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Now showing items 31-40 of 59

### On Functional Sure Independence Screening (fSIS) and Dynamic Spectral Featuring Extraction for Neuroscience Data

(2021-12-07)

This dissertation is composed of two parts. The first part introduces a methodology for high-dimensional functional variable screening and selection--the functional sure independent screening (fSIS). The fSIS method is an ...

### Maximal Sets of Hamilton Cycles in Complete Multipartite Graphs IV

(2021-12-06)

Finding the values of s for which there exists a maximal set of s edge-disjoint Hamilton cycles in the complete multipartite graph K_n^p has been considered in papers for over 20 years. This paper finally settles the problem ...

### 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 ...