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Numerical Analysis and Scientific Computing

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Machine Learning

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Full-Text Articles in Physical Sciences and Mathematics

Mathematical Models Yield Insights Into Cnns: Applications In Natural Image Restoration And Population Genetics, Ryan Cecil Aug 2022

Mathematical Models Yield Insights Into Cnns: Applications In Natural Image Restoration And Population Genetics, Ryan Cecil

Electronic Theses and Dissertations

Due to a rise in computational power, machine learning (ML) methods have become the state-of-the-art in a variety of fields. Known to be black-box approaches, however, these methods are oftentimes not well understood. In this work, we utilize our understanding of model-based approaches to derive insights into Convolutional Neural Networks (CNNs). In the field of Natural Image Restoration, we focus on the image denoising problem. Recent work have demonstrated the potential of mathematically motivated CNN architectures that learn both `geometric' and nonlinear higher order features and corresponding regularizers. We extend this work by showing that not only can geometric features …


Knot Flow Classification And Its Applications In Vehicular Ad-Hoc Networks (Vanet), David Schmidt May 2020

Knot Flow Classification And Its Applications In Vehicular Ad-Hoc Networks (Vanet), David Schmidt

Electronic Theses and Dissertations

Intrusion detection systems (IDSs) play a crucial role in the identification and mitigation for attacks on host systems. Of these systems, vehicular ad hoc networks (VANETs) are difficult to protect due to the dynamic nature of their clients and their necessity for constant interaction with their respective cyber-physical systems. Currently, there is a need for a VANET-specific IDS that meets this criterion. To this end, a spline-based intrusion detection system has been pioneered as a solution. By combining clustering with spline-based general linear model classification, this knot flow classification method (KFC) allows for robust intrusion detection to occur. Due its …