Programming Experience

My computational experience is diverse. My university coursework required using Java, C++, or Matlab (10-15’). I used C++98 or ANSI-C extensively for the AFIT-affiliated projects, occasionally writing high level scripts in Python or Matlab (+MEX) (13-15’). I used either the R project (+Rcpp) or Python (+Cython) for the majority of the projects I was involved in, preferring the former (15-19’). Since 2020, interfacing Python with modern C++ FFIs (e.g. pybind11) has been my primary development workflow.

Projects

Spectral relaxations of persistent rank invariants


TopologyPersistenceLinear Algebra

We introduce a framework for constructing families of continuous relaxations of the persistent rank invariant for persistence modules indexed over the real line. Applications to multi-parameter persistence, parameter optimization, and shape classification are also presented.

Move Schedules: Fast persistence computations in coarse dynamic settings


TopologyAlgorithmsPersistence

Persistence diagrams are known to vary continuously with respect to their input, motivating the study of their computation for time-varying filtered complexes. Computationally, simulating persistence dynamically can be reduced to maintaining a valid decomposition under adjacent transpositions in the filtration order. Since there are quadratically many such transpositions, this maintenance procedure exhibits limited scalability and often is too fine for many applications. We propose a coarser strategy for maintaining the decomposition over a 1-parameter family of filtrations that requires only subquadratic time and linear space to construct.

Efficient Multiscale Simplicial Complex Generation for Mapper


ClusteringTopologyR Package

The primary result of the Mapper framework is the geometric realization of a simplicial complex, depicting topological relationships and structures suitable for visualizing, analyzing, and comparing high dimensional data...

Automating Point of Interest Discovery in Geospatial Contexts


ClusteringGeospatial analysisNetwork modeling

With the rapid development and widespread deployment of sensors dedicated to location-acquisition, new types of models have emerged to predict macroscopic patterns that manifest in large data sets representing "significant" group behavior. Partially due to the immense scale of geospatial data, current approaches to discover these macroscopic patterns are primarily driven by inherently heuristic detection methods. Although useful in practice, the inductive bias adopted by such mainstream detection schemes is often unstated or simply unknown. Inspired by recent theoretical advances in efficient non-parametric density level set estimation techniques, in this research effort we describe a semi-supervised framework for automating point of interest discovery in geospatial contexts. We outline the flexibility and utility of our approach through numerous examples, and give a systematic framework for incorporating semisupervised information while retaining finite-sample estimation guarantees.

Bringing High Performance Density-based Clustering to R


ClusteringR PackageHigh performance computing

Density-based clustering techniques have become extremely popular in the past decade. It's often conjectured that the reason for the success of these methods is due to their ability of identify 'natural groups' in data. These groups are often non-convex (in terms of shape), deviating the typical premise of 'minimal variance' that underlies parametric, model-based approaches, and often appear in very large data sets. As the era of 'Big Data' continues to rise in popularity, it seems that typical notions having access to scalable, easy-to-use, and scalable implementations of these density-based methods is paramount. In this research effort, we provide fast, state-of-the-art density-based algorithms in the form of an open-source package in R. We also provide several related density-based clustering tools to help bring make state of the art density-based clustering accessible to people with large, computationally difficult problems.

Towards Autonomous Aerial Refueling: Massive Parallel Iterative Closest Point


GeometryPoint registrationHigh performance computing

The Iterative Closest Point (ICP) problem is now a well-studied problem that seeks to align a given query point cloud to a fixed reference point cloud. The ICP problem computationally is dominated by the first phase, a pairwise distance minimization. The ''brute-force'' approach, an embarrassingly parallel problem amenable to GPU-acceleration..

Employment

  1. Graduate Research Assistant

    Perea Lab

    Fall 2019 - Present

    MSU/NEU


    Topological Data AnalysisLinear AlgebraMachine Learning

    Motivated by my previous work on the foundations of density-based clustering, I focused on implementing and extending the Mapper algorithm, a popular and very general method which has been used successfully for data analysis.

  2. SCaN Intern

    National Aeronautics and Space Administration

    Summer 2022

    John H. Glenn Research Center at Lewis Field, OH


    Space networkingGraph TheoryFlow algorithms

    Towards enabling delay-tolerant satellite communications in uncertain space environments, I was re-hired back at NASA as part of the Space Communications and Navigation (SCaN) program to expand the algorithmic theory on time-dependent routing.

  3. Research Associate

    Oak Ridge Institute for Science and Education

    Fall 2017, Fall 2018 - Fall 2019

    Air Force Research Laboratory, WPAFB


    TopologyMapperR package

    Motivated by my previous work on the foundations of density-based clustering, I focused on implementing and extending the Mapper algorithm, a popular and very general method which has been used successfully for data analysis.

  4. Graduate Research Assistant

    Web and Complex Systems Group

    Spring 2016 - Fall 2018

    Wright State University


    ClusteringNetwork analysisMachine Learning

    Motivated by my previous work on the foundations of density-based clustering, I focused on implementing and extending the Mapper algorithm, a popular and very general method which has been used successfully for data analysis.

  5. LERCIP Intern

    National Aeronautics and Space Administration

    Summer 2018

    John H. Glenn Research Center at Lewis Field, OH


    Experimental designMachine learningMaterial science

    Towards accelerating the design and discovery materials for use in extreme environments, I was hired by Dr. Steven Arnold under NASAs 10-week LERCIP program to apply Machine Learning to a specific Material Science problem.

  6. Student Participant

    Google Summer of Code

    Summer 2017

    R Project for Statistical Computing


    ClusteringLearning theoryR package

    Towards unifying recent developments related the theory and utility of density-based clustering, this project involved a mixture of research and code development which culminated in the form of an R package for estimating the empirical cluster tree.

  7. Civilian Research Assistant

    Oak Ridge Institute for Science and Education

    Spring 2014 - Spring 2015

    Air Force Institute of Technology, WPAFB


    OptimizationGraph theoryFlow algorithms

    Towards the end of my undergraduate degree, my contract at the [Air Force Institute of Technology](https://www.afit.edu/) (AFIT) was extended under ORISE, where I continued working with the LOREnet group under Dr. Andrew Terzuoli

  8. Civilian Research Assistant

    Southwestern Ohio Council For Higher Education

    December 2013 - June 2014

    Air Force Institute of Technology, WPAFB


    OptimizationGraph theoryFlow algorithms

    As my first experience doing undergraduate research, I worked in a heavily multi-disciplinary team called the Low Orbitals Radar and Electromagnetism group, where I worked on a diverse set of projects involving computational, statistical, or physics-based requirements

Education

  1. Doctorate in CS (Pursuing)

    Khoury College of Computer Sciences

    Northeastern University, 2021-Present

    Advisor: Jose Perea


    Click for teaching experience, coursework taken, and other details...

  2. Doctorate in CMSE (Transferred)

    Computational Mathematics, Science and Engineering

    Michigan State University, 2019-2021

    Advisor: Jose Perea


    Click for teaching experience, coursework taken, and other details...

  3. Masters of Science in CS

    College of Engineering and Computer Science

    Wright State University, 2015-2018

    Advisor: Derek Doran


    Click for teaching experience, coursework taken, and other details...

  4. Bachelor of Science in CS (+STT)

    College of Engineering and Computer Science

    Wright State University, 2010-2015


    Click for teaching experience, coursework taken, and other details...