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...
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 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...
Friction severely limits performance in precise positioning systems. This thesis investigates one possible approach to counter friction related performance losses, friction cancellation. In this method a friction observer is used to estimate...
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 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...
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...
Let K be the function field over a finite field of odd order, and let H be a definite quaternion algebra over K. If Α is an order of level M in H , we define theta series for each ideal I of Α using the reduced norm on H. Using harmonic analysis...
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...
The brain is a vastly interconnected information processing network. In humans, this network supports the rich mental space at the root of the imagination and enables many flexible cognitive abilities such as scientific and artistic creativity. How...
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...
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...
Chapter 1: Munchnones and mesoionic heterocycles The reactivity, regioselectivity, and synthetic applications of munchnones (1,3-oxazolium-5-olates) is a common theme which runs through Chapters 2-5. The definition, structure, and reactivity of...
Brain tissue mechanics are an important biomarker for neurological disorders, yet methods to obtain tissue information yield inconsistent conclusions. These techniques can be invasive or require excised tissue, where tissue function is altered from...
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...
PDZ protein-protein interaction domains recognize short linear motif (SLiM) sequences typically at the extreme C-terminus of a target protein. These domains often act as scaffolds, connecting target proteins to additional interaction and catalytic...
Gustatory pheromones regulate mating behaviors in Drosophila melanogaster and represent an important model for understanding how sensory stimuli can drive behavior. However, the genes and cells involved in pheromone detection have remained poorly...
Black-throated blue warbler -- Habitat. Black-throated blue warbler -- Behavior. Black-throated blue warbler -- Food. Black-throated blue warbler -- Nests.
Two experiments were designed to investigate the effects of brain damage on source monitoring. Source monitoring is the process of making decisions about the origins of memories. Previous research has demonstrated that source monitoring judgments...
Ice mechanics. Compressibility. Fracture mechanics. Strains and stresses. Brittleness.
This work describes the effect of triaxial compressive confinement on the strength of columnar S2 ice loaded under conditions leading to brittle failure. Cubes of columnar S2 ice were tested at -10 °C under triaxial (proportional) loading where...