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...
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,...
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...
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...
Since its discovery in the 1930's, the Cherenkov effect has been paramount in the development of high-energy physics research. It results in light emission from charged particles traveling faster than the local speed of light in a dielectric...
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...
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 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...
We start by introducing avoidance coupling of Markov chains, with an overview of existing results. We then introduce and motivate a new notion, uniform coupling. We show that the only Markovian avoidance coupling on a cycle is of this type, and...
Auroras -- Alaska -- Observations. Magnetospheric currents. Electric currents. Magnetic fields.
Auroral downward-current regions balance the upward currents of visible auroral arcs. FAST satellite data show conclusive evidence to confirm that these downward current regions (DCR) contain positive potential structures with diverging DC electric...
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...
Currently, the hypothesis that discrete auroral arcs are produced by fluxes of magnetospheric electrons accelerated along the ambient magnetic field into the ionosphere by linear/non-linear mechanisms associated with magnetic field-aligned currents...
This thesis presents data from ground camera observations of the aurora conducted from Alaska during the winters of 2005 through 2007. In conjunction with these camera observations, conjugate radar observations of the auroral ionosphere were...
The auroral zone is a rich source of natural radio emissions that can be observed in space and at ground-level. By studying these waves, scientists can gain insight into the plasma processes that generate them and use the near-Earth space...
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...
Digital integrated circuits -- Testing. Digital integrated circuits -- Testing -- Mathematical models. Digital integrated circuits -- Design and construction.
Computer input-output equipment. ; Computational grids (Computer systems). ; High performance computing. ; Electronic data processing -- Distributed processing.
High-performance computing increasingly occurs on computational grids composed of heterogeneous and geographically distributed systems of computers, networks, and storage devices that collectively act as a single virtual computer. A key challenge...
While Cherenkov emission was discovered more than eighty years ago, the potential applications of imaging this during radiation therapy have just recently been explored. With approximately half of all cancer patients being treated by radiation at...
Wnt/[beta]-catenin signaling directs metazoan development and is aberrantly activated in many cancers; however, effective inhibitors to treat Wnt-driven cancers have long been elusive. Following the recent discovery that the ADPribose polymerase...
Since their discovery in laboratory plasmas in the 1920s, Langmuir waves have been observed to be ubiquitous in plasma environments, particularly in space plasmas. From the greater solar wind to planetary foreshocks and the auroral ionosphere,...
Sudden infant death syndrome (SIDS) occurs when a sleeping infant experiences a challenge to cardiorespiratory homeostasis which it fails to overcome. Analyses of brain tissue from SIDS cases from around the world consistently show abnormalities in...
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...
The Wnt/β-catenin signaling pathway controls numerous biological processes from embryogenesis to adult homeostasis; aberrant Wnt signaling underlies a wide range of human diseases. In the absence of Wnt stimulation, a multiprotein “destruction...