Enumeration of rises and falls by position

AbstractLet π=(π1, π2,…,πn) denote a permutation of Zn = {1, 2,…, n}. The pair (πi, πi+1) is a rise if πi<πi+1 or a fall if πi>πi+1. Also a conventional rise is counted at the beginning of π and a conventional fall at the end. Let k be a fixed integer ≥ 1. The rise πi,πi+1 is said to be in a in a j (mod k) position if i ≡ j (mod k); similarly for a fall. The conventional rise at the beginning is in a 0 (mod k) position, while the conventional fall at the end is in an n (mod k) position. Let Pn≡Pn(r0,…,rk−1,ƒ0,…,ƒ;k−1) denote the number of permutations having ri rises i (mod k) positions and ƒ;i falls in i (mod k) positions. A generating function for Pn is obtained. In particular, for k = 2 the generating function is quite explicit and also, for certain special cases when k = 4

What are the indications for tonsillectomy in children?

Tonsillectomy with or without adenoidectomy is minimally effective when combined with tympanostomy tube placement in preventing recurrent otitis media in the 3 years following surgery. The risks of surgery must be weighed against potential benefit. (Grade of recommendation: B, based on low-quality randomized controlled trials [RCTs]). The evidence supporting tonsillectomy for recurrence of sore throat is controversial. There is insufficient evidence to recommend other potential indications. (Grade of recommendation: C, based on case series.

Dynamically Driven Evolution of the Interstellar Medium in M51

We report the highest-fidelity observations of the spiral galaxy M51 in CO emission, revealing the evolution of giant molecular clouds (GMCs) vis-a-vis the large-scale galactic structure and dynamics. The most massive GMCs (so-called GMAs) are first assembled and then broken up as the gas flow through the spiral arms. The GMAs and their H2 molecules are not fully dissociated into atomic gas as predicted in stellar feedback scenarios, but are fragmented into smaller GMCs upon leaving the spiral arms. The remnants of GMAs are detected as the chains of GMCs that emerge from the spiral arms into interarm regions. The kinematic shear within the spiral arms is sufficient to unbind the GMAs against self-gravity. We conclude that the evolution of GMCs is driven by large-scale galactic dynamics --their coagulation into GMAs is due to spiral arm streaming motions upon entering the arms, followed by fragmentation due to shear as they leave the arms on the downstream side. In M51, the majority of the gas remains molecular from arm entry through the inter-arm region and into the next spiral arm passage.Comment: 6 pages, including 3 figures. Accepted, ApJ

Grizzly bear monitoring by the Heiltsuk people as a crucible for First Nation conservation practice

Guided by deeply held cultural values, First Nations in Canada are rapidly regaining legal authority to manage natural resources. We present a research collaboration among academics, tribal government, provincial and federal government, resource managers, conservation practitioners, and community leaders supporting First Nation resource authority and stewardship. First, we present results from a molecular genetics study of grizzly bears inhabiting an important conservation area within the territory of the Heiltsuk First Nation in coastal British Columbia. Noninvasive hair sampling occurred between 2006 and 2009 in the Koeye watershed, a stronghold for grizzly bears, salmon, and Heiltsuk people. Molecular demographic analyses revealed a regionally significant population of bears, which congregate at the Koeye each salmon-spawning season. There was a minimum of 57 individual bears detected during the study period. Results also pointed to a larger than expected source geography for salmon-feeding bears in the study area (\u3e 1000 km²), as well as early evidence of a declining trend in the bear population potentially explained by declining salmon numbers. Second, we demonstrate and discuss the power of integrating scientific research with a culturally appropriate research agenda developed by indigenous people. Guided explicitly by principles from Gvi’ilas or customary law, this research methodology is coupled with Heiltsuk culture, enabling results of applied conservation science to involve and resonate with tribal leadership in ways that have eluded previous scientific endeavors. In this context, we discuss the effectiveness of research partnerships that, from the outset, create both scientific programs and integrated communities of action that can implement change. We argue that indigenous resource management requires collaborative approaches like ours, in which science-based management is embedded within a socially and culturally appropriate context. We emerge not only with a set of guiding principles for resource management by the Heiltsuk, but a broadly applicable strategy that fosters intimacy with traditional lands and resources and provides a powerful engine for conservation

SMA CO(J=6-5) and 435 micron interferometric imaging of the nuclear region of Arp 220

We have used the Submillimeter Array (SMA) to make the first interferometric observations (beam size ~1") of the 12CO J=6-5 line and 435 micron (690 GHz) continuum emission toward the central region of the nearby ULIRG Arp 220. These observations resolve the eastern and western nuclei from each other, in both the molecular line and dust continuum emission. At 435 micron, the peak intensity of the western nucleus is stronger than the eastern nucleus, and the difference in peak intensities is less than at longer wavelengths. Fitting a simple model to the dust emission observed between 1.3 mm and 435 micron suggests that dust emissivity power law index in the western nucleus is near unity and steeper in the eastern nucleus, about 2, and that the dust emission is optically thick at the shorter wavelength. Comparison with single dish measurements indicate that the interferometer observations are missing ~60% of the dust emission, most likely from a spatially extended component to which these observations are not sensitive. The 12CO J=6-5 line observations clearly resolve kinematically the two nuclei. The distribution and kinematics of the 12CO J=6-5 line appear to be very similar to lower J CO lies observed at similar resolution. Analysis of multiple 12CO line intensities indicates that the molecular gas in both nuclei have similar excitation conditions, although the western nucleus is warmer and denser. The excitation conditions are similar to those found in other extreme environments, including M82, Mrk 231, and BR 1202-0725. Simultaneous lower resolution observations of the 12CO, 13CO, and C18O J=2-1 lines show that the 13CO and C18O lines have similar intensities, which suggests that both of these lines are optically thick, or possibly that extreme high mass star formation has produced in an overabundance of C18O.Comment: 13 pages (emulateapj), 10 figures, Accepted for publication in Ap

Estimating Luminosity Function Constraints from High-Redshift Galaxy Surveys

The installation of the Wide Field Camera 3 (WFC3) on the Hubble Space Telescope (HST) will revolutionize the study of high-redshift galaxy populations. Initial observations of the HST Ultra Deep Field (UDF) have yielded multiple z>~7 dropout candidates. Supplemented by the Great Observatory Origins Deep Survey (GOODS) Early Release Science (ERS) and further UDF pointings, these data will provide crucial information about the most distant known galaxies. However, achieving tight constraints on the z~7 galaxy luminosity function (LF) will require even more ambitious photometric surveys. Using a Fisher matrix approach to fully account for Poisson and cosmic sample variance, as well as covariances in the data, we estimate the uncertainties on LF parameters achieved by surveys of a given area and depth. Applying this method to WFC3 z~7 dropout galaxy samples, we forecast the LF parameter uncertainties for a variety of model surveys. We demonstrate that performing a wide area (~1 deg^2) survey to H_AB~27 depth or increasing the UDF depth to H_AB~30 provides excellent constraints on the high-z LF when combined with the existing UDF GO and GOODS ERS data. We also show that the shape of the matter power spectrum may limit the possible gain of splitting wide area (>~0.5 deg^2) high-redshift surveys into multiple fields to probe statistically independent regions; the increased root-mean-squared density fluctuations in smaller volumes mostly offset the improved variance gained from independent samples.Comment: Version accepted by ApJ

The Grizzly, April 20, 1993

Two Officers Guilty in King Trial • U.C. Tutoring Program Benefits Local Students • Open Your Minds Ursinus: Give Art a Chance • Men\u27s Tennis Ups Record to 5-3 • Better Days on the Diamond • Men\u27s LaX Facing Tough Competitionhttps://digitalcommons.ursinus.edu/grizzlynews/1315/thumbnail.jp

The Grizzly, April 28, 1992

Earth Day 1992: Fun for All • CoreStates Grants Grant • UC History Majors Present Papers • U.C. a hit at U.N. • Holocaust Survivor Speaks • Scholarly Hat Trick in Biology • Political Cartoonist To Speak • Strunk Runs for Office • Spring Weekend Great Success • Concert Band & Jazz Ensemble Perform • Exam Schedule • Student Art Exhibition Opens, Awards Presented • Wismer\u27s Modern Art Spy • First Friends First • Sophomore Chats Tell All • Letter: Strunk Thanks Democrats • Men\u27s Lacrosse Splits Weekendhttps://digitalcommons.ursinus.edu/grizzlynews/1296/thumbnail.jp

Mass of the Southern Black Hole in NGC 6240 from Laser Guide Star Adaptive Optics

NGC 6240 is a pair of colliding disk galaxies, each with a black hole in its core. We have used laser guide star adaptive optics on the Keck II telescope to obtain high-resolution ($\sim 0.06$") near-infrared integral-field spectra of the region surrounding the supermassive black hole in the south nucleus of this galaxy merger. We use the K-band CO absorption bandheads to trace stellar kinematics. We obtain a spatial resolution of about 20 pc and thus directly resolve the sphere of gravitational influence of the massive black hole. We explore two different methods to measure the black hole mass. Using a Jeans Axisymmetric Multi-Gaussian mass model, we investigate the limit that a relaxed mass distribution produces all of the measured velocity dispersion, and find an upper limit on the black hole mass at 2.0 \pm 0.2 \times 10^9 M_{\sun}. When assuming the young stars whose spectra we observe remain in a thin disk, we compare Keplerian velocity fields to the measured two-dimensional velocity field measured and fit for a mass profile containing a black hole point mass plus a radially-varying spherical component, which suggests a lower limit for the black hole mass of 8.7 \pm 0.3 \times 10^8 M_{\sun}. Our measurements of the stellar velocity dispersion place this AGN within the scatter of the $M_{BH}$-$\sigma_{*}$ relation. As NGC 6240 is a merging system, this may indicate that the relation is preserved during a merger at least until the final coalescence of the two nuclei.Comment: 10 pages, 12 figures; accepted to Ap