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My research builds rigorous, explainable methods for finding structure in data: how patterns form, cluster, and spread across space. At its center is my dissertation, which introduces a Markov chain diffusion distance that extends Moran’s I, the classical measure of spatial clustering, using optimal transport and spectral theory. The same questions about scale and shape carry into topological data analysis, where I co-mentor undergraduate researchers, and into spaceflight biology, where I contribute to NASA’s Open Science Data Repository.
My research builds rigorous, explainable methods for finding structure in data: how patterns form, cluster, and spread across space. At its center is my dissertation, which introduces a Markov chain diffusion distance that extends Moran’s I, the classical measure of spatial clustering, using optimal transport and spectral theory. The same questions about scale and shape carry into topological data analysis, where I co-mentor undergraduate researchers, and into spaceflight biology, where I contribute to NASA’s Open Science Data Repository.
Quick Links
Quick Links
New Preprint
New Preprint
Measuring Spatial Clustering via Metropolis–Hastings Diffusion Distance
T. Weighill and C. Williams · arXiv:2607.14880 · 2026
How do you tell whether a map’s clustering is real structure or just noise? This paper introduces the diffusion distance, a measure of how long a random walk on a graph takes to smooth a spatial pattern into uniformity. It extends Moran’s I, the classical clustering statistic, which turns out to be exactly its first step. We prove spectral and optimal-transport bounds, derive significance tests that need no permutation sampling, and test the measure on census-tract maps of 100 U.S. cities.
Diffusion Distance in Practice
Diffusion Distance in Practice
Presenting “Diffusion Distance and Permutations for Spatial Autocorrelation Analysis” at the 21st Annual UNCG Regional Mathematics and Statistics Conference, November 2025. Read more on LinkedIn
Chyf: AI‑Assisted Micro‑Planning for Streamlined Focus and Execution
Chyf: AI‑Assisted Micro‑Planning for Streamlined Focus and Execution
From scattered tasks to a clear, doable plan.
Chyf (said "chief") is an LLM‑assisted micro‑planning companion that harnesses large language models to support everyday focus and task execution. Given a free‑form or highly structured description of what someone wants to do, Chyf generates a refined, humane sequence of steps—adding buffers, re‑ordering for cognitive load, and suggesting small but meaningful adjustments rather than simply mirroring the input. It lives at the intersection of human‑computer interaction, productivity support, and calm, assistive AI. You are invited to explore the Chyf web app and read my reflection on LinkedIn.
SpartyWiz: Human-Centered AI Innovation
SpartyWiz: Human-Centered AI Innovation
Our final pitch round slide, UNCG AI Innovation Challenge, October 2025.
SpartyWiz is an AI-powered campus assistant redefining how students access information. Via Retrieval-Augmented Generation (RAG) and Large Language Models, SpartyWiz connects UNCG’s internal knowledge bases with conversational AI to provide accurate, real-time, and inclusive 24/7 support for all students. SpartyWiz won First Runner-Up and the Viewer’s Choice Award at the inaugural 2025 UNCG AI Innovation Challenge. Read more about it here: Campus Weekly, Math & Stats News, Research, LinkedIn.
Co-Mentoring Undergraduate Research
Co-Mentoring Undergraduate Research
During the summers of 2025 and 2026, I co-mentored undergraduate research teams with Dr. Thomas Weighill in UNC Greensboro’s NSF-supported Computational Statistics REU, Complex Data Analysis Using Statistical and Machine Learning Tools. Our projects explored topological data analysis and its applications, including questions about scale and structure in data. I guided students in computational methods, data analysis, and model evaluation, and worked with them as their results were written up and prepared for publication. Each team presented its research at the end of the program, where the students received certificates recognizing their work.
REU 2025 · UNCG Computational Statistics REU cohort
The 2025 research team at their final presentation
REU 2026 · UNCG Computational Statistics REU cohort
Innovative Instructional Methods Harnessing Geospatial Data
Innovative Instructional Methods Harnessing Geospatial Data
I developed Adaptive Socio-Spatial Learning (ASSL), a geospatially informed instructional method that integrates data analysis and computational techniques to improve learning outcomes across institutional levels. In classroom deployments at the middle‑school and undergraduate levels, ASSL increased student understanding, retention, and overall performance; middle‑school students taught with ASSL outperformed peers on a statewide exam. I presented these results at the 2025 North East Regional Computing Conference (NERCOMP), sponsored by EDUCAUSE, and the work was featured in UNCG’s Research Magazine for Social Innovation. I was also honored with the 2024 Tutor Spotlight Award for this instructional innovation.
Invited Poster Presentation
NERCOMP 2025
Invited Poster Presentation
NERCOMP 2025
ASSL uses geospatial data to understand the barriers students face outside the classroom, such as access to technology, financial strain, and support at home, and adapts instruction to meet them. I applied it in seventh-grade math through UNCG’s Tutoring Collaborative and in my own undergraduate courses.
NERCOMP Annual Conference (an EDUCAUSE event), Providence, RI, April 1, 2025. Attendance supported by EDUCAUSE and NERCOMP conference funding.
ASSL poster, NERCOMP 2025 Annual Conference (EDUCAUSE), Providence, RI.
Math Learning Specialist, NC A&T State University
Academic Recovery & Pre-College Workshops · Summer 2024
Math Learning Specialist, NC A&T State University
Academic Recovery & Pre-College Workshops · Summer 2024
As a Math Learning Specialist at North Carolina A&T State University, I worked with students in the Math Scholars Institute (MSI), an academic recovery program giving students a second chance to pass College Algebra and Calculus. I designed and led a 10-workshop series with coaching and advising sessions, sharing strategies for breaking down problems, understanding complex questions, and building independent analytical skills.
I also led workshops for the Aggie Success Academy’s residential pre-college program, including S.I.S.T.E.R.S., a mathematics mentorship program for female students. Each workshop opened with the question “Why?”, connecting math to fields from language and engineering to cybersecurity and finance, so students could see mathematics as an exciting journey of problem-solving rather than something “difficult” or “irrelevant.”
Workshop Topics (Summer 2024)
Workshop Topics (Summer 2024)
Math Scholars Institute: Academic Recovery Program
Unlocking Your Math Potential: Embracing Your Learning Style
Decoding Complex Problems: Analytical Skills Bootcamp
Mastering Math Study Skills: Techniques for Effective Learning and Retention
Mastering Math: Advanced Study Techniques for Complex Concepts
Aggie Success Academy: Residential Pre-College Program & S.I.S.T.E.R.S. Female Students Mentorship in Mathematics
Math Unveiled: Unlocking the Power of Numbers in Your Future
Math Empowerment: Transforming Mindsets, Accelerating Skills
Math Fundamentals: Learning FUN-damentals
Math Refresher: Mastering Linear Inequalities in Two Variables
Math Refresher II: Navigating Quadratic Functions
Celebrating Female Mathematicians Who Excelled Against All Odds (final workshop, July 31, 2024)
NC A&T Center for Academic Excellence: S.I.S.T.E.R.S Summer of Success
Small-group photo: Working with students during a S.I.S.T.E.R.S. mathematics session, Summer 2024.
Photo courtesy of the NC A&T Aggie Success Academy.
Lecture photo: Leading a Math Scholars Institute workshop on study strategies, NC A&T, Summer 2024.
Title slide from my final workshop, “Celebrating Female Mathematicians Who Excelled Against All Odds,” Aggie Success Academy, July 31, 2024.
2025 NASA Student Launch Challenge
2025 NASA Student Launch Challenge
At the launch field with the Aggie Rocketry team, 2025.
Image credit: National Aeronautics and Space Administration (NASA)
As a volunteer member of NC A&T’s Aggie Rocketry team, I performed computational analysis for the 2024–2025 NASA Student Launch Challenge. I modeled the rocket’s three-dimensional velocity from its inertial measurement unit (IMU) data, combining accelerometer, gyroscope, and magnetometer readings, and my predictions closely matched the measured flight path. The team advanced to the finals near NASA’s Marshall Space Flight Center in Huntsville, Alabama, launching at Bragg Farms in Toney, Alabama, in May 2025.
Publications, Talks & Projects.
Publications, Talks & Projects.
Talks & Presentations
Talks & Presentations
2026
American Society for Gravitational and Space Research (ASGSR) Annual Conference (upcoming)
Oral presentation on spaceflight retinal data. Crystal City, Virginia, December 2026.
Optimal Transport Seminar, UNC Charlotte (upcoming)
Williams, C. C. (2026). Markov Chain and Optimal Transport Measures of Spatial Clustering. Charlotte, North Carolina, November 4, 2026.
UNCG Mathematics and Statistics Graduate Research Seminar
Williams, C. C. (2026). Measuring Spatial Clustering via Metropolis–Hastings Diffusion Distance. Greensboro, North Carolina, October 16, 2026.
UNCG Computational Statistics REU (invited)
Williams, C. C. (2026). Measuring Spatial Clustering via Metropolis–Hastings Diffusion Distance. Greensboro, North Carolina, Summer 2026.
2025
2025
21st Annual Regional Mathematics and Statistics Conference
Ezugwu, C. (2025). Diffusion Distance and Permutations for Spatial Autocorrelation Analysis. Presented at the 21st Annual Regional Mathematics and Statistics Conference, Greensboro, North Carolina.
UNCG Mathematics and Statistics | Graduate Research Seminar
Ezugwu, C. (2025). Diffusion Distance and Permutations for Spatial Autocorrelation Analysis. Presented at the Mathematics and Statistics Graduate Research Seminar, Greensboro, North Carolina.
NorthEast Regional Computing Program (NERCOMP) and EDUCAUSE Annual Conference 2025, Rhode Island, USA
Ezugwu, Chidinma. "Innovative Instructional Methods for Diverse Learners in a Post-Pandemic World: Adaptive Socio-Spatial Learning." Presented at the NERCOMP Annual Conference 2025. Graduate Teaching Associate, Department of Mathematics and Statistics, University of North Carolina at Greensboro
Links to Session Abstract and Poster.
2023
2023
19th Annual Regional Mathematics and Statistics Conference
Ezugwu, C. (2023). Reducing the Number of Node Expansions by DIBBS. Presented at the 19th Annual Regional Mathematics and Statistics Conference, Greensboro, North Carolina. National Science Foundation Grant no. DMS-2324883.
Institute for Partners in Education & GCS Tutors Conference
Ezugwu, C. (2023). Momentous Little Efforts: Going the Extra Mile as a Tutor. Presented at The Inaugural Annual Tutoring Conference | Guilford County Schools & Institute for Partners in Education (Tutoring Collaborative), Greensboro, North Carolina.
2021
2021
Castleton University 234th Commencement Ceremony
Ezugwu, C. C. (2021). Invited Keynote Speaker. Castleton, Vermont.
2017
2017
International Women's Day Featured Speaker
Ezugwu, C. (2017). Keynote Speaker, “Every Woman Has a Story – Cross-Atlantic Educational Journey in STEM. Presented at International Women's Day Series | Castleton University, Vermont.
Papers & Articles
Papers & Articles
Research
Weighill, T., and Williams, C. C. (2026). Measuring Spatial Clustering via Metropolis–Hastings Diffusion Distance. arXiv preprint arXiv:2607.14880. Paper link
Ezugwu, C. C. (2021). Reducing the Number of Node Expansions by DIBBS (M.S. thesis, Department of Mathematics and Statistics, Southern Illinois University Edwardsville). Thesis link
Ezugwu, C. C. (2017). Stagflation in Nigeria: A New Theory and Case Study. https://doi.org/10.13140/RG.2.2.23147.31528. Paper link
Articles & Essays
Ezugwu, C. C. (2021, May 20). A Voyage for the Light [LinkedIn Article]. LinkedIn. Article link
Williams, C. C. (2024, November 24). Emerging Trends in Retail Credit and Spending. LinkedIn. Article link
Williams, C. C. (2024, November 24). Borrowed Time: Mapping the Geography of Household Credit Distress in the U.S. LinkedIn. Article link
Williams, C. C. (2025, December 3). Launching CHYF: A Gentle Planner for a Loud World. LinkedIn. Article link
Software & Tools
Software & Tools
Applications I’ve Built
CHYF (Chidinma Helps You Focus): an AI planning assistant that turns goals into clear, humane steps. Built with Flask, Groq LLMs, and RAG, and deployed on Render. [Link]
SpartyWiz: an AI assistant for UNCG students, built with team Campus AI Solutions. First Runner-Up and Viewer’s Choice Award, UNCG AI Innovation Challenge, 2025.
Tools
Languages: Python (NumPy, SciPy, NetworkX), R, MATLAB, SAS, JavaScript, HTML/CSS
Machine Learning & AI: scikit-learn, TensorFlow, Groq and OpenAI APIs, RAG
Statistical Software: SAS OnDemand, IBM SPSS Statistics
Web & Apps: Flask, R Shiny, REST APIs, Git/GitHub, Render
Visualization: Tableau, Plotly, Matplotlib/Seaborn
Simulation: Arena (discrete-event simulation)
Writing: LaTeX (TikZ, Beamer)
Areas of Application: computational mathematics, geospatial data analysis, optimal transport, Markov chains, graph and network analysis, simulation and optimization, statistical computing, and machine learning.
Selected Projects
Selected Projects
2024
2024
“Customer Churn Prediction” | Graduate Capstone, Solving Problems with Data Analysis
For this capstone project, I built a statistical model to predict which customers of a fictional online nutrition company were likely to cancel within six months, and estimated what retaining them would be worth. Working with more than 600,000 customer records and 50 behavioral and spending variables, I narrowed the predictors to six key drivers of churn. To do that, I combined Lasso regularization, backward stepwise selection, best subset selection, and likelihood ratio tests. The final logistic regression model correctly identified about 80% of customers who went on to churn, with an AUROC of 0.76. A customer-lifetime-value analysis showed that retaining even 1–2% of at-risk customers could add $260,000–$520,000 a year over a baseline approach, enough to recover the company’s $250,000 investment in the model.
2023
2023
"Enhancing MRI Classification through Optimal Thresholding in Machine Learning" - Big Data and Machine Learning
This study investigates advanced methodologies for the classification of brain MRI scans, employing sophisticated image processing techniques and machine learning algorithms to differentiate between neoplastic and non-neoplastic cases. While previous research has focused on maximizing the F1 score for threshold selection, this approach may negatively impact other performance metrics. To address this, the study evaluates various thresholding methods to enhance overall model performance. Additionally, it incorporates principal component analysis (PCA) to create new feature spaces from the original data, allowing for a comprehensive exploration of informative features. By improving thresholding strategies and utilizing PCA, the study offers deeper insights into model performance and enhancing the accuracy of brain tumor predictions using machine learning algorithms.
2022
2022
“Performance Evaluation of Resampling Methods in Claims Reserving” - Statistical Computing Project at UNC Greensboro
In this paper, we evaluate the performance of prominent resampling methods in claims reserving. This graduate study focused on resampling Pearson residuals obtained from fitting a quasi-Poisson model to loss data and utilized the predicted future losses in computing future reserves. Via numerical analysis, we determine the more effective resampling methods based on computed prediction errors and other pertinent metrics.
2021
2021
“Reducing the Number of Node Expansions by DIBBS” - Southern Illinois University Master's Thesis
This paper discovers and proves various interesting and useful properties of a new Bidirectional Heuristic Search (BHS) algorithm that dynamically improves the bounds during its execution. The algorithm, Dynamically Improved Bounds Bidirectional Search (DIBBS), has the property that it always terminates on or before the forward search meets the backward search. It also has the ability to solve certain problems while expanding fewer nodes than prominent BHS algorithms like GBFHS and MMe. Ultimately, we present a theorem that can be used in reducing the number of nodes expanded by DIBBS in solving a shortest path problem. SIUE, Spring 2021.
2019
2019
(Team) Solved the Institute of Industrial Engineers and Rockwell Automation’s Third Annual Contest Problem 3 | Graduate Advanced Simulation Course Final project
This work is a collaborative project with colleagues in the Advanced Simulation Modeling course at SIUE. Using ARENA Event Simulation software, we model, analyze, and solve –with remarkable results—the Institute of Industrial Engineers and Rockwell Automation’s Third Annual Contest Problem 3: Sally Model’s SM Pizza Shop. SIUE, Fall 2019.
2018
2018
“Cognitive Learning Preferences” | Applied Statistics with SPSS
This project (supervised by Dr. A. Rajia) used IBM SPSS to identify the cognitive learning preferences of Castleton University Applied Statistics students. Findings were analyzed to inform instructional strategies and better align course delivery with the diverse ways students process and retain quantitative information.
Market Research for Student Recruitment at Vermont State University, Castleton | Integrated Marketing and Communications Practicum, Mathematics Department
I was selected by the VSU University Dean of Advancement to conduct research on recruiting new mathematics majors. I developed and executed recruitment strategies in collaboration with the department head, including targeted engagement emails and announcements, managing the departmental email inbox, redesigning the website to attract prospective students, and optimizing overall math department student engagement.
2017
2017
“Economic Development Research” at The Chamber & Economic Development of the Rutland Region
While working as the Economic Development Intern, I conducted research, analyzing Rutland County census and demographic data to identify trends and business development opportunities to inform decision-making for regional improvement. I conducted stakeholder interviews, collaborated with community leaders — including the Paramount Theater Executive Director and university outreach managers — and led a semester-long, data-driven study on strategies to strengthen Rutland's economic sector. Additional contributions included executive report writing and a website content audit with optimization recommendations.
Blog & Portfolios
Blog & Portfolios
The Spirit-Filled Heart (SFH) Faith-Inspired Blog
The Spirit-Filled Heart is a labor of love: a warm, faith-inspired blog sharing uplifting content, encouragement, and Christ-centered reflections.
You are welcome to explore the blog here: Spirit-Filled Heart.
Adobe Education Institute (AEI) 2026 Session Portfolio
Editorial-style research content website created during the "Building Clear, Engaging Webpages with Adobe Express" workshop offered during AEI 2026.
View the portfolio here: Chidinma Williams' AEI 2026 Portfolio.
View the website here: Chidinma Williams' Adobe Website.
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