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Dynamics and Optimal Control of the Growth of the Gut Microbiome with Varying Nutrient
(2023-07-27)
The human gut microbiome consists of all the microbes that make up the human intestinal tract, and many diseases are associated with certain microbial compositions in the gut. First, a mathematical model describing the ...
Intersections of Graph Theory and Combinatorial Commutative Algebra
(2023-07-27)
In this dissertation, we explore three problems in the fields of graph theory and combinatorial commutative algebra, and their intersections. First, we prove a higher upper bound for the slow coloring number of a certain ...
A Study of Space-time Fractional SPDE in Bounded Domains
(2023-07-24)
This dissertation considers space-time fractional stochastic heat equation on a regular bounded domain B in R^d, d ⩾ 1 with Dirichlet boundary condition:
∂βt ut(x) = −(−Δ)α2 ut(x) + I1−βt [λσ(ut(x)) ˙W (t, x)] for x ∈ B ...
Intersection Structures on Secants of Grassmannians
(2023-08-02)
Restricted secant varieties of Grassmannians are constructed from sums of points corresponding to k-planes with the restriction that their intersection has a prescribed dimension. This thesis calculates dimensions of ...
THEORY OF HIGH-DIMENSIONAL ℓ1-PENALIZED LOGISTIC REGRESSION
(2023-08-04)
n the setting where sample size n is sufficiently large relative to the number of features p, a classical result is that fitting a logistic model by means of maximum likelihood produces estimates that are approximately ...
Containment Relations and Line Graphs
(2023-08-07)
This dissertation studies several problems involving containment relations and line graphs. First, motivated by Reed and Seymour's 2004 result that Hadwiger's Conjecture holds for line graphs, we provide a partial result ...
Elementary Submodels of Function Spaces
(2023-08-11)
In this thesis we develop the now-standard tool of elementary submodels and apply the technique to topological function spaces. We show that many cardinal relations regarding function spaces hold in suitable models. ...
On Translative Packing Densities in $E^2$ and $E^3$
(2023-12-01)
The theory of packing and covering is an essential part of discrete geometry. In this dissertation we focus on and contribute to the knowledge on the densities of translative and lattice packings in $E^{2}$ and ...