Browsing Combinatorics and Optimization by Title
Now showing items 338-357 of 434
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A quadratic programming approach to find faces in robust nonnegative matrix factorization
(University of Waterloo, 2017-08-29)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 ... -
Quadratically Dense Matroids
(University of Waterloo, 2020-07-08)This thesis is concerned with finding the maximum density of rank-$n$ matroids in a minor-closed class. The extremal function of a non-empty minor-closed class $\mathcal M$ of matroids which excludes a rank-2 uniform ... -
Quantum algorithms for searching, resampling, and hidden shift problems
(University of Waterloo, 2012-09-21)This thesis is on quantum algorithms. It has three main themes: (1) quantum walk based search algorithms, (2) quantum rejection sampling, and (3) the Boolean function hidden shift problem. The first two parts deal with ... -
Quantum Compression and Quantum Learning via Information Theory
(University of Waterloo, 2020-12-21)This thesis consists of two parts: quantum compression and quantum learning theory. A common theme between these problems is that we study them through the lens of information theory. We first study the task of visible ... -
Quantum Cost Models for Cryptanalysis of Isogenies
(University of Waterloo, 2019-05-01)Isogeny-based cryptography uses keys large enough to resist a far-future attack from Tani’s algorithm, a quantum random walk on Johnson graphs. The key size is based on an analysis in the query model. Queries do not ... -
Quantum independence and chromatic numbers
(University of Waterloo, 2019-08-28)In this thesis we are studying the cases when quantum independence and quantum chromatic numbers coincide with or differ from their classical counterparts. Knowing about the relation of chromatic numbers separation to the ... -
Quantum Information Processing with Adversarial Devices
(University of Waterloo, 2010-06-09)We consider several applications in black-box quantum computation in which untrusted physical quantum devices are connected together to produce an experiment. By examining the outcome statistics of such an experiment, and ... -
Quantum Random Access Codes with Shared Randomness
(University of Waterloo, 2009-05-22)We consider a communication method, where the sender encodes n classical bits into 1 qubit and sends it to the receiver who performs a certain measurement depending on which of the initial bits must be recovered. This ... -
Quantum Rejection Sampling
(University of Waterloo, 2015-01-21)Let H be a finite dimensional Hilbert space and ρ, σ ∈ D(H) be quantum states in H such that S(ρ||σ) is finite. In this thesis, we consider the following communication task involving two parties Alice and Bob. Suppose ... -
Quantum Speed-ups for Boolean Satisfiability and Derivative-Free Optimization
(University of Waterloo, 2014-04-21)In this thesis, we have considered two important problems, Boolean satisfiability (SAT) and derivative free optimization in the context of large scale quantum computers. In the first part, we survey well known classical ... -
Quantum State Transfer in Graphs
(University of Waterloo, 2014-08-13)Let X be a graph, A its adjacency matrix, and t a non-negative real number. The matrix exp(i t A) determines the evolution in time of a certain quantum system defined on the graph. It represents a continuous-time quantum ... -
Quantum Walks and Pretty Good State transfer on Paths
(University of Waterloo, 2019-08-23)Quantum computing is believed to provide many advantages over traditional computing, particularly considering the speed at which computations can be performed. One of the challenges that needs to be resolved in order to ... -
Quantum Walks on Oriented Graphs
(University of Waterloo, 2019-01-11)This thesis extends results about periodicity and perfect state transfer to oriented graphs. We prove that if a vertex a is periodic, then elements of the eigenvalue support lie in Z √∆ for some squarefree negative ... -
Quantum Walks on Strongly Regular Graphs
(University of Waterloo, 2010-08-30)This thesis studies the transition matrix of a quantum walk on strongly regular graphs. It is proposed by Emms, Hancock, Severini and Wilson in 2006, that the spectrum of a matrix based on the amplitudes of walks in the ... -
A Quick-and-Dirty Approach to Robustness in Linear Optimization
(University of Waterloo, 2013-01-07)We introduce methods for dealing with linear programming (LP) problems with uncertain data, using the notion of weighted analytic centers. Our methods are based on high interaction with the decision maker (DM) and try ... -
Ramsey-nice families of graphs
(Elsevier, 2018-08)For a finite family $\cF$ of fixed graphs let $R_k(\cF)$ be the smallest integer $n$ for which every $k$-coloring of the edges of the complete graph $K_n$ yields a monochromatic copy of some $F\in\cF$. We say that $\cF$ ... -
Rayleigh Property of Lattice Path Matroids
(University of Waterloo, 2015-09-22)In this work, we studied the class of lattice path matroids $\mathcal{L}$, which was first introduced by J.E. Bonin. A.D. Mier, and M. Noy in [\ref{Bonin 2002}]. Lattice path matroids are transversal, and $\mathcal{L}$ is ... -
Real equiangular lines and related codes
(University of Waterloo, 2020-01-24)We consider real equiangular lines and related codes. The driving question is to find the maximum number of equiangular lines in a given dimension. In the real case, this is controlled by combinatorial phenomena, and until ... -
Recognizing Even-Cycle and Even-Cut Matroids
(University of Waterloo, 2016-04-27)Even-cycle and even-cut matroids are classes of binary matroids that generalize respectively graphic and cographic matroids. We give algorithms to check membership for these classes of matroids. We assume that the matroids ... -
Recovery Guarantees for Graph Clustering Problems
(University of Waterloo, 2021-12-06)Graph clustering is widely-studied unsupervised learning problem in which the task is to group similar entities together based on observed pairwise entity interactions. This problem has applications in diverse domains such ...