2022 Student Abstracts


Grace Stoh – 5:30 pm (Wisconsin Lutheran College)
Room: GMS 1097

Title: Mountain Glacier Segmentation Method Using L*a*b* Color Space

Abstract: Change in a glacier’s size can be used as a physical indicator of the rate of climate change. However, the remote nature of glaciers renders direct measurement impractical. For this reason, researchers have been working to find an accurate remote measurement technique to calculate the area of glaciers. Since there are almost 200,000 glaciers around the world, such a technique also needs to be efficient and ideally automated. This project used Landsat satellite images to identify glaciers and segment them from their surroundings. A color-based image segmentation method was developed to find the area of glaciers from Landsat images, then implemented on images of Gorner Glacier in Switzerland and Franz Josef Glacier in New Zealand. Three satellite color bands were compiled into a false color image and then segmented in the L*a*b* color space. The transformation from the typical RGB colorspace to the L*a*b color space allowed the red “land” pixels to be easily eliminated, leaving behind the blue pixels of the glacier for area calculation.

Grace is currently taking guitar lessons and a journaling art class to force herself to make time for fun things. 🙂

Nicole Xie – 5:30 pm (Lawrence University)
Room: GMS 1096

Title: Symmetric Union Presentation and Beta Invariant

Abstract: The symmetric union presentation of knots is a field of knot theory that has recently come to people’s attention. Its fundamental challenge is identifying knot invariants in order to distinguish between various knots. In this talk, we will investigate a new way of constructing a family of knot invariants, the beta value of a Symmetric Union K and its partial knot J, defined as β(J, K) = 2b(J) − b(K) − 1 where b() is the bridge invariant, and the beta invariant of J is the maximum beta value we can have for β(J, K). We found the upper bound and lower bound for β(J), providing some insight about the relationship between β(J) and β(K), connecting the beta value of each symmetrical union presentation with its partial knot. The research presented here was carried out as part of the Ploymath Jr. 2022 online program under the direction of Associate Professor Alex Zupan at the University of Nebraska-Lincoln and Ana Wright, a fifth-year PhD student for the project Symmetric union presentations for ribbon links.

Nicole used to want to be a bank teller when she was little. The reason is she saw how they took the money from her mom and put it in their drawer, then thought it meant the money was all theirs, so she wanted to be them.

Ted Reimer – 5:50 pm (Carthage College)
Room: GMS 1097

Title: Coincidence Isometries of 3D Lattices

Abstract: Crystal structures are important to the material and geographic sciences, so it is reasonable to desire a mathematical model for their study. We do this using lattices: these are integer linear combinations of a set of basis vectors which we will represent as a single matrix. Rotating, shifting, and otherwise altering these lattices can help us represent crystal defects, which occur where two different crystals meet. In this work we review coincidence site lattices, that is, new lattices made of points where a lattice and the image of its transformation intersect. Our primary concern is determining when a rotation actually results in a coincidence site lattice. We cover the matrices for three dimensional crystals with two complex eigenvalues and one real eigenvalue, and we prove that we can consider this case as a rotation of lattices with a real diagonal basis matrix.

Ted is the captain and treasurer of Carthage’s Ultimate Frisbee team, Blitz, and plays upright bass for the Carthage Jazz Ensemble. 

Melissa Miller – 6:10 pm (MSOE)
Room: GMS 1097

Title: Advancing Aviation Safety with Linear Algebra

Abstract: My research focused on improving aviation safety through linear algebra. Aircraft landing and takeoff are heavily influenced by the variable of airflow, which in turn is influenced by gust fronts, wakes, sea breezes, and induced flows. These segments of air travel are particularly dangerous due to the pilot’s limited time to react to resulting hazardous situations. Aviation safety can therefore be improved by a deeper understanding and interpretation of airflow using various dynamical system identification tools typically found in linear algebra. The overarching objective is to apply these tools to time-sensitive data and then relay the results to pilots in order to potentially delay landing or takeoff. This project relied on heavy usage of MATLAB to apply singular value decomposition (SVD), dynamic mode decomposition (DMD), and proper orthogonal decomposition (POD) to data gathered from the Hong Kong International Airport.

Melissa loves to draw in her spare time (especially cars), and has eaten both a scorpion and fish eyeball. 

Crimson Groh – 6:30 pm (SNC)
Room: GMS 1097

Title: Redistricting: Gini Index, Calculations, Restrictions, and Applications

Abstract: The debate between what is considered fair political redistricting has been around for years. Occasionally politicians manipulate boundaries in order to assist their party in elections. Due to this, there exist many methods to determine the level of inequality presented in political redistricting plans, one of which is to use the Partisan Gini Index. We explore various ways to calculate this index, what restrictions exist, and how we can apply this to other voting methods.

Crimson’s minor is Spanish and she traveled to Peru for a summer.  She’s the youngest of 6 kids and  will be a first generation college graduate.

Alexandra Bennett – 6:50 pm (SNC)
Room: GMS 1097

Title: Measuring Partisan Bias with Randomly Generated District Maps

Abstract: In order to analyze partisan bias in the redistricting process, we constructed an ensemble of random district maps for Iowa.  Then using historical voting data, we evaluated the constructed maps using the Partisan Gini Index and compared them to the district maps actually used by Iowa.

Ali started downhill skiing with my family at 2 years old. 

GMS 1097

Zoua Xiong – 9:00 am (UW-Green Bay)
Title: Regression Model Selection

Abstract: One important aspect of research that is often overlooked is the process of choosing the best statistical model to represent the relationships between the variables in a data set. In this presentation, we study the factors that affect female infertility. A readily available R data set is used in the analysis. The participants consisted of 333 women who were having trouble getting pregnant. A key method for assessing fertility is a count of antral follicles (LowAFC), which is performed with noninvasive ultrasound. We are interested in how the following variables are related to these counts: age, maximum follicle stimulating hormone level (FSH), fertility level (E2), maximum fertility level (MaxE2), maximum daily gonadotropin level (MaxDailyGn), total gonadotropin level (TotalGn), number of egg cells (Oocytes), and number of embryos (Embryos). Various methods are used to obtain different statistical models for the data set, including but not limited to, T-tests, nested F-tests, interaction effects, and multicollinearity. Finally, based on model assumptions and model selection criteria, the best regression model was chosen.

Zoua enjoys hiking and doing yoga in her free time.

Zachariah Kline – 9:20 am (Wisconsin Lutheran College)
Title: A Performance Comparison of Principal Component Analysis and Non-Negative Matrix Factorization on Optical Spectroscopy Data

Abstract: The nuclear energy industry is one of many industries that are actively seeking ways to improve measurement collection accuracy. Data containing information about the elemental and isotopic compositions of nuclear materials found in spent fuel rods is one example of a dataset that needs to be tremendously accurate in order to ensure the safety of facilities and the workers inside. One popular method of collecting unique atomic information about a chemical species is through absorption spectroscopy. These measurements are then used for quantification analysis; to better understand the chemical makeup of a particular solution. However, the amount of data required to effectively predict concentrations negatively impacts the overall analysis due to one problem: high dimensionality. In this research, we use linear algebra techniques such as principal component analysis (PCA) and non-negative matrix factorization (NNMF) to solve the issue of high dimensionality. These different techniques complete this task by reducing the total number of dimensions and numerical complexity of our absorption measurements of different samples of plutonium (IV) in nitric acid. After applying PCA and NNMF on our given dataset, statistical methods are used to generate concentration prediction models for both solution components. Using metrics created from the prediction models – such as the coefficient of determination, root mean squared error, and reconstruction error – we compare the efficiency of PCA and NNMF in relation to their dimensionality reduction capabilities, computational complexity, statistical explainability, and general analysis.

Andrew Radicker – 9:40 am (Bradley University)
Title: Double Nim

Abstract: Nim is a simple combinatorial game with finitely many possibilities. Unlike many games of a similar description, Nim is not simply a single game, but a set of games. The general premise in Nim is as follows: players take turns removing sticks from some number of piles, subject to some constraint. The win conditions vary. In this talk, we will explore “Double Nim,” a variant with a single pile, in which a player may not take more than double the number of sticks the previous player took, where the winner is the player who takes the last stick. We will find that, as we analyze games with different pile sizes, a familiar sequence of numbers emerges. 

Andrew is the president of Bradley’s Chess Club and Bradley’s Math Club. He is also the current Bradley University Spotlight Speech Competition champion. Andrew has a passion for both puzzles and yo-yoing.

Nathaniel Woltman – 10:05 am (St Norbert University)
Title: Pure Taxicab Geometry and Euclid: Investigating How Circles, Chords, and Angles Behave

Abstract: We investigate what happens when we change the distance metric allowing it to affect geometric constructs such as circles, chords, and angles, forming what is now known as pure taxicab geometry. We also investigate some of Euclid’s Book I and Book III propositions which deal with chords and angles through the lens of pure taxicab geometry to see how they are preserved and under what restrictions.

Nathaniel knows how to play three instruments: piano, trumpet, and recorder. 

Kyle Pulvermacher – 10:35 am (UW-Stevens Point)
Title: Statistical Sampling in a Library: The Unexpected Challenges of Data Collection

Abstract: In a world increasingly focused on data-driven decision-making, our techniques for statistical analysis depend on the reliability of data collection itself.  However, as I found out while analyzing fiction and nonfiction literature at the UWSP library, collecting representative samples of data often poses significant challenges.  In this presentation, I will first explain how I implemented stratified random sampling to gather library data, followed by a discussion of the results and lessons learned.

Outside of studying math and being involved in campus activities, Kyle enjoys spending time outside biking newly discovered trails, relaxing at Schmeeckle Reserve in Stevens Point, playing tennis/pickleball, kayaking, and trout fishing.  He also has fun playing trombone during the summer for the Waupaca City Band!

Luke Kovscek – 10:55 am (Lawrence University)
Title:  T-Singularities on KSBA Stable Surfaces

Abstract: Algebraic varieties are locally described by polynomials. We study algebraic varieties of dimension two, known as algebraic surfaces. Quotient singularities, which commonly appear on algebraic surfaces, have nice combinatorial constructions. We describe some of these constructions and present a set of novel examples that correspond to singular algebraic surfaces.

Luke is currently studying classical saxophone.