Inference For Time Series In Change Points And Statistical Learning,
2024
Washington University in St. Louis
Inference For Time Series In Change Points And Statistical Learning, Jiaqi Li
Arts & Sciences Graduate Student Theses and Dissertations
This study aims to develop a comprehensive framework for inference theory in time series, with a focus on change-point detection and online learning. First, we introduce an $\ell^2$-based inference approach for multiple change-point detection in high-dimensional time series, which targets dense or spatially clustered signals by a novel Two-Way MOSUM (moving sum) test statistic. We derive the limiting distribution of this $\ell^2$-aggregated statistic by extending the high-dimensional Gaussian approximation to non-stationary spatial-temporal processes. Simulation exhibits promising performance of our test in detecting non-sparse weak signals, and the application to COVID-19 analysis shows the real-world relevance of our method. Next, we …
Art And Math Via Cubic Polynomials, Polynomiography And Modulus Visualization,
2024
Rutgers University
Art And Math Via Cubic Polynomials, Polynomiography And Modulus Visualization, Bahman Kalantari
LASER Journal
Throughout history, both quadratic and cubic polynomials have been rich sources for the discovery and development of deep mathematical properties, concepts, and algorithms. In this article, we explore both classical and modern findings concerning three key attributes of polynomials: roots, fixed points, and modulus. Not only do these concepts lead to fertile ground for exploring sophisticated mathematics and engaging educational tools, but they also serve as artistic activities. By utilizing innovative practices like polynomiography—visualizations associated with polynomial root finding methods—as well as visualizations based on polynomial modulus properties, we argue that individuals can unlock their creative potential. From crafting captivating …
Classification Of Topological Defects In Cosmological Models,
2024
University of Mary Washington
Classification Of Topological Defects In Cosmological Models, Abigail Swanson
Departmental Honors & Graduate Capstone Projects
In nature, symmetries play an extremely significant role. Understanding the symmetries of a system can tell us important information and help us make predictions. However, these symmetries can break and form a new type of symmetry in the system. Most notably, this occurs when the system goes through a phase transition. Sometimes, a symmetry can break and produce a tear, known as a topological defect, in the system. These defects cannot be removed through a continuous transformation and can have major consequences on the system as a whole. It is helpful to know what type of defect is produced when …
An Investigation Into The Causes Of Home Field Advantage In Professional Soccer,
2024
Macalester College
An Investigation Into The Causes Of Home Field Advantage In Professional Soccer, Paige E. Tomer
Mathematics, Statistics, and Computer Science Honors Projects
Home-field advantage is the sporting phenomenon in which the home team outperforms the away team. Despite its widespread occurrence across sports, the underlying reasons for home-field advantage remain uncertain. In this paper, we employ a range of statistical methods to explore the causal relationships of potential determinants of home-field advantage. We measure home-field advantage using match outcomes and differential metrics (e.g., differences in yellow cards received). In an attempt to narrow the research disparity between men’s and women’s sports, we utilize data from the National Women’s Soccer League (NWSL) and the English Premier League (EPL) to investigate potential causes of …
A Discussion On Estimation Of The Best Constant For Spherical Restriction Inequalities,
2024
University of Michigan Ann Arbor
A Discussion On Estimation Of The Best Constant For Spherical Restriction Inequalities, Hongyi Liu
Mathematics, Statistics, and Computer Science Honors Projects
The restriction conjecture asks for a meaningful restriction of the Fourier transform of a function to a sufficiently curved lower dimensional manifold. It then conjectures certain size estimates for this restriction in terms of the size of the original function. It has been proven in 2 dimensions, but it is open in dimensions 3 and larger, and is an area of much recent active effort. In our study, instead of aiming to prove the restriction conjecture, we target understanding its worst-case scenarios within known estimates. Specifically, we investigate the extension operator applied to antipodally concentrating profiles, examining the ratio of …
Representation Theory And Burnside's Theorem,
2024
University of Minnesota - Morris
Representation Theory And Burnside's Theorem, Nathan Fronk
Senior Seminars and Capstones
In this paper we give a brief introduction to the representation theory of finite groups, and by extension character theory. These tools are extensions of group theory into linear algebra, that can then be applied back to group theory to prove propositions that are based entirely in group theory. We discuss the importance of simple groups and the Jordan-Hölder theorem in order to prepare for the statement of Burnside’s pq theorem. Lastly, we provide a proof of Burnside’s theorem that utilizes the character theory we covered earlier in the paper.
Numerical Investigation To Produce A Fundamental Polygon,
2024
Murray State University
Numerical Investigation To Produce A Fundamental Polygon, Elizabeth Sipes
Honors College Theses
There exist multiple types of geometry, differing in the postulates they are based on, and therefore the theorems and proofs that make up said geometry. Hyperbolic geometry differs from others by allowing there to exist multiple lines through a single point not on a given line, that are parallel to the given line. Every geometry has the idea of distance and isometries, distance preserving maps. By considering special collections of isometries called discrete groups, we can construct interesting surfaces, such as the torus and genus-g surface. The connection between the surface and the discrete group can be understood through …
Largeness And Accessibility Of Sparse Sets,
2024
Bridgewater State University
Largeness And Accessibility Of Sparse Sets, Oscar Quester
Honors Program Theses and Projects
One of the main goals in the study of Ramsey Theory is to find “order” in seemingly “random” structures. For example, Van der Waerden’s Theorem tells us that given any r-coloring of the positive integers, there will exist arbitrarily long monochromatic arithmetic progressions. The theorem places no requirement on the gap (common difference), d, of the arithmetic progression – it can be any natural number. With this in mind, we ask if we are still guaranteed arbitrarily long monochromatic arithmetic progressions when we restrict the possible values of d to some subset D ⊆ N. We also ask a similar …
A Tale Of Two Toroidal Graphs,
2024
Western Michigan University
A Tale Of Two Toroidal Graphs, Akshat Gulgulia
Honors Theses
A graph is toroidal if it can be embedded on a torus which is a doughnut-shaped surface. Two well-known examples of toroidal graphs are the complete graph K5 and the complete bipartite graph K3,3. In this thesis we elucidate the association of the subject matter with two renowned enigmas in graph theory, namely the Five Princes Problem and the Three Utilities Problems. Additionally, we look at their association with several renowned theorems in topological graph theory. We explore the link between these two graphs and a contemporary labeling concept.
Euler Archive Spotlight: Multiple Search Options,
2024
University of the Pacific
Euler Archive Spotlight: Multiple Search Options, Christopher Goff
Euleriana
The Euler Archive houses PDF versions of almost all of Euler's original publications. While most visitors search the archive via a work's Eneström number, the Archive can be searched via source publication name, date written, or decade of publication. The Archive also provides context for Euler's publications through short pieces of historical information.
Euler And A Proof Of The Functional Equation For The Riemann Zeta-Function He Could Have Given,
2024
Johannes Gutenberg Universitat, Mainz
Euler And A Proof Of The Functional Equation For The Riemann Zeta-Function He Could Have Given, Alexander Aycock
Euleriana
We explain how Euler could have proved a functional equation, which is equivalent to the one for the Riemann zeta-function, that he conjectured in his paper {\it ``Remarques sur un beau rapport entre les series des puissances tant directes que reciproques"} \cite{E352} (E352: ``Remarks on the beautiful relation between the series of the direct and reciprocal powers").
Euler And The Gaussian Summation Formula For The Hypergeometric Series,
2024
Johannes Gutenberg Universitat, Mainz
Euler And The Gaussian Summation Formula For The Hypergeometric Series, Alexander Aycock
Euleriana
We show that in his paper {\it ``Plenior expositio serierum illarum memorabilium, quae ex unciis potestatum binomii formantur"} \cite{E663} (E663: ``A more thorough exposition of those memorable series that are formed from the binomial coefficients") Euler could have found the Gaussian summation formula for the hypergeometric series from his own formulas in that same paper, if he actually set the task for himself.
Euler And Homogeneous Difference Equations With Linear Coefficients,
2024
Johannes Gutenberg Universitat, Mainz
Euler And Homogeneous Difference Equations With Linear Coefficients, Alexander Aycock
Euleriana
We present a method outlined by Euler in his paper{\it ``De fractionibus continuis observationes"} \cite{E123} (E123: ``Observations on continued fractions") that can be used to solve homogeneous difference equations with linear coefficients. We will illustrate his ideas by applying it to two familiar examples and explain how it can be understood from a more modern point of view.
On The Cases In Which The Formula X^4+Kxxyy+Y^4 Can Be Reduced To A Square,
2024
Oak Ridge National Laboratory
On The Cases In Which The Formula X^4+Kxxyy+Y^4 Can Be Reduced To A Square, Georg Ehlers
Euleriana
Euler’s key idea for equating the Quartic in the title to a square is to set k=P+surd(Q). From this he derives P=f·x^2 and Q=4f·y^2+4 and solves the Pell equation for y. He then discusses various extensions to rational numbers that leave k an integer. Euler provides incomplete tables for integers k with |k|square.
Research On Arithmetic,
2024
University of Washington – Tacoma
Research On Arithmetic, Erik R. Tou
Euleriana
In this English translation, some of Joseph-Louis Lagrange's early number theory is presented. Here, he laid out a theory of binary quadratic forms with special attention to the representation problem: determining those integers which may be represented by a given form, and cataloguing the possible forms of their divisors.
Number Theory And More,
2024
University of the Pacific
Number Theory And More, Christopher Goff, Erik Tou
Euleriana
An introduction to the contents in Issue 1, Volume 4 of Euleriana.
Finite State And Sequential Automata,
2024
Western Michigan University
Finite State And Sequential Automata, Kriti Gulgulia
Honors Theses
No abstract provided.
Caterpillar, Lobster, X Graphs,
2024
College of Saint Benedict/Saint John's University
Caterpillar, Lobster, X Graphs, Gerald Melin, Landon Seward, Will Mahowald, Xavier Jones
Celebrating Scholarship and Creativity Day (2018-)
We studied a combinatorial game played between two players ("Alpha", who goes first, and "Beta", who goes second). The idea is that there are a lot of lightbulbs in a large warehouse, and they take turns turning a light bulb on. When a light bulb is turned on, it illuminates the area directly by it as well as the areas immediately surrounding it. The player who is the one to make all of the warehouse illuminated is the winner. This can be modeled on a graph. The two players take turns (1) selecting a vertex that has not yet been …
Skeletal 2-Groups And Category Theory,
2024
Providence College
Skeletal 2-Groups And Category Theory, Nicholas Small '25, Alexander Stepanov '26, Haley Waiksnis '25
Mathematics & Computer Science Student Scholarship
Nicholas Small ’25, Mathematics and Computer Science major
Alexander Stepanov ’26, Mathematics and Studio Art major
Haley Waiksnis ’25, Mathematics major
Faculty Mentor: Dr. Laura Murray, Mathematics and Computer Science
Autonomous Remote Erosion Monitoring Using Computer Vision,
2024
Providence College
Autonomous Remote Erosion Monitoring Using Computer Vision, Emily Gelchie '24, Gabriel Benz '25
Mathematics & Computer Science Student Scholarship
Emily Gelchie ’24, Computer Science major
Gabriel Benz ’25, Computer Science major
Faculty Mentor: Dr. Martin Helwig, Mathematics and Computer Science
