Browsing Mathematics URC Student Scholarship by Issue Date
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Differential Posets and kribbon Tableaux
(20050101)In this study we examine a class of partially ordered sets (posets). Differential posets were first introduced by R. Stanley in 1988 and are a group of posets which meet criteria set forth by Stanley. After examining Young's ... 
On Induced Subgraphs of Johnson Graphs and Move, Rotation, and Jump Graphs
(20050101)A graph is a set of vertices (points) and edges (lines) connecting some of the vertices to each other. We study how different two graphs are by measuring various "distances" between them, e.g., the number of edges that ... 
PostTonal Theory: Musical Technology For New Modes of Expression and Representation
(20070101)My research this summer explored posttonal music theory, a system of organizing the twelvepitch classes of the Western musical scale such that the harmonic hierarchy that exists in conventional music is deconstructed and ... 
Calcium Waves in Pregnant Uterine Contractions
(20070101)Uterine contractions during childbirth stem from cellular processes. This complex process occurs when pacemaker cells generate action potentials that trigger intercellular calcium waves which result in contraction of the ... 
Calculable Congestion: Modeling Effects of Traffic Light on Traffic Flow Using ODEs and PDEs
(20080101)The study analyzes the effect of traffic lights on traffic flow using ordinary differential equation (ODE) and partial differential equations (PDE) models. I consider several different cases. First, I assume constant inflow ... 
Discovering New Intrinsically Knotted Graphs Nancy Moore and Michael Wade
(20080101)In the field of topology, intrinsically knotted graphs are rare graphs in which all embeddings contain a nontrivial knot. There are a finite number of these graphs and only a handful of graphs have been proven to be ... 
Investigations of Multidimensional PredatorPrey Models
(20090101)The GauseLotkaVolterra (GLV) equations are an idealized model for competition between n species. The nRPS and May Leonard competing species models are specific cases of (GLV) which define interaction between various ... 
Proving Graphs are Minor Minimal
(20090101)In the field of topology, a graph is a set of vertices with certain vertices connected to each other by edges. An intrinsically knotted graph is a graph that is guaranteed to contain a knot no matter which way you arrange ... 
Sound Dining: An Analysis of the Soundscape in New York Fine Dining Restaurants
(20100101)In the early nineteenth century, travelers from across the globe who visited Paris remarked on what they called a distinctly Parisian phenomenon: the restaurant. By the 1820s, the ?restaurants of the French capital?closely ... 
Film Franchises and the EdwardsBuckmire Model: An Examination of the Financial Performance of Movie Sequels
(20100101)The EdwardsBuckmire Model (EBM) is a mathematical model which utilizes a system of three nonlinear coupled ordinary differential equations to model the boxoffice dynamics of films released theatrically in North America. ... 
Expressive Musical Terms Index: A Case for WebBased Technology as a Means of Interpreting Musical Scores
(20110101)One of the most commonplace elements of the graphic notation of music is the most elusive element to interpret: the Italian expressive terms that populate most music scores. Nowhere is this more the case than in the music ... 
Mathematical Modeling of Single Nucleotide Polymorphisms via MicroArray Analysis
(20110101)In this project, our goal is to create a mathematical model that can accurately simulate a sample of specific DNA when run through a microarray slide. A microarray slide has probes calibrated to bind onto specific target ... 
A Study of Intrinsic Knots and Links: a Tale of Two Graphs Alex Barylskiy and Hannah Schwartz
(20110101)Our research focused on two questions in graph and knot theory. Our first question addressed the complete graph of nine vertices (K9) and whether or not a 3linkless straightedge embedding is realizable in 3space. A ... 
Classifying and Documenting TYRealizable Trees
(20110101)This project centers around Triangle Y  moves (TYmoves). TYmoves are an operation on graphs (collections of vertices and edges), where we remove the edges AB, AC, and BC of a triangle with vertices A, B, and C, insert ... 
TriangleY Families of Complete Graphs
(20110101)I attempt to determine the triangley (TY) family of any given complete graph. I present a method for determining the number of TY cousins on any level of the family diagram, and give sizes for the first five levels of any ...