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- 2Department of Biological Sciences
- 2Department of Mechanical Engineering
- 1Department of Civil and Environmental Engineering
- 1Department of Computing Science
- 1Department of Public Health Sciences
- 7Frei, Christoph (Mathematical and Statistical Sciences)
- 7Hillen, Thomas (Mathematical and Statistical Sciences)
- 7Kong, Linglong (Mathematical and Statistical Sciences)
- 7Lewis, Mark (Mathematical and Statistical Sciences)
- 6Han, Bin (Mathematical and Statistical Sciences)
- 6Kashlak, Adam (Mathematical and Statistical Sciences)
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Spring 2015
For a smooth projective variety defined over a number field, Beilinson (and independently Bloch) constructed a `height' pairing under very reasonable assumptions and with a number of conjectural properties. A folklore conjecture related to this pairing states that the rational Griffiths...
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Fall 2021
Topological Recursion began its life as a series of recursive equations aimed at solving constraints which occur in matrix models of Quantum Field Theory. After its inception, Topological Recursion was given a more abstract formulation in terms of Quantum Airy Structures and has since been of...
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Fall 2019
One of the main difficulties in extending Macdonald’s theory of spherical functions from p-adic Chevalley groups to p-adic Kac-Moody groups is the absence of Haar measure in the infinite dimensional case. Related to this problem is the question of how to generalize the integral defining...
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Fall 2013
In this thesis, two robust and efficient methods of estimation are examined in dose-response studies context. In particular, we investigate the minimum Hellinger distance estimation and symmetric chi-squared distance methods of estimation. We support our theoretical results with extensive finite...
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Spring 2016
This thesis contains the following three parts: \egin{description} \item[Part 1(Chapters 1-5):] Spherical $h$-harmonic analysis. \item[Part 2:] Reverse H\"{o}lder's inequality for spherical harmonics. \item[Part 3:] Multivariate Lagrange and Hermite approximation and pointwise limits...
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Fall 2012
The main goal of this thesis is to explore various applications of persistent homology in statistical analysis of point-cloud data. In the introduction, after a brief historical overview, we provide some of the underlying concepts of persistence. Starting from Chapter 2 the focus is on analysis...
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Fall 2021
Risk can be decomposed along two dimensions: risk allocation and risk attribution. On the one hand, the total risk of a company can be allocated to its divisions, using that the company’s profit/loss is the sum of the divisions’ profits/losses. On the other hand, risk is attributed to risk...