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Now showing items 1-10 of 1157

#### Error-Tolerant Coding and the Genetic Code

(University of Waterloo, 2006)

The following thesis is a project in mathematical biology building upon the so-called "error minimization hypothesis" of the genetic code. After introducing the biological context of this hypothesis, I proceed to develop ...

#### Two- and Three-Dimensional Coding Schemes for Wavelet and Fractal-Wavelet Image Compression

(University of Waterloo, 2001)

This thesis presents two novel coding schemes and applications to both two- and three-dimensional image compression. Image compression can be viewed as methods of functional approximation under a constraint on the amount ...

#### Approximate Private Quantum Channels

(University of Waterloo, 2006)

This thesis includes a survey of the results known for private and approximate private quantum channels. We develop the best known upper bound for ε-randomizing maps,

**n**+ 2log(1/ε) +**c**bits required to ε-randomize an arbitrary**n**-qubit state by improving a scheme of Ambainis and Smith [5] based on small bias spaces [16, 3]. We show by a probabilistic argument that in fact the great majority of random schemes using slightly more than this many bits of key are also ε-randomizing. We provide the first known nontrivial lower bound for ε-randomizing maps, and develop several conditions on them which we hope may be useful in proving stronger lower bounds in the future....#### On the Role of Partition Inequalities in Classical Algorithms for Steiner Problems in Graphs

(University of Waterloo, 2006)

The Steiner tree problem is a classical, well-studied, $\mathcal{NP}$-hard optimization problem. Here we are given an undirected graph $G=(V,E)$, a subset $R$ of $V$ of terminals, and non-negative costs $c_e$ for all ...

#### A Statistical Analysis of the Aggregation of Crowdsourced Labels

(University of Waterloo, 2015-10-29)

Crowdsourcing, due to its inexpensive and timely nature, has become a popular method of collecting data that is difficult for computers to generate. We focus on using this method of human computation to gather labels for ...

#### Physically-based Simulation of Tornadoes

(University of Waterloo, 2005)

In this physically-based tornado simulation, the tornado-scale approach techniques are applied to simulate the tornado formation environment. The three-dimensional Navier-Stokes equations for incompressible viscous ...

#### A Web-based Statistical Analysis Framework

(University of Waterloo, 2007-04-26)

Statistical software packages have been used for decades to perform statistical analyses. Recently, the emergence of the Internet has expanded the potential for these packages. However, none of the existing packages have ...

#### Algorithms for the Optimization of Quantum Circuits

(University of Waterloo, 2013-08-30)

This thesis investigates techniques for the automated optimization of quantum circuits. In the first part we develop an exponential time algorithm for synthesizing minimal depth quantum circuits. We combine this with ...

#### On 2-crossing-critical graphs with a V8-minor

(University of Waterloo, 2014-05-22)

The crossing number of a graph is the minimum number of pairwise edge crossings in a drawing of a graph. A graph $G$ is $k$-crossing-critical if it has crossing number at least $k$, and any subgraph of $G$ has crossing ...

#### Genetic Programming for the Evolution of Functions with a Discrete Unbounded Domain

(University of Waterloo, 2013-05-16)

The idea of automatic programming using the genetic programming paradigm is a concept that has been explored in the work of Koza and several works since. Most problems attempted using genetic programming are finite in size, ...