SIURO | Volume 17 | SIAM
 

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SIAM Undergraduate Research Online

Volume 17


SIAM Undergraduate Research Online Volume 12

Identifying Priority Areas for Expanding Mental Health Facilities with Mixed Integer Linear Programming

Published electronically January 25, 2024
DOI: 10.1137/23S1547755

Authors: Junyuan Quan (Corresponding author – Denison University)
Project Advisor: Dr. Anthony Bonifonte (Denison University)

Abstract: This research attempts to estimate the unmet mental health services demand at a census tract level and identify new mental health facility locations in Ohio to maximize the number of new individuals with serious mental illness (SMI) who receive treatment. We find that among the 765,304 individuals with SMI in Ohio, 469,549 (61.4%) perceive an unmet need for mental health services due to the lack of geographic access and limited service capacity. Using estimates of the capacity of existing facilities, unmet demand in each census tract, and the distance between each census tract center, we modeled a mixed integer linear program to maximize coverage of newly opened facilities. The model suggests 10 new potential mental health facilities could provide geographic access to 418,228 new patients, comprising 89.1% of the total SMI population that currently has unmet mental health services demand in Ohio. The findings of this research could make recommendations for identifying hot spots for individuals with SMI and priority areas for expanding mental health facilities.

From Pole to Podium: Adjusting Elo Method to Separate Car and Driver in Formula One Racing

Published electronically February 06, 2024
DOI: 10.1137/22S1522899

Authors: Zijian Xun (Corresponding author – Carleton College)
Project Advisor: Timothy P. Chartier (Davidson College)

Abstract: This article presents a novel approach to separating and quantifying the effect of a car’s performance and a driver’s skill on Formula 1(F1) race outcomes. By analyzing data from the past decade, we propose a formula to measure F1 drivers’ ability. This approach could be used to predict race outcomes for a given driver in cars with different performance levels, thereby aiding teams in optimizing resource allocation for car development.

How to be #1 in the IOI? A Study on Rating Nations Participating in the International Informatics Olympiad

Published electronically February 09, 2024
DOI: 10.1137/23S1586951

Authors: Mohamed Mahmoud (Corresponding author – STEM High School for Boys, Giza, Egypt)
Project Advisor: Timothy P. Chartier (Davidson College)

Abstract: This paper investigates the reliability of using Elo, TrueSkill, and Top Coder rating methods in analyzing the performance of nations participating in the International Informatics Olympiad from 2011-2022. This investigation aims to utilize the ratings to assist nations in improving and achieving more medals in future IOI contests. Based on ratings for whole contests and each problem category, including but not limited to graph theory, ad hoc, and data structures, we prove and compare the reliability of the rating methods by measuring their predictive accuracies. By taking Egypt as a case study, we show how to extract useful information from rating changes over time to assist in improvement. In addition, we use standardization and percentiles in locating Egypt, or any nation, in each category among other nations to find which categories weaken the whole contests ratings of Egypt. Thus, Egypt can focus on these categories for improvements. Moreover, we relate each specific range of whole contests percentiles to medal achievements, showing that nations in each range have nearly the same number and types of medals, which means that a country needs to get to a higher specific range of percentiles to get more and better in type medals. Ultimately, we set recommendations for future work, encompassing a sensitive analysis of which category is easier to improve and the usage of a modified Elo version.

Predator-Prey Oscillations in a Cellular Automaton of Huffaker's Mite Experiment

Published electronically February 13, 2024
DOI: 10.1137/22S1529452
Supplementary materials

Authors: Haley Zsoldos (Corresponding author – Pennsylvania State University) and Isabelle Stepler (Pennsylvania State University)
Project Advisor: Jessica M. Conway (Pennsylvania State University) and Timothy Reluga (Pennsylvania State University)

Abstract: Predator-prey interactions are commonly modeled using the Lotka-Volterra ordinary differential equations, producing intertwined predator and prey population oscillations. Scientists have attempted to reproduce these oscillations, such as Carl Huffaker and his 1958 experiment with mites and oranges. However, Huffaker was only able to produce sustained oscillations after adjusting his system’s spatial factors. Particularly, increased space per orange and increased mite dispersal have a significant impact on achieving predator-prey oscillations. To address and confirm this result, we developed a cellular automaton model of Huffaker’s mite experiment. We simplified his system to fit automata criteria, created rules to govern mite dynamics, tested model parameters relating to mite lifetime and fertility, and increased patches per orange and mite dispersal by wooden posts to determine the conditions for successful oscillations. The results of our simulations show that increasing prey dispersal and the number of patches available per orange is sufficient for producing lasting oscillations in our model. Secondarily, we concluded that a certain disparity between reproduction and lifetime parameters for the predators and prey is sufficient for oscillations as well. In conclusion, spatial complexity must be considered when attempting to achieve predator-prey oscillations experimentally.