Convergence analysis of block Gibbs samplers for Bayesian linear mixed models with p>Np>N

Exploration of the intractable posterior distributions associated with Bayesian versions of the general linear mixed model is often performed using Markov chain Monte Carlo. In particular, if a conditionally conjugate prior is used, then there is a simple two-block Gibbs sampler available. Rom\'{a}n and Hobert [Linear Algebra Appl. 473 (2015) 54-77] showed that, when the priors are proper and the $X$ matrix has full column rank, the Markov chains underlying these Gibbs samplers are nearly always geometrically ergodic. In this paper, Rom\'{a}n and Hobert's (2015) result is extended by allowing improper priors on the variance components, and, more importantly, by removing all assumptions on the $X$ matrix. So, not only is $X$ allowed to be (column) rank deficient, which provides additional flexibility in parameterizing the fixed effects, it is also allowed to have more columns than rows, which is necessary in the increasingly important situation where $p>N$. The full rank assumption on $X$ is at the heart of Rom\'{a}n and Hobert's (2015) proof. Consequently, the extension to unrestricted $X$ requires a substantially different analysis.Comment: Published at http://dx.doi.org/10.3150/15-BEJ749 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Geometric Multicut

We study the following separation problem: Given a collection of colored objects in the plane, compute a shortest “fence” F, i.e., a union of curves of minimum total length, that separates every two objects of different colors. Two objects are separated if F contains a simple closed curve that has one object in the interior and the other in the exterior. We refer to the problem as GEOMETRIC k-CUT, where k is the number of different colors, as it can be seen as a geometric analogue to the well-studied multicut problem on graphs. We first give an O(n4log3n)-time algorithm that computes an optimal fence for the case where the input consists of polygons of two colors and n corners in total. We then show that the problem is NP-hard for the case of three colors. Finally, we give a (2−4/3k)-approximation algorithm

High-threshold mechanosensitive ion channels blocked by a novel conopeptide mediate pressure-evoked pain

Little is known about the molecular basis of somatosensory mechanotransduction in mammals. We screened a library of peptide toxins for effects on mechanically activated currents in cultured dorsal root ganglion neurons. One conopeptide analogue, termed NMB-1 for noxious mechanosensation blocker 1, selectively inhibits (IC50 1 µM) sustained mechanically activated currents in a subset of sensory neurons. Biotinylated NMB-1 retains activity and binds selectively to peripherin-positive nociceptive sensory neurons. The selectivity of NMB-1 was confirmed by the fact that it has no inhibitory effects on voltage-gated sodium and calcium channels, or ligand-gated channels such as acid-sensing ion channels or TRPA1 channels. Conversely, the tarantula toxin, GsMTx-4, which inhibits stretch-activated ion channels, had no effects on mechanically activated currents in sensory neurons. In behavioral assays, NMB-1 inhibits responses only to high intensity, painful mechanical stimulation and has no effects on low intensity mechanical stimulation or thermosensation. Unexpectedly, NMB-1 was found to also be an inhibitor of rapid FM1-43 loading (a measure of mechanotransduction) in cochlear hair cells. These data demonstrate that pharmacologically distinct channels respond to distinct types of mechanical stimuli and suggest that mechanically activated sustained currents underlie noxious mechanosensation. NMB-1 thus provides a novel diagnostic tool for the molecular definition of channels involved in hearing and pressure-evoked pain

Phonon-induced quadrupolar ordering of the magnetic superconductor TmNi2_2B2_2C

We present synchrotron x-ray diffraction studies revealing that the lattice of thulium borocarbide is distorted below T_Q = 13.5 K at zero field. T_Q increases and the amplitude of the displacements is drastically enhanced, by a factor of 10 at 60 kOe, when a magnetic field is applied along [100]. The distortion occurs at the same wave vector as the antiferromagnetic ordering induced by the a-axis field. A model is presented that accounts for the properties of the quadrupolar phase and explains the peculiar behavior of the antiferromagnetic ordering previously observed in this compound.Comment: submitted to PR

Pauli Paramagnetic Effects on Vortices in Superconducting TmNi2B2C

The magnetic field distribution around the vortices in TmNi2B2C in the paramagnetic phase was studied experimentally as well as theoretically. The vortex form factor, measured by small-angle neutron scattering, is found to be field independent up to 0.6 Hc2 followed by a sharp decrease at higher fields. The data are fitted well by solutions to the Eilenberger equations when paramagnetic effects due to the exchange interaction with the localized 4f Tm moments are included. The induced paramagnetic moments around the vortex cores act to maintain the field contrast probed by the form factor.Comment: 4 pages, 4 figure

Circulation, retention, and mixing of waters within the Weddell-Scotia Confluence, Southern Ocean:The role of stratified Taylor columns

The waters of the Weddell-Scotia Confluence (WSC) lie above the rugged topography of the South Scotia Ridge in the Southern Ocean. Meridional exchanges across the WSC transfer water and tracers between the Antarctic Circumpolar Current (ACC) to the north and the subpolar Weddell Gyre to the south. Here, we examine the role of topographic interactions in mediating these exchanges, and in modifying the waters transferred. A case study is presented using data from a free-drifting, intermediate-depth float, which circulated anticyclonically over Discovery Bank on the South Scotia Ridge for close to 4 years. Dimensional analysis indicates that the local conditions are conducive to the formation of Taylor columns. Contemporaneous ship-derived transient tracer data enable estimation of the rate of isopycnal mixing associated with this column, with values of O(1000 m2/s) obtained. Although necessarily coarse, this is of the same order as the rate of isopycnal mixing induced by transient mesoscale eddies within the ACC. A picture emerges of the Taylor column acting as a slow, steady blender, retaining the waters in the vicinity of the WSC for lengthy periods during which they can be subject to significant modification. A full regional float data set, bathymetric data, and a Southern Ocean state estimate are used to identify other potential sites for Taylor column formation. We find that they are likely to be sufficiently widespread to exert a significant influence on water mass modification and meridional fluxes across the southern edge of the ACC in this sector of the Southern Ocean

Optimal Design and Tolerancing of Compressor Blades Subject to Manufacturing Variability

This paper presents a computational approach for optimal robust design and tolerancing of turbomachinery compressor blades that are subject to geometric variability. This approach simultaneously determines the optimal blade geometry and manufacturing tolerances to minimize the overall cost of producing and operating the resulting compressor blades. A pathwise sensitivity method is used to compute gradient information that is in turn used to optimize the design and tolerances. Results for a two-dimensional subsonic compressor are presented, demonstrating the significant performance improvements that can be achieved using the proposed approach.Pratt & Whitney Aircraft CompanyBoeing Compan