Other Mathematics Commons^™

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, …

Some Progress On Random Matrix Theory (Rmt), Feiying Yang

Undergraduate Student Research Internships Conference

This is a research report about Random Matrix Theory (RMT), which studies Gaussian Orthogonal Ensemble (GOE), Gaussian Unitary Ensemble (GUE) and Gaussian Symplectic Ensemble (GSE), the purpose is to prove Wigner’s semicircle law.

Contemporary Mathematical Approaches To Computability Theory, Luis Guilherme Mazzali De Almeida

Undergraduate Student Research Internships Conference

In this paper, I present an introduction to computability theory and adopt contemporary mathematical definitions of computable numbers and computable functions to prove important theorems in computability theory. I start by exploring the history of computability theory, as well as Turing Machines, undecidability, partial recursive functions, computable numbers, and computable real functions. I then prove important theorems in computability theory, such that the computable numbers form a field and that the computable real functions are continuous.

Categorical Aspects Of Graphs, Jacob D. Ender

Undergraduate Student Research Internships Conference

In this article, we introduce a categorical characterization of directed and undirected graphs, and explore subcategories of reflexive and simple graphs. We show that there are a number of adjunctions between such subcategories, exploring varying combinations of graph types.

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 …