Heegaard diagrams and surgery descriptions for twisted face-pairing 3-manifolds

The twisted face-pairing construction of our earlier papers gives an efficient way of generating, mechanically and with little effort, myriads of relatively simple face-pairing descriptions of interesting closed 3-manifolds. The corresponding description in terms of surgery, or Dehn-filling, reveals the twist construction as a carefully organized surgery on a link. In this paper, we work out the relationship between the twisted face-pairing description of closed 3-manifolds and the more common descriptions by surgery and Heegaard diagrams. We show that all Heegaard diagrams have a natural decomposition into subdiagrams called Heegaard cylinders, each of which has a natural shape given by the ratio of two positive integers. We characterize the Heegaard diagrams arising naturally from a twisted face-pairing description as those whose Heegaard cylinders all have integral shape. This characterization allows us to use the Kirby calculus and standard tools of Heegaard theory to attack the problem of finding which closed, orientable 3-manifolds have a twisted face-pairing description.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-10.abs.htm

Forest diagrams for elements of Thompson's group F

We introduce forest diagrams to represent elements of Thompson's group F. These diagrams relate to a certain action of F on the real line in the same way that tree diagrams relate to the standard action of F on the unit interval. Using forest diagrams, we give a conceptually simple length formula for elements of F with respect to the {x_0,x_1} generating set, and we discuss the construction of minimum-length words for positive elements. Finally, we use forest diagrams and the length formula to examine the structure of the Cayley graph of F.Comment: 44 pages, 70 figure

Point vortices on the hyperbolic plane

We investigate some properties of the dynamical system of point vortices on the hyperboloid. This system has noncompact symmetry SL(2, R) and a coadjoint equivariant momentum map J. The relative equilibrium conditions are found and the trajectories of relative equilibria with non-zero momentum value are described. We also provide the classification of relative equilibria and the stability criteria for a number of cases, focusing on N=2, 3. Contrary to the system on the sphere, relative equilibria with non-compact momentum isotropy subgroup are found, and are used to illustrate the different stability types of relative equilibria.Comment: To appear in J. Mathematical Physic

On Hyperbolic once-punctured-torus bundles II. Fractal tessellations of the plane

We describe fractal tessellations of the complex plane that arise naturally from Cannon-Thurston maps associated to complete, hyperbolic, once-punctured-torus bundles. We determine the symmetry groups of these tessellations

On the bounded cohomology of semi-simple groups, S-arithmetic groups and products

We prove vanishing results for Lie groups and algebraic groups (over any local field) in bounded cohomology. The main result is a vanishing below twice the rank for semi-simple groups. Related rigidity results are established for S-arithmetic groups and groups over global fields. We also establish vanishing and cohomological rigidity results for products of general locally compact groups and their lattices

Use of a Distal Radius Endoprosthesis Following Resection of a Bone Tumour: A Case Report

Limited literature is available on the reconstruction of the distal radius using prosthetic replacement following resection of a bone tumour. We present the first reported case, in the English literature, of the use of an entirely metal endoprosthesis for the reconstruction of the distal radius. This case involves a 66-year-old male who was treated for giant cell tumour of the distal radius with surgical excision of the lesion and replacement of the defect using a predominantly titanium endoprosthesis. He was followed-up for 56 months following surgery and had a good functional outcome with no associated pain or complications. We propose that the use of a primarily titanium endoprosthesis for the reconstruction of a bone defect of the distal radius is a suitable alternative, providing good function of the forearm with satisfactory range of movement at the wrist and adequate pain relief

An Integrated Imaging Approach to the Study of Oxidative Stress Generation by Mitochondrial Dysfunction in Living Cells

BACKGROUND: The mechanisms of action of many environmental agents commonly involve oxidative stress resulting from mitochondrial dysfunction. Zinc is a common environmental metallic contaminant that has been implicated in a variety of oxidant-dependent toxicological responses. Unlike ions of other transition metals such as iron, copper, and vanadium, Zn(2+) does not generate reactive oxygen species (ROS) through redox cycling. OBJECTIVE: To characterize the role of oxidative stress in zinc-induced toxicity. METHODS: We used an integrated imaging approach that employs the hydrogen peroxide (H2O2)-specific fluorophore Peroxy Green 1 (PG1), the mitochondrial potential sensor 5,5 ,6,6 -tetrachloro-1,1 ,3,3 -tetraethylbenzimidazolylcarbocyanine iodide (JC-1), and the mitochondria-targeted form of the redox-sensitive genetically encoded fluorophore MTroGFP1 in living cells. RESULTS: Zinc treatment in the presence of the Zn(2+) ionophore pyrithione of A431 skin carcinoma cells preloaded with the H(2)O(2)-specific indicator PG1 resulted in a significant increase in H(2)O(2) production that could be significantly inhibited with the mitochondrial inhibitor carbonyl cyanide 3-chlorophenylhydrazone. Mitochondria were further implicated as the source of zinc-induced H(2)O(2) formation by the observation that exposure to zinc caused a loss of mitochondrial membrane potential. Using MTroGFP1, we showed that zinc exposure of A431 cells induces a rapid loss of reducing redox potential in mitochondria. We also demonstrated that zinc exposure results in rapid swelling of mitochondria isolated from mouse hearts. CONCLUSION: Taken together, these findings show a disruption of mitochondrial integrity, H(2)O(2) formation, and a shift toward positive redox potential in cells exposed to zinc. These data demonstrate the utility of real-time, live-cell imaging to study the role of oxidative stress in toxicological responses

1952: Abilene Christian College Bible Lectures - Full Text

Delivered in the Auditorium of Abilene Christian College, February, 1952 ABILENE, TEXAS PRICE, $3.00 firm foundation publishing house Box 77 Austin Cl, Texa

High-throughput SNP discovery through deep resequencing of a reduced representation library to anchor and orient scaffolds in the soybean whole genome sequence

Background: The Soybean Consensus Map 4.0 facilitated the anchoring of 95.6% of the soybean whole genome sequence developed by the Joint Genome Institute, Department of Energy, but its marker density was only sufficient to properly orient 66% of the sequence scaffolds. The discovery and genetic mapping of more single nucleotide polymorphism (SNP) markers were needed to anchor and orient the remaining genome sequence. To that end, next generation sequencing and high-throughput genotyping were combined to obtain a much higher resolution genetic map that could be used to anchor and orient most of the remaining sequence and to help validate the integrity of the existing scaffold builds. Results: A total of 7,108 to 25,047 predicted SNPs were discovered using a reduced representation library that was subsequently sequenced by the Illumina sequence-by-synthesis method on the clonal single molecule array platform. Using multiple SNP prediction methods, the validation rate of these SNPs ranged from 79% to 92.5%. A high resolution genetic map using 444 recombinant inbred lines was created with 1,790 SNP markers. Of the 1,790 mapped SNP markers, 1,240 markers had been selectively chosen to target existing un-anchored or un-oriented sequence scaffolds, thereby increasing the amount of anchored sequence to 97%. Conclusion: We have demonstrated how next generation sequencing was combined with high-throughput SNP detection assays to quickly discover large numbers of SNPs. Those SNPs were then used to create a high resolution genetic map that assisted in the assembly of scaffolds from the 8× whole genome shotgun sequences into pseudomolecules corresponding to chromosomes of the organism