On consecutive pattern-avoiding permutations of length 4, 5 and beyond

We review and extend what is known about the generating functions for consecutive pattern-avoiding permutations of length 4, 5 and beyond, and their asymptotic behaviour. There are respectively, seven length-4 and twenty-five length-5 consecutive-Wilf classes. D-finite differential equations are known for the reciprocal of the exponential generating functions for four of the length-4 and eight of the length-5 classes. We give the solutions of some of these ODEs. An unsolved functional equation is known for one more class of length-4, length-5 and beyond. We give the solution of this functional equation, and use it to show that the solution is not D-finite. For three further length-5 c-Wilf classes we give recurrences for two and a differential-functional equation for a third. For a fourth class we find a new algebraic solution. We give a polynomial-time algorithm to generate the coefficients of the generating functions which is faster than existing algorithms, and use this to (a) calculate the asymptotics for all classes of length 4 and length 5 to significantly greater precision than previously, and (b) use these extended series to search, unsuccessfully, for D-finite solutions for the unsolved classes, leading us to conjecture that the solutions are not D-finite. We have also searched, unsuccessfully, for differentially algebraic solutions.Comment: 23 pages, 2 figures (update of references, plus web link to enumeration data). Minor update. Typos corrected. One additional referenc

TOI-150: A transiting hot Jupiter in the TESS southern CVZ

We report the detection of a hot Jupiter ($M_{p}=1.75_{-0.17}^{+0.14}\ M_{J}$,$R_{p}=1.38\pm0.04\ R_{J}$) orbiting a middle-aged star ($\log g=4.152^{+0.030}_{-0.043}$) in the Transiting Exoplanet Survey Satellite (TESS) southern continuous viewing zone ($\beta=-79.59^{\circ}$). We confirm the planetary nature of the candidate TOI-150.01 using radial velocity observations from the APOGEE-2 South spectrograph and the Carnegie Planet Finder Spectrograph, ground-based photometric observations from the robotic Three-hundred MilliMeter Telescope at Las Campanas Observatory, and Gaia distance estimates. Large-scale spectroscopic surveys, such as APOGEE/APOGEE-2, now have sufficient radial velocity precision to directly confirm the signature of giant exoplanets, making such data sets valuable tools in the TESS era. Continual monitoring of TOI-150 by TESS can reveal additional planets and subsequent observations can provide insights into planetary system architectures involving a hot Jupiter around a star about halfway through its main-sequence life.Comment: 13 pages, 3 figures, 2 tables, accepted to ApJ

Standard Galactic Field RR Lyrae II: A Gaia DR2 calibration of the period-Wesenheit-metallicity relation

RR Lyrae stars have long been popular standard candles, but significant advances in methodology and technology have been made in recent years to increase their precision as distance indicators. We present multi-wavelength (optical $UBVR_cI_c$ and Gaia $G, BP, RP$; near-infrared $JHK_s$; mid-infrared $[3.6], [4.5]$) period-luminosity-metallicity (PLZ), period-Wesenheit-metallicity (PWZ) relations, calibrated using photometry obtained from The Carnegie RR Lyrae Program and parallaxes from the Gaia second data release for 55 Galactic field RR Lyrae stars. The metallicity slope, which has long been predicted by theoretical relations, can now be measured in all passbands. The scatter in the PLZ relations is on the order of 0.2 mag, and is still dominated by uncertainties in the parallaxes. As a consistency check of our PLZ relations, we also measure the distance modulus to the globular cluster M4, the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC), and our results are in excellent agreement with estimates from previous studies.Comment: Accepted for publication in MNRAS, 15 pages, 14 figure

The Carnegie-Chicago Hubble Program. VIII. An Independent Determination of the Hubble Constant Based on the Tip of the Red Giant Branch

We present a new and independent determination of the local value of the Hubble constant based on a calibration of the tip of the red giant branch (TRGB) applied to Type Ia supernovae (SNe Ia). We find a value of H0 = 69.8 ± 0.8 (±1.1% stat) ± 1.7 (±2.4% sys) km s−1 Mpc−1. The TRGB method is both precise and accurate and is parallel to but independent of the Cepheid distance scale. Our value sits midway in the range defined by the current Hubble tension. It agrees at the 1.2σ level with that of the Planck Collaboration et al. estimate and at the 1.7σ level with the Hubble Space Telescope (HST) SHoES measurement of H0 based on the Cepheid distance scale. The TRGB distances have been measured using deep HST Advanced Camera for Surveys imaging of galaxy halos. The zero-point of the TRGB calibration is set with a distance modulus to the Large Magellanic Cloud of 18.477 ± 0.004 (stat) ± 0.020 (sys) mag, based on measurement of 20 late-type detached eclipsing binary stars, combined with an HST parallax calibration of a 3.6 μm Cepheid Leavitt law based on Spitzer observations. We anchor the TRGB distances to galaxies that extend our measurement into the Hubble flow using the recently completed Carnegie Supernova Project I ( CSP-I ) sample containing about 100 well-observed SNe Ia . There are several advantages of halo TRGB distance measurements relative to Cepheid variables; these include low halo reddening, minimal effects of crowding or blending of the photometry, only a shallow (calibrated) sensitivity to metallicity in the I band, and no need for multiple epochs of observations or concerns of different slopes with period. In addition, the host masses of our TRGB host-galaxy sample are higher, on average, than those of the Cepheid sample, better matching the range of host-galaxy masses in the CSP-I distant sample and reducing potential systematic effects in the SNe Ia measurements

The Carnegie-Chicago Hubble Program. VIII. An Independent Determination of the Hubble Constant Based on the Tip of the Red Giant Branch

We present a new and independent determination of the local value of the Hubble constant based on a calibration of the Tip of the Red Giant Branch (TRGB) applied to Type Ia supernovae (SNeIa). We find a value of Ho = 69.8 +/- 0.8 (+/-1.1\% stat) +/- 1.7 (+/-2.4\% sys) km/sec/Mpc. The TRGB method is both precise and accurate, and is parallel to, but independent of the Cepheid distance scale. Our value sits midway in the range defined by the current Hubble tension. It agrees at the 1.2-sigma level with that of the Planck 2018 estimate, and at the 1.7-sigma level with the SHoES measurement of Ho based on the Cepheid distance scale. The TRGB distances have been measured using deep Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) imaging of galaxy halos. The zero point of the TRGB calibration is set with a distance modulus to the Large Magellanic Cloud of 18.477 +/- 0.004 (stat) +/-0.020 (sys) mag, based on measurement of 20 late-type detached eclipsing binary (DEB) stars, combined with an HST parallax calibration of a 3.6 micron Cepheid Leavitt law based on Spitzer observations. We anchor the TRGB distances to galaxies that extend our measurement into the Hubble flow using the recently completed Carnegie Supernova Project I sample containing about 100 well-observed SNeIa. There are several advantages of halo TRGB distance measurements relative to Cepheid variables: these include low halo reddening, minimal effects of crowding or blending of the photometry, only a shallow (calibrated) sensitivity to metallicity in the I-band, and no need for multiple epochs of observations or concerns of different slopes with period. In addition, the host masses of our TRGB host-galaxy sample are higher on average than the Cepheid sample, better matching the range of host-galaxy masses in the CSP distant sample, and reducing potential systematic effects in the SNeIa measurements.Comment: 60 pages, 20 figures, accepted for publication in the Astrophysical Journa

Discovery and Early Evolution of ASASSN-19bt, the First TDE Detected by TESS

We present the discovery and early evolution of ASASSN-19bt, a tidal disruption event (TDE) discovered by the All-Sky Automated Survey for Supernovae (ASAS-SN) at a distance of $d\simeq115$ Mpc and the first TDE to be detected by TESS. As the TDE is located in the TESS Continuous Viewing Zone, our dataset includes 30-minute cadence observations starting on 2018 July 25, and we precisely measure that the TDE begins to brighten $\sim8.3$ days before its discovery. Our dataset also includes 18 epochs of Swift UVOT and XRT observations, 2 epochs of XMM-Newton observations, 13 spectroscopic observations, and ground data from the Las Cumbres Observatory telescope network, spanning from 32 days before peak through 37 days after peak. ASASSN-19bt thus has the most detailed pre-peak dataset for any TDE. The TESS light curve indicates that the transient began to brighten on 2019 January 21.6 and that for the first 15 days its rise was consistent with a flux $\propto t^2$ power-law model. The optical/UV emission is well-fit by a blackbody SED, and ASASSN-19bt exhibits an early spike in its luminosity and temperature roughly 32 rest-frame days before peak and spanning up to 14 days that has not been seen in other TDEs, possibly because UV observations were not triggered early enough to detect it. It peaked on 2019 March 04.9 at a luminosity of $L\simeq1.3\times10^{44}$ ergs s$^{-1}$ and radiated $E\simeq3.2\times10^{50}$ ergs during the 41-day rise to peak. X-ray observations after peak indicate a softening of the hard X-ray emission prior to peak, reminiscent of the hard/soft states in X-ray binaries.Comment: 23 pages, 14 figures, 5 tables. A machine-readable table containing the host-subtracted photometry presented in this manuscript is included as an ancillary fil

Conservative management versus open reduction and internal fixation for mid-shaft clavicle fractures in adults - The Clavicle Trial: Study protocol for a multicentre randomized controlled trial

Background: Clavicle fractures account for around 4% of all fractures and up to 44% of fractures of the shoulder girdle. Fractures of the middle third (or mid-shaft) account for approximately 80% of all clavicle fractures. Management of this group of fractures is often challenging and the outcome can be unsatisfactory. In particular it is not clear whether surgery produces better outcomes than non-surgical management. Currently there is much variation in the use of surgery and a lack of good quality evidence to inform our decision.Methods/Design: We aim to undertake a multicentre randomised controlled trial evaluating the effectiveness and safety of conservative management versus open reduction and internal fixation for displaced mid-shaft clavicle fractures in adults. Surgical treatment will be performed using the Acumed clavicle fixation system. Conservative management will consist of immobilisation in a sling at the side in internal rotation for 6 weeks or until clinical or radiological union. We aim to recruit 300 patients. These patients will be followed-up for at least 9 months. The primary endpoint will be the rate of non-union at 3 months following treatment. Secondary endpoints will be limb function measured using the Constant-Murley Score and the Disabilities of the Arm, Shoulder and Hand (DASH) Score at 3 and 9 months post-operatively.Discussion: This article presents the protocol for a multicentre randomised controlled trial. It gives extensive details of, and the basis for, the chosen methods, and describes the key measures taken to avoid bias and to ensure validity.Trial Registration: United Kingdom Clinical Research Network ID: 8665. The date of registration of the trial is 07/09/2006. The date the first patient was recruited is 18/12/2007. © 2011 Longo et al; licensee BioMed Central Ltd