Quotients of S2×S2S^2\times{S^2}

We consider closed topological 4-manifolds $M$ with universal cover ${S^2\times{S^2}}$ and Euler characteristic $\chi(M) = 1$. All such manifolds with $\pi=\pi_1(M)\cong {\mathbb Z}/4$ are homotopy equivalent. In this case, we show that there are four homeomorphism types, and propose a candidate for a smooth example which is not homeomorphic to the geometric quotient. If $\pi\cong {\mathbb Z}/2 \times {\mathbb Z}/2$, we show that there are three homotopy types (and between 6 and 24 homeomorphism types).Comment: 18 page

Continued fractions and Pell conics

The classic method of continued fractions is applied to finding rational integer points of Pell conics

Validation of the frequency modulation technique applied to the pulsating Sct- Dor eclipsing binary star KIC 8569819

KIC 8569819 is an eclipsing binary star with an early F primary and G secondary in a 20.85-d eccentric orbit. The primary is a δ Sct–γ Dor star pulsating in both p modes and g modes. Using four years of Kepler Mission photometric data, we independently model the light curve using the traditional technique with the modelling code PHOEBE, and we study the orbital characteristics using the new frequency modulation technique. We show that both methods provide the equivalent orbital period, eccentricity and argument of periastron, thus illustrating and validating the FM technique. In the amplitude spectrum of the p-mode pulsations, we also discovered an FM signal compatible with a third body in the system, a low-mass M dwarf in an 861-d orbit around the primary pair. However, the eclipses show no timing variations, indicating that the FM signal is a consequence of the intrinsic change in pulsation frequency, thus providing a cautionary tale. Our analysis shows the potential of the FM technique using Kepler data, and we discuss the prospects to detect planets and brown dwarfs in Kepler data for A and F stars even in the absence of transits and with no spectroscopic radial velocity curves. This opens the possibility of finding planets orbiting hotter stars that cannot be found by traditional techniques

Heartbeat stars and the ringing of tidal pulsations

With the advent of high precision photometry from satellites such as Kepler and CoRoT, a whole new layer of interesting and astounding astronomical objects has been revealed: heartbeat stars are an example of such objects. Heartbeat stars are eccen- tric ellipsoidal variables that undergo strong tidal interactions when the stars are almost in contact at the time of closest approach. These interactions deform of the stars and cause a notable light curve variation in the form of a tidal pulse. A subset of these objects (∼20%) show prominent tidally induced pulsations: pulsations forced by the binary orbit. We now have a fully functional code that models binary star features (using phoebe) and stellar pulsations simultaneously, enabling a complete and accurate heartbeat star model to be determined. In this paper we show the results of our new code, which uses emcee, a variant of mcmc, to generate a full set of stellar parameters. We further highlight the interesting features of KIC 8164262, including its tidally induced pulsations and resonantly locked pulsations

Measurement and predictors of adherence in a trial of HSV suppressive therapy in Tanzania.

This study estimates adherence and identifies predictors of good adherence among 1305 Tanzanian women participating in a randomised, double-blind, placebo-controlled trial of HSV suppressive therapy to reduce HIV incidence or genital HIV shedding. Women were randomised to acyclovir 400mg BD or placebo and followed every three months for 12-30 months. Adherence was assessed by tablet counts. Random urine samples, collected between 6 and 24 months, were tested for acyclovir. At 12, 24 and 30 month visits, 56%, 52% and 54% of women on treatment had adherence >or=90%, respectively. Factors independently associated with good adherence (taking >or=90% of tablets in the preceding 3-months) included older age, understanding trial concepts at enrolment, living >2 years in the screening site, receiving an unannounced tablet check visit, using oral contraception at screening, living in the same site and house as the previous visit, accessing VCT during the trial, recent malaria and not having a positive pregnancy test. Overall, 55% of urine samples from women randomised to acyclovir had detectable acyclovir. Additional, tailored adherence strategies may be needed for younger, more mobile women and those who have not used oral contraception, which may sensitise them to daily tablet-taking. Use of biomarkers may alert investigators to adherence problems

Impact of Rubin Observatory LSST Template Acquisition Strategies on Early Science from the Transients and Variable Stars Science Collaboration: Non-time-critical Science Cases

Vera C. Rubin Observatory Legacy Survey of Space and Time, LSST, will revolutionize modern astronomy by producing an extremely deep (coadded depth ~27 mag) depth-limited survey of the entire southern sky (LSST Science Collaboration et al. 2009). The 8.4 m large-aperture, wide-field telescope, which is based in Cerro Pachón, will image the entire Southern sky every three nights in multiple bands (SDSS-u, g, r, i, z, y) and produce a fire-hose of data, 20 Tb each night, concluding in a 60 petabyte data set as the legacy of the 10 yr survey. Extracting meaningful light curves from variable objects requires difference imaging to both identify variability and calibrate light curve data products. Templates, co-added groups of visits that act as an image of the "static" sky, are a key component of Difference Imaging Analysis (DIA) and as such are of paramount importance for all science that involves variable objects. As the "non-time-critical" science cases discussed here are mostly periodic, they generally do not depend upon the survey alert stream; however, templates are still crucial for performing science and calibrations during the first year. We provide recommendations for observing strategies for template acquisition starting from commissioning and through Year 1 of the survey

Phoebe 2.0 – Triple and multiple systems

Some close binary formation theories require the presence of a third body so that the binary orbit can shrink over time. Tidal friction and Kozai cycles transfer energy from the binary to its companion, resulting in a close inner binary and a wide third body orbit. Spectroscopy and imaging studies have found 40% of binaries with periods less than 10 days, and 96% with periods less than 3 days, have a wide tertiary companion. With recent advancements in large photometric surveys, we are now beginning to detect many of these triple systems by observing tertiary eclipses or through the effect they have on the eclipse timing variations (ETVs) of the inner-binary. In the sample of 2600 Kepler EBs, we have detected the possible presence of a third body in ∼20%, including several circumbinary planets. Some multiple systems are quite dynamical and feature disappearing and reappearing eclipses, apsidal motion, and large disruptions to the inner-binary. phoebe is a freely available binary modeling code which can dynamically model all of these systems, allowing us to better test formation theories and probe the physics of eclipsing binaries

PHOEBE 2.0 – Where no model has gone before

phoebe 2.0 is an open source framework bridging the gap between stellar observations and models. It allows to create and fit models simultaneously and consistently to a wide range of observational data such as photometry, spectroscopy, spectrapolarimetry, interferometry and astrometry. To reach the level of precision required by the newest generation of instruments such as Kepler, GAIA and the arrays of large telescopes, the code is set up to handle a wide range of phenomena such as multiplicity, rotation, pulsations and magnetic fields, and to model the involved physics to a new level

Effect of dead space on avalanche speed

The effects of dead space (the minimum distance travelled by a carrier before acquiring enough energy to impact ionize) on the current impulse response and bandwidth of an avalanche multiplication process are obtained from a numerical model that maintains a constant carrier velocity but allows for a random distribution of impact ionization path lengths. The results show that the main mechanism responsible for the increase in response time with dead space is the increase in the number of carrier groups, which qualitatively describes the length of multiplication chains. When the dead space is negligible, the bandwidth follows the behavior predicted by Emmons but decreases as dead space increase