Speaker : Michael Yampolsky (University of Toronto)

Title : Computability of Julia sets.

Abstract : Informally speaking, a compact set in the plane is computable if there exists an algorithm to draw it on a computer screen with an arbitrary resolution. Julia sets are some of the best-known mathematical images, however, the questions of their computability and computational complexity are surprisingly subtle. I will survey joint results with M. Braverman and others on computability and complexity of Julia sets.

Speaker: Gideon Zamba (U. Iowa)

Title: Recurrence of Subsequent Malignancies following Diagnosis of and Treatment for Hodgkin Lymphoma Diagnosis

Abstract: Hodgkin’s Lymphoma (HL) is a type of cancer that affects the lymphatic system and compromises the body’s ability to fight infection. HL typically starts in white blood cells. HL occurs when a specific type of cell, the Reed-Stenberg cell, is present in the host’s system, causing the body’s infection fighting cells to develop a mutation in their DNA. Each year, there are several thousand people in the United States and worldwide who develop HL. Although there are many prognostic factors for HL and post treatment malignancies, it has also been hypothesized that initial treatment after diagnosis may be associated with subsequent new malignancies or death. We explored the association between prognostic factors and subsequent malignancies using the Oncology Registry at the University of Iowa Hospitals and Clinics. In this exploration we account for subject random effect through a gamma frailty model for recurrent events, which acts multiplicatively and jointly on both the hazard of new malignancies and the hazard of death. The parameters of the model were iteratively estimated using a penalized marginal likelihood approach. The findings suggest a significant within subject correlation, and a significant treatment effect on both the hazard of recurrence and the hazard of death.

Speaker: Elizabeth Gross (San Jose State U.)

Title: Goodness of fit of statistical network models

Abstract: Exponential random graph models (ERGMs) are families of distributions defined by a set of network statistics and, thus, give rise to interesting graph theoretic questions. Indeed, goodness-of-fit testing for these models can be achieved if we know how to sample uniformly from the space of all graphs with the same network statistics as the observed network. Examples of commonly used network statistics include edge count, degree sequences, k-star counts, and triangle counts. In this talk, we will introduce exponential random graph models, discuss the geometry of these models, and show the role toric ideals play in determining the quality of model fit.

Speaker:

Leslie Hogben

Iowa State University and American Institute of Mathematics

Title:

Power domination and zero forcing: Using graphs to model real-world problems

Abstract:

A graph $G = (V, E)$ is a set of vertices $V = {1, dots , n}$ and set of edges $E$ of

two element sets of vertices. A graph can be used to model connections between

vertices, such as airline routes between cities, internet connections, a quantum

system, or an electric power network.

Power domination and zero forcing are related coloring processes on graphs.

We start with a set of vertices colored blue and the rest colored white. We apply

a color change rule to color the white vertices blue. A set of blue vertices that

can color all vertices blue by using the power domination color change rule (or

zero forcing color change rule) is called a power dominating set (or a zero forcing

set). Finding a such set allows us to solve various problems, and a minimum

such set can provide an optimal solution.

In an electric power network, a power dominating set (blue vertices) gives

a set of locations from which monitoring units can observe the entire network.

In a quantum system, a zero forcing set (blue vertices) gives a set of locations

from which the entire system can be controlled.

This talk will describe power domination and zero forcing processes on

graphs and some of their applications.

This semester the Logic Seminar continues at a new day and time, Fridays at 2:30 in Keller 314.

For the first meeting this Friday I will (probably) speak about _Skolem polynomials_:

Abstract:

Over 100 years ago Hardy proved that a certain large class of real functions

was linearly ordered by eventual domination. In 1956 Skolem asked

whether the subclass of integer exponential polynomials is *well*-ordered

by the Hardy ordering, and conjectured that its order type

is epsilon_0. (This class is the smallest containing 1, x, and closed

under +, x, and f^g.) In 1973 Ehrenfeucht proved that the class is

well-ordered, and since then there has been some progress on the order

type.

The proof of well-ordering is rather remarkable and very short, and I

will attempt to expose it (which is to say, cover it) in the hour.

David Ross

Mushfeq Khan will speak on amenability and symbolic dynamics.

As usual the seminar is in Keller 314.