Other Mathematics Commons^™

Counting Hamiltonian Cycles In Quartic Circulant Graphs, Allison Hilliard

Seaver College Research And Scholarly Achievement Symposium

We consider the problem of counting Hamiltonian cycles in circulant graphs $C^K_n$ where $n$ is the number of vertices and $K$ is a set containing elements that correspond to the allowed edges in the circulant graphs. After sorting the cycles by a topological invariant called the winding number, we use a modified transfer matrix method to convert local data into global structures. The result is a generating function that counts the number of Hamiltonian cycles in a circulant graph with $n$ vertices. The results for $K=\{1,2\}$ and $K=\{1,3\}$ have been found by previous authors. We focus on the case where …

Analysis Of Solutions To Research Methods: Navigating The Infinite Content Of Mathematics, Jesus Navarro

Student Scholar Symposium

In the infinite realm of mathematical research, understanding and communicating complex concepts require structured and logical approaches. However, a variety of research methods are employed in mathematical studies; these may differ in approach, historical context, and other important considerations which can contribute to confusion and a lack of effective communication. The genesis of this research began with personal confusion during my research on "Counting the Uncountable: Life in a World Without Numbers", setting the stage for the central challenge: How do mathematicians explain their research? To answer this issue, we analyzed a variety of mathematical research articles to highlight their …

Turning Papers And Class Notes Into Books, Olcay Akman, Christopher Hay-Jahans

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Counting Hamiltonian Cycles In Quartic Circulant Graphs, Allison Hilliard

Seaver College Research And Scholarly Achievement Symposium

We consider the problem of counting Hamiltonian cycles in circulant graphs $C_n^{1,k}$. Our method is to partition the set of Hamiltonian cycles according to their winding numbers. Then, we construct a weighted digraph that allows us to produce a generating function that counts the number of Hamiltonian cycles for each winding number. Summing these generating functions derives a formula for the total number of Hamiltonian cycles in a circulant graph with $n$ vertices.

Learning With Errors Parameter Analysis, Archana Parameswaran

Cybersecurity Undergraduate Research Showcase

We implement a systematic approach for generating, evaluating, and benchmarking Learning with Errors implementations in Sage Math by varying lattice dimensions, moduli, error standard deviations, and multiple error distributions to observe concrete security-efficiency tradeoffs. The security estimator maps parameter sets to concrete security levels and bits, while performance metrics measured computational efficiency and memory requirements. Results indicate that various distribution types do not significantly impact security, though binomial distributions require more computational overhead than discrete gaussian or uniform. Memory requirements increased when modulus q increased from 12289 to 65537. Larger dimensions have an exponentially growing requirement for memory, but this …

Rsa Algorithm, Evalisbeth Garcia Diazbarriga

ATU Scholars Symposium

I will be presenting about the RSA method in cryptology which is the coding and decoding of messages. My research will focus on proving that the method works and how it is used to communicate secretly.

Msis-Capaldi: Modelling The Winter Tick Epizootic In Moose, Charlotte Beckford

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Integrating Quantitative Skills Into Biology Courses, Kathleen Hoffman, Sarah Leupen, Hannah Pie, Michelle Starz-Gaiano, Patricia Turner, Tory Williams

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modelling Impact Of Diverse Vegetation On Crop-Pollinator Interactions, Morgan N. Beetler

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Most Popular Genre's Of Videogames To Play For Hu Students, Asheria Upsher, Jean Orejuela, Joshua Scott

Harrisburg University Research Symposium: Highlighting Research, Innovation, & Creativity

Our Poster will show the most played and favored videogame genre's according to HU students.

Reducing Uncertainty In Sea-Level Rise Prediction: A Spatial-Variability-Aware Approach, Subhankar Ghosh, Shuai An, Arun Sharma, Jayant Gupta, Shashi Shekhar, Aneesh Subramanian

I-GUIDE Forum

Given multi-model ensemble climate projections, the goal is to accurately and reliably predict future sea-level rise while lowering the uncertainty. This problem is important because sea-level rise affects millions of people in coastal communities and beyond due to climate change's impacts on polar ice sheets and the ocean. This problem is challenging due to spatial variability and unknowns such as possible tipping points (e.g., collapse of Greenland or West Antarctic ice-shelf), climate feedback loops (e.g., clouds, permafrost thawing), future policy decisions, and human actions. Most existing climate modeling approaches use the same set of weights globally, during either regression or …

Problem Of The Week: A Student-Led Initiative To Bring Mathematics To A Broader Audience, Jordan M. Sahs, Brad Horner

UNO Student Research and Creative Activity Fair

Problem of the Week (POW!) is a weekly undergraduate mathematics competition hosted by two graduate students from the UNO Math Department. It started with the goal to showcase variety, creativity, and intrigue in math to those who normally feel math is dry, rote, and formulaic. Problems shine light on both hidden gems and popular recreational math, both math history and contemporary research, both iconic topics and nontraditional ones, both pure abstraction and real-world application. Now POW! aims to increase availability and visibility in Omaha and beyond. Select problems from Fall 2021 to Spring 2023 are highlighted here: these received noteworthy …

Using Graph Theoretical Methods And Traceroute To Visually Represent Hidden Networks, Jordan M. Sahs

UNO Student Research and Creative Activity Fair

Within the scope of a Wide Area Network (WAN), a large geographical communication network in which a collection of networking devices communicate data to each other, an example being the spanning communication network, known as the Internet, around continents. Within WANs exists a collection of Routers that transfer network packets to other devices. An issue pertinent to WANs is their immeasurable size and density, as we are not sure of the amount, or the scope, of all the devices that exists within the network. By tracing the routes and transits of data that traverses within the WAN, we can identify …

Unomaha Problem Of The Week (2021-2022 Edition), Brad Horner, Jordan M. Sahs

UNO Student Research and Creative Activity Fair

The University of Omaha math department's Problem of the Week was taken over in Fall 2019 from faculty by the authors. The structure: each semester (Fall and Spring), three problems are given per week for twelve weeks, with each problem worth ten points - mimicking the structure of arguably the most well-regarded university math competition around, the Putnam Competition, with prizes awarded to top-scorers at semester's end. The weekly competition was halted midway through Spring 2020 due to COVID-19, but relaunched again in Fall 2021, with massive changes.

Now there are three difficulty tiers to POW problems, roughly corresponding to …

Estimating Glutamate Transporter Surface Density In Mouse Hippocampal Astrocytes, Anca R. Radulescu, Annalisa Scimemi

Biology and Medicine Through Mathematics Conference

No abstract provided.

Optimal Time-Dependent Classification For Diagnostic Testing, Prajakta P. Bedekar, Paul Patrone, Anthony Kearsley

Biology and Medicine Through Mathematics Conference

No abstract provided.

Equitable Coloring Of Complete Tripartitle Graphs, Maxwell Vlam, Bailey Orehosky, Dominic Ditizio

Capstone Showcase

In this paper, we prove the Equitable Coloring Conjecture for variations of complete tripartite graphs with graphs K_n,n,n, K_n,n,2n, K_n,n,n+2, and K_n,n+2,n+4.

Connecting People To Food: A Network Approach To Alleviating Food Deserts, Anna Sisk

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Eulerian Walk And Dna Sequence Assembly, Yifan Zhu

Symposium of Student Scholars

Children like jigsaw puzzles, and the way to assemble the puzzle is by putting together pieces that match, one by one, till the puzzle is complete. DNA sequence assembly could be thought of as something similar: when a strand of DNA is passed into a particular “sequencing machine”, it gives a large number of short reads of the DNA sequence. This type of technology is called shotgun sequencing. These reads form the jigsaw pieces in the puzzle and one must put together these pieces in an intelligent way to obtain the original sequence. There is, however, a catch here; apriori, …

Understanding The Effect Of Adaptive Mutations On The Three-Dimensional Structure Of Rna, Justin Cook

Undergraduate Research and Scholarship Symposium

Single-nucleotide polymorphisms (SNPs) are variations in the genome where one base pair can differ between individuals.¹ SNPs occur throughout the genome and can correlate to a disease-state if they occur in a functional region of DNA.¹According to the central dogma of molecular biology, any variation in the DNA sequence will have a direct effect on the RNA sequence and will potentially alter the identity or conformation of a protein product. A single RNA molecule, due to intramolecular base pairing, can acquire a plethora of 3-D conformations that are described by its structural ensemble. One SNP, rs12477830, which …

Optimizing Networking Topologies With Shortest Path Algorithms, Jordan Sahs

UNO Student Research and Creative Activity Fair

Communication networks tend to contain redundant devices and mediums of transmission, thus the need to locate, document, and optimize networks is increasingly becoming necessary. However, many people do not know where to start the optimization progress. What is network topology? What is this “Shortest Path Problem”, and how can it be used to better my network? These questions are presented, taught, and answered within this paper. To supplement the reader’s understanding there are thirty-eight figures in the paper that are used to help convey and compartmentalize the learning process needed to grasp the materials presented in the ending sections.

In …

Ethnomathematics: Art, Culture, And Social Justice, John R. Jungck

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Community-Based Curriculum: A Novel Approach In Collaborative Teaching, Christopher Hay-Jahans

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Testing The Effect Of Acetaminophen Overdose On The Liver And The Role Of Biomarkers To Predict Death Or Survival, Christine Brasic

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Climate Change Models, Lauren Fie

Capstone Showcase

As a result of the changing climate, global temperatures and global mean sea levels (GMSL) have been increasing rapidly. The complex physical systems surrounding this growth make it difficult to form an accurate model. This paper looks at a simplified model proposed and supported by Aral, Guan, and Chang. This model consists of a system of ordinary differential equations that are simplified and solved theoretically, then applied using python to calculate precise values and form predictions.

Modeling Control Methods To Manage The Sylvatic Plague In Black-Tailed Prairie Dog Towns, David C. Elzinga, Shelby R. Stowe, Leland Russell

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Using Agent-Based Modeling To Investigate The Existence Of Herd Immunity Thresholds For Infectious Diseases On Randomly Generated Contact Networks, Hannah Callender Highlander, Owen Price

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Model For Cross-Institutional Collaboration: Addressing Diminishing Resources In Academia, Claudia Kolakowski

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

University Scholar Series: Tatiana Shubin, Tatiana Shubin

University Scholar Series

Moving in Circles: the Beauty and Joy of Mathematics for Everyone

Tatiana Shubin joined the faculty of San Jose State University in 1985 after earning her Ph.D. in Math­ematics from University of California, Santa Barbara. In 1998, she founded San Jose Math Circle and the Bay Area Math Adventures. In 2006, Shubin became a co-founder of the first Math Teachers' Circle in the US. This circle proved to be a seed which germinated to produce the entire Math Teachers' Circle Network. She launched the Navajo Nation Math Circles project in 2012, became a co-founder and co-director of the Alliance of …

Heterogeneous Boolean Networks With Two Totalistic Rules, Katherine Toh

UNO Student Research and Creative Activity Fair

Boolean Networks are being used to analyze models in biology, economics, social sciences, and many other areas. These models simplify the reality by assuming that each element in the network can take on only two possible values, such as ON and OFF. The node evolution is governed by its interaction with other nodes in its neighborhood, which is described mathematically by a Boolean function or rule. For simplicity reasons, many models assume that all nodes follow the same Boolean rule. However, real networks often use more than one Boolean rule and therefore are heterogeneous networks. Heterogeneous networks have not yet …