A new algorithm is presented which uses maximum likelihood (ML) estimation and convex constraints to restore edge information in a robust and accurate way for microscope images. The convex constraints are spatially variant bounds on the image...
Protein complexes play vital roles in cellular processes within living organisms. They are formed by interactions between either different proteins (hetero-oligomers) or identical proteins (homo-oligomers). In order to understand the functions of...
Goldman and Turaev constructed a Lie bialgebra structure on the free Z-module generated by free homotopy classes of loops on an oriented surface. Turaev conjectured that the cobracket of A is zero if and only if A is a power of a simple class. Chas...
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...
In this thesis we study 1=k-geodesics, those closed geodesics that minimize on any subinterval of length L=k, where L is the length of the geodesic. These curves arise as critical points of the uniform energy, a function introduced in Morse theory...
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...
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....
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...
Motivated by quantum mechanics and geometric optics, it is a long-standing problem whether the length spectrum of a compact Riemannian manifold can be recovered from its Laplace spectrum. One route to proving that the length spectrum depends on the...
Emergency medical response requires timely and efficient assessment and treatment of casualties. Mass casualty situations, in particular, strain the resources of emergency responders, prompting the need for a well-organized, effective, automated...
In image-guided neurosurgery, preoperative magnetic resonance images (pMR) are typically used intraoperatively for neuronavigation. The accuracy of image guidance using preoperative images can be significantly compromised by intraoperative brain...
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,...
Lung cancer is the leading cause of cancer-related death in the USA and worldwide causing 160,000 and 1.5 million deaths per year, respectively. Due to the late stage of diagnosis, poor efficacy of chemotherapies (targeted and pleiotropic), and...
We present new forensic tools that are capable of detecting traces of tampering in digital images without the use of watermarks or specialized hardware. These tools operate under the assumption that images contain natural properties from a variety...
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...
Breast cancer is the most common cancer in women. The discovery of breast tumor subtypes and the subsequent development of treatments aimed at them has allowed a reduction in the mortality of breast cancer. However, tumors with similar...
Annual screening mammograms are recommended for all women above 40 years of age for early detection of breast cancer, and are known to improve cancer mortality rates. However, mammography is hampered by low sensitivity and a high rate of false...
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...
Internet -- Security measures. Public key infrastructure (Computer security). Digital signatures. Peer-to-peer architecture (Computer networks) -- Security measures.
The Internet has become a virtual place where people not only operate in isolation but also interact with other Internet users. Collaborative systems are becoming more popular. Applications now being introduced could provide better remote education...
Pseudomonas aeruginosa is a virulent opportunistic pathogen that is frequently cultured from infectious sites, and is estimated to cause ~12% of nosocomial infections worldwide [1]. P. aeruginosa infections occur in a majority of adults with 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....
Gene set testing has become a critical tool for interpreting the results of high-throughput genomic experiments. Despite the development of robust statistical methods and extensive gene set collections, however, the results from gene set testing...
Increased fetal hemoglobin (HbF) expression is beneficial for [beta]-hemoglobinopathy patients; however, most inducing agents do not possess the ideal combination of efficacy, safety and availability. Better understanding the mechanisms involved in...
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...
How is concrete conceptual information represented in the brain? Little is known about the neural organization for details of concrete objects when presented as words. The goal of the first two studies was to investigate this. In the third study,...
For many scientific applications, the data set cannot entirely fit in main memory. The data must reside out-of-core, i.e., on parallel disks. For many basic data-movement operations such as permuting, if the programmer does not design efficient...