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SIAM Undergraduate Research Online

Volume 12


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Computing shape DNA using the closest point method

Published electronically January 13, 2019
DOI: 10.1137/18S016801

Authors: Rachel Han (University of British Columbia) and Chingyi Tsoi (Hong Kong Baptist University)
Sponsor: Colin Macdonald (University of British Columbia)

Abstract: We demonstrate an application of the closest point method to numerically computing the truncated spectrum of the Laplace-Beltrami operator. This is known as the “Shape DNA" and it can be used to identify objects in various applications. We prove a result about the null-eigenvectors of the numerical discretization. We also investigate the effectiveness of the method with respect to invariants of the Shape DNA. Finally we experiment with clustering similar objects via a multi-dimensional scaling algorithm.

Opinion Formation Dynamics with Contrarians and Zealots

Published electronically February 12, 2019
DOI: 10.1137/18S017314

Author: Kaitlyn Eekhoff (Calvin College)
Sponsor: Todd Kapitula (Calvin College)

Abstract: Mean-field type ODE models for opinion dynamics often assume that the entire population is comprised of congregators, who are agreeable. On the other hand, a contrarian opinion dynamics ODE model assumes the population has two personality types: congregators, and contrarians, who are disagreeable. In this paper we broadly study how contrarians influence the ability of the population to form a fixed and stable opinion. In particular, we re-examine the dynamics associated with the model introduced by Tanabe and Masuda [12] by looking at how the parameters effect the formation of stable periodic solutions (whose existence implies there is no fixed consensus opinion). Afterwards, we refine and analyze the model under two new hypotheses: (a) the contrarians bow to peer pressure and change their personality type to congregators if a large enough proportion of the entire population agrees on an opinion, and (b) there are zealots associated with one of the opinions. We conclude with a brief discussion on possible extensions of this work.

A Bayesian Model for the Prediction of United States Presidential Elections

Published electronically February 18, 2019
DOI: 10.1137/17S016166

Author: Brittany Alexander (Texas Tech University)
Sponsor: Leif Ellingson (Texas Tech University)

Abstract: Using a combination of polling data and previous election results, FiveThirtyEight successfully predicted the Electoral College distribution in the presidential election in 2008 with 98% accuracy and in 2012 with 100% accuracy. This study applies a Bayesian analysis of polls, assuming a normal distribution of poll results using a normal conjugate prior. The data were taken from the Huffington Post's Pollster. States were divided into categories based on past results and current demographics. Each category used a different poll source for the prior. This model was originally used to predict the 2016 election, but later it was applied to the poll data for 2008 and 2012. For 2016, the model had 88% accuracy for the 50 states. For 2008 and 2012, the model had the same Electoral College Prediction as FiveThirtyEight. The method of using state and national polls as a prior in election prediction seems promising and further study is needed.

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