# Dissertations and Theses - Mathematics

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• (2019-09-13)
The Toda lattice is an important dynamical system studied in the theory of integrable systems. It is known that the Toda lattice is related to other integrable systems: the DST system and the XXX model. We will generalize ...

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• (2019-12-13)
In this thesis, we show how to deploy machine learning techniques such as Gaussian process regression to approximate the European basket option prices. For the underlying asset of European basket option, we assume it follows ...

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• (2019-12-06)
This dissertation develops a theory of networks of hybrid open systems and morphisms. This theory builds upon a framework of networks of continuous-time open systems as product and interconnection. We work out categorical ...

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• (2019-07-03)
Motivic Donaldson-Thomas (DT) invariant is a categorification of the classical DT invariant which contains more information of the local structure of a moduli space. In this thesis, we give three (partial) studies on the ...

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• (2019-07-10)
Fix a Weierstrass cubic curve $E$, and an element $\sigma$ in the Jacobian variety $\Jac E$ corresponding to the line bundle $\mathcal L_\sigma$. We introduce a space $\mathsf{RS}_{\sigma, n}(E, V)$ of pure 1-dimensional ...

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