Digital Commons Network^™

Data Visualization, Dimensionality Reduction, And Data Alignment Via Manifold Learning, Andrés Felipe Duque Correa

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The high dimensionality of modern data introduces significant challenges in descriptive and exploratory data analysis. These challenges gave rise to extensive work on dimensionality reduction and manifold learning aiming to provide low dimensional representations that preserve or uncover intrinsic patterns and structures in the data. In this thesis, we expand the current literature in manifold learning developing two methods called DIG (Dynamical Information Geometry) and GRAE (Geometry Regularized Autoencoders). DIG is a method capable of finding low-dimensional representations of high-frequency multivariate time series data, especially suited for visualization. GRAE is a general framework which splices the well-established machinery from kernel …

Symplectic Reduction Along A Submanifold, Peter Crooks, Maxence Mayrand

Mathematics and Statistics Faculty Publications

We introduce the process of symplectic reduction along a submanifold as a uniform approach to taking quotients in symplectic geometry. This construction holds in the categories of smooth manifolds, complex analytic spaces, and complex algebraic varieties, and has an interpretation in terms of derived stacks in shifted symplectic geometry. It also encompasses Marsden-Weinstein-Meyer reduction, Mikami-Weinstein reduction, the pre-images of Poisson transversals under moment maps, symplectic cutting, symplectic implosion, and the Ginzburg-Kazhdan construction of Moore-Tachikawa varieties in topological quantum field theory. A key feature of our construction is a concrete and systematic association of a Hamiltonian G-space 𝔐_𝐺,𝑆 to …

Applying Expansive Framing To An Integrated Mathematics-Computer Science Unit, Kimberly Evagelatos Beck, Jessica F. Shumway

Publications

In this research report for the National Council of Teachers of Mathematics 2022 Research Conference, we discuss the theory of Expansive Framing and its application to an interdisciplinary mathematics-computer science curricular unit.

Leveraging The "Large" In Large Lecture Statistics Classes, Kady Schneiter, Kimberleigh Felix Hadfield, Jenny Lee Clements

Mathematics and Statistics Faculty Publications

Being a teacher or a student in a class with a large enrollment can be intimidating. Often, teachers view comforts that are common to small classes as unattainable in a larger class, including knowing students’ names, using active learning, employing group work, and creating group discussion. Students in large classes may find that the class size leads to isolation. At Utah State University, we offer introductory statistics classes for various audiences using a large lecture format. The authors have collectively led these large lectures dozens of times and found that, despite its shortcomings, the large lecture format can be an …

Recognizing And Reducing Ambiguity In Mathematics Curriculum And Relations Of Θ-Functions In Genus One And Two: A Geometric Perspective, Shantel Spatig

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

Anxiety and mathematics come hand in hand for many individuals. This is due, in
part, to the fact that the only experience they have with mathematics is what some
mathematics educators refer to as "schoolmath," which uses a somewhat different
language than real mathematics. The language of schoolmath can cause individu-
als to have confusion and develop misconceptions related to several mathematical
concepts. One such concept is a fraction. In chapter one of this report, one possible
reason for this is discussed and a possible solution is purposed.
In chapter three of this report, genus-two curves admitting an elliptic involution …

Developing Confidence And Interest In Teaching Relevant Mathematical Modeling Lessons, Jacy Beck

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

What is mathematical modeling and how can inservice and pre-service teachers develop the skills and competencies necessary to increase confidence and interest in teaching relevant mathematical modeling lessons? Mathematical modeling is “the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions” (CSSM, 2010, p. 72). By providing students with an opportunity to engage in relevant mathematical modeling prompts, we provide them with transferable skills and knowledge. The aim of this paper will be to provide insight into the relevance of teaching mathematical modeling, provide resources for integrating modeling …

Dynamic System Discovery With Recursive Physics-Informed Neural Networks, Jarrod Mau

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This thesis presents a novel method, recursive Physics informed neural network, to learn the right hand side of differential equations. The neural network takes in data, then trains, and then acts as a proxy for the differential equation which can be used for modeling. We show the theoretical superiority of the recursive approach. We also use computer simulations to demonstrate the proved properties.

Defining Areas Of Interest Using Voronoi And Modified Voronoi Tesselations To Analyze Eye-Tracking Data, Joanna D. Coltrin

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Eye tracking is a technology used to track where someone is looking. Eye-tracking technology is often used to study what people focus on when looking at a photo of another person. The eye-tracking technology records points on a photo that a person is looking at. When the photo being looked at shows a person, the points can be categorized by body part such as head, right hand, left hand, and torso. This thesis presents the use of partially circular areas to define the body parts of the person in the photo and therefore categorize the points collected by the eye-tracker. …

Contributions To Random Forest Variable Importance With Applications In R, Kelvyn K. Bladen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A major focus in statistics is building and improving computational algorithms that can use data to predict a response. Two fundamental camps of research arise from such a goal. The first camp is researching ways to get more accurate predictions. Many sophisticated methods, collectively known as machine learning methods, have been developed for this very purpose. One such method that is widely used across industry and many other areas of investigation is called Random Forests.

The second camp of research is that of improving the interpretability of machine learning methods. This is worthy of attention when analysts desire to optimize …

Using The Reshetikhin-Turaev Link Invariant Approach With Non-Semisimple Categories, Adam Robertson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Invariants of knots and links are useful because they give rise to invariants of 3-manifolds. In particular, combinatorial link invariants give rise to combinatorial invariants of 3-manifolds, which are hard to come by using traditional methods from classical topology. The Reshetikhin–Turaev approach, which is based in quantum topology, develops link invariants using semisimple ribbon categories. However, a large class of algebraically interesting ribbon categories are non-semisimple and so give trivial link invariants via the Reshetikhin–Turaev method. We modify the Reshetikhin–Turaev method to make it suitable for non-semisimple ribbon categories. We discuss explicitly the following three examples: semisimple modules for the …

Joint Invariants Of Primitive Homogenous Spaces, Illia Hayes

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Joint invariants are motivated by the study of congruence problems in Euclidean geometry, where they provide necessary and sufficient conditions for congruence. More recently joint invariants have been used in computer image recognition problems. This thesis develops new methods to compute joint invariants by developing a reduction technique, and applies the reduction to a number of important examples.

Extensions To The Syrjala Test With Eye-Tracking Data Analysis Applications In R, Eric D. Mckinney

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Eye tracking is a process for measuring the movement of an individual’s eye(s) when that individual is looking at something. Many eye-tracking technologies exist to aid in calculating and recording data associated with what a person focuses their visual attention on. For example, eye-tracking technology can record points on an image that a person is looking at. Often the question arises as to whether two people, or groups of people, are looking at the same thing(s). This dissertation presents a new way (or test) to quantify those differences while taking into consideration the randomness associated with such data. Hence, the …

Introduction To Classical Field Theory, Charles G. Torre

All Complete Monographs

This is an introduction to classical field theory. Topics treated include: Klein-Gordon field, electromagnetic field, scalar electrodynamics, Dirac field, Yang-Mills field, gravitational field, Noether theorems relating symmetries and conservation laws, spontaneous symmetry breaking, Lagrangian and Hamiltonian formalisms.

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 …

The Influence Of A Course On Assessment For Inservice Secondary Mathematics Teachers, Natalie M. Anderson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Many mathematics teachers are not prepared to design valid and usable measurements of their students’ mathematical achievements. There are relatively few opportunities for mathematics teachers to improve their assessment literacy. The purpose of this study is to (1) design a course on assessment for inservice mathematics teachers and (2) evaluate the effectiveness of the course. This paper recounts the development of the course and its influence on 16 teachers. Teachers who completed the course submitted a unit outline with learning objectives, a test blueprint, and a unit test. These artifacts influenced my evaluation on the effectiveness of the course. All …

Dynamical Systems Analysis In Adaptive And Metapopulation Ecology With Applications To Conservation Management, Guenchik Grosklos

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The ability for a species to persist largely relies on how well they adapt to the environment and their interactions with local and global communities. Specifically, if adaptation occurs quickly enough or nearby communities sufficiently promote growth rates, populations at risk of extinction may persist. In this dissertation, we first develop a method that estimates and compares rates of change in time series data of population densities and measurable traits (phenotypes). Additionally, we compare between genetic (evolutionary) and non-genetic (plastic) trait change to determine whether phenotypes change faster when driven by evolutionary or plastic change. We then focus on metapopulation …

Visions Of Science: An Art Historical Exploration Of Medieval Scientific Manuscripts, Olivia Brock

Undergraduate Honors Capstone Projects

The late 16th century saw a new movement in the world of science to push scientific ideas and practice out of academia and into the hands of the layman. No longer were scholars the sole proprietors of science –everyday laborers, craftsman, and artists now had practical scientific principles at their fingertips that they could incorporate into their professions. This new spread of science was facilitated in several ways, including the publication of books incorporating detailed, explanatory images, new utilitarian instruments, and public lectures. Though science was disseminated through a variety of means, I have been particularly interested in the ways …

Manifold Alignment With Inter-Domain Diffusion, Andres Duque

Student Research Symposium

The integration of multimodal data presents a challenge in cases when the study of a given phenomena by different instruments or conditions generates distinct but related domains. In this paper, we propose Diffusion Transport Alignment (DTA) a semi-supervised manifold alignment method that exploits prior correspondence knowledge between distinct data views. DTA finds a bijection between two domains, which by assumption, share a similar geometrical structure coming from the same underlying data generating process. We empirically demonstrate the effectiveness of our method to integrate multimodal data, as well as how it can improve the performance of machine learning tasks, otherwise less …

Analyzing Suicidal Text Using Natural Language Processing, Cassandra Barton

Student Research Symposium

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 …

Modeling The Spread Of Curly Top Disease In Tomato Crops, Rachel Frantz

Student Research Symposium

Curly Top disease (CT), caused by a family of curtoviruses, infects a wide variety of agricultural crops. Historically, CT has caused extensive damage in tomato crops resulting in substantial economic loss for the tomato industry. Control methods for CT are scarce, and methods for predicting and assessing the scope of CT outbreaks are limited. In this paper, we formulate two theoretical models, a deterministic model and a stochastic model, for the spread of CT in a heterogeneous environment consisting of beets (preferred host) and tomatoes. The models are composed of two susceptible classes and two infected classes (infectious beets and …

The Outdoor Fashion Industry Is Not Sustainable, Joshua Hillam

Student Research Symposium

Outdoor fashion companies are responsible for a large amount of waste and pollution worldwide. I believe they are ethically bound to make changes in their manufacturing process to decrease their footprint because their products are used in outdoor environments that are impacted negatively by waste and pollution. The fashion industry as a whole is responsible for 10% of the carbon emissions worldwide. Research was conducted by first understanding what being sustainable means from the EPA, from individuals who work in the fashion industry, and from companies that advocate for more sustainable clothing. I then investigated what materials are the most …

Finding Higher Order Interactions Using Local Corex, Thomas Kerby

Student Research Symposium

In applications such as financial markets, social networks, and gene expression data, the variables often interact in complex ways. Yet accurately characterizing pairwise variable interactions can be a difficult task, let alone efficiently characterizing complex higher-order interactions, which is an unsolved problem. This difficulty is exacerbated when variable interactions change across the data. For example, gene interactions in single-cell RNA-sequencing (scRNA-seq) data will typically differ from one cell type to another. To solve these problems, we propose a new method called Local Correlation Explanation (CorEx). Local CorEx captures higher-order variable interactions at a local scale by first clustering data points …

Modeling The Extended Low And Sudden High Periods Of Activity In Infectious Diseases, Dana Strong

Student Research Symposium

This research explores how the aggregation of individuals during disease spread may, in conjunction with noise, explain how some diseases’ trajectories spend some time at low numbers after which there is a sudden outbreak.

Ensemble Kernel Density Estimation, Ethan Ancell

Student Research Symposium

The problem of estimating a probability density function from data has many applications in machine learning and data science. Nonparametric estimators are useful in this context as they require relatively few assumptions on the densities. Unfortunately, standard nonparametric methods such as kernel density estimationtend to converge slowly to the true value in high dimensions as a function of the data sample size. Recent work has shown that optimally weighted ensembles of nonparametric estimators can be used to achieve a fast convergence rate when estimating information theoretic functionals such as information divergence. We explore the extension of this theory to density …

Development Of Particle Image Velocimetry Learning Tool: Learnpiv.Org, Kevin Roberts

Student Research Symposium

Particle Image Velocimetry (PIV) is an experimental measurement technique used for quantitative and visual analysis of the velocity distribution in a flow field. Researchers conduct PIV by using lasers to illuminate particles in a flow field of interest, digital cameras to record images of these illuminated particles, and PIV software to analyze the recorded images, producing a velocity vector field. Applying proper techniques to gather useful images and identifying PIV processing algorithm parameters to the collected images is a challenging task for novice PIV users who are unaware of the inner workings of PIV algorithms. Recognizing this problem, we created …

A New Non-Inheriting Homogeneous Solution Of The Einstein-Maxwell Equations With Cosmological Term, Ian M. Anderson, Charles G. Torre

Publications

We find a new homogeneous solution to the Einstein-Maxwell equations with a cos- mological term. The spacetime manifold is R × S3. The spacetime metric admits a simply transitive isometry group G = R × SU(2) and is Petrov type I. The spacetime is geodesically complete and globally hyperbolic. The electromagnetic field is non- null and non-inheriting: it is only invariant with respect to the SU(2) subgroup and is time-dependent in a stationary reference frame.