Browsing Theses by Title
Now showing items 2121-2140 of 15618
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Colour Vision Test for Railway Dispatchers
(University of Waterloo, 2009-04-29)Introduction Colour codes are used extensively in railways to convey specific information governing movement of trains and equipment on the track. One such task is the railway traffic control display that uses colour coded ... -
Colouring Cayley Graphs
(University of Waterloo, 2005)We will discuss three ways to bound the chromatic number on a Cayley graph. 1. If the connection set contains information about a smaller graph, then these two graphs are related. Using this information, we will ... -
Colouring Subspaces
(University of Waterloo, 2005)This thesis was originally motivated by considering vector space analogues of problems in extremal set theory, but our main results concern colouring a graph that is intimately related to these vector space analogues. ... -
Combination of Chemotherapy and Antiangiogenic Therapies: A Mathematical Modelling Approach
(University of Waterloo, 2009-09-08)A brief introduction to cancer biology and treatment is presented with a focus on current clinical advances in the delivery of chemotherapy and antiangiogenic therapies. Mathematical oncology is then surveyed with summaries ... -
Combination of Levene-Type Tests and a Finite-Intersection Method for Testing Trends in Variances
(University of Waterloo, 2009-04-30)The problem of detecting monotonic increasing/decreasing trends in variances from k samples is widely met in many applications, e.g. financial data analysis, medical and environmental studies. However, most of the tests ... -
Combinatorial Algorithms for Submodular Function Minimization and Related Problems
(University of Waterloo, 2015-05-19)Submodular functions are common in combinatorics; examples include the cut capacity function of a graph and the rank function of a matroid. The submodular function minimization problem generalizes the classical minimum cut ... -
Combinatorial and Probabilistic Approaches to Motif Recognition
(University of Waterloo, 2010-11-10)Short substrings of genomic data that are responsible for biological processes, such as gene expression, are referred to as motifs. Motifs with the same function may not entirely match, due to mutation events at a few of ... -
Combinatorial Approaches To The Jacobian Conjecture
(University of Waterloo, 2007-08-24)The Jacobian Conjecture is a long-standing open problem in algebraic geometry. Though the problem is inherently algebraic, it crops up in fields throughout mathematics including perturbation theory, quantum field theory ... -
Combinatorial Arithmetic on Elliptic Curves
(University of Waterloo, 2017-09-27)We propose a scalar multiplication technique on an elliptic curve, which operates on triples of collinear points. The computation of this operation requires a new approach to operation chains, with similarities to Montgomery ... -
Combinatorial aspects of braids with applications to cryptography
(University of Waterloo, 2015-08-25)This thesis is a collection of different results on braids, and draws connections between them. We first introduce braids by showcasing a number of equivalent ways of describing what a braid is, and how those representations ... -
Combinatorial Constructions for Transitive Factorizations in the Symmetric Group
(University of Waterloo, 2004)We consider the problem of counting <i>transitive factorizations</i> of permutations; that is, we study tuples (σ<i>r</i>,. . . ,σ1) of permutations on {1,. . . ,<i>n</i>} such that (1) the product ... -
Combinatorial Generalizations of Sieve Methods and Characterizing Hamiltonicity via Induced Subgraphs
(University of Waterloo, 2022-08-17)A sieve method is in effect an application of the inclusion-exclusion counting principle, and the estimation methods to avoid computing the explicit formula. Sieve methods have been used in number theory for over a hundred ... -
A Combinatorial Interpretation of Minimal Transitive Factorizations into Transpositions for Permutations with two Disjoint Cycles
(University of Waterloo, 2008-01-24)This thesis is about minimal transitive factorizations of permutations into transpositions. We focus on finding direct combinatorial proofs for the cases where no such direct combinatorial proofs were known. We give a ... -
Combinatorial Methods for Enumerating Maps in Surfaces of Arbitrary Genus
(University of Waterloo, 2016-06-10)The problem of map enumeration is one that has been studied intensely for the past half century. Early work on this subject included the works of Tutte for various types of rooted planar maps and the works of Brown for ... -
Combinatorial Problems in Compiler Optimization
(University of Waterloo, 2013-04-22)Several important compiler optimizations such as instruction scheduling and register allocation are fundamentally hard and are usually solved using heuristics or approximate solutions. In contrast, this thesis examines ... -
A Combinatorial Tale of Two Scattering Amplitudes: See Two Bijections
(University of Waterloo, 2022-01-07)In this thesis, we take a journey through two different but not dissimilar stories with an underlying theme of combinatorics emerging from scattering amplitudes in quantum field theories. The first part tells the tale ... -
Combinatorially Thin Trees and Spectrally Thin Trees in Structured Graphs
(University of Waterloo, 2023-12-19)Given a graph $G=(V,E)$, finding simpler estimates of $G$ with possibly fewer edges or vertices while capturing some of its specific properties has been used in order to design efficient algorithms. The concept of estimating ... -
Combinatorics and the KP Hierarchy
(University of Waterloo, 2009-10-01)The study of the infinite (countable) family of partial differential equations known as the Kadomtzev - Petviashvili (KP) hierarchy has received much interest in the mathematical and theoretical physics community for ... -
Combinatorics of Grassmannian Decompositions
(University of Waterloo, 2019-08-22)This thesis studies several combinatorially defined families of subsets of the Grassmannian. We introduce and study a family of subsets called “basis shape loci” associated to transversal matroids. Additionally, we study ... -
The combinatorics of the Jack parameter and the genus series for topological maps
(University of Waterloo, 2009-08-19)Informally, a rooted map is a topologically pointed embedding of a graph in a surface. This thesis examines two problems in the enumerative theory of rooted maps. The b-Conjecture, due to Goulden and Jackson, predicts ...