## Williams Hall, Room 310

## Abstract

In biological systems, decision-making is an integral factor in organismal behavior, yet we still do not understand the processes behind it. Modeling the behavior of simple organisms helps us to understand the mechanisms and reasoning that directly result in the behavior of an organism.Single-celled slime mold Physarum polycephalumis capable of making complex decisions, all while lacking a nervous system or any nerve-like structures. What is unique about P. polycephalumis that it has external memory in the form of the secretion of a repellent chemical trail, which deters the slime mold from returning to previously explored areas. The attractive Keller-Segel model is a well-known model for predicting how slime mold Dictyosteliummoves. Preliminary numerical analysis ofthe one-dimensional repulsive Keller-Segel model using a pseudospectral method confirm the resultsof our stability analysis on the model, and suggest that it can be applied to the movement of P.polycephalumas it navigates a U-shaped trap.

## Abstract

I will discuss the existence of prime numbers in between consecutive Fibonacci numbers and in between terms of other linear recursive sequences.This work was conducted with Emma (Emily) Hampston.

## Abstract

It is commonly believed within the collegiate debate circuit that the current structure of debate tournaments is systematically flawed as some of the best teams frequently do not advance out of the preliminary rounds. In other words, debate tournaments, under the current structure, are bad at correctly ranking teams. We developed a computational discrete model to simulate British parliamentary debate tournaments. Through computationally intensive manipulation of various model parameters, we explored alternative tournament structures. To evaluate the correctness of various structures, we developed metrics for the fairness or accuracy of the resulting rankings. In this talk, we will outline what makes debate tournaments unlike other competitions, consider various ranking metrics to use with incomplete and nontransitive tournament outcomes, and highlight a couple of tournament structures that improve the fairness of debate tournaments.

## Abstract

I will discuss a recent conjecture of George Miliakos concerning a relation between consecutive prime numbers. I will show counterexamples and will address some similar statements.

## Abstract

Let $x_1$, $x_2$, and $x_3$ be real numbers and consider the three statements \[x_1 >x_2, x_2>x_3, \text{ and } x_3> x_1.\qquad (1)\] Clearly, these statements cannot all be true because if that were the case, it would follow, for example, that $x_1>x_1$, which is a contradiction. But, suppose that $x_1$, $x_2$, and $x_3$ are realizations of the random variables $X_1$, $X_2$, and $X_3$ respectively and that each of the statements corresponding to those in (1) is true with the same probability $p$. That is, \[Pr(X_1>X_2) = Pr(X_2>X_3)=Pr(X_3>X_1) = p.\] Since $p$ cannot be equal to one, the following question arises: how close to one can $p$ be? Can $p$ be greater than $\frac{1}{2}$? Can $p=0.7$? One can ask an analogous question for $n$ random variables. To answer these questions, we derive an upper bound for a cyclic sum of $n$ probabilities, each of which involves inequalities for $L$ random variables that are consecutively-indexed mod $n$, where $L \in \{2,\ldots,n\}$.

## Abstract

I will show that a certain sequence related to the sequence of prime numbers is increasing.

## Abstract

We develop a method of detecting change points in high-dimensional online data using means. A new stopping rule is proposed that relies on the spatial dependence of the data but does not assume the data follows a Gaussian distribution. We study the asymptotic properties of this new stopping rule. An explicit expression for the average run length (ARL) is derived when there is no change. When there is a change point, an upper bound is established for the expected detection delay (EDD) which demonstrates the impact of data dimensionality and dependence. Our method is applied to simulated data in order to verify its accuracy under a range of parameters. We apply our results to data collected in Beijing, measuring the level of pollutant PM2.5 in the atmosphere. This research was conducted under NSF grant DMS-1916239.This project was undertaken as a collaboration between Olivia Beck (Colorado State University), Isabelle Hauge (University of MassachusettsAmherst), and Molly Noel (Ithaca College) with faculty advisor Jun Li (Kent State University).

## Abstract

In this talk, we derive an alternate form to the recurrence relation of the determinant of a tridiagonal matrix using continued fractions. We then apply our derivation to obtain properties of the eigenvalues of a general threshold graph including the alternating behavior of the magnitudes of the eigenvalues about the value $-1/2$ as well as obtaining equations whose intersections yield the eigenvalues of any threshold graph.

## Abstract

Continuing the work of Greg Fredrickson, Julia Martin, and Elizabeth Wilcox, for my summer research project I dove into studying folding polyominoes from one-level to two-levels. I classified a few infinite sets of polyominoes that are and are not foldable when restricted to two “legal moves” and along the way I also determined an algorithm to efficiently create foldable polyominoes from non-foldable ones.