Professor Inga Johnson, Willamette University
Professor Johnson discusses Knot Theory, introducing the topic of knot colorings and how to determine whether or not a knot has a valid coloring with p-colors.
Breeann Flesch, Western Oregon University
Approval Gap of Weighted K-Majority Tournaments
A tournament is an oriented complete graph. A k-majority tournament T on a finite set of vertices V is defined by a set of 2k-1 linear orders on V, with an edge uv in T if u>v in a majority of the linear orders. We think of the linear orders as voter preferences and the vertices of T as candidates, with an edge uv in T if a majority of voters prefer candidate u to candidate v. In this talk we introduce weighted k-majority tournaments, with each edge uv weighted by the number of voters preferring u. We define the maximum approval gap of T, a measure by which any dominating set of T beats the next most popular candidate. We will give background and definitions, some results, including some short proofs, and open questions.
Inga Johnson, Willamette University
An Introduction to Topological Data Analysis
This talk will be an introduction to topology and the concept of persistent homology. We will use persistent homology to a look at examples of how topological ideas can be used to give new and surprising insight towards understanding data. This talk will include some technical details but I'll emphasize examples and concepts. If time permits, we will discuss an application or two including results from a 2014 REU project I worked on with Professor Jordan Purdy, and four undergrads, Christopher Cericola, Johanna Torrence, Mitchell Krock, and Joshua Kiers.
Josh Laison, Willamette University
Distinguishing, Determining, Fixing, Stamping, and Otherwise Breaking Graph Symmetries
Graph symmetry breaking is a field of research combining graph and group theory, although I won't assume knowledge of those fields for this presentation.
In graph symmetry breaking, the goal is to make a graph asymmetric by adding distinguishing features (i.e., coloring its vertices or faces with different colors). We can ask how few colors we need to do this, or how few vertices or faces we need to color. Each of these is a parameter of the graph (the distinguishing number, determining number, stamping number, etc., of the graph).
In this presentation I'll introduce some of the problems I've worked on in this field with different groups of researchers, including some Willamette students.
Heather Kitada, Reed College
Exploring Model Specification and Imputation Methods to Address Bias in Surveys
Due to differences in cognitive and social stimuli, survey researchers must deal with the consequences of mode of administration differences. Mode choice affects data quality, measurement error, and estimation, and has vast implications on inference. Modes of data collection may change due to newer modes potentially having lower cost, greater convenience, and more representative sampling frames. Data collected from repeated surveys may have incorporated different data collection modes. Changes in mode present a problem due to an inability to detect changing opinions over time because of confounding. This motivates research in performing statistical adjustments to create data under a unified mode.
A biennial survey of Oregon residents has been conducted assessing satisfaction with highways and determining the most important issues facing the Oregon Department of Transportation (ODOT) for the last two decades. All surveys were based on stratified random samples of Oregon residents. A series of experiments were conducted on the general population to determine the impact of mode on survey results and to examine the demographics of respondents for each of these modes over time.
Synthetic data, based on historical ODOT observations, were created and used to study the performance of adjustment methods in large simulation studies that account for the complexities of the sampling mechanism. These adjustment methods include a design-based additive approach, an inverse logit application of the delta method, and a truncated latent logistic multiple imputation. Each method is assessed for model misspecification, adjusted estimate bias, and proper inference calibration.
Harbour Harrison & Brandon Nelson, Willamette University
Advancement of Statistics, Data, and Technology in Baseball
It is a common misconception that sports such as baseball are detached from educational subjects such as math and science. In reality, baseball has become the most data driven sport in the world, changing the way the game is played, coached, and evaluated. The interests of computer scientists, statisticians, and physicists are no longer mutually exclusive to those of a baseball organization. The Moneyball philosophy triggered a surge in advanced statistics for baseball and the newest technology has given teams access to even more data to explore for evaluating their team.
Evgenia Chunikhina, Oregon State University
Statistical Machine Learning for Recommender systems: LDA and K-means
Recommender systems are one of the most popular and successful applications of statistical machine learning in e-commerce. Recommender systems use algorithms to provide users with service or product recommendations. A large variety of methods have been proposed for recommendation, including collaborative, content-based, and knowledge-based techniques. In this talk I will consider two classical algorithms from statistical machine learning: Linear Discriminant Analysis (LDA) for classification and K-means for clustering. Both algorithms are extensively used in recommender systems because of their relative simplicity and effectiveness.
Professor Nancy Ann Neudauer, Pacific University
Extending Fixing Numbers of Graphs to Matroids
A subset S of the vertices of a graph G is a fixing set for G if and only if the identity automorphism is the only automorphism of G that fixes every vertex of S. That is, each automorphism of G is completely determined by its action on a fixing set S. The fixing number of G, denoted fix(G), is the cardinality of the smallest fixing set of G. Automorphism groups and fixing numbers allow us to describe the symmetry properties and structural complexity of a graph. We begin by examining the automorphism groups and fixing numbers of various classes of graphs, show that two graphs with isomorphic automorphism groups may not have the same fixing number, and consider some bounds for fixing numbers.
We then consider whether we can extend this to matroids. We find the fixing number for specific examples of matroids and give some results for fixing numbers of binary, transversal, and bicircular matroids. No prior knowledge of graphs, matroids, or groups is assumed.
Professor Steve Bleiler, Portland State University
Exploring the Geometry of Music with Technology
For over two millennia now, when faced with this very famous statement from the father of nearly all Western mathematics, people have asked what really is this geometry of humming strings or music of the spheres? This talk explores how modern computational software capabilities grant us new ways of visualizing geometrical and hearing musical landscapes. This happy trick is performed via the elimination of various arithmetical and computational barriers that have previously stymied those untrained in musical theory or mathematical and arithmetical techniques from fully appreciating Pythagoras’ remarkable observation. No mathematics beyond ordinary arithmetic or knowledge of music theory required.
Professor Josh Laison, Willamette University
Prime Distance Graphs: Making Difficult Problems Seem Easier Using Pretty Diagrams
A graph is a prime distance graph if its vertices can be labeled with distinct integers
such that for any two adjacent vertices, the difference of their labels is prime. Surprisingly, some well-known theorems and longstanding conjectures in number theory are closely connected to questions about prime distance graphs. In this talk, we’ll investigate some of these connections and fail to prove any of the longstanding conjectures. This talk is based on two research projects with Willamette Math professor, Colin Starr, and Willamette Math alums, Yumi Kaneda, Jeffrey Schreiner-McGraw, and Andrea Walker.