Quantum Geometry and Diffusion

We study the diffusion equation in two-dimensional quantum gravity, and show that the spectral dimension is two despite the fact that the intrinsic Hausdorff dimension of the ensemble of two-dimensional geometries is very different from two. We determine the scaling properties of the quantum gravity averaged diffusion kernel.Comment: latex2e, 10 pages, 4 figure

Involvement of (pro)renin receptor in the glomerular filtration barrier

(Pro)renin receptor-bound prorenin not only causes the generation of angiotensin II via the nonproteolytic activation of prorenin, it also activates the receptor’s own intracellular signaling pathways independent of the generated angiotensin II. Within the kidneys, the (pro)renin receptor is not only present in the glomerular mesangium, it is also abundant in podocytes, which play an important role in the maintenance of the glomerular filtration barrier. Recent in vivo studies have demonstrated that the overexpression of the (pro)renin receptor to a degree similar to that observed in hypertensive rat kidneys leads to slowly progressive nephropathy with proteinuria. In addition, the handle region peptide, which acts as a decoy peptide and competitively inhibits the binding of prorenin to the receptor, is more beneficial than an angiotensin-converting enzyme inhibitor with regard to alleviating proteinuria and glomerulosclerosis in experimental animal models of diabetes and essential hypertension. Thus, the (pro)renin receptor may be upregulated in podocytes under hypertensive conditions and may contribute to the breakdown of the glomerular filtration barrier

On the Large Time Behavior of Solutions of Hamilton-Jacobi Equations Associated with Nonlinear Boundary Conditions

In this article, we study the large time behavior of solutions of first-order Hamilton-Jacobi Equations, set in a bounded domain with nonlinear Neumann boundary conditions, including the case of dynamical boundary conditions. We establish general convergence results for viscosity solutions of these Cauchy-Neumann problems by using two fairly different methods : the first one relies only on partial differential equations methods, which provides results even when the Hamiltonians are not convex, and the second one is an optimal control/dynamical system approach, named the "weak KAM approach" which requires the convexity of Hamiltonians and gives formulas for asymptotic solutions based on Aubry-Mather sets

Thin presentation of knots and lens spaces

This paper concerns thin presentations of knots K in closed 3-manifolds M^3 which produce S^3 by Dehn surgery, for some slope gamma. If M does not have a lens space as a connected summand, we first prove that all such thin presentations, with respect to any spine of M have only local maxima. If M is a lens space and K has an essential thin presentation with respect to a given standard spine (of lens space M) with only local maxima, then we show that K is a 0-bridge or 1-bridge braid in M; furthermore, we prove the minimal intersection between K and such spines to be at least three, and finally, if the core of the surgery K_gamma yields S^3 by r-Dehn surgery, then we prove the following inequality: |r| <= 2g, where g is the genus of K_gamma.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-23.abs.htm