Research

Current Projects

Evolving Voter Models

Voter Models were originally conceived as spatial conflict models by Clifford and Sudburry in 1973. In a static voter model, one has a graph of voters and relationships, a set of opinions such that each voter is assigned an opinion, and an update rule to re-assign opinions. These models have been studied extensively and many of their features are well understood. For an evolving voter model, in addition to having a dynamical process on the network, the network itself is dynamic such that the update rule may also create or break relationships.

Profanity on Reddit

The function of profanity is an active area of research in linguistics, psychology, sociology, and many other fields. Here, we employ tools from network theory to explore the usage of profanity (used synonymously with swearing and swear words) particularly on the Internet discussion website Reddit. Analysis of the textual content of Reddit threads suggests certain behavioral trends. We also investigate thread centrality and communities as well as word similarity communities.


TDA

Under Construction

Opinion Dynamics

Under Construction


Past Projects

Research in Industrial Projects for Students

From left: Mohit Agrawal, Leah Rosenbaum, Leah Birch, and Yacoub Kureh In the summer of 2011, I participated in Research in Industrial Projects for Students (RIPS), a summer research program for undergraduate students in mathematics. Students work in teams of four on projects proposed by industry sponsors, such as IBM, the Los Angeles Police Department, and S&P. Each team is advised by an academic mentor and works closely with one or more mentors from the industry sponsor. RIPS is organized by the Institute for Pure and Applied Mathematics at UCLA.

I worked with a team of students on a project for The Aerospace Corporation, a federal R&D center that manages the design, launch, and maintenance of satellites. Below is the abstract of that work, along with our paper, our final presentation and PowerPoint, and a draft of a paper that we submitted to an IEEE conference. Leah Rosenbaum and I participated in the student poster session at the Joint Mathematics Meetings in Boston where we won Outstanding Presentation awards.

Abstract: Many satellite communication (SATCOM) systems currently use a static resource allocation scheme, which is known to provide excellent service to high-priority jobs. However, this static allocation method is inefficient, as it makes valuable network resources inaccessible to low-priority jobs even when resources are available. We developed stochastic models that approximate the SATCOM systems and studied their statistical properties. We began by reviewing the standard M/M/m model from classic queueing theory and used Markov chains to extend the classic models to include multi-class jobs, more suitably approximating SATCOM systems. Then, by way of simulation, we isolated and characterized the system’s key performance trends in terms of its statistical characteristics. Properties under consideration include the probability of call blocking, preemption, satisfaction, and the expected server utilization, all as a function of priority and bandwidth.

Files: Presentation Slides, Final Report, IEEE Paper, and Video of our final presentation (Thanks to Mohit Agrawal for posting).