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This collection contains theses and dissertations by students in the Department of Mathematics and Statistics at Washington State University.

### Recent Submissions

• #### TAIL MUTUAL INFORMATION OF VINE COPULAS ﻿

(2019)
Multivariate mutual information describes the amount of uncertainty among several random variables, whose scale-invariant dependence is captured by the copula of the joint distribution. In this dissertation, we first show ...
• #### A Modified Chang-Wilson-Wolff Inequality Via the Bellman Function ﻿

(2019)
We produce the optimal constant in an inequality bounding the exponential integral of a function by the exponential integral of its dyadic square function. This work is motivated by a well known result due to Chang, Wilson, ...
• #### EXPERIMENTS IN MEDICAL IMAGE SEGMENTATIONS ﻿

(2019)
Non-invasive Radiology Imaging (e.g. CT, MRI, and PET) have been utilized tremendously in medical study for disease diagnosis, prognostication, and monitoring therapeutic response. And segmenting medical image for regions ...
• #### Spectrally Arbitrary Patterns Over Various Rings ﻿

(2019)
A pattern $\mathcal{A}$ is a matrix where the location, but not the magnitude, of the nonzero entries are known. A subpattern of $\mathcal{A}$, say $\mathcal{B}$, is pattern where a nonzero entry from $\mathcal{A}$ may be ...
• #### Median Shapes ﻿

(2018)
In this paper, we generalized the variational definition of median numbers to median shapes. We represent shapes with currents and use flat norms as the distances between currents. Under this setting, the median shapes ...
• #### Boundary Measures and Cubical Covers of Sets in R^n ﻿

(2018)
The art of analysis involves the subtle combination of approximation, inequalities, and geometric intuition as well as being able to work at different scales. Even the restriction to sets in R^n affords us the opportunity ...
• #### MATHEMATICAL MODELING AND BAYESIAN PARAMETER ESTIMATION IN CANCER ﻿

(2018)
Recent works have highlighted the role of the differentiation of fibroblast into myofibroblast in cancer initiation and progression. Fibroblasts respond in a variety of ways to concentrations of activated transforming ...
• #### Stability Analysis, Convex Hulls of Matrix Powers and their Relations to P-matrices ﻿

(2018)
Invertibility of all convex combinations of an $n\times n$ matrix $A$ and the $n\times n$ identity matrix $I$ is equivalent to the real eigenvalues of $A$, if any, being positive. Moreover, invertibility of all matrices ...
• #### High School Student Representational Adaptivity and Transfer in Multiplying Polynomials ﻿

(2018)
While there is an extensive amount of research on representations for solving problems involving functions, there are few studies on high school student use of multiple representations for multiplying polynomials. This ...
• #### AN ENERGY-BASED INTERACTION MODEL FOR POPULATION OPINION DYNAMICS WITH TOPIC COUPLING ﻿

(2017)
Opinion dynamics, also called the opinion game, has gained a great deal of attention during past several decades. It tries to model and explain the evolution of opinions of people in a society. How individuals learn, how ...
• #### Eventual Cone Invariance ﻿

(2017)
If $K$ is a proper cone in $\RR^{n}$ some results in the theory of eventually (entrywise) nonnegative matrices have equivalent analogues in eventual $K$-invariance. We develop these analogues using the classical ...
• #### Studying and supporting the teaching practice of calculus teaching assistants ﻿

(2017)
Graduate teaching assistants (TAs) are an important group of math instructors whose practice deserves to be supported and studied. In this action research study, I lead a customized regimen of professional development ...
• #### Examining Student Agency in an Active-Learning Business Calculus Course ﻿

(2017)
This study explored student agency in an active-learning business calculus course. The lecture-style instructional practices typically used in this course at this institution allow few opportunities for students to interact ...
• #### On the computation of eigenvalues, spectral bounds, and Hessenberg form for matrix polynomials ﻿

(2016)
In this dissertation we focus on root-finding methods, such as Laguerre's method, for solving the polynomial eigenvalue problem. Serious consideration is given to the initial conditions and stopping criteria. Cost efficient ...
• #### Interior Point Algorithms for Stochastic Semidefinite Programming ﻿

(2016)
Two-stage stochastic semidefinite programming with recourse (SSDP) has been proposed and studied during the last 10 years, as a two-stage stochastic counterpart of semidefinite programming (SDP). To design efficient ...
• #### Portfolio Optimization on Jump Diffusion ﻿

(2016)
Portfolio optimization problem is an important research topic in financial applications. In this research, we focus on a consumption process and a terminal wealth problem. A portfolio including a riskless asset, a zero ...
• #### Identification and Establishment of Social and Sociomathematical Norms Associated with Mathematically Productive Discourse ﻿

(2016)
For some time, the mathematics education community has sought to involve students more actively in classroom mathematical discourse, but realizing this goal has been problematic. This study has two goals: the first is to ...
• #### Numerical Methods for American Option Pricing with Nonlinear Volatility ﻿

(2015)
Options are a fundamental and important type of financial derivatives with stocks as the underlying asset. Investors frequently trade options, making option pricing an important research area in both finance and applied ...
• #### First Collegiate Mathematics Grade and Persistence to Graduation in STEM ﻿

(2015)
This study explores the relationship between college students’ first mathematics course and persistence to graduation with a bachelor’s degree in a Scientific, Technical, Engineering, or Mathematical (STEM) field. Half of ...
• #### On alpha-critical graphs and their construction ﻿

(2015)
A graph G is alpha-critical (or removal-critical) if alpha(G-e)=alpha(G)+1 for all edges e in E(G), where alpha(G) is the vertex independence number of G. Similarly, a graph G is contraction-critical if alpha(G\setminus ...