Gaussian Process Regression with Spectral Mixture Kernel for Brain Pressure Data Analysis

Johns Hopkins University

Mentors: Tamás Budavári (JHU Applied Math and Statistics), Rohan Mathur (JHU School of Medicine)

• Using machine learning to predict if brain pressure of patients are at cautionary levels.

• Research in progress.

Mathematical Optimization Approaches to Radiation Therapy Treatments of Brain Metastases

NCSU REU (DRUMS) 2021

Mentors: David Papp, Maria Macaulay.

• Ideated and tested large-scale, mixed integer optimization models that assessed the benefits of non-uniformly fractionated treatment plans.

Line Solitons in the Kadomstev-Petviashvili Equations

Brown University

Mentor: Justin Holmer

• Coded numerical simulations to investigate the stability of line solitons in KP equations.

Real Power of Monomial Ideals

Polymath Jr. REU 2020

Mentors: Alexandra Seceleanu,  Benjamin Drabkin, Tingting Tang.

• Designed 3 algorithms that compute the real power of monomial ideals and implemented in Macaulay2.

Sparse Recovery Using Basis Pursuit and Orthogonal Matching Pursuit

• Recovered sparse images using probabilistic algorithms. With Justin Bennett and Ryan Pilgrim.

High-dimensional Approximation, Probability, and Statistical Learning, Spring 2023.

Chirp Signal Detection using Wavelets

• Designed an algorithm to detect chirp signals masked in random noise. 

Wavelets and Applications, Spring 2021.

pdf | code

Knot (dis)equivalence by knot-coloring

• 15-min lesson on distinguishing between knots using knot-coloring.  With Alexander Ivanov. 

Topology, Fall 2020.

video

Age-structured Population Models

• Group study on Chapter 5.1 of Logan's Applied PDE, 3rd Edition.  Plotted numerical solutions for textbook exercises. With Bill Ma, Daniel Park, Jason Senthil. 

Applied PDE, Fall 2020.

pdf | code

Pattern Formation in Sandpile Models

• Used computer simulations to investigate symmetries and stability of sandpile avalanches. 

Applied Dynamical Systems, Spring 2020.

pdf | images/videos | simulator (p5)

Connect 4

• Terminal based game of Connect 4, written in ReasonML. Players can be Human or AI. Joint-winner of the class' AI tournament. With Will Chen. 

Computer Science: An Integrated Introduction, Fall 2019.

Vector Calculus Solutions Guide

Full homework solutions for Honors Calculus (MATH 0350, Spring 2021) at Brown University. Available to Brown instructors/TA on request.

Textbook: Vector Calculus (6th Ed), Marsden & Tromba.

sample pdf | MATLAB code for plots