Now showing items 1-6 of 6
Augmentation Rank of Satellites with Braid Pattern
Given a knot $K$ in $S^3$, a question raised by Cappell and Shaneson asks if the meridional rank of $K$ equals the bridge number of $K$. Using augmentations in knot contact homology we consider the persistence of equality ...
Efficient Partition Function Estimation in Computational Protein Design: Probabalistic Guarantees and Characterization of a Novel Algorithm
By computational protein design we mean the use of computer algorithms to design new proteins or redesign existing ones. A significant challenge in this field involves computing the partition function of the ensemble of ...
Dynamic Random Network Model for Human Papilloma Virus Transmission
Human Papilloma Virus (HPV) is a widespread sexually transmitted disease which can lead to cervical cancer. Understanding the factors influencing HPV transmission has been a challenge for scientists and policy makers. We ...
Stochastic Study of Gerrymandering
In the 2012 election for the US House of Representatives, only four of North Carolina’s thirteen congressional districts elected a democrat, despite a majority democratic vote. This raises the question of whether gerrymandering, ...
Geometry of Impressionist Music
My project, using both geometrical and statistical methods, nds an appropriate way of determining distances between scales, calculated using appropriate metrics, in the context of impressionist music.
Modeling the Dynamics of Cancerous Tumors in Vivo
A key area of interest in cancer research is understanding tumor dynamics, so that tumor growth can be predicted more easily and treated more reliably. We explored in vivo tumor dynamics starting from simple exponential ...