On the number of tetrahedra with minimum, unit, and distinct volumes in three-space

We formulate and give partial answers to several combinatorial problems on volumes of simplices determined by $n$ points in 3-space, and in general in $d$ dimensions. (i) The number of tetrahedra of minimum (nonzero) volume spanned by $n$ points in \RR^3 is at most ${2/3}n^3-O(n^2)$, and there are point sets for which this number is ${3/16}n^3-O(n^2)$. We also present an $O(n^3)$ time algorithm for reporting all tetrahedra of minimum nonzero volume, and thereby extend an algorithm of Edelsbrunner, O'Rourke, and Seidel. In general, for every k,d\in \NN, $1\leq k \leq d$, the maximum number of $k$-dimensional simplices of minimum (nonzero) volume spanned by $n$ points in \RR^d is $\Theta(n^k)$. (ii) The number of unit-volume tetrahedra determined by $n$ points in \RR^3 is $O(n^{7/2})$, and there are point sets for which this number is $\Omega(n^3 \log \log{n})$. (iii) For every d\in \NN, the minimum number of distinct volumes of all full-dimensional simplices determined by $n$ points in \RR^d, not all on a hyperplane, is $\Theta(n)$.Comment: 19 pages, 3 figures, a preliminary version has appeard in proceedings of the ACM-SIAM Symposium on Discrete Algorithms, 200

Simulations of small-scale explosive events on the Sun

Small-scale explosive events or microflares occur throughout the chromospheric network of the Sun. They are seen as sudden bursts of highly Doppler shifted spectral lines of ions formed at temperatures in the range 2x10^4 - 5x10^5 K. They tend to occur near regions of cancelling photospheric magnetic fields and are thought to be directly associated with magnetic field reconnection. Recent observations have revealed that they have a bi-directional jet structure reminiscent of Petschek reconnection. In this paper compressible MHD simulations of the evolution of a current sheet to a steady Petschek, jet-like configuration are computed using the Versatile Advection Code. We obtain velocity profiles that can be compared with recent ultraviolet line profile observations. By choosing initial conditions representative of magnetic loops in the solar corona and chromosphere, it is possible to explain the fact that jets flowing outward into the corona are more extended and appear before jets flowing towards the chromosphere. This model can reproduce the high Doppler shifted components of the line profiles but the brightening at low velocities, near the centre of the bi-directional jet, cannot be explained by this simple MHD model.Comment: 16 pages, 8 figures. To be published in Solar Physic

Bayesian Estimation Under Informative Sampling

Bayesian analysis is increasingly popular for use in social science and other application areas where the data are observations from an informative sample. An informative sampling design leads to inclusion probabilities that are correlated with the response variable of interest. Model inference performed on the observed sample taken from the population will be biased for the population generative model under informative sampling since the balance of information in the sample data is different from that for the population. Typical approaches to account for an informative sampling design under Bayesian estimation are often difficult to implement because they require re-parameterization of the hypothesized generating model, or focus on design, rather than model-based, inference. We propose to construct a pseudo-posterior distribution that utilizes sampling weights based on the marginal inclusion probabilities to exponentiate the likelihood contribution of each sampled unit, which weights the information in the sample back to the population. Our approach provides a nearly automated estimation procedure applicable to any model specified by the data analyst for the population and retains the population model parameterization and posterior sampling geometry. We construct conditions on known marginal and pairwise inclusion probabilities that define a class of sampling designs where $L_{1}$ consistency of the pseudo posterior is guaranteed. We demonstrate our method on an application concerning the Bureau of Labor Statistics Job Openings and Labor Turnover Survey.Comment: 24 pages, 3 figure

On distinct distances in homogeneous sets in the Euclidean space

A homogeneous set of $n$ points in the $d$-dimensional Euclidean space determines at least $\Omega(n^{2d/(d^2+1)} / \log^{c(d)} n)$ distinct distances for a constant $c(d)>0$. In three-space, we slightly improve our general bound and show that a homogeneous set of $n$ points determines at least $\Omega(n^{.6091})$ distinct distances

An Evaluation of The Host Response to An Interspinous Process Device Based on A Series of Spine Explants: Device for Intervertebral Assisted Motion (DIAM®)

Background: The objective of this study was to evaluate the host response to an interspinous process device [Device for Intervertebral Assisted Motion (DIAM®)] based on a series of nine spine explants with a mean post-operative explant time of 35 months. Methods: Explanted periprosthetic tissues were processed for histology and stained with H&E, Wright-Giemsa stain, and Oil Red O. Brightfield and polarized light microscopy were used to evaluate the host response to the device and the resultant particulate debris. The host response was graded per ASTM F981-04. Quantitative histomorphometry was used to characterize particle size, shape, and area per ASTM F1877-05. The presence or absence of bone resorption was also evaluated when bony tissue samples were provided. Results: Periprosthetic tissues demonstrated a non-specific foreign body response composed of macrophages and foreign body giant cells to the DIAM® device in most of the accessions. The foreign body reaction was not the stated reason for explantation in any of the accessions. Per ASTM F981-04, a “very slight” to “mild” to “moderate” chronic inflammatory response was observed to the biomaterials and particulate, and this varied by tissue sample and accession. Particle sizes were consistent amongst the explant patients with mean particle size on the order of several microns. Osteolysis, signs of toxicity, necrosis, an immune response, and/or device related infection were not observed. Conclusions: Cyclic loading of the spine can cause wear in dynamic stabilization systems such as DIAM®. The fabric nature of the DIAM® device’s polyethylene terephthalate jacket coupled with the generation of polymeric particulate debris predisposes the device to a foreign body reaction consisting of macrophages and foreign body giant cells. Although not all patients are aware of symptoms associated with a foreign body reaction to a deeply implanted device, surgeons should be aware of the host response to this device

Fabrication of tungsten wire reinforced nickel-base alloy composites

Fabrication methods for tungsten fiber reinforced nickel-base superalloy composites were investigated. Three matrix alloys in pre-alloyed powder or rolled sheet form were evaluated in terms of fabricability into composite monotape and multi-ply forms. The utility of monotapes for fabricating more complex shapes was demonstrated. Preliminary 1093C (2000F) stress rupture tests indicated that efficient utilization of fiber strength was achieved in composites fabricated by diffusion bonding processes. The fabrication of thermal fatigue specimens is also described

HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics

We describe a conservative, shock-capturing scheme for evolving the equations of general relativistic magnetohydrodynamics. The fluxes are calculated using the Harten, Lax, and van Leer scheme. A variant of constrained transport, proposed earlier by T\'oth, is used to maintain a divergence free magnetic field. Only the covariant form of the metric in a coordinate basis is required to specify the geometry. We describe code performance on a full suite of test problems in both special and general relativity. On smooth flows we show that it converges at second order. We conclude by showing some results from the evolution of a magnetized torus near a rotating black hole.Comment: 38 pages, 18 figures, submitted to Ap

Ezetimibe therapy: mechanism of action and clinical update.

The lowering of low-density lipoprotein cholesterol (LDL-C) is the primary target of therapy in the primary and secondary prevention of cardiovascular events. Although statin therapy is the mainstay for LDL-C lowering, a significant percentage of patients prescribed these agents either do not achieve targets with statin therapy alone or have partial or complete intolerance to them. For such patients, the use of adjuvant therapy capable of providing incremental LDL-C reduction is advised. One such agent is ezetimibe, a cholesterol absorption inhibitor that targets uptake at the jejunal enterocyte brush border. Its primary target of action is the cholesterol transport protein Nieman Pick C1 like 1 protein. Ezetimibe is an effective LDL-C lowering agent and is safe and well tolerated. In response to significant controversy surrounding the use and therapeutic effectiveness of this drug, we provide an update on the biochemical mechanism of action for ezetimibe, its safety and efficacy, as well as the results of recent randomized studies that support its use in a variety of clinical scenarios