# 2019 Fall - Student Talks

## Williams Hall, Room 310

Time: 07:15 am - 07:25 am
Title: Modeling Slime Mold Decision-making: The U-shaped Trap Problem
Speaker: Laynie Jensen (SUNY Cortland)
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.

Time: 07:30 am - 07:40 am
Title: Prime Numbers in between Fibonacci Numbers
Speaker: Justin Kipp (SUNY Brockport)
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.

Time: 07:45 am - 07:55 am
Title: Optimizing Fairness in British Parliamentary Debates
Speaker: Hugh McKenny (Hobart and William Smith Colleges)
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.

Time: 08:00 am - 08:10 am
Title: A Conjecture of George Miliakos
Speaker: Briana Palmer (SUNY Brockport)
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.

Time: 09:30 am - 09:40 am
Title: An Upper Bound for the Sum of Cyclic Probabilities
Speaker: Quinn Kolt (Rochester Institute of Technology)
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 $L \in \{2,\ldots,n\}$.

Time: 09:45 am - 09:55 am
Title: A Monotone Sequence Related to Prime Numbers
Speaker: Nicole Zhe (SUNY Brockport)
Abstract

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

Time: 10:00 am - 10:20 am
Title: Online Change-Point Detection in the Mean of High-Dimensional Data
Speaker: Molly Noel (Ithaca College)
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).

Time: 10:25 am - 10:45 am
Title: Tridiagonal Matrices with Continued Fractions
Speaker: Matthew Ficarra (SUNY Geneseo)
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.

Time: 10:50 am - 11:10 am
Title: Folding Polyominoes
Speaker: Ryan Gelnett (SUNY Oswego)
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.

## Williams Hall, Room 317

Time: 07:15 am - 07:25 am
Title: Prime Numbers in between Fibonacci Numbers
Speaker: Emily Hampston (SUNY Brockport)
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 Justin Kipp.

Time: 07:30 am - 07:40 am
Title: Coding with Application
Speaker: Alexandra Lewis (SUNY Oneonta)
Abstract

Using RStudio application, we developed an R Dashboard Shiny App for ranking 4-year colleges and universities in the US in terms of their 4-year graduation rates. We created functions that read an external data file and returned the name of a 4-year college or university that has the“best” or the “worst” 4-year graduation rate in a particular state. Other graduation outcomes was also be considered. In addition, the App has the ability to take in arguments, such as the name of a state, and a ranking value of a 4-year college or university in that state. Then, the App will return the name of the college that has the specified rankings requested. Moreover, the App can also be used to display a leaflet map and information about the names of the 4-year colleges or universities that are the “best” or “worse” in their respective states based on their 4-year graduation rates and other outcomes.  Authors: Alexandra Lewis, Ryan Minges, and Christopher Robertson (SUNYOneonta).

Time: 07:45 am - 07:55 am
Title: Three Squares in a Circle
Speaker: Morgan Sherwood (SUNY Brockport)
Abstract

I will discuss a recent problem posted on the internet concerning 3 squares in a circle. I will show why the problem is wrong, how to fix it, and how to solve it.

Time: 08:00 am - 08:10 am
Title: Cocycle Invariant and Oriented Singular Knots
Speaker: Nicolas van Kempen (SUNY Oswego)
Abstract

Finding an efficient way to compute whether or not two knot diagrams are representations of the same knot is one of the most researched problems in knot theory, with few efficient solutions.In this presentation, we will introduce a new way to compare knots diagrams, the cocyle invariant, which provides an enhancement of current methods to more easily differentiate topologically distinct knots. We will present algebraic structures such as quandles and singquandles, which will enable us to work with oriented singular knots. We will explain and provide examples of how these structures can be related to knot diagrams. We will then present the notion of a quandle cocyle invariant on oriented singular knots, defining precisely the invariant, giving a quick overview of the algorithm we had to develop for this project, and once more providing examples to confirm and illustrate the theory. While researching this invariant over the past summer, we have obtained many promising results, and are still working to further better the invariant.

Time: 09:30 am - 09:40 am
Title: An Alternate Method of Finding Maximum and Minimum of a Multivariable Function
Speaker: Megan Hardenbrook (SUNY Brockport)
Abstract

I will show how the extrema of a multivariable function can be found using one variable techniques.

Time: 09:45 am - 09:55 am
Title: Probabilities in Number Theory
Speaker: Una MacDonald (SUNY Brockport)
Abstract

I will discuss what is the probability that certain sums end up with the same digits.

Time: 10:00 am - 10:20 am
Title: Standing in a Room Full of Mirrors
Speaker: Molly Marshall (SUNY Geneseo)
Abstract

Imagine yourself standing in a room full of mirrors, each direction you look there are surrounding copies of you, following each movement. This is what it is like to stand in a platycosm. There exist only 10 varieties of this effect, and in this presentation we will discuss what each of them are, how they look, and how they are created. As well as what it would be like to stand in one, like you are standing in a room full of mirrors. Then I will conclude with how we may be living in a universe that looks just like this, possibly, an infinitely large room of mirrors

Time: 10:25 am - 10:45 am
Title: The Congruence of Curves in the Three Dimensional Space
Speaker: Andrew Ditzel (SUNY Oneonta)
Abstract

In this presentation, we will discuss the notion of congruence for curves in the three dimensional space. In particular, we will see that a necessary and sufficient condition for two curves to be congruent is that they have the same curvature and torsion. Some authors claim that this theorem represents in fact an analogue for curves of the criteria of the congruence of triangles from the two dimensional plane. In order to understand these concepts, we will start by discussing isometries and we will follow the so-called Frenet approach to differentiable curves. Among other things, we will see how the basic Frenet vector fields look like and how to express their derivatives in terms of the vector fields themselves.

Time: 10:50 am - 11:10 am
Title: Critical Groups of Strongly Regular Graphs
Speaker: Eric Piato (SUNY Geneseo)
Abstract

Let $G=(V,E)$ be a simple graph.  The critical group (also called the sandpile group), denoted $K(G)$, is a fine abelian group associated with $G$.  Concretely, viewing the Laplacian matrix $L$ as a linear mapping $\mathbb{Z}^{|V|}\rightarrow \mathbb{Z}^{|V|}$, it turns out that $\mathbb{Z}^V /\, \text{Im}(L)\equiv \mathbb{Z}\oplus K(G)$.  In this talk, we discuss our results regarding the critical group of strongly regular graphs $\Gamma$.  In particular, we provide a complete characterization of $K(\Gamma)$ under certain assumptions regarding the associated eigenvalues of $\Gamma$.  In other cases, when the eigenvalues of $\Gamma$ satisfy different (weaker) conditions, we are able to provide constraints on the form of the critical group. We conclude with a brief discussion regarding the question of existence of a strongly regular graph with given parameters, and explore how our work could be used to resolve this inquiry.