Graduate Students Seminar

Speaker 1: Harrison Lewis

Title

Spanning a Vector Space with One Vector: An Exploration of the Strange Geometry of De Bruijn Graphs

Abstract

We consider a Graph Theory informed alternative to the usual basis of Rⁿ with the hopes of connecting Linear Algebraic and Graph Theoretic concepts. This results in a deceptively familiar algorithm for constructing a basis which may be cheaper to store in computer memory, but which comes with its own flaws and drawbacks. We also consider the use of this new perspective on both fields, enumerating results which may be demonstrated in a new light.

Speaker 2: Fei Han

Title

Relationship between Event Prevalence Rate and Gini Coefficient of Risk Predictive Model

Abstract

Risk predictive models are currently used for early intervention to help identify patients with a high risk of adverse events.  Assessing the accuracy of such models is a crucial part of the development process. To measure the predictive performance of a scoring model, quantitative indices such as the C-statistic and calibration curve are used. This study discusses the relationship between Gini coefficients and event prevalence rates. The main contribution is a proof of the relationship between the Gini coefficient and event prevalence rate.