On thin plate spline interpolation

We present a simple, PDE-based proof of the result [M. Johnson, 2001] that the error estimates of [J. Duchon, 1978] for thin plate spline interpolation can be improved by $h^{1/2}$. We illustrate that ${\mathcal H}$-matrix techniques can successfully be employed to solve very large thin plate spline interpolation problem

Genetic clustering on the hippocampal surface for genome-wide association studies

Imaging genetics aims to discover how variants in the human genome influence brain measures derived from images. Genome-wide association scans (GWAS) can screen the genome for common differences in our DNA that relate to brain measures. In small samples, GWAS has low power as individual gene effects are weak and one must also correct for multiple comparisons across the genome and the image. Here we extend recent work on genetic clustering of images, to analyze surface-based models of anatomy using GWAS. We performed spherical harmonic analysis of hippocampal surfaces, automatically extracted from brain MRI scans of 1254 subjects. We clustered hippocampal surface regions with common genetic influences by examining genetic correlations (rg) between the normalized deformation values at all pairs of surface points. Using genetic correlations to cluster surface measures, we were able to boost effect sizes for genetic associations, compared to clustering with traditional phenotypic correlations using Pearson's r

Antagonistic effects of transforming growth factor-beta on vitamin D3 enhancement of osteocalcin and osteopontin transcription: reduced interactions of vitamin D receptor/retinoid X receptor complexes with vitamin E response elements

Osteocalcin and osteopontin are noncollagenous proteins secreted by osteoblasts and regulated by a complex interplay of systemic and locally produced factors, including growth factors and steroid hormones. We investigated the mechanism by which transforming growth factor-beta (TGF beta) inhibits 1,25-dihydroxyvitamin D3 (1,25-(OH)2D3)-enhanced expression of the osteocalcin (OC) and osteopontin (OP) genes. ROS 17/2.8 cells, in which both genes are expressed, were transfected with reporter constructs driven by native (i.e. wild-type) rat OC and mouse OP promoters. TGF beta abrogated the 1,25-(OH)2D3 enhanced transcription of both the OC and OP genes. The inhibitory TGF beta response for each requires vitamin D response element (VDRE) sequences, although there are additional contributions from proximal basal regulatory elements. These transcriptional effects were further investigated for contribution of the trans-activating factors, which interact with OC and OP VDREs, involving the vitamin D receptor (VDR) and retinoid X receptor (RXR). Gel mobility shift assays show that TGF beta significantly reduces induction of the heterodimers VDR/RXR complexes in 1,25-(OH)2D3-treated ROS 17/2.8 cells. However, Western blot and ligand binding analysis reveal that TGF beta does not affect nuclear availability of the VDR. We also show that activator protein-1 activity is up-regulated by TGF beta; thus, activator protein-1 binding sites in the OC promoter may potentially contribute to inhibitory effects of TGF beta on basal transcription. Our studies demonstrate that the inhibitory action of TGF beta on the 1,25-(OH)2D3 enhancement of OC and OP transcription in osteoblastic cells results from modulations of protein-DNA interactions at the OC and OP VDRE, which cannot be accounted for by changes in VDR protein levels. As OC and OP participate in bone turnover, our results provide insight into the contributions of TGF beta and 1,25-(OH)2D3 to VDR-mediated gene regulatory mechanism operative in bone formation and/or resorption events

Nonlinear porous medium flow with fractional potential pressure

We study a porous medium equation, with nonlocal diffusion effects given by an inverse fractional Laplacian operator. We pose the problem in n-dimensional space for all t>0 with bounded and compactly supported initial data, and prove existence of a weak and bounded solution that propagates with finite speed, a property that is nor shared by other fractional diffusion models.Comment: 32 pages, Late

Charge Fluctuations on Membrane Surfaces in Water

We generalize the predictions for attractions between over-all neutral surfaces induced by charge fluctuations/correlations to non-uniform systems that include dielectric discontinuities, as is the case for mixed charged lipid membranes in an aqueous solution. We show that the induced interactions depend in a non-trivial way on the dielectric constants of membrane and water and show different scaling with distance depending on these properties. The generality of the calculations also allows us to predict under which dielectric conditions the interaction will change sign and become repulsive

Implementation and Validation of Schapery-Rand Anisotropic Viscoelasticity Model for Super-Pressure Balloons

The thin film used for the NASA Ultra Long Duration Balloons (ULDB) shows con-siderable time-dependent behaviour. Furthermore, experiments on scaled ULDB balloons have revealed that wrinkles are present over a wide range of pressures. A numerical model has been developed describing the nonlinear anisotropic viscoelastic material behaviour by means of a Schapery-type model and this model has been extended to model wrinkling by means of a user-defined subroutine in the finite-element package ABAQUS. After a description of the viscoelastic modelling approach, a lobe of a 48 gore ULDB flat facet balloon is modelled and compared to experimental results. Additionally two test cases of anisotropic wrinkling are presented, one involving a flat membrane and one a cylindrical balloon structure. I

Imprints of the Quantum World in Classical Mechanics

The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show Using no physical hypotheses) that the Schroedinger equation for a nonrelativistic system of spinless particles is a classical equation which is equivalent to Hamilton's equations.Comment: Paper submitted to Foundations of Physic

A dynamical model of lipoprotein metabolism

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