Mathematics Commons^™

Video Event Understanding With Pattern Theory, Fillipe Souza, Sudeep Sarkar, Anuj Srivastava, Jingyong Su

MODVIS Workshop

We propose a combinatorial approach built on Grenander’s pattern theory to generate semantic interpretations of video events of human activities. The basic units of representations, termed generators, are linked with each other using pairwise connections, termed bonds, that satisfy predefined relations. Different generators are specified for different levels, from (image) features at the bottom level to (human) actions at the highest, providing a rich representation of items in a scene. The resulting configurations of connected generators provide scene interpretations; the inference goal is to parse given video data and generate high-probability configurations. The probabilistic structures are imposed using energies that …

Non-Orientable Objects As Gaming Surfaces, Haley P. Bourke, Paul Latiolais

Student Research Symposium

Developed in Python, Klein Space Fighter is an interactive learning tool and mathematically themed arcade game that allows the player to combat on different mathematical surfaces including a 2D Klein bottle. The app is available for Android and desktop devices, and will be made available for iOS in the future.

To receive an invitation to download the app through Google Play, contact me at [email protected]

The Smallest Intersecting Ball Problem, Daniel J. Giles, Mau Nam Nguyen

Student Research Symposium

The smallest intersecting ball problem involves finding the minimal radius necessary to intersect a collection of closed convex sets. This poster discusses relevant tools of convex optimization and explores three methods of finding the optimal solution: the subgradient method, log-exponential smoothing, and an original approach using target set expansion. A fourth algorithm based on weighted projections is given, but its convergence is yet unproven. Numerical tests and comparison between methods are also presented.

Topological Data Analysis Of Biological Aggregation Models, Chad M. Topaz, Lori B. Ziegelmeir, Tom Halverson

Faculty Publications

No abstract provided.

Exploring Residents’ Attitudes Toward Solar Photovoltaic System Adoption In China, Yaqin Sun

Honors Program Theses and Projects

As the largest energy consuming country, China is facing environmental deterioration, which results from the overuse of non-renewable conventional energy such as coal. Solar photovoltaic (PV) energy, an unlimited and clean energy with minimal impacts on the environment, is considered to be a good alternative to alleviate this severe issue. A survey was designed and conducted among residents in some major cities. Based on the first hand data, basic statistical methods were utilized to examine Chinese residents’ knowledge of, concerns, and attitudes towards PV adoption. The research aims to identify the drivers and dynamics that most encourage customers to install …

Life On The Floodplain: An Analysis Of Falmouth, Massachusetts And Osaka, Japan, Shellie Johnson

Honors Program Theses and Projects

After Hurricane Katrina in 2005, the awareness of flooding threats to coastal areas increased. For Massachusetts in particular, Cape Cod is still at high risk of flooding with any storm that comes and goes. However, all of these recent devastating floods and natural disasters have caused insurance prices to skyrocket. With my research, I specifically looked at Falmouth, Massachusetts and the possibilities to lessen the risks and which of these options would be the most financially sound for a homeowner. The possibilities include elevating a house in a high flood risk zone, selling a current house to move in to …

An Analysis Of Numerical Methods On Traffic Flow Models, Terry Mullen

Honors Program Theses and Projects

In this thesis, we implement Euler's method and the Runge-Kutta method to solve initial value problems. A goal of the project is to compare the two methods on preliminary problems illustrating limitations and advantages. We also apply the Runge-Kutta method to a mathematical model of traffic flow. This thesis sheds light on how the fourth-order Runge-Kutta method is implemented to solve the Optimal Velocity Model (Kurata & Nagatani, 2003). We identify initial conditions and base cases to run simulations of the model. We consider one-car and two-car systems to validate the application of the fourth-order Runge-Kutta method and the Optimal …

How Does Tutoring To Develop Conceptual Understanding Impact Student Understanding?, Kelsey Cummings

Honors Program Theses and Projects

No abstract provided.

Exploring The Calkin-Wilf Tree: Subtrees And The Births Of Numbers, Kayla Javier

Honors Program Theses and Projects

No abstract provided.

Mountain Passes And Saddle Points, James Bisgard

All Faculty Scholarship for the College of the Sciences

Variational methods find solutions of equations by considering a solution as a critical point of an appropriately chosen function. Local minima and maxima are well-known types of critical points. We explore methods for finding critical points that are neither local maxima or minima, but instead are mountain passes or saddle points. Criteria for the existence of minima or maxima are well known, but those for mountain passes or saddle points are less well known. We give an accessible treatment of some criteria for the existence of such points (including the mountain pass lemma), as well as describe a method that …

On The Sum Of The Reciprocals Of Squares, Hussam Ibrahim

Celebration of Learning

The Fourier Series has always been a great tool by turning the most complicated functions into a simple approximation by several sine and cosine terms. However, given the fact that its called an approximation arouses the question of how accurate is this approximation, especially with functions that have a corner at x values. In this project, we will show how the series that is the sum of the reciprocals of squares arises in the study of Fourier series. We will discuss the convergence and the rate of convergence of this series. This result arose during exploration on mathematical software Sage. …

Differential Geometry: Curvature And Holonomy, Austin Christian

Math Theses

We develop the basic language of differential geometry, including smooth manifolds, bundles, and differential forms. Once this background is established, we explore parallelism in smooth manifolds -- in particular, in Riemannian manifolds -- and conclude by presenting a proof of the Ambrose-Singer theorem, which relates parallelism (holonomy) to curvature in principal bundles.

The P -Royden And P -Harmonic Boundaries For Metric Measure Spaces, Marcello Lucia, Michael J. Puls

Publications and Research

Let p be a real number greater than one and let X be a locally compact, noncompact metric measure space that satisfy certain conditions. The p-Royden and p-harmonic boundaries of X are constructed by using the p-Royden algebra of functions on X and a Dirichlet type problem is solved for the p-Royden boundary. We also characterize the metric measure spaces whose p-harmonic boundary is empty.

Using Maya And Mathematica To Create Mathematical Art, Allison Carr

Honors Projects

The project consists of six pieces of art that were created in Maya using mathematical objects created in Mathematica. Accompanying the art are artist statements for each piece, the mathematics behind each object used, and the Mathematica codes used to generate the objects.

Section Abstracts: Astronomy, Mathematics And Physics With Material Science

Virginia Journal of Science

Abstracts of the Astronomy, Mathematics, and Physics with Material Science Section for the 93rd Annual Meeting of the Virginia Academy of Science, May 21-23, 2015, James Madison University, Richmond, Virginia

Book Review: How To Bake Pi: An Edible Exploration Of The Mathematics Of Mathematics, Darren B. Glass

Math Faculty Publications

If you think about it, mathematics is really just one big analogy. For one example, the very concept of the number three is an drawing an analogy between a pile with three rocks, a collection of three books, and a plate with three carrots on it. For another, the idea of a group is drawing an analogy between adding real numbers, multiplying matrices, and many other mathematical structures. So much of what we do as mathematicians involves abstracting concrete things, and what is abstraction other than a big analogy? [excerpt]

Standing On The Shoulders Of The Giants: Why Constructive Mathematics, Probability Theory, Interval Mathematics, And Fuzzy Mathematics Are Important, Vladik Kreinovich

Departmental Technical Reports (CS)

Recent death of Ray Moore, one of the fathers of interval mathematics, inspired these thoughts on why interval computations -- and several other related areas of study -- are important, and what we can learn from the successes of these areas' founders and promoters.

Ua66 Ogden College Of Science & Engineering Newsletter, Cheryl Stevens, Dean

Ogden College of Science & Engineering Publications

No abstract provided.

Counting Convex Sets On Products Of Totally Ordered Sets, Brandy Amanda Barnette

Masters Theses & Specialist Projects

The main purpose of this thesis is to find the number of convex sets on a product of two totally ordered spaces. We will give formulas to find this number for specific cases and describe a process to obtain this number for all such spaces. In the first chapter we briefly discuss the motivation behind the work presented in this thesis. Also, the definitions and notation used throughout the paper are introduced here The second chapter starts with examining the product spaces of the form {1; 2; : : : ;n} × {1; 2}. That is, we begin by analyzing …

Analysis Of Discrete Fractional Operators And Discrete Fractional Rheological Models, Meltem Uyanik

Masters Theses & Specialist Projects

This thesis is comprised of two main parts: Monotonicity results on discrete fractional operators and discrete fractional rheological constitutive equations. In the first part of the thesis, we introduce and prove new monotonicity concepts in discrete fractional calculus. In the remainder, we carry previous results about fractional rheological models to the discrete fractional case. The discrete method is expected to provide a better understanding of the concept than the continuous case as this has been the case in the past. In the first chapter, we give brief information about the main results. In the second chapter, we present some fundamental …