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...
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...
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....
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...
Arctic soils in the permafrost region store substantially more carbon than is contained in the atmosphere, and are undergoing rapid change associated with anthropogenic climate change. Soil decomposition is an important component of ecosystem...
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,...
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...
The retinoids exert potent growth and differentiation effects on normal, embryonic and neoplastic cells. Although retinoids are known to regulate gene transcription through activation of retinoid receptors, the direct target genes of retinoid...
Nuclear magnetic resonance spectroscopy -- Data processing. ; Proteins -- Analysis -- Mathematical models. ; Computer algorithms.
Our aim is to enhance high-throughput applications of Nuclear Magnetic Resonance (NMR) through the development of efficient computational methods that operate on sparse (minimal) sets of experimental NMR data. We have developed a family of four...
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...
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...
Cancer cells -- Proliferation -- Molecular aspects. Biological control systems. Cancer cells -- Growth -- Regulation. Breast -- Cancer -- Genetic aspects. p53 protein. Cell cycle. DNA damage. Cellular signal transduction. Carcinogenesis --...
Cells respond to DNA damage by activating signal transduction pathways that cause cell cycle arrest at checkpoints in G 1 , S, or G 2 phases of the cell cycle; this allows time for repair of damaged DNA. The G 1 checkpoint is dependent upon the...
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...
Brain -- Physiology -- Mathematical models.
Brain stem -- Effect of chemicals on.
Basal ganglia -- Physiology.
Understanding how the brain works remains one of the toughest problems in science, despite the progress in scientific technology available for its study. The difficulty lies in the fact that the brain is a dynamic system, while the body of facts...
Oligomers -- Structure -- Mathematical models. Nuclear magnetic resonance spectroscopy.
Medical Term: Nuclear Magnetic Resonance, Biomolecular.
Protein complexes play vital roles in the fundamental processes of life. In particular, homo-oligomers are involved in cell signaling, regulation, and transport. To make detailed studies of these symmetric proteins, they need to be discovered, and...