I am very interested in mathematical biology research, particularly disease modeling and epidemiology. I have also dabbled in some machine learning and data analytics. Though I have my preferences, I'm open to any research that can be applied to real world problems and proves useful to people. Currently, I'm working with Dr. Christina Yu. We are finishing up a project on Principle Component Analysis for Tensors.
Current and Past Projects
PCA for Tensors (2021, ongoing)
In collaboration with Dr. Christina Yu and Sean Sinclair
ORSuite: Benchmarking Suite for Sequential Operations Models (2021)
Vaccine Distribution Environment and Simulation
Reinforcement learning is a natural model for problems involving real-time sequential decision making. In these models, a principal interacts with a system having stochastic transitions and rewards and aims to control the system online (by exploring available actions using real-time feedback) or offline (by exploiting known properties of the system). This project revolves around providing a unified landscape on scaling reinforcement learning algorithms to operations research domains. I worked specifically on setting up a vaccine allocation environment, as well as a framework for simulating the impact of different vaccine allocation policies on disease spread through a population.
Combinatorics (2019, Mathematical Sciences Research Institute)
Properties of Peaks in Parking Functions
In 2013, Billey, Burdzy, and Sagan proved that there are 2n−1 permutations of length n with no peaks. In this paper, we discuss generalizations of their results where instead of permutations, we investigate parking functions with no peaks. In particular, we study certain subsets of parking functions and enumerate peaks by analyzing their valleys and plateaus. We also analyze the bijection between nondecreasing parking functions with repeating digits and certain labeled Dyck paths. For full list of collaborators, click "More" below.
Object Detection, Machine Learning (2019, CSU Channel Islands)
Finding Waldo: An Investigation into Machine Learning for Object Detection
One of the resources that Amazon Web Services provides is a platform for researchers and professionals to create, train and use models that can detect specific objects in image or video data. These object detection/recognition (ODR) models are used to detect people, cars, wildlife and other objects. The applications of ODR models extend to environmental health, public safety and general everyday-life improvement. These models allow us to use video data to do things like enumerate the number of people who are at a particular beach or to detect malfunctions on solar panels. We present an ODR model to detect the Waldo character in the popular children’s series “Where’s Waldo?” We use our results to motivate further investigations in machine learning and ODR modeling. By identifying key limitations and issues during the development of the project, we gain a better understanding of how to present project material to a population of people interested in learning more about machine learning, data collecting, and ODR modeling through AWS Sagemaker. We also discuss how we can extend “finding Waldo” to other problems, such as classifying whales by their tails or detecting faces in a video feed.
Object Detection (2018, CSU Channel Islands)
Solar Panel Hotspot Detection
Although solar panels allow us to harness clean energy, their location can make maintaining them difficult. Collections of solar panels that are placed on top of tall buildings without easy roof access pose a danger and challenge to inspecting technicians. We present a possible solution to this problem in a two-part process. Using computer vision techniques and tools, we work to develop a collection of python scripts that allow for real-time detection of solar panels in an image and their hotspots using drone technology (as hotspots are a good indication of a broken solar panel). We use our results to provide a roadmap for future investigations on how to use drones to inspect solar arrays for potential malfunctions.
Disease Modeling (2018, St. Mary's College of Maryland)
Combating Tuberculosis: Using Time-Dependent Sensitivity Analysis to Develop Strategies for Treatment and Prevention
Although many organizations throughout the world have worked tirelessly to control tuber- culosis (TB) epidemics, no country has yet been able to eradicate the disease completely. We present two compartmental models representing the spread of a TB epidemic through a population. The first is a general TB model; the second is an adaptation for regions in which HIV is prevalent, accounting for the effects of TB/HIV co-infection. Using active subspaces, we conduct time-dependent sensitivity analysis on both models to explore the significance of certain parameters with respect to the spread of TB. We use the results of this sensitivity analysis to determine the most effective strategies for treatment and prevention throughout the epidemic.