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

Viewed by 166

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

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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

Viewed by 138

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)

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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

Viewed by 155

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

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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

Viewed by 165

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)

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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

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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

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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

Viewed by 184

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)

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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

Viewed by 257

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)

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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

Viewed by 266

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

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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

Viewed by 300

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

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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

Viewed by 248

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)

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Math. Comput. Appl., Volume 30, Issue 3 (June 2025) – 11 articles

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