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...
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...
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...
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...
Robot hands -- Design and construction. Robots -- Motion -- Mathematical models. Manipulators (Mechanism) -- Design and construction. Textile fabrics. Knots and splices. String.
Flexible objects are a challenge to manipulate. Their motions are hard to predict, and the high number of degrees of freedom makes sensing, control, and planning difficult. Additionally, they have more complex friction and contact issues than rigid...
Epilepsy is associated with cognitive impairments which often manifest as a higher prevalence of memory impairments. Memory impairments in patients with epilepsy may persist even with sufficient control of seizures, suggesting other factors may...
Metal ions confer structural stability and reactivity to a large number of proteins that use the amino acids histidine (His) and cysteine (Cys) to form stable metal-ligand complexes. The stability of metal-His and metal-Cys interactions and their...
Perceptual-motor learning -- Physiological aspects. ; Language acquisition -- Physiological aspects. ; Motor ability -- Physiological aspects. ; Knots and splices.
The studies presented in this dissertation explore several points of intersection between action perception and production within the human brain. One's ability to use perceptual information about another individual's actions to guide and inform...
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...
How the genome is shaped directly influences how it is expressed. In fact, the genome is organized at many different levels, each imparting specific regulation over transcription. Fundamental principles regulating genome organization are poorly...
Vibrio cholerae is a gram-negative bacterial pathogen that causes the severe diarrheal disease cholera. Several bacterial factors have been identified that are critical for V. cholerae intestinal colonization. The best characterized of these...
We present results from a modeling effort of simple shock phenomena in the Cygnus Loop and Cassiopeia A. Using multi-epoch MDM observations of a small, isolated cloud in the southwest region of the Cygnus Loop, we measure the velocity of the...
In the late 1960s, Ihara began work that led to the Ihara zeta function, a zeta function which is defined on a finite graph. This function is an interesting graph invariant which gives information on expansion properties of the graph. It also...
The human female reproductive tract (FRT) maintains a state of immune tolerance to spermatozoa and fetal allografts, while retaining the capacity to respond to a number of sexually transmitted infections (STIs) including human immunodeficiecy virus...
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...