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...
RNA binding proteins are fundamental components of crucial biological processes in all domains of life. The development of techniques to study RNA binding protein complexes is, therefore, broadly impactful. I employed multiple genome-wide...
The BCL2 family of proteins control intrinsic apoptosis at the mitochondria through a delicate balance of pro and anti-apoptotic proteins. Anti-apoptotic proteins are frequently relied upon by cancer cells, making them ideal targets for...
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...
Medical imaging methods have become increasingly important in diagnosing diseases and assisting therapeutic treatment. In particular, early detection of breast cancer is considered as a critical factor in reducing the mortality rate of women....
We prove the existence of nontrivial multiparameter isospectral deformations of metrics on the classical compact simple Lie groups SO (n) (n = 9, n ≥11), Spin(n) (n = 9, n ≥11), SU (n) (n ≥7), and Sp (n) (n ≥5). The proof breaks into three...
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...
For ordinary knots in R 3 , there are no degree one Vassiliev invariants. For virtual knots, however, the space of degree one Vassiliev invariants is infinite dimensional. We introduce a sequence of three degree one Vassiliev invariants of virtual...
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...
We study motion planning problems, finding trajectories that connect two configurations of a system, from two different perspectives: optimality and survivability. For the problem of finding optimal trajectories, we provide a model in which the...
Brain mapping via EEG activation is a useful tool of basic neuroscience, and has wide clinical applications as well. The mapping is achieved by means of Event Related Potentials (ERPs), task-related changes in EEG time series. The methodology of...
The main theme of this thesis is to investigate the origins of photosensitizer pharmacokinetic variability, how this pharmacokinetic variation affects photodynamic therapy (PDT), and to search for innovative strategies to reduce the...
Problem Statement Patient safety in the modern hospital is supported by multiple human and technological systems, and this type of high-risk/high-complexity domain requires multiple layers of protection against harm. This fault-tolerant approach is...
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...
I consider the problem of extending certain invariants of subsets of natural numbers to their equivalents for subsets of larger cardinals. The two specific questions I will address are the extension of the off-branch number [Special characters...
Digital video -- Analysis. Forensic sciences. Image processing -- Digital techniques.
We present new forensic tools that are capable of detecting traces of tampering in digital video without the use of watermarks or specialized hardware. These tools operate under the assumption that video contain naturally occurring properties which...
A metric structure on a set gives a concept of distance between any two elements of that set, and it induces a topology. In this thesis, we provide several ways to put a metric structure on the collection of CW complexes. We accomplish this by...
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...
This thesis considers the two special sensor networks for future sensor network design: mobile sensor networks and hybrid network of sensors and robots. To investigate two types of networks, we abstract two most important aspects that are ingrained...
Single cycle electromagnetic pulses have been difficult to experimentally generate and to theoretically analyze. With the recent development of terahertz systems based on near infrared femtosecond lasers it has become possible to perform single...
Coal combustion remains an important source of toxic metal emissions. Dilute concentrations and poor understanding of their chemistries hinders reduction of these emissions. This thesis examines the chemistry of the trace metals arsenic and mercury...
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...
Introduction -- Snow, Ice, and Permafrost Glossary: Introductory Note -- Glossary of Snow, Ice, and Permafrost Terms -- Outline of the Economic Geology of Alaska -- Physiography of Alaska -- Stratigraphy and Geologic History of Alaska --...