My name is Greg DePaul. I am a fifth year doctoral student at UC Davis studying Applied Mathematics. My advisor is Erik Carlsson. My research interests are in computational topology and algebraic geometry and their applications to data science and machine learning. Specifically, my work is in topological inference and algebraic statistics. In my free time, I also enjoy road cycling.
Ph.D. Applied Mathematics
M.S. Statistics
2019-2025
M.S. Computational and Mathematical Engineering
2016-2018
B.S. Computer Engineering
B.S. Double Major in Mathematics and Computer Science
2012-2016
June 2024 - September 2024
Working with Ads Infrastructure team for better ML training Strategies.
April 2023 - June 2023
Work on combining local knowledge bases with conversational agents.
June 2021 - Sept 2022
Working on data science problems related to the new interest discovery system called Pincepts.
August 2018 - September 2019
Powerpoint Data Analytics and Machine Learning Team. Worked in a variety of projects dealing with Text2Content features as well as aiding in the release of the new Rehearsal Coach feature.
June 2017 - September 2017
Research Assistant for Data Analytics Department. Project focused on Machine Learning techniques and Computational linguistics for Information Extraction.
June 2016 - September 2016
Worked with FIRST Engineering Department to develop technologies that will benefit robotics teams in order to compete for the 2017 FIRST Robotics Competition (FRC).
Winter 2023
Graduate-Level Research in Industrial Projects for Students (GRIPS) will offer gradgripsuate students in mathematics and related disciplines the opportunity to work on industry-sponsored research problems. Students from the U.S. and Germany will work on cross-cultural teams on three research problems designed by the industrial sponsor. The projects will be of serious interest to the sponsor and will offer a stimulating challenge to students; most will involve both analytic and computational work. At the end of the program, the teams will present the results of their work and prepare a final report. English is the only language required for participation.
Spring 2021
Yueh-Jing (Jean) Lin and Chau-Hsiung (Mike) Chuang are alumni of UC Davis who met while they were graduate students on campus. This endowment provides scholarship support to one or more mathematics students each year who are high-achieving mathematics students, either undergraduate or graduate.
Spring 2018
Awarded to aspiring engineers who travel to support conservation efforts on the UNESCO World Heritage site of Chavin de Huantar, Peru.
Winter 2017
The Schlumberger Innovation Fellows program recognizes aspiring scholars in the fields of machine learning, deep learning, high performance computing, and 3D modeling and data visualization. The award was established to encourage scholarship and research in these emerging technology areas, which hold great promise across many industries to improve performance, lower costs, increase accuracy and provide new research and business insights.
Spring 2014
Awarded to students majoring in Mathematics that demonstrate academic merit, particularly in mathematics courses at the UA.
Spring 2014
Awarded to students majoring in Engineering that demonstrate academic merit to support and ensure those awarded success as students and practicing professionals.
Spring 2012
Established by the Arizona Board of Regents to recognize Arizona high school students for outstanding academic achievements as demonstrated through high school courses and test scores (AIMS).
May 2024
The study of the closest point(s) on a statistical model from a given distribution in the probability simplex with respect to a fixed Wasserstein metric gives rise to a polyhedral norm distance optimization problem. There are two components to the complexity of determining the Wasserstein distance from a data point to a model. One is the combinatorial complexity that is governed by the combinatorics of the Lipschitz polytope of the finite metric to be used. Another is the algebraic complexity, which is governed by the polar degrees of the Zariski closure of the model. We find formulas for the polar degrees of rational normal scrolls and graphical models whose underlying graphs are star trees. Also, the polar degrees of the graphical models with four binary random variables where the graphs are a path on four vertices and the four-cycle, as well as for small, nothree-way interaction models, were computed. We investigate the algebraic degree of computing the Wasserstein distance to a small subset of these models. It was observed that this algebraic degree is typically smaller than the corresponding polar degree. Read Paper
Summer 2023
We survey the necessary architectural develops that lead to the development of FlowSSM [1]. We also engineer a sequence model to perform the integration of the identified flow trajectories surrounding a mean shape. Read Paper Access Code
Summer 2019
A method and system for speech rehearsal assistant during a presentation rehearsal includes receiving audio data from a speech rehearsal session over a network, receiving a transcript for the audio data, the transcript including a plurality of words spoken during the speech rehearsal session, calculating a real time speaking rate for the speech rehearsal session, determining if the speaking rate is within a threshold range, detecting utterance of a filler phrase or sound during the speech rehearsal session using at least in part a machine learning model trained for identifying filler phrases and sounds in a text, and upon determining the speaking rate falls outside the threshold range or detecting the utterance of the filler phrase or sound, enabling real time display of a notification on a display device. Read Patent
Spring 2019
A textual user input is received and a plurality of different text-to-content models are run on the textual user input. A selection system attempts to identify a suggested content item, based upon the outputs of the text-to-content models. The selection system first attempts to generate a completed suggestion based on outputs from a single text-to-content model. It then attempts to mix the outputs of the text-to-content models to obtain a completed content suggestion. Read Patent
Summer 2018
While working in an archeological site, I was given the opportunity to help aide in Archeo-accoustic research. Lot of fun! Read Paper
Summer 2018
Spent the summer working in an archeological site, developing remote sensing modules which are used to gather valuable data for archeological conservation. Read Paper
Spring 2018
Supervised by Michael Saunders, Stephanie Sanchez and I worked to develop industry level code for Saunder's Modified USYMQR Algorithm for Julia. Read Paper
Spring 2018
We set out to build a model that, given satellite imagery and structured covariate data, is able to provide a reasonable estimate of the performance of a school district. Read Paper
Fall 2016
We perform smoothing over the raw velocity spectrum data, and then apply methods of unsupervised classification to emphasize features of nonuniformity. We then create a heuristic-driven graphical overlay for accelerating subsurface fault-line/mineral deposit identification based on reflection seismology. Read Paper
Spring 2016
Implement an LED grid on top of your everyday coffee table. This grid is reconfigurable through a Bluetooth connected android device. Read Paper See Video
Spring 2016
Create an implementation of Huffman Encoding for an arbitrary subset of ASCII characters. This implementation makes explicit use of data structures to ease processing. Read Paper Download Code
Fall 2015
My team was given the task of design a data acquisition module that is both versatile in its ability to collect different sensory data by alternating sensor units, while also being portable, particularly capable of fitting within the average pocket. The final module is also cost effective, estimated to cost a mere twenty US dollars in order produce a single module. Read Paper
Spring 2015
Developed a simple, collaborative editor in Java, using the command design pattern, that provided users the ability to edit the same document simultaneously. Download Code
November 7-12, 2024
Mérida (Yucatán), México
Presented a three class course on TDA using Python, Gudhi, and Sage.
October 21-25, 2024
Atlanta, Georgia, U.S
Presenting Leveraging Derived Statistics from Differential Geometry for Understanding High-Dimensional TDA
October 7-19, 2023
Saclay, France
April 5-7, 2023
Ohio State University
Presenting on the Successes and Failures of Starting a Spectra Chapter
April 7-12, 2023
Banff International Research Station
Attending as a spectator.
January 22-26, 2024
Isaac Newton Institute for Mathematical Sciences (attended virtually)
Attending as a spectator.
January 8-13, 2023
Mérida (Yucatán), México
Presenting work from "A novel filtered complex from multidimensional Gaussian balls"
January 3-6, 2024
San Francisco
Presenting work from "Adding Differential Topology and Statistical Robustness to TDA"
October 9-13, 2023
IMSI, University of Chicago
Purely attended, although enjoyed much of the work on algebraic models dealing with unbounded sequences of finite states, specifically phylogenetics.
October 2-6, 2023
IMSI, University of Chicago
Presented some of the joint work with Ikenna Nometa and Nilava Metya under the supervision of Dr. Serkan Hosten on computing the Wasserstein Distance to certain independence models.
April 14th, 2023
University of Calfironai, Merced
Presented on "Novel Resolution of Singularities within Point Cloud Data using TDA"