Problem Statement Patient safety in the modern hospital is supported by multiple human and technological systems, and this type of high-risk/high-complexity domain requires multiple layers of protection against harm. This fault-tolerant approach is...
We begin with a presentation of the current state of Poljak and Turzik's conjecture that a matroid is sticky if and only if it is modular as described in [5] and [1]. We show that all graphic, cographic, and regular matroids must satisfy the...
In this thesis, we present different approaches to tying knots using robots by enforcing different types of constraints. We attack the problem from three different directions; mechanical design, motion planning with simple control strategies, and...
In Chapter 2 we look at the distribution of permutation statistics in the context of pattern-avoiding permutations. The first part of this chapter deals with a recursively defined bijection of Robertson [37] between 123- and 132-avoiding...
In the Firefighter Problem, a fire starts at a vertex of a graph, and in discrete time units, it spreads from burned vertices to their neighbors, unless they are protected by one of the f firefighters that are deployed every turn. Once burned or...
Over the past decade, a pair of instructions called load-linked (LL) and store-conditional (SC) have emerged as the most suitable synchronization instructions for the design of lock-free algorithms. However, current architectures do not support...
Manifolds (Mathematics) Geodesics (Mathematics) Space and time.
We investigate weak and strong refocusing of light rays in a space-time and related concepts. A strongly causal space-time ( X^ n +1 , g ) is emphstrongly refocusing at x ∈ X if there is a point y ≠ x such that all null-geodesics through y pass...
A yearly breast contrast-MR scan is recommended to high-risk women because of MR's high sensitivity to breast tumors. However, breast contrast-MR yields a high number of false positives that lead to expensive and sometimes unnecessary biopsy...
Continual improvements to clinical breast imaging technologies have led to ever earlier detections and increasingly accurate localizations of female breast cancers. While these advancements have certainly improved the prognoses of many patients,...
As the visual effect and movie industries are striving for realism and high fidelity images, physically based lighting, global illumination, realistic materials, and highly tessellated geometry are gradually accepted and used in movie and game...
Thermodynamics, and the classic balance between entropy and enthalpy, provides a proverbial zoo of exotic phase behaviour that chemists can harness to create new materials out of simple liquids and polymers. The diversity of self-assembling...
The purpose of this thesis is to describe methods for detecting hidden crevasses on glaciers in Polar regions. Crevasses form in ice sheets as a result of forces imposed upon the brittle ice. The crevasses are hidden from view by bridges of soft...
Patients with cystic fibrosis (CF) are susceptible to respiratory tract infections at an early age; with the most frequent initial isolate being the Gram-positive pathogen Staphylococcus aureus. Subsequently, these patients become chronically...
We begin with a result on the refocussing of null geodesics in space-times. We show that all oriented refocussing 2-dimensional Lorentz manifolds are also strongly refocussing. We also introduce a theory of virtual Legendrian knots. We show that...
Recent years have witnessed a new class of monitoring applications that need to continuously collect information from remote data sources. Those data sources, such as web click-streams, stock quotes, and sensor data, are often characterized as...
This thesis contains material relating to two separate subjects. The first section determines when the C*-algebra affiliated to a directed graph has continuous trace. We use groupoid methods and the focus is on producing conditions on a graph that...
At the heart of computer games and computer generated films lies 3D content creation. A student wanting to learn how to create and edit 3D meshes can quickly find thousands of videos explaining the workflow process. These videos are a popular...
This project focuses on the development of research tools and methods that are used to study the relationship between neural activity and subsequent hemodynamic responses in the human brain. This relationship, referred to as neurovascular coupling,...
Diffuse optical imaging techniques can be combined with standard imaging technologies such as computed tomography (CT) and magnetic resonance (MR) imaging to allow measurement of spectroscopic signals pertaining to the molecular components of...
In this thesis, we consider several problems relating to cyclic subgroups of the group [mathematical equation]. Each element of [mathematical equation] has a unique representative in one of the two intervals [mathematical equation] and...
Magneto-spectroscopy is used to characterize the confinement properties of strain-induced quantum wires and dots. The wires and dots are low energy regions in an ordinary GaAs/AlGaAs quantum well that are formed when microscopic...
Hematopoietic stem cells (HSCs) are the cells that can give rise to all different lineages of differentiated/mature blood cells. HSCs are capable of self-renewal and maintaining the homeostasis of differentiated cells for specific functions. The...
Digital integrated circuits -- Testing. Digital integrated circuits -- Testing -- Mathematical models. Digital integrated circuits -- Design and construction.