PhD DefensesSummer 2016 Tuesday, June 28, 2016 Spring 2016 Thursday, March 17, 2016 Friday, March 18, 2016 Thursday, March 24, 2016 Friday, March 25, 2016 Friday, March 25, 2016 The MAMS Department will host a reception to celebrate our PhD students’ successful dissertation defenses, with cake and beverages provided. All department faculty, students, staff, and visitors are welcome. Thursday, April 28, 2016 Spring 2014 Monday, March 3, 2014 Tuesday, March 4, 2014 Friday, March 7, 2014 Thursday, March 20, 2014 Monday, March 24, 2014 Friday, March 28, 2014 
MS Thesis DefensesSummer 2015 Monday, August 3, 2015 Spring 2015 Wednesday, April 29, 2015 Spring 2014 Friday, May 16, 2014 Tuesday, March 25, 2014 
Senior Capstone PresentationsFall 2016 Wednesday, Dec. 7, 2016 Title: Familywise Discovery Rate and False Discovery Rate Abstract: This project compares the Bonferroni correction, which controls familywise discovery rate (FWER) in multiple testing and the BenjaminiHochberg procedure (BH method), which controls false discovery rate (FDR). The goal of this project is to look at the cons of FWER and reasons for FDR’s growing popularity. As this project goes on, different distributions of pvalues under two conditions, all nulls are true, and not all nulls are true, are studied. This will affect the ways to choose the upper bound q when using BH method. Wednesday, Dec. 7, 2016 Title: Spatial Analysis About Soil Moisture Abstract: This senior project applied methods from spatial statistics to analysis spatial relationship about soil moisture between two random locations in each block. Data is collected from University Farm. The presentation will show some basic ideas used in spatial analysis, such as variogram and kriging. Monday, Dec. 12, 2016 Student: Grace Cammarn Title: Assessing the Public Health of 50 U.S. Cities Abstract: In April 2016, the Aetna Foundation announced the start of the Healthiest Cities & Counties Challenge. In the Challenge, 50 cities and counties would be competing to improve the public health of their targeted areas. I will simulate the Healthiest Cities & Counties Challenge by selecting 50 random U.S. cities and comparing different public health metrics in order to determine what factors lead to healthier cities. Public health, the science of protecting and improving the health of communities through policies and the promotion of athome healthy lifestyles is not an easy thing to measure. There is no single index or measure that indicates the overall health of a community. Public health metrics must cover areas of personal health behaviors, the built environment, socioeconomic factors, community safety, and other environmental exposures. My simulation revealed that at present, there is not a robust data source that would allow the public health of different U.S. cities to be accurately compared. I will recommend that publicly available public health data be used on a regionbyregion basis, not as comparison metrics. I will also recommend that U.S. census procedures inquire about more public health related topics. Student: Jenna Ehrle Title: Women’s Rights and Economic Performance Abstract: This project analyzes a merged data set of levels of women’s rights in different countries in 2014 from the Organization for Economic Cooperation and Development and GDP per capita of different countries in the years 20052015 from The World Bank. The goal of this project is to explore the connection between women’s rights and economic performance and development, hopefully to find that higher levels of women’s rights have a positive effect on economic performance. This project utilizes the application of exploratory data analysis, linear regression, and additional data analysis techniques. Student: Yinger Fan Title: Investigation on the Correlations between HIV, Literacy Rate, and Socioeconomic Status Abstract: Simple regression models and chisquare tests were used to investigate the relationships between HIV, literacy rate, and socioeconomic status. Data are collected from demographic and health surveys, EFA global reports, AIDS indicator surveys, and readymade research on wealth and poverty linking to HIV in Africa. R software was used in the analysis. The relationship between literacy rate and HIV prevalence in several African countries was investigated by using simple linear regression. The relationship between socioeconomic status and HIV prevalence in 12 African countries was investigated using the chisquare test. Thursday, Dec. 15, 2016 Title: A Numerical Investigation of Lagrangian Coherent Structures in Fluid Flow Abstract: Lagrangian Coherent Structures are useful for determining the behavior of dynamical systems, and in particular they are useful for separating fluid flow into distinct regions. LCS has been used to study flow patterns in blood flow, flow past an airfoil, and ocean currents. However, rigorous numerical testing and validation of existing software packages, such FlowVC is lacking. In this work, we test the numerical convergence of the numerical methods used in the FlowVC software to determine LCS. We perform various convergence tests to determine the validity of data output used to defined the coherent structures. Specifically we test the following incompressible velocity fields: uniform fluid flow, vortex flow, double gyre flow, and flow past a sphere. Results show that the methods do not converge due to large numerical error on the boundary. Therefore, we recommend using LCS on a smaller domain away from the physical boundary of the system where we show first convergence in space can be achieved. 11:30 a.m. in Yost 306 Title: Two characterizations of inversepositive matrices Abstract: A matrix M is called inversepositive if M is nonsingular and the inverse of M has all nonnegative entries. I will talk about two characterizations of inversepositive matrices and examples of them.
Spring 2016 Tuesday, March 29, 2016 Title: Independent Component Analysis Abstract: Independent Component Analysis (ICA) is a powerful computational tool for separating independently generated signals from each other based on a multichannel registration of the mixed signal. The classic example is the cocktail party problem, in which the goal is to separate several simultaneous speakers from each other. ICA is widely used, e.g., in medical applications such as electroencephalography (EEG) to discern the different brain signals from the noisy registration. The talk reviews the basic idea behind the ICA. Monday, April 25, 2016 Title: A Comparison of Public Market Equivalent Calculations Abstract: Generally, the Private Equity industry calculates Internal Rates of Return (IRR) and Market Multiples to weigh the performance of an investment or fund. However, while these calculations can be used to compare between private investments, it cannot be used to compare private investments with other asset classes, requiring the calculation of a public market equivalent. A public market equivalent (PME) acts as a measure of the performance of a private equity fund by comparing it against a benchmark in the public market (in our case the S&P500). While several methods have been created to calculate PMEs have been found, we will take a closer look at three methods of calculating PME: LongNickels method, KaplanSchoar method, and Direct Alpha method. We will look at how each equation and/or algorithm to calculate PME affects its ability to accurately depict the performance of an investment. We will also look at using these methods to then determine the best one among the three to be a basis for a predictive model. MATH 352 Senior Capstone Presentation Session Thursday, April 28, 2016 Title: Finding Bestsellers? An Application of Data Analysis with Open Source Data Abstract: This project analyzes a historical data set containing the daily top 100 bestselling shoe products on amazon.com over a 2andahalfyear period. The project goal is to identify characteristics which may be indicative of successful products, success being defined as the amount of days a product is listed in the top 100 bestsellers, and to attempt to predict the amount of days a product will appear on the best sellers list. This project will showcase the practical application of data analysis techniques such as linear regression, principal components analysis, Poisson regression, time series analysis, and exploratory data analysis among other techniques. Fall 2015 Tuesday, December 15, 2015 Abstract: The RMS Titanic sank in 1912, what can we still learn from it today? This talk will discuss the steps, process and outcome of using R to create a predictive model. This model will be used to predict the “survivability” of individuals based off of key characteristics. This talk will also discuss how creating a predictive model is useful in other catastrophic situations. Summer 2015 Tuesday, August 4, 2015 Spring 2015 Tuesday, May 5, 2015 Thursday, May 7, 2015 Fall 2014 Wednesday, December 10, 2014 Abstract: I investigated the game of Craps because I enjoy gambling and I have been successful playing Craps at casinos. While at the casino, I have done some mental math and found some parts of the game to have good odds. However, I had never done any of the hard mathematics. This project allowed me the opportunity to research something that I enjoy and to see whether or not it was possible to make money. In order to figure out the odds of each game and to see if it was possible to make a profit, I used an assortment of different probability techniques. This included anything as simple as figuring out the chance that a two will roll next to the probability of a seven coming before a ten given that a ten has already been rolled. Spring 2014 Tuesday, April 29, 2014 Abstract: The cost of attending a private university in America has become a financial burden for many degreeseeking students. Some private colleges, however, have much higher price tags than others. Our question of interest pertains to what factors influence tuition rates at private universities in America. Do the universities with similar tuition rates also share some similar qualities? Given certain publicly available characteristics of a university, can we fit a linear regression model that allows us to predict that university’s “correct” tuition rate with a rather high degree of accuracy? In this talk, I describe the process I took in an attempt to seek answers to these questions through a statistical analysis.
Friday, May 2, 2014 Abstract: In 2010, Eguchi, Ooguri and Tachikawa discovered an incredible and mysterious connection between the Mathieu group M24 and K3 surfaces. In 2012, Cheng, Duncan and Harvey further related moonshine to certain mock theta functions discovered by Ramanujan. In this project, by using the data from the paper “Umbral Moonshine and the Niemeier Lattices”, we found evidence that for a Niemeier root system X and its corresponding vector valued weak harmonic Maass form, a conjectural generalization the Borcherds lift (for a given admissible pair) coincides with a rational function in an eta product defined by the Coxeter element of X. This project contains five examples from two root systems with discriminants of different class numbers. These examples provide interesting data for understanding the hidden, mysterious nature of moonshine.
Monday, May 5, 2014 Abstract: Simpson’s Paradox may lead to intuitive but invalid conclusion on the correlation between variables. For this talk, I will describe how I applied the existing contingency table approach to analysis the paradox under a real world paradoxical data – Economic Recession: 1982 vs.2009. The study also includes an attempt to summarize the conditions of conditional probabilities, based on which I can construct my own paradoxical data. Finally, to compare the accuracies of the Chisquare and Bsquare tests in determining the measure of association between two variables, a simulation process is used.
Thursday, May 8, 2014 Abstract: Using a matrix action, matrices in the group SL 2 mod n can act on homogenous polynomials in two variables. We find homogenous (bivariate) polynomials of any given degree are closed under the matrix action, and that the mappings from a polynomial to the result of the action on it lay the foundation for certain patterns that we describe.
Thursday, May 8, 2014 Abstract: With the prospect of quantum computers on the horizon, the most widely used cryptosystems may soon be rendered obsolete. A possible solution is latticebased cryptosystems, for which there are no known quantum attacks. Signature schemes based on the hardness of lattice problems are theoretically very efficient and secure, although a large key size is required to make lattice reduction attacks infeasible in practice. I focus on latticebased signature schemes, their development over the past two decades and a modern onetime signature scheme due to Micciancio and Lubyshevsky (and I give a basic improvement of the scheme using Merkle Trees).
Friday, May 16, 2014 Abstract: There is a known correspondence between a particular set of conjugacy classes of the group M_{24} and the nodes of the affine Dynkin diagram arising from the E_{8} lattice. More specifically, the nine conjugacy classes of M_{24} that arise as compositions of two 2A class involutions correspond to the nine nodes of the affine E_{8} diagram. As M_{24} is known to be the automorphism group of the extended binary Golay code C_{24}, we investigate how this correspondence appears in the context of C_{24}. Namely, we attach to each 2A involution of M_{24} a unique subcode of C_{24} isomorphic to the extended binary Hamming code H_{8}. We then characterize the relationship between any two 2A involutions and the corresponding copies of H_{8} and relate these pairs of H_{8} copies to the nodes of the affine E_{8} diagram.
