Mathematics Commons^™

Iterated Line Graphs On Bi-Regular Graphs And Trees, Brenden Balch

Rose-Hulman Undergraduate Mathematics Journal

In 1965, van Rooij and Wilf considered sequences of line graphs, in which they grouped sequences of line graphs into four categories. We’ll add to their research by presenting results on sequences of line graphs for star graphs and bi-regular graphs. We will then investigate slight variations of star graphs.

A Connection Between Quadratic Rational Maps And Linear Fractional Maps, Laura Schlesinger, Anna Marek, Ella White, Danqi Yin

Rose-Hulman Undergraduate Mathematics Journal

This research project is an investigation into quadratic rational maps, $\vp$, of one complex variable that map the unit disk to itself. Previous research \cite{brittney} shows that for each $\vp$, a corresponding linear fractional map $\zeta$ can be found using the coefficients of $\vp$, and this $\zeta$ can be used to characterize functions in the kernel of the adjoint of the composition operator with symbol $\vp$, defined on a space of analytic functions. In this paper, we show sufficient conditions to ensure that certain cases of $\vp$ map the unit disk to itself and find all the forms of $\zeta$. …

Discrete Models And Algorithms For Analyzing Dna Rearrangements, Jasper Braun

USF Tampa Graduate Theses and Dissertations

In this work, language and tools are introduced, which model many-to-many mappings that comprise DNA rearrangements in nature. Existing theoretical models and data processing methods depend on the premise that DNA segments in the rearrangement precursor are in a clear one-to-one correspondence with their destinations in the recombined product. However, ambiguities in the rearrangement maps obtained from the ciliate species Oxytricha trifallax violate this assumption demonstrating a necessity for the adaptation of theory and practice.

In order to take into account the ambiguities in the rearrangement maps, generalizations of existing recombination models are proposed. Edges in an ordered graph model …

Effective Number Theory: Counting The Identities Of A Quantum State, Ivan Horváth, Robert Mendris

Anesthesiology Faculty Publications

Quantum physics frequently involves a need to count the states, subspaces, measurement outcomes, and other elements of quantum dynamics. However, with quantum mechanics assigning probabilities to such objects, it is often desirable to work with the notion of a “total” that takes into account their varied relevance. For example, such an effective count of position states available to a lattice electron could characterize its localization properties. Similarly, the effective total of outcomes in the measurement step of a quantum computation relates to the efficiency of the quantum algorithm. Despite a broad need for effective counting, a well-founded prescription has not …

New Proper Orthogonal Decomposition Approximation Theory For Pde Solution Data, Sarah Locke, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

In our previous work [J. R. Singler, SIAM J. Numer. Anal., 52 (2014), pp. 852- 876], we considered the proper orthogonal decomposition (POD) of time varying PDE solution data taking values in two different Hilbert spaces. We considered various POD projections of the data and obtained new results concerning POD projection errors and error bounds for POD reduced order models of PDEs. In this work, we improve on our earlier results concerning POD projections by extending to a more general framework that allows for nonorthogonal POD projections and seminorms. We obtain new exact error formulas and convergence results for POD …

On Some Problems On Polynomial Interpolation In Several Variables, Brian Jon Tuesink

USF Tampa Graduate Theses and Dissertations

Polynomial approximation is a long studied process, with a history dating back to the 1700s, At which time Lagrange, Newton and Taylor developed their famed approximation methods. At that time, it was discovered that every Taylor projection (projector) is the pointwise limit of Lagrange projections. This leaves open a rather large and intriguing question, What happens in several variables?

To this end we define a linear idempotent operator to be an ideal projector whenever its kernel is an ideal. No matter the number of variables, Taylor projections and Lagrange projections are always ideal projectors, and it is well known that …

Quantum Markov Chains Associated With Unitary Quantum Walks, Chul Ki Ko, Hyun Jae Yoo

Journal of Stochastic Analysis

No abstract provided.

Invariant Projections For Covariant Quantum Markov Semigroups, Franco Fagnola, Emanuela Sasso, Veronica Umanità

Journal of Stochastic Analysis

No abstract provided.

Pauli Matrices: A Triple Of Accardi Complementary Observables, Stephen Bruce Sontz

Journal of Stochastic Analysis

No abstract provided.

Preface, Julius Esunge, Brian C. Hall, Ambar N. Sengupta, Aurel Stan

Journal of Stochastic Analysis

No abstract provided.

Supporting Our Struggling Students: Details Of A Hybrid Mathematics Summer Bridge Program, Anita White, Patrick Davis, Marti Shirley

Faculty Publications & Research

It goes without saying that the schools in the consortium are used to dealing with gifted and talented students. However with such high-caliber students, we also have high expectations. What resources do we offer to the students who struggle at our institutions? This presentation will detail the setup and results of EXCEL2 - a summer bridge program offered at the Illinois Mathematics & Science Academy to help students who were unable to meet course expectations. The program operated through a hybrid online/in-person model - with instruction primarily given through video conferencing but coupled with an on-campus experience.

Geometric Approaches And Bifurcations In The Dichotomous Decision Model, Abdelrahim Mousa

Journal of the Arab American University مجلة الجامعة العربية الامريكية للبحوث

Resorting to the Dichotomous decision model, where individuals can make alternative decisions, we study two geometric approaches to construct all possible decisions tiling. Each decision tiling indicates the way the Nash equilibria co-exist and change with the relative decision preferences of the individuals. We find the Nash domains for the pure and mixed strategies and characterize the space of all parameters where the pure Nash equilibria are either cohesive or disparate. We show how the coordinates of the influence matrix together with the total number of individuals affect significantly the occurrence of bifurcations with and without overlaps between the pure …

A Natural Frenet Frame For Null Curves On The Lightlike Cone In Minkowski Space ℝ⁴₂, Nemat Abazari, Martin Bohner, Ilgin Sağer, Alireza Sedaghatdoost, Yusuf Yayli

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we investigate the representation of curves on the lightlike cone ℚ³₂ in Minkowski space ℝ⁴₂ by structure functions. In addition, with this representation, we classify all of the null curves on the lightlike cone ℚ³₂ in four types, and we obtain a natural Frenet frame for these null curves. Furthermore, for this natural Frenet frame, we calculate curvature functions of a null curve, especially the curvature function κ₂ = 0 , and we show that any null curve on the lightlike cone is a helix. Finally, we find all curves with constant curvature functions.

The Decline Of The Mid-Range Jump Shot In Basketball: A Study Of The Impact Of Data Analytics On Shooting Habits In The Nba, Shawn Kilcoyne

Honors Projects in Mathematics

The purpose of this thesis paper is to investigate the strategic shift away from the mid-range jump shot in basketball over the past decade. This paper will cover the rationale for the decline of the mid-range, as well as the general impact of data analytics on the way the game of basketball is played at the professional level. Following a review of the existing literature relating to the use of analytics in the NBA, this paper will analyze the differences in shooting habits between two seven-season periods. Data visualization tools, including boxplots, statistical trends, and distribution plots, will be used …

Why Quantiles Are A Good Description Of Volatility In Economics: A Pedagogical Explanation, Sean R. Aguilar, Vladik Kreinovich, Uyen Pham

Departmental Technical Reports (CS)

To make investment decisions, we need to know, for each financial instrument, not only its expected return -- but also how the actual return may deviate from its expected value. A numerical measure of such deviations is known as volatility. Originally, volatility was measured by the srabdard deviation from the expected price, but it turned out that this measure does not always adequately describe our perception of volatility. Empirically, it turned out that quantiles are a more adequate description of volatility. In this paper, we provide an explanation of this empirical phenomenon.

Analyzing Yankees And Red Sox Sentiment Over The Course Of A Season, Connor Koch

Honors Projects in Data Science

This paper investigates data collected on twitter which references the Yankees or Red Sox during the 2020 Major League Baseball (MLB) season. The objective is to analyze the sentiment of tweets referencing the Yankees and Red Sox over the course of the season. In addition, an investigation of the networks within the data and the topics that were prevalent will be conducted. The 2020 MLB season was started late because of the COVID-19 pandemic and was a season like no other. The expectation of a dataset revolving around baseball is that the topics discussed would be about baseball. The findings …

A Natural Formalization Of Changing-One's-Mind Leads To Square Root Of "Not" And To Complex-Valued Fuzzy Logic, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

We show that a natural formalization of the process of changing one's mind leads to such seemingly non-intuitive ideas as square root of "not" and complex-valued fuzzy degrees.

Why Ancient Egyptians Preferred Some Sum-Of-Inverses Representations Of Fractions?, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Ancient Egyptians represented a fraction as a sum of inverses of natural numbers, with the smallest possible number of terms. In our previous paper, we explained that this representation makes sense since it leads to the optimal way of solving a problem frequently mentioned in the Egyptian papyri: dividing bread between workers. However, this does not explain why ancient Egyptians preferred some representations with the same number of terms but not others. For example, to represent 2/3, they used the sum 1/2 + 1/6 but not the sum 1/3 + 1/3 with the same number of terms. In this paper, …

Instrumental Vs. Expressive: A Study Of Voter Behavior Models Through The Lens Of Identity In The 2016 Presidential Election, Kaitlyn Fales

Honors Projects in History and Social Sciences

Studying voter behavior through the lens of identity is central to making sense of the 2016 presidential election. The traditional models for explaining voter behavior are rational choice and behavioralism. The former is grounded in instrumental partisanship and a voter’s issue positions, with the latter grounded in an expressive, psychological attachment to partisanship. More recent, social identity theory related models discuss voter behavior through group belonging and the partisan mega-identity (Mason 2018). My analysis used the ANES 2016 Time Series Study. To measure a voter’s issue positions, I created a new Identity Index alongside the expansion of an established Issue …

Yet Another Possible Explanation Of Egyptian Fractions: Motivated By Fairness, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Ancient Egyptians represented fractions as sums of inverses of natural numbers, and they made sure that all these natural numbers are different. The representation as a sum of inverses makes some sense: it is known to lead to an optimal solution to the problem of dividing bread between workers, a problem often described in the Egyptian papyri. However, this does not explain why the corresponding natural numbers should be all different: some representations with the same natural number repeated several times lead to the same smallest number of cuts as the representations that the ancient Egyptians actually used. In this …