Browsing Mathematics (Faculty of) by Title
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A Framework for MachineAssisted Software Architecture Validation
(University of Waterloo, 2000)In this thesis we propose a formal framework for specifying and validating properties of software system architectures. The framework is founded on a model of software architecture description languages (ADLs) and uses ... 
A Framework for Records Management in Relational Database Systems
(University of Waterloo, 20080514)The problem of records retention is often viewed as simply deleting records when they have outlived their purpose. However, in the world of relational databases there is no standardized notion of a business record and its ... 
A Framework for Resource Allocation in Time Critical Dynamic Environments Based on Social Welfare and Local Search and its Application to Healthcare
(University of Waterloo, 20140214)This thesis provides an artificial intelligence approach for the problem of resource allocation in timecritical dynamic environments. Motivated by healthcare scenarios such as mass casualty incidents, we are concerned ... 
A Framework for Software Component Interface Specification and Analysis
(University of Waterloo, 2001)Although markets are emerging for commercial offtheshelf components (such as Sun JavaBeans), there are many barriers to widespread component adoption. This is due to the inherent `blackbox' nature of software ... 
A Framework for the Generation of Textures Representing TimeDependent Changes in the Appearance of Dust Layers
(University of Waterloo, 20220419)The perception of realism in computer generated images can be significantly enhanced by subtle visual cues. Among those, one can highlight the presence of dust on synthetic objects, which is often subject to temporal ... 
Frameworks for Quantum Algorithms
(University of Waterloo, 20140826)Due to the difficulty of constructing new quantum algorithms, frameworks that facilitate this construction are of great importance in quantum computing. These frameworks reduce the problem of coming up with a quantum ... 
Free semigroup algebras and the structure of an isometric tuple
(University of Waterloo, 20110628)An ntuple of operators V=(V_1,…,V_n) acting on a Hilbert space H is said to be isometric if the corresponding row operator is an isometry. A free semigroup algebra is the weakly closed algebra generated by an isometric ... 
FrictionalMonolith: A Monolithic Optimizationbased Approach for Granular Flow with ContactAware RigidBody Coupling
(Association for Computing Machinery, 2021)We propose FrictionalMonolith, a monolithic pressurefrictioncontact solver for more accurately, robustly, and efficiently simulating twoway interactions of rigid bodies with continuum granular materials or inviscid ... 
The Frobenius Problem in a Free Monoid
(University of Waterloo, 20090821)Given positive integers c1,c2,...,ck with gcd(c1,c2,...,ck) = 1, the Frobenius problem (FP) is to compute the largest integer g(c1,c2,...,ck) that cannot be written as a nonnegative integer linear combination of c1,c2,...,ck. ... 
From Astrophysics of Galaxies to Binary Black Hole Mergers: Theoretical Modelling of the GravitationalWave Bias Parameter
(University of Waterloo, 20230104)In the past few decades, the field of cosmology has become a fascinating field of study in physics. The computational advances and precision observational measurements such as Cosmic Microwave Background (CMB) measurements ... 
From Atoms to the Solar System: Generating Lexical Analogies from Text
(University of Waterloo, 2006)A <em>lexical analogy</em> is two pairs of words (<em>w</em><sub>1</sub>, <em>w</em><sub>2</sub>) and (<em>w</em><sub>3</sub>, <em>w</em><sub>4</sub>) such that the relation between <em>w</em><sub>1</sub> and <em>w</em>< ... 
From Fundamentals to Spectroscopic Applications of Density Functional Theory
(University of Waterloo, 20200529)Density functional theory (DFT) and its timedependent counterpart (TDDFT) are crucial tools in material discovery, drug design, biochemistry, catalysis, and nanoscience. However, despite its exact theoretical basis, ... 
From Gravity to Hopf Algebra Lattice Models
(University of Waterloo, 20191002)This thesis addresses three different problems related to quantum gravity. In the first problem we will discuss the two natural ways to encode gravity through geometric structures. One is the much acclaimed Einstein's ... 
Fully Automated Translation of BoxTalk to Promela
(University of Waterloo, 20110826)Telecommunication systems are structured to enable incremental growth, so that new telecommunication features can be added to the set of existing features. With the addition of more features, certain existing features may ... 
Functionvalued Mappings and SSIMbased Optimization in Imaging
(University of Waterloo, 20150827)In a few words, this thesis is concerned with two alternative approaches to imag ing, namely, Functionvalued Mappings (FVMs) and Structural Similarity Index Measure (SSIM)based Optimization. Briefly, a FVM is a mathematical ... 
Fundamental Limitations of SemiSupervised Learning
(University of Waterloo, 20090505)The emergence of a new paradigm in machine learning known as semisupervised learning (SSL) has seen benefits to many applications where labeled data is expensive to obtain. However, unlike supervised learning (SL), which ... 
A Fundamentally Topological Perspective on Graph Theory
(University of Waterloo, 2005)We adopt a novel topological approach for graphs, in which edges are modelled as points as opposed to arcs. The model of classical <i>topologized graphs</i> translates graph isomorphism into topological homeomorphism, ... 
Funding Liquidity and Limits to Arbitrage
(University of Waterloo, 20120614)Arbitrageurs play an important role in keeping market prices close to their fundamental values by providing market liquidity. Most arbitrageurs however use leverage. When funding conditions worsen they are forced to ... 
Future Sight: Dynamic Story Generation with Large Pretrained Language Models
(University of Waterloo, 20220823)Automated story generation has been an open problem in computing for many decades. Only with the recent wave of deep learning research have neural networks been applied to automated story generation tasks. Current deep ... 
A Fuzzylogic based Alert Prioritization Engine for IDSs: Architecture and Configuration
(University of Waterloo, 20080116)Intrusion Detection Systems (IDSs) are designed to monitor a networked environment and generate alerts whenever abnormal activities are detected. The number of these alerts can be very large making their evaluation by ...