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.

Title:  Cyclotomic Factors of the Descent Set Polynomial

Abstract:  The descent set polynomial is defined in terms of the descent set statistics of a permutation and was first introduced by Chebikin, Ehrenborg, Pylyavskyy, and Readdy.  This polynomial was found to have many factors which are cyclotomic polynomials.  In this talk, we will explore why these cyclotomic factors exist, focusing on instances of the 2pth cyclotomic polynomial for a prime p.

We will also discuss activities for next semester and talk about organizing practice sessions for the math modeling contest

People often like to say things along the lines of “Well, we're either gonna win the game, or we're not.  So I'd say the odds are fifty-fifty."  This is, of course, rarely the case.

We will look at some problems and try to determine what the odds really are. Consider the following problem. A plane has 100 seats and 100 passengers. They enter the plane, one-by-one, in order. The first passenger is lazy and selfish, and picks a random seat to sit in. The rest of the passengers try to sit in their assigned seats, but if they find another passenger there, they choose another seat at random. What are the odds that the last passenger sits in his/her assigned seat?