# By the Numb3rs Spring 2021 - Undergraduate

## 2021 MathFest

The 2021 MATHFEST was held virtually on Friday, April 9th, 2021, from 2:30 pm to 5:00 pm. The COVID related constraints did not stop our students from showcasing their research. With the participation of undergraduate students, graduate students, and faculty, there were always as least 25 participants present throughout the event, with the maximum being 39; participants devoted their Friday afternoon to discuss their work in various problems, both in applied and fundamental mathematics.

We had three presentations, in Section 1, by a combined total of 9 students who reported on their work on Math 1103 BIG Ideas. The discussed Natural Gas Production, optimizing defensive alignments in baseball, and predicting post-peak baseball player performance. Our keynote speaker, Derek Orr, described for us his path from BS to PhD in Mathematics; he earned both degrees in our department, having defended his thesis in March 2021 and begun a financial analyst position at BNY Mellon. In the second Session, we heard from four more undergraduates, Sebastian Cohn, Caroline Kulczycky, Marissa Porco, and Juliet Flynn, who reported on their work done in Math 1902 Undergraduate Research in Mathematics. They discussed problems in neural networks, fractal visualization, and combinatorial game theory.

## Painter Research Fellowship/Pitt Day of Giving

The faculty, staff and students of the Mathematics Department would like to take this opportunity to express our thanks to the Painter family for their new endowment for undergraduate research and to our community-at-large for their support and generosity during the recent successful Pitt Day of Giving campaign.

During recent years faculty-mentored undergraduate research in the Mathematics Department has expanded rapidly and become an integral part of a student’s training and experience. A research experience of this sort complements traditional course work with specialized training that can help to prepare undergraduate students for rewarding careers in meaningful research. Our highly successful academic-year undergraduate research program now culminates in an annual MathFest highlighting students’ accomplishments. However, time limitations and academic demands can significantly impact a student’s progress in a research project when conducted during the academic year. As a result, it became increasingly important to identify funding to support projects during the summer, allowing students to continue working full time in Pittsburgh with their chosen faculty advisor.

The Painter family established an endowment in 2019 to fund such scholarly initiatives in the Mathematics Department. The Painter Fellowship fund was created to acknowledge the contributions of Dr. James A. Painter. Dr. Painter’s career in Mathematics began at the University of Pittsburgh where he received a BS degree in Mathematics in 1951. After serving in Korea, he returned to the University of Pittsburgh on the GI Bill to earn an MS in Mathematics in 1954. This was followed with a PhD in Computer Science from Stanford University. After a long and distinguished career at IBM he and his family settled in the DC area where Dr. Painter continued to contribute as an active researcher, consultant and entrepreneur in the computer industry until he passed away in 2018. His family says that Dr. Painter was a big believer in the value of education and that his time at the University of Pittsburgh, especially as a student in the Mathematics Department, proved important in launching his own career. This new endowment created by the family in honor of Dr. Painter provides a $2000 stipend for each of three Painter Undergraduate Research Fellows (PURF) to pursue their research initiatives for 8 weeks during the summer, beginning in 2021. Building on the Painter family efforts, and in view of the significant student interest in summer research opportunities, the Mathematics Department formally requested to initiate a targeted fundraising effort to support additional research students. The Arts & Sciences Development Office approved the proposal and selected it for a Dean’s Challenge during the recent successful Pitt Day of Giving. The response to the Dean’s Challenge was extraordinarily positive among the Pitt Mathematics community. The original challenge level was quickly met through 84 donors’ support. This community of alumni, friends and faculty of the Mathematics Department came together to raise over 10,000 USD, ranking highest of all departmental initiatives during the Pitt Day of Giving. Thanks to the support and generosity of these Pitt Day of Giving donors, two additional Department of Mathematics Summer Undergraduate Research Fellows (DMSURF) will also be funded at the$2000 level this summer.

In closing, we again thank the Painter family and the community-at-large for supporting the Mathematics Department’s efforts to provide important, expanded and extended undergraduate research experiences during the summer for our students. Finally, and importantly, we are pleased to recognize and congratulate the student applicants who were selected for financial support for this summer.

Thanks to the generosity of the Painter family, we were able to fund 8-week Summer Undergraduate Research Experiences for:

• Madeline McCrea, mentored by Jon Rubin and Bard Ermentrout
• Riley Debski, mentored by Carl Wang-Erickson
• Gabriel Weiner, mentored by Thomas Gilton.

Thanks to the generosity of the Pitt Day of Giving donors we were able to fund 8-week Summer Undergraduate Research experiences for:

• Benjamin Finley, mentored by Michael Neilan
• David Poling, mentored by Carl Wang-Erickson

In each case the stipend is \$2,000.

## BIG Problems Spring 2021

This Spring’s offering of Math 1103 – Mathematical Problems in Business, Industry and Government (BIG Problems) was a tremendous success with 24 participants including students from Mathematics (one PhD), Engineering, Computer Science, and Economics as well as three Mathematics majors from Carnegie Mellon University. The BIG students initially considered 5 projects with one from an energy company and four from two separate Major League Baseball organizations. After some initial work, the baseball projects merged into single projects for each organization.

Teams were tasked with providing their client a deliverable by the end of the semester. Initially, all teams had to work with their client to firm up a clear understanding of the their task. The next step for everyone was to sort and clean the large data sets they were given. No team’s first approach was their final approach, but each team did obtain a result and present a deliverable to their client by semester’s end.

In addition to their presentations to their clients, the three BIG teams prepared a separate talk for a more mathematical audience and

• presented at the Spring Sectional Meeting of the Allegheny Mountain Section of the Mathematical Association of America. The talks were very well attended and the students answered many questions from the audience;
• presented to Pitt’s Math Club; and
• participated in this year’s departmental MathFest by preparing a poster and giving a talk.

In addition to this talks, some of the students are considering presenting their team’s work at

• CMU’s sports analytics club,
• SIAM, and
• the MAA’s MathFest 2021.

Summaries of the team’s works are:

### 1. CX Energy for M&P Law

The MATH1103 Energy Team was tasked by Morascyzk & Polochak Attorneys at Law to analyze oil and natural gas production trends for the state of Pennsylvania over the last six years. Using the data of oil and gas production in the state the team would present how the industry has changed over time, especially in the southwestern and northeastern counties of Allegheny, Beaver, Washington, Green, Fayette, Westmoreland, and Tioga, and Bradford, Susquehanna, Lycoming, Sullivan, and Wyoming, respectively. Most notably, the team was able to visualize and model the data and predict optimal well locations. The team was able to accomplish project objectives by utilizing decline curve analysis in R, machine learning techniques in Python, and user-friendly interfaces via Dash by Plotly. Decline curve analysis is an industry standard in gas and oil production in which wells can be described by their output. Wells will exhibit three periods over their lifetime: increase in production (described by a linear line), plateau period in production (described by a horizontal line), and decline period (currently described by hyperbolic or exponential decline). The

decline curve portion is utilized to determine the economic limit of a well, or when a well is no longer a good financial investment. Using this information, the team was able to create a model for each period of the well’s life. Instead of using an exponential, hyperbolic or harmonic decline, the decline period was modeled using a sixth-degree polynomial regression, improving on the industry standard. The modeling code would output coefficients for the polynomial and the time allotted in each of the three periods. From these variables, the team was able to develop a machine learning code in python that can predict optimal well location. The location of the well can be determined with a root-mean-square-error of 0.005.

Finally, the team offered as a deliverable a user-friendly interface that allows for the geographical and time-series visualization of each well, as well as import of new data to allow continuation of use of the interface. Overall, the team was able to accomplish visualization, modeling, and prediction of the well behavior. The team would recommend the continuation of data uploads into this new application in order to create a more holistic view of Pennsylvania gas and oil production.

The client said of the student team:

“We appreciate all of the hard work the students did on their analysis for our company. The students showed great professionalism and willingness to think outside the box in tackling the decline curve project. They were engaged throughout and showed great interest in finding a solution to a very real world data problem that we use in our day to day work. We have looked through their results, are pleased with the outcomes and will be able to use the models presented to make decisions that will impact our business in a positive way.”

Zane Haverlack, Director of Technology for CX-Energy

Jeremy Stragand, VP of Operations

### 2. Pittsburgh Pirates

This semester, a team of 12 worked on a project titled “Optimizing Defensive Alignments in Major League Baseball.” The Pittsburgh Pirates - specifically their Director of Baseball Informatics, Dan Fox – tasked the students with the following problem: create a method to optimize starting defensive alignments for a set of hitters to reduce the expected number of runs conceded.

To solve the problem, the team first visualized the over 200,000 data points they had been provided, with specific focus on different variables such as hit type and bat side. Next, the team attempted several initial approaches including the use of machine learning (PCA and k-means clustering) or a probability graph (Parzen window). However, these approaches had significant limitations, including data biases, and a moved to an optimization approach was selected. The objective was to minimize the distance between the predicted ball position when caught and the total distance between the players, while constraining the area in which each player was allowed to be and the minimum distance between the players themselves. However, since both infield and

outfield players “saw” the same data, the players tended to cluster around one point for a given hitter, which is not a realistic (or beneficial) alignment in practice. Creating a more complex optimization problem, including splitting the outfielders and infielders, produced better results but still had room for improvement. The team’s final attempt was to use a two-part probability simulator to maximize the number of outs for each player. Although it is still a work in progress, this two-part probability simulator has produced the best and most realistic defensive alignments.

In addition to presentations listed above, the ream presenting their approaches and results to Pirates’ employees Dan Fox and Dan Gustafson.

Dan Fox, who brought the shift to MLB, said of the team’s work: “We were impressed with the varied approaches the students used to tackle the problem and how well they communicated their findings. It was a pleasure to be a part of the project,”

### 3. Undisclosed MLB Team

The third BIG team worked on the project “Predicting Post-Peak MLB Player Performance Per Position” for an undisclosed MLB team. The project’s goal was to use past performance and playing history to create a predictive model that evaluates a position player’s ability to play each defensive position. The students from Carnegie Mellon and Pitt present their work to the fictitious Plaid Panthers (= CMU + Pitt).

Their target variable was Defensive Runs Saved (DRS) which measures how many runs a player saved or cost his team in the field compared to others at his position. Data was obtained from Fangraphs and Baseball Savant’s Statcast, which consisted of variables such as the season and the age, position, DRS, and other defensive metrics for players. After doing some exploratory data analysis, the team observed a correlation between the different variables used in the model. The team decided to use the Mahalanobis distance, which accounts for existing relationships between variables, to calculate the similarity between two different players. The results of the Mahalanobis distance calculation were used to find clusters of similar players to a given player. Based on these clusters, linear models were determined for the components of DRS to find the expected DRS for that given player. The team also explored the impact of age on DRS, and considered methods such as the delta method and semiparametric regression. For future work, the team plans on adding analysis on aging curves into its modeling approach to improve model predictions.

In addition to presentations of their work at the University of Pittsburgh’s MathFest, the Allegheny Mountain Section of the MAA student talk session, and the Pitt Mathematics Club, the team had the opportunity to present to Mark Simon and colleagues at industry sports analytics leader Sports Info Solutions. SIS was excited to learn of the Mahalanobis distance, to see how it is used, and said, in general, of the team’s work:

• “This really impressed me. I think they're really interesting approaches and probably better approaches than most people have used to attack this sort of a problem before."
• "I think this is a fantastic work congratulations."

#### Student Testimonial:

“Excellent career building class! I used my experience from the BIG Problems math class in an interview and was offered a job the next day! I highly recommend taking the course!”

– Katherine Brosky, Chemical Engineer, University of Pittsburgh, Class of 2021