Hi, my name is William Oakley. I'm a PhD candidate at UCLA specializing in dynamical systems on networks. Currently, I am involved in three research projects: 1.) modeling, prediction, and inference of messaging in online social networks, 2.) multi-scale belief dynamics on networks, and 3.) multi-scale network games. On my website you will find information about my research and notes on C++ and development tools.

I am seeking a career that will allow me to use the skills that I have developed throughout my PhD--a career requiring the solution of difficult and intricate technical problems, backend software development, collaboration, and project management. My technical skills in programming and mathematics from writing tens of thousands of lines of code in C++, Matlab, Javascript, and many other languages as well as from countless hours on calculations and proofs in many areas of mathematics will allow me to accomplish difficult analytical tasks. Additionally, the research projects that I have led and participated in have given me years of experience in planning and pushing difficult projects to completion as well as collaborating with and managing other researchers. Below, I elaborate on my technical, research, collaborative, and managerial experience.

In a nutshell, my PhD research has been to develop mathematical models of the behaviors of individuals within their social networks, to study these models both mathematically and computationally, and to develop applications of these models. As part of a $6.25m project with the DoD's Multidisciplinary Research Initiative Program (MURI), I developed a belief dynamics model to investigate how group-based communication, such as meetings of individuals, affects belief trajectories when individuals have a bias towards conformity. Using properties I discovered about the model, I suggested practical methods by which an outside influencer could accelerate convergence to a consensus of beliefs within the network. We will be submitting the first paper of this project during the next month.

As part of my thesis research, I have thousands of hours of experience in software development and statistical computing. First, I developed a probabilistic model of user messaging patterns based on the queueing structure of online social networks. Second, I developed an algorithm for parameter estimation and discovered important mathematical properties of the model. Thirdly, I used the algorithm and mathematical properties to apply the model to both estimation and inference: estimation of the messaging patterns of users online and inference of missing data from social network datasets. My thesis and corresponding papers are in preparation and will be completed over the coming months.

As part of the MURI project, I have gained experience collaborating, designing and executing a research plan, communicating research ideas and goals, and managing relationships with other members of the research team. I have worked extensively with researchers at UCLA, USC, and Washington University in St. Louis. I initiated, planned, and led the belief dynamics project discussed above, creating a research plan and suggesting ways other members of the research team can get involved based upon their strengths. Recently, I was tasked with starting a new collaboration with researchers at Washington University: I flew to St. Louis as a liaison to communicate research ideas and decide on and initialize new focus areas for the project.

Above, I sketched out a few of the formative projects and experiences I have had throughout my PhD. I look forward to discussing ways I can contribute to the business of your company.


University of California, Los Angeles

PhD in Applied Mathematics
Los Angeles, CA

North Carolina State University

MS in Mathematics
Raleigh, NC
Cum. GPA: 4.0/4.0

North Carolina State University

BS in Mathematics
Raleigh, NC
Cum. GPA: 4.0/4.0




  • Mathematical Modeling
  • Network Science
  • Social Networks
  • Graph Theory
  • Dynamical Systems
  • PDE and ODE Theory
  • Numerical Analysis
  • Scientific Computing
  • Probability Theory
  • Convex Optimization
  • Statistical Learning


  • Over 50000 lines:
    • C++
    • LaTeX
  • Over 5000 lines:
    • Matlab
    • JavaScript
  • Over 1000 lines:
    • HTML
    • CSS
    • Python
    • PHP
    • Mathematica
  • Familiar:
    • Shell Scripting
    • MySQL
    • regex

Research Experience

Multi-scale Network Games of Collusion and Competition

University of California, Los Angeles
  • Collaborative $6.25m project between five academic institutions funded by the Department of Defense's Multidisciplinary Research Initiative Program and led by Mingyan Liu at the University of Michigan - Anne Arbor
  • Originated and led a subsidiary research project to derive a belief dynamics model under sociological constraints, to prove results on the model's behavior, and to write simulation software to computationally study the model
  • Preprint to be placed on the arXiv by Nov. 1
  • Faculty Advisor: P. Jeffrey Brantingham

Queueing Models of Online Social Network Dynamics: Inference and Prediction

University of California, Los Angeles
  • Originated and led research to develop and study a queueing model of messaging dynamics on online social networks and created techniques for inference and prediction using the model
  • Preprint to be placed on the arXiv by Dec. 19.
  • Faculty Advisor: Mason A. Porter

Hidden Boundary Smoothness for some Classes of Partial Differential Equations

North Carolina State University
  • Masters project in which I proved regularity results on the boundary of a domain for certain classes of differential equations
  • Faculty Advisor: Lorena Bociu

Well-posedness of an ODE Boundary Value Problem on an Invariant Set.

Undergraduate Researcher
North Carolina State University
  • Undergraduate thesis in which I proved existence and uniqueness of an ODE with forcing conditions on the ODE to stay in a set
  • Faculty Advisor: Robert H. Martin, Jr.

Gaps in the Spectrum of the Laplacian on 3N-Gaskets

REU Participant
University of Connecticut
  • Undergraduate research experience in which we characterized and proved results about the eigenvalues of the graph Laplacian on the Sierpinski Gasket
  • Faculty Advisor: Alexander Teplyaev

Work Experience

Verizon Digital Media Services

Software Engineering Intern
Playa Vista, CA
  • Created and deployed a tool to detect malicious activity in web traffic
  • Modified and added functionality to legacy code


2014-2016 Dean's Scholarship UCLA
2012-2013 Hubert V. and Mary Alice Park Scholarship NC State


  • D. Kelleher, N. Gupta, M. Margenot, J. Marsh, W. Oakley, and A. Teplyaev. Gaps in the spectrum of the laplacian on 3n-gaskets. Communications on Pure Applied Analysis, 14(6):2509-2533, 2015.