Quantifying Iron Overload Using Mri, Active Contours, And Convolutional Neural Networks,
2019
Duquesne University
Quantifying Iron Overload Using Mri, Active Contours, And Convolutional Neural Networks, Andrea Sajewski, Stacey Levine
Undergraduate Research and Scholarship Symposium
Iron overload, a complication of repeated blood transfusions, can cause tissue damage and organ failure. The body has no regulatory mechanism to excrete excess iron, so iron overload must be closely monitored to guide therapy and measure treatment response. The concentration of iron in the liver is a reliable marker for total body iron content and is now measured noninvasively with magnetic resonance imaging (MRI). MRI produces a diagnostic image by measuring the signals emitted from the body in the presence of a constant magnetic field and radiofrequency pulses. At each pixel, the signal decay constant, T2*, can be calculated, …
Patterns, Symmetries, And Mathematical Structures In The Arts,
2019
Georgia Southern University
Patterns, Symmetries, And Mathematical Structures In The Arts, Sarah C. Deloach
Honors College Theses
Mathematics is a discipline of academia that can be found everywhere in the world around us. Mathematicians and scientists are not the only people who need to be proficient in numbers. Those involved in social sciences and even the arts can benefit from a background in math. In fact, connections between mathematics and various forms of art have been discovered since as early as the fourth century BC. In this thesis we will study such connections and related concepts in mathematics, dances, and music.
Connectedness- Its Evolution And Applications,
2019
Ursinus College
Connectedness- Its Evolution And Applications, Nicholas A. Scoville
Topology
No abstract provided.
Accurate Inference For Repeated Measures In High Dimensions,
2019
Loyola University Chicago
Accurate Inference For Repeated Measures In High Dimensions, Xiaoli Kong, Solomon W. Harrar
Mathematics and Statistics: Faculty Publications and Other Works
This paper proposes inferential methods for high-dimensional repeated measures in factorial designs. High-dimensional refers to the situation where the dimension is growing with sample size such that either one could be larger than the other. The most important contribution relates to high-accuracy of the methods in the sense that p-values, for example, are accurate up to the second-order. Second-order accuracy in sample size as well as dimension is achieved by obtaining asymptotic expansion of the distribution of the test statistics, and estimation of the parameters of the approximate distribution with second-order consistency. The methods are presented in a unified and …
Confidence Intervals For The Area Under The Receiver Operating Characteristic Curve In The Presence Of Ignorable Missing Data,
2019
University of North Carolina at Chapel Hill
Confidence Intervals For The Area Under The Receiver Operating Characteristic Curve In The Presence Of Ignorable Missing Data, Hunyong Cho, Gregory J. Matthews, Ofer Harel
Mathematics and Statistics: Faculty Publications and Other Works
Receiver operating characteristic curves are widely used as a measure of accuracy of diagnostic tests and can be summarised using the area under the receiver operating characteristic curve (AUC). Often, it is useful to construct a confidence interval for the AUC; however, because there are a number of different proposed methods to measure variance of the AUC, there are thus many different resulting methods for constructing these intervals. In this article, we compare different methods of constructing Wald‐type confidence interval in the presence of missing data where the missingness mechanism is ignorable. We find that constructing confidence intervals using multiple …
Leveraging Variation Of Historical Number Systems To Build Understanding Of The Base-Ten Place-Value System,
2019
Portland State University
Leveraging Variation Of Historical Number Systems To Build Understanding Of The Base-Ten Place-Value System, Eva Thanheiser, Kathleen Melhuish
Mathematics and Statistics Faculty Publications and Presentations
Prospective elementary school teachers (PTs) come to their mathematics courses fluent in using procedures for adding and subtracting multidigit whole numbers, but many are unaware of the essential features inherent in understanding the base-ten place-value system (i.e., grouping, place value, base). Understanding these features is crucial to understanding and teaching number and place value. The research aims of this paper are (1) to present a local instructional theory (LIT), designed to familiarize PTs with these features through comparison with historical number systems and (2) to present the effects of using the LIT in the PT classroom. A theory of learning …
Folding Mathematics: A Mathematical Approach To Origami,
2019
Louisiana Tech University
Folding Mathematics: A Mathematical Approach To Origami, Zachary Davis
Mathematics Senior Capstone Papers
From constructing a midpoint on a line to observing specific divisions of a plane, the art form of Origami borrows many mathematical tools in order to create complex, and often symmetrical, patterns in a paper medium known as a fold. For this project, the traditional fold known as the Origami Crane/Swan will be thoroughly examined as it contains the unique property to lie completely flat when complete. This phenomenon occurs because the vertices holding the fold together are not all considered to be flat folds. The different types of vertices interacting with each other create a natural locking mechanism within …
Pisano Periods: A Comparison Study,
2019
Louisiana Tech University
Pisano Periods: A Comparison Study, Katherine Willrich
Mathematics Senior Capstone Papers
The Pisano period, denoted π(n), is the period during which the Fibonacci sequence repeats after reducing the original sequence modulo n. More generally, one can similarly define Pisano periods for any linear recurrence sequence; in this paper we compare the Pisano periods of certain linear recurrence sequences with the Pisano periods of the Fibonacci sequence. We first construct recurrence sequences, defining the initial values as integers from 2 to 1000 and second values as 1. This paper discusses how the constructed sequences are related to the matrix M = [(first row) 1 1 (second row) 1 0] reduced modulo n. …
Mathematical Analysis Of The Duck Migration To Louisiana,
2019
Louisiana Tech University
Mathematical Analysis Of The Duck Migration To Louisiana, Brandon Garcia
Mathematics Senior Capstone Papers
The purpose of this project is to research the relationship between duck migration and weather patterns, more specifically trying to determine if the rainfall and temperature in a given year affects the migration patterns of ducks. Duck hunters and conservation- ists alike have observed an overall decrease in the duck population in Louisiana over the past 70 years. Though some years have seen an increase, the population has not recovered to the level from the 1950s. These observations have led to many questions about what have happened to the ducks or where have the ducks gone. Using differ- ent forms …
The Riemann Curvature Tensor,
2019
Louisiana Tech University
The Riemann Curvature Tensor, Jennifer Cox
Mathematics Senior Capstone Papers
A tensor is a mathematical object that has applications in areas including physics, psychology, and artificial intelligence. The Riemann curvature tensor is a tool used to describe the curvature of n-dimensional spaces such as Riemannian manifolds in the field of differential geometry. The Riemann tensor plays an important role in the theories of general relativity and gravity as well as the curvature of spacetime. This paper will provide an overview of tensors and tensor operations. In particular, properties of the Riemann tensor will be examined. Calculations of the Riemann tensor for several two and three dimensional surfaces such as that …
Personality & How Sound Affects Moods,
2019
Louisiana Tech University
Personality & How Sound Affects Moods, Joe Pham
Mathematics Senior Capstone Papers
This research seeks to determine the personality and relationship between current moods of individuals at Louisiana Tech University by conducting a sound test of a can opening with a pre and post mood assessment, Brief Mood Introspection Scale (BMIS). The real question is “Can a sound test change mood?” Using one-way analysis of variance (ANOVA), the study is intended to examine the relationship between the pre and post (BMIS). The results indicate that there is a statistically significant relationship between both BMIS assessments. To determine if the data is significant, we must show the analysis of both BMIS and its …
Semiclassically Modeling Hydrogen At Rydberg States Immersed In Electromagnetic Fields,
2019
Louisiana Tech University
Semiclassically Modeling Hydrogen At Rydberg States Immersed In Electromagnetic Fields, Jaron Williams
Mathematics Senior Capstone Papers
Originally, closed-orbit theory was developed in order to analyze oscillations in the near ionization threshold (Rydberg) densities of states for atoms in strong external electric and magnetic fields. Oscillations in the density of states were ascribed to classical orbits that began and ended near the atom. In essence, observed outgoing waves following the classical path return and interfere with original outgoing waves, giving rise to oscillations. Elastic scattering from one closed orbit to another gives additional oscillations in the cross-section. This study examines how quantum theory can be properly used in combination with classical orbit theory in order to study …
Making The Cut: Receivers Of The National Football League,
2019
Louisiana Tech University
Making The Cut: Receivers Of The National Football League, Anthony Kent Davis
Mathematics Senior Capstone Papers
In this paper the prospects of the National Football League, or NFL, are studied in order to determine the relationships between past college statistics, other “measurables,” and how they translate to successful careers in the league. When referring to measurables, this consists of all of the numerical data from each player that should, in theory, help teams get an idea of the players strengths or weaknesses. The data being used comes from an annual scouting combine for NFL teams that is held prior to each season. Information about the player’s college statistics and pre-draft measurables are being compared to several …
Blackjack: The Math Behind The Cards,
2019
Louisiana Tech University
Blackjack: The Math Behind The Cards, Hanna Blanchard
Mathematics Senior Capstone Papers
In this paper the reader will learn about the math behind the cards in the game of Blackjack. Blackjack or “21” has been played around the world with various rules and regulations in both professional and informal environments. The ultimate objective of the game is to receive a total card value of 21, or as close to 21 as possible without exceeding it, from the cards in a player’s hand in order to beat the dealer’s total. The goal of this project is to calculate the probabilities of various hands to determine the best strategies to win 21. The probabilities …
Generalizations Of Markov Chain Discretizations,
2019
Elizabethtown College
Generalizations Of Markov Chain Discretizations, John E. Kampmeyer Iii
Mathematical Science: Student Scholarship & Creative Works
Markov chains have famously been a crucial tool in understanding stochastic processes and queuing systems, among many other applications. Both discrete-time chains and continuoustime chains have been important centers in both research and application. These two cases are described by transition matrices. Continuous-time chains are difficult to model because this matrix is rather hard to compute in general. One attack to this problem is approximating a continuous-time chain with one that evolves in discrete time. The transition matrix is still difficult to compute exactly but can also be approximated to any order. The first-order approximation of this quantity is well-known. …
Interview Of Stephen Andrilli, Ph.D.,
2019
La Salle University
Interview Of Stephen Andrilli, Ph.D., Stephen Francis Andrilli Ph.D., Jane Highley
All Oral Histories
Stephen Francis Andrilli was born in August 1952 in Bryn Mawr, PA. He was born to Francis and Leatrice Andrilli. Dr. Andrilli is the oldest of four children; his three sisters are Carol (now Carol Strosser), Patricia (now Patricia Kempczynski), and Barbara (now Barbara Parkes). Aside from a few years of living in Gettysburg, Dr. Andrilli has lived in the Philadelphia area for most of his life. He attended St. Jerome School, where he finished 8th grade. He then attended LaSalle College High School, where he graduated in 1969 at age 16. He entered La Salle University (formerly La Salle …
How To Calculate Pi: Buffon's Needle (Non-Calculus Version),
2019
Central Washington University
How To Calculate Pi: Buffon's Needle (Non-Calculus Version), Dominic Klyve
Pre-calculus and Trigonometry
No abstract provided.
Greatest Common Divisor: Algorithm And Proof,
2019
University of St. Thomas - Houston
Greatest Common Divisor: Algorithm And Proof, Mary K. Flagg
Number Theory
No abstract provided.
The Name Tag Problem,
2019
Boise State University
The Name Tag Problem, Christian Carley
Mathematics Undergraduate Theses
A group of n people sit around a table, according to an assignment of name tags in which only one person is paired with the correct name tag. Curious to see if it will improve the number of correct pairings, everybody passes their name tag to the person on their left. Oddly, a new person, and only that person, receives the correct name tag. Indeed, every rotation provides the correct name tag to exactly one new person, until the nth rotation, whereby every person has received the correct name tag one at a time. Given any group of people, …
The Hyperreals: Do You Prefer Non-Standard Analysis Over Standard Analysis?,
2019
Boise State University
The Hyperreals: Do You Prefer Non-Standard Analysis Over Standard Analysis?, Chloe Munroe
Mathematics Undergraduate Theses
The hyperreal number system *ℝ forms an ordered field that contains ℝ as a subfield as well as infinitely many large and small numbers. A number is defined to be infinitely large if |ω| > n for all n = 1, 2, 3, ... and infinitely small if |ε| < 1/n for all n = 1, 2, 3... This number system is built out of the real number system analogous to Cantor’s construcion of ℝ out of ℚ. The new entities in *ℝ and the relationship between the reals and hyperreals provides an appealing alternate approach to real (standard) analysis …
