Physical Sciences and Mathematics Commons^™

A Classification Of Tensors In Ecsk Theory, Joshua James Leiter

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

You might have heard of Einstein’s theory of General relativity (GR): it is the one where mass and energy curve the fabric of spacetime to create gravity. This is the major theory which allows communication through satellites and our GPS to work too! Wormholes have interested me, but there are some issues about forming them in GR. Interestingly enough, elementary particles are also characterized by their spin in the standard model. However, intrinsic spin is nowhere geometrically coupled to the geometry of spacetime in Einstein’s theory. Later, Élie Cartan, Dennis Sciama, and Tom Kibble all flushed out adding different aspects …

Deep Learning With Attention Mechanisms In Breast Ultrasound Image Segmentation And Classification, Meng Xu

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Breast cancer is a great threat to women’s health. Breast ultrasound (BUS) imaging is commonly used in the early detection of breast cancer as a portable, valuable, and widely available diagnosis tool. Automated BUS image analysis can assist radiologists in making accurate and fast decisions. Generally, automated BUS image analysis includes BUS image segmentation and classification. BUS image segmentation automatically extracts tumor regions from a BUS image. BUS image classification automatically classifies breast tumors into benign or malignant categories. Multi-task learning accomplishes segmentation and classification simultaneously, which makes it more appealing and practical than an either individual task. Deep neural …

Data-Driven Recommendation Of Academic Options Based On Personality Traits, Aashish Ghimire

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The choice of academic major and, subsequently, an academic institution has a massive effect on a person’s career. It not only determines their career path but their earning potential, professional happiness, etc. [1] About 40% of people who are admitted to a college do not graduate within six years. Yet, very limited resources are available for students to help make those decisions, and each guidance counselor is responsible for roughly 400 to 900 students across the United States. A tool to help these decisions would benefit students, parents, and guidance counselors.

Various research studies have shown that personality traits affect …

Development And Identification Of Metrics To Predict The Impact Of Dimension Reduction Techniques On Classical Machine Learning Algorithms For Still Highway Images, Wasim Akram Khan

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We are witnessing an influx of data - images, texts, video, etc. Their high dimensionality and large volume make it challenging to apply machine learning to obtain actionable insight. This thesis explores several aspects pertaining to dimensional reduction: dimension reduction methods, metrics to measure distortion, image preprocessing, etc. Faster training and inference time on reduced data and smaller models which can be deployed on commodity hardware are a critical advantage of dimension reduction. For this study, classical machine learning methods were explored owing to their solid mathematical foundation and interpretability.

The dataset used is a time series of images from …

Classification Of Isometry Algebras Of Solutions Of Einstein's Field Equations, Eugene Hwang

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Since Schwarzschild found the first solution of the Einstein’s equations, more than 800 solutions were found. Solutions of Einstein’s equations are classified according to their Lie algebras of isometries and their isotropy subalgebras. Solutions were taken from the USU electronic library of solutions of Einstein’s field equations and the classification used Maple code developed at USU. This classification adds to the data contained in the library of solutions and provides additional tools for addressing the equivalence problem for solutions to the Einstein field equations. In this thesis, homogeneous spacetimes, hypersurface-homogeneous spacetimes, Robinson-Trautman solutions, and some famous black hole solutions have …

Real Simple Lie Algebras: Cartan Subalgebras, Cayley Transforms, And Classification, Hannah M. Lewis

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The differential geometry software package in Maple has the necessary tools and commands to automate the classification process for complex simple Lie algebras. The purpose of this thesis is to write the programs to complete the classification for real simple Lie algebras. This classification is difficult because the Cartan subalgebras are not all conjugate as they are in the complex case. For the process of the real classification, one must first identify a maximally noncompact Cartan subalgebra. The process of the Cayley transform is used to find this specific Cartan subalgebra. This Cartan subalgebra is used to find the simple …

Extensions And Improvements To Random Forests For Classification, Anna Quach

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The motivation of my dissertation is to improve two weaknesses of Random Forests. One, the failure to detect genetic interactions between two single nucleotide polymorphisms (SNPs) in higher dimensions when the interacting SNPs both have weak main effects and two, the difficulty of interpretation in comparison to parametric methods such as logistic regression, linear discriminant analysis, and linear regression.

We focus on detecting pairwise SNP interactions in genome case-control studies. We determine the best parameter settings to optimize the detection of SNP interactions and improve the efficiency of Random Forests and present an efficient filtering method. The filtering method is …

Classification Of Five-Dimensional Lie Algebras With One-Dimensional Subalgebras Acting As Subalgebras Of The Lorentz Algebra, Jordan Rozum

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Motivated by A. Z. Petrov's classification of four-dimensional Lorentzian metrics, we provide an algebraic classification of the isometry-isotropy pairs of four-dimensional pseudo-Riemannian metrics admitting local slices with five-dimensional isometries contained in the Lorentz algebra. A purely Lie algebraic approach is applied with emphasis on the use of Lie theoretic invariants to distinguish invariant algebra-subalgebra pairs. This method yields an algorithm for identifying isometry-isotropy pairs subject to the aforementioned constraints.

Enhancement Of Random Forests Using Trees With Oblique Splits, Andrejus Parfionovas

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Statistical classification is widely used in many areas where there is a need to make a data-driven decision, or to classify complicated cases or objects. For instance: disease diagnostics (is a patient sick or healthy, based on the blood test results?); weather forecasting (will there be a storm tomorrow, based on today's atmospheric pressure, air temperature, and wind velocity?); speech recognition (what was said over the phone, based on the caller's voice level and articulation); spam detection (can the unsolicited commercial e-mails be identified by their content?); and so on.

Classification trees …

A Classification Of Real Indecomposable Solvable Lie Algebras Of Small Dimension With Codimension One Nilradicals, Alan R. Parry

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This thesis was concerned with classifying the real indecomposable solvable Lie algebras with codimension one nilradicals of dimensions two through seven. This thesis was organized into three chapters.

In the first, we described the necessary concepts and definitions about Lie algebras as well as a few helpful theorems that are necessary to understand the project. We also reviewed many concepts from linear algebra that are essential to the research.

The second chapter was occupied with a description of how we went about classifying the Lie algebras. In particular, it outlined the basic premise of the classification: that we can use …

Lorentz Homogeneous Spaces And The Petrov Classification, Adam Bowers

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A. Z. Petrov gave a complete list of all local group actions on a four-dimensional space-time that admit an invariant Lorentz metric, up to an equivalence relation. His list was compiled by directly constructing all possible Lie algebras of infinitesimal generators of group actions that preserve a Lorentz metric. The goal of this paper was to verify that classification by algebraically constructing a list of all possible three-dimensional homogeneous spaces and calculating which among them have a non-degenerate invariant metric.

A New Perspective On Classification, Guohua Zhao

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The idea of voting multiple decision rules was introduced in to statistics by Breiman. He used bootstrap samples to build different decision rules, and then aggregated them by majority voting (bagging). In regression, bagging gives improved predictors by reducing the variance (random variation), while keeping the bias (systematic error) the same. Breiman introduced the idea of bias and variance for classification to explain how bagging works. However, Friedman showed that for the two-class situation, bias and variance influence the classification error in a very different way than they do in the regression case.

In the first part of …