# Search Research Symposium Abstracts

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## A Graph Theoretic Approach to Regularity of Toric Ideals

One measure of the complexity of an ideal is its regularity, which may be difficult to compute with algebraic tools. To study the regularity of certain toric ideals (prime ideals generated by differences of monomials) with quadratic initial ideals, we instead make use of correspondences between the initial ideals and graphs. Moreover, a key theorem by [Read More...]

**Presenter:**Beth Anne Castellano, Lafayette College

**Authors:**Beth Anne Castellano, Marcella Manivel

**Symposium Year:**2022

**Session:**Poster Presentation

**Presentation Time:**June 17, 2022; 2:45 pm

## Minimal Cycle Representatives in Persistent Homology using Linear Programming: an Empirical Study with User's Guide

Cycle representatives of persistent homology classes can be used to provide descriptions of topological features in data. However, the non-uniqueness of these representatives creates ambiguity and can lead to many different interpretations of the same set of classes. One approach to solving this problem is to optimize the choice of representative against [Read More...]

**Presenter:**Lu Li,

**Authors:**Lu Li, Connor Thompson, Gregory Henselman-Petrusek, Chad Giusti, Lori Ziegelmeier

**Symposium Year:**2022

**Session:**Poster Presentation

**Presentation Time:**June 17, 2022; 2:45 pm

## Topological effects in Tau-protein aggregation

Tau-proteins form aggregates that are associated with neurodegenerative diseases such as Alzheimer's disease and dementia. The mechanisms by which tau protein spatially organizes into aggregates remain largely unknown. We use Molecular Dynamics (MD) simulations to model tau proteins in solution and we apply methods from topology to rigorously [Read More...]

**Presenter:**Masumi Sugiyama, University of Tennessee at Chattanooga

**Symposium Year:**2022

**Session:**Poster Presentation

**Presentation Time:**June 17, 2022; 2:45 pm

## Approaches for Incomplete Large-Scale Data

Due to advances in technology, data is available at rates never before seen. For example, wearable devices allow us to have data on health metrics such as heart rate, number of steps per day, and even blood O2 levels virtually at every minute of every day. However, it's not often the case that data is always accessible or complete. In fact, many real [Read More...]

**Presenter:**Anna Ma, UC Irvine

**Symposium Year:**2022

**Session:**Poster Presentation

**Presentation Time:**June 17, 2022; 2:45 pm

## Tilings generated by Pisot numbers

Consider the question of expanding a real number in a non-integer base with a set of specified digits as coefficients. For some cases, there exist expansions with desirable properties--in particular, using a Pisot number $\beta$ (a real algebraic integer greater than 1 with all Galois conjugates inside the open unit disk) as a base and all nonnegative [Read More...]

**Presenter:**Laura Seaberg, Boston College

**Symposium Year:**2022

**Session:**Poster Presentation

**Presentation Time:**June 17, 2022; 2:45 pm

## Modeling the Effects of Napping and Non-napping Light Schedules on the Human Circadian Oscillator

A major developmental milestone during early childhood is the consolidation of sleep from a biphasic sleep-wake pattern (afternoon nap and nighttime sleep episodes) to a single monophasic nighttime sleep episode. An advance in the timing of the circadian system is associated with reduced napping behavior, but it is unknown if this advance is a feature of the [Read More...]

**Presenter:**Shelby Stowe, Colorado School of Mines

**Authors:**Shelby Stowe MS, Monique LeBourgeois PhD, Cecilia Diniz Behn PhD

**Symposium Year:**2022

**Session:**Poster Presentation

**Presentation Time:**June 17, 2022; 2:45 pm

## Modeling Enzyme Kinetics in the Presence of Lipids

Blood coagulation is a network of biochemical reactions whereby dozens of proteins act collectively to initiate a rapid clotting response. Coagulation reactions are lipid-surface dependent, and this dependence is thought to help localize coagulation to the site of injury and enhance the association between reactants. Current models of coagulation fail to [Read More...]

**Presenter:**Jamie Madrigal,

**Authors:**Jamie Madrigal, Dougald Monroe, PhD, Suzanne Sindi, PhD, Karin Leiderman, PhD

**Symposium Year:**2022

**Session:**Poster Presentation

**Presentation Time:**June 17, 2022; 2:45 pm

## A Statistical Analysis of Strategies of Machi Koro

Machi Koro is a game where players take turns rolling dice and buying different “properties”, or cards, for their “town.” Each card has a number which corresponds to a dice roll. If a player rolls that particular number, they make money. There are many different strategies that can be used but players are often forced to think about probabilities and [Read More...]

**Presenter:**Danya Morman, University of Wisconsin Eau-Claire

**Authors:**Danya Morman

**Symposium Year:**2022

**Session:**Poster Presentation

**Presentation Time:**June 17, 2022; 2:45 pm

## Global attractors for a wave equation subject to nonlinear boundary dissipation and nonlinear interior/boundary sources with critical exponents.

In this poster we shall consider a wave model in 3D on a bounded domain which contains nonlinear sources with critical exponent in the interior/boundary and nonlinear feedback dissipation on the boundary. Similar models with simpler nonlinear boundary terms have been already studied broadly whereas the generality of our model is not only the presence of [Read More...]

**Presenter:**MADHUMITA ROY, GA, University of Memphis

**Authors:**Jose H. Rodrigues and Madhumita Roy

**Symposium Year:**2022

**Session:**Poster Presentation

**Presentation Time:**June 17, 2022; 2:45 pm

## The Hereditary Closure of the Unigraphs

A graph with degree sequence $\pi$ is a $\textit{unigraph}$ if it is isomorphic to every graph that has degree sequence $\pi$. The class of unigraphs is not hereditary, but there are two related hereditary classes. Barrus (2012) characterized the largest hereditary class contained within the unigraphs, and in this work, we study the smallest hereditary [Read More...]

**Presenter:**Rebecca Whitman, University of California, Berkeley

**Authors:**Michael Barrus, Ann Trenk, Rebecca Whitman

**Symposium Year:**2022

**Session:**Poster Presentation

**Presentation Time:**June 17, 2022; 2:45 pm

## Resolving powers of the maximal ideal with a hole

Let $k$ be a field, $S=k[x_{1},\dots, x_{n}]$ a polynomial ring and $\mathbf{m}=(x_{1},\dots, x_{n}$ the maximal ideal. Let $I=\mathbf{m}^{d}$ for some $d$. Then $I$ is a Borel ideal which is generated by all monomials of degree $d$, say $m_{1},\dots, m_{s}$. Let $\widehat{I}_{I}=(m_{1},\dots, \widehat{m_{I}},\dots, m_{s})$. Observe that if [Read More...]

**Presenter:**Hoai Dao, Oklahoma State University

**Authors:**Hoai Dao

**Symposium Year:**2022

**Session:**Poster Presentation

**Presentation Time:**June 17, 2022; 2:45 pm

## The Jones polynomial of collections of open curves in 3-space

Measuring the entanglement complexity of collections of open curves in 3-space has been an intractable, yet pressing mathematical problem, relevant to a plethora of physical systems, such as in polymers and biopolymers. In this manuscript, we give a novel definition of the Jones polynomial that generalizes the classic Jones polynomial to collections of [Read More...]

**Presenter:**Kasturi Barkataki, University of Tennessee at Chattanooga

**Authors:**Kasturi Barkataki, Eleni Panagiotou

**Symposium Year:**2022

**Session:**Poster Presentation

**Presentation Time:**June 17, 2022; 2:45 pm

## Nonlinear Schrödinger Equation with Combined Nonlinearities

We consider the one-dimensional nonlinear Schrödinger equation with the nonlinearity term that is expressed as a sum of powers, possibly infinite The combined nonlinearities appear in various physical applications such as chemical super fluidity, or the description of elementary particles such as bosons and defectons, or other subatomic structures, and in [Read More...]

**Presenter:**Gia Azcoitia, Florida International University

**Authors:**Gia Azcoitia, Alex David Roudriguez, Svetlana Roudenko, Oscar Riano, Hannah Wubben

**Symposium Year:**2022

**Session:**Poster Presentation

**Presentation Time:**June 17, 2022; 2:45 pm

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