Open Access. Powered by Scholars. Published by Universities.®
- Discipline
Articles 1 - 2 of 2
Full-Text Articles in Applied Mathematics
Exploration And Implementation Of Neural Ordinary Differential Equations, Long Huu Nguyen, Andy Malinsky
Exploration And Implementation Of Neural Ordinary Differential Equations, Long Huu Nguyen, Andy Malinsky
Capstone Showcase
Neural ordinary differential equations (ODEs) have recently emerged as a novel ap- proach to deep learning, leveraging the knowledge of two previously separate domains, neural networks and differential equations. In this paper, we first examine the back- ground and lay the foundation for traditional artificial neural networks. We then present neural ODEs from a rigorous mathematical perspective, and explore their advantages and trade-offs compared to traditional neural nets.
Modeling Gene Expression With Differential Equations, Madison Kuduk
Modeling Gene Expression With Differential Equations, Madison Kuduk
Capstone Showcase
Gene expression is the process by which the information stored in DNA is convertedinto a functional gene product, such as protein. The two main functions that makeup the process of gene expression are transcription and translation. Transcriptionand translation are controlled by the number of mRNA and protein in the cell. Geneexpression can be represented as a system of first order differential equations for the rateof change of mRNA and proteins. These equations involve transcription, translation,degradation and feedback loops. In this paper, I investigate a system of first orderdifferential equations to model gene expression proposed by Hunt, Laplace, Miller andPham in …