Browsing Mathematics (Faculty of) by Title
Now showing items 1943-1962 of 2993
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On the Representation Theory of Semisimple Lie Groups
(University of Waterloo, 2010-08-30)This thesis is an expository account of three central theorems in the representation theory of semisimple Lie groups, namely the theorems of Borel-Weil-Bott, Casselman-Osborne and Kostant. The first of these realizes all ... -
On the Role of Partition Inequalities in Classical Algorithms for Steiner Problems in Graphs
(University of Waterloo, 2006)The Steiner tree problem is a classical, well-studied, $\mathcal{NP}$-hard optimization problem. Here we are given an undirected graph $G=(V,E)$, a subset $R$ of $V$ of terminals, and non-negative costs $c_e$ for all ... -
On the roughness of paths and processes
(University of Waterloo, 2021-09-10)In recent years, a significant amount of the stochastic volatility literature has focused on modelling the ``roughness" or irregularity of the unobserved volatility time series and its effect on option pricing. In many ... -
On the Security of Leakage Resilient Public Key Cryptography
(University of Waterloo, 2012-04-30)Side channel attacks, where an attacker learns some physical information about the state of a device, are one of the ways in which cryptographic schemes are broken in practice. "Provably secure" schemes are subject to these ... -
On the Security of Some Variants of RSA
(University of Waterloo, 2007-05-10)The RSA cryptosystem, named after its inventors, Rivest, Shamir and Adleman, is the most widely known and widely used public-key cryptosystem in the world today. Compared to other public-key cryptosystems, such as elliptic ... -
On the Similarity of Operator Algebras to C*-Algebras
(University of Waterloo, 2006)This is an expository thesis which addresses the requirements for an operator algebra to be similar to a <em>C</em>*-algebra. It has been conjectured that this similarity condition is equivalent to either amenability ... -
On the Solution of the Hamilton-Jacobi Equation by the Method of Separation of Variables
(University of Waterloo, 2000)The method of separation of variables facilitates the integration of the Hamilton-Jacobi equation by reducing its solution to a series of quadratures in the separable coordinates. The case in which the metric tensor is ... -
On the Strongly Connected Components of Random Directed Graphs with Given Degree Sequences
(University of Waterloo, 2016-08-24)A strongly connected component of a directed graph G is a maximal subgraph H of G such that for each pair of vertices u and v in H, there is a directed path from u to v and a directed path from v to u in H. A strongly ... -
On the structure of invertible elements in certain Fourier-Stieltjes algebras
(University of Waterloo, 2021-08-27)Let $G$ be a locally compact group. The Fourier-Stieltjes and Fourier algebras, $B(G)$ and $A(G)$ are defined by Eymard to act as dual objects of the measure and group algebras, $M(G)$ and $L^1(G)$, in a sense generalizing ... -
On the Structure of Nonnegative Semigroups of Matrices
(University of Waterloo, 2009-08-18)The results presented here are concerned with questions of decomposability of multiplicative semigroups of matrices with nonnegative entries. Chapter 1 covers some preliminary results which become useful in the remainder ... -
On the Succinct Representation of Equivalence Classes
(University of Waterloo, 2014-12-17)Given a set of n elements that are partitioned into equivalence classes, we study the problem of assigning unique labels to these elements in order to support the query that asks whether the elements corresponding to two ... -
On the TVD property of second order methods for 2D scalar conservation laws
(arXiv, 2021-10-05)The total variation diminishing (TVD) property is an important tool for ensuring nonlinear stability and convergence of numerical solutions of one-dimensional scalar conservation laws. However, it proved to be challenging ... -
On the Utility of Adding An Abstract Domain and Attribute Paths to SQL
(University of Waterloo, 2018-04-30)Albeit its popularity today, RDBMS and the relational model still have many limitations. For example, one needs to pay premature attention to naming issues in the schema designing phase; and the syntax for conjunctive ... -
On Tolerant Testing and Tolerant Junta Testing
(University of Waterloo, 2020-07-08)Over the past few decades property testing has became an active field of study in theoretical computer science. The algorithmic task is to determine, given access to an unknown large object (e.g., function, graph, probability ... -
On Transcendence of Irrationals with Non-eventually Periodic b-adic Expansions
(University of Waterloo, 2010-05-18)It is known that almost all numbers are transcendental in the sense of Lebesgue measure. However there is no simple rule to separate transcendental numbers from algebraic numbers. Today research in this direction is about ... -
On Using Embeddings for Ownership Verification of Graph Neural Networks
(University of Waterloo, 2023-08-11)Graph neural networks (GNNs) have emerged as a state-of-the-art approach to model and draw inferences from large scale graph-structured data in various application settings such as social networking. The primary goal of a ... -
On Using Storage and Genset for Mitigating Power Grid Failures
(University of Waterloo, 2013-04-25)Although modern society is critically reliant on power grids, even modern power grids are subject to unavoidable outages due to storms, lightning strikes, and equipment failures. The situation in developing countries is ... -
On Vegh's Strongly Polynomial Algorithm for Generalized Flows
(University of Waterloo, 2014-05-22)This thesis contains an exposition of the new strongly polynomial algorithm for the generalized flow problem by Laszlo Vegh (2013). It has been a long-standing open question whether such an algorithm exists, until it was ... -
One-Dimensional Population Density Approaches To Recurrently Coupled Networks Of Neurons With Noise
(Society for Industrial and Applied Mathematics, 2015)Mean-field systems have been previously derived for networks of coupled, two-dimensional, integrate-and-fire neurons such as the Izhikevich, adapting exponential, and quartic integrate-and-fire, among others. Unfortunately, ... -
An Online Analytical System for Multi-Tagged Document Collections
(University of Waterloo, 2015-12-03)The New York Times Annotated Corpus and the ACM Digital Library are two prototypical examples of document collections in which each document is tagged with keywords and significant phrases. Such collections can be viewed ...