David Carcaño Ventura Lil María Xibai Rodríguez-Henríquez Saúl E. Pomares Hernández

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.

Mathematical and Computational Applications doi: 10.3390/mca31010026

Authors: Gianluigi Rozza Oliver Schütze Nicholas Fantuzzi

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 [...]

Mathematical and Computational Applications doi: 10.3390/mca31010025

Authors: Qimeng Zhang Wensheng Yu

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.

Mathematical and Computational Applications doi: 10.3390/mca31010024

Authors: Yaping Wang Xuebing Wei Xiaofei Zhu Lili Wan Zihui Zhao

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.

Mathematical and Computational Applications doi: 10.3390/mca31010023

Authors: Weicheng Fu Yisen Wang

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.

Mathematical and Computational Applications doi: 10.3390/mca31010022

Authors: Yu-Shan Bai Jin Wang Yan-Ting Ren Yu-Xiang Li

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.

Mathematical and Computational Applications doi: 10.3390/mca31010021

Authors: Obiora C. Collins Oludolapo A. Olanrewaju

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.

Mathematical and Computational Applications doi: 10.3390/mca31010020

Authors: Miguel A. García-Morales Rubén Salas-Cabrera Bárbara María-Esther García-Morales Juan Frausto-Solís Joel Rodríguez-Guillén

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.

Mathematical and Computational Applications doi: 10.3390/mca31010019

Authors: Maashele Kholofelo Metwane Daniel Maposa Caston Sigauke

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.

Mathematical and Computational Applications doi: 10.3390/mca31010018

Authors: Ange Gabriel Belinga Stéphane Cédric Tékouabou Koumetio Mohammed El Haziti

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.

Mathematical and Computational Applications doi: 10.3390/mca31010017

Authors: Hao Hu Jinshun Cai Chenke Xu

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.

Mathematical and Computational Applications doi: 10.3390/mca31010016

Authors: Eric O’Sullivan Ken Kennedy Jean Mohammadi-Aragh

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.

Mathematical and Computational Applications doi: 10.3390/mca31010015

Authors: Huajun Ran Xian Huang Jiahao Dong Jiefei Yang

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.

Mathematical and Computational Applications doi: 10.3390/mca31010014

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

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.

Mathematical and Computational Applications doi: 10.3390/mca31010013

Authors: Ata Jahangir Moshayedi Zeashan Khan Zhonghua Wang Mehran Emadi Andani

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.

Mathematical and Computational Applications doi: 10.3390/mca31010012

Authors: Zibo Yang Jiale Guo Rui Li Guoqing An Kai Zhang Jiawei Liu Long Zhang

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.

Mathematical and Computational Applications doi: 10.3390/mca31010011

Authors: Fangyuan Li

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.

Mathematical and Computational Applications doi: 10.3390/mca31010010

Authors: Katalina Oviedo Rodríguez Alda Carvalho Rodrigo Valente José Xavier António Cruz Tomás

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.

Mathematical and Computational Applications doi: 10.3390/mca31010009

Authors: Moster Zhangazha Alex Somto Arinze Alochukwu Elizabeth Jonck Ronald John Maartens Eunice Mphako-Banda Simon Mukwembi Farai Nyabadza

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.

Mathematical and Computational Applications doi: 10.3390/mca31010008

Authors: 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 Ana Guadalupe Vélez-Chong

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.

Mathematical and Computational Applications doi: 10.3390/mca31010007

Authors: Fazlollah Lak Emrah Altun Morad Alizadeh Javier E. Contreras-Reyes Hamid Esmaeili

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.

Mathematical and Computational Applications doi: 10.3390/mca31010006

Authors: Hulisani Lutombo Daniel Maposa Simon Setsweke Nkoane

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.

Mathematical and Computational Applications doi: 10.3390/mca31010005

Authors: Yulong Du Huping Mao

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.

Mathematical and Computational Applications doi: 10.3390/mca31010004

Authors: Suresha Kharvi Muhammed Rasheed Irshad Christophe Chesneau Jabir Kakkottakath Valappil Thekkepurayil

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.

Mathematical and Computational Applications doi: 10.3390/mca31010003

Authors: Abuduwali Abudukeremu Mairemunisa Abudusaimaiti

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.

Mathematical and Computational Applications doi: 10.3390/mca31010002

Authors: Aure Flo Oraya Eugene Herrera Guillermo Tabios

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.

Mathematical and Computational Applications doi: 10.3390/mca31010001

Authors: Muhammad Asif Javairia Gul Mehnaz Shakeel Ioan-Lucian Popa

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∞ 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.

Mathematical and Computational Applications doi: 10.3390/mca30060140

Authors: Mostafa Aboulnour Salem Zeyad Aly Khalil

Early identification of students at risk for low academic confidence, poor problem-solving skills, or poor academic performance is crucial to achieving equitable and sustainable learning outcomes. This research presents a hybrid artificial intelligence (AI) framework that combines feature selection using a Random Forest (RF) algorithm with data classification via an Artificial Neural Network (ANN) to predict risks related to Academic Confidence and Problem-Solving Skills (ACPS) among higher education students. Three real-world datasets from Saudi universities were used: MSAP, EAAAM, and MES. Data preprocessing included Min–Max normalisation, class balancing using SMOTE (Synthetic Minority Oversampling Technique), and recursive feature elimination. Model performance was evaluated using five-fold cross-validation and a paired t-test. The proposed model (RF-ANN) achieved an average accuracy of 98.02%, outperforming benchmark models such as XGBoost, TabNet, and an Autoencoder–ANN. Statistical tests confirmed the significant performance improvement (p < 0.05; Cohen’s d = 1.1–2.7). Feature importance and explainability analysis using a Random Forest and Shapley Additive Explanations (SHAP) showed that psychological and behavioural factors—particularly study hours, academic engagement, and stress indicators—were the most influential drivers of ACPS risk. Hence, the findings demonstrate that the proposed framework combines high predictive accuracy with interpretability, computational efficiency, and scalability. Practically, the model supports Sustainable Development Goal 4 (Quality Education) by enabling early, transparent identification of at-risk students, thereby empowering educators and academic advisors to deliver timely, targeted, and data-driven interventions.

Mathematical and Computational Applications doi: 10.3390/mca30060139

Authors: Jingxuan Zhang Yanfei Jin Xueli Wang

In disciplines such as epidemiology, economics, and public health, inference and estimation of heterogeneous treatment effects (HTE) are critical. This approach helps reveal differences in treatment effect estimates between subgroups, which supports personalized decision-making processes. While a variety of meta-learners (e.g., S-, T-, X-learners) have been proposed for estimating HTE, there is a lack of consensus on their relative strengths and weaknesses under different data conditions. To address this gap and provide actionable guidance for applied researchers, this study conducts a comprehensive simulation-based comparison of these methods. We first introduce the causal inference framework and review the underlying principles of the methods used to estimate these effects. We then simulate different data generating processes (DGPs) and compare the performance of S-, T-, X-, DR-, and R-learners with the causal forest, highlighting the potential of meta-learners for HTE estimation. Our evaluation reveals that each learner excels under distinct conditions: the S-learner yields the least bias and is most robust when the conditional average treatment effect (CATE) is approximately zero; the T-learner provides accurate estimates when the response functions differ significantly between the treatment and control groups, resulting in a complex CATE structure, and the X-learner can accurately estimate the HTE in imbalanced data.Additionally, by integrating Z-bias—a bias that may arise when adjusting the covariate only affects the treatment variable—with a specific sensitivity analysis, this study demonstrates its effectiveness in reducing the bias of causal effect estimates. Finally, through an empirical analysis of the Trends in International Mathematics and Science Study (TIMSS) 2019 data, we illustrate how to implement these insights in practice, showcasing a workflow for HTE assessment within the meta-learner framework.

Mathematical and Computational Applications doi: 10.3390/mca30060138

Authors: Hui Xia Jinhong Jiang Qin Wang

In recent years, financial statement fraud schemes have evolved to become markedly more sophisticated and concealed, thereby posing severe threats to both social stability and economic health. Traditional detection methods, which rely primarily on fragmented corporate data, exhibit significant limitations in capturing the dynamic evolution and spatial diffusion characteristics of fraudulent behaviors over time and space. To address this issue, in this study, we undertake a thorough analysis of the intrinsic nature of fraud risk from a sociotechnical systems perspective and construct a multi-level indicator system to comprehensively quantify risk elements. Furthermore, recognizing the dynamic evolution nature and propagating characteristics of fraud risk, we propose a novel financial statement fraud detection framework to capture behavior patterns in temporal and spatial dimensions. Experiments on A-share-listed companies of high-risk industries in China demonstrate that the proposed framework significantly outperforms other mainstream machine learning and deep learning techniques. In addition, we open the “black box” of the detection framework and empirically validate fraud risk patterns with respect to social–technical elements by leveraging explainable AI techniques. Practically, the proposed framework and interpretable analysis are capable of providing precise early warnings and supervision.

Mathematical and Computational Applications doi: 10.3390/mca30060137

Authors: Sadegh Ghavami Hamed Naseri

Conducting laboratory tests in geotechnical engineering is a costly, time-consuming, and labor-intensive process. As an alternative solution, this study employs various machine learning methods to predict the unconfined compressive strength (UCS) of fine-grained soils stabilized by combining chemical additives (such as Portland cement, lime, and industrial and agricultural waste) and nanosilica. After preparing a comprehensive database of a collection of studies from the literature, ten machine learning models were developed for modeling, and their performances were compared using various metrics. After comparing the performance of the models in predicting the UCS with experimental results, the CatBoost model was determined as the optimal model. The variables of curing time, liquid limit of soil, and additive contents were identified as the most effective parameters on the stabilized soil’s UCS. The best-performing model on the applied dataset was determined and compared with experimental models. After determining the effective parameters for predicting the strength of stabilized soil, the nonlinear relationships between the most important variables and the stabilized soil’s UCS were analyzed and investigated.

Mathematical and Computational Applications doi: 10.3390/mca30060136

Authors: Sangeeta Saha Roderick Melnik

Understanding how emotions and psychological states influence both individual and collective actions is critical for expressing the real complexity of biosocial and ecological systems. Recent breakthroughs in mathematical modeling have created new opportunities for systematically integrating these emotion-specific elements into dynamic frameworks ranging from human health to animal ecology and socio-technical systems. This review builds on mathematical modeling approaches by bringing together insights from neuroscience, psychology, epidemiology, ecology, and artificial intelligence to investigate how psychological effects such as fear, stress, and perception, as well as memory, motivation, and adaptation, can be integrated into modeling efforts. This article begins by examining the influence of psychological factors on brain networks, mental illness, and chronic physical diseases (CPDs), followed by a comparative discussion of model structures in human and animal psychology. It then turns to ecological systems, focusing on predator–prey interactions, and investigates how behavioral responses such as prey refuge, inducible defense, cooperative hunting, group behavior, etc., modulate population dynamics. Further sections investigate psychological impacts in epidemiological models, in which risk perception and fear-driven behavior greatly affect disease spread. This review article also covers newly developing uses in artificial intelligence, economics, and decision-making, where psychological realism improves model accuracy. Through combining these several strands, this paper argues for a more subtle, emotionally conscious way to replicate intricate adaptive systems. In fact, this study emphasizes the need to include emotion and cognition in quantitative models to improve their descriptive and predictive ability in many biosocial and environmental contexts.

Mathematical and Computational Applications doi: 10.3390/mca30060135

Authors: Yaozong Tang

A spherically constrained nonlinear eigenvalue problem (NEPv) arising in Bose–Einstein condensates (BEC) is investigated. The Projected Gradient Method (PGM) is proposed and analyzed in detail. Rigorous theoretical analysis establishes its global convergence for both “easy” and “hard” cases, including Lipschitz continuity of the gradient, monotonic objective decrease, and convergence to optimality. Numerical experiments in 1D, 2D, and 3D BEC models demonstrate that PGM achieves competitive accuracy compared to other methods while offering significant advantages in computational efficiency and scalability, enabling large-scale simulations.

Mathematical and Computational Applications doi: 10.3390/mca30060134

Authors: Fatemeh Tavakoli Davud Mohammadpur Javad Salimi Sartakhti Mohammad Hossein Manshaei

In this paper, we present an integrative framework based on Evolutionary Stackelberg Game Theory to model the strategic interaction between a physician, acting as a rational leader, and a heterogeneous population of treatment-sensitive and treatment-resistant breast cancer cells. The model incorporates ecological competition, evolutionary adaptation, and spatial heterogeneity, enabling prediction of tumor progression under clinically relevant treatment protocols. Using tumor volume data obtained from breast cancer-bearing mice treated with Capecitabine and Gemcitabine, we estimated treatment and subject-specific parameters via the GEKKO optimization package in Python. Benchmarking against classical tumor growth models (Exponential, Logistic, and Gompertz) showed that while classical models capture monotonic growth, they fail to reproduce complex, non-monotonic behaviors such as treatment-induced regression, rebound, and phenotypic switching. The game-theoretic approach achieved superior alignment with experimental data across Maximum Tolerated Dose, Dose-Modulation Adaptive Therapy, and Intermittent Adaptive Therapy protocols. To enhance adaptability, we integrated reinforcement learning (RL) for both single-agent and combination chemotherapy. The RL agent learned dosing policies that maximized tumor regression while minimizing cumulative drug exposure and resistance, with combination therapy exploiting dose diversification to improve control without exceeding total dose budgets. Incorporating reaction diffusion equations allowed the model to capture spatial dispersal of sensitive (cooperative) and resistant (defector) phenotypes, revealing that spatially aware adaptive strategies more effectively suppress resistant clones than non-spatial approaches. These results demonstrate that evolutionarily informed, spatially explicit, and computationally optimized strategies can outperform conventional fixed-dose regimens in reducing resistance, lowering toxicity, and improving efficacy. This framework offers a biologically interpretable tool for guiding evolution-aware, patient-tailored cancer therapies toward improved long-term outcomes.

Mathematical and Computational Applications doi: 10.3390/mca30060133

Authors: Faisal Bilal Muhammad Asif Mehnaz Shakeel Ioan-Lucian Popa

Time-fractional interface problems arise in systems where interacting materials exhibit memory effects or anomalous diffusion. These models provide a more realistic description of physical processes than classical formulations and appear in heat conduction, fluid flow, porous media diffusion, and electromagnetic wave propagation. However, the presence of complex interfaces and the nonlocal nature of fractional derivatives makes their numerical treatment challenging. This article presents a numerical scheme that combines radial basis functions (RBFs) with the finite difference method (FDM) to solve time-fractional partial differential equations involving interfaces. The proposed approach applies to both linear and nonlinear models with constant or variable coefficients. Spatial derivatives are approximated using RBFs, while the Caputo definition is employed for the time-fractional term. First-order time derivatives are discretized using the FDM. Linear systems are solved via Gaussian elimination, and for nonlinear problems, two linearization strategies, a quasi-Newton method and a splitting technique, are implemented to improve efficiency and accuracy. The method’s performance is assessed using maximum absolute and root mean square errors across various grid resolutions. Numerical experiments demonstrate that the scheme effectively resolves sharp gradients and discontinuities while maintaining stability. Overall, the results confirm the robustness, accuracy, and broad applicability of the proposed technique.

Mathematical and Computational Applications doi: 10.3390/mca30060132

Authors: Yang Li Xinhang Li Ke Shen Yacong Li Dong Sui Maozu Guo

Ensuring the structural integrity of road infrastructure is vital for transportation safety and long-term sustainability. This study presents a lightweight and accurate pavement crack detection framework named SpcNet, which integrates a Sparse Encoding Module, ConvNeXt V2-based decoder, and a Binary Attention Module (BAM) within an asymmetric encoder–decoder architecture. The proposed method first applies a random masking strategy to generate sparse pixel inputs and employs sparse convolution to enhance computational efficiency. A ConvNeXt V2 decoder with Global Response Normalization (GRN) and GELU activation further stabilizes feature extraction, while the BAM, in conjunction with Channel and Spatial Attention Bridge (CAB/SAB) modules, strengthens global dependency modeling and multi-scale feature fusion. Comprehensive experiments on four public datasets demonstrate that SpcNet achieves state-of-the-art performance with significantly fewer parameters and lower computational cost. On the Crack500 dataset, the method achieves a precision of 91.0%, recall of 85.1%, F1 score of 88.0%, and mIoU of 79.8%, surpassing existing deep-learning-based approaches. These results confirm that SpcNet effectively balances detection accuracy and efficiency, making it well-suited for real-world pavement condition monitoring.

Mathematical and Computational Applications doi: 10.3390/mca30060131

Authors: Belkacem Bekhiti Kamel Hariche Vasilii Zaitsev Guangren R. Duan Abdel-Nasser Sharkawy

This paper develops an algebraic framework for operator matrix polynomials and demonstrates its application to control-design problems in aeroservoelastic systems. We present constructive spectral-factorization and linearization tools (block spectral divisors, companion forms and realization algorithms) that enable systematic block-pole assignment for large-scale MIMO models. Building on this theory, an adaptive block-pole placement strategy is proposed and cast in a practical implementation that augments a nominal state-feedback law with a compact neural-network compensator (single hidden layer) to handle un-modeled nonlinearities and uncertainty. The method requires state feedback and the system’s nominal model and admits Laplace-domain analysis and straightforward implementation for a two-degree-of-freedom aeroelastic wing with cubic stiffness nonlinearity and Roger aerodynamic lag is validated in MATLAB R2023a. Comprehensive simulations (Runge–Kutta 4) for different excitations and step disturbances demonstrate the approach’s advantages: compared with Eigenstructure assignment, LQR and H2-control, the proposed method achieves markedly better robustness and transient performance (e.g., closed-loop Hiω2 ≈ 4.64, condition number χ ≈ 11.19, and reduced control efforts μ ≈ 0.41, while delivering faster transients and tighter regulation (rise time ≈ 0.35 s, settling time ≈ 1.10 s, overshoot ≈ 6.2%, steady-state error ≈ 0.9%, disturbance-rejection ≈ 92%). These results confirm that algebraic operator-polynomial techniques, combined with a compact adaptive NN augmentation, provide a well-conditioned, low-effort solution for robust control of aeroelastic systems.

Mathematical and Computational Applications doi: 10.3390/mca30060130

Authors: Muhammad Asad Arshed Ştefan Cristian Gherghina Iqra Khalil Hasnain Muavia Anum Saleem Hajran Saleem

The extensive use of large language models (LLMs), particularly in the finance sector, raises concerns about the authenticity and reliability of generated text. Developing a robust method for distinguishing between human-written and AI-generated financial content is therefore essential. This study addressed this challenge by constructing a dataset based on financial tweets, where original financial tweet texts were regenerated using six LLMs, resulting in seven distinct classes: human-authored text, LLaMA3.2, Phi3.5, Gemma2, Qwen2.5, Mistral, and LLaVA. A context-aware representation-learning-based model, namely DeBERTa, was extensively fine-tuned for this task. Its performance was compared to that of other transformer variants (DistilBERT, BERT Base Uncased, ELECTRA, and ALBERT Base V1) as well as traditional machine learning models (logistic regression, naive Bayes, random forest, decision trees, XGBoost, AdaBoost, and voting (AdaBoost, GradientBoosting, XGBoost)) using Word2Vec embeddings. The proposed DeBERTa-based model achieved an impressive test accuracy, precision, recall, and F1-score, all reaching 94%. In contrast, competing transformer models achieved test accuracies ranging from 0.78 to 0.80, while traditional machine learning models yielded a significantly lower performance (0.39–0.80). These results highlight the effectiveness of context-aware representation learning in distinguishing between human-written and AI-generated financial text, with significant implications for text authentication, authorship verification, and financial information security.

Mathematical and Computational Applications doi: 10.3390/mca30060129

Authors: Petar Curkovic

This study presents a systematic comparison of five crossover operators used in genetic algorithms (GA) for the Traveling Salesman Problem (TSP). Partially Mapped Crossover (PMX), Order Crossover (OX), Cycle Crossover (CX), Edge Recombination (ERX), and Alternating Edges (AEX) are evaluated within an identical GA framework using tournament selection, inversion mutation, generational replacement, and elitism. Experiments were conducted on seven datasets, including three TSPLIB benchmarks, a clustered synthetic instance, a uniformly random instance, and two real-world Croatian city sets of 50 and 100 cities. Thirty independent GA runs per operator were analyzed using the Friedman test followed by Holm-corrected Wilcoxon pairwise comparisons. The Friedman test shows highly significant global performance differences. After applying Holm correction, the top four operators (PMX, OX, CX, and ERX) are statistically comparable on most datasets, as the correction eliminates most pairwise differences among them. All pairwise comparisons involving AEX remain significant across every dataset, confirming its consistently inferior performance. OX achieves the best average ranks across all datasets consistently, while PMX, CX, and ERX exhibit comparable mid-range performance. To illustrate practical relevance, optimized routes for Croatian instances were used to estimate fuel consumption and CO2 emissions for petrol, diesel, and electric vehicles. The results demonstrate meaningful sustainability benefits achievable through optimized routing.

Mathematical and Computational Applications doi: 10.3390/mca30060128

Authors: Junyu Liu Dayou Guan Xi Liu

Recycled aggregate concrete (RAC) is a sustainable alternative to conventional concrete, reducing environmental hazards and conserving resources. Accurate compressive strength (CS) prediction is critical for its broader acceptance. This study uses machine learning (ML) models (elastic net regression, KNN, ANN, SVR, RF, XGBoost, CatBoost, symbolic regression, stacking) trained on 1030 conventional concrete mixtures from UCI to support RAC’s CS prediction. The best model achieved R2 = 0.92; performance order: CatBoost > XGBoost > RF > SVR > ANN > symbolic regression > KNN > elastic net regression. Stacking improved RMSE by 6% over CatBoost. During the testing, sensitivity analysis revealed that CS exhibits pronounced sensitivity to the cement (C) content and testing age (TA). This aligns with existing experimental research. External validation, which is often neglected by prediction model research, was performed, from which a high-quality evaluating model was used for generalizability and reliability, enhancing the heterogenicity of its usefulness. Lastly, a user-friendly graphical interface was developed that allows users to input custom parameters to obtain sustainable RAC mixtures. This study offers insights into optimizing concrete mix designs for RAC, improving its performance and sustainability. It also advances the knowledge of cementitious materials, aligning with industrial and environmental objectives.

Mathematical and Computational Applications doi: 10.3390/mca30060127

Authors: Atmane Babni Ismail Jamiai José Alberto Rodrigues

In this paper, we address the challenge of solving differential equations using physics-informed neural networks (PINNs), an innovative approach that integrates known physical laws into neural network training. The PINN approach involves three main steps: constructing a neural-network-based solution ansatz, defining a suitable loss function, and minimizing this loss via gradient-based optimization. We review two primary PINN formulations: the standard PINN I and an enhanced PINN II. The latter explicitly incorporates initial, final, or boundary conditions. Focusing on first-order differential equations, PINN II methods typically express the approximate solution as u˜(x,θ)=P(x)+Q(x)N(x,θ), where N(x,θ) is the neural network output with parameters θ, and P(x) and Q(x) are polynomial functions. We generalize this formulation by replacing the polynomial Q(x) with a more flexible function ϕ(x). We demonstrate that this generalized form yields a uniform approximation of the true solution, based on Cybenko’s universal approximation theorem. We further show that the approximation error diminishes as the loss function converges. Numerical experiments validate our theoretical findings and illustrate the advantages of the proposed choice of ϕ(x). Finally, we outline how this framework can be extended to higher-order or other classes of differential equations.