# News & Events 2023-2024

## 2023 - 2024

#### 4/8 Department Picnic

12:00 - 2:00pm

Front of Tutt Science Center

Join us in front on Tutt Science for games, crafts, and, of course, some yummy food! We all made it to the end of the year and our seniors are about to graduate, so it’s time to celebrate! See you guys there!

## Capstone Presentations 5/2/2024

#### David Wine

###### An Analysis of Racial Disparity in Police Stops in Illinois

In this paper, I will perform analysis of a large data set containing information on police stops in the state of Illinois in an attempt to find potential racial biases. This is done by comparing the rate at which races are stopped to the rate at which those stops are ‘successful’, or which of those stops turned up contraband or led to further investigation or arrest. I found that Black or Hispanic drivers are stopped at a higher rate while also having a lower rate of success, indicating bias. I also completed the ‘Veil of Darkness’ test, comparing stop rates at a time of day when it is light outside during some part of the year and dark outside during another.

## Capstone Presentations 4/11/2024

#### Yousheng Tang

###### Harmonic Mappings and the Hexasquare

This study explains the foundational principles required for the creation of the "Hexasquare Minimal Surface". This study covers the main theorems, proofs, and examples related to analytic functions, conformal mappings, and Riemann Mapping Theorem. Building upon the fundamental theories, this study also includes a systematic exposition of the Schwarz-Christoffel Mapping, Poisson Integral Formula, Sheil-Small Theory, and their relation to the Hexasquare. Using harmonic functions defined on the unit disk, this study explains the mapping to hexagons that extends the properties of the harmonic mapping connected with the classical Scherk minimal surface. The new Hexasquare surface changes its boundary heights more frequently, and expands our understanding of Jenkins-Serrin Surfaces and their geometric properties.

#### Trey Crawford

###### Beyond Buzzer Beaters

This thesis provides an analysis of National Collegiate Athletic Association (NCAA) basketball stats and their relationship with winning percentage as determined by the outcome of individual games. It strives to identify the "Four Factors" that contribute the most to the outcomes of Division 1 (D1) College Basketball games during the 2016 season. Using a mathematical technique called \textbf{Logistic Regression}, the method can solve for weights or coefficients that test how important each stat relates to wins and losses. The findings of this study will further our understanding of the complex and dynamic nature of college basketball as the game keeps evolving and provide insights into the crucial statistics that influence game outcomes.

#### Silas Blanchard and Quinn Sebso

###### Esports Computer Availability

Our program aims to address a fundamental problem with the Colorado College esports lab; there is no way to know how busy the lab is without being there. For many students, particularly in cold months, the walk to the lab could be a huge wasted effort if they find it full. Our project is a website, built using node js, that displays which computers are in use and which are free. Additionally, it displays the calendar, something only available through Discord currently, and supports customization by gaming lab staff. Available to anyone on the Colorado College campus (and using a Colorado College network), this project is currently deployed and visitable at http://esportscomm.coloradocollege.edu.

#### Eric Uerling, Ethan Fuentes

###### Boys and Girls Country App

This project is to make an IOS app for Boys and Girls Country of Houston (BGC), a nonprofit children’s home. The app contains content about donating, placing a child, with the goal of creating an emotional connection and encouraging users to get involved with BGC. Another feature was the Clothing Closet, which allows BGC to upload their stock of donated clothes so that children and staff can easily view and order clothes.

## Capstone Presentations 4/9/2024

#### Gwen Hardwick

###### Supersingular Isogeny Diffie-Hellman Cryptography

In today's digital era, the need for secure communication is prominent. While traditional systems like RSA and ECDH fend off classical threats, quantum computers pose a new challenge. The Supersingular Isogeny Diffie-Hellman (SIDH) protocol emerged as a promising candidate, being one of three finalists in the NIST Post-Quantum Computing replacement campaign, prior to the groundbreaking Castryck-Decru Attack being published in July 2022. Its foundation lies in traversal over an isogeny graph made of supersingular elliptic curves.

#### Esa Chen, Junhao Qu

###### MonsterVault: Budgeting App

In an era where effective financial management is paramount yet challenging for many, MonsterVault, an iOS app, revolutionizes financial management by incorporating a virtual pet care system, encouraging expenses and income tracking with features like receipt scanning, object detection, and manual entry. For each recorded tracking, users accumulate points that can be exchanged for pet food, connecting users’ budgeting actions with the growth of pets. This gamification aspect makes financial management a more engaging and rewarding process, aiming to cultivate lasting financial discipline among users. MonsterVault enhances financial literacy through insights into spending patterns by offering a visual representation of spending habits and budget status. MonsterVault turns the routine task of budget management into an enjoyable activity, fostering financial discipline and literacy uniquely and interactively.

#### Fremont Fosberg

###### Async Co.

Async Co. is a software application designed for a theoretical Venture Capital company, inspired by a past work experience. Aysnc Co. is meant to be a centralized workplace for multiple workflows. The application allows the user to see data stored in a database about Investments, Investors, the relationship between Investors and Investments, as well as KPI data that would theoretically be acquired each quarter from the Investments to track growth.

#### Louisa Penrice, Blanche Stora

###### RoCCy Rides

As many of us know, the closest major airport to Colorado College is in Denver, an hour and fifteen minute drive away. Ride share applications, shuttles, and long term parking are expensive, and those with their own cars are forced to waste gas (and money) on a ride for themselves. Every school break, student group chats are flooded with inquiries hoping to connect with others flying in or out of the airport at similar times. RoCCy Rides is an iOS application built in Swift that streamlines this process by allowing students to post, chat, and connect with one another regarding airport transportation based on flight times. Thanks to this app, students will have one less thing to worry about when traveling.

#### Clay Arnold, Omar Castro-Frederick, Tom Heffernan, Jackson Kaib

###### A Machine Learning Approach to Detecting Credit Card Fraud

Credit card fraud poses a challenge for financial institutions, leading to losses and erosion of customer trust. We have developed Fraud Finders, a machine learning-based system designed to detect fraudulent credit card transactions. With models including Random Forest and XGBoost, our system looks at fraud data to identify patterns of fraud. We use Machine Learning Models trained on historical data, and a dashboard to visualize the results. We aim to make a solution that is scalable and secure. Our system hopes to mitigate risk and protect consumers.

## Capstone Presentations 4/8/2024

#### Jack Dresser, Lucy Flanagan, Jay Moran

###### TigerList

TigerList is a website for Colorado College students to buy, sell, or exchange goods and services. Mimicking an online marketplace, TigerList allows only Colorado College students to use the platform. Unlike other online marketplaces, TigerList guarantees products are within walking distance, are in safe locations and are only amongst other students. This improves safety and equity, while also encouraging good sustainability practices. Currently, Colorado College students have no single interface to message each other about buying and selling goods. Messages end up in class GroupMes, on Instagram stories, or by word of mouth, where everything typically gets drowned out, and also creates an equity concern of who gets what items. TigerList is a confluence for students to buy and sell goods without going to extreme measures.

#### Mai Nguyen, Khawla Douah, Calvin Than, Dylan Chapell

###### CoralLabeler: A better way to label large datasets

We built the CoralLabeler application to assist our clients, Dr. Cory Scott from Colorado College and Dr. Amber Stubler at Occidental College, in labeling a large dataset of underwater corals. We built tools into this application to manually label parts of the image and developed an API to allow a configurable machine-learning model to predict image labels. Once the labels have been produced, they will be used to train more effective machine-learning models for coral classification and generate statistics relevant to coral research.

#### Haoru Yang

###### The Winning Strategies of RISK: the Game Dynamic of Rolling More Dice with s Sides

The board game RISK has many interesting but complicated probabilistic problems. The classic version of RISK involves 3 attacking and 2 defending dice with 6 sides. This work investigated the modified versions of RISK with t × m battles, which involves t attacking dice and m defending dice with s sides. The paper presents the generic formulas for all possible outcomes of a single attack in 3 × 2 and 3 × 3 battles, and the simulated results of a single attack in other t×m battles. These results for each attack allow the estimation of actual conquer probabilities by normal approximation, and the estimation helps find the winning strategies and discuss game dynamics in modified games. The winning strategies show the number of attacking armies needed to conquer an enemy territory with approximately 50% and 80% chance of successful conquer, for example, the attacker needs 1.71 times of the defending armies to have over 50% chance of success in 3 × 3 battles. The paper also introduces a concept called ”balance of power” that measures the equivalence between the attacker and defender, for example, 3 × 2 battles with 6-sided dice favor the attacker and 3 × 3 battles with 6-sided dice favor the defender. The balance of power helps players understand the game dynamics and make reasonable decisions.

#### Obie Kahn

###### Chaotic Orbits and Random Fibonacci Sequences

From sequences (of numbers, of events, of movements) there can emerge a great deal of information. This thesis explores two types of sequences: (1) sequences, or "orbits," generated by repeatedly applying the same function to an initial value, and (2) variations of the famous Fibonacci Sequence, which we define recursively. By studying "period three" orbits in particular, we demonstrate how mathematical "chaos" arises in deterministic systems that have seemingly random behavior. We then harness randomness to construct variations of the Fibonacci Sequence with one random process and explore their growth rates, using these rates to offer a guess for the growth rate of a Fibonacci Sequence generated by two random processes.

#### Jingyi Liu

###### Comparative Analysis of Frequentist and Bayesian Variable Selection Methods on Mental Health Datasets

Variable selection remains an important problem researchers encounter when building a statistical model. While frequentist methods have been widely used in many fields, the Bayesian variable selection received less attention due to its complexity. In this paper, we review variable selection methods from both frequentist and Bayesian perspectives. We evaluate the performance of such algorithms via simulation studies using cross-validation. We argue that Bayesian variable selection is advantageous as it shows superior performance in identifying the true underlying process. The predictive performance of frequentist and Bayesian variable selection was assessed on international students' mental health during the pandemic as an application in psychology.

## Capstone Presentations 4/4/2024

#### John Lê

###### Bayesian Optimization: Theory and Applications

Optimization is a crucial process in mathematics, especially used in real-world scenarios such as economics, engineering, and machine learning. This is because optimization can give us information about an ideal solution in a scenario, underlying phenomenon given specific parameters, and etc. However, when dealing with black-box functions where we do not know anything about their usages and characteristics, Bayesian Optimization is a powerful tool that can be used to find global optimums in unfamiliar environments. This thesis provides a theoretical framework to Bayesian Optimization by understanding the foundations of Bayesian Inference.  Alongside the theory, this thesis explores the implementation of Python to employ Bayesian Optimization in various computational problems. Specifically, we will look at data in optimizing parameters for ferroelectric materials.

#### Zhiqi Yao

###### Comparison of the Predictive Ability of Different Financial Models for Stock Prices

This study compares the predictive abilities of two time series analysis models, the Geometric Brownian Motion (GBM) model and the Autoregressive Integrated Moving Average (ARIMA) model, in forecasting the stock prices of the S&P 500 index over both long-term and short-term periods. The performance of each model is evaluated using two error measures: the Root Mean Square Error (RMSE) and the Mean Absolute Percentage Error (MAPE). The results show that the ARIMA model outperforms the GBM model in predicting stock prices for both long-term and short-term periods.

#### Dan Conlin, Alisha Bloom, Elliot Triplett

###### Black and Pink Resource Portal and Data Visualization Page

The Southern Colorado chapter of Black and Pink is a prison abolition group that focuses on providing support for members of the community who have recently been unincarecerated. This project adds two pages to their website: one for folks to find reentry resources, and one aimed at educating people about the importance of prison abolition. Some of the resources include housing equity, LGBTQ+ centers, centers for people transitioning out of prison, food resources, and employment opportunities. The portal is easy to use, and easy for Black and Pink volunteers to update. The data visualization page provides clear visual portrayals of racial and other inequalities in the prison industrial complex within Colorado and the greater United States.

#### Dan Phuong, Teva Tannenbaum, Gwen Hardwick

###### College Marketplace App

To address the issue of college students’ wasteful behavior and transportation challenges, we developed a marketplace iOS app tailored for student needs. The app, designed with sustainability in mind, offers a platform for students to buy and sell items conveniently. With a user-friendly interface and a swiping mechanic reminiscent of popular social media apps, it encourages engagement and addresses safety concerns by facilitating transactions within the student community. A variety of other features are also included to contribute to the user experience.

#### Hayley Heineken

###### Pattern Formation in Arid Grasslands

Arid grasslands cover an estimated 35% of the earth’s surface and exist in nearly every continent (Archibold 2012). Low rainfall amounts and limited growth characterize these landscapes. As the changing climate threatens a continued decrease in rainfall, ecologists and applied mathematicians seek to quantify the point of ecosystem collapse and explore the effect of different conditions on observed patterns. We offer a model consisting of two partial differential equations that interact in a Turing manner to instigate pattern formation. Ultimately, we were able to quantify the point of ecosystem collapse under different parameter conditions, figures that will contribute to future conservation efforts. Additionally, we offer an in-depth analysis of the effect of different rates of water advection and diffusion on the types of patterns produced. This paper seeks to add to the existing ecological and mathematical knowledge on this topic through the introduction of a simple differential model that captures the most important aspects of more complex models on this topic.

#### Daniela Santillan

###### Pattern Finding: A Curriculum for the Stroud Scholars Program

This project consists of building a 3-week mathematics curriculum on pattern-finding for the quantitative reasoning course on the third and final summer of the Stroud program, which is a program that provides under-resourced high school students the experience of academic preparation and the opportunity to earn admission to Colorado College. The objective of the curriculum is for students to identify patterns, describe them mathematically, and demonstrate how pure math can be applied in the real world. Patterns we explore include number sequences, symmetry of figures, and fractals.

## 2023 - 2024

#### Friday 3/29 Paraprof Info Session

1:30 - 2:00pm

TSC 215 (Paraprof office)

The math and CS paraprof applications are open and just waiting to be applied to! If you are thinking about applying (this year or any year in the future) but want some more info, then drop by the paraprof info session after Nails & Pizza this Friday (3/29) from 1:30 to 2PM in Tutt Science 215 (the paraprof office!), with snacks provided. Find out about the regular responsibilities and fun opportunities that come with the positions!

#### Friday 3/29 Nails & Pizza

12:00 - 1:30pm

Math & CS Lounge

Our second and final of the semester! Join us in the Math and CS Lounge this Friday (3/29) from 12 to 1:30PM for the classic event. Come for yummy pizza, come for pretty nails, come for the hot, juicy gossip!

#### Friday 3/8 Pi Day!

Sadly the 14th of March falls over Spring Break, but that will not stop us from celebrating the most iconic number that math has to offer! On third Friday (3/8) at 2PM, join us for the Pi K walk/run, pie eating, and fun having!

## Capstone Presentations 3/6/2024

#### Tiia Shea

###### Integrating more real-data into Calculus I courses: An exploration and adaptation of Maximum Likelihood Estimation for math curriculum

How can students be motivated to invest in their own learning? This paper addresses the lack of real-world data in pure math curricula by adapting the maximum likelihood estimation method for usage in a Calculus I class. This is achieved through the creation of a small MLE-based calculus module.

Maximum likelihood estimation (MLE) is a statistical procedure used to estimate the parameter(s) of a probability distribution that best describes a data set. By using optimization of single-variable equations, MLE can be used to bring more real data into math classrooms.

Results of module implementation in Blocks 3 & 4 primarily show that students' perceptions about math applicability (where and how math can be useful in the real-world) and self-efficacy improved. Work in mathematics education is crucial to improving math curricula and making mathematics more applicable and accessible to all students.

#### Leo Fries

###### Positive Steady-State Varieties of 2-Reaction Chemical Reaction Networks

Chemical reaction network theory is a field of applied mathematics concerned with modeling chemical systems. It is used in many areas of science, for example in systems biology to understand cellular signaling networks. This research seeks to understand networks’ biologically relevant equilibrium points through the lens of algebraic geometry, by translating the networks into systems of polynomial equations and computing the positive portion of their solution sets. Currently, there is no algorithm to calculate this positive steady-state variety in general, or to determine if the variety is nonempty. This thesis provides the conditions for 2-reaction networks to produce a nonempty positive steady-state variety and a more in-depth classification of the varieties produced by 2- and 3-species, 2-reaction networks, grounded in combinatorial and algebraic properties.

#### Walt Jones and James Settles

###### Heat Sheet Cheat Sheet

The Accurate Heat Sheets project will allow a NCAA college track coaches to see competitor information for any race in one button click. The coach will upload a heat sheet to accurate-heat-sheet.com and will receive every runner’s personal best time, season-best time, and other relevant information about the runners so that the coach may make accurate race strategy decisions for their athletes. Initially, this will be deployed as a web application, and the database will support the 800, 1500, 3,000 steeplechase, 5,000 and 10,000 meter distances.

#### Kaija van Zante, Kathleen Shea, Lizzie Blaschke, and August Knox

###### Cutler Publications App

Get access to all of Culter’s publications on-the-go! Currently, Cutler sponsors five different publications, all of which have different release schedules and limited physical copies, making it difficult to keep up with the variety of writing and art that students are producing. Our iOS application allows users to view content from The Catalyst, Cipher, Leviathan, Anamnesis, and The Disincentive. Exciting features include favoriting articles for easy access later, the ability to search by keywords and article content across all publications, and receiving notifications from authors/publications users subscribe to. By bringing all of Cutler’s writers and artists together under one mobile platform, we hope to boost readership and retention for Colorado College’s numerous publications.

#### Tyler Chang and Simay Cural

###### Preserve: Reduce Waste at Home

The FDA indicates that the typical household wastes around 32% of purchased foods. Preserve, an iOS mobile application, serves as a solution by keeping track of ingredients within refrigerators, pantries, and freezers accompanied by reminder notifications of when an item is about to go bad. Users can import food from the physical world to the digital world through barcode scanning, receipt scanning, or manual entry. Each imported item is assigned an estimated shelf life based on a dataset from the USDA. Users are then reminded of products that are about to or have expired. Additionally, Preserve recommends recipes that use produce that are soon to go bad in the inventory. With these tools, Preserve provides intuitive ways to prevent food waste.

## More 2023 - 2024 Events

#### Block 6 First Monday 2/19

Monday, February 19 (Week 1)

Gates Commons

3:30 - 5:00pm

In their First Monday presentation, Professors Cory Scott, Blake Jackson, and Ben Nye discuss the history and context of machine intelligence, fundamentals of how these systems work, what's happening at the cutting edge, and how we can strike a balance between powerful technology and social benefit.

#### Nails & Pizza 2/9

Friday, February 9 (Week 3)

Math & CS Lounge

12:00 - 1:00pm

#### JMM 24

##### Galileo Fries wins an outstanding speaker award at the 2024 Joint Mathematics Meetings’ Conference.  Congratulations Galileo!
Fries presenting at JMM 2024

#### JMM 24

CC Group at JMM 2024

L-R:  Nathan Mankovich, Hanson Smith, Joseph Rennie,

Sam Johnson, Isak Larson, Brendan McCune, Galileo Fries,

Sarah Wolff, Beth Malmskog, Sophie Aiken, Molly Moran

#### The Ethics of ChatGPT

Thursday 12/14/23, 12:15 pm

South Hall Commons

#### Snowflakes + Snacks!

Tuesday, December 3 (Week 2)

Math & CS Lounge

1:00 - 2:00 pm

Attractions include:

❄️Cutting out snowflakes and making other paper crafts❄️

💅Wintery nail painting🌨️

🖌️Face Painting🎨

🍫Drinking hot chocolate☕

🍿Other snacks like popcorn + fruit🍓

… And so much more!!

#### Fearless Friday 11/3

Friday, November 3 (Week 2)

TSC 122

12:00 - Pizza!

12:30 – 1:30 pm:  Faculty Research Bytes

1:30 - 3:00:  Student poster fair

Zoom

#### Nails & Pizza 9/29

Friday, September 29 (Week 1)

Math & CS Lounge

12:00 - 1:30

## 2022 - 2023

#### End of Year Celebration!

In lieu of the traditional picnic, the department will hold a fun-filled gathering indoors, featuring a mashup of some of our favorite activities from the year! Request food, nail polish colors, and activity ideas here.

## Capstone Presentations 2023

#### Olivia Bouthot

###### An Exploration of Symmetry Groups

Humans are drawn to patterns, whether that be in the reflective symmetry of butterflies or repetition of musical beats. In exploring pattern classification through geometric means, it becomes clear how math always informs the structure of our world, including beauty. This thesis explores the classification of frieze and wallpaper groups. We follow the methodology of William Barker and Roger Howe in their book Continuous symmetry: From Euclid to Klein. We categorize 7 isomorphism classes for frieze groups, and 17 for wallpaper groups. The method is similar for frieze and wallpaper groups, illuminating the possibility of higher dimensional pattern classification.

#### Tim Somerset

###### Prior sensitivity analysis of Bayesian hidden Markov models for hospital infection data

Analyzing hospital infection data presents a number of difficulties from the structure of the data – sparse, low counts, and auto correlated – to the nature of the data generation process – transmission through largely unobserved infections. A natural solution is to use a hidden Markov model. This talk focuses on a Bayesian methodology to this model, a key step of which is to define our prior belief of key transmission parameter values. Due to the size of the dataset, our prior belief has a large impact on the output of the analysis. What is this impact? And is there a predictable pattern we can identify?

Topics covered in the talk include: Bayesian/frequentist statistics, Monte-Carlo Markov chain sampling, and hidden Markov models.

#### Edie Brazil

###### Mathematical Model of Stochastic Differential Equations of Population Recovery Dynamics with a Non-Constant Carrying Capacity

Stochastic models integrate randomness into the model which allows us to analyze systems and processes and their dynamics in the presence of noise. We use the methods outlined by Gillespie in his paper, “The Chemical Langevin Equation” to develop a mathematical model of stochastic differential equations modeling population dynamics with a nonconstant carrying capacity in the wake of an assumed population devastating event. We are interested in how the aggregation of noise contributed by the individuals of a population affects population recovery dynamics. This presentation will include an overview of our model and its derivation and underlying assumptions and an analysis of our simulation results.

#### 3:30 – 3:55 pm

###### The Quantitative Reasoning Center Scheduling System (QSS)

The QSS is an online application that will be used by the directors of the Quantitative Reasoning Center (QRC) for scheduling tutors’ walk-in shifts. The QSS will utilize a variety of tutor inputs to determine the schedule by allocating the best set of shifts to each tutor. The website will allow the heads of the QRC to manage all aspects of the scheduling while giving the tutors the ability to select which shifts they would like to sign up for. With this application, blockly meetings between QRC tutors and administrators will become much more efficient and organized.

#### Will Barber, Tucker Hale, Bryan Moreno, Ronak Patel

###### Find Your Fun: Building Your Calendar With A Little Help from AI

Search engines today have made it extremely easy to find anything and everything, too easy in fact! When it comes to adding to your personal schedule, too many options on what to do can make adding events and planning unnecessarily cumbersome. Our web application seeks to make the process of finding things to do in your local area easy and convenient. Our web app offers a concise selection of events its users can chose from. We use Natural Language Processing (Python spaCy) to look through the descriptions of events hosted on our website to assign it the most relevant tags to further tailor user experience.

## Capstone Presentations 2023

#### Marcus Behenna, Quattro Musser, Moses Solomon

###### Visualizing Sodomitical Paris

Accounts of homosexual practices in 18th century Europe are few and far between. The scarcity of these accounts often limits historians to analysis of individuals, obscuring larger scale community dynamics. 18th century records of the Parisian Police give historians a rare opportunity to study homosexual practices on the level of communities, through a wealth of data on masculine homosexual practices, and the policing thereof. The project “Policing Male Homosexuality in 18th Century Paris,” (PHS) founded in 2016, is working to translate these documents into English, publish them online, and supply the tools necessary for community scale analysis of these records. For our thesis project we developed two such tools: a web map and a data dashboard. The web map allows users to visualize, query, and filter all locational data the project has translated. The data dashboard allows users to explore non-locational data and create their own charts with custom filters.

#### William Holtz, Daniel Lewinsohn, Ben Modlin, Max Perozek

###### scSHARP: Python and R Packages for Robust Single-Cell RNA Sequencing Cell Type Annotation

Single-cell RNA sequencing (scRNA-seq) data, annotated by cell type, are useful in a variety of downstream biological applications, such as profiling gene expression at the single-cell level. However, manually assigning these annotations with known marker genes is both time-consuming and subjective. We present scSHARP, a combination of Python and R packages that is easily installable and usable for bioinformatics researchers. Our R package, R4scSHARP, implements five state-of-the-art cell type annotation tools which allow us to find cells with highly confident assignments through consensus. Our Python package, scSHARP, provides a semi-supervised Graph Convolutional Network (GCN) and other methods to spread these confident labels and interpret the results. As a result, scSHARP provides highly accurate and interpretable cell type annotations in an easy-to-use format.

#### Henry Jones

###### Explorations in Diffusion and the Mean First Passage Time

The subject of interest in a variety of applied and theoretical fields, the Mean First Passage Time (MFPT) is a solution to a particular Poisson equation deeply connected to the classical diffusion equation. Within the scope of this thesis, the MFPT is interpreted as the average time for a diffusing particle or random walker to arrive or 'react' at an absorbing boundary. This thesis aims to contextualize the study of diffusion and random walks and examine comparisons between the discrete and continuous. We begin with several foundational derivations before delving into some analytical and numerical results for a particularly interesting MFPT problem.

#### Na’ama Nevo

###### Error Correcting Codes

Error Correcting Codes are algorithms used to maximize accurate data transmission in networks between a sender and receiver. Data transmission is often hindered by random errors which can flip bits of a message to the wrong symbols. The goals of error correcting codes is both to be able to detect as many errors as possible and to be able correct as many errors as possible, while also maximizing the length of possible messages and minimizing the amount of storage space required. Hermitian-Lifted Codes were first described in a paper by Lopez, Malmskog, Matthews, Pinero-Gonzales, Wootters, and have many advantageous properties such as maximal length and good locality and availability. Additionally, the Hermitian-Lifted Code has a large dimension, which is an improvements from previous similar codes.

#### Emerson Worrell

###### An Exploration of Connect Sums of Knots Using the Trip Matrix

In the field of knot theory, we use knot invariants to determine if two knots are the same or distinct. The trip matrix provides a method of computing a knot invariant known as the Jones Polynomial that requires only linear algebra. The encapsulation of so much information in a matrix over Z_2 provides an interesting opportunity to see what other tasks the trip matrix can be used to perform. We utilize the trip matrix method to give an alternative proof that the Jones Polynomial is multiplicative under connect sums, and then use the structure of the trip matrix itself as a method to determine if a given knot diagram with minimal crossing representation is prime or composite.

#### Davidson Cheng

###### Lattice-based Cryptography on Quantum Computer

Lattice-based crypto systems are currently the prime candidates for quantum-secure crypto systems. This talk will cover an introduction to hard lattice problems, which are at the core of lattice-based cryptography. I will also illustrate how a specific instance of a hard lattice problem might be solved efficiently on a general purpose quantum computer.

## Capstone Presentations 2023

#### Mike Romer

###### Exploring the Rubik’s Cube Group

The Rubik’s Cube was invented in 1974 by architecture professor Ernő Rubik. Since then, it has become the most popular puzzle in history according to the national museum of play. Despite the cube’s popularity, its underlying algebraic structure is rarely discussed outside of college math departments. This is understandable as configurations of the Rubik’s Cube can be represented by a mathematical group with over forty-three quintillion elements. This project investigated the structure of this group and its subgroups and used them to create an original solution to the puzzle.

#### Casmali Lopez

###### Phylogenetic Networks: Combinatorics and Algebra

This presentation will demonstrate the applications of combinatorics and algebra to the field of phylogenetics. Phylogenetics is the study of the evolutionary relationships between organisms. The goal of phylogenetics is to use biological data from a collection of individuals or species to infer a tree or network that describes how they are related evolutionary. Phylogenetic networks, an expansion of phylogenetic trees, are more accurate in certain biological circumstances but provide increased complexity and therefore increased mathematical challenges. The first section of this presentation will work through counting results related to phylogenetic networks. The second section of this presentation focuses on the statistical algebra of phylogenetic networks and their use in inferring phylogenetic networks.

#### Cooper Doe

###### Effect of Randomness on Behavior of Gene Transcription in Certain Motifs

Transcription of genes within organisms can be characterized as a Gene Regulatory Network of different smaller patterns, called motifs. The Feed Forward Loop (FFL), a three-gene motif, is characterized by a first gene X that has a direct effect on second gene Y, and a direct effect on final gene Z. Gene Y also has a direct effect on the final gene Z. FFLs are 'incoherent' if the indirect and direct pathways have an opposite effect (e.g. upregulation or downregulation). The first IFFL is the most biologically abundant incoherent loop. We find that certain deterministically predicted functions of the I1-FFL are not reproducible in our models with added stochasticity, and some functions are heavily dependent on intra-cell gene particle density.

#### Ethan Lebowitz, Tony Mastromarino, Mac O’Brien

###### QuickCheck: Rapid Formative Assessment for K-12 Teachers

There's been a push in the education sphere towards formative assessment; as opposed to tests and quizzes, which happen at the end of a unit, formative assessment establishes an understanding of student knowledge at the time of teaching. This allows teachers to adjust their lesson plans and ensure that the entire class is on the same page. Like most things within the education, there's been little support with this; so, working with science teaching coach Monica Tino, we developed a web app that allows teachers to set up their classes and assessments on their computers and quickly perform the assessments while teaching on their phones, capturing data in a way that empowers teachers to do what they do best.

#### Davidson Cheng, Hset Hset Naing, Richard Wang

###### Mesh Feature Learning

It is difficult for computers to understand “shapes”: an apple and a plane both appear as a sequence of bits. But there is one specific
way to convey “shape” information to a computer: graphs! In our project, we developed a model that extracts structural information from graphs using adversarial machine learning, and we put it to the test by comparing our feature extraction method with a traditionally robust feature extraction method: heat kernel signature.

## Capstone Presentations 2023

#### Lena Fleischer, Ellen Moore, Miranda Hunter

###### Sun Chase: A Machine Learning-Based iOS App Predicting the Beauty of Sunrises and Sunsets

Have you ever woken up early to watch the sunrise, only to be disappointed by gray skies? Our mission is to create an iOS application which predicts the aesthetic quality of sunrises and sunsets, encouraging users to get outside when skies are beautiful. The app takes in user location and gathers corresponding weather data which it passes into a machine learning algorithm. We have trained a neural network to recognize weather patterns that are highly correlated with beautiful skies, using geotagged image data (Flickr API) in tandem with historical weather data (Visual Crossing API). This model, trained in Python (PyTorch), is then packaged into an iOS application built using Swift. The final product, Sun Chase, is an intuitive application which displays sunrise and sunset predictions.

#### Liz Seero

###### Recovery Connection

According to the most recent SAMHSA National Survey on Drug Use and Health (NSDUH) detailing
Mental Illness and Substance Use Levels in 2021, 46.3 million people meet the DSM-5 criteria for having
a substance use disorder in the past year. The same study found that in that same year, 94% of people
aged 12 or older with a substance use disorder did not receive any treatment. The project aimed to
focus on recovery through the lens of Human Computer Interaction utilizing an Agile Design process.
Recovery Connection is a life tracking and reflection application that allows for users to record and
analyze information about relationships, activities, and substances. To test usability, I conducted two
user studies and implemented program changes inspired by the results. Available on both mobile and
desktop, Recovery Connection is a tool that was built to protect integrity, provide a non-judgmental
place to store and revisit private information, and above all, provide help to under-served communities.

## Springs 2023 Events

#### Beans and Board Games!

Friday, March 3rd, 2023

Come play board and card games with the Math & CS paraprofs, and eat Chipotle! All students, staff, and faculty welcome!

Request games and food using this form!

Math & CS Lounge
(Tutt Science, 2nd Floor, North)
12:00 - 1:30 PM
Friday, March 3rd

#### Nails and Pizza!

Friday, February 17th, 2023

• Hang out with the math & CS paraprofs!
• Give your nails a spiffy new look!
• Eat pizza!