Volume 17

DOI: 10.1137/24S1658528

Authors

John C. Breedis (Corresponding author – University of Texas at Austin)

Project Advisors

Dr. Tan Bui-Thanh (University of Texas at Austin)

Abstract

We provide a new perspective on comparing activation functions via neural network approximate identity (nAI), a family of bell-curve activation functions Bθ with parameter θ > 0. This was done by comparing the performance of several neural networks across multiple data sets, where each neural network has one hidden layer and uses nAI as activation functions. The data sets used include polynomial, discontinuous, and non-differentiable regression problems, as well as MNIST classification. Across all regression problems, hinge activation functions outperformed sigmoidal activation functions. For classification, sigmoidal activation functions perform slightly better than hinge functions. In addition to traditional neural networks, we develop a machine learning architecture that utilizes integral convolution and quadrature by fixing the initial weight and bias matrices of the network. Supplemental modifications were implemented to improve the accuracy of these networks. This modified architecture was used alongside standard Feedforward networks across each regression problem with similar efficacy.

DOI: 10.1137/24S1649848

Authors

Gianluca Barone (Corresponding author – Rowan University), Aashrit Cunchala (University of Pittsburgh), Rudy Nunez (Emory University)

Project Advisors

Nicole Yang (Emory University)

Abstract

Standard classification theory assumes that the distribution of images in the test and training sets are identical. Unfortunately, real-life scenarios typically feature unseen data (“out-of-distribution data”) which is different from data in the training distribution (“in-distribution”). This issue is most prevalent in social justice problems where data from under-represented groups may appear in the test data without representing an equal proportion of the training data. This may result in a model returning confidently wrong decisions and predictions. We are interested in the following question: Can the performance of a neural network improve on facial images of out-of-distribution data when it is trained simultaneously on multiple datasets of in-distribution data? We approach this problem by incorporating the Outlier Exposure model and investigate how the model’s performance changes when other datasets of facial images were implemented. We observe that the accuracy and other metrics of the model can be increased by applying Outlier Exposure, incorporating a trainable weight parameter to increase the machine’s emphasis on outlier images, and by re-weighting the importance of different class labels. We also experimented with whether sorting the images and determining outliers via image features would have more of an effect on the metrics than sorting by average pixel value, and found no conclusive results. Our goal was to make models not only more accurate but also more fair by scanning a more expanded range of images. Utilizing Python and the Pytorch package, we found models utilizing outlier exposure could result in more fair classification.

DOI: 10.1137/24S1646911

Authors

Renjing Wang (Corresponding author – Xi'an Jiaotong-Liverpool University, China)

Project Advisors

Dr. Yichen Liu (Xi'an Jiaotong-Liverpool University, China)

Abstract

This paper aims to maximize the energy functionals of the Cauchy problem for one-dimensional wave and heat equations through a rearrangement class of initial conditions. The energy functional is defined to be the classical physical energy on a restricted interval. The corresponding result of wave equations is considered separately for three cases and that of heat equations can be generalized to higher dimensions. Moreover, uniqueness of the solution and stability problems are studied for heat equations.

DOI: 10.1137/24S1667427

Authors

Alexandra Lawryshyn (Corresponding author – University of Guelph, Ontario, Canada)

Project Advisors

Dr. Hermann J. Eberl (University of Guelph, Ontario, Canada)

Abstract

In this paper, we study the diffusive Streeter-Phelps equations, consisting of two weakly coupled diffusion-advection-reaction equations that describe biological oxygen demand (BOD) and dissolved oxygen (DO) in a river. The Streeter-Phelps equations were first introduced in 1925 but are still used in river quality modelling to this day. We investigate travelling wave solutions to this system with non-linear BOD decay instead of traditional linear decay. We prove the existence of spectrally stable monotone wavefront solutions to the BOD equation and corresponding solutions to the DO equation. We also discuss the existence and instability of non-monotone travelling waves and give an approximation of stable solutions to the BOD equation. Our analytical findings are illustrated numerically.

DOI: 10.1137/24S1662618

Authors

Han Chen (Corresponding author – Tsinghua University)

Project Advisors

Hien Tran (North Carolina State University)

Abstract

The online hotel reservation channels have caused increased cancellations, which is a revenue-diminishing factor for the hotels to deal with. Therefore, it is important to understand the bookers’ behavior and make good prediction on the cancellation decision. In this work, we analyzed the characteristics of distinct sub-populations among the bookers by a hotel reservation data. We built a range of machine learning models to make predictions on whether a customer is going to cancel the reservation. We also improved our methods by selecting the important features in the data. Moreover, we investigated deep into the important features to find rational explanation on the effect. Hopefully, our work can provide suggestions on room management for hotels.

DOI: 10.1137/24S1678489

Authors

Romina Mahinpei (Corresponding author – University of British Columbia)

Project Advisors

Dr. Chen Greif (University of British Columbia)

Abstract

Within the scientific computing community, there is a growing interest in using lower precision formats, such as single and half precision, given the potential for increased speed, reduced energy, and reduced communication costs. Mixed precision algorithms, which combine different precisions, offer a promising avenue to balance speed and accuracy. However, the applicability of mixed precision algorithms varies across different problem domains, thus requiring domain-specific investigations. This paper addresses a gap in the domain of sparse preconditioned saddle-point problems, proposing two mixed precision variants of the Minimal Residual (MINRES) method that vary the arithmetic and storage precision of the preconditioner solves and the matrix-vector products. Using CUDA C, these variants are implemented and then used to make performance measurements on NVIDIA’s GeForce RTX 3070 Ti graphics card for Maxwell and Stokes saddle-point problems. Our numerical results suggest that low precision preconditioning is an effective optimization strategy for reducing the runtime of the MINRES iterative solver when applied to the chosen saddle-point problems while also maintaining the desired accuracy of the final solution.

DOI: 10.1137/24S163493X

Authors

Kenneth Kau (Corresponding author – University of Hawaii West Oahu)

Project Advisors

Esther Widiasih, PhD (University of Hawaii West Oahu)

Abstract

In this paper, we apply an alternative two-dimensional Lotka-Volterra system, traditionally used in ecology to model species competition, to the field of industrial organization. We investigate whether this model can effectively represent the competitive interactions between firms in technology sector markets. The study focuses on determining if the model can provide realistic predictions of future market shares, aligning with observed trends. Additionally, we explore the general implications of changes in dynamic variables within the competitive framework. This approach helps draw parallels between ecological and economic competition, suggesting that this Lotka-Volterra model offers valuable insights for market strategy development. This paper lays the groundwork for further research, including the incorporation of stochastic elements and the analysis of more complex competitive scenarios involving multiple firms.

DOI: 10.1137/23S1592018

Authors

Meha Patel (Corresponding author – California State University, Long Beach), Samuel Rath (San Diego State University), Chupeng Zheng (University of Chicago)

Project Advisors

Anna Ma (Project advisor – University of California, Irvine)

Abstract

As big data problems become more prevalent, the need to accurately approximate solutions to largescale linear systems increases. Many real-world big data problems are also accompanied by the risk of missing or incomplete data, further complicating the linear models assigned to them. Current methods to address missing data involve deletion or zero imputation, which introduces bias to the model. We propose a model that adapts Stochastic Coordinate Descent (SCD) to handle missing data in linear systems and utilizes μ-imputation to retrieve a better approximation of the original data. We prove that in expectation, our proposed algorithm, μ-imputation mSCD utilizes an unbiased estimator of the gradient of the least-squares objective function when using mean imputation in the absence of data. Furthermore, we compare our algorithm’s performance on synthetic data to closely related algorithms: zero-imputation mSCD and SCD. Finally, we apply μ-imputation mSCD on real-world data to demonstrate the usefulness and viability of our proposed algorithm.

DOI: 10.1137/23S1611282

Authors

Caleb Fikes (Corresponding author – Rice University), Keira Behal (Emory University), Jiayi Chen (Emory University), Sophia Xiao (Emory University)

Project Advisors

Yuanzhe Xi, PhD (Emory University)

Abstract

In the field of healthcare, electronic health records (EHR) serve as crucial training data for developing machine learning models for diagnosis, treatment, and the management of healthcare resources. However, medical datasets are often imbalanced in terms of sensitive attributes such as race/ethnicity, gender, and age. Machine learning models trained on class-imbalanced EHR datasets perform significantly worse in deployment for individuals of the minority classes compared to those from majority classes, which may lead to inequitable healthcare outcomes for minority groups. To address this challenge, we propose Minority Class Rebalancing through Augmentation by Generative modeling (MCRAGE), a novel approach to augment imbalanced datasets using samples generated by a deep generative model. The MCRAGE process involves training a Conditional Denoising Diffusion Probabilistic Model (CDDPM) capable of generating high-quality synthetic EHR samples from underrepresented classes. We use this synthetic data to augment the existing imbalanced dataset, resulting in a more balanced distribution across all classes, which can be used to train less biased downstream models. We measure the performance of MCRAGE versus alternative approaches using Accuracy, F1 score and AUROC of these downstream models. We provide theoretical justification for our method in terms of recent convergence results for DDPMs.

DOI: 10.1137/23S161793X

Authors

Hannah Simpson-Clancy (Corresponding author – University of Huddersfield)

Project Advisors

Dr. Ann Smith (University of Huddersfield)

Abstract

A small number of epithelial ovarian cancer cases are deemed preventable and its overall survival rates are low. The developments in omics data analysis paves a way for biomarker discovery for epithelial ovarian cancer in order to improve survival rates and prevent its development. This report provides analysis of gene expression data for epithelial ovarian cancer to compare the gene expression of 99 epithelial ovarian cancer samples and 4 non-cancerous ovary samples. Serous and endometrioid epithelial ovarian cancer subtypes were most similar based on hierarchical clustering. Serous was the subtype with the most differentially expressed genes when compared with normal ovary samples whereas mucinous had the least by the Wilcoxon Rank-Sum test (Benjamini Hochberg, p < 0.05). The number of down-regulated genes exceeded the number of up-regulated genes when comparing each cancer subtype with normal ovary samples. In this case, the clear cell subtype had the greatest number of dysregulated genes when compared to normal ovaries whereas endometrioid had the least. The dysregulated genes were found by fold change analysis (FC > 2 or FC < 0.5). Differences in gene expression levels between epithelial ovarian cancer subtypes were suggested due to 11, 181 differentially expressed genes identified when comparing expression levels in all sample groups by the Kruskal-Wallis test (Benjamini Hochberg, p < 0.05). Genes proposed as biomarkers for (1) epithelial ovarian cancer and (2) individual epithelial ovarian cancer subtypes, when compared with normal ovaries included MUC1, SCNN1A, CD24, ITM2A, AGR2 and WFDC2.

Supplementary Materials

DOI: 10.1137/23S1615838

Authors

Tuan M. Le (Corresponding author – DePauw University), Evan Sajtar (DePauw University)

Project Advisors

McKenzie Lamb, PhD (DePauw University)

Abstract

The objective of this study is to explore the feasibility and effectiveness of using smartphone accelerometer data, combined with advanced machine learning techniques, to accurately classify three distinct motions– pushing, pumping, and coasting–that a longboarder might engage in over the course of a ride. The final goal is to integrate these concepts into a closed system of classification in the form of a mobile application. Utilizing a dataset collected from a smartphone carried by a longboarded, we apply a series of data processing techniques, including rotation matrices for orientation normalization, Verlet integration for handling unevenly-spaced time series data, and the discrete Fourier transform for feature extraction. We experiment with various machine learning algorithms, with a particular focus on the Random Forest classifier, which achieves an F1 Score of 96.8% in classifying the three primary longboarding actions. The F1 Score, a harmonic mean of precision and recall, serves as a critical metric in evaluating the model’s accuracy, particularly in the context of imbalanced datasets. This study not only demonstrates a novel application of portable technology in sports analytics but also contributes to the broader field of machine learning by presenting an efficient approach to processing and classifying telemetric data from motion sensors. The implications of this research extend beyond longboarding, offering potential applications in enhancing athletic performance across a range of sports through accessible and real-time motion analysis.

DOI: 10.1137/24S1636083

Authors

Allen Joseph Minch (Corresponding author – Brandeis University), Hung Anh Dinh Vu (University of Maryland), Anne Marie Warren (University of Minnesota)

Project Advisors

Elizabeth Newman (Emory University)

Abstract

This project explores adversarial training techniques to develop fairer Deep Neural Networks (DNNs) to mitigate the inherent bias they are known to exhibit. DNNs are susceptible to inheriting bias with respect to sensitive attributes such as race and gender, which can lead to life-altering outcomes (e.g., demographic bias in facial recognition software used to arrest a suspect). We propose a robust optimization problem, which we demonstrate can improve fairness in several datasets, both synthetic and real-world, using an affine linear model. Leveraging second order information, we are able to find a solution to our optimization problem more efficiently than with a purely first order method.

DOI: 10.1137/23S1612032

Authors

Eunkyu Kim (Corresponding author – The Cooper Union, New York), Lucia Rhode (The Cooper Union, New York)

Project Advisors

Mili Shah (The Cooper Union, New York)

Abstract

This paper introduces a linear algebra-based formulation of camera calibration algorithms, focusing on two methods: the regular method and the linearized method. The regular method is computationally more efficient while the linearized method can be adapted to an iterative process to enhance calibration accuracy. To demonstrate the effectiveness of these methods, a marker-based motion tracking experiment utilizing real-life data is conducted. The results showcase the regular method’s computational efficiency, while the linearized method’s ability to remove outliers is demonstrated through reverse coordinate computation. With a 2.00 mm upper limit threshold, reverse coordinate computation achieved accuracy up to a Frobenius norm of 0.18 mm.

DOI: 10.1137/23S1577055

Authors

Yong Hong Ivan Tan (Corresponding author – National University of Singapore)

Project Advisors

Delin Chu (National University of Singapore), Timo Sprekeler (National University of Singapore), Johannes J. Brust (Arizona State University)

Abstract

The main objective of this article is to find the group testing strategy which minimizes the number of groups to test while identifying all positives. This manuscript explores the Hypercube Approach, the Kirkman Triple and Polynomial Pools Algorithms which are used to design group testing strategies. This work enhances the Polynomial Pools Algorithm with the Projective Geometry Design and proposes an algorithm which returns an effective group testing strategy when compared to other well-known algorithms.

Supplementary Materials

DOI: 10.1137/23S1591980

Authors

Li Yuan (Corresponding author – University of Michigan), Weilin Cheng (University of California, Davis), Hengyuan Liu (University of California, Davis), Kathy Mo (University of California, Davis), Sida Tian (University of Michigan)

Project Advisors

Ambuj Tewari (University of Michigan)

Abstract

This research uniquely focuses on predicting the likelihood of H5N1 outbreaks in the United States at the county level. Unlike previous studies, which either excluded the United States or used outdated data, we utilized diverse statistical techniques and publicly available H5N1- related data from January 2022 to March 2023. Employing logistic regression, regularization methods, cross-validation, and eXtreme Gradient Boosting (XGBoost), our models demonstrated remarkable predictive efficacy. Notably, the XGBoost model, trained with 10-fold cross-validation, outperformed others in terms of ROC-AUC. This research provides valuable epidemiological insights, proposes intervention strategies for H5N1 in the United States, and suggests future research directions.

DOI: 10.1137/23S1574269

Authors

Zhuorong Mao (Corresponding author – College of William & Mary), Sarah Kunkler (College of William & Mary)

Project Advisors

Susana Furtado (Universidade do Porto), Charles R. Johnson (College of William & Mary)

Abstract

Approval Voting over several alternatives asks each voter to choose a subset of the alternatives of which they “approve”. Then, the alternative (or, perhaps, alternatives) approved by the most voters is selected. The outcome is then not only a function of the profile of individual voter preferences alone, but also the protocols (number of alternatives approved) chosen by each voter. We quantify the differences in outcome that result from differences in protocols in several ways, regarding hypotheses about individual preferences. Considered are the two natural protocols when there are three alternatives, for both small and large numbers of voters. For more alternatives, we consider all possible pure protocols. Mixed protocols are also considered to quantify protocol effects. Several methods were employed for varying numbers of voters. Consistent numbers result from all methods. We find that differences in outcome, due to differences in protocol alone, can be quite frequent and often rival preferences as a determinant of the outcome.

DOI: 10.1137/23S1560756

Authors

Sara Peter (Corresponding author – Clarkson University)

Project Advisors

Marko Budišić (Clarkson University)

Abstract

We present a dynamical system model to show the Potsdam, NY campus of Clarkson University is 100% renewable with the university’s new contract as of 2019 with Brookfield Renewable. The model creates periodic functions simulating energy inputs which can be used to generate alternative past and future scenarios. Clarkson University changed their source of electrical energy to Brookfield Renewable in July 2019 as they moved towards their 2025 goal of being 100% renewable. To claim that a MWh of electricity used by campus is renewably generated, a Renewable Energy Credit (REC) has to be purchased or generated and applied to it. The new contract with Brookfield Renewable provides each supplied MWh with its own REC. Combined with Clarkson University’s other renewable energy sources, 95% of electricity consumed by campus can be certified as renewable. To model the remaining portion of electricity consumed by off-campus properties, we rely on data that accounts for consumed and delivered electricity, prices for that electricity, and monetary credits generated by local energy sources. Our developed dynamical system models the monetary credit generation, debt accumulation, and REC accrual over 34 months using real university data. As not all data parameters were explicitly available, we explore estimating parameters in three ways: directly from the data as time-varying functions, as constants, and stochastically, as random variables with distributions consistent with the provided data. We validate the alternative models against the data and estimate sensitivity to parameters.

DOI: 10.1137/23S1606411

Authors

Sophia Y. Rong (Corresponding author – Buchholz High School, Gainesville, FL) , Alice X. Li (Eastside High School, Gainesville, FL)

Project Advisors

Shasha Gao (Jiangxi Normal University, China, and University of Florida), Chunmei Wang (University of Florida)

Abstract

Infectious diseases present persistent challenges to global public health, demanding a comprehensive understanding of their dynamics to develop effective prevention and control strategies. The presence of asymptomatic carriers, individuals capable of transmitting pathogens without displaying symptoms, challenges conventional containment approaches focused on symptomatic cases. Waning immunity, the decline in protective response following natural recovery or vaccination, introduces further complexity to disease dynamics. In this paper, we developed a mathematical model to investigate the interplay between these factors, aiming to inform strategies for the management of infectious diseases. We derived the basic reproduction number for the model and showed that the disease would die out when this number falls below 1. We obtained a formula to estimate the relative contributions of asymptomatic and symptomatic transmission to the basic reproduction number, which remains unchanged when vaccination is included in the model. Through computer simulations with parameter values tailored for COVID-19 and sensitivity analysis, we demonstrated that population susceptibility significantly impacts the timing and magnitude of infection peaks. Populations with lower susceptibility experience delayed and less severe outbreaks. Vaccination was shown to play a crucial role in disease control, with an increased vaccination rate, extended immunity, and heightened vaccine efficacy proving pivotal. However, the effectiveness of these strategies hinges on maintaining a low vaccine escape proportion. Taken together, this study underscores the need for multifaceted, adaptable approaches to infectious disease management, highlighting the central role of vaccination in mitigating disease spread. Further research and validation with disease-specific data will enhance parameter estimates, improve model predictions, and inform evidence-based disease control strategies.

DOI: 10.1137/22S1529452

Authors

Haley Zsoldos (Corresponding author – Pennsylvania State University) , Isabelle Stepler (Pennsylvania State University)

Project Advisors

Jessica M. Conway (Pennsylvania State University) , 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.

Supplementary Materials

DOI: 10.1137/23S1586951

Authors

Mohamed Mahmoud (Corresponding author – STEM High School for Boys, Giza, Egypt)

Project Advisors

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.

DOI: 10.1137/22S1522899

Authors

Zijian Xun (Corresponding author – Carleton College)

Project Advisors

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.

DOI: 10.1137/23S1547755

Authors

Junyuan Quan (Corresponding author – Denison University)

Project Advisors

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.