Advanced Mathematical Methods for Machine Learning in Biomedical Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E3: Mathematical Biology".

Deadline for manuscript submissions: 31 August 2026 | Viewed by 763

Special Issue Editors

School of Computer, National University of Defense Technology, No. 109 Deya Road, Changsha 410073, China
Interests: machine learning; bioinformatics; graph learning; multi-modal information fusion
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Guest Editor
College of Computer Science and Software Engineering, Hohai University, Nanjing, China
Interests: computer vision; medical image analysis; deep learning; continual learning; few-shot learning
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Special Issue Information

Dear Colleagues,

The integration of machine learning (ML) into biomedical research is transforming our capacity to decode complex biological systems and enhance healthcare outcomes. However, the unique characteristics of biomedical data—such as high dimensionality, heterogeneity, and inherent noise—pose substantial challenges that require sophisticated mathematical approaches. This Special Issue seeks to bridge this gap by emphasizing the pivotal role of advanced mathematical methods in driving the next generation of biomedical machine learning.

We aim to compile cutting-edge research that develops and applies novel mathematical and computational models to tackle pressing challenges in biomedicine. The scope of this Special Issue is broad, encompassing innovative studies on the development of ML algorithms grounded in rigorous mathematical theory, advanced techniques for multimodal data integration and feature extraction, and novel mathematical frameworks to manage data imbalance and bias, thereby enhancing model robustness and fairness. We invite submissions of original research and comprehensive review articles. By bringing together diverse expertise, this collection will demonstrate how advanced mathematics is fundamental to realizing the full potential of machine learning in addressing complex challenges in biology and medicine.

Dr. Dayu Hu
Dr. Jinghua Zhang
Guest Editors

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Keywords

  • machine learning
  • biomedical data analysis
  • computational modeling
  • multimodal learning
  • data imbalance
  • algorithmic fairness
  • graph neural networks
  • feature extraction
  • mathematical methods in biomedicine

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Published Papers (1 paper)

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Research

31 pages, 3003 KB  
Article
A Two-Phase Nonlocal Integral Continuum Model Combined with Machine Learning for Flexural Wave Propagation in Small-Scale Breast Ducts
by Ali Farajpour and Wendy V. Ingman
Mathematics 2026, 14(4), 720; https://doi.org/10.3390/math14040720 - 19 Feb 2026
Viewed by 452
Abstract
The majority of breast malignancies arise from breast ducts at the small-scale level. Understanding the wave characteristics of breast ducts may assist in developing new technologies to detect very early changes that precede breast cancer. In this study, a two-phase nonlocal integral model [...] Read more.
The majority of breast malignancies arise from breast ducts at the small-scale level. Understanding the wave characteristics of breast ducts may assist in developing new technologies to detect very early changes that precede breast cancer. In this study, a two-phase nonlocal integral model is developed to analyse the biomechanical behavior of breast ducts under flexural wave propagation. The influence of surface stiffness, surface residual stress, stress nonlocality, and stromal matrix is taken into consideration. The breast duct consists of different biological layers, including the basement membrane, myoepithelial cells, and luminal epithelial cells. Surface properties are calculated for the outer basement membrane and inner luminal epithelial cell layer. The results of the two-phase nonlocal integral model are validated using available molecular dynamics simulations. In addition, various machine learning algorithms, such as a neural network model, gradient boosting, random forest, logistic regression, and Ridge regression, are developed and integrated with the two-phase nonlocal model to better understand the flexural wave characteristics of breast ducts. Incorporation of two-phase nonlocal integral stress effects, surface energy, and residual stress reduces the root mean square error from 4.16 to 0.24 when compared against molecular dynamics simulation data. Full article
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