Towson Regional Mathematics Undergraduate Conference

On Saturday, April 7, 2018, three UD math undergraduate students presented results from their summer research projects at the 2018 Towson Regional Mathematics Undergraduate Conference.  UD provided the largest contingent of talks at the conference, which drew participants from four states.

The following students presented their research:

Chunxu Ji - Graph Edge Coloring (with Sebastian Cioaba)

In this note, we study graph edge coloring on strongly regular graphs. The main tools are Vizing theorem and spectral
graph theory. We start with analyzing the chromatic index of a very special strongly regular graph { Petersen graph. We
then prove a property that the chromatic index of a regular graph with even order preserves if an arbitrary vertex and
all the edges induced by it are removed from the original graph. Moreover, spectral theory is applied when we compare
graph edge coloring problems with matching problems.

Claire Lubash - Mathematical Modeling of Plankton Behavior: Photosynthesis (with Lou Rossi)

The goal of this research is to create a three-dimensional model of the motion and aggregation patterns of Heterosigma
Akashiwo, a species of plankton known to cause algal blooms with detrimental ecological impacts. In order to eventually
mitigate these blooms, we want to understand how plankton signal each other via photosynthesis and chemical signaling.
To obtain raw data and gain insight for our model, experiments were conducted to determine what variables aected the
photosystems and behaviors of the plankton. From our model and experimental data, we see the number of plankton
aggregations decaying exponentially with time, and the ecology eventually forming a rotating quasi-equilibrium. We
have constructed a number of reduced computational and analytical models focusing on how plankton aggregate through
chemotaxis and phototaxis. In the future, we hope to create more realistic models and further our understanding of the
variables aecting aggregation patterns and the eventual quasi-equilibrium it attains.

Lucas Onisk - Multi-Site Reaction Rate Constant Evaluation (with David Edwards)

Scientists interested in biomolecular interaction analysis often ow a stream of ligands through a uid-lled volume
over which receptors are bound. This procedure coupled with current instrumentation allows researchers to measure
reaction rate constants of multiple simultaneous reactions. New interests now lie in determining multiple rate constants
associated with coupled reactions from a single coalesced signal. Current instrumentation however, cannot ascribe rate
constants to specic reacting species from a single signal. In this work, we present use of MATLAB code which is
optimized to take real experimental data, break it down into two experimental phases, and elucidate both the size of the
reacting system as well as its rate constants. We present two similar algorithms which achieve these goals, and explore
eects of introduced data error on code reliability. This work is expected to be robust enough to discern the dierences
in systems whose data appears alike to the user.

Congratulations to all the UD participants!  We hope that even more students will participate in this conference next year!