Recent Submissions

• Linear Forms in Logarithms and Fibonacci Numbers ﻿

The main work included in these pages is from a paper co-written by myself and my brother, Simon Earp-Lynch, under the supervision of Omar Kihel, pertaining to Diophantine triples of Fibonacci numbers. To go along with ...
• Diophantine Triples and Linear Forms in Logarithms ﻿

This is the thesis for my master's degree in mathematics which I undertook with Dr. Omar Kihel. Over the last couple of years I have studied number theory with the aim being to develop a broader understanding of the theory ...
• Upper Bounds for the Number of solutions for the Diophantine Equation $y^2=px(Ax^2-C), C \in {2, \pm 1, \pm 4}$ ﻿

A Diophantine equation is an equation of more than one variable where we are looking for strictly integer solutions. The purpose of this paper is to give a new upper bounds for the number of positive solutions for the ...
• Towards a New Algorithm for Event Recommendation System ﻿

We develop a recommendation algorithm for a local entertainment and ticket provider company. The recommender system predicts the score of items, i.e. event, for each user. The special feature of these events, which makes ...
• Dynamics in large scale networks ﻿

In this thesis we study the properties of two large dynamic networks, the competition network of advertisers on the Google and Bing search engines and the dynamic network of friend relationships among avatars in the ...
• Community Detection in Multi-Layer Networks ﻿

In the scope of the current thesis we review and analyse networks that are formed by nodes with several attributes. We suppose that different layers of communities are embedded in such networks, besides each of the layers ...
• Optimal and Robust Designs of Step-stress Accelerated Life Testing Experiments for Proportional Hazards Models ﻿

Accelerated life testing (ALT) is widely used to obtain reliability information about a product within a limited time frame. The Cox s proportional hazards (PH) model is often utilized for reliability prediction. My ...
• Backbone Colouring of Graphs ﻿

Consider an undirected graph G and a subgraph of G, H. A q-backbone k-colouring of (G,H) is a mapping f: V(G) {1, 2, ..., k} such that G is properly coloured and for each edge of H, the colours of its endpoints differ by ...
• Using PageRank Algorithm in Analyzing Dictionary Graphs and PageRank in Dynamic Graphs ﻿

In this thesis we are going to analyze the dictionary graphs and some other kinds of graphs using the PagerRank algorithm. We calculated the correlation between the degree and PageRank of all nodes for a graph obtained ...
• Prime Rational Functions and Integral Polynomials ﻿

(Brock University, 2015-01-05)
Let f(x) be a complex rational function. In this work, we study conditions under which f(x) cannot be written as the composition of two rational functions which are not units under the operation of function composition. ...
• A game-theoretic network formation model ﻿

(Brock University, 2014-07-23)
We study the dynamics of a game-theoretic network formation model that yields large-scale small-world networks. So far, mostly stochastic frameworks have been utilized to explain the emergence of these networks. On the ...
• Edge-choosability of Planar Graphs ﻿

(Brock University, 2013-09-26)
According to the List Colouring Conjecture, if G is a multigraph then χ' (G)=χl' (G) . In this thesis, we discuss a relaxed version of this conjecture that every simple graph G is edge-(∆ + 1)-choosable as by Vizing’s ...
• Rings, Group Rings, and Their Graphs ﻿

(Brock University, 2013-09-05)
We associate some graphs to a ring R and we investigate the interplay between the ring-theoretic properties of R and the graph-theoretic properties of the graphs associated to R. Let Z(R) be the set of zero-divisors of R. ...
• Acyclic 5-Choosability of Planar Graphs Without Adjacent Short Cycles ﻿

(Brock University, 2013-09-05)
The conjecture claiming that every planar graph is acyclic 5-choosable[Borodin et al., 2002] has been verified for several restricted classes of planargraphs. Recently, O. V. Borodin and A. O. Ivanova, [Journal of Graph ...
• Square Root Finding In Graphs ﻿

(Brock University, 2013-01-24)
Abstract: Root and root finding are concepts familiar to most branches of mathematics. In graph theory, H is a square root of G and G is the square of H if two vertices x,y have an edge in G if and only if x,y are of ...
• Response curves of deterministic and probabilistic cellular automata in one and two dimensions ﻿

(2012-04-02)
One of the most important problems in the theory of cellular automata (CA) is determining the proportion of cells in a specific state after a given number of time iterations. We approach this problem using patterns in ...
• The von Neumann Minimax Theorem and its relatives and a study of externality in on-line auctions ﻿

(2012-03-30)
This work consists of a theoretical part and an experimental one. The first part provides a simple treatment of the celebrated von Neumann minimax theorem as formulated by Nikaid6 and Sion. It also discusses its relationships ...
• Zero-sum problems in finite cyclic groups ﻿

(Brock University, 2009-01-28)
The purpose of this thesis is to investigate some open problems in the area of combinatorial number theory referred to as zero-sum theory. A zero-sequence in a finite cyclic group G is said to have the basic property if ...