Students will present an interesting application of matrix algebra that could supplement a Math 322 class.

Title: R as a vector space over Q, with an interesting consequence

Speaker: Dustin Hedmark

Abstract: We will look at the real numbers as a vector space over the rational numbers. After reviewing relevant linear algebra terminology, we will show that this is an infinite dimensional vector space. Next, we will use the vector space R over Q to show that there does not exist a tiling of a rectangle of dimensions 1 by x with squares, where x is an irrational number.

David Murrugarra will talking about some research he did over the past year with two UKY undergraduate students. The title and abstract of his talk are below. Please come and ahangout with other mathematically minded students. There will be pizza.

Title: Estimating Propensity Parameters using Google PageRank and Genetic Algorithms

Abstract: Stochastic Boolean networks, or more generally stochastic discrete networks, are an important class of computational models for molecular interaction networks. The stochasticity stems from the updating schedule. The standard updating schedules include the synchronous update, where all the nodes are updated at the same time and gives a deterministic dynamic, and the asynchronous update, where a random node is updated at each time step that gives a stochastic dynamics. A more general stochastic setting considers propensity parameters for updating each node. SDDS is a modeling framework that considers two propensity values for updating each node, one when the update has a positive impact on the variable, that is, when the update causes the variable to increase its value, and the other when the update is negative, that is, when the update causes it to decrease its value. This extension adds a complexity in parameter estimation of the propensity parameters. This talk presents a method for estimating the propensity parameters for SDDS. The method is based on adding noise to the system using the Google PageRank approach to make the system ergodic and thus guaranteeing the existence of a stationary distribution and then with the use of a genetic algorithm the propensity parameters are estimated.

You may have encountered the concept of Euler characteristic when thinking about soccer balls or Euclidean solids. We'll discuss counting and Euler characteristic: counting points, counting potatoes, and counting holes. We will then approach the Euler characteristic from the perspective a topologist by trying to understand it via its properties rather than by explicitly counting--after all, even mathematicians can only count so high in practice!