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Algorithms
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Mathematical Modelling in Engineering and Human Behaviour (3rd Edition)
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Mathematical Modelling in Engineering and Human Behaviour (3rd Edition)

A special issue of Algorithms (ISSN 1999-4893). This special issue belongs to the section "Algorithms for Multidisciplinary Applications".

Deadline for manuscript submissions: closed (31 July 2025) | Viewed by 19147

Special Issue Editors

Prof. Dr. Alicia Cordero

E-Mail Website
Guest Editor
School of Telecommunications Engineering, Universitat Politècnica de València, 46022 Valencia, Spain
Interests: numerical analysis; iterative methods; nonlinear problems; discrete dynamics; real and complex
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Juan Ramón Torregrosa Sánchez

E-Mail Website
Guest Editor
Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain
Interests: iterative processes; matrix analysis; numerical analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The aim of this Special Issue, entitled “Mathematical Modelling in Engineering and Human Behaviour (3rd Edition)”, is to develop an interdisciplinary forum for research in Medicine, Sociology, Business and Engineering, where experts in cross-disciplinary areas can discuss recent advances in mathematical techniques in a common and understandable language. This Special Issue hopes to connect researchers who utilize mathematics for the formulation and analysis of models.

The scope of this Special Issue includes, but is not limited to, the following topics:

  • Mathematical models in epidemiology and medicine；
  • Mathematical models in engineering；
  • Applications of linear algebra；
  • Iterative methods for nonlinear problems；
  • Simulations in civil engineering and railway engineering；
  • Networks and applications；
  • Financial mathematics；
  • Uncertainty quantification and modelling；
  • Optimization, least squares and applications；
  • Machine learning and neuronal networks；
  • Mathematics for decision-making.

Prof. Dr. Alicia Cordero
Prof. Dr. Juan Ramón Torregrosa Sánchez
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematical models in epidemiology and medicine
  • mathematical models in engineering
  • applications of linear algebra
  • iterative methods for nonlinear problems
  • simulations in civil engineering and railway engineering
  • networks and applications
  • financial mathematics
  • uncertainty quantification and modelling optimization, least squares and applications
  • machine learning and neuronal networks
  • mathematics for decision making

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Published Papers (23 papers)

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Research

19 pages, 1318 KB  
Article
Hybrid Stochastic–Machine Learning Framework for Postprandial Glucose Prediction in Type 1 Diabetes
by Irina Naskinova, Mikhail Kolev, Dilyana Karova and Mariyan Milev
Algorithms 2025, 18(10), 623; https://doi.org/10.3390/a18100623 - 1 Oct 2025
Viewed by 340
Abstract
This research introduces a hybrid framework that integrates stochastic modeling and machine learning for predicting postprandial glucose levels in individuals with Type 1 Diabetes (T1D). The primary aim is to enhance the accuracy of glucose predictions by merging a biophysical Glucose–Insulin–Meal (GIM) model [...] Read more.
This research introduces a hybrid framework that integrates stochastic modeling and machine learning for predicting postprandial glucose levels in individuals with Type 1 Diabetes (T1D). The primary aim is to enhance the accuracy of glucose predictions by merging a biophysical Glucose–Insulin–Meal (GIM) model with advanced machine learning techniques. This framework is tailored to utilize the Kaggle BRIST1D dataset, which comprises real-world data from continuous glucose monitoring (CGM), insulin administration, and meal intake records. The methodology employs the GIM model as a physiological prior to generate simulated glucose and insulin trajectories, which are then utilized as input features for the machine learning (ML) component. For this component, the study leverages the Light Gradient Boosting Machine (LightGBM) due to its efficiency and strong performance with tabular data, while Long Short-Term Memory (LSTM) networks are applied to capture temporal dependencies. Additionally, Bayesian regression is integrated to assess prediction uncertainty. A key advancement of this research is the transition from a deterministic GIM formulation to a stochastic differential equation (SDE) framework, which allows the model to represent the probabilistic range of physiological responses and improves uncertainty management when working with real-world data. The findings reveal that this hybrid methodology enhances both the precision and applicability of glucose predictions by integrating the physiological insights of Glucose Interaction Models (GIM) with the flexibility of data-driven machine learning techniques to accommodate real-world variability. This innovative framework facilitates the creation of robust, transparent, and personalized decision-support systems aimed at improving diabetes management. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
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14 pages, 1027 KB  
Article
A Hybrid Steffensen–Genetic Algorithm for Finding Multi-Roots of Nonlinear Equations and Applications to Biomedical Engineering
by Fiza Zafar, Alicia Cordero, Sadia Mujtaba and Juan R. Torregrosa
Algorithms 2025, 18(9), 582; https://doi.org/10.3390/a18090582 - 13 Sep 2025
Viewed by 471
Abstract
A new hybrid of a Steffensen-type method and genetic algorithm is developed for the efficient simultaneous computation of roots of nonlinear equations, particularly in all cases involving non-differentiable functions and multiple roots. Traditional numerical methods often fail to handle these complexities effectively, highlighting [...] Read more.
A new hybrid of a Steffensen-type method and genetic algorithm is developed for the efficient simultaneous computation of roots of nonlinear equations, particularly in all cases involving non-differentiable functions and multiple roots. Traditional numerical methods often fail to handle these complexities effectively, highlighting the need for a more robust solution. The proposed algorithm combines the global search strength of the genetic algorithm (GA) with the local refinement capabilities of a derivative-free optimal fourth-order Steffensen method. This integration enhances both exploration and exploitation capabilities, leading to improved convergence and computational accuracy. By uniting the GA’s global optimization with the local refinement of iterative solvers, the algorithm forms a higher-order framework capable of locating all roots concurrently. This study validates the performance of this hybrid strategy through diverse applications in biomedical engineering problems. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
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27 pages, 6213 KB  
Article
Mathematical Modelling and Numerical Analysis of Turbulence Models (In a Two-Stage Laboratory Turbine)
by Vesna Antoska Knights, Tatjana Atanasova-Pacemska and Jasenka Gajdoš Kljusurić
Algorithms 2025, 18(9), 578; https://doi.org/10.3390/a18090578 - 13 Sep 2025
Viewed by 477
Abstract
This paper presents a mathematical modeling and numerical analysis of fluid-thermal processes in a two-stage steam turbine cascade, focusing on the application and comparative assessment of turbulence models in computational fluid dynamics (CFD) simulations. Using the finite volume method implemented in the ANSYS [...] Read more.
This paper presents a mathematical modeling and numerical analysis of fluid-thermal processes in a two-stage steam turbine cascade, focusing on the application and comparative assessment of turbulence models in computational fluid dynamics (CFD) simulations. Using the finite volume method implemented in the ANSYS CFX-Task Flow (ANSYS CFX 2022 R2) workflow, the study investigates the performance of standard k-ε, k-ω, and SST turbulence models in predicting flow structures, pressure fields, and velocity distributions within the turbine flow passages. The governing equations, including the Reynolds-Averaged Navier–Stokes (RANS) equations and associated energy and constitutive relations, are solved in conservative form under compressible flow conditions. Experimental data from turbine tests performed at the Institute of Fluid Machinery at Lodz University of Technology are used for validation. Results demonstrate that turbulence modeling significantly influences the accuracy of predicted flow phenomena. The study identifies strengths and limitations of the models in capturing complex three-dimensional flow structures and provides quantitative error margins and practical guidance for their application in industrial turbine flow simulations. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
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28 pages, 16152 KB  
Article
A Smooth-Delayed Phase-Type Mixture Model for Human-Driven Process Duration Modeling
by Dongwei Wang, Sally McClean, Lingkai Yang, Ian McChesney and Zeeshan Tariq
Algorithms 2025, 18(9), 575; https://doi.org/10.3390/a18090575 - 11 Sep 2025
Viewed by 354
Abstract
Activities in business processes primarily depend on human behavior for completion. Due to human agency, the behavior underlying individual activities may occur in multiple phases and can vary in execution. As a result, the execution duration and nature of such activities may exhibit [...] Read more.
Activities in business processes primarily depend on human behavior for completion. Due to human agency, the behavior underlying individual activities may occur in multiple phases and can vary in execution. As a result, the execution duration and nature of such activities may exhibit complex multimodal characteristics. Phase-type distributions are useful for analyzing the underlying behavioral structure, which may consist of multiple sub-activities. The phenomenon of delayed start is also common in such activities, possibly due to the minimum task completion time or prerequisite tasks. As a result, the distribution of durations or certain components does not start at zero but has a minimum value, and the probability below this value is zero. When using phase-type models to fit such distributions, a large number of phases are often required, which exceed the actual number of sub-activities. This reduces the interpretability of the parameters and may also lead to optimization difficulties due to overparameterization. In this paper, we propose a smooth-delayed phase-type mixture model that introduces delay parameters to address the difficulty of fitting this kind of distribution. Since durations shorter than the delay should have zero probability, such hard truncation renders the parameter not estimable under the Expectation–Maximization (EM) framework. To overcome this, we design a soft-truncation mechanism to improve model convergence. We further develop an inference framework that combines the EM algorithm, Bayesian inference, and Sequential Least Squares Programming for comprehensive and efficient parameter estimation. The method is validated on a synthetic dataset and two real-world datasets. Results demonstrate that the proposed approach maintains a suitable performance comparable to purely data-driven methods while providing good interpretability to reveal the potential underlying structure behind human-driven activities. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
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11 pages, 474 KB  
Article
Secant-Type Iterative Classes for Nonlinear Equations with Multiple Roots
by Francisco I. Chicharro, Neus Garrido-Saez and Julissa H. Jerezano
Algorithms 2025, 18(9), 568; https://doi.org/10.3390/a18090568 - 9 Sep 2025
Viewed by 395
Abstract
General-purpose iterative methods for solving nonlinear equations provide approximations to solving problems without closed-form solutions. However, these methods lose some properties when the problems have multiple roots or are not differentiable, in which case specific methods are used. However, in most problems the [...] Read more.
General-purpose iterative methods for solving nonlinear equations provide approximations to solving problems without closed-form solutions. However, these methods lose some properties when the problems have multiple roots or are not differentiable, in which case specific methods are used. However, in most problems the multiplicity of the root is unknown, which reduces the range of methods available to us. In this work we propose two iterative classes with memory for solving multiple-root nonlinear equations without knowing the multiplicity. One of the proposals includes derivatives, but the other is derivative-free, obtained from the previous one using divided differences and a parameter in its iterative expression. The order of convergence of the proposed schemes is analyzed. The stability of the methods is studied using real dynamics, showing the good behavior of the methods. A numerical benchmark confirms the theoretical study. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
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12 pages, 1451 KB  
Article
Machine Learning Models for Predicting Postoperative Complications and Hospitalization After Percutaneous Nephrolithotomy
by Laura Shalabayeva, Pilar Bahílo Mateu, Marc Romeu Ferras, Javier Díaz-Carnicero, Alberto Budía and David Vivas-Consuelo
Algorithms 2025, 18(9), 558; https://doi.org/10.3390/a18090558 - 4 Sep 2025
Viewed by 681
Abstract
PCNL treatment is often associated with complications of hemorrhagic or infectious origin, which can result in prolonged hospitalization. This study aims to develop predictive models using machine learning (ML) techniques to anticipate these outcomes. Multiple ML algorithms—including Logistic Regression, Decision Tree, Random Forest, [...] Read more.
PCNL treatment is often associated with complications of hemorrhagic or infectious origin, which can result in prolonged hospitalization. This study aims to develop predictive models using machine learning (ML) techniques to anticipate these outcomes. Multiple ML algorithms—including Logistic Regression, Decision Tree, Random Forest, and Extreme Gradient Boosting—were evaluated on separate validation and test datasets. The Random Forest model achieved the highest predictive performance for hospitalization need (AUC 0.726/0.736) and infectious complications (AUC 0.799/0.735). Threshold adjustment was applied to increase sensitivity, reducing false negatives. The interpretability of the models was ensured through SHAP analysis, identifying clinically meaningful variables. Risk factors for both hospitalization and infectious complications models included nephrostomy drainage, a neutrophils percentage higher than 80, Guy’s score of grade 4, leukocytes level higher than 15 or lower than 4.5, and balloon dilation, while protective features included tubeless intervention, easy localization of a stone, negative culture, and microorganism results. However, no model achieved acceptable performance for predicting hemorrhagic complications, likely due to limited data. These results suggest that AI-based models can contribute to risk stratification after PCNL. Further experiments with larger, multi-center datasets are needed to confirm these findings and improve the generalizability of the models. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
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21 pages, 1814 KB  
Article
Data-Driven Prior Construction in Hilbert Spaces for Bayesian Optimization
by Carol Santos Almonte, Oscar Sanchez Jimenez, Eduardo Souza de Cursi and Emmanuel Pagnacco
Algorithms 2025, 18(9), 557; https://doi.org/10.3390/a18090557 - 3 Sep 2025
Viewed by 801
Abstract
We propose a variant of Bayesian optimization in which probability distributions are constructed using uncertainty quantification (UQ) techniques. In this context, UQ techniques rely on a Hilbert basis expansion to infer probability distributions from limited experimental data. These distributions act as prior knowledge [...] Read more.
We propose a variant of Bayesian optimization in which probability distributions are constructed using uncertainty quantification (UQ) techniques. In this context, UQ techniques rely on a Hilbert basis expansion to infer probability distributions from limited experimental data. These distributions act as prior knowledge of the search space and are incorporated into the acquisition function to guide the selection of enrichment points more effectively. Several variants of the method are examined, depending on the distribution type (normal, log-normal, etc.), and benchmarked against traditional Bayesian optimization on test functions. The results show competitive performance, with selective improvements depending on the problem structure, and faster convergence in specific cases. As a practical application, we address a structural shape optimization problem. The initial geometry is an L-shaped plate, where the goal is to minimize the volume under a horizontal displacement constraint expressed as a penalty. Our approach first identifies a promising region while efficiently training the surrogate model. A subsequent gradient-based optimization step then refines the design using the trained surrogate, achieving a volume reduction of more than 30% while satisfying the displacement constraint, without requiring any additional evaluations of the objective function. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
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16 pages, 1007 KB  
Article
Learning SMILES Semantics: Word2Vec and Transformer Embeddings for Molecular Property Prediction
by Saya Hashemian, Zak Khan, Pulkit Kalhan and Yang Liu
Algorithms 2025, 18(9), 547; https://doi.org/10.3390/a18090547 - 1 Sep 2025
Viewed by 776
Abstract
This paper investigates the effectiveness of Word2Vec-based molecular representation learning on SMILES (Simplified Molecular Input Line Entry System) strings for a downstream prediction task related to the market approvability of chemical compounds. Here, market approvability is treated as a proxy classification label derived [...] Read more.
This paper investigates the effectiveness of Word2Vec-based molecular representation learning on SMILES (Simplified Molecular Input Line Entry System) strings for a downstream prediction task related to the market approvability of chemical compounds. Here, market approvability is treated as a proxy classification label derived from approval status, where only the molecular structure is analyzed. We train character-level embeddings using Continuous Bag of Words (CBOW) and Skip-Gram with Negative Sampling architectures and apply the resulting embeddings in a downstream classification task using a multi-layer perceptron (MLP). To evaluate the utility of these lightweight embedding techniques, we conduct experiments on a curated SMILES dataset labeled by approval status under both imbalanced and SMOTE-balanced training conditions. In addition to our Word2Vec-based models, we include a ChemBERTa-based baseline using the pretrained ChemBERTa-77M model. Our findings show that while ChemBERTa achieves a higher performance, the Word2Vec-based models offer a favorable trade-off between accuracy and computational efficiency. This efficiency is especially relevant in large-scale compound screening, where rapid exploration of the chemical space can support early-stage cheminformatics workflows. These results suggest that traditional embedding models can serve as viable alternatives for scalable and interpretable cheminformatics pipelines, particularly in resource-constrained environments. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
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21 pages, 914 KB  
Article
Modeling How the Different Parts of the Immune System Fight Viruses
by Benito Chen-Charpentier
Algorithms 2025, 18(9), 544; https://doi.org/10.3390/a18090544 - 29 Aug 2025
Viewed by 491
Abstract
Viruses cause a large number of diseases. After penetrating into a host, the virus starts infecting healthy cells. Then it uses the RNA or DNA of the cell to replicate and afterward it explodes the infected cell, letting out many copies of the [...] Read more.
Viruses cause a large number of diseases. After penetrating into a host, the virus starts infecting healthy cells. Then it uses the RNA or DNA of the cell to replicate and afterward it explodes the infected cell, letting out many copies of the virus that can infect new cells. The innate and adaptive parts of the immune system defend the body by eliminating both the free viruses and the infected cells. Neutrophils, macrophages, natural killer cells, helper T cells (CD4+) and cytotoxic T lymphocytes (CD8+) are among the participating immune cells. The interactions are complex and not fully understood. In this paper, we present and study three mathematical models based on ordinary differential equations of virus and immune system interactions with different complexities, and also introduce possible treatments. We discuss the advantages and disadvantages of each model. We do global sensitivity analysis and numerical simulations. Finally, we present conclusions including comments about the complexity of mathematical models. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
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20 pages, 2367 KB  
Article
Hybrid Machine Learning Model for Blast-Induced Peak Particle Velocity Estimation in Surface Mining: Application of Sparrow Search Algorithm in ANN Optimization
by Kesalopa Gaopale, Takashi Sasaoka, Akihiro Hamanaka and Hideki Shimada
Algorithms 2025, 18(9), 543; https://doi.org/10.3390/a18090543 - 27 Aug 2025
Viewed by 627
Abstract
Blast-induced ground vibrations present substantial safety and environmental hazards in surface mining operations. This study proposes and evaluates the Sparrow Search Algorithm-optimized ANN (SSA-ANN) against artificial neural network (ANN), Genetic Algorithm-optimized ANN (GA-ANN), and empirical formula (USBM) to estimate peak particle velocity (PPV). [...] Read more.
Blast-induced ground vibrations present substantial safety and environmental hazards in surface mining operations. This study proposes and evaluates the Sparrow Search Algorithm-optimized ANN (SSA-ANN) against artificial neural network (ANN), Genetic Algorithm-optimized ANN (GA-ANN), and empirical formula (USBM) to estimate peak particle velocity (PPV). In addition, the input parameters include key blasting design parameters and rock mass features (GSI and UCS). The SSA-ANN demonstrated superior prediction accuracy, attaining an average R2 of 0.51 using bootstrap validation, surpassing GA-ANN (0.41) and standard ANN (0.26). Furthermore, the incorporation of GSI enhanced the model’s geotechnical sensitivity. These results illustrate that the application of SSA-ANN alongside comprehensive rock mass characteristics can substantially decrease uncertainty in PPV prediction, therefore enhancing safety within the blast area and improving vibration control methods in blasting operations. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
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19 pages, 650 KB  
Article
Algorithmic Efficiency Analysis in Innovation-Driven Labor Markets: A Super-SBM and Malmquist Productivity Index Approach
by Chia-Nan Wang and Giovanni Cahilig
Algorithms 2025, 18(8), 518; https://doi.org/10.3390/a18080518 - 15 Aug 2025
Viewed by 892
Abstract
Innovation-driven labor markets play a pivotal role in economic development, yet significant disparities exist in how efficiently countries transform innovation inputs into labor market outcomes. This study addresses the critical gap in benchmarking multi-stage innovation efficiency by developing an integrated framework combining Data [...] Read more.
Innovation-driven labor markets play a pivotal role in economic development, yet significant disparities exist in how efficiently countries transform innovation inputs into labor market outcomes. This study addresses the critical gap in benchmarking multi-stage innovation efficiency by developing an integrated framework combining Data Envelopment Analysis (DEA) Super Slack-Based Measure (Super-SBM) for static efficiency evaluation and the Malmquist Productivity Index (MPI) for dynamic productivity decomposition, enhanced with cooperative game theory for robustness testing. Focusing on the top 20 innovative economies over a 5-year period, we analyze key inputs (Innovation Index, GDP, trade openness) and outputs (labor force, unemployment rates), revealing stark efficiency contrasts: China, Luxembourg, and the U.S. demonstrate optimal performance (mean scores > 1.9), while Singapore and the Netherlands show significant underutilization (scores < 0.4). Our results identify a critical productivity shift period (average MPI = 1.325) driven primarily by technological advancements. This study contributes a replicable, data-driven model for cross-domain efficiency assessment and provides empirical evidence for policymakers to optimize innovation-labor market conversion. The methodological framework offers scalable applications for future research in computational economics and productivity analysis. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
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9 pages, 354 KB  
Communication
Algorithm Providing Ordered Integer Sequences for Sampling with Replacement Confidence Intervals
by Lorentz Jäntschi
Algorithms 2025, 18(8), 459; https://doi.org/10.3390/a18080459 - 24 Jul 2025
Viewed by 490
Abstract
Sampling with replacement occurs when drawing without removing individuals from finite populations. It is a common distribution technique used in physics, biology, and medicine. It is used in state analysis of qubits, the physics of particle interactions, studies of genetic variation and variability, [...] Read more.
Sampling with replacement occurs when drawing without removing individuals from finite populations. It is a common distribution technique used in physics, biology, and medicine. It is used in state analysis of qubits, the physics of particle interactions, studies of genetic variation and variability, and analyzing the treatment effects from clinical trial analyses. When applied, sample statistics should be accompanied by confidence intervals. The major difficulty in expressing the confidence intervals in sampling with replacement consists of discreetness regarding the probability distribution. As a result, no mathematical formula can handle an optimum solution. Using a simple algorithm is proposed in order to obtain confidence intervals for sampling with replacement variables (x from m trials with replacement) and their proportion (x/m). A question-based discussion is presented. Traditional confidence intervals often require large sample sizes. Confidence intervals, constructed in a deterministic way provided by the proposed algorithm for sampling with replacement, allow constructing intervals without constraints. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
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23 pages, 1473 KB  
Article
Integrating Inferential Statistics and Systems Dynamics: A Study of Short-Term Happiness Evolution in Response to a Dose of Alcohol and Caffeine
by Salvador Amigó, Antonio Caselles, Joan C. Micó and Pantaleón D. Romero
Algorithms 2025, 18(7), 447; https://doi.org/10.3390/a18070447 - 21 Jul 2025
Viewed by 461
Abstract
This paper compares two methods, inferential statistics and Systems Dynamics, to study the evolution of individual happiness after a single dose of drug consumption. In an application case, the effect of alcohol and caffeine on happiness is analyzed through a single-case experimental design, [...] Read more.
This paper compares two methods, inferential statistics and Systems Dynamics, to study the evolution of individual happiness after a single dose of drug consumption. In an application case, the effect of alcohol and caffeine on happiness is analyzed through a single-case experimental design, with replication, involving two participants. Both inferential statistical analysis and Systems Dynamics methods have been used to analyze the results. Two scales were used to measure happiness—the Euphoria Scale (ES) and the Smiling Face Scale (SFS)—in trait and state format. A single-case experimental ABC design was used. Phase A had no treatment, and Phases B and C saw both subjects receiving 26.51 mL of alcohol and 330 mg of caffeine, respectively. The participants filled in a form with both scales in a state format every 10 min over a 3 h period, operating in each one of the three phases A, B and C. The main conclusion of the analysis performed is that both methods provide similar results about the evolution of individual happiness after single dose consumption. Therefore, the article shows that inferential statistics and the stimulus response model derived from the Systems Dynamics approach can be used in a complementary and enriching way to obtain prediction results. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
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20 pages, 359 KB  
Article
Iterative Matrix Techniques Based on Averages
by María A. Navascués
Algorithms 2025, 18(7), 439; https://doi.org/10.3390/a18070439 - 17 Jul 2025
Viewed by 384
Abstract
Matrices have an important role in modern engineering problems like artificial intelligence, biomedicine, machine learning, etc. The present paper proposes new algorithms to solve linear problems involving finite matrices as well as operators in infinite dimensions. It is well known that the power [...] Read more.
Matrices have an important role in modern engineering problems like artificial intelligence, biomedicine, machine learning, etc. The present paper proposes new algorithms to solve linear problems involving finite matrices as well as operators in infinite dimensions. It is well known that the power method to find an eigenvalue and an eigenvector of a matrix requires the existence of a dominant eigenvalue. This article proposes an iterative method to find eigenvalues of matrices without a dominant eigenvalue. This algorithm is based on a procedure involving averages of the mapping and the independent variable. The second contribution is the computation of an eigenvector associated with a known eigenvalue of linear operators or matrices. Then, a novel numerical method for solving a linear system of equations is studied. The algorithm is especially suitable for cases where the iteration matrix has a norm equal to one or the standard iterative method based on fixed point approximation converges very slowly. These procedures are applied to the resolution of Fredholm integral equations of the first kind with an arbitrary kernel by means of orthogonal polynomials, and in a particular case where the kernel is separable. Regarding the latter case, this paper studies the properties of the associated Fredholm operator. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
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23 pages, 3338 KB  
Article
European Efficiency Schemes for Domestic Gas Boilers: Estimation of Savings in Heating of Settlements
by Dejan Brkić
Algorithms 2025, 18(7), 416; https://doi.org/10.3390/a18070416 - 6 Jul 2025
Cited by 1 | Viewed by 2719
Abstract
This article aims to evaluate the seasonal efficiency of natural gas boilers used in European households, highlighting the cost effectiveness, environmental benefits, and user comfort associated with higher-efficiency models, particularly those based on condensing technology. The study applies a standardized algorithm used in [...] Read more.
This article aims to evaluate the seasonal efficiency of natural gas boilers used in European households, highlighting the cost effectiveness, environmental benefits, and user comfort associated with higher-efficiency models, particularly those based on condensing technology. The study applies a standardized algorithm used in European energy labeling schemes to calculate the seasonal efficiency of household gas boilers. It further includes a comparative analysis of selected boiler models available on the Serbian market and outlines a step-by-step method for estimating gas savings when replacing older, less efficient boilers with modern units. Condensing boilers demonstrate significantly higher seasonal efficiency than standard models by recovering additional heat from exhaust gases. These improved boilers produce lower greenhouse gas emissions and offer annual fuel savings of approximately 10% to 30%, depending on the boiler’s age, system design, and usage patterns. The results also confirm the direct correlation between seasonal efficiency and annual fuel consumption, validating the use of efficiency-based cost comparisons. The analysis focuses on residential gas boilers available in the Serbian market, although the models examined are commonly distributed across Europe. The findings highlight the important role of energy efficiency labels—based on a standardized algorithm—in guiding boiler selection, helping consumers and policymakers make informed decisions that promote energy savings and reduce environmental impact. This article contributes to the theoretical and practical understanding of gas boiler efficiency by integrating algorithm-based evaluation with market data and user-centered considerations. It offers actionable insights for consumers, energy advisors, and policymakers in the context of Europe’s energy transition. Verifying the efficiency calculations of gas boilers requires a careful combination of theoretical methods, measured data, and adherence to standards. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
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23 pages, 676 KB  
Article
Numerical and Theoretical Treatments of the Optimal Control Model for the Interaction Between Diabetes and Tuberculosis
by Saburi Rasheed, Olaniyi S. Iyiola, Segun I. Oke and Bruce A. Wade
Algorithms 2025, 18(6), 348; https://doi.org/10.3390/a18060348 - 5 Jun 2025
Viewed by 1180
Abstract
We primarily focus on the formulation, theoretical, and numerical analyses of a non-autonomous model for tuberculosis (TB) prevention and control programs in a population where individuals suffering from the double trouble of tuberculosis and diabetes are present. The model incorporates four time-dependent control [...] Read more.
We primarily focus on the formulation, theoretical, and numerical analyses of a non-autonomous model for tuberculosis (TB) prevention and control programs in a population where individuals suffering from the double trouble of tuberculosis and diabetes are present. The model incorporates four time-dependent control functions, saturated treatment of non-infectious individuals harboring tuberculosis, and saturated incidence rate. Furthermore, the basic reproduction number of the autonomous form of the proposed optimal control mathematical model is calculated. Sensitivity indexes regarding the constant control parameters reveal that the proposed control and preventive measures will reduce the tuberculosis burden in the population. This study establishes that the combination of campaigns that teach people how the development of tuberculosis and diabetes can be prevented, a treatment strategy that provides saturated treatment to non-infectious individuals exposed to tuberculosis infections, and prompt effective treatment of individuals infected with tuberculosis disease is the optimal strategy to achieve zero TB by 2035. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
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14 pages, 698 KB  
Article
Inferring the Timing of Antiretroviral Therapy by Zero-Inflated Random Change Point Models Using Longitudinal Data Subject to Left-Censoring
by Hongbin Zhang, McKaylee Robertson, Sarah L. Braunstein, David B. Hanna, Uriel R. Felsen, Levi Waldron and Denis Nash
Algorithms 2025, 18(6), 346; https://doi.org/10.3390/a18060346 - 5 Jun 2025
Viewed by 932
Abstract
We propose a new random change point model that utilizes routinely recorded individual-level HIV viral load data to estimate the timing of antiretroviral therapy (ART) initiation in people living with HIV. The change point distribution is assumed to follow a zero-inflated exponential distribution [...] Read more.
We propose a new random change point model that utilizes routinely recorded individual-level HIV viral load data to estimate the timing of antiretroviral therapy (ART) initiation in people living with HIV. The change point distribution is assumed to follow a zero-inflated exponential distribution for the longitudinal data, which is also subject to left-censoring, and the underlying data-generating mechanism is a nonlinear mixed-effects model. We extend the Stochastic EM (StEM) algorithm by combining a Gibbs sampler with a Metropolis–Hastings sampling. We apply the method to real HIV data to infer the timing of ART initiation since diagnosis. Additionally, we conduct simulation studies to assess the performance of our proposed method. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
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18 pages, 934 KB  
Article
Optimization of PFMEA Team Composition in the Automotive Industry Using the IPF-RADAR Approach
by Nikola Komatina and Dragan Marinković
Algorithms 2025, 18(6), 342; https://doi.org/10.3390/a18060342 - 4 Jun 2025
Cited by 4 | Viewed by 1064
Abstract
In the automotive industry, the implementation of Process Failure Mode and Effect Analysis (PFMEA) is conducted by a PFMEA team comprising employees who are connected to the production process or a specific product. Core PFMEA team members are actively engaged in PFMEA execution [...] Read more.
In the automotive industry, the implementation of Process Failure Mode and Effect Analysis (PFMEA) is conducted by a PFMEA team comprising employees who are connected to the production process or a specific product. Core PFMEA team members are actively engaged in PFMEA execution through meetings, analysis, and the implementation of corrective actions. Although the current handbook provides guidelines on the potential composition of the PFMEA team, it does not strictly define its members, allowing companies the flexibility to determine the team structure independently. This study aims to identify the core PFMEA team members by adhering to criteria based on the recommended knowledge and competencies outlined in the current handbook. By applying the RAnking based on the Distances and Range (RADAR) approach, extended with Interval-Valued Pythagorean Fuzzy Numbers (IVPFNs), a ranking of potential candidates was conducted. A case study was performed in a Tier-1 supplier company within the automotive supply chain. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
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22 pages, 8623 KB  
Article
Polarization in Political Rallies: A Markovian Agent-Based Model for Opinion Dynamics
by Marco Scarpa, Marco Garofalo, Francesco Longo and Salvatore Serrano
Algorithms 2025, 18(6), 308; https://doi.org/10.3390/a18060308 - 23 May 2025
Viewed by 762
Abstract
One of the most studied problems among researchers in recent years is how individuals form their opinions. This problem has become more urgent with the advent of social networks, which can easily influence a huge number of followers and have become increasingly pervasive [...] Read more.
One of the most studied problems among researchers in recent years is how individuals form their opinions. This problem has become more urgent with the advent of social networks, which can easily influence a huge number of followers and have become increasingly pervasive over time. The produced effect is the rise of polarized opinions among different groups of people. Understanding polarization is of great relevance across various application domains, such as economics and politics. Opinion dynamics has often been studied by exploiting the popular Friedkin–Johnsen model. In this paper, we propose a different modeling approach based on the Markovian agents paradigm for deriving metrics characterizing polarized opinions. The main goal of this work is to demonstrate the potential of the Markovian agent modeling paradigm for the analysis of opinion dynamics. The main advantages of Markovian agents are the ease of setting a large number of behavioral parameters, spatial distribution of agents, scalability, and numerical tractability. We extend our previous work, in which we analyzed a peer assembly and validated it against other commonly used modeling approaches. In our opinion, the Markovian agent approach offers an effective modeling framework due to its scalability and flexibility in handling parameters that describe the behavior of individuals in the opinion formation process. The context we will discuss is inspired by election rallies, where an assembly attends a speech by a political candidate. The crowd consists of individuals with diverse initial political opinions, and the candidate seeks to polarize them toward his/her own political stance. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
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22 pages, 1552 KB  
Article
A Regret-Enhanced DEA Approach to Mapping Renewable Energy Efficiency in Asia’s Growth Economies
by Chia-Nan Wang, Nhat-Luong Nhieu and Yu-Cin Ye
Algorithms 2025, 18(5), 297; https://doi.org/10.3390/a18050297 - 20 May 2025
Viewed by 808
Abstract
Renewable energy (RE) is pivotal to achieving both environmental sustainability and long-term energy security, yet systematic evidence on the efficiency of RE investment across South and Southeast Asia remains sparse. This study introduces a rejoice–regret utility cross-efficiency DEA (RRUCE-DEA) framework that fuses conventional [...] Read more.
Renewable energy (RE) is pivotal to achieving both environmental sustainability and long-term energy security, yet systematic evidence on the efficiency of RE investment across South and Southeast Asia remains sparse. This study introduces a rejoice–regret utility cross-efficiency DEA (RRUCE-DEA) framework that fuses conventional quantitative efficiency measurement with the behavioral insights of regret theory. Applying the model to 16 countries shows India as the benchmark for efficient RE investment allocation, followed closely by Pakistan and Indonesia. The Philippines, Malaysia, and Vietnam also post strong results, whereas Sri Lanka and Thailand reveal moderate performance with clear room for improvement. At the lower end of the spectrum, Cambodia, Myanmar, and Afghanistan encounter significant hurdles that must be overcome to achieve a successful clean energy transition. A sensitivity analysis further explores how variations in the regret aversion and rejoice–regret coefficients affect the RRUCE-DEA outcomes. The findings provide actionable guidance for policymakers and investors seeking to channel resources toward a cleaner, more sustainable regional energy portfolio. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
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25 pages, 339 KB  
Article
Existence and Mittag–Leffler Stability for the Solution of a Fuzzy Fractional System with Application of Laplace Transforms to Solve Fractional Differential Systems
by Mohammad Saeid Abolhassanifar, Reza Saadati, Mohammad Bagher Ghaemi and Donal O’Regan
Algorithms 2025, 18(5), 264; https://doi.org/10.3390/a18050264 - 3 May 2025
Viewed by 593
Abstract
This study explores the existence and Mittag–Leffler stability of solutions for fuzzy fractional systems that include Caputo derivatives and ordinary derivatives with non-local conditions using the Schauder fixed-point theorem. Following this, we employ the Laplace transform method and numerical techniques to create iterative [...] Read more.
This study explores the existence and Mittag–Leffler stability of solutions for fuzzy fractional systems that include Caputo derivatives and ordinary derivatives with non-local conditions using the Schauder fixed-point theorem. Following this, we employ the Laplace transform method and numerical techniques to create iterative methods for obtaining exact and approximate solutions. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
31 pages, 9472 KB  
Article
Mathematics-Driven Analysis of Offshore Green Hydrogen Stations
by Álvaro García-Ruiz, Pablo Fernández-Arias and Diego Vergara
Algorithms 2025, 18(4), 237; https://doi.org/10.3390/a18040237 - 21 Apr 2025
Viewed by 1003
Abstract
Renewable energy technologies have become an increasingly important component of the global energy supply. In recent years, photovoltaic and wind energy have been the fastest-growing renewable sources. Although oceans present harsh environments, their estimated energy generation potential is among the highest. Ocean-based solutions [...] Read more.
Renewable energy technologies have become an increasingly important component of the global energy supply. In recent years, photovoltaic and wind energy have been the fastest-growing renewable sources. Although oceans present harsh environments, their estimated energy generation potential is among the highest. Ocean-based solutions are gaining significant momentum, driven by the advancement of offshore wind, floating solar, tidal, and wave energy, among others. The integration of various marine energy sources with green hydrogen production can facilitate the exploitation and transportation of renewable energy. This paper presents a mathematics-driven analysis for the simulation of a technical model designed as a generic framework applicable to any location worldwide and developed to analyze the integration of solar energy generation and green hydrogen production. It evaluates the impact of key factors such as solar irradiance, atmospheric conditions, water surface flatness, as well as the parameters of photovoltaic panels, electrolyzers, and adiabatic compressors, on both energy generation and hydrogen production capacity. The proposed mathematics-based framework serves as an innovative tool for conducting multivariable parametric analyses, selecting optimal design configurations based on specific solar energy and/or hydrogen production requirements, and performing a range of additional assessments including, but not limited to, risk evaluations, cause–effect analyses, and/or degradation studies. Enhancing the efficiency of solar energy generation and hydrogen production processes can reduce the required photovoltaic surface area, thereby simplifying structural and anchoring requirements and lowering associated costs. Simpler, more reliable, and cost-effective designs will foster the expansion of floating solar energy and green hydrogen production in marine environments. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
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18 pages, 974 KB  
Article
On the Q-Convergence and Dynamics of a Modified Weierstrass Method for the Simultaneous Extraction of Polynomial Zeros
by Plamena I. Marcheva, Ivan K. Ivanov and Stoil I. Ivanov
Algorithms 2025, 18(4), 205; https://doi.org/10.3390/a18040205 - 5 Apr 2025
Cited by 1 | Viewed by 673
Abstract
In the present paper, we prove a new local convergence theorem with initial conditions and error estimates that ensure the Q-quadratic convergence of a modification of the famous Weierstrass method. Afterward, we prove a semilocal convergence theorem that is of great practical importance [...] Read more.
In the present paper, we prove a new local convergence theorem with initial conditions and error estimates that ensure the Q-quadratic convergence of a modification of the famous Weierstrass method. Afterward, we prove a semilocal convergence theorem that is of great practical importance owing to its computable initial condition. The obtained theorems improve and complement all existing such kind of convergence results about this method. At the end of the paper, we provide three numerical examples to show the applicability of our semilocal theorem to some physics problems. Within the examples, we propose a new algorithm for the experimental study of the dynamics of the simultaneous methods and compare the convergence and dynamical behaviors of the modified and the classical Weierstrass methods. Full article
(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))
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