Topological graph theory. Aperiodicity. Paths and cycles (Graph theory)
The condition ""every cycle has an entry"" first appeared in the literature in Kumjian, Pask, and Raeburn's paper on Cuntz-Krieger algebras of directed graphs, where it was called Condition (L). It provides a necessary condition for simplicity of...
We present a number of findings concerning groupoid dynamical systems and groupoid crossed products. The primary result is an identification of the spectrum of the groupoid crossed product when the groupoid has continuously varying abelian...
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...
We study the bijective combinatorics of reduced words. These are fundamental objects in the study of Coxeter groups. We restrict our focus to reduced words of permutations and signed permutations. Our results can all be situated within the context...
This thesis constitutes the first steps in the author's program to investigate the question of when a homotopy of 2-cocycles Ï‰ = {Ï‰[subscript t]}[subscript tâˆŠ[0,1]] on a locally compact Hausdorff groupoid Æ“ induces an isomorphism of the...
The focus of this thesis is the study of nuclearity and exactness for groupoid crossed product C*-algebras. In particular, we present generalizations of two well-known facts from group dynamical systems and crossed products to the groupoid setting....
In the past few years there has been a tremendous growth in the usage of digital images. Users can now access millions of photos, a fact that poses the need of having methods that can efficiently and effectively search the visual information of...
From deciding what to eat first or what stock to invest in, the order in which we prefer to experience events and the amount of risk we are willing to undertake are factors that influence our choices. However, the mechanisms underlying order and...
Quantitative Risk Analysis of Computer Networks (QSRA) addresses the problem of risk opacity of software in networks. It allows risk managers to get a detailed and comprehensive snapshot of the constitutive software on the network, assess its risk...
Information retrieval -- Mathematical models. ; Electronic information resource searching. ; Computer algorithms. ; Decision making -- Data processing. ; Mathematical optimization.
This thesis presents a unified method for simultaneous solution of three problems in Information Retrieval--metasearch (the fusion of ranked lists returned by retrieval systems to elicit improved performance), efficient system evaluation (the...
The problem of moving rigid bodies efficiently is of particular interest in robotics because the simplest model of a mobile robot or of a manipulated object is often a rigid body. Path planning, controller design and robot design may all benefit...
Earlier work has suggested that various neurological or neuropsychiatric disorders may result in characteristic spatial patterns in brain activation, potentially allowing their detection from maps of brain activity under different conditions....
Clinical medicine -- Decision making. ; Medical informatics. ; Patient participation. ; Osteoarthritis -- Treatment. ; Knee -- Diseases -- Treatment. ; Decision Making. ; Decision Support Techniques.
Problem Statement. Effective patients' decision aids (PtDAs) help patients understand clinical information and reduce decisional conflict. PtDAs that also explicitly provide guidance through four """"Deliberative Steps"""" may achieve additional...
Polynomials. Finite fields (Algebra). Algebraic functions. Number theory.
The ring of univariate polynomials over a finite field shares many foundational arithmetic properties with the ring of rational integers. This similarity makes it possible for many problems in elementary number theory to be translated 'through the...
A nocturnal activity pattern is central to almost all hypotheses on the adaptive origins of primates but this view has been challenged recently on the basis of variation in the cone opsin genes of nocturnal primates. The diversity among primates in...
This thesis centers around a generalization of the classical discrete Fourier transform. We first present a general diagrammatic approach to the construction of efficient algorithms for computing the Fourier transform of a function on a finite...
The performance of machine learning algorithms largely depends on data representation. As a critical step in machine learning, representation learning (feature learning) learns a transformation of training data to give a new representation that can...
'Orthogonal modular forms are algebraic modular forms arising from lattices in quadratic spaces. In this thesis, we define orthogonal modular forms, establish their basic properties, and then apply them to a case of ternary quadratic spaces to...
There are no Vassiliev invariants of degree one for classical knots. A. Henrich proved the existence of a sequence of three Vassiliev invariants of degree one for virtual knots. The invariants get stronger and stronger, and the final invariant is...
'The control of waves using periodic structures is crucial for modern optical, electromagnetic and acoustic devices such as diffraction gratings, filters, photonic crystals, solar cells, sensors, and absorbers. We present a high-order accurate...
Networks that model relationships in the real world have attracted much attention in the past few years. The "link prediction problem" plays a central role in the network area. In this thesis, we explore the link prediction problem in a...
In this thesis we develop a theory of Fourier analysis and fast Fourier transforms (FFTs) for finite inverse semigroups. Our results generalize results in the theory of Fourier analysis for finite groups. There is a general method for generating...
The recognition of foreign peptides by MHC (Major Histocompatibility Complex) proteins is a critical step in the immune response mounted by higher vertebrates against pathogens. MHC proteins have many allelic variants, each recognizing different...
Modern distributed systems scatter sensors, storage, and computation throughout the environment. Ideally these devices communicate and share resources, but there is seldom motivation for a device''s owner to yield control to another user. We...
This thesis is divided into 2 parts. In the first part of the thesis, we describe a software based approach to speeding up the Magnetic Resonance Imaging modality. In the second part of the thesis, we describe Significance Tree Quantization, which...
Siegel domains. Modular groups. Hecke algebras. Forms
In the 1960s Satake proved the existence of an isomorphism between the local Hecke algebra and the ring of polynomials invariant under the action of the signed permutation group W n (the Weyl group associated to Sp n over a local field)....
Coronary artery bypass graft (CABG) surgery is a leading treatment option for extending and/or improving the quality of life for patients suffering from heart disease. While we have witnessed improvements in mortality and morbidity secondary to...
Most current multiprocessor file systems are designed to use multiple disks in parallel, using the high aggregate bandwidth to meet the growing I/O requirements of parallel scientific applications. Most multiprocessor file systems provide...