Browsing Mathematics (Faculty of) by Title
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Proportionality and Fairness in Voting and Ranking Systems
(University of Waterloo, 20230818)Fairness through proportionality has received significant attention in recent social choice research, leading to the development of advanced tools, methods, and algorithms aimed at ensuring fairness in democratic institutions. ... 
Protein De novo Sequencing
(University of Waterloo, 20160513)In the proteomic mass spectrometry field, peptide and protein identification can be classified into two categories: database search that relies on existing peptide and protein databases and de novo sequencing with no prior ... 
Protein Loop Prediction by Fragment Assembly
(University of Waterloo, 20070119)If the primary sequence of a protein is known, what is its threedimensional structure? This is one of the most challenging problems in molecular biology and has many applications in proteomics. During the last three ... 
Protein Structure Elastic Network Models and the Rank 3 Positive Semidefinite Matrix Manifold
(University of Waterloo, 20190109)This thesis is a contribution to the study of protein dynamics using elastic network models (ENMs). An ENM is an abstraction of a protein structure where interatomic interactions are assumed to be modelled by a Hookean ... 
A protocol for constructing a domainspecific ontology for use in biomedical information extraction using lexicalchaining analysis
(University of Waterloo, 20070119)In order to do more semanticsbased information extraction, we require specialized domain models. We develop a hybrid approach for constructing such a domainspecific ontology, which integrates key concepts from the ... 
The ProuhetTarryEscott problem
(University of Waterloo, 20130115)Given natural numbers n and k, with n>k, the ProuhetTarryEscott (PTE) problem asks for distinct subsets of Z, say X={x_1,...,x_n} and Y={y_1,...,y_n}, such that x_1^i+...+x_n^i=y_1^i+...+y_n^i\] for i=1,...,k. ... 
Providing Freshness for Cached Data in Unstructured PeertoPeer Systems
(University of Waterloo, 20130417)Replication is a popular technique for increasing data availability and improving perfor mance in peertopeer systems. Maintaining freshness of replicated data is challenging due to the high cost of update management. ... 
Proving Properties of Fibonacci Representations via Automata Theory
(University of Waterloo, 20240122)In this work, we introduce a novel framework for mechanically testing the completeness and unambiguity of Fibonaccibased representations via automata theory. We call a representation (or a number system) complete and ... 
PRSONA: Private Reputation Supporting Ongoing Network Avatars
(University of Waterloo, 20211209)Trust and usergenerated feedback have become increasingly vital to the normal functioning of the modern internet. However, deployed systems that currently incorporate such feedback do not guarantee users much in the way ... 
PStorM: Profile Storage and Matching for FeedbackBased Tuning of MapReduce Jobs
(University of Waterloo, 20130102)The MapReduce programming model has become widely adopted for large scale analytics on big data. MapReduce systems such as Hadoop have many tuning parameters, many of which have a significant impact on performance. The map ... 
PUPy: A Generalized, Optimistic Context Detection Framework
(University of Waterloo, 20210428)In modern life, the usage of smart devices like smartphones and laptops that allow for access to information, communication with friends and colleagues and other indispensable services has become ubiquitous. People have ... 
Pure Pairs VI. Excluding an Ordered Tree.
(Society for Industrial and Applied Mathematics Journal on Discrete Mathematics, 202201)A pure pair in a graph G is a pair (Z1,Z2) of disjoint sets of vertices such that either every vertex in Z1 is adjacent to every vertex in Z2, or there are no edges between Z1 and Z2. With Maria Chudnovsky, we recently ... 
Pure pairs. I. Trees and linear anticomplete pairs
(Elsevier, 20201202)The ErdősHajnal conjecture asserts that for every graph H there is a constant c > 0 such that every graph G that does not contain H as an induced subgraph has a clique or stable set of cardinality at least Gc. In this ... 
Pure pairs. II. Excluding all subdivisions of a graph
(Springer Nature, 20210601)We prove for every graph H there exists ɛ > 0 such that, for every graph G with G≥2, if no induced subgraph of G is a subdivision of H, then either some vertex of G has at least ɛG neighbours, or there are two disjoint ... 
Pure pairs. III. Sparse graphs with no polynomialsized anticomplete pairs
(Wiley, 202011)A graph is Hfree if it has no induced subgraph isomorphic to H, and G denotes the number of vertices of G. A conjecture of Conlon, Sudakov and the second author asserts that:  For every graph H, there exists ∈ > 0 ... 
Purely topdown software rebuilding
(University of Waterloo, 20070122)Software rebuilding is the process of deriving a deployable software system from its primitive source objects. A build tool helps maintain consistency between the derived objects and source objects by ensuring that all ... 
A PuzzleBased Synthesis Algorithm For a Triple Intersection of Schubert Varieties
(University of Waterloo, 20100129)This thesis develops an algorithm for the Schubert calculus of the Grassmanian. Specifically, we state a puzzlebased, synthesis algorithm for a triple intersection of Schubert varieties. Our algorithm is a reformulation ... 
qdeformed LQG in three dimensional spacetime
(University of Waterloo, 20220823)Loop quantum gravity (LQG) is a canonical, backgroundindependent and nonperturbative approach to quantum gravity. This thesis is devoted to studying threedimensional (3D) quantum gravity with a nonvanishing cosmological ... 
Quadratic Hedging with Margin Requirements and Portfolio Constraints
(University of Waterloo, 20100428)We consider a meanvariance portfolio optimization problem, namely, a problem of minimizing the variance of the ﬁnal wealth that results from trading over a ﬁxed ﬁnite horizon in a continuoustime complete market in the ... 
A quadratic programming approach to find faces in robust nonnegative matrix factorization
(University of Waterloo, 20170829)Nonnegative matrix factorization (NMF) is a popular dimensionality reduction technique because it is easily interpretable and can discern useful features. For a given matrix M (dimension n x m) whose entries are nonnegative ...