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Now showing items 1-10 of 141

#### On Excluded Minors for Even Cut Matroids

(University of Waterloo, 2007-01-22)

In this thesis we will present two main theorems that can be used to study
minor minimal non even cut matroids.
Given any signed graph we can associate an even cut matroid. However, given
an even cut matroid, there are ...

#### Variations on a Theme: Graph Homomorphisms

(University of Waterloo, 2013-08-30)

This thesis investigates three areas of the theory of graph homomorphisms: cores of graphs, the homomorphism order, and quantum homomorphisms.
A core of a graph X is a vertex minimal subgraph to which X admits a ...

#### Geometric Ramifications of the Lovász Theta Function and Their Interplay with Duality

(University of Waterloo, 2013-08-30)

The Lovasz theta function and the associated convex sets known as theta bodies are fundamental objects in combinatorial and
semidefinite optimization. They are accompanied by a rich duality theory and
deep connections ...

#### Probabilistic Choice Models for Product Pricing Using Reservation Prices

(University of Waterloo, 2007-01-22)

The problem of pricing a product line to maximize profits is an important challenge faced by many companies. To address this problem, we discuss four different probabilistic choice models that are based on reservation ...

#### Transmitting Quantum Information Reliably across Various Quantum Channels

(University of Waterloo, 2013-05-01)

Transmitting quantum information across quantum channels is an important task. However quantum information is delicate, and is easily corrupted. We address the task of protecting quantum information from an information ...

#### Algebraic Methods and Monotone Hurwitz Numbers

(University of Waterloo, 2012-09-21)

We develop algebraic methods to solve join-cut equations, which are partial differential equations that arise in the study of permutation factorizations. Using these techniques, we give a detailed study of the recently ...

#### On Efficient Semidefinite Relaxations for Quadratically Constrained Quadratic Programming

(University of Waterloo, 2007-05-18)

Two important topics in the study of Quadratically Constrained Quadratic Programming (QCQP) are how to exactly solve a QCQP with few constraints in polynomial time and how to find an inexpensive and strong relaxation bound ...

#### Convex relaxation for the planted clique, biclique, and clustering problems

(University of Waterloo, 2011-08-24)

A clique of a graph G is a set of pairwise adjacent nodes of G. Similarly, a biclique (U, V ) of a bipartite graph G is a pair of disjoint, independent vertex sets such that each node in U is adjacent to every node in V ...

#### Modularity and Structure in Matroids

(University of Waterloo, 2013-04-22)

This thesis concerns sufficient conditions for a matroid to admit one of two types of structural characterization: a representation over a finite field or a description as a frame matroid.
We call a restriction N of a ...

#### Implementing the Schoof-Elkies-Atkin Algorithm with NTL

(University of Waterloo, 2013-04-30)

In elliptic curve cryptography, cryptosystems are based on an additive subgroup of an elliptic curve defined over a finite field, and the hardness of the Elliptic Curve Discrete Logarithm Problem is dependent on the order ...