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Now showing items 1-10 of 12

### Statistical Inference for High-Dimensional Regularized Huber Regression

(2023-04-18)

With the rapid advancement of technology, the amount of available data for extracting interesting insights and meaningful patterns has grown exponentially, resulting in a significant increase in the dimensionality of ...

### Existence of L_d(n) and ML_d(n,k)

(2023-04-28)

We are given an n x n array, ML(n,k), with integers n, d, k > 0 such that n=mk and each symbol in {0, ..., m-1} appears in each row and column of the ML(n,k) exactly k times. We aim to construct an ML_d(n,k) with the ...

### Embedding and Coloring Designs

(2023-05-04)

This dissertation focuses on two problems in design theory. Techniques from graph theory are frequently utilized and therefore the proofs may also be of interest to graph theorists.
The first problem focuses on ...

### Forbidding Monchromatic and Rainbow Cycles and Families of Cycles

(2023-05-01)

In this dissertation, we avoid certain cycles and families of cycles in complete graphs. Introduced by Axenovich and Choi \cite{2011NoteMonotonicity}, the mixed Ramsey spectrum, $\mrs{F}{H}$,
is the set of numbers $k$ ...

### Probability Equivalent Level of Value at Risk and Expected Shortfall

(2023-05-02)

Probability Equivalent Level of Value at Risk and Expected Shortfall (PELVE) is a novel risk measure proposed and explored by Li and Wang (2020), in [16]. It is motivated by the transition from 99% Value-at-Risk (VaR) to ...

### 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 ...