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Browsing by Degree "Mathematics and Statistics"

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Browsing by Degree "Mathematics and Statistics"

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  • Hall, Bailey Thomas (Wake Forest University, 2017)
    Given a field $k$ of characteristic zero, let $R = k_{-1}[x_1, ..., x_n]$ denote the $(-1)$ skew-polynomial ring; i.e., the ring generated from $n$ indeterminates $\{x_i\}_{i=1}^n$ over $k$ such that $x_i x_j = - x_j x_i$ ...
  • Tague, Mitchell Carlson (Wake Forest University, 2020)
    Network analysis is a burgeoning field, showing success at explaining various characteristics in social network contexts. Centrality is a key property used in analysis of real world networks. Many different measures for ...
  • Fries, William (Wake Forest University, 2018)
    In this paper we explore the introductory theory of modeling epidemics on networks and the significance of the spectral radius in their analysis. We look to establish properties of the spectral radius that would better ...
  • Lidral-Porter, Brendan (Wake Forest University, 2017)
    In this thesis, we consider broadly the concept of choice in a variety of settings, focusing on equity in selection. In particular, we introduce the concept of (pair-wise) domination graphs for hypergraphs endowed with a ...
  • Cerchia, Michael (Wake Forest University, 2019)
    Let $E$ be an elliptic curve without complex multiplication over a number field $F$, let $\ell$ be a prime, and let $\alpha\in E(F)$ be a point of infinite order such that $\alpha+T$ is not $\ell$ times a point over $F$ ...
  • Zhang, Teng (Wake Forest University, 2016)
    Clustering analysis aims to detect the topological community-structure of networks (connected graphs with n vertices and m edges), and studies inherent relations behind partitions. In this thesis, we consider far-reaching ...
  • Xia, Jinxin (Wake Forest University, 2021)
    The computational power growth nowadays does not match the demands of the datasize growth. Efficient algorithms are needed in almost every large numerical optimization task. Decades ago Broyden, Fletcher, Goldfarb, and ...
  • Roberts, Sarah Elizabeth (Wake Forest University, 2017)
    In this thesis, we tabulate some previously undocumented link mosaic diagrams. Next we prove an upper and lower bound on crossing number of certain mosaic diagrams of knots in terms of winding number for knot diagrams that ...
  • Han, Yichen (Wake Forest University, 2020)
    This thesis studies the friendship paradox under random attachment via the configuration model. In particular, we build upon recent work regarding degree-wise comparisons in expected value for varying length walks on a ...
  • Zhang, Xinyu (Wake Forest University, 2020)
    Occupancy models for different species have been used by researchers to estimatespecies’ migratory trends and to understand how the environmental and human fac-tors are affecting it. Developed from the original single ...
  • Farmer, Charles Matthew (Wake Forest University, 2018)
    Let G be a graph with a finite vertex set and edge set. A bond of G is a spanning subgraph of G whose connected components are induced. This collection of bonds form a partially ordered set which is also a lattice. This ...
  • Nichols, David E (Wake Forest University, 2020)
    Motivated by Richard Stanley's e-positivity conjecture, we explore the relationships between line graphs, modified line graphs, and incomparability graphs. We show that line graphs and modified line graphs will fail to ...
  • Lee, Ariella (Wake Forest University, 2021)
    We find the $K$-points on the curve\begin{align*}X\colon\begin{cases}y^{2}z=x^{3}-2xz^{2}\\w^{2}z=-4x^{2}y-4xyz-y^{3}\end{cases}\end{align*}in which $K=\Q(\sqrt{-p})$ for some prime $p\equiv3\pmod{8}$.
  • Greene, Katherine Anne (Wake Forest University, 2017)
    We introduce a new combinatorial three-player partizan game called Rhombination and expand some ideas from two-player game theory into three-player game theory.
  • Yu, Kejia (Wake Forest University, 2020)
    In this paper, we fit models to the occurrence and intensity of flood in North America to study risk for insurance purposes. North America is separated into 625 hydro basins with unique hydro graphic information. We collected ...
  • Rezek, Maximilian (Wake Forest University, 2019)
    In the non-Euclidean model of elasticity, growth is modeled by a Riemannian metric that encodes local changes in distance. In response to the growth, the sheet deforms to minimize an elastic energy. The elastic energy ...
  • Jiang, Hongyi (Wake Forest University, 2017)
    This thesis studies the friendship paradox for weighted and directed networks, from a probabilistic perspective. We consolidate and extend recent results of Cao and Ross and Kramer, Cutler and Radcliffe, to weighted networks. ...
  • Turnage, John Michael (Wake Forest University, 2022)
    We present a study of the optimal time of flight of a vertical rolling disk on a surface of revolution. This is a twist on the classic problem of a disk rolling without slipping on the plane, which is a canonical example ...
  • Gilbert, Cody (Wake Forest University, 2018)
    In this paper, we work towards understanding a counterexample found in Lukas Katthan's "A non-Golod Ring with a Trivial Product on its Koszul Homology". In this counterexample, Katthan disproved a claim made by Berglund ...
  • Holley, Lydia Jane (Wake Forest University, 2020)
    A link is a collection of disjoint, smoothly embedded circles in $\mathbb{R}^3$. We might think of this object as a chain of knots in physical space. We will consider an arbitrary $n$-component link $L$, and ask the question ...