On UT 29 June 2015, the occultation by Pluto of a bright star (r′ = 11.9) was observed from the Stratospheric Observatory for Infrared Astronomy (SOFIA) and several ground-based stations in New ...Zealand and Australia. Pre-event astrometry allowed for an in-flight update to the SOFIA team with the result that SOFIA was deep within the central flash zone (~22 km from center). Analysis of the combined data leads to the result that Pluto's middle atmosphere is essentially unchanged from 2011 and 2013 (Person et al. 2013; Bosh et al. 2015); there has been no significant expansion or contraction of the atmosphere. Additionally, our multi-wavelength observations allow us to conclude that a haze component in the atmosphere is required to reproduce the light curves obtained. This haze scenario has implications for understanding the photochemistry of Pluto's atmosphere.
•We observed an occultation of the brightest star ever in our series of Pluto occultations, 12th magnitude.•The event was only about two Pluto-days (and 15 Earth-days) before the flyby of NASA's New ...Horizons spacecraft.•Our observations from the Mt. John Observatory and Auckland in New Zealand were simultaneous to SOFIA observations with its 100-inch telescope and occultation photometer HIPO, overflying not far from Mt. John.•At Mt. John, with the 1-m telescope, we were so close to the center of the occultation that we observed a central flash, enabling us to study the atmosphere close to the limb than ever before.•We observed a number of bright spikes in the light curve during ingress and egress from both Mt. John and Auckland, showing structure in Pluto's atmosphere.•With the subsequent determination of Pluto's size from New Horizons, we have a more accurate scale for the atmosphere than from previous occultation observations.
We observed the occultation by Pluto of a 12th magnitude star, one of the two brightest occultation stars ever in our dozen years of continual monitoring of Pluto's atmosphere through such studies, on 2015 June 29 UTC.At the Univ. of Canterbury Mt. John Observatory (New Zealand), under clear skies throughout, we used a POETS frame-transfer CCD at 10Hz with GPS timing on the 1-m McLellan telescope as well as an infrared camera on an 0.6-m telescope and three-color photometry at a slower cadence on a second 0.6-m telescope. At the Auckland Observatory, we used a POETS and a PICO on 0.5-m and 0.4-m telescopes, with 0.4s and 2s cadences, respectively, obtaining ingress observations before clouds moved in. The Mt. John light curves show a central flash, indicating that we were close to the center of the occultation path. Analysis of our light curves show that Pluto's atmosphere remains robust.The presence of spikes at both sites in the egress and ingress shows atmospheric layering. We coordinated our observations with aircraft observations (Bosh et al., 2017) with the Stratospheric Observatory for Infrared Astronomy (SOFIA). Our chords helped constrain the path across Pluto that SOFIA saw. Our ground-based and airborne stellar-occultation effort came only just over two weeks of Earth days and two Pluto days before the flyby of NASA's New Horizons spacecraft.
Benford's law describes a common phenomenon among many naturally occurring data sets and distributions in which the leading digits of the data are distributed with the probability of a first digit of ...\(d\) base \(B\) being \(\log_{B}{\frac{d+1}{d}}\). As it often successfully detects fraud in medical trials, voting, science and finance, significant effort has been made to understand when and how distributions exhibit Benford behavior. Most of the previous work has been restricted to cases of independent variables, and little is known about situations involving dependence. We use copulas to investigate the Benford behavior of the product of \(n\) dependent random variables. We develop a method for approximating the Benford behavior of a product of \(n\) dependent random variables modeled by a copula distribution \(C\) and quantify and bound a copula distribution's distance from Benford behavior. We then investigate the Benford behavior of various copulas under varying dependence parameters and number of marginals. Our investigations show that the convergence to Benford behavior seen with independent random variables as the number of variables in the product increases is not necessarily preserved when the variables are dependent and modeled by a copula. Furthermore, there is strong indication that the preservation of Benford behavior of the product of dependent random variables may be linked more to the structure of the copula than to the Benford behavior of the marginal distributions.
Let \(n\) points be in crescent configurations in \(\mathbb{R}^d\) if they lie in general position in \(\mathbb{R}^d\) and determine \(n-1\) distinct distances, such that for every \(1 \leq i \leq ...n-1\) there is a distance that occurs exactly \(i\) times. Since Erdős' conjecture in 1989 on the existence of \(N\) sufficiently large such that no crescent configurations exist on \(N\) or more points, he, Pomerance, and Palásti have given constructions for \(n\) up to \(8\) but nothing is yet known for \(n \geq 9\). Most recently, Burt et. al. had proven that a crescent configuration on \(n\) points exists in \(\mathbb{R}^{n-2}\) for \(n \geq 3\). In this paper, we study the classification of these configurations on \(4\) and \(5\) points through graph isomorphism and rigidity. Our techniques, which can be generalized to higher dimensions, offer a new viewpoint on the problem through the lens of distance geometry and provide a systematic way to construct crescent configurations.
According to Benford's Law, many data sets have a bias towards lower leading digits (about \(30\%\) are \(1\)'s). The applications of Benford's Law vary: from detecting tax, voter and image fraud to ...determining the possibility of match-fixing in competitive sports. There are many common distributions that exhibit such bias, i.e. they are almost Benford. These include the exponential and the Weibull distributions. Motivated by these examples and the fact that the underlying distribution of factors in protein structure follows an inverse gamma distribution, we determine the closeness of this distribution to a Benford distribution as its parameters change.
Recent Genome-Wide Association Studies (GWAS) have identified four low-penetrance ovarian cancer susceptibility loci. We hypothesized that further moderate- or low-penetrance variants exist among the ...subset of single-nucleotide polymorphisms (SNPs) not well tagged by the genotyping arrays used in the previous studies, which would account for some of the remaining risk. We therefore conducted a time- and cost-effective stage 1 GWAS on 342 invasive serous cases and 643 controls genotyped on pooled DNA using the high-density Illumina 1M-Duo array. We followed up 20 of the most significantly associated SNPs, which are not well tagged by the lower density arrays used by the published GWAS, and genotyping them on individual DNA. Most of the top 20 SNPs were clearly validated by individually genotyping the samples used in the pools. However, none of the 20 SNPs replicated when tested for association in a much larger stage 2 set of 4,651 cases and 6,966 controls from the Ovarian Cancer Association Consortium. Given that most of the top 20 SNPs from pooling were validated in the same samples by individual genotyping, the lack of replication is likely to be due to the relatively small sample size in our stage 1 GWAS rather than due to problems with the pooling approach. We conclude that there are unlikely to be any moderate or large effects on ovarian cancer risk untagged by less dense arrays. However, our study lacked power to make clear statements on the existence of hitherto untagged small-effect variants.
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