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Skip to Search Results- 7Frei, Christoph (Mathematical and Statistical Sciences)
- 7Kong, Linglong (Mathematical and Statistical Sciences)
- 7Lewis, Mark (Mathematical and Statistical Sciences)
- 6Han, Bin (Mathematical and Statistical Sciences)
- 6Hillen, Thomas (Mathematical and Statistical Sciences)
- 6Mizera, Ivan (Mathematical and Statistical Sciences)
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Fall 2023
Determinantal point processes (DPPs) arise as important tools in various aspects of mathematics, such as stochastic processes, random matrices, and combinatorics. Over the last decade, DPPs have also been widely used in ma- chine learning community; they are especially popular in subset selection...
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Spring 2023
In present thesis I focus on development of method of market completions and its applications to various problems in pricing and hedging of contingent claims. Since theory of mathematical finance is well developed on complete markets, and corresponding solutions are well understood, method of...
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Fall 2009
Let $A1$ denote the first Weyl algebra over a field $K$ of characteristic 0; that is, $A1$ is generated over $K$ by elements $p$, $q$ that satisfy the relation $pq-qp=1$. One can view $A1$ as an algebra of differential operators by setting $q=X$, $p=d/dX$. The basic questions which are addressed...
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Dimensionality Reduction via the Johnson and Lindenstrauss Lemma: Mathematical and Computational Improvements
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In an increasingly data-driven society, there is a growing need to simplify high-dimensional data sets. Over the course of the past three decades, the Johnson and Lindenstrauss (JL) lemma has evolved from a highly abstract mathematical result into a useful tool for dealing with data sets of...
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Fall 2014
This thesis presents recent developments in direct numerical simulations of fluid-structure interaction occurring in biological systems, with particular interest in the modeling of particle deposition within the human respiratory system. Two numerical techniques are proposed. The first one is...
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Direction-Dependent Communication Mechanisms in Individual-Based Models of Collective Behaviour
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In this thesis, we study direction-dependent communication mechanisms in individual-based models (IBMs) of collective behaviour. Previously, direction-dependent communication mechanism were incorporated into a non-local hyperbolic PDE model for collective behaviour. The PDE model exhibits...
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Fall 2013
This thesis introduces a new temporally second-order accurate direction-splitting scheme for implicitly solving parabolic or elliptic partial differential equations in complex-shaped domains. While some other splitting schemes can be unstable in such domains, numerical evidence suggests that the...
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Spring 2016
A cell centered finite difference scheme for 2D parabolic problems on grids with a local refinement is presented. Peaceman and Rachford directional splitting is used in the discretization of time. The scheme is unconditionally stable and proven to be of second order convergence in time. Numerical...
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Fall 2015
This thesis concentrates on the construction of directional tensor product complex tight framelets. It uses a complex tight framelet filter bank in one dimension and the tensor product of the one-dimensional filter bank to obtain high-dimensional filter bank. It has a number of advantages over...