• Data analysis of salmonid environmental DNA measurements obtained via controlled experiments and from several Pacific streams 

  Sneiderman, Robert (2021-01-13)

  Standard sampling and monitoring of fish populations are invasive and time- consuming techniques. The ongoing development of statistical techniques to analyze environmental DNA (eDNA) introduces a possible solution to these ...
• Generating function approach for the effective degree SIR Model 

  Manke, Kurtis (2021-01-05)

  The effective degree model has been applied to both SIR and SIS type diseases (those which confer permanent immunity and those which do not, respectively) with great success. The original model considers a large system ...
• The hot, magnetized, relativistic Vlasov Maxwell system 

  Preissl, Dayton (2021-01-04)

  This master thesis is devoted to the kinetic description in phase space of strongly magnetized plasmas. It addresses the problem of stability near equilibria for magnetically confined plasmas modeled by the relativistic ...
• Ramp function approximations of Michaelis-Menten functions in biochemical dynamical systems 

  Dore-Hall, Skye (2020-12-22)

  In 2019, Adams, Ehlting, and Edwards developed a four-variable system of ordinary differential equations modelling phenylalanine metabolism in plants according to Michaelis-Menten kinetics. Analysis of the model suggested ...
• Sarvate-beam group divisible designs and related multigraph decomposition problems 

  Niezen, Joanna (2020-09-30)

  A design is a set of points, V, together with a set of subsets of V called blocks. A classic type of design is a balanced incomplete block design, where every pair of points occurs together in a block the same number of ...
• Obstructions for local tournament orientation completions 

  Hsu, Kevin (2020-08-23)

  The orientation completion problem for a hereditary class C of oriented graphs asks whether a given partially oriented graph can be completed to a graph belonging to C. This problem was introduced recently and is a ...
• Directional constraint qualifications and optimality conditions with application to bilevel programs 

  Bai, Kuang (2020-07-18)

  The main purpose of this dissertation is to investigate directional constraint qualifications and necessary optimality conditions for nonsmooth set-constrained mathematical programs. First, we study sufficient conditions ...
• Enumerating digitally convex sets in graphs 

  Carr, MacKenzie (2020-07-18)

  Given a finite set V, a convexity, C, is a collection of subsets of V that contains both the empty set and the set V and is closed under intersections. The elements of C are called convex sets. We can define several different ...
• New and existing results on circular words 

  Johnson, Jesse T. (2020-05-08)

  Circular words, also known as necklaces, are combinatorial objects closely related to linear words. A brief history of circular words is given, from their early conception to present results. We introduce the concept of a ...
• Spectral gap and asymptotics for a family of cocycles of Perron-Frobenius operators 

  Horan, Joseph Anthony (2020-05-06)

  At its core, a dynamical system is a set of things and rules for how they change. In the study of dynamical systems, we often ask questions about long-term or average phenomena: whether or not there is an equilibrium for ...
• N-mixture models with auxiliary populations and for large population abundances 

  Parker, Matthew R. P. (2020-04-29)

  The key results of this thesis are (1) an extension of N-mixture models to incorporate the additional layer of obfuscation brought by observing counts from a related auxiliary population (rather than the target population), ...
• A population approach to systems of Izhikevich neurons: can neuron interaction cause bursting? 

  Xie, Rongzheng (2020-04-29)

  In 2007, Modolo and colleagues derived a population density equation for a population of Izhekevich neurons. This population density equation can describe oscillations in the brain that occur in Parkinson’s disease. ...
• C*-algebras from actions of congruence monoids 

  Bruce, Chris (2020-04-20)

  We initiate the study of a new class of semigroup C*-algebras arising from number-theoretic considerations; namely, we generalize the construction of Cuntz, Deninger, and Laca by considering the left regular C*-algebras ...
• Poincaré self-duality of A_θ 

  Duwenig, Anna (2020-04-09)

  The irrational rotation algebra A_θ is known to be Poincaré self-dual in the KK-theoretic sense. The spectral triple representing the required K-homology fundamental class was constructed by Connes out of the Dolbeault ...
• Limited broadcast domination 

  Yang, Feiran (2020-01-03)

  Let G = (V,E) be a graph and f be a function such that f : V -> {0,1,2,..., k}. Let V_f^+ = {v : f(v) > 0}. If for every vertex v not in V_f^+ there exists a vertex w in V_f^+ such that d(v,w) ≤ f(w) then f is called ...
• Cops, robber, and pre-calculus skills 

  Halliday, Felicia (2020-01-02)

  This thesis is partitioned into three parts: improving pre-calculus skills of students in an introductory calculus course, the game of Cops and Robber on oriented graphs, and the generalized game of Cops and Robber. In the ...
• Localized structure in graph decompositions 

  Bowditch, Flora Caroline (2019-12-20)

  Let v ∈ Z+ and G be a simple graph. A G-decomposition of Kv is a collection F={F1,F2,...,Ft} of subgraphs of Kv such that every edge of Kv occurs in exactlyone of the subgraphs and every graph Fi ∈ F is isomorphic to G. A ...
• Effect of equatorially trapped waves on the tropical cyclone drift 

  Hyungeun, Shin (2019-10-03)

  The movement of tropical cyclones (TC) is studied numerically based on a two-dimensional barotropic model, using a previously developed non-oscillatory balanced scheme. The model of TC used here takes an exponential form, ...
• Broadcast independence in graphs 

  Neilson, Linda (2019-08-29)

  The usual graph parameters related to independent and dominating sets can be adapted to broadcasts on graphs. We examine some possible definitions for an inde- pendent broadcast. We determine the minimum maximal and the ...
• On chordal digraphs and semi-strict chordal digraphs 

  Ye, Ying Ying (2019-08-29)

  Chordal graphs are an important class of perfect graphs. The beautiful theory surrounding their study varies from natural applications to elegant characterizations in terms of forbidden subgraphs, subtree representations, ...

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