Physical Sciences and Mathematics Commons^™

Automated Feature Extraction From Large Cardiac Electrophysiological Data Sets, And A Population Dynamics Approach To The Distribution Of Space Debris In Low-Earth Orbit, John Jurkiewicz

Theses and Dissertations

We present two applications of mathematics to relevant real-world situations.

In the first chapter, we discuss an automated method for the extraction of useful data from large file-size readings of cardiac data. We begin by describing the history of electrophysiology and the background of the work's setting, wherein a new multi-electrode array-based application for the long-term recording of action potentials from electrogenic cells makes large-scale readings of relevant data possible, opening the way for exciting cardiac electrophysiology studies in health and disease. With hundreds of simultaneous electrode recordings being acquired over a period of days, the main challenge becomes achieving …

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 …

Analyzing Suicidal Text Using Natural Language Processing, Cassandra Barton

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Using Natural Language Processing (NLP), we are able to analyze text from suicidal individuals. This can be done using a variety of methods. I analyzed a dataset of a girl named Victoria that died by suicide. I used a machine learning method to train a different dataset and tested it on her diary entries to classify her text into two categories: suicidal vs non-suicidal. I used topic modeling to find out unique topics in each subset. I also found a pattern in her diary entries. NLP allows us to help individuals that are suicidal and their family members and close …

Quadratic Neural Network Architecture As Evaluated Relative To Conventional Neural Network Architecture, Reid Taylor

Senior Theses

Current work in the field of deep learning and neural networks revolves around several variations of the same mathematical model for associative learning. These variations, while significant and exceptionally applicable in the real world, fail to push the limits of modern computational prowess. This research does just that: by leveraging high order tensors in place of 2nd order tensors, quadratic neural networks can be developed and can allow for substantially more complex machine learning models which allow for self-interactions of collected and analyzed data. This research shows the theorization and development of mathematical model necessary for such an idea to …

Reinforcement Learning: Low Discrepancy Action Selection For Continuous States And Actions, Jedidiah Lindborg

Electronic Theses and Dissertations

In reinforcement learning the process of selecting an action during the exploration or exploitation stage is difficult to optimize. The purpose of this thesis is to create an action selection process for an agent by employing a low discrepancy action selection (LDAS) method. This should allow the agent to quickly determine the utility of its actions by prioritizing actions that are dissimilar to ones that it has already picked. In this way the learning process should be faster for the agent and result in more optimal policies.