Mathematics Commons^™

Volume 12, Haleigh James, Hannah Meyls, Hope Irvin, Megan E. Hlavaty, Samara L. Gall, Austin J. Funk, Karyn Keane, Sarah Ghali, Antonio Harvey, Andrew Jones, Rachel Hazelwood, Madison Schmitz, Marija Venta, Haley Tebo, Jeremiah Gilmer, Bridget Dunn, Benjamin Sullivan, Mckenzie Johnson

Incite: The Journal of Undergraduate Scholarship

Introduction, Dr. Roger A. Byrne, Dean

From the Editor, Dr. Larissa "Kat" Tracy

From the Designers, Rachel English, Rachel Hanson

Immortality in the Mortal World: Otherworldly Intervention in "Lanval" and "The Wife of Bath's Tale" by Haleigh James

Analysis of Phenolic Compounds in Moroccan Olive Oils by HPLC by Hannah Meyls

Art by Hope Irvin

The Effects of Cell Phone Use on Gameplay Enjoyment and Frustration by Megan E. Hlavaty, Samara L. Gall, and Austin J. Funk

Care, No Matter What: Planned Parenthood's Use of Organizational Rhetoric to Expand its Reputation by Karyn Keane

Analysis of Petroleum Products for …

Simplexity Of The N-Cube, Peter Graziano

Mathematics & Computer Science Student Scholarship

Major: Mathematics and Classics

Faculty Mentor: Dr. Su-Jeong Kang, Mathematics

The process of dividing shapes into triangles is called triangulation, and it is possible to abstract the idea of a triangle to higher dimensions, where it will be called a simplex in n-dimensions, or an n-simplex. I studied this process of generalized triangulation, or decomposition, in order to find an optimal decomposition of a 5-cube to help improve the bounds on the general case of an n-cube.

Self-Supervised Learning For Single-Molecule Localization Microscopy, Clare Minnerath

Mathematics & Computer Science Student Scholarship

Major: Mathematics and Computer Science

Faculty Mentor: Dr. Lynette Boos, Mathematics

We evaluate the ability of self-supervised deep learning for Poisson denoising of Single-Molecule Localization Microscopy (SMLM) in addition to the impact denoising can have on the ability to locate molecules within the Single-Molecule Localization Microscopy images. SMLM images are predominantly corrupted with Poisson noise. There is a need for a superior technique to provide accurate SMLM images in order for scientists to gain a better understanding of the functions of live cells at the nanoscale. By denoising SMLM images prior to the images undergoing the current state- of-the-art super-resolution …

Application Of Black-Scholes-Merton Model In Option Pricing And Intangibles Assets, Giang Nguyen-Hoang

Mathematics & Computer Science Student Scholarship

Major: Finance and Mathematics

Faculty Mentor: Dr. Joseph Shomberg, Mathematics

The Black-Scholes model was developed by Fisher Black and Myron Scholes in the 1970s to price stock options. Since then the model has been suited to price so-called intangible assets such as trademarks and patents. In this paper, we investigate the related Black-Scholes-Merton model and the relevant characteristics of patents in order to associate patents as real options. After describing patents as options, we apply the Black-Scholes-Merton model to the valuation of the intangible assets. Special attention is given to modeling volatility and the cost of delay in order to …

Research In Sabermetrics: The Cape Cod Baseball League, Thomas Zinzarella

Mathematics & Computer Science Student Scholarship

Major: Sports Media

Faculty Mentor: Fr. Humbert Kilanowski O.P, Mathematics and Computer Science

We analyzed data from the Cape Cod Baseball League, a prestigious summer baseball league, where we looked at sabermetric statistics such as WAR (Wins above replacement). Stats like these can help evaluate a player and project whether they are a future MLB player or not. Especially on the Cape, where 1 in 7 current Major League Baseball players have played in the league.

Universal Vector Neural Machine Translation With Effective Attention, Joshua Yi, Satish Mylapore, Ryan Paul, Robert Slater

SMU Data Science Review

Neural Machine Translation (NMT) leverages one or more trained neural networks for the translation of phrases. Sutskever intro- duced a sequence to sequence based encoder decoder model which be- came the standard for NMT based systems. Attention mechanisms were later introduced to address the issues with the translation of long sen- tences and improving overall accuracy. In this paper, we propose two improvements to the encoder decoder based NMT approach. Most trans- lation models are trained as one model for one translation. We introduce a neutral/universal model representation that can be used to predict more than one language depending on …

Inductive Constructions In Logic And Graph Theory, Davis Deaton

Honors Scholars Collaborative Projects

Just as much as mathematics is about results, mathematics is about methods. This thesis focuses on one method: induction. Induction, in short, allows building complex mathemati- cal objects from simple ones. These mathematical objects include the foundational, like logical statements, and the abstract, like cell complexes. Non-mathematicians struggle to find a common thread throughout all of mathematics, but I present induction as such a common thread here. In particular, this thesis discusses everything from the very foundations of mathematics all the way to combina- torial manifolds. I intend to be casual and opinionated while still providing all necessary formal rigor. …

On A Vizing-Type Integer Domination Conjecture, Elliot Krop, Randy R. Davila

Theory & Applications of Graphs

Given a simple graph G, a dominating set in G is a set of vertices S such that every vertex not in S has a neighbor in S. Denote the domination number, which is the size of any minimum dominating set of G, by γ(G). For any integer k ≥ 1, a function f : V (G) → {0, 1, . . ., k} is called a {k}-dominating function if the sum of its function values over any closed neighborhood is at least k. The weight of a {k}-dominating function is the sum of its values over all …

Identifying Cloud Forest Landslides In Satellite Imagery: A Machine Learning Approach, Eric Leu

19th Annual Celebration of Undergraduate Research and Creative Activity (2020)

Landslide formation is a significant contributor to montane rainforest biodiversity, opening gaps in the tree canopy and leading to the germination of pioneer plants. In order to study the spatio-temporal patterns of landslide formation, we developed a technique using a machine learning algorithm (random forest) to automatically identify landslides in high resolution satellite imagery. Using 4-band Planetscope and 5-band RapidEye satellite imagery, we identified landslides associated with major rain events over the Monteverde Cloud Forest Reserve in Costa Rica. The classifier uses reflectance values along with texture measures and topographic slope to sort pixels into different landscape classes. Slope was …

Entropy In Quantum Mechanics And Applications To Nonequilibrium Thermodynamics, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

Classical formulations of the entropy concept and its interpretation are introduced. This is to motivate the definition of the quantum von Neumann entropy. Some general properties of quantum entropy are developed, such as the quantum entropy which always increases. The current state of the area that includes thermodynamics and quantum mechanics is reviewed. This interaction shall be critical for the development of nonequilibrium thermodynamics. The Jarzynski inequality is developed in two separate but related ways. The nature of irreversibility and its role in physics are considered as well. Finally, a specific quantum spin model is defined and is studied in …

"Using A Multimeter And Graphing: Voltage And Math”, Kelly W. Remijan

Teacher Resources

No abstract provided.

Response To Pitkanen’S Solar System Model: Towards Gross-Pitaevskiian Description Of Solar System And Galaxies And More Evidence Of Chiral Superfluid Vortices, Victor Christianto, Florentin Smarandache, Yunita Umniyati

Branch Mathematics and Statistics Faculty and Staff Publications

In a new paper in recent issue of this journal (PSTJ), Prof. M. Pitkanen describes a solar system model inspired by spiral galaxies. While we appreciate his new approach, we find it lacks substantial discussion on the nature of vortices and chirality in galaxy. Therefore we submit a viewpoint that Gross-Pitaevskii model can be a more complete description of both solar system and also spiral galaxies, especially taking into account the nature of chirality and vortices in galaxies. In this article, we also hope to bring out some correspondence among existing models, so we discuss shortly: the topological vortice approach, …

Nonlinear Least Squares 3-D Geolocation Solutions Using Time Differences Of Arrival, Michael V. Bredemann

Mathematics & Statistics ETDs

This thesis uses a geometric approach to derive and solve nonlinear least squares minimization problems to geolocate a signal source in three dimensions using time differences of arrival at multiple sensor locations. There is no restriction on the maximum number of sensors used. Residual errors reach the numerical limits of machine precision. Symmetric sensor orientations are found that prevent closed form solutions of source locations lying within the null space. Maximum uncertainties in relative sensor positions and time difference of arrivals, required to locate a source within a maximum specified error, are found from these results. Examples illustrate potential requirements …

An Experiential Report On The Thayer Method Of Teaching Across College-Level Chemistry, Biology, Math, And Physics Courses, Kevin P. O'Halloran, Sairam Tangirala, Fengjie Sun, Leonard E. Anagho, Gerald Agbegha, Clay Runck, David Roth, Amy H. Erickson

Georgia Journal of Science

The Thayer method of instruction is a little-known active learning technique that dates back to 1817 at the U.S. Military Academy. This study describes the implementation and statistical evaluation of an adaptation of the Thayer method in a variety of college science and math courses. All courses had five characteristics in common: (i) students were given a daily reading schedule and instructed to prepare before class, (ii) each class started with a question and answer session, (iii) class time minimized the use of lecture, (iv) class time maximized the use of active learning, and (v) students were frequently quizzed. A …

Examining The Effect Of Personal Classroom Friendships With Online Learning, Alicia T. Lamere, Kristin T. Kennedy

Mathematics Faculty Journal Articles

Friendships within learning environments have been established as valuable aspects of supporting student success. The literature clearly shows that: 1) a student can achieve a better grade depending on how he/she perceives the task in terms of level of difficulty, and 2) a student can perceive the level of difficulty to be more or less difficult, depending on who is in the room with him/her during the task. If task difficulty can be linked to perceived friendships in the room, then fostering friendships in a classroom could play a crucial role to improving performance. As universities continue to embrace online …

Storage Management Strategy In Mobile Phones For Photo Crowdsensing, En Wang, Zhengdao Qu, Xinyao Liang, Xiangyu Meng, Yongjian Yang, Dawei Li, Weibin Meng

Department of Computer Science Faculty Scholarship and Creative Works

In mobile crowdsensing, some users jointly finish a sensing task through the sensors equipped in their intelligent terminals. In particular, the photo crowdsensing based on Mobile Edge Computing (MEC) collects pictures for some specific targets or events and uploads them to nearby edge servers, which leads to richer data content and more efficient data storage compared with the common mobile crowdsensing; hence, it has attracted an important amount of attention recently. However, the mobile users prefer uploading the photos through Wifi APs (PoIs) rather than cellular networks. Therefore, photos stored in mobile phones are exchanged among users, in order to …

Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya

Department of Mathematics Faculty Scholarship and Creative Works

Fluid mechanics occupies a privileged position in the sciences; it is taught in various science departments including physics, mathematics, environmental sciences and mechanical, chemical and civil engineering, with each highlighting a different aspect or interpretation of the foundation and applications of fluids. Doll’s fluid analogy [5] for this idea is especially relevant to this issue: “Emergence of creativity from complex flow of knowledge—example of Benard convection pattern as an analogy—dissipation or dispersal of knowledge (complex knowledge) results in emergent structures, i.e., creativity which in the context of education should be thought of as a unique way to arrange information so …

Parameter Identification For Gompertz And Logistic Dynamic Equations, Elvan Akin, Neslihan Nesliye Pelen, Ismail Ugur Tiryaki, Fusun Yalcin

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we generalize and compare Gompertz and Logistic dynamic equations in order to describe the growth patterns of bacteria and tumor. First of all, we introduce two types of Gompertz equations, where the first type 4-paramater and 3-parameter Gompertz curves do not include the logarithm of the number of individuals, and then we derive 4-parameter and 3-parameter Logistic equations. We notice that Logistic curves are better in modeling bacteria whereas the growth pattern of tumor is described better by Gompertz curves. Increasing the number of parameters of Logistic curves give favorable results for bacteria while decreasing the number …

Reliability Improvement On Feasibility Study For Selection Of Infrastructure Projects Using Data Mining And Machine Learning, Xi Hu

Theses and Dissertations

With the progressive development of infrastructure construction, conventional analytical methods such as correlation index, quantifying factors, and peer review are no longer satisfactory in support for decision-making of implementing an infrastructure project in the age of big data. This study proposes using a mathematical model named Fuzzy-Neural Comprehensive Evaluation Model (FNCEM) to improve the reliability of the feasibility study of infrastructure projects by using data mining and machine learning. Specifically, the data collection on time-series data, including traffic videos (278 Gigabytes) and historical weather data, uses transportation cameras and online searching, respectively. Meanwhile, the researcher sent out a questionnaire for …

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.