Farthest-Polygon Voronoi Diagrams

Given a family of k disjoint connected polygonal sites in general position and of total complexity n, we consider the farthest-site Voronoi diagram of these sites, where the distance to a site is the distance to a closest point on it. We show that the complexity of this diagram is O(n), and give an O(n log^3 n) time algorithm to compute it. We also prove a number of structural properties of this diagram. In particular, a Voronoi region may consist of k-1 connected components, but if one component is bounded, then it is equal to the entire region

Between umbra and penumbra

International audienceComputing shadow boundaries is a difficult problem in the case of non-point light sources. A point is in the umbra if it does not see any part of any light source; it is in full light if it sees entirely all the light sources; otherwise, it is in the penumbra. While the common boundary of the penumbra and the full light is well understood, less is known about the boundary of the umbra. In this paper we prove various bounds on the complexity of the umbra and the penumbra cast by a segment or polygonal light source on a plane in the presence of polygon or polytope obstacles. In particular, we show that a single segment light source may cast on a plane, in the presence of two triangles, four connected components of umbra and that two fat convex obstacles of total complexity n can engender Omega(n) connected components of umbra. In a scene consisting of a segment light source and k disjoint polytopes of total complexity n, we prove an Omega(nk^2+k^4) lower bound on the maximum number of connected components of the umbra and a O(nk^3) upper bound on its complexity. We also prove that, in the presence of k disjoint polytopes of total complexity n, some of which being light sources, the umbra cast on a plane may have Omega(n^2k^3 + nk^5) connected components and has complexity O(n^3k^3). These are the first bounds on the size of the umbra in terms of both k and n. These results prove that the umbra, which is bounded by arcs of conics, is intrinsically much more intricate than the full light/penumbra boundary which is bounded by line segments and whose worst-case complexity is in Omega(n alpha(k) +km +k^2) and O(n alpha(k) +km alpha(k) +k^2), where m is the complexity of the polygonal light source

Candidate X-ray-Emitting OB Stars in the Carina Nebula Identified Via Infrared Spectral Energy Distributions

We report the results of a new survey of massive, OB stars throughout the Carina Nebula using the X-ray point source catalog provided by the Chandra Carina Complex Project (CCCP) in conjunction with infrared (IR) photometry from the Two Micron All-Sky Survey and the Spitzer Space Telescope Vela--Carina survey. Mid-IR photometry is relatively unaffected by extinction, hence it provides strong constraints on the luminosities of OB stars, assuming that their association with the Carina Nebula, and hence their distance, is confirmed. We fit model stellar atmospheres to the optical (UBV) and IR spectral energy distributions (SEDs) of 182 OB stars with known spectral types and measure the bolometric luminosity and extinction for each star. We find that the extinction law measured toward the OB stars has two components: Av=1--1.5 mag produced by foreground dust with a ratio of total-to-selective absorption Rv=3.1 plus a contribution from local dust with Rv>4.0 in the Carina molecular clouds that increases as Av increases. Using X-ray emission as a strong indicator of association with Carina, we identify 94 candidate OB stars with Lbol\geq10^4 Lsun by fitting their IR SEDs. If the candidate OB stars are eventually confirmed by follow-up spectroscopic observations, the number of cataloged OB stars in the Carina Nebula will increase by ~50%. Correcting for incompleteness due to OB stars falling below the Lbol cutoff or the CCCP detection limit, these results potentially double the size of the young massive stellar population.Comment: 19 pages, 8 figures, accepted for the ApJS Special Issue on the Chandra Carina Complex Project (CCCP), scheduled for publication in May 2011. All 16 CCCP Special Issue papers, including a version of this article with high-quality figures, are available at http://cochise.astro.psu.edu/Carina_public/special_issue.html (through 2011 at least

Rationale and design of the randomized, controlled early valve replacement guided by biomarkers of left ventricular decompensation in asymptomatic patients with severe aortic stenosis (EVOLVED) trial

Background: The optimal timing of aortic valve replacement in asymptomatic patients with aortic stenosis is uncertain. Replacement fibrosis, as assessed by midwall (nonischemic) late gadolinium enhancement (LGE) on cardiac magnetic resonance (CMR) imaging, is an irreversible marker of left ventricular decompensation in aortic stenosis. Once established, it progresses rapidly and is associated with poor long-term prognosis in a dose-dependent manner. // Trial design: The objective of this multicenter prospective randomized controlled trial is to determine whether early aortic valve replacement in asymptomatic patients with severe aortic stenosis can improve the adverse prognosis associated with midwall LGE. Patients will be screened for likelihood of having LGE with electrocardiography or high-sensitivity troponin I. Those at high risk will proceed to CMR imaging. Approximately 400 patients with midwall LGE will be randomized 1:1 to early valve replacement or routine care. Those who do not exhibit midwall LGE will continue with routine care and be randomized to a study registry or no further follow-up. Follow-up will be annual for approximately 3 years until the number of required outcome events is achieved. The primary endpoint is a composite of all-cause mortality and unplanned aortic stenosis–related hospitalization. The expected event rate is 25.0% in the routine care arm and 13.4% in the early intervention arm over the first 2 years; 88 observed primary outcome events will give 90% power at 5% significance level. Key secondary endpoints include all-cause mortality, sudden cardiac death, stroke, and symptomatic status. // Conclusion: The EVOLVED trial is the first multicenter randomized controlled trial to compare early aortic valve replacement to routine care in asymptomatic patients with severe aortic stenosis and midwall LGE