Selection Lemmas for various geometric objects

Selection lemmas are classical results in discrete geometry that have been well studied and have applications in many geometric problems like weak epsilon nets and slimming Delaunay triangulations. Selection lemma type results typically show that there exists a point that is contained in many objects that are induced (spanned) by an underlying point set. In the first selection lemma, we consider the set of all the objects induced (spanned) by a point set $P$. This question has been widely explored for simplices in $\mathbb{R}^d$, with tight bounds in $\mathbb{R}^2$. In our paper, we prove first selection lemma for other classes of geometric objects. We also consider the strong variant of this problem where we add the constraint that the piercing point comes from $P$. We prove an exact result on the strong and the weak variant of the first selection lemma for axis-parallel rectangles, special subclasses of axis-parallel rectangles like quadrants and slabs, disks (for centrally symmetric point sets). We also show non-trivial bounds on the first selection lemma for axis-parallel boxes and hyperspheres in $\mathbb{R}^d$. In the second selection lemma, we consider an arbitrary $m$ sized subset of the set of all objects induced by $P$. We study this problem for axis-parallel rectangles and show that there exists an point in the plane that is contained in $\frac{m^3}{24n^4}$ rectangles. This is an improvement over the previous bound by Smorodinsky and Sharir when $m$ is almost quadratic

Ram Selection and Ewe Culling

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Evidence-Informed Case Rates: A New Health Care Payment Model

Suggests a new payment model whereby providers are paid a single, risk-adjusted payment across inpatient and outpatient settings to care for a patient diagnosed with a specific condition

Morphological Dependence of Star Formation Properties for the Galaxies in the Merging Galaxy Cluster A2255

The merging cluster of galaxies A2255 is covered by the Sloan Digital Sky Survey (SDSS) survey. In this paper we perform a morphological classification on the basis of the SDSS imaging and spectral data, and investigate the morphological dependence of the star formation rates (SFRs) for these member galaxies. As we expect, a tight correlation between the normalized SFR by stellar mass (SFR/M$_*$) and the H$\alpha$ equivalent width is found for the late-type galaxies in A2255. The correlation of SFR/M$_*$ with the continuum break strength at 4000 \AA is also confirmed. The SFR/M$_*$ - M$_*$ correlation is found for both the early- and late-type galaxies, indicating that the star formation activity tends to be suppressed when the assembled stellar mass M$_*$) increases, and this correlation is tighter and steeper for the late-type cluster galaxies. Compared with the mass range of field spiral galaxies, only two massive late-type galaxies with M$_*>10^{11}$ M$_{\odot}$ are survived in A2255, suggesting that the gas disks of massive spiral galaxies could have been tidally stripped during cluster formation. Additionally, the SFR variation with the projected radial distance are found to be heavily dependent upon galaxy morphology: the early-type galaxies have a very weak inner decrease in SFR/M$_*$, while the inner late-type galaxies tend to have higher SFR/M$_*$ values than the outer late-types. This may suggest that the galaxy-scale turbulence stimulated by the merging of subclusters might have played different roles on early- and late-type galaxies, which leads to a suppression of the star formation activity for E/S0 galaxies and a SFR enhancement for spiral and irregular galaxies.Comment: 21 pages, including 7 EPS figures and 1 tables, uses aastex.cls, Accepted by the A

Obscured AGN at z~1 from the zCOSMOS-Bright Survey I. Selection and Optical Properties of a [Ne v]-selected sample

A sample of 94 narrow line AGN with 0.65<z<1.20 has been selected from the 20k-Bright zCOSMOS galaxy sample by detection of the high-ionization [NeV]3426 line. Taking advantage of the large amount of data available in the COSMOS field, the properties of the [NeV]-selected Type-2 AGN have been investigated, focusing on their host galaxies, X-ray emission, and optical line flux ratios. Finally, the diagnostic developed by Gilli et al. (2010), based on the X-ray to [NeV] luminosity ratio, has been exploited to search for the more heavily obscured AGN. We found that [Ne v]-selected narrow line AGN have Seyfert 2-like optical spectra, although with emission line ratios diluted by a star-forming component. The ACS morphologies and stellar component in the optical spectra indicate a preference for our Type-2 AGN to be hosted in early-spirals with stellar masses greater than 10^(9.5-10)Msun, on average higher than those of the galaxy parent sample. The fraction of galaxies hosting [NeV]-selected obscured AGN increases with the stellar mass, reaching a maximum of about 3% at 2x10^11 Msun. A comparison with other selection techniques at z~1 shows that the detection of the [Ne v] line is an effective method to select AGN in the optical band, in particular the most heavily obscured ones, but can not provide by itself a complete census of AGN2. Finally, the high fraction of [NeV]-selected Type-2 AGN not detected in medium-deep Chandra observations (67%) is suggestive of the inclusion of Compton-thick sources in our sample. The presence of a population of heavily obscured AGN is corroborated by the X-ray to [NeV] ratio; we estimated, by mean of X-ray stacking technique and simulations, that the Compton-thick fraction in our sample of Type-2 AGN is 43+-4%, in good agreement with standard assumptions by the XRB synthesis models.Comment: 14 pages, 12 figures, accepted for publication in A&