Physical Sciences and Mathematics Commons^™

Proving Dirichlet's Theorem On Arithmetic Progressions, Owen T. Abma

Undergraduate Student Research Internships Conference

First proved by German mathematician Dirichlet in 1837, this important theorem states that for coprime integers a, m, there are an infinite number of primes p such that p = a (mod m). This is one of many extensions of Euclid’s theorem that there are infinitely many prime numbers. In this paper, we will formulate a rather elegant proof of Dirichlet’s theorem using ideas from complex analysis and group theory.

Iceact Monitoring And Data Analysis, Andre Sierra Alderete, John W. Hewitt, Warren Huelsnitz

Showcase of Osprey Advancements in Research and Scholarship (SOARS)

The goal of the IceACT project is to establish an array of small ACTs deployed at the South Pole for neutrino detection, CR composition studies and high energy gamma ray detection. The IceCube Neutrino Observatory at the South Pole has detected these massless subatomic particles called neutrinos. These high-energy astronomical messengers provide us information to investigate the most violent astrophysical sources: events like exploding stars, gamma-ray bursts, and cataclysmic phenomena involving black holes and neutron stars. In particular, these neutrinos have no charge, and can travel across the universe without being scattered by interstellar magnetic fields. The main background for …

Tournaments And A Fibonacci Link, Michael Long, Daniela Genova

Showcase of Osprey Advancements in Research and Scholarship (SOARS)

Round robin tournaments are a type of directed graphs with applications to athletic competitions and transportation logistics. The presentation begins with a brief series of informative theorems and properties of directed graphs, which are imperative to our understanding of the properties that make directed graphs (and, subsequently, round robin tournaments) uniquely interesting. We then present a number of results about the properties of tournaments (defined as a complete directed graph), including transitivity–a relatively uncommon property used to determine domination in a round robin tournament–and connectivity, which can most often be seen in determining means of transportation between any two locations. …

Predator-Prey Model With Herding Behavior And Hunting Quota, Randy Lee, Mahbubar Rahman Phd

Showcase of Osprey Advancements in Research and Scholarship (SOARS)

The Lotka-Volterra predator-prey model is widely studied and used in many disciplines such as biology, ecology and economics. It is used to describe the growth and coexistence of two interacting populations. The model consists of a pair of first-order nonlinear differential equations. In this paper, we studied steady states, stability of steady states, existence of limit cycles, and bifurcation behavior of the predator-prey model by modifying the existing model with hunting quota. We also illustrated our results with numerical simulations.

Block Designs, Lucien Poulin, Daniela Genova

Showcase of Osprey Advancements in Research and Scholarship (SOARS)

Block designs are a type of combinatorial structures that can be used to model many different types of problems ranging from experimental design to computer software testing. They can be used to construct schemes that ensure complete optimization and efficiency of the given experiment. We focus mainly on Steiner and Kirkman triple systems, as well as, on different ways for constructing block designs. Well known results in combinatorics such as Fisher’s inequality and Kirkman’s schoolgirl problem are also discussed.

Game Theory Based Distributed Coordination With Multi-Agent Reinforcement Learning, Charlotte M. Morrison

Showcase of Osprey Advancements in Research and Scholarship (SOARS)

We study the problem of automated object manipulation using two arms of a Baxter robot. The robot uses a novel multi-agent reinforcement learning strategy to learn how to complete the task without any prior experience. It learns what actions to take by storing its interactions with the environment and uses these experiences to create a policy that guides future actions. Each of Baxter’s arms is modeled as an independent agent that can move and learn separately from the other. Each arm learns independent policies (i.e., environment state to robot action mapping) about how to best move in order to complete …

Simulation Environment For Object Manipulation With Soft Robots In Shared Autonomy, Devin Hunter, Fabio Stroppa, Allison Okamura

Showcase of Osprey Advancements in Research and Scholarship (SOARS)

The robots of today have grown to be of much more significant use than their predecessors. Robots are now being used in industries outside of the factory setting which can be seen primarily in the medical, transportation, and social fields. With robots taking on all of these new roles within our society, the establishment of robust human-robot collaboration is crucial in order for robots to be able to successfully complete desired tasks without becoming a hinderance to nearby humans. We explored this concept by implementing a shared-autonomy algorithm named MBSA (Motion Based Smart Assistance) to a soft robot simulation and …

Embedding Graphs On Surfaces And Graph Minors, Tracy Leung, Mya Salas, Dylan Wilson

Showcase of Osprey Advancements in Research and Scholarship (SOARS)

A planar graph is a graph that can be drawn in such a way in the plane, so that no edges cross each other. In other words, it is a graph that can be embedded in the plane. We discuss the conditions that make a graph embeddable on a sphere with k handles. Then, using vertex deletions and edge contractions, which produce graph minors, we examine if a graph is minimally nonembeddable on a surface. To conclude, we discuss an important result, that the set of minimally nonembeddable graphs on a surface is finite.

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 …

07. Criminal Justice, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.

04. Botany, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.

06. Computer Science, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.

03. Biology, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.

08. Engineering, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.

10. Forensic Science, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.

11. Genetics, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.

14. Optometry, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.

16. Physics, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.

17. Psychology, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.

13. Mathematics, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.

18. Statistics, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.

02. Animal Science, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.

05. Chemistry, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.

09. Environmental Science, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.

12. Kinesiology, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.

15. Pharmacy, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.

19. Zoology, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.