Browsing Mathematics (Faculty of) by Title
Now showing items 891-910 of 2993
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The Enigma History and Mathematics
(University of Waterloo, 2016-10-25)In this thesis we look at the solution to the German code machine, the Enigma machine. This solution was originally found by Polish cryptologists. We look at the solution from a historical perspective, but most importantly, ... -
Entanglement Entropy in Quantum Gravity
(University of Waterloo, 2008-05-22)We study a proposed statistical explanation for the Bekenstein-Hawking entropy of a black hole in which entropy arises quantum-mechanically as a result of entanglement. Arguments for the identification of black hole entropy ... -
Entanglement in single-shot quantum channel discrimination
(University of Waterloo, 2018-08-30)Single-shot quantum channel discrimination is the fundamental task of determining, given only a single use, which of two known quantum channels is acting on a system. In this thesis we investigate the well-known phenomenon ... -
Entire Solutions to Dirichlet Type Problems
(University of Waterloo, 2007-08-02)In this thesis, we examined some Dirichlet type problems of the form: \begin{eqnarray*} \triangle u & = & 0\ {\rm in\ } \mathbb{R}^n \\ u & = & f\ {\rm on\ } \psi = 0, \end{eqnarray*} and we were particularly ... -
Entity Matching and Disambiguation Across Multiple Knowledge Graphs
(University of Waterloo, 2019-06-10)Knowledge graphs are considered an important representation that lie between free text on one hand and fully-structured relational data on the other. Knowledge graphs are a back-bone of many applications on the Web. With ... -
Entropic Matroids and Their Representation
(Multidisciplinary Digital Publishing Institute, 2019)This paper investigates entropic matroids, that is, matroids whose rank function is given as the Shannon entropy of random variables. In particular, we consider p-entropic matroids, for which the random variables each have ... -
Entropy and Graphs
(University of Waterloo, 2014-01-23)The entropy of a graph is a functional depending both on the graph itself and on a probability distribution on its vertex set. This graph functional originated from the problem of source coding in information theory and ... -
Entropy-based aggregate posterior alignment techniques for deterministic autoencoders and implications for adversarial examples
(University of Waterloo, 2020-08-27)We present results obtained in the context of generative neural models — specifically autoencoders — utilizing standard results from coding theory. The methods are fairly elementary in principle, yet, combined with the ... -
Entropy-Stable Positivity-Preserving Schemes for Multiphase Flows
(University of Waterloo, 2024-01-22)High-intensity focused ultrasound is a promising non-invasive medical technology that has been successfully used to ablate tumors, as well as in the treatment of other conditions. Researchers believe high-intensity focused ... -
Enumerating matroid extensions
(University of Waterloo, 2023-09-01)This thesis investigates the problem of enumerating the extensions of certain matroids. A matroid M is an extension of a matroid N if M delete e is equal to N for some element e of M. Similarly, a matroid M is a coextension ... -
Enumerating Query Plans via Conditional Tableau Interpolation
(University of Waterloo, 2023-04-21)Database query optimization studies the problem of finding equivalent and efficient query execution plans for user queries under schema constraints. Logic-based approaches to query optimization leverage automated theorem ... -
Enumeration of Factorizations in the Symmetric Group: From Centrality to Non-centrality
(University of Waterloo, 2011-04-25)The character theory of the symmetric group is a powerful method of studying enu- merative questions about factorizations of permutations, which arise in areas including topology, geometry, and mathematical physics. This ... -
Enumerative Applications of Integrable Hierarchies
(University of Waterloo, 2015-05-21)Countably infinite families of partial differential equations such as the Kadomtzev - Petviashvili (KP) hierarchy and the B-type KP (BKP) hierarchy have received much interest in the mathematical and theoretical physics ... -
Enumerative perspectives on chord diagrams
(University of Waterloo, 2022-10-07)The topic of this thesis is enumerating certain classes of chord diagrams, perfect matchings of the interval $\{1, 2, \ldots, 2n\}$. We consider hereditary classes of chord diagrams that are restricted to satisfy one of ... -
Epidemic Models with Pulse Vaccination and Time Delay
(University of Waterloo, 2011-08-22)In this thesis we discuss deterministic compartmental epidemic models. We study the asymp- totic stability of the disease-free solution of models with pulse vaccination campaigns. The main contributions of this thesis ... -
Equality of Number-Theoretic Functions over Consecutive Integers
(University of Waterloo, 2009-04-30)This thesis will survey a group of problems related to certain number-theoretic functions. In particular, for said functions, these problems take the form of when and how often they are equal over consecutive integers, n ... -
Equality Operators for Constant-weight Codewords with Applications in (Keyword) PIR
(University of Waterloo, 2021-09-21)Homomorphic encryption allows computation to be performed on data while in encrypted form. However, the computational overhead of a circuit that is run using homomorphic encryption depends on the number of multiplications ... -
Equiangular Lines and Antipodal Covers
(University of Waterloo, 2010-09-22)It is not hard to see that the number of equiangular lines in a complex space of dimension $d$ is at most $d^{2}$. A set of $d^{2}$ equiangular lines in a $d$-dimensional complex space is of significant importance in Quantum ... -
Equivalence of Queries with Nested Aggregation
(University of Waterloo, 2009-12-11)Query equivalence is a fundamental problem within database theory. The correctness of all forms of logical query rewriting—join minimization, view flattening, rewriting over materialized views, various semantic optimizations ... -
The Erdős Pentagon Problem
(University of Waterloo, 2018-12-20)The Erdős pentagon problem asks about the maximum number of copies of C_5 that one can find in a triangle-free graph. This problem was posed in 1984, but was not resolved until 2012. In this thesis, we aim to capture the ...