The Fourier Coefficients Of Modular Forms,
2015
Brigham Young University
The Fourier Coefficients Of Modular Forms, Kyle Pratt, Dr. Paul Jenkins
Journal of Undergraduate Research
Modular forms are complex analytic functions with remarkable properties. Modular forms possess interesting and surprising connections to many different branches of mathematics. For example, it is well-known that Andrew Wiles’ proof of Fermat’s Last Theorem, a conjecture that had been unresolved for more than three centuries, utilized modular forms in a crucial way.
Poincaré Disc: Hear The Whole Mind Sing,
2015
University of Alabama in Huntsville
Poincaré Disc: Hear The Whole Mind Sing, Laura Moss, John T. Shrontz
Research Horizons Day Posters
No abstract provided.
Stochastic Comparisons Of Weighted Sums Of Arrangement Increasing Random Variables,
2015
University of Science and Technology of China
Stochastic Comparisons Of Weighted Sums Of Arrangement Increasing Random Variables, Xiaoqing Pan, Min Yuan, Subhash C. Kochar
Mathematics and Statistics Faculty Publications and Presentations
Assuming that the joint density of random variables X1,X2, . . . ,Xn is arrangement increasing (AI), we obtain some stochastic comparison results on weighted sums of Xi’s under some additional conditions. An application to optimal capital allocation is also given.
Multivariate Statistical Methodologies Applied In Biomedical Raman Spectroscopy: Assessing The Validity Of Partial Least Squares Regression Using Simulated Model Datasets.,
2015
Technological University Dublin
Multivariate Statistical Methodologies Applied In Biomedical Raman Spectroscopy: Assessing The Validity Of Partial Least Squares Regression Using Simulated Model Datasets., Mark Keating
Articles
Raman spectroscopy is fast becoming a valuable analytical tool in a number of biomedical scenarios, most notably disease diagnostics. Importantly, the technique has also shown increasing promise in the assessment of drug interactions on a cellular and subcellular level, particularly when coupled with multivariate statistical analysis. However, an important consideration, both with Raman spectroscopy and the associated statistical methodologies, is the accuracy of these techniques and more specifically the sensitivities which can be achieved and ultimately the limits of detection of the various methods. The purpose of this study is thus the construction of a model simulated data set with …
Review: On Pairs Of Generalized And Hypergeneralized Projections In A Hilbert Space,
2015
Pomona College
Review: On Pairs Of Generalized And Hypergeneralized Projections In A Hilbert Space, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
Zeros Of Poincare Series Of Level 2,
2015
Brigham Young University
Zeros Of Poincare Series Of Level 2, Andrew Haddock, Paul Jenkins
Journal of Undergraduate Research
Introduction Poincaré series are a certain type of modular form. Modular forms are complex-valued functions that satisfy certain symmetry properties. There are many different types of modular forms, and one way to classify modular forms is by their level, such as 1, 2, 3, etc. They are of much interest as a research subject because they are connected in surprising ways to many different fields in number theory—e.g., elliptic curves, quadratic forms, and partition functions, to name just a few. As we gain more insight into the various properties of modular forms, we gain more insight into how these various …
Does Being Bilingual Make You Better At Math?,
2015
Bryant University
Does Being Bilingual Make You Better At Math?, Enxhi Elezi
Honors Projects in Mathematics
The purpose of this study is to examine if there is any relationship between being bilingual, defined as speaking your native language at home and another language in school, and your mathematical ability. Data from the National Longitudinal Study of Adolescent Health was used to compare the math grades of students who were not born in the US and speak English, Spanish, or Other at home. Also, data from the Bryant University first year students was used to test if students who speak a different language at home have a higher mathematical average than their monolingual peers. Results show that …
Mathematical Modeling Of Trending Topics On Twitter,
2015
Bryant University
Mathematical Modeling Of Trending Topics On Twitter, Jonathan S. Skaza
Honors Projects in Mathematics
Created in 2006, Twitter is an online social networking service in which users share and read 140-character messages called Tweets. The site has approximately 288 million monthly active users who produce about 500 million Tweets per day. This study applies dynamical and statistical modeling strategies to quantify the spread of information on Twitter. Parameter estimates for the rates of infection and recovery are obtained using Bayesian Markov Chain Monte Carlo (MCMC) methods. The methodological strategy employed is an extension of techniques traditionally used in an epidemiological and biomedical context (particularly in the spread of infectious disease). This study, which addresses …
Analysis Of Random Metric Spaces Explains Emergence Phenomenon And Suggests Discreteness Of Physical Space,
2015
The University of Texas at El Paso
Analysis Of Random Metric Spaces Explains Emergence Phenomenon And Suggests Discreteness Of Physical Space, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, systems follow the pattern set by the second law of thermodynamics: they evolve from an organized inhomogeneous state into a homogeneous structure-free state. In many other practical situations, however, we observe the opposite emergence phenomenon: in an originally homogeneous structure-free state, an inhomogeneous structure spontaneously appears. In this paper, we show that the analysis of random metric spaces provides a possible explanation for this phenomenon. We also show that a similar analysis supports space-time models in which proper space is discrete.
Bytes Of Π, Spring 2015,
2015
Bridgewater State University
Bytes Of Π, Spring 2015, Department Of Mathematics, Bridgewater State University
Department of Mathematics Newsletter
No abstract provided.
Topological Manifolds,
2015
University of Southern Maine
Topological Manifolds, Grant Wilson
Thinking Matters Symposium Archive
Topological Manifolds are abstract spaces that locally resemble Euclidean space. For example, consider a round globe and a flat map. The map is a 2-dimensional representation of a 3-dimensional space. Given any point on the globe we can find a corresponding position on the map, and vice versa. This correspondence is called a chart. With a sufficient number of charts, we can describe the whole space. Such a collection of charts is called an Atlas. It is possible to construct different Atlases for the same space, allowing us to move from one chart, to the space, to another chart. This …
Inside Out: Properties Of The Klein Bottle,
2015
University of Southern Maine
Inside Out: Properties Of The Klein Bottle, Andrew Pogg, Jennifer Daigle, Deirdra Brown
Thinking Matters Symposium Archive
A Klein Bottle is a two-dimensional manifold in mathematics that, despite appearing like an ordinary bottle, is actually completely closed and completely open at the same time. The Klein Bottle, which can be represented in three dimensions with self-intersection, is a four dimensional object with no intersection of material. In this presentation we illustrate some topological properties of the Klein Bottle, use the Möbius Strip to help demonstrate the construction of the Klein Bottle, and use mathematical properties to show that the Klein Bottle intersection that appears in ℝ3 does not exist in ℝ4. Introduction: Topology
Parallel Symmetric Eigenvalue Problem Solvers,
2015
Purdue University
Parallel Symmetric Eigenvalue Problem Solvers, Alicia Marie Klinvex
Open Access Dissertations
Sparse symmetric eigenvalue problems arise in many computational science and engineering applications: in structural mechanics, nanoelectronics, and spectral reordering, for example. Often, the large size of these problems requires the development of eigensolvers that scale well on parallel computing platforms. In this dissertation, we describe two such eigensolvers, TraceMin and TraceMin-Davidson. These methods are different from many other eigensolvers in that they do not require accurate linear solves to be performed at each iteration in order to find the smallest eigenvalues and their associated eigenvectors. After introducing these closely related eigensolvers, we discuss alternative methods for solving the saddle point …
Why Big-O And Little-O In Algorithm Complexity: A Pedagogical Remark,
2015
The University of Texas at El Paso
Why Big-O And Little-O In Algorithm Complexity: A Pedagogical Remark, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In the comparative analysis of different algorithm, O- and o-notions are frequently used. While their use is productive, most textbooks do not provide a convincing student-oriented explanation of why these particular notations are useful in algorithm analysis. In this note, we provide such an explanation.
Sometimes, It Is Beneficial To Process Different Types Of Uncertainty Separately,
2015
Technical Educational Institute of Epirus
Sometimes, It Is Beneficial To Process Different Types Of Uncertainty Separately, Chrysostomos D. Stylios, Andrzej Pownuk, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, we make predictions based on the measured and/or estimated values of different physical quantities. The accuracy of these predictions depends on the accuracy of the corresponding measurements and expert estimates. Often, for each quantity, there are several different sources of inaccuracy. Usually, to estimate the prediction accuracy, we first combine, for each input, inaccuracies from different sources into a single expression, and then use these expressions to estimate the prediction accuracy. In this paper, we show that it is often more computationally efficient to process different types of uncertainty separately, i.e., to estimate inaccuracies in the …
Symbolic Aggregate Approximation (Sax) Under Interval Uncertainty,
2015
Technical Educational Institute of Epirus
Symbolic Aggregate Approximation (Sax) Under Interval Uncertainty, Chrysostomos D. Stylios, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, we monitor a system by continuously measuring the corresponding quantities, to make sure that an abnormal deviation is detected as early as possible. Often, we do not have ready algorithms to detect abnormality, so we need to use machine learning techniques. For these techniques to be efficient, we first need to compress the data. One of the most successful methods of data compression is the technique of Symbolic Aggregate approXimation (SAX). While this technique is motivated by measurement uncertainty, it does not explicitly take this uncertainty into account. In this paper, we show that we can …
A Simplified Explanation Of What It Means To Assign A Finite Value To An Infinite Sum,
2015
The University of Texas at El Paso
A Simplified Explanation Of What It Means To Assign A Finite Value To An Infinite Sum, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Recently, a video made rounds that explained that it often makes sense to assign finite values to infinite sums. For example, it makes sense to claim that the sum of all natural numbers is equal to -1/12. This has picked up interested in media. However, judged by the viewers' and readers' comments, for many viewers and readers, neither the video, not the corresponding articles seem to explain the meaning of the above inequality clearly enough. One of the main stumbling blocks is the fact that the infinite sum is clearly divergent, so a natural value of the infinite sum is …
An Analysis Of Strategic Treatment Interruptions During Imatinib Treatment Of Chronic Myelogenous Leukemia With Imatinib-Resistant Mutations,
2015
California Polytechnic State University - San Luis Obispo
An Analysis Of Strategic Treatment Interruptions During Imatinib Treatment Of Chronic Myelogenous Leukemia With Imatinib-Resistant Mutations, Dana Paquin, David Sacco, John Shamshoian
Mathematics
Chronic myelogenous leukemia (CML) is a cancer of the white blood cells that results from increased and uncontrolled growth of myeloid cells in the bone marrow and the accumulation of these cells in the blood. The most common form of treatment for CML is imatinib, a tyrosine kinase inhibitor. Although imatinib is an effective treatment for CML and most patients treated with imatinib do attain some form of remission, imatinib does not completely eradicate all leukemia cells, and if treatment is stopped, all patients eventually relapse (Cortes, 2005). In Kim (2008), the authors developed a mathematical model for the dynamics …
Mathematical Explorations Of Card Tricks,
2015
John Carroll University
Mathematical Explorations Of Card Tricks, Timothy R. Weeks
Senior Honors Projects
In this project, we explore various mathematical topics as they apply to an assortment of card tricks. We will focus on an examination of theorems applied to the manipulation of cards in an attempt to prove why certain card tricks work. These theorems utilize abstract algebra, probability, number theory, and combinatorics. Many tricks can be explained this way, instead of singularly by sleight of hand or other “magical” methods. We will rigorously prove the theorems and principles that explain these concepts, focusing primarily on the card tricks and examples presented in Mathematical Card Magic by Colm Mulcahy (2013).
Hyperbolic Geometry And Mobius Transformations,
2015
John Carroll University
Hyperbolic Geometry And Mobius Transformations, Emmalee Stevens
Masters Essays
Imagine a world in which there are infinitely many lines through a single point that are all parallel to the same line; this world is referred to as the hyperbolic plane. It starts with a brief history of the development of hyperbolic geometry and the mathematicians who contributed their explorations of the hyperbolic plane. The reader will be reminded of some of the important aspects of Euclidean geometry and some of the basic properties that will later be adjusted to develop hyperbolic geometry. The hyperbolic plane will be constructed from the pseudosphere and the properties of the Poincare Upper Half …
