Applied Mathematics Commons^™

Comparative Study Of Variable Selection Methods For Genetic Data, Anna-Lena Kubillus

Theses and Dissertations

Association studies for genetic data are essential to understand the genetic basis of complex traits. However, analyzing such high-dimensional data needs suitable feature selection methods. For this reason, we compare three methods, Lasso Regression, Bayesian Lasso Regression, and Ridge Regression combined with significance tests, to identify the most effective method for modeling quantitative trait expression in genetic data. All methods are applied to both simulated and real genetic data and evaluated in terms of various measures of model performance, such as the mean absolute error, the mean squared error, the Akaike information criterion, and the Bayesian information criterion. The results …

Dictionary-Based Data Generation For Fine-Tuning Bert For Adverbial Paraphrasing Tasks, Mark Anthony Carthon

Theses and Dissertations

Recent advances in natural language processing technology have led to the emergence of

large and deep pre-trained neural networks. The use and focus of these networks are on transfer

learning. More specifically, retraining or fine-tuning such pre-trained networks to achieve state

of the art performance in a variety of challenging natural language processing/understanding

(NLP/NLU) tasks. In this thesis, we focus on identifying paraphrases at the sentence level using

the network Bidirectional Encoder Representations from Transformers (BERT). It is well

understood that in deep learning the volume and quality of training data is a determining factor

of performance. The objective of …

Stability Analysis For The Equilibria Of A Monkeypox Model, Rachel Elizabeth Tewinkel

Theses and Dissertations

Monkeypox virus was first identified in 1958 and has since been an ongoing problem in Central and Western Africa. Although the smallpox vaccine provides partial immunity against monkeypox, the number of cases has greatly increased since the eradication of smallpox made its vaccination unnecessary. Although studied by epidemiologists, monkeypox has not been thoroughly studied by mathematicians to the extent of other serious diseases. Currently, to our knowledge, only three mathematical models of monkeypox have been proposed and studied. We present the first of these models, which is related to the second, and discuss the global and local asymptotic stability of …

Density Estimation For Lifetime Distributions Under Semi-Parametric Random Censorship Models, Carsten Harlass

Theses and Dissertations

We derive product limit estimators of survival times and failure rates for randomly right censored data as the numerical solution of identifying Volterra integral equations by employing explicit and implicit Euler schemes. While the first approach results in some known estimators, the latter leads to a new general type of product limit estimator. Plugging in established methods to approximate the conditional probability of the censoring indicator given the observation, we introduce new semi-parametric and presmoothed Kaplan-Meier type estimators. In the case of the semi-parametric random censorship model, i.e. the latter probability belonging to some parametric family, we study the strong …

An Exponential Time Differencing Scheme With A Real Distinct Poles Rational Function For Advection-Diffusion Reaction Equations, Emmanuel Owusu Asante-Asamani

Theses and Dissertations

A second order Exponential Time Differencing (ETD) scheme for advection-diffusion reaction systems is developed by using a real distinct poles rational function for approximating the underlying matrix exponential. The scheme is proved to be second order convergent. It is demonstrated to be robust for reaction-diffusion systems with non-smooth initial and boundary conditions, sharp solution gradients, and stiff reaction terms. In order to apply the scheme efficiently to higher dimensional problems, a dimensional splitting technique is also developed. This technique can be applied to all ETD schemes and has been found, in the test problems considered, to reduce computational time by …

Nonlocal Debye-Hückel Equations And Nonlocal Linearized Poisson-Boltzmann Equations For Electrostatics Of Electrolytes, Yi Jiang

Theses and Dissertations

Dielectric continuum models have been widely applied to the study of aqueous electrolytes since the early work done by Debye and Hückel in 1910s. Traditionally, they treat the water solvent as a simple dielectric medium with a permittivity constant without considering any correlation among water molecules. In the first part of this thesis, a nonlocal dielectric continuum model is proposed for predicting the electrostatics of electrolytes caused by any external charges. This model can be regarded as an extension of the traditional Debye Hückel equation. For this reason, it is called the nonlocal Debye-Hückel equation. As one important application, this …

Longitudinal Data Models With Nonparametric Random Effect Distributions, Hartmut Jakob Stenz

Theses and Dissertations

There is the saying which says you cannot see the woods for the trees. This

thesis aims to circumvent this unfortunate situation: Longitudinal data on

tree growth, as an example of multiple observations of similar individuals

pooled together in one data set, are modeled simultaneously rather than

each individual separately. This is done under the assumption that one

model is suitable for all individuals but its parameters vary following un-

known nonparametric random effect distributions. The goal is a maximum

likelihood estimation of these distributions considering all provided data and

using basis-spline-approximations for the densities of each distribution func-

tion …

Newton's Method Backpropagation For Complex-Valued Holomorphic Neural Networks: Algebraic And Analytic Properties, Diana Thomson La Corte

Theses and Dissertations

The study of Newton's method in complex-valued neural networks (CVNNs) faces many difficulties. In this dissertation, we derive Newton's method backpropagation algorithms for complex-valued holomorphic multilayer perceptrons (MLPs), and we investigate the convergence of the one-step Newton steplength algorithm for the minimization of real-valued complex functions via Newton's method. The problem of singular Hessian matrices provides an obstacle to the use of Newton's method backpropagation to train CVNNs. We approach this problem by developing an adaptive underrelaxation factor algorithm that avoids singularity of the Hessian matrices for the minimization of real-valued complex polynomial functions.

To provide experimental support for the …