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Fall 2024

Biswas, Amitakshar

Motivated by Elizabeth Meckes’ work on concentration inequalities using the group SO(n) (see [9]), this thesis explores the use of random rotations for detecting autocorrelation in time series data. Traditional tests like the Durbin Watson test assess autocorrelation by analyzing quadratic forms...

Fall 2010

Zhao, Wei

In this thesis, we investigate Riesz bases of wavelets and their applications to numerical solutions of elliptic equations. Compared with the finite difference and finite element methods, the wavelet method for solving elliptic equations is relatively young but powerful. In the wavelet Galerkin...

Fall 2018

Xu,Chuang

Approximation of probability measures, quantization, Kantorovich metric, Levy metric, Kolmogorov metric, Benford's Law, slowly changing sequences, asymptotic distribution, invariance property.","This thesis is based on four papers. The first two papers fall into the field of approximation of...

Fall 2024

Fan, Xinyi

In the field of sleep research, the quantitative analysis of electroencephalography (EEG) data acquired during sleep offers invaluable insights. However, the presence of artifacts in such data can severely distort analytical outcomes. Therefore, this study aims to develop an innovative artifact...

Fall 2020

Chidambaram, Nitin Kumar

In this thesis, we study some aspects of algebraic geometry that have had a significant influx of ideas from physics. The first part focuses on the Eynard- Orantin topological recursion and its variants as a theory of enumerative ge- ometry. We investigate the conjectural relationship between the...

Spring 2020

Riedler, Wolfgang

This thesis studies various aspects of the theory of vertex algebras. It has been shown that the moonshine module for Conway’s group C0 has close ties to the equivariant elliptic genera of sigma models with a K3 surface as target space. This is taken as a motivation to investigate conditions...

Fall 2024

Ding, Lei

This thesis presents a comprehensive exploration of social biases embedded within texts and Natural Language Processing (NLP) models. It develops innovative algorithms to evaluate and mitigate these biases, thereby enhancing the fairness and effectiveness of NLP applications. The initial phase of...

Fall 2023

Zhang, Junxi

Bayesian nonparametric models have gained increasing attention due to their flexibility in modelling natural and social phenomena and have been widely applied in machine learning, biology, social science and so on. Unlike traditional Bayesian parametric models, Bayesian nonparametric models place...

2003

Sarı, Bünyamin

Fall 2013

Chang, Zhihua

Given a conformal superalgebra A over an algebraically closed field k of characteristic zero, a twisted loop conformal superalgebra L based on A has a differential conformal superalgebra structure over the differential Laurent polynomial ring D. In this context, L is a Dm/D–form of A \otimes D...