Minimizers of higher order gauge invariant functionals

We introduce higher order variants of the Yang-Mills functional that involve $(n-2)$th order derivatives of the curvature. We prove coercivity and smoothness of critical points in Uhlenbeck gauge in dimensions $\mathrm{dim}M\le 2n$. These results are then used to establish the existence of smooth minimizers on a given principal bundle $P\to M$ for subcritical dimensions $\mathrm{dim}M<2n$. In the case of critical dimension $\mathrm{dim}M=2n$ we construct a minimizer on a bundle which might differ from the prescribed one, but has the same Chern classes $c_1,\ldots,c_{n-1}$. A key result is a removable singularity theorem for bundles carrying a $W^{n-1,2}$-connection. This generalizes a recent result by Petrache and Rivi\`ere

Vitamin D supplementation in the pediatric rheumatology clinic.

Vitamin D is capturing the attention of healthy and chronically ill populations for its potential skeletal and nonskeletal benefits. New information suggesting a role in immune modulation has led to a surge of interest among rheumatologists. Although the epidemiologic data are limited, it appears that many children with rheumatic conditions are at risk of vitamin D deficiency. However, understanding this phenomenon requires an appreciation for how vitamin D status is assessed, and options for supplementation. Although a "more-is-better" attitude is tempting when considering the medicinal effects of a nutritional supplement, we suggest a cautious approach and suggest that further studies are needed to clarify the potential benefits and risks among children with rheumatic conditions

Higher integrability for doubly nonlinear parabolic systems

This paper proves a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems. The new feature of the argument is that the intrinsic geometry involves the solution as well as its spatial gradient. The main result holds true for a range of parameters suggested by other nonlinear parabolic systems

Glial cell line-derived neurotrophic factor influences proliferation of osteoblastic cells

Little is known about the role of neurotrophic growth factors in bone metabolism. This study investigated the short-term effects of glial cell line-derived neurotrophic factor (GDNF) on calvarial-derived MC3T3-E1 osteoblasts. MC3T3-E1 expressed GDNF as well as its canonical receptors, GFRα1 and RET. Addition of recombinant GDNF to cultures in serum-containing medium modestly inhibited cell growth at high concentrations; however, under serum-free culture conditions GDNF dose-dependently increased cell proliferation. GDNF effects on cell growth were inversely correlated with its effect on alkaline phosphatase (ALP) activity showing a significant dose-dependent inhibition of relative ALP activity with increasing concentrations of GDNF in serum-free culture medium. Live/dead and lactate dehydrogenase assays demonstrated GDNF did not significantly affect cell death or survival under serum-containing and serum-free conditions. The effect of GDNF on cell growth was abolished in the presence of inhibitors to GFR α 1 and RET indicating that GDNF stimulated calvarial osteoblasts via its canonical receptors. Finally, this study found that GDNF synergistically increased tumor necrosis factor-α (TNF-α)-stimulated MC3T3-E1 cell growth suggesting that GDNF interacted with TNF-α-induced signaling in osteoblastic cells. In conclusion, this study provides evidence for a direct, receptor-mediated effect of GDNF on osteoblasts highlighting a novel role for GDNF in bone physiology. \ud \u