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,...
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....
Given graded C *-algebras A and B , we define the notion of an admissible pair ([straight phi], D ) for A and B . Associated to an admissible pair ([straight phi], D ) is an equivalence class of asymptotic morphisms from A to B . Under certain...
We describe a set of natural image statistics that are built upon two multi-scale image decompositions, the quadrature mirror filter pyramid decomposition and the local angular harmonic decomposition. These image statistics consist of first- and...
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...
This thesis contains some results concerning groupoid dynamical systems and crossed products. We introduce the notion of a proper groupoid dynamical system and of its generalized fixed point algebra. We show that our notion of proper groupoid...
Casimir effect. Zero-point field. Electric conductivity. Quantum electrodynamics.
The Casimir force arises from an alteration of boundary condition in vacuum and is often regarded as a manifestation of quantum zero point energy. Considerable progress has been made in the last decade with an impressive achievement of experimental...
This thesis explores practical and theoretical aspects of several privacy-providing technologies, including tools for anonymous web-browsing, verifiable electronic voting schemes, and private information retrieval from databases. State-of-art...
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...
Human locomotion -- Computer-assisted instruction. ; Real-time data processing. ; Human-computer interaction.
Teaching physical motions such as riding, exercising, swimming, etc. to human beings is hard. Coaches face difficulties in communicating their feedback verbally and cannot correct the student mid-action; teaching videos are two dimensional and...
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....
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...
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...
We start by introducing avoidance coupling of Markov chains, with an overview of existing results. We then introduce and motivate a new notion, uniform coupling. We show that the only Markovian avoidance coupling on a cycle is of this type, and...
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...
Arabidopsis -- Effect of metals on. ; Zinc -- Physiological transport. ; Iron -- Physiological transport. ; Plants -- Effect of iron on. ; Plants -- Effect of zinc on.
Iron and zinc deficiency commonly limit plant growth and crop yields. Furthermore, deficiencies in both of these micronutrients are common throughout the world, particularly in developing countries where people may only consume simple diets...
Despite great progress in object recognition techniques, there is a mismatch between traditional approaches and the characteristics of real world vision tasks. We highlight in particular, three closely related areas of mismatch: i) recognition...
Multiresolution image transformations have become commonplace tools for analyzing images for a number of applications, including enhancement and restoration. Powerful models for these applications have been developed in the transform domain of...
We examine variations of cops and robbers games on graphs. Our goals are to introduce some randomness into their study, and to estimate (expected) capture time. We show that a cop chasing a random walker can capture him in expected time n + o(n)....
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...
Molecular imaging of cancer features is a critical part of advancing better tools for oncology management and drug discovery, yet it is still evolving as a useful tool. Diffuse Fluorescence Tomography (FT) is one approach to molecular imaging, used...
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...
The multisubunit eukaryotic Mediator complex integrates diverse positive and negative gene regulatory signals and transmits them to the core transcription machinery. It is also involved in chromatin structure related epigenetic silencing through...
Operating systems and low-level applications are usually written in languages like C and assembly, which provide access to low-level abstractions. These languages have unsafe type systems that allow many bugs to slip by programmers. For example, in...
Optical tomography. ; Near infrared spectroscopy. ; Image analysis -- Mathematical models. ; Imaging systems -- Image quality -- Mathematical models. ; Image reconstruction -- Mathematical models. ; Least squares. Breast -- Tomography.
Diffuse optical tomography (DOT) has the potential to become a non-invasive and non-ionizing diagnostic imaging technique for breast cancer imaging. DOT uses near-infrared (NIR) light to illuminate the breast, generally through the use of fiber...
In the past decade, the use of ordinal patterns in the analysis of time series and dynamical systems has become an important tool. Ordinal patterns (otherwise known as a permutation patterns) are found in time series by taking n data points at...
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...