Mathematics Commons^™

(2,3)-Cordial Digraphs, Jonathan Mousley, Manuel Santana

Fall Student Research Symposium 2020

This presentation is about graphs (the vertex-edge kind, not the y = f(x) kind). A graph is a mathematical object that represents objects and some relationship among them; the objects are represented by vertices and the relationships are represented by the edges. Graphs have applications in just about every field imaginable, including artificial intelligence, social network theory, and parallel computing theory. A directed graph is a type of graph used to represent relationships that are one-sided or not symmetric. We discuss a graph labeling scheme on directed graphs introduced by LeRoy Beasley called a (2,3)-cordial labeling. In …

Addendum For The Article Radio Graceful Labelling Of Graphs, Laxman Saha, Alamgir Rahaman Basunia

Theory & Applications of Graphs

Additional references listed for the article: Saha, Laxman and Basunia, Alamgir Rahaman (2020) "Radio Graceful Labelling of Graphs," Theory and Applications of Graphs: Vol. 7: Iss. 1, Article 7. DOI: 10.20429/tag.2020.070107

R(P,Q) Analogs Of Discrete Distributions: General Formalism And Applications, Mahouton Norbert Hounkonnou, Fridolin Melong

Journal of Stochastic Analysis

No abstract provided.

The Yang-Mills Heat Equation On Three-Manifolds With Boundary, Nelia Charalambous

Journal of Stochastic Analysis

No abstract provided.

Emergence Of Quantum Theories From Classical Probability: Historical Origins, Developments, And Open Problems, Luigi Accardi, Yun-Gang Lu

Journal of Stochastic Analysis

No abstract provided.

Quantitatively Hyper-Positive Real Functions, Daniel Alpay, Izchak Lewkowicz

Mathematics, Physics, and Computer Science Faculty Articles and Research

Hyper-positive real, matrix-valued, rational functions are associated with absolute stability (the Lurie problem). Here, quantitative subsets of Hyper-positive functions, related through nested inclusions, are introduced. Structurally, this family of functions turns out to be matrix-convex and closed under inversion.

A state-space characterization of these functions through a corresponding Kalman-Yakubovich-Popov Lemma, is given. Technically, the classical Linear Matrix Inclusions, associated with passive systems, are here substituted by Quadratic Matrix Inclusions.

An Enticing Study Of Prime Numbers Of The Shape �� = ��^2 + ��^2, Xiaona Zhou

Publications and Research

We will study and prove important results on primes of the shape ��² + ��² using number theoretic techniques. Our analysis involves maps, actions over sets, fixed points and involutions. This presentation is readily accessible to an advanced undergraduate student and lay the groundwork for future studies.

An Asymptotic Formula For Integrals Of Products Of Jacobi Polynomials, Maxim Derevyagin, Nicholas Juricic

Journal of Stochastic Analysis

No abstract provided.

So How Were The Tents Of Israel Placed? A Bible-Inspired Geometric Problem, Julio Urenda, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In one of the Biblical stories, prophet Balaam blesses the tents of Israel for being good. But what can be so good about the tents? A traditional Rabbinical interpretation is that the placement of the tents provided full privacy: from each entrance, one could not see what is happening at any other entrance. This motivates a natural geometric question: how exactly were these tents placed? In this paper, we provide an answer to this question.

Need For Shift-Invariant Fractional Differentiation Explains The Appearance Of Complex Numbers In Physics, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Complex numbers are ubiquitous in physics, they lead to a natural description of different physical processes and to efficient algorithms for solving the corresponding problems. But why this seemingly counterintuitive mathematical construction is so natural here? In this paper, we provide a possible explanation of this phenomenon: namely, we show that complex numbers appear if take into account that some physical system are described by derivatives of fractional order and that a physically meaningful analysis of such derivatives naturally leads to complex numbers.

Using The Chi-Square Test To Analyze Voter Behavior, Bailey Fadden

Mathematics Senior Showcase 2020

We explain the Chi-Square Test and how to use it to analyze voter behavior. Specifically we look at the behavior of U.S citizens and whether or not they voted in the 2016 U.S presidential election, and how this relates to income.

Economics And Game Theory, Jeremiah Patrick Prenn

Mathematics Senior Showcase 2020

Game theory is one of the major fields of mathematics. Game theory is the study of how games, their players, and players’ strategies are defined, and how the games might play out. The outcomes of games are ultimately based on decisions, much like in the science of economics. Economics analyzes how scarce resources are to be allocated to suit unlimited needs. Every decision has an economic cost, and every decision has a utility value (utility being a quantitative measure of usefulness). Economics and game theory go hand in hand: Both analyze the effects of decisions and the rules imposed on …

Morse-Code Encoded Eye Blinking As A Source Of Biometric Authentication Via Eeg, Ben Adams, Meghan Edgerton, Gabe Miles, Callum Young

Mathematics Senior Showcase 2020

Brain-Computer Interfaces (BCIs) have historically provided many uses in the medical field, including mobility for individuals with differing levels of paralysis. Present day research is focused around testing the efficacy of such devices on mental diseases such as Alzheimer's, Dementia, and Parkinson's. Leading companies that are spearheading the research of such devices, are looking at BCI's as a tool for solving many of the problems that these diseases produce, with the end goal of generalizing BCIs to appeal to the healthy layperson by providing an additional interface between them and the technological world. If such devices were present in society …

Internal Sorting Methods, Rebekah Marie Bitikofer

Mathematics Senior Showcase 2020

Internal sorting methods are possible when all of the items to be accessed fit in a computer's high-speed internal memory. There are quite a few (Knuth's third volume of The Art of Computer Programming covers 14 in total) but I will go over the four I found to be most versatile and useful. Each algorithm that I cover has a specific benefit that merits its' use in computer science. Some have faster run times (Heapsort), simpler code (Straight Insertion), run with a smaller memory space (Quicksort), or work well with large sets (Radix Sorting). Different sorting tasks lead users to …

A Distance Based Multisample Test For High-Dimensional Compositional Data With Applications To The Human Microbiome, Qingyang Zhang, Thy Dao

Mathematical Sciences Faculty Publications and Presentations

Background

Compositional data refer to the data that lie on a simplex, which are common in many scientific domains such as genomics, geology and economics. As the components in a composition must sum to one, traditional tests based on unconstrained data become inappropriate, and new statistical methods are needed to analyze this special type of data.

Results

In this paper, we consider a general problem of testing for the compositional difference between K populations. Motivated by microbiome and metagenomics studies, where the data are often over-dispersed and high-dimensional, we formulate a well-posed hypothesis from a Bayesian point of view and …

The History And Application Of Benford's Law, Hunter Clark

Mathematics Senior Showcase 2020

My Poster is on the history and application of Benford’s law. This is a law that states that the leading digit of a set of numbers will be the number 1 approximately 30% of the time. This is a natural phenomenon and what I mean by that is that in order for this law to hold the numbers cannot be assigned. They must be random as in financial statements or logs. This law does not work on sets that are assigned such as time sheets and addresses. You will see in my poster that the original person to discover this …

Stochastic Risk Measures For The Lundberg Model With Reinsurance And Investment, Benie Justine N'Gozan

Mathematics Dissertations - Archive

Risk measures emerge in fields such as economics, insurance, finance and are concerned with a stochastic representation of uncertainties stemming from the unpredictability of the real world events. In essence, risk analysis amounts to quantifying the chances of undesirable events and developing a model that limits the impact of potential losses. Assets and liabilities in the Insurance industry, as well as financial goals of Investment companies rely on calculating the probability that their respective portfolios satisfy the preset constraints. On the flip side, risk measures serve both industries by providing optimal strategies for minimizing losses. Our research is concerned with …

On The Local Theory Of Profinite Groups, Mohammad Shatnawi

Dissertations

Let G be a finite group, and H be a subgroup of G. The transfer homomorphism emerges from the natural action of G on the cosets of H. The transfer was first introduced by Schur in 1902 [22] as a construction in group theory, which produce a homomorphism from a finite group G into H/H^' an abelian group where H is a subgroup of G and H' is the derived group of H. One important first application is Burnside’s normal p-complement theorem [5] in 1911, although he did not use the transfer homomorphism explicitly to prove it. …

Proving Pairwise Intransitivity In Sets Of Dice, Erika Clary

Honors Projects

Prior research has been conducted regarding the intransitivity of a set of dice when a single die from a set is rolled against another die from that set and when two of the same dice are rolled against a different pair of two of the same dice. This project examines and proves that an intransitive cycle exists in every set of at least five dice when two different dice are rolled against two other different dice.

Nato And The Ifrc: A Comparative Case Study, Abigail Kosiak

Undergraduate Honors Capstone Projects

This research analyzes the North Atlantic Treaty Organization's (NATO) Multinational Telemedicine System (MnTS) Project and works to answer five main questions:

1) What challenges did the NATO MnTS Project face that are directly related to the fact that the project included members from different countries and worked to create a system that operates across national borders?

2) How do these challenges compare to those faced by a non-governmental organization (NGO) like the International Federation of the Red Cross and Red Crescent Societies (IFRC)?

3) What successes has the IFRC had with its current operational model?

4) In what ways could …