In this thesis we look at several problems that lie in the intersection between combinatorial and multiplicative number theory. A common theme of many of these problems are estimates for and properties of the smooth numbers, those integers not...
Proteins -- Structure -- Data processing. Proteins -- Analysis -- Data processing. Nuclear magnetic resonance spectroscopy. Oligomers -- Analysis -- Data processing.
Symmetric homo-oligomers (protein complexes with similar subunits arranged symmetrically) play pivotal roles in complex biological processes such as ion transport and cellular regulation. Structure determination of these complexes is necessary in...
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...
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 this thesis, we study the dynamics of magnetic flows on compact nilmanifolds. Magnetic flows are generalizations of geodesic flows. They model the motion of a particle of unit mass and unit charge in a smooth manifold M in the presence of a...
The thesis is dedicated to the understanding and characterization of brittle compressive fracture of columnar S2 ice. The work quantifies the strength of fresh-water S2 ice and investigates its characteristic brittle failure modes under biaxial...
Laser speckle monitoring is a way to measure the motion of an optically rough surface without making physical contact to that surface. Laser speckle is inherently sensitive to motion in the plane of the reflecting surface, which gives speckle...
A variety of forensic methods have been developed to identify falsified photos, each unified by the ability to estimate and detect properties of a photo that are perturbed by forgery. There exist, however, many photos in which the required...
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...
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...
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...
Riemannian manifolds. Singularities (Mathematics). Laplacian operator. Spectral theory (Mathematics). Riemann surfaces. Curves on surfaces. Geometry
Historically, inverse spectral theory has been concerned with the relationship between the geometry and the spectrum of compact Riemannian manifolds, where spectrum means the eigenvalue spectrum of the Laplace operator as it acts on smooth...
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 processes affecting gas transport through the firn column are important to understand in order to accurately interpret climate records from ice cores. Historically, density measurements have been used to estimate open and closed porosity in the...
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...
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,...
Opinion dynamics is a complex procedure that entails a cognitive process when it deals with how a person integrates influential opinions to form revised opinion. Early research on opinion formation and social influence can be traced back to the...
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...
Proteins are ubiquitous in cells and are essential to a wide range of biological processes. Since existing proteins occupy only a small portion of the space of possible amino acid composition, understanding their sequence-structure-function...
Partially ordered sets. ; Convex polytopes. ; Representations of groups.
This thesis deals with geometric representations of ordered sets. In a geometric representation, each element of the ordered set is assigned a geometric object, with two elements incomparable in the ordered set if and only if the corresponding...
The effects of process parameters on the microstructural and textural evolution during directional recrystallization processing were investigated. Microstructural evolution during primary directional recrystallization of 80% cold-rolled, single...
A double-acceleration stage linear time of flight mass spectrometer (TOF MS) with Nd/YAG laser ablation cluster source was designed and constructed for cluster production, study and deposition. Cumulenic polycarbons SC n S ( n = 2-27) were...
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...
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...