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#### The Estimation of Stochastic Models in Finance with Volatility and Jump Intensity

(University of Waterloo, 2018-10-26)

This thesis covers the parametric estimation of models with stochastic volatility, jumps, and stochastic jump intensity, by FFT. The first primary contribution is a parametric minimum relative entropy optimal Q-measure ...

#### Linearized Stability of Partial Differential Equations with Application to Stabilization of the Kuramoto--Sivashinsky Equation

(Society for Industrial and Applied Mathematics, 2018-01-05)

Linearization is a useful tool for analyzing the stability of nonlinear differential equations. Unfortunately, the proof of the validity of this approach for ordinary differential equations does not generalize to all ...

#### The Erdős Pentagon Problem

(University of Waterloo, 2018-12-20)

The Erdős pentagon problem asks about the maximum number of copies of C_5 that one can find in a triangle-free graph. This problem was posed in 1984, but was not resolved until 2012. In this thesis, we aim to capture the ...

#### Ideal Clutters

(University of Waterloo, 2018-04-24)

Let E be a finite set of elements, and let C be a family of subsets of E called members. We say that C is a clutter over ground set E if no member is contained in another. The clutter C is ideal if every extreme point of ...

#### Enhanced Multi-Touch Gestures for Complex Tasks

(University of Waterloo, 2018-12-21)

Recent technological advances have resulted in a major shift, from high-performance notebook and desktop computers -- devices that rely on keyboard and mouse for input -- towards smaller, personal devices like smartphones, ...

#### Privately Constrained Testable Pseudorandom Functions

(University of Waterloo, 2018-09-20)

Privately Constrained Pseudorandom Functions allow a PRF key to be delegated to some
evaluator in a constrained manner, such that the key’s functionality is restricted with
respect to some secret predicate. Variants of ...

#### An Experimental Analysis of Multi-Perspective Convolutional Neural Networks

(University of Waterloo, 2018-05-16)

Modelling the similarity of sentence pairs is an important problem in natural language processing and information retrieval, with applications in tasks such as paraphrase identification and answer selection in question ...

#### The Capacitated Matroid Median Problem

(University of Waterloo, 2018-05-18)

In this thesis, we study the capacitated generalization of the Matroid Median Problem which is a generalization of the classical clustering problem called the k-Median problem. In the capacitated matroid median problem, ...

#### Finite Element Exterior Calculus with Applications to the Numerical Solution of the Green–Naghdi Equations

(University of Waterloo, 2018-08-09)

The study of finite element methods for the numerical solution of differential equations is one of the gems of modern mathematics, boasting rigorous analytical foundations as well as unambiguously useful scientific ...

#### Compatibility Problems of Probability Measures for Stochastic Processes

(University of Waterloo, 2018-07-27)

In this thesis, we address three topics in the area of compatibility for probability measures. By "compatibility", we mean the problems concerning the existence of random variables/stochastic processes which generate certain ...