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Now showing items 1-10 of 13

### New Statistical Learning for Next-Generation Functional Data and Spatial Data

(2022-03-18)

Advancements of modern technology have enabled the collection of sophisticated, high-dimensional data sets, such as 3D images, high dimensional data and other objects living in a functional space. As such, boosting the ...

### Hybrid Sampling for Uncertainty Quantification in Systems with High Dimensional Parameter Spaces

(2022-05-02)

Spatial models formulated as partial differential equations, often include space dependent parameters that are not readily estimable and are therefore uncertain.
There are two broad classes of methods for computing ...

### Evaluation of Statistical and Machine Learning Methods on Predicting One-way Shear Strength of Reinforced Concrete Beams

(2022-02-10)

It is a well-known fact that predicting shear strength of concrete beams is a very complex topic. The traditional approach is to assume that the shear strength is the sum of the concrete contribution (Vc) and the shear ...

### Mathematical Studies of Population Models in Stochastic Environments

(2022-04-28)

This dissertation is devoted to the study of population models in stochastic environments. We will investigate a two-species lottery model in non-stationary stochastic environment, an $N-$species lottery model in stationary ...

### Isoperimetric Properties of the Circle

(2022-05-03)

Jakob Steiner and Karl Weierstrass provided formal proofs of the isoperimetric property of the circle in the late 1830s. New mathematical tools, proof language, and concepts were needed to prove this rather obvious fact, ...

### Nonlocal Dispersal Equations with Almost Periodic Dependence

(2022-07-28)

Nonlocal dispersal equations are used to model the population dynamics of species that exhibit long-range dispersal mechanisms. This model of spatial spread is obtained by replacing the Laplacian in the usual reaction-diffusion ...

### Robust Estimation and Selection for Semi-Varying Coefficient Models

(2022-07-28)

Varying coefficient models have gained popularity in recent years due to their
exibility
in modeling more realistic problems. On the other hand, parametric models provide better
interpretability. Model selection can ...

### The Numerical Approximation of Blow-Up Times for Fractional Reaction-Diffusion Equations

(2022-07-28)

We investigate the numerical estimation of blow-up phenomena of the space fractional reaction-diffusion equation \[ \partial_t u +(-\Delta)^{\alpha/2}u=f(u), \quad x \in \Omega, t>0 \] with non-negative initial and Dirichlet ...

### An Introduction to Bernstein-Gel’fand-Gel’fand Correspondence

(2022-08-04)

This master's thesis serves as an introduction to the Bernstein-Gel'fand-Gel'fand correspondence first written in 1978. We shall cover some of the fundamental objects that the reader may not be familiar with, mainly tensor ...

### Color Trades on Graphs

(2022-08-03)

Edge-colorings of graphs have a rich history and are widely studied. Trade spectra of
graphs are relatively new and ripe for study. The color-trade-spectrum of a graph G is defined
to be the set of all t for which there ...