Lombardi Drawings of Graphs

We introduce the notion of Lombardi graph drawings, named after the American abstract artist Mark Lombardi. In these drawings, edges are represented as circular arcs rather than as line segments or polylines, and the vertices have perfect angular resolution: the edges are equally spaced around each vertex. We describe algorithms for finding Lombardi drawings of regular graphs, graphs of bounded degeneracy, and certain families of planar graphs.Comment: Expanded version of paper appearing in the 18th International Symposium on Graph Drawing (GD 2010). 13 pages, 7 figure

The Role of Vortices in the Mutual Coupling of Superconducting and Normal-Metal Films

I propose a possible explanation to a recently observed ``cross-talk'' effect in metal-insulator-metal trilayers, indicating a sharp peak near a superconducting transition in one of the metal films. Coulomb interactions are excluded as a dominant coupling mechanism, and an alternative is suggested, based on the local fluctuating electric field induced by mobile vortices in the superconducting layer. This scenario is compatible with the magnitude of the peak signal and its shape; most importantly, it addresses the {\it non-reciprocity} of the effect in exchanging the roles of the films.Comment: 13 pages, RevTe

The Quantum Hall Effect in Drag: Inter-layer Friction in Strong Magnetic Fields

We study the Coulomb drag between two spatially separated electron systems in a strong magnetic field, one of which exhibits the quantum Hall effect. At a fixed temperature, the drag mimics the behavior of $\sigma_{xx}$ in the quantum Hall system, in that it is sharply peaked near the transitions between neighboring plateaux. We assess the impact of critical fluctuations near the transitions, and find that the low temperature behavior of the drag measures an exponent $\eta$ that characterizes anomalous low frequency dissipation; the latter is believed to be present following the work of Chalker.Comment: 13 pages, Revtex 2.0, 1 figure upon request, P-93-11-09

Open Problems on Central Simple Algebras

We provide a survey of past research and a list of open problems regarding central simple algebras and the Brauer group over a field, intended both for experts and for beginners.Comment: v2 has some small revisions to the text. Some items are re-numbered, compared to v

1,25(OH)2D3 Alters Growth Plate Maturation and Bone Architecture in Young Rats with Normal Renal Function

Whereas detrimental effects of vitamin D deficiency are known over century, the effects of vitamin D receptor activation by 1,25(OH)2D3, the principal hormonal form of vitamin D, on the growing bone and its growth plate are less clear. Currently, 1,25(OH)2D3 is used in pediatric patients with chronic kidney disease and mineral and bone disorder (CKD-MBD) and is strongly associated with growth retardation. Here, we investigate the effect of 1,25(OH)2D3 treatment on bone development in normal young rats, unrelated to renal insufficiency. Young rats received daily i.p. injections of 1 µg/kg 1,25(OH)2D3 for one week, or intermittent 3 µg/kg 1,25(OH)2D3 for one month. Histological analysis revealed narrower tibial growth plates, predominantly in the hypertrophic zone of 1,25(OH)2D3-treated animals in both experimental protocols. This phenotype was supported by narrower distribution of aggrecan, collagens II and X mRNA, shown by in situ hybridization. Concomitant with altered chondrocyte maturation, 1,25(OH)2D3 increased chondrocyte proliferation and apoptosis in terminal hypertrophic cells. In vitro treatment of the chondrocytic cell line ATDC5 with 1,25(OH)2D3 lowered differentiation and increased proliferation dose and time-dependently. Micro-CT analysis of femurs from 1-week 1,25(OH)2D3-treated group revealed reduced cortical thickness, elevated cortical porosity, and higher trabecular number and thickness. 1-month administration resulted in a similar cortical phenotype but without effect on trabecular bone. Evaluation of fluorochrome binding with confocal microscopy revealed inhibiting effects of 1,25(OH)2D3 on intracortical bone formation. This study shows negative effects of 1,25(OH)2D3 on growth plate and bone which may contribute to the exacerbation of MBD in the CKD pediatric patients

Essential Role of the Small GTPase Ran in Postnatal Pancreatic Islet Development

The small GTPase Ran orchestrates pleiotropic cellular responses of nucleo-cytoplasmic shuttling, mitosis and subcellular trafficking, but whether deregulation of these pathways contributes to disease pathogenesis has remained elusive. Here, we generated transgenic mice expressing wild type (WT) Ran, loss-of-function Ran T24N mutant or constitutively active Ran G19V mutant in pancreatic islet β cells under the control of the rat insulin promoter. Embryonic pancreas and islet development, including emergence of insulin+ β cells, was indistinguishable in control or transgenic mice. However, by one month after birth, transgenic mice expressing any of the three Ran variants exhibited overt diabetes, with hyperglycemia, reduced insulin production, and nearly complete loss of islet number and islet mass, in vivo. Deregulated Ran signaling in transgenic mice, adenoviral over-expression of WT or mutant Ran in isolated islets, or short hairpin RNA (shRNA) silencing of endogenous Ran in model insulinoma INS-1 cells, all resulted in decreased expression of the pancreatic and duodenal homeobox transcription factor, PDX-1, and reduced β cell proliferation, in vivo. These data demonstrate that a finely-tuned balance of Ran GTPase signaling is essential for postnatal pancreatic islet development and glucose homeostasis, in vivo