Mathematics Commons^™

Data Science For Engineers, Heidi Moulton

Undergraduate Honors Capstone Projects

Undergraduate research is a core pillar of Utah State University’s College of Engineering. Many students become involved with research during their Junior and Senior years and begin to generate various forms of data. Most students, however, have received little formal education on how to process data, and there are currently no readily available resources within the College of Engineering. As a Mechanical Engineering and Data Science double major, I found the data processing techniques I learned in my Data Science courses invaluable as an undergraduate researcher, and now as a Mechanical Engineer at Apogee Instruments, I frequently draw upon these …

Geometric Algebra For Field Theory In Curved Spacetime, Kevin Rhine

All Graduate Reports and Creative Projects, Fall 2023 to Present

Physics seeks to understand the universe by uncovering the fundamental laws that govern matter, energy, space, and time. At its heart lies the challenge of unification: finding a mathematical framework that consistently describes these interactions across all scales, from the subatomic to the cosmological.

This thesis explores geometric algebra, a mathematical language that unifies algebra and geometry, as a tool for advancing this understanding. By extending this framework to curved spacetimes, where gravity influences the structure of space and time, we investigate its ability to describe physical phenomena such as electromagnetism and general relativity. A notable contribution includes the geometric …

Development Of Saddlepoint Methodologies For Sparse Sample Multiple Parameter Generalized Linear Models And Correlated Data Scenarios, Christopher Johnson

All Graduate Theses and Dissertations, Fall 2023 to Present

Parameter estimation using maximum likelihood techniques may be biased when sample sizes are small, event rates are low, or otherwise sparse counts exist in a parametric model. This in turn may lead researchers to draw invalid statistical conclusions when conventional methods are utilized. The saddlepoint approximation has potential to lessen the degree of bias in sparse data conditions through its use of moments beyond the mean and variance, which allows for more accurate approximations using a smaller number of observations. We propose two novel saddlepoint methods for use in practical analysis scenarios, as an alternative to maximum likelihood estimation. First, …

A Survey Of Master's Qualifying Exam Practices And Content In Real Analysis, Zachary M. Coverstone

All Graduate Theses and Dissertations, Fall 2023 to Present

Graduate programs in mathematics are intended to develop experts in mathematics. As part of a graduate program, many students are expected to engage in a qualifying examination that can serve myriad purposes. This dissertation investigates real analysis qualifying examinations at the master's level through a nation-wide survey of institutions in the Association of Public and Land-Grant Universities (APLU). This study reveals the practices in administration of real analysis qualifying exams, institutions reported offering traditional, pencil-and-paper exams and generally asked students to prepare individually using previously administered exams. The survey results show that approximately two in three APLU institutions offering master's …

Data Science For Engineers, Heidi Moulton

Student Research Symposium

30% of USU undergraduate students participate in some sort of research, and for engineering students this often means generating large amounts of data.

Data Science for Engineers is a series of four modules that introduce students to data processing, visualization, and graphing in the Python programming language using Pandas DataFrames and Juypter Notebooks.

The modules are intended for students with a basic understanding of programming in Python, specifically those who have taken CS 1400 Introduction to Computer Science.

The Stem Gender Gap: Can It Be Closed?, Makenna Roberts

Student Research Symposium

Introduction

While many industries have achieved gender parity, women remain underrepresented in STEM fields, with participation stagnating between 32% and 35% from 2011 to 2021. Research suggests this gap is influenced by relative cognitive strengths and social/societal factors. This study analyzes two datasets: (1) SAT score report data from the National College Board and (2) employment data from the 2021 NCSES Survey of Recent College Graduates. Findings highlight disparities at the highest percentiles and lower workforce participation among female STEM graduates.

The Applicability Of A/B Testing In Clinical Trials, Carlie Prinster

Student Research Symposium

• A/B Testing is a study method that allows researchers to compare two different options in a variety of different contexts, most usually in a business context (i.e.: font color).

• A/B Testing is starting to used in biostatistical application, such as for clinical trial recruitment improvement.

• A study done by previous researchers aimed to apply A/B Testing to clinical trial recruitment improvement.

• My goal was to build a model that used the data from this study but implement a dependent structure.

On Mach's Principle In General Relativistic Cosmological Models, Zach Zito

Student Research Symposium

General Relativity

1. Gravity is the mechanism by which matter influences inertia
2. This influence happens across a spacelike hypersurface
3. Geometrodynamic equations mathematically describe this influence

Exploring The Geometry Of Einstein's Field Equations: Understanding The Mathematics Behind Curved Spacetime, Morgan Maxwell

Student Research Symposium

Einstein's equations describe how spacetime bends in response to mass and energy:

Fiber Bundles Of The Complex Projective Space And Their Relation To Quantum Physics, Emily Wessman

Student Research Symposium

The complex projective space CPⁿ is the space of lines through the origin in Cⁿ⁺¹ with an equivalence relation defined by Z ~ λZ' for λ ∈ C*. We define the points under the equivalence relation as homogeneous coordinates, represented by [Z₀ : Z₁ : ... Z_n]. Since all Z,sub>i cannot equal zero, we can find a unique set of n coordinates (z₁,...,z_n) such that [Z₀ : Z₁ : ... : Z_n] ~ [1 : z₁ : ... : z_n] where z …

Supplementary Files For: "Structure Identification For High-Dimensional Data In The Vicinity Of Bear Lake", Ben Shaw, Haley Burger, Brennan Bean, Kevin Moon

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This report focuses on seven water quality measurements taken at 43 different depths on the Bear Lake for the months of June - November in the years 2018 - 2023. These measurements create a high-dimensional dataset on which we apply state-of-the-art machine learning (ML) techniques to look for low-dimensional structure in the data. A similar effort was made for weather measurements taken near the lake. Our analysis revealed that water quality measurements tend to cluster (i.e., group together) by year, while weather measurements tend to cluster by time of the year. This suggests that the structure observed in the water …

Cost-Effective Strategies For Feral Swine Control: Exploring Trapping Equipment Cooperatives, Phil Kenkel, Riza Radmehr, Rodney Holcomb, Mckenzie Boyce

Human–Wildlife Interactions

Feral swine (Sus scrofa) in the United States have become a growing concern, with a population of ≥6 million and causing annual damages of ≥$1.5 billion USD. Because of their high reproductive capacity, effective control methods are crucial to reducing or slowing their population growth. While remotely monitored and triggered traps have proven to be an effective control strategy, the cost of sophisticated trapping equipment, which can cost ≥$7,000 USD, is often cost prohibitive for many landowners. Despite the pressing need to address the challenge of making effective feral swine control methods more affordable, there are few studies …

Mathematical And Statistical Methods To Harness Limited Data In Models For Ecological Space Use Under Global Change, Sarah C. Bogen

All Graduate Theses and Dissertations, Fall 2023 to Present

The dynamics of how plants and animals use space in their habitats has important implications for the fields of ecology and conservation. However, understanding and responding to these spatial and temporal dynamics is often limited by data availability, financial resources and biases. As average global temperatures increase, suitable habitats shift poleward and require local populations to move with suitable habitat, adapt to the changing environment, or risk extinction. Capacity to persist without movement may be estimated by considering changes to a combination of habitat characteristics. Capacity to track suitable habitat may be modeled through synthesizing information on species demographic mechanisms …

Discrete Time Series Forecasting Of Hive Weight, In-Hive Temperature, And Hive Entrance Traffic In Non-Invasive Monitoring Of Managed Honey Bee Colonies: Part I, Vladimir A. Kulyukin, Daniel Coster, Aleksey V. Kulyukin, William Meikle, Milagra Weiss

Computer Science Faculty and Staff Publications

From June to October, 2022, we recorded the weight, the internal temperature, and the hive entrance video traffic of ten managed honey bee (Apis mellifera) colonies at a research apiary of the Carl Hayden Bee Research Center in Tucson, AZ, USA. The weight and temperature were recorded every five minutes around the clock. The 30 s videos were recorded every five minutes daily from 7:00 to 20:55. We curated the collected data into a dataset of 758,703 records (208,760–weight; 322,570–temperature; 155,373–video). A principal objective of Part I of our investigation was to use the curated dataset to investigate …

Quantifying The Impact Of Rain-On-Snow Induced Flooding In The Western United States, Brennan Lynn Bean, Emma Watts

Mathematics and Statistics Faculty Publications

The potentially destructive flooding resulting from rain-on-snow (ROS) events motivates efforts to better incorporate these events and their residual effects into flood-related infrastructure design. This paper examines relationships between measured streamflow surges at streamgages across the Western United States and the meteorological conditions preceding them at SNOTEL stations within the same water catchment. Relevant stream surges are identified using a peak detection algorithm via time series analysis, which are then labeled ROS- or non-ROS-induced based on the preceding meteorological conditions. Both empirical and model-derived differences between ROS- and non-ROS-induced stream surges are then explored, which suggest that ROS-induced stream surges …

A Preliminary Fuzzy Inference System For Predicting Atmospheric Ozone In An Intermountain Basin, John R. Lawson, Seth N. Lyman

Mathematics and Statistics Faculty Publications

High concentrations of ozone in the Uinta Basin, Utah, can occur after sufficient snowfall and a strong atmospheric anticyclone creates a persistent cold pool that traps emissions from oil and gas operations, where sustained photolysis of the precursors builds ozone to unhealthy concentrations. The basin's winter-ozone system is well understood by domain experts and supported by archives of atmospheric observations. Rules of the system can be formulated in natural language ("sufficient snowfall and high pressure leads to high ozone"), lending itself to analysis with a fuzzy-logic inference system. This method encodes human expertise as machine intelligence in a more prescribed …

Dynamic Optimization With Timing Risk, Erin Cottle Hunt, Frank N. Caliendo

Economics and Finance Faculty Publications

Timing risk refers to a situation in which the timing of an economically important event is unknown (risky) from the perspective of an economic decision maker. While this special class of dynamic stochastic control problems has many applications in economics, the methods used to solve them are not easily accessible within a single, comprehensive survey. We provide a survey of dynamic optimization methods under comprehensive assumptions about the nature of timing risk. We also relax the assumption of full information and summarize optimization with limited information, ambiguity, imperfect hedging, and dynamic inconsistency. Our goal is to provide a concise user …

Bootstrap Methods For Bias-Correcting Probability Distribution Parameters Characterizing Extreme Snow Accumulations, Kenneth Pomeyie, Brennan Bean

Mathematics and Statistics Student Research and Class Projects

Accurately quantifying the threat of collapse due to the weight of settled snow on the roof of a structure is crucial for ensuring structural safety. This quantification relies upon direct measurements of the snow water equivalent (SWE) of settled snow, though most weather stations in the United States only measure snow depth. The absence of direct load measurements necessitates the use of modeled estimates of SWE, which often results in the underestimation of the scale/variance parameter of the distribution of annual maximum SWE. This paper introduces a novel bias correction method that employs a bootstrap technique with regression-based models to …

Supplementary Files For "Using Digitized Building And Weather Records To Improve The Accuracy Of Ground To Roof Snow Load Ratio Estimations", Gideon Parry, Brennan Bean

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Reliability targeted snow loads (RTLs) measure the weight in accumulated snow (i.e. snow load) that a roof is required to support to ensure the probability of failure is suf- ficiently low. This calculation has historically relied upon a probability distribution that characterizes the ratio between the annual maximum ground snow load to the annual max- imum roof snow load, a quantity referred to as Gr. The best available data for estimating Gr comes from Canadian case studies from the 1950s and 1960s. However, much of the data was never digitized, with only approximations of data being made available in scanned …

Supplementary Files For: "Interactive Modeling Of Bear Lake Elevations In A Future Climate", Benjamin D. Shaw, Scout Jarman, Brennan Bean, Kevin R. Moon, Wei Zhang, Nathan Butler, Tommy Bolton, April Knight, Emeline Haroldsen, Abby Funk, Rebecca Higbee

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The water level, or elevation, of Bear Lake has a significant impact on agriculture, power, infrastructure, and recreation for communities around the lake. Climatological variables, such as precipitation, temperature, and snowfall, all have an impact on the elevation of Bear Lake. As the climate changes due to greenhouse gas emissions, the typical behaviors of these climate variables change, leading to new behaviors in Bear Lake elevation. Because of the importance of Bear Lake, it is vital to be able to model and understand how Bear Lake's elevation may change in the face of different climate scenarios and to gain further …

Sustained Ifn Signaling Is Associated With Delayed Development Of Sars-Cov-2-Specific Immunity, Elsa Brunet-Ratnasingham, Sacha Sacha, Haley E. Randolph, Marjorie Labrecque, Justin Bélair, Raphaël Lima-Barbosa, Amélie Pagliuzza, Lorie Marchitto, Michael Hultström, Julia Niessl, Rose Cloutier, Alina M. Flores, Nathalie Brassard, Mehdi Benlarbi, Jérémie Prévost, Shilei Ding, Sai Priya Anand, Gérémy Sannier, Amanda Marks, Dick Wågsäter, Eric Bareke, Hugo Zeberg, Miklos Lipcsey, Robert Frithiof, Anders Larsson, Sirui Zhou, Tomoko Nakanishi, David Morrison, Dani Vezina, Catherine Bourassa, Gabrielle Gendron-Lepage, Halima Medjahed, Floriane Point, Jonathan Richard, Catherine Larochelle, Alexandre Prat, Janet L. Cunningham, Nathalie Arbour, Madeleine Durand, J. Brent Richards, Kevin Moon, Nicolas Chomont, Andrés Finzi, Martine Tétreault, Luis Barreiro, Guy Wolf, Daniel E. Kaufmann

Mathematics and Statistics Faculty Presentations

Plasma RNAemia, delayed antibody responses and inflammation predict COVID-19 outcomes, but the mechanisms underlying these immunovirological patterns are poorly understood. We profile 782 longitudinal plasma samples from 318 hospitalized patients with COVID-19. Integrated analysis using k-means reveals four patient clusters in a discovery cohort: mechanically ventilated critically-ill cases are subdivided into good prognosis and high-fatality clusters (reproduced in a validation cohort), while non-critical survivors segregate into high and low early antibody responders. Only the high-fatality cluster is enriched for transcriptomic signatures associated with COVID-19 severity, and each cluster has distinct RBD-specific antibody elicitation kinetics. Both critical and non-critical clusters with …

Landscape Influences On Thermal Sensitivity And Predicted Spatial Variability Among Brook Trout Streams In The Southeastern Usa, George P. Valentine, Xinyi Lu, C. Andrew Dolloff, Craig N. Roghair, Jacob M. Rash, Mevin B. Hooten, Yoichiro Kanno

Mathematics and Statistics Faculty Publications

Warming water temperatures as a result of climate change pose a major threat to coldwater organisms. However, the rate of warming is not spatially uniform due to surface-ground-water interactions and stream and watershed characteristics. Coldwater habitats that are most resistant to warming serve as thermal refugia and identifying their locations is critical to regional aquatic conservation planning. We quantified the thermal sensitivity of 203 streams providing current and potential habitat for brook trout (Salvelinus fontinalis) across nearly 1000 linear km of their native range in the southern and central Appalachian Mountains region, USA, and characterized their spatial variability …

Using Multi-Scale Spatial Models Of Dendritic Ecosystems To Infer Abundance Of A Stream Salmonid, Xinyi Lu, Yoichiro Kanno, George P. Valentine, Jacob M. Rash, Mevin B. Hooten

Mathematics and Statistics Faculty Publications

1. Understanding patterns of species abundance is essential for planning landscape-level conservation. The complex hierarchies of dendritic ecosystems result in different levels of heterogeneity at distinct geographic scales. Species responses to dynamic environmental drivers may also vary spatially depending on their interactions with landscape features. Monitoring abundance by explicitly quantifying their spatial and temporal variation is important for strategic management.

2. We analysed brook trout (Salvelinus fontinalis) count data collected from 173 sites in western North Carolina between 1989 and 2015. We developed a Bayesian hierarchical model that used single- and multi-pass electro-fishing data and characterized their respective …

Calculations From On The Existence Of Periodic Traveling-Wave Solutions To Certain Systems Of Nonlinear, Dispersive Wave Equations, Jacob Daniels

Mathematics and Statistics Student Research and Class Projects

In the field of nonlinear waves, particular interest is given to periodic traveling-wave solutions of nonlinear, dispersive wave equations. This thesis aims to determine the existence of periodic traveling-wave solutions for several systems of water wave equations. These systems are the Schr¨odinger KdV-KdV, Schr¨odinger BBM-BBM, Schr¨odinger KdV-BBM, and Schr¨odinger BBM-KdV systems, and the abcd-system. In particular, it is shown that periodic traveling-wave solutions exist and are explicitly given in terms of cnoidal, the Jacobi elliptic function. Certain solitary-wave solutions are also established as a limiting case of the periodic traveling-wave solutions, that is, as the elliptic modulus approaches one.

Tasks For Learning Trigonometry, Sydnee Andreasen

All Graduate Reports and Creative Projects, Fall 2023 to Present

Many studies have been done using task-based learning within different mathematics courses. Within the field of trigonometry, task-based learning is lacking. The following research aimed to create engaging, mathematically rich tasks that meet the standards for the current trigonometry course at Utah State University and align with the State of Utah Core Standards for 7th through 12th grades. Four lessons were selected and developed based on the alignment of standards, the relevance to the remainder of the trigonometry course, and the relevance to courses beyond trigonometry. The four lessons that were chosen and developed were related to trigonometric ratios, graphing …

On The Existence Of Periodic Traveling-Wave Solutions To Certain Systems Of Nonlinear, Dispersive Wave Equations, Jacob Daniels

All Graduate Theses and Dissertations, Fall 2023 to Present

A variety of physical phenomena can be modeled by systems of nonlinear, dispersive wave equations. Such examples include the propagation of a wave through a canal, deep ocean waves with small amplitude and long wavelength, and even the propagation of long-crested waves on the surface of lakes. An important task in the study of water wave equations is to determine whether a solution exists. This thesis aims to determine whether there exists solutions that both travel at a constant speed and are periodic for several systems of water wave equations. The work done in this thesis contributes to the subfields …

Vectors And Vector Borne Disease: Models For The Spread Of Curly Top Disease And Culex Mosquito Abundance, Rachel M. (Frantz) Georges

All Graduate Theses and Dissertations, Fall 2023 to Present

Mathematical models are useful tools in managing infectious disease. When designed appropriately, these models can provide insight into disease incidence patterns and transmission rates. In this work, we present several models that provide information that is useful in monitoring diseases spread by insects.

In the first part of this dissertation, we present two models that predict disease incidence patterns for Curly Top disease (CT) in tomato crops. CT affects a wide variety of plants and is spread through the bite of the Beet Leafhopper. This disease is particularly devastating to tomato crops. When infected, tomato plants present with stunted growth …

A Comprehensive Uncertainty Quantification Methodology For Metrology Calibration And Method Comparison Problems Via Numeric Solutions To Maximum Likelihood Estimation And Parametric Bootstrapping, Aloka B. S. N. Dayarathne

All Graduate Theses and Dissertations, Fall 2023 to Present

In metrology, the science of measurements, straight line calibration models are frequently employed. These models help understand the instrumental response to an analyte, whose chemical constituents are unknown, and predict the analyte’s concentration in a sample. Techniques such as ordinary least squares and generalized least squares are commonly used to fit these calibration curves. However, these methods may yield biased estimates of slope and intercept when the calibrant, substance used to calibrate an analytical procedure with known chemical constituents (x-values), carries uncertainty. To address this, Ripley and Thompson (1987) proposed functional relationship estimation by maximum likelihood (FREML), which considers uncertainties …

Towards Fast, Realistic Gas Plume Simulation For Lwir Hyperspectral Images To Improve Deep Learning Identification Models, Scout Jarman

Student Research Symposium

• Longwave infrared (LWIR) hyperspectral images (HSI) are taken from airborne platforms and can be used to find gas plumes.
• Detection and identification of gas plumes has applications in environmental monitoring, disaster response, and national security
• Deep learning can be used to identify gases from a large library of materials,  but can be difficult to apply in practice

Inferring Inertial Navigation Errors From Sar Image Distortions Using A Convolutional Neural Network, Teresa White

Student Research Symposium

Precise navigation data is necessary for autonomous vehicles. In normal circumstances: GPS is typically used.