Mathematical and Computational Applications

16 pages, 40466 KiB

Open AccessArticle

Hybrid Neural Network Approach with Physical Constraints for Predicting the Potential Occupancy Set of Surrounding Vehicles

by Bin Sun, Shichun Yang, Jiayi Lu, Yu Wang, Xinjie Feng and Yaoguang Cao

Math. Comput. Appl. 2025, 30(3), 56; https://doi.org/10.3390/mca30030056 - 15 May 2025

Abstract

The reliable and uncertainty-aware prediction of surrounding vehicles remains a key challenge in autonomous driving. However, existing methods often struggle to quantify and incorporate uncertainty effectively. To address these challenges, we propose a hybrid architecture that combines a data-driven neural trajectory predictor with [...] Read more.

The reliable and uncertainty-aware prediction of surrounding vehicles remains a key challenge in autonomous driving. However, existing methods often struggle to quantify and incorporate uncertainty effectively. To address these challenges, we propose a hybrid architecture that combines a data-driven neural trajectory predictor with physically grounded constraints to forecast future vehicle occupancy. Specifically, the physical constraints are derived from vehicle kinematic principles and embedded into the network as additional loss terms during training. This integration ensures that predicted trajectories conform to feasible and physically realistic motion boundaries. Furthermore, a mixture density network (MDN) is employed to estimate predictive uncertainty, transforming deterministic trajectory predictions into spatial probability distributions. This enables a probabilistic occupancy representation, offering a richer and more informative description of the potential future positions of surrounding vehicles. The proposed model is trained and evaluated on the Aerial Dataset for China’s Congested Highways and Expressways (AD4CHE), which contains representative driving scenarios in China. Experimental results demonstrate that the model achieves strong fitting performance while maintaining high physical plausibility in its predictions. Full article

► Show Figures

Figure 1

28 pages, 7329 KiB

Open AccessArticle

Causal Diagnosability Optimization Design for UAVs Based on Maximum Mean Covariance Difference and the Gray Wolf Optimization Algorithm

by Xuping Gu and Xianjun Shi

Math. Comput. Appl. 2025, 30(3), 55; https://doi.org/10.3390/mca30030055 - 14 May 2025

Abstract

Given the growing complexity and variability of application scenarios, coupled with increasing operational demands, unmanned aerial vehicles (UAVs) are prone to faults. To enhance diagnosability and reliability in this context, this study proposes a causal diagnosability optimization strategy based on the Maximum Mean [...] Read more.

Given the growing complexity and variability of application scenarios, coupled with increasing operational demands, unmanned aerial vehicles (UAVs) are prone to faults. To enhance diagnosability and reliability in this context, this study proposes a causal diagnosability optimization strategy based on the Maximum Mean and Covariance Discrepancy (MMCD) metric and the Grey Wolf Optimization (GWO) algorithm. First, a qualitative assessment method for causal diagnosability is introduced, leveraging structural analysis to evaluate the detectability and isolability of faults. Next, residuals are generated using Minimal Structurally Overdetermined (MSO) sets, and a quantitative diagnosability assessment framework is developed based on the MMCD metric. This framework measures the complexity of diagnosability through the analysis of residual deviations under fault conditions. Finally, a diagnosability optimization technique utilizing the GWO algorithm is proposed. This approach minimizes diagnostic system design costs while maximizing its performance. Simulation results for a UAV structural model demonstrate that the proposed strategy achieves a 100% fault detection rate and fault isolation rate while reducing design costs by 70.59%. Full article

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

► Show Figures

Figure 1

27 pages, 1842 KiB

Open AccessArticle

Penalty Strategies in Semiparametric Regression Models

by Ayuba Jack Alhassan, S. Ejaz Ahmed, Dursun Aydin and Ersin Yilmaz

Math. Comput. Appl. 2025, 30(3), 54; https://doi.org/10.3390/mca30030054 - 12 May 2025

Abstract

This study includes a comprehensive evaluation of six penalty estimation strategies for partially linear models (PLRMs), focusing on their performance in the presence of multicollinearity and their ability to handle both parametric and nonparametric components. The methods under consideration include Ridge regression, Lasso, [...] Read more.

This study includes a comprehensive evaluation of six penalty estimation strategies for partially linear models (PLRMs), focusing on their performance in the presence of multicollinearity and their ability to handle both parametric and nonparametric components. The methods under consideration include Ridge regression, Lasso, Adaptive Lasso (aLasso), smoothly clipped absolute deviation (SCAD), ElasticNet, and minimax concave penalty (MCP). In addition to these established methods, we also incorporate Stein-type shrinkage estimation techniques that are standard and positive shrinkage and assess their effectiveness in this context. To estimate the PLRMs, we consider a kernel smoothing technique grounded in penalized least squares. Our investigation involves a theoretical analysis of the estimators’ asymptotic properties and a detailed simulation study designed to compare their performance under a variety of conditions, including different sample sizes, numbers of predictors, and levels of multicollinearity. The simulation results reveal that aLasso and shrinkage estimators, particularly the positive shrinkage estimator, consistently outperform the other methods in terms of Mean Squared Error (MSE) relative efficiencies (RE), especially when the sample size is small and multicollinearity is high. Furthermore, we present a real data analysis using the Hitters dataset to demonstrate the applicability of these methods in a practical setting. The results of the real data analysis align with the simulation findings, highlighting the superior predictive accuracy of aLasso and the shrinkage estimators in the presence of multicollinearity. The findings of this study offer valuable insights into the strengths and limitations of these penalty and shrinkage strategies, guiding their application in future research and practice involving semiparametric regression. Full article

► Show Figures

Figure 1

35 pages, 3870 KiB

Open AccessArticle

Induction of Convolutional Decision Trees for Semantic Segmentation of Color Images Using Differential Evolution and Time and Memory Reduction Techniques

by Adriana-Laura López-Lobato, Héctor-Gabriel Acosta-Mesa and Efrén Mezura-Montes

Math. Comput. Appl. 2025, 30(3), 53; https://doi.org/10.3390/mca30030053 - 10 May 2025

Abstract

Convolutional Decision Trees (CDTs) are machine learning models utilized as interpretable methods for image segmentation. Their graphical structure enables a relatively simple interpretation of how the tree successively divides the image pixels into two classes, distinguishing between objects of interest and the image [...] Read more.

Convolutional Decision Trees (CDTs) are machine learning models utilized as interpretable methods for image segmentation. Their graphical structure enables a relatively simple interpretation of how the tree successively divides the image pixels into two classes, distinguishing between objects of interest and the image background. Several techniques have been proposed to induce CDTs. However, they have primarily been focused on analyzing grayscale images due to the computational cost of the Differential Evolution (DE) algorithm, which is employed in these techniques. This paper proposes a generalization of the induction process of a CDT with the DE algorithm using color images, implementing two techniques to reduce the computational time and memory employed in the induction process: the median selection technique and a memory of previously evaluated solutions. The first technique is applied to select a representative sample of pixels from an image for the model’s training process, and the second technique is implemented to reduce the number of evaluations in the fitness function considered in the DE process. The efficacy of these techniques was evaluated using the Weizmann Horse and DRIVE datasets, resulting in favorable outcomes in terms of the segmentation performance of the induced CDTs, and the processing time and memory required for the induction process. Full article

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

► Show Figures

Figure 1

15 pages, 296 KiB

Open AccessArticle

New Results on Gevrey Well Posedness for the Schrödinger–Korteweg–De Vries System

by Feriel Boudersa, Abdelaziz Mennouni and Ravi P. Agarwal

Math. Comput. Appl. 2025, 30(3), 52; https://doi.org/10.3390/mca30030052 - 7 May 2025

Abstract

In this work, we prove that the initial value problem for the Schrödinger–Korteweg–de Vries (SKdV) system is locally well posed in Gevrey spaces for

s > - \frac{3}{4}

and

k \geq 0

. This advancement extends recent findings regarding the well posedness [...] Read more.

In this work, we prove that the initial value problem for the Schrödinger–Korteweg–de Vries (SKdV) system is locally well posed in Gevrey spaces for

s > - \frac{3}{4}

and

k \geq 0

. This advancement extends recent findings regarding the well posedness of this model within Sobolev spaces and investigates the regularity properties of its solutions. Full article

13 pages, 210 KiB

Open AccessEditorial

Recent Advances and New Challenges in Coupled Systems and Networks: Theory, Modelling, and Applications (Special Issue in Honor of Professor Roderick Melnik)

by Sundeep Singh and Weizhong Dai

Math. Comput. Appl. 2025, 30(3), 51; https://doi.org/10.3390/mca30030051 - 7 May 2025

Abstract

Coupled systems and networks are ubiquitous across all branches of science and engineering, while mathematical and computational models play a fundamental role in their studies [...] Full article

(This article belongs to the Special Issue Recent Advances and New Challenges in Coupled Systems and Networks: Theory, Modelling, and Applications)

20 pages, 350 KiB

Open AccessArticle

A Family of Newton and Quasi-Newton Methods for Power Flow Analysis in Bipolar Direct Current Networks with Constant Power Loads

by Oscar Danilo Montoya, Juan Diego Pulgarín Rivera, Luis Fernando Grisales-Noreña, Walter Gil-González and Fabio Andrade-Rengifo

Math. Comput. Appl. 2025, 30(3), 50; https://doi.org/10.3390/mca30030050 - 6 May 2025

Abstract

This paper presents a comprehensive study on the formulation and solution of the power flow problem in bipolar direct current (DC) distribution networks with unbalanced constant power loads. Using the nodal voltage method, a unified nonlinear model is proposed which accurately captures both [...] Read more.

This paper presents a comprehensive study on the formulation and solution of the power flow problem in bipolar direct current (DC) distribution networks with unbalanced constant power loads. Using the nodal voltage method, a unified nonlinear model is proposed which accurately captures both monopolar and bipolar load configurations as well as the voltage coupling between conductors. The model assumes a solid grounding of the neutral conductor and known system parameters, ensuring reproducibility and physical consistency. Seven iterative algorithms are developed and compared, including three Newton–Raphson-based formulations and four quasi-Newton methods with constant Jacobian approximations. The proposed techniques are validated on two benchmark networks comprising 21 and 85 buses. Numerical results demonstrate that Newton-based methods exhibit quadratic convergence and high accuracy, while quasi-Newton approaches significantly reduce computational time, making them more suitable for large-scale systems. The findings highlight the trade-offs between convergence speed and computational efficiency, and they provide valuable insights for the planning and operation of modern bipolar DC grids. Full article

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

► Show Figures

Figure 1

22 pages, 3576 KiB

Open AccessArticle

A Deep Learning Approach to Unveil Types of Mental Illness by Analyzing Social Media Posts

by Rajashree Dash, Spandan Udgata, Rupesh K. Mohapatra, Vishanka Dash and Ashrita Das

Math. Comput. Appl. 2025, 30(3), 49; https://doi.org/10.3390/mca30030049 - 3 May 2025

Abstract

Mental illness has emerged as a widespread global health concern, often unnoticed and unspoken. In this era of digitization, social media has provided a prominent space for people to express their feelings and find solutions faster. Thus, this area of study with a [...] Read more.

Mental illness has emerged as a widespread global health concern, often unnoticed and unspoken. In this era of digitization, social media has provided a prominent space for people to express their feelings and find solutions faster. Thus, this area of study with a sheer amount of information, which refers to users’ behavioral attributes combined with the power of machine learning (ML), can be explored to make the entire diagnosis process smooth. In this study, an efficient ML model using Long Short-Term Memory (LSTM) is developed to determine the kind of mental illness a user may have using a random text made by the user on their social media. This study is based on natural language processing, where the prerequisites involve data collection from different social media sites and then pre-processing the collected data as per the requirements through stemming, lemmatization, stop word removal, etc. After examining the linguistic patterns of different social media posts, a reduced feature space is generated using appropriate feature engineering, which is further fed as input to the LSTM model to identify a type of mental illness. The performance of the proposed model is also compared with three other ML models, which includes using the full feature space and the reduced one. The optimal resulting model is selected by training and testing all of the models on the publicly available Reddit Mental Health Dataset. Overall, utilizing deep learning (DL) for mental health analysis can offer a promising avenue toward improved interventions, outcomes, and a better understanding of mental health issues at both the individual and population levels, aiding in decision-making processes. Full article

(This article belongs to the Section Engineering)

► Show Figures

Figure 1

31 pages, 4470 KiB

Open AccessArticle

RHADaMAnTe: An Astro Code to Estimate the Spectral Energy Distribution of a Curved Wall of a Gap Opened by a Forming Planet in a Protoplanetary Disk

by Francisco Rendón

Math. Comput. Appl. 2025, 30(3), 48; https://doi.org/10.3390/mca30030048 - 30 Apr 2025

Abstract

When a star is born, a protoplanetary disk made of gas and dust surrounds the star. The disk can show gaps opened by different astrophysical mechanisms. The gap has a wall emitting radiation, which contributes to the spectral energy distribution (SED) of the [...] Read more.

When a star is born, a protoplanetary disk made of gas and dust surrounds the star. The disk can show gaps opened by different astrophysical mechanisms. The gap has a wall emitting radiation, which contributes to the spectral energy distribution (SED) of the whole system (star, disk and planet) in the IR band. As these newborn stars are far away from us, it is difficult to know whether the gap is opened by a forming planet. I have developed RHADaMAnTe, a computational astro code based on the geometry of the wall of a gap coming from hydrodynamics 3D simulations of protoplanetary disks. With this code, it is possible to make models of disks to estimate the synthetic SEDs of the wall and prove whether the gap was opened by a forming planet. An implementation of this code was used to study the stellar system LkCa 15. It was found that a planet of 10 Jupiter masses is capable of opening a gap with a curved wall with a height of 12.9 AU. However, the synthetic SED does not fit to Spitzer IRS SED (

χ^{2}

∼4.5) from

5 μ

m to

35 μ

m. This implies that there is an optically thin region inside the gap. Full article

► Show Figures

Graphical abstract

18 pages, 4321 KiB

Open AccessArticle

Integrating Equation Coding with Residual Networks for Efficient ODE Approximation in Biological Research

by Ziyue Yi

Math. Comput. Appl. 2025, 30(3), 47; https://doi.org/10.3390/mca30030047 - 27 Apr 2025

Abstract

Biological research traditionally relies on experimental methods, which can be inefficient and hinder knowledge transfer due to redundant trial-and-error processes and difficulties in standardizing results. The complexity of biological systems, combined with large volumes of data, necessitates precise mathematical models like ordinary differential [...] Read more.

Biological research traditionally relies on experimental methods, which can be inefficient and hinder knowledge transfer due to redundant trial-and-error processes and difficulties in standardizing results. The complexity of biological systems, combined with large volumes of data, necessitates precise mathematical models like ordinary differential equations (ODEs) to describe interactions within these systems. However, the practical use of ODE-based models is limited by the need for curated data, making them less accessible for routine research. To overcome these challenges, we introduce LazyNet, a novel machine learning model that integrates logarithmic and exponential functions within a Residual Network (ResNet) to approximate ODEs. LazyNet reduces the complexity of mathematical operations, enabling faster model training with fewer data and lower computational costs. We evaluate LazyNet across several biological applications, including HIV dynamics, gene regulatory networks, and mass spectrometry analysis of small molecules. Our findings show that LazyNet effectively predicts complex biological phenomena, accelerating model development while reducing the need for extensive experimental data. This approach offers a promising advancement in computational biology, enhancing the efficiency and accuracy of biological research. Full article

► Show Figures

Figure 1

16 pages, 2341 KiB

Open AccessArticle

TAE Predict: An Ensemble Methodology for Multivariate Time Series Forecasting of Climate Variables in the Context of Climate Change

by Juan Frausto Solís, Erick Estrada-Patiño, Mirna Ponce Flores, Juan Paulo Sánchez-Hernández, Guadalupe Castilla-Valdez and Javier González-Barbosa

Math. Comput. Appl. 2025, 30(3), 46; https://doi.org/10.3390/mca30030046 - 25 Apr 2025

Abstract

Climate change presents significant challenges due to the increasing frequency and intensity of extreme weather events. Mexico, with its diverse climate and geographic position, is particularly vulnerable, underscoring the need for robust strategies to predict atmospheric variables. This work presents TAE Predict (Time [...] Read more.

Climate change presents significant challenges due to the increasing frequency and intensity of extreme weather events. Mexico, with its diverse climate and geographic position, is particularly vulnerable, underscoring the need for robust strategies to predict atmospheric variables. This work presents TAE Predict (Time series Analysis and Ensemble-based Prediction with relevant feature selection) based on relevant feature selection and ensemble models of machine learning. Dimensionality in multivariate time series is reduced through Principal Component Analysis, ensuring interpretability and efficiency. Additionally, data remediation techniques improve data set quality. The ensemble combines Long Short-Term Memory neural networks, Random Forest regression, and Support Vector Machines, optimizing their contributions using heuristic algorithms such as Particle Swarm Optimization. Experimental results from meteorological time series in key Mexican cities demonstrate that the proposed strategy outperforms individual models in accuracy and robustness. This methodology provides a replicable framework for climate variable forecasting, delivering analytical tools that support decision-making in critical sectors, such as agriculture and water resource management. The findings highlight the potential of integrating modern techniques to address complex, high-dimensional problems. By combining advanced prediction models and feature selection strategies, this study advances the reliability of climate forecasts and contributes to the development of effective adaptation and mitigation measures in response to climate change challenges. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2024)

► Show Figures

Figure 1

35 pages, 1960 KiB

Open AccessArticle

Bio-Inspired Multiobjective Optimization for Designing Content Distribution Networks

by Gerardo Goñi, Sergio Nesmachnow, Diego Rossit, Pedro Moreno-Bernal and Andrei Tchernykh

Math. Comput. Appl. 2025, 30(2), 45; https://doi.org/10.3390/mca30020045 - 21 Apr 2025

Abstract

This article studies the effective design of content distribution networks over cloud computing platforms. This problem is relevant nowadays to provide fast and reliable access to content on the internet. A bio-inspired evolutionary multiobjective optimization approach is applied as a viable alternative to [...] Read more.

This article studies the effective design of content distribution networks over cloud computing platforms. This problem is relevant nowadays to provide fast and reliable access to content on the internet. A bio-inspired evolutionary multiobjective optimization approach is applied as a viable alternative to solve realistic problem instances where exact optimization methods are not applicable. Ad hoc representation and search operators are applied to optimize relevant metrics from the point of view of both system administrators and users. In the evaluation of problem instances built using real data, the evolutionary multiobjective optimization approach was able to compute more accurate solutions in terms of cost and quality of service when compared to the exact resolution method. The obtained results represent an improvement over greedy heuristics from 47.6% to 93.3% in terms of cost while maintaining competitive quality of service. In addition, the computed solutions had different tradeoffs between the problem objectives. This can provide different options for content distribution network design, allowing for a fast configuration that fulfills specific quality of service demands. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2024)

► Show Figures

Figure 1

13 pages, 4627 KiB

Open AccessArticle

Detection of Abnormal Pedestrian Flows with Automatic Contextualization Using Pre-Trained YOLO11n

by Adrián Núñez-Vieyra, Juan C. Olivares-Rojas, Rogelio Ferreira-Escutia, Arturo Méndez-Patiño, José A. Gutiérrez-Gnecchi and Enrique Reyes-Archundia

Math. Comput. Appl. 2025, 30(2), 44; https://doi.org/10.3390/mca30020044 - 17 Apr 2025

Abstract

Recently, video surveillance systems have evolved from expensive, human-operated monitoring systems that were only useful after the crime was committed to systems that monitor 24/7, in real time, and with less and less human involvement. This is partly due to the use of [...] Read more.

Recently, video surveillance systems have evolved from expensive, human-operated monitoring systems that were only useful after the crime was committed to systems that monitor 24/7, in real time, and with less and less human involvement. This is partly due to the use of smart cameras, the improvement of the Internet, and AI-based algorithms that allow the classifying and tracking of objects in images and in some cases identifying them as threats. Threats are often associated with abnormal or unexpected situations such as the presence of unauthorized persons in a given place or time, the manifestation of a different behavior by one or more persons compared to the behavior of the majority, or simply an unexpected number of people in the place, which depends largely on the available information of their context, i.e., place, date, and time of capture. In this work, we propose a model to automatically contextualize video capture scenarios, generating data such as location, date, time, and flow of people in the scene. A strategy to measure the accuracy of the data generated for such contextualization is also proposed. The pre-trained YOLO11n algorithm and the Bot-SORT algorithm gave the best results in person detection and tracking, respectively. Full article

(This article belongs to the Special Issue New Trends in Computational Intelligence and Applications 2024)

► Show Figures

Figure 1

15 pages, 674 KiB

Open AccessArticle

Thau Observer for Insulin Estimation Considering the Effect of Beta-Cell Dynamics for a Diabetes Mellitus Model

by Diana Gamboa, Tonalli C. Galicia and Paul J. Campos

Math. Comput. Appl. 2025, 30(2), 43; https://doi.org/10.3390/mca30020043 - 17 Apr 2025

Abstract

In this work, a Thau observer is designed based on a nonlinear third-order mathematical model described by ODEs, which captures the dynamics among insulin levels,

β

-cells, and glucose concentration. The novelty of this research lies in its interdisciplinary approach to understanding a [...] Read more.

In this work, a Thau observer is designed based on a nonlinear third-order mathematical model described by ODEs, which captures the dynamics among insulin levels,

β

-cells, and glucose concentration. The novelty of this research lies in its interdisciplinary approach to understanding a complex biological system. The observer’s mathematical validation is established using the Localization of Compact Invariant Sets to determine the domain of attraction and global knowledge about the system’s dynamic bounds. These bounds are used to compute the Lipschitz constant and the elements of the free gain matrix that satisfy the constraints for designing a Thau observer, such as the stability matrix and asymptotic stability. This analysis provides insights into how insulin levels evolve over time at various glucose concentrations, an essential step toward hardware implementation due to the system’s chaotic behavior. It also establishes a mathematical background that could contribute to treatment planning in future Digital Twins studies. Numerical simulations demonstrate that the observer can accurately track the dynamic behavior of the Diabetes Mellitus model analyzed in this work through in silico methods. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2024)

► Show Figures

Figure 1

24 pages, 485 KiB

Open AccessArticle

The Weighted Flexible Weibull Model: Properties, Applications, and Analysis for Extreme Events

by Ziaurrahman Ramaki, Morad Alizadeh, Saeid Tahmasebi, Mahmoud Afshari, Javier E. Contreras-Reyes and Haitham M. Yousof

Math. Comput. Appl. 2025, 30(2), 42; https://doi.org/10.3390/mca30020042 - 16 Apr 2025

Abstract

The weighted flexible Weibull distribution focuses on its unique point of flaunting a bathtub-shaped hazard rate, characterized by an initial increase followed by a drop over time. This property plays a major role in reliability analysis. In this paper, this distribution and its [...] Read more.

The weighted flexible Weibull distribution focuses on its unique point of flaunting a bathtub-shaped hazard rate, characterized by an initial increase followed by a drop over time. This property plays a major role in reliability analysis. In this paper, this distribution and its main properties are examined, and the parameters are estimated using several estimation methods. In addition, a simulation study is done for different sample sizes. The performance of the proposed model is illustrated through two real-world applications: component failure times and COVID-19 mortality. Moreover, the value-at-risk (VaR), tail value-at-risk (TVaR), peaks over a random threshold VaR (PORT-VaR), the mean of order P (

{MOP}_{[P]}

) analysis, and optimal order of P due to the true mean value can help identify and characterize critical events or outliers in failure events and COVID-19 death data across different counties. Finally, the PORT-VaR estimators are provided under a risk analysis for both applications. Full article

(This article belongs to the Section Social Sciences)

► Show Figures

Figure 1

23 pages, 5543 KiB

Open AccessArticle

Enhanced Synchrosqueezing Transform for Detecting Non-Traditional Flight Modes in High Angle of Attack Maneuvers

by Seyed Amin Bagherzadeh, Hamed Mohammadkarimi and Mohammad Hossein Alizadeh

Math. Comput. Appl. 2025, 30(2), 41; https://doi.org/10.3390/mca30020041 - 12 Apr 2025

Abstract

Due to nonlinear aerodynamics, “non-traditional” flight modes may appear in longitudinal and lateral/directional dynamics once an aircraft experiences a high angle of attack and rapid maneuvers. Signal decomposition techniques are required to uncover these modes since they are hidden in flight characteristics. This [...] Read more.

Due to nonlinear aerodynamics, “non-traditional” flight modes may appear in longitudinal and lateral/directional dynamics once an aircraft experiences a high angle of attack and rapid maneuvers. Signal decomposition techniques are required to uncover these modes since they are hidden in flight characteristics. This study represents the Enhanced SynchroSqueezing Transform (ESST) for the extraction of “non-traditional” flight modes from flight data. Developed in the framework of the SynchroSqueezing Transform (SST), the ESST decomposes an Amplitude- and Frequency-Modulated (AMFM) signal into Intrinsic Mode Functions (IMFs). This process is optimized using the Genetic Algorithm (GA). Numerical investigations are performed to confirm the validity of the ESST. Both quantitative criteria for the fitness of the IMFs and qualitative study of the Time–Frequency Representations (TFRs) suggest that the ESST may perform better than the SST in decomposing nonlinear and non-stationary signals. Then, a method is proposed to find the instantaneous characteristics of the flight modes obtained by the ESST. The ESST analyzes an aircraft’s longitudinal and lateral flight data in post-stall maneuvers. The TFRs of flight parameters verify the existence of identical flight modes at different flight conditions. The IMFs are separated, and their instantaneous characteristics are computed. In addition, the ESST modes are compared to conventional modes. The results indicate that the ESST is capable of obtaining both classical oscillatory modes, such as Short Period (SP) and Dutch Roll (DR), and “non-traditional” modes. In the end, coupled modes are identified by comparing longitudinal and lateral IMFs. Full article

(This article belongs to the Section Engineering)

► Show Figures

Figure 1

21 pages, 1482 KiB

Open AccessArticle

Fractional Diffusion: A Structured Approach to Application with Examples

by Kathrin Kulmus, Christopher Essex, Karl Heinz Hoffmann and Janett Prehl

Math. Comput. Appl. 2025, 30(2), 40; https://doi.org/10.3390/mca30020040 - 9 Apr 2025

Abstract

Time-fractional evolution equations for probability distributions provide a means of representing an important class of stochastic processes. Their solutions have features that are important in modeling anomalous diffusion and a variety of other real-world applications, like the search patterns of predators or queuing [...] Read more.

Time-fractional evolution equations for probability distributions provide a means of representing an important class of stochastic processes. Their solutions have features that are important in modeling anomalous diffusion and a variety of other real-world applications, like the search patterns of predators or queuing problems. However, these equations are usually not included in current physics education, as the underlying mathematics might be considered too advanced. In the following, we present a novel approach to understanding time-fractional diffusion equations and their solutions for practical applications. This approach shifts the focus to the physical rather than the in-depth mathematical properties typically studied for this topic. We introduce the fractional differential operator simply as an identity operation on generalizations of exponential functions. This shifts the emphasis to the actual functions of fractional derivatives instead of what they are. This concept is applied to a discrete one-dimensional time-fractional diffusion equation on a finite interval modeling anomalous subdiffusion. Examples and tasks are provided for readers to allow interactive learning. Full article

(This article belongs to the Section Natural Sciences)

► Show Figures

Figure 1

21 pages, 3138 KiB

Open AccessArticle

An Evolutionary Strategy Based on the Generalized Mallows Model Applied to the Mixed No-Idle Permutation Flow Shop Scheduling Problem

by Elvi M. Sánchez Márquez, Ricardo Pérez-Rodríguez, Manuel Ornelas-Rodriguez and Héctor J. Puga-Soberanes

Math. Comput. Appl. 2025, 30(2), 39; https://doi.org/10.3390/mca30020039 - 3 Apr 2025

Abstract

The Mixed No-Idle Permutation Flow Shop Scheduling Problem (MNPFSSP) represents a specific case within regular flow scheduling problems. In this problem, some machines allow idle times between consecutive jobs or operations while other machines do not. Traditionally, the MNPFSSP has been addressed using [...] Read more.

The Mixed No-Idle Permutation Flow Shop Scheduling Problem (MNPFSSP) represents a specific case within regular flow scheduling problems. In this problem, some machines allow idle times between consecutive jobs or operations while other machines do not. Traditionally, the MNPFSSP has been addressed using the metaheuristics and exact methods. This work proposes an Evolutionary Strategy Based on the Generalized Mallows Model (ES-GMM) to solve the issue. Additionally, its advanced version, ES-GMMc, is developed, incorporating operating conditions to improve execution times without compromising solution quality. The proposed approaches are compared with algorithms previously used for the problem under study. Statistical tests of the experimental results show that the ES-GMMc achieved reductions in execution time, especially standing out in large instances, where the shortest computing times were obtained in 23 of 30 instances, without affecting the quality of the solutions. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2024)

► Show Figures

Figure 1

32 pages, 5759 KiB

Open AccessReview

by Bálint Molnár, József Szőlősi, Attila Gludovátz and Mátyás Andó

Math. Comput. Appl. 2025, 30(2), 38; https://doi.org/10.3390/mca30020038 - 31 Mar 2025

Abstract

IT (Information Technology) support plays a major role in CPSs (cyber-physical systems). More and more IT solutions and CIS (complex information system) modules are being developed to help engineering systems to a higher level of efficiency. The different specificities of different technological environments [...] Read more.

IT (Information Technology) support plays a major role in CPSs (cyber-physical systems). More and more IT solutions and CIS (complex information system) modules are being developed to help engineering systems to a higher level of efficiency. The different specificities of different technological environments require a very different IT approach. Increasing the efficiency of different manufacturing processes requires an appropriate architecture. The Zachman framework guidelines were applied to design a suitable framework architecture for the welding process. A literature search was conducted to explore the conditions for component matching to a complex information system, in which advanced data management and data protection are important. In order to effectively manage the standards, a dedicated module needs to be created that can be integrated into the MES-ERP (Manufacturing Execution System-Enterprise Resource Planning) architecture. The result of the study is the creation of business UML (Unified Modeling Language) and BPMN (Business Process Model and Notation) diagrams and a roadmap to start a concrete application development. The paper concludes with an example to illustrate ideas for the way forward. Full article

(This article belongs to the Section Engineering)

► Show Figures

Figure 1

Journal Description

Mathematical and Computational Applications

Latest Articles

Journal Menu

Journal Browser

Highly Accessed Articles

Latest Books

E-Mail Alert

News

Topics

Conferences

Special Issues

Topical Collections

Further Information

Guidelines

MDPI Initiatives

Follow MDPI