Personal Interests
I am interested in leverging mathematical and computational approaches to image-based biomedical research problems.
Current Work
After completing an internship at Lawrence Berkeley National Laboratory between the Applied Math Department and the Molecular Biophysics and Integrated Bioimaging Division, I have returned as a research associate to complete our study of data-driven denoising methods for cryogenic electron tomography. Our study undertakes a rigorous assessment of the modern denoising methods using simulated and experimental data to investigate the possible introduction of artifacts and loss of critical high-frequency information.
Prior Postbaccalaureate Work
In the spring of 2024 I was an intern in the Center for Computational Science and Engineering (CCSE) at Lawrence Berkeley National Laboratory. The Department of Energy (DOE)'s Exascale Computing Project has funded the development of massively-parellel solvers designed for next-generation supercomputers. During my internship I helped develop the analysis pipeline for the introduction of mesh refinement to the WarpX code, built on the AMReX framwork, for the further study of magnetic reconnection. In addition to this work resulting in an upcoming publication in the Physics of Plasmas Journal, I added support for AMReX-based simulation data to the popular open-source analysis and visualization library yt.
Undergraduate Work
A broad natural science foundation grounds my computational and biomedical interests.
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Signal and Image Processing
Solving image-based problems using statistical and computational tools is of great interest to me.
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Biomedical Imaging
Current imaging technology continues to enable next-generation analytics yet to be fully realized.
Selected Undergraduate Papers
Undergraduate Thesis
An exploration of particle diffusion and the mean first passage time in bounded domains inspired by cellular diffusion. In this project I considered the effects of domain geometry and various boundary conditions on the time-evolution of diffusive particles and their "escape" from such domains. This project makes an interesting comparison between the discrete and continuous with a vectorized random walk implementation and analytical work using conformal mappings and the Fourier Transform.
Semantic Segmentation Computer Vision
Written with a computer science major, I covered the theoretical introduction to single-layer convolutional neural networks(CNNs) and an R implementation while my partner completed the Python implementation. This paper covers the theory behind CNNs and implements a model on a Kaggle dataset.
Method of Finite-Differences
The final paper for my numerical anlysis course, an introduction to the finite-difference method(FDM) for linear and non-linear ODE's is given, before a conceptual introduction to the FDM for the classical wave equation. A Python implementation of the FDM for the heat equation was completed in conjunction with this paper and is available on my GitHub linked at the bottom of this website.
Atmospheric Dynamics Report: Atmospheric River Event in California
In this co-authored report, an introduction to atmospheric rivers and the particularities of the December 2021 event are given. Using Total Precipitable Water satellite imagery and NOAA HYSPLIT back-trajectories in conjuction with the analysis provided by the Center for Western Water and Weather Extremes, we were able to provide a detailed analysis of the atmospheric processes which produced this event.
Confidence Scores of Neural Networks
In this co-authored paper we provide an introduction and exploration of neural network confidence scores. Modern neural networks for classification tasks are often over-confident compared to expected sample accuracy despite ever-increasing generalization accuracy in testing. This trend is a form of overfitting related to the use of particular loss functions and reflects poor calibration. In this paper an introduction to the Expected Calibration Error(ECE) as an informative calibration statistic precedes an implementation by my co-author comparing the ECE scores for three popular pre-trained, deep convolutional neural networks: ResNet, ShuffleNet, and DenseNet.
An Introduction to Harmonic Theory
Written for my complex analysis course, this paper introduces harmonic functions and relies on earlier theorems for analytic functions to establish results for harmonic functions. Such results include the Local and Global Maximum Principal for Harmonic functions, Uniqueness of the Dirichlet Problem for harmonic functions, and the Poisson Integral formula on the disk in the complex plane.