Mathematical and Computational Applications

36 pages, 5967 KiB

Open AccessArticle

Color Identification on Heterogeneous Bean Landrace Seeds Using Gaussian Mixture Models in CIE L*a*b* Color Space

by Adriana-Laura López-Lobato, Martha-Lorena Avendaño-Garrido, Héctor-Gabriel Acosta-Mesa, José-Luis Morales-Reyes and Elia-Nora Aquino-Bolaños

Math. Comput. Appl. 2025, 30(3), 64; https://doi.org/10.3390/mca30030064 - 6 Jun 2025

Viewed by 81

Abstract

The classification of bean landraces based on their coloration is of particular interest, as the color of these plants is associated with the nutritional components present in their seeds. In this paper, the authors propose a procedure to identify the colors of heterogeneous [...] Read more.

The classification of bean landraces based on their coloration is of particular interest, as the color of these plants is associated with the nutritional components present in their seeds. In this paper, the authors propose a procedure to identify the colors of heterogeneous color bean landraces based on the information from their digital images. The proposed methodology employs a three-dimensional histogram representation of the estimated color, expressed in the CIE L*a*b* color space, with an unsupervised learning method called the Gaussian Mixture Model. This approach facilitates the acquisition of representative information for the colors of a bean landrace, represented as points in the CIE L*a*b* color space. Furthermore, the K-

n n

method can be trained with these punctual representations to identify colors, yielding satisfactory results on landraces with homogeneous and heterogeneous seeds. Full article

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

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13 pages, 384 KiB

Open AccessArticle

On the Study of Wealth Distribution with Non-Maxwellian Collision Kernels and Variable Trading Propensity

by Yaxue Liu, Miao Liu and Shaoyong Lai

Math. Comput. Appl. 2025, 30(3), 63; https://doi.org/10.3390/mca30030063 - 5 Jun 2025

Viewed by 110

Abstract

A class of dynamic equations containing a non-Maxwellian collision kernel is used to investigate the distribution of wealth. A trading rule, in which the trading propensity

γ

of agents is a function of wealth w (namely,

γ = γ (w)

), [...] Read more.

A class of dynamic equations containing a non-Maxwellian collision kernel is used to investigate the distribution of wealth. A trading rule, in which the trading propensity

γ

of agents is a function of wealth w (namely,

γ = γ (w)

), is considered. Two different trading propensity functions are discussed. One is that

γ (w)

increases with wealth. The other is that

γ (w)

decreases with the increase in wealth. In a single transaction, when the transaction tendency increases with the increase in wealth, the rich invest more in transactions. The gap between the rich and the poor in society is reduced under suitable conditions. Through numerical simulation, we conclude that an escalation in market risk intensifies the inequality in wealth distribution. Full article

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30 pages, 787 KiB

Open AccessArticle

A New Logistic Distribution and Its Properties, Applications and PORT-VaR Analysis for Extreme Financial Claims

by Piotr Sulewski, Morad Alizadeh, Jondeep Das, Gholamhossein G. Hamedani, Partha Jyoti Hazarika, Javier E. Contreras-Reyes and Haitham M. Yousof

Math. Comput. Appl. 2025, 30(3), 62; https://doi.org/10.3390/mca30030062 - 4 Jun 2025

Viewed by 89

Abstract

This paper introduces a new extension of exponentiated standard logistic distribution. Some important statistical properties of the novel family of distributions are discussed. A simulation study is also conducted to observe the behavior of the estimated parameter using several estimation methods. The adaptability [...] Read more.

This paper introduces a new extension of exponentiated standard logistic distribution. Some important statistical properties of the novel family of distributions are discussed. A simulation study is also conducted to observe the behavior of the estimated parameter using several estimation methods. The adaptability as well as the flexibility of the new model is checked through two real-life applications. A comprehensive financial risk assessment is conducted using multiple actuarial risk measures: Peaks Over Random Threshold Value-at-Risk, Value-at-Risk, Tail Value-at-Risk, the risk-adjusted return on capital and the Mean of Order P. These indicators offer a nuanced view of risk by capturing different aspects of tail behavior, which are critical in understanding potential extreme losses. These risk indicators are applied to analyze actuarial financial claims data, providing a robust framework for assessing financial stability and decision-making in the face of uncertainty. Full article

(This article belongs to the Section Social Sciences)

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5 pages, 166 KiB

Open AccessEditorial

Numerical and Evolutionary Optimization 2024

by Marcela Quiroz-Castellanos, Oliver Cuate, Leonardo Trujillo and Oliver Schütze

Math. Comput. Appl. 2025, 30(3), 61; https://doi.org/10.3390/mca30030061 - 1 Jun 2025

Viewed by 180

Abstract

This Special Issue was inspired by the 11th International Workshop on Numerical and Evolutionary Optimization (NEO 2024), held from 3 to 6 September 2024 in Mexico City, Mexico, and hosted by Cinvestav [...] Full article

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

24 pages, 4242 KiB

Open AccessArticle

Numerical Simulation of Drilling Fluid-Wellbore Interactions in Permeable and Fractured Zones

by Diego A. Vargas Silva, Zuly H. Calderón, Darwin C. Mateus and Gustavo E. Ramírez

Math. Comput. Appl. 2025, 30(3), 60; https://doi.org/10.3390/mca30030060 - 30 May 2025

Viewed by 243

Abstract

In well drilling operations, interactions between drilling fluid water-based and the well-bore present significant challenges, often escalating project costs and timelines. Particularly, fractures (both induced and natural) and permeable zones at the wellbore can result in substantial mud loss or increased filtration. Addressing [...] Read more.

In well drilling operations, interactions between drilling fluid water-based and the well-bore present significant challenges, often escalating project costs and timelines. Particularly, fractures (both induced and natural) and permeable zones at the wellbore can result in substantial mud loss or increased filtration. Addressing these challenges, our research introduces a novel coupled numerical model designed to precisely calculate fluid losses in fractured and permeable zones. For the permeable zone, fundamental variables such as filtration velocity, filtrate concentration variations, permeability reduction, and fluid cake growth are calculated, all based on the law of continuity and convection-dispersion theory. For the fracture zone, the fluid velocity profile is determined using the momentum balance equation and both Newtonian and non-Newtonian rheology. The model was validated against laboratory data and physical models, and adapted for field applications. Our findings emphasize that factors like mud particle size, shear stress, and pressure differential are pivotal. Effectively managing these factors can significantly reduce fluid loss and mitigate formation damage caused by fluid invasion. Furthermore, the understanding gathered from studying mud behavior in both permeable and fractured zones equips drilling personnel with valuable information related to the optimal rheological properties according to field conditions. This knowledge is crucial for optimizing mud formulations and strategies, ultimately aiding in the reduction of non-productive time (NPT) associated with wellbore stability issues. Full article

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18 pages, 1166 KiB

Open AccessArticle

Hybrid Deep Learning Models for Predicting Student Academic Performance

by Kuburat Oyeranti Adefemi, Murimo Bethel Mutanga and Vikash Jugoo

Math. Comput. Appl. 2025, 30(3), 59; https://doi.org/10.3390/mca30030059 - 23 May 2025

Viewed by 416

Abstract

Educational data mining (EDM) is instrumental in the early detection of students at risk of academic underperformance, enabling timely and targeted interventions. Given that many undergraduate students face challenges leading to high failure and dropout rates, utilizing EDM to analyze student data becomes [...] Read more.

Educational data mining (EDM) is instrumental in the early detection of students at risk of academic underperformance, enabling timely and targeted interventions. Given that many undergraduate students face challenges leading to high failure and dropout rates, utilizing EDM to analyze student data becomes crucial. By predicting academic success and identifying at-risk individuals, EDM provides a data-driven approach to enhance student performance. However, accurately predicting student performance is challenging, as it depends on multiple factors, including academic history, behavioral patterns, and health-related metrics. This study aims to bridge this gap by proposing a deep learning model to predict student academic performance with greater accuracy. The approach combines a convolutional neural network (CNN) and a bidirectional gated recurrent unit (BiGRU) network to enhance predictive capabilities. To improve the model’s performance, we address key data preprocessing challenges, including handling missing data, addressing class imbalance, and selecting relevant features. Additionally, we incorporate optimization techniques to fine-tune hyperparameters to determine the best model architecture. Using key performance metrics such as accuracy, precision, recall, and F-score, our experimental results show that our proposed model achieves improved prediction accuracy of 97.48%, 90.90%, and 95.97% across the three datasets. Full article

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

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23 pages, 1322 KiB

Open AccessArticle

Comparative Analysis of ALE Method Implementation in Time Integration Schemes for Pile Penetration Modeling

by Ihab Bendida Bourokba, Abdelmadjid Berga, Patrick Staubach and Nazihe Terfaya

Math. Comput. Appl. 2025, 30(3), 58; https://doi.org/10.3390/mca30030058 - 22 May 2025

Viewed by 254

Abstract

This study investigates the full penetration simulation of piles from the ground surface, focusing on frictional contact modeling without mesh distortion. To overcome issues related to mesh distortion and improve solution convergence, the Arbitrary Lagrangian–Eulerian (ALE) adaptive mesh technique was implemented within both [...] Read more.

This study investigates the full penetration simulation of piles from the ground surface, focusing on frictional contact modeling without mesh distortion. To overcome issues related to mesh distortion and improve solution convergence, the Arbitrary Lagrangian–Eulerian (ALE) adaptive mesh technique was implemented within both explicit and implicit time integration schemes. The numerical model was validated against field experiments conducted at Bothkennar, Scotland, using the Imperial College instrumented displacement pile (ICP) in soft clay, where the soil behavior was effectively represented using the modified Cam-Clay model and the Mohr–Coulomb model. The primary objectives of this study are to evaluate the ALE method performance in handling mesh distortion; analyze the effects of soil–pile interface friction, pile dimensions, and various dilation angles on pile resistance; and compare the effectiveness of explicit and implicit time integration schemes in terms of stability, computational efficiency, and solution accuracy. The ALE method effectively modeled pile penetration in Bothkennar clay, validating the numerical model against field experiments. Comparative analysis revealed the explicit time integration method as more robust and computationally efficient, particularly for complex soil–pile interactions with higher friction coefficients. Full article

(This article belongs to the Topic Numerical Methods for Partial Differential Equations)

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18 pages, 1692 KiB

Open AccessArticle

Multiple-Feature Construction for Image Segmentation Based on Genetic Programming

by David Herrera-Sánchez, José-Antonio Fuentes-Tomás, Héctor-Gabriel Acosta-Mesa, Efrén Mezura-Montes and José-Luis Morales-Reyes

Math. Comput. Appl. 2025, 30(3), 57; https://doi.org/10.3390/mca30030057 - 21 May 2025

Viewed by 155

Abstract

Within the medical field, computer vision has an important role in different tasks, such as health anomaly detection, diagnosis, treatment, and monitoring medical conditions. Image segmentation is one of the most used techniques for medical support to identify regions of interest in different [...] Read more.

Within the medical field, computer vision has an important role in different tasks, such as health anomaly detection, diagnosis, treatment, and monitoring medical conditions. Image segmentation is one of the most used techniques for medical support to identify regions of interest in different organs. However, performing accurate segmentation is difficult due to image variations. In this way, this work proposes an automated multiple-feature construction approach for image segmentation, working with magnetic resonance images, computed tomography, and RGB digital images. Genetic programming is used to automatically create and construct pipelines to extract meaningful features for segmentation tasks. Additionally, a co-evolution strategy is proposed within the evolution process to increase diversity without affecting segmentation performance. The segmentation is addressed as a pixel classification task; in this way, a wrapper approach is used, and the classification model’s segmentation performance determines the fitness. To validate the effectiveness of the proposed method, four datasets were used to measure the capability of the proposal to deal with different types of medical images. The results demonstrate that the proposal achieves values of the DICE similarity coefficient of more than 0.6 in MRI and C.T. images. Additionally, the proposal is compared with SOTA GP-based methods and the convolutional neural networks used within the medical field. The method proposed outperforms these methods, achieving improvements greater than

20 %

in DICE, specificity, and sensitivity. Additionally, the qualitative results demonstrate that the proposal accurately identifies the region of interest. Full article

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

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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 272

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 198

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, 6617 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 230

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 234

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

Viewed by 185

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

Viewed by 195

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 318

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 438

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 310

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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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 428

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 393

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) – 19 articles

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