Improving Dodgson scoring techniques

The Dodgson score problem is part of the Dodgson election scheme invented by Charles Dodgson and presented in his manuscript. One of the system\u27s strengths (and motivations for its study) is that it satisfies the Condorcet criterion (which states that any candidate who defeats all other candidates in pairwise elections will be declared the winner). It is unfortunate, though, that in a given election no Condorcet winner may exist. Dodgson\u27s election system chooses the winner closest to being the Condorcet winner in the sense that it requires the shortest sequence of edits (swapping of adjacent candidates in the voters\u27 preference rankings) to the votes in order to make it one. The length of this sequence is known as the Dodgson score. The problem of finding the Dodgson score of a candidate is computationally intractable. Thus an approximation is necessary. This paper puts forth MCDodgsonScore, a polynomialtime computable (ln(m) + 1)-approximation of that problem. This approximation is optimal, meaning that an approximation with an asymptotically tighter error bound does not exist. MCDodgsonScore builds on a technique introduced by Homan and Hemaspaandra in 2006. A nice feature of MCDodgsonScore is that, when treated as its own voting rule, it will also satisfy the Condorcet criterion

Statistical Searches for Microlensing Events in Large, Non-Uniformly Sampled Time-Domain Surveys: A Test Using Palomar Transient Factory Data

Many photometric time-domain surveys are driven by specific goals, such as searches for supernovae or transiting exoplanets, which set the cadence with which fields are re-imaged. In the case of the Palomar Transient Factory (PTF), several sub-surveys are conducted in parallel, leading to non-uniform sampling over its $\sim$$20,000 \mathrm{deg}^2$ footprint. While the median $7.26 \mathrm{deg}^2$ PTF field has been imaged $\sim$40 times in \textit{R}-band, $\sim$$2300 \mathrm{deg}^2$ have been observed $>$100 times. We use PTF data to study the trade-off between searching for microlensing events in a survey whose footprint is much larger than that of typical microlensing searches, but with far-from-optimal time sampling. To examine the probability that microlensing events can be recovered in these data, we test statistics used on uniformly sampled data to identify variables and transients. We find that the von Neumann ratio performs best for identifying simulated microlensing events in our data. We develop a selection method using this statistic and apply it to data from fields with $>$10 $R$-band observations, $1.1\times10^9$ light curves, uncovering three candidate microlensing events. We lack simultaneous, multi-color photometry to confirm these as microlensing events. However, their number is consistent with predictions for the event rate in the PTF footprint over the survey's three years of operations, as estimated from near-field microlensing models. This work can help constrain all-sky event rate predictions and tests microlensing signal recovery in large data sets, which will be useful to future time-domain surveys, such as that planned with the Large Synoptic Survey Telescope.Comment: 13 pages, 14 figures; accepted for publication in ApJ. fixed author lis

Untangling the Galaxy. IV. Empirical Constraints on Angular Momentum Evolution and Gyrochronology for Young Stars in the Field

We present a catalog of ~100,000 periodic variable stars in TESS FFI data among members of widely distributed moving groups identified with Gaia in the previous papers in the series. By combining the periods from our catalog attributable to rotation with previously derived rotation periods for benchmark open clusters, we develop an empirical gyrochronology relation of angular momentum evolution that is valid for stars with ages 10-1000 Myr. Excluding stars rotating faster than 2 days, which we find are predominantly binaries, we achieve a typical age precision of ~0.2-0.3 dex and improving at older ages. Importantly, these empirical relations apply to not only FGK-type stars but also M-type stars, due to the angular momentum distribution being much smoother, simpler, continuous and monotonic as compared to the rotation period distribution. As a result, we are also able to begin tracing in fine detail the nature of angular momentum loss in low-mass stars as functions of mass and age. We characterize the stellar variability amplitudes of the cool stars as functions of mass and age, which may correlate with the starspot covering fractions. We also identify pulsating variables among the hotter stars in the catalog, including $\delta$ Scuti, $\gamma$ Dor and SPB-type variables. These data represent an important step forward in being able to estimate precise ages of FGK- and M-type stars in the field, starting as early as the pre-main-sequence phase of evolution.Comment: 24 pages, 14 figures, accepted to A

WHY ARE RAPIDLY ROTATING M DWARFS IN THE PLEIADES SO (INFRA)RED? NEW PERIOD MEASUREMENTS CONFIRM ROTATION-DEPENDENT COLOR OFFSETS FROM THE CLUSTER SEQUENCE

Stellar rotation periods ( P {sub rot}) measured in open clusters have proved to be extremely useful for studying stars’ angular momentum content and rotationally driven magnetic activity, which are both age- and mass-dependent processes. While P {sub rot} measurements have been obtained for hundreds of solar-mass members of the Pleiades, measurements exist for only a few low-mass (<0.5 M {sub ⊙}) members of this key laboratory for stellar evolution theory. To fill this gap, we report P {sub rot} for 132 low-mass Pleiades members (including nearly 100 with M ≤ 0.45 M {sub ⊙}), measured from photometric monitoring of the cluster conducted by the Palomar Transient Factory in late 2011 and early 2012. These periods extend the portrait of stellar rotation at 125 Myr to the lowest-mass stars and re-establish the Pleiades as a key benchmark for models of the transport and evolution of stellar angular momentum. Combining our new P {sub rot} with precise BVIJHK photometry reported by Stauffer et al. and Kamai et al., we investigate known anomalies in the photometric properties of K and M Pleiades members. We confirm the correlation detected by Kamai et al. between a star's P {sub rot} and position relative tomore » the main sequence in the cluster's color–magnitude diagram. We find that rapid rotators have redder ( V − K ) colors than slower rotators at the same V , indicating that rapid and slow rotators have different binary frequencies and/or photospheric properties. We find no difference in the photometric amplitudes of rapid and slow rotators, indicating that asymmetries in the longitudinal distribution of starspots do not scale grossly with rotation rate.« les

The APOGEE-2 Survey of the Orion Star Forming Complex: I. Target Selection and Validation with early observations

The Orion Star Forming Complex (OSFC) is a central target for the APOGEE-2 Young Cluster Survey. Existing membership catalogs span limited portions of the OSFC, reflecting the difficulty of selecting targets homogeneously across this extended, highly structured region. We have used data from wide field photometric surveys to produce a less biased parent sample of young stellar objects (YSOs) with infrared (IR) excesses indicative of warm circumstellar material or photometric variability at optical wavelengths across the full 420 square degrees extent of the OSFC. When restricted to YSO candidates with H < 12.4, to ensure S/N ~100 for a six visit source, this uniformly selected sample includes 1307 IR excess sources selected using criteria vetted by Koenig & Liesawitz and 990 optical variables identified in the Pan-STARRS1 3$\pi$ survey: 319 sources exhibit both optical variability and evidence of circumstellar disks through IR excess. Objects from this uniformly selected sample received the highest priority for targeting, but required fewer than half of the fibers on each APOGEE-2 plate. We fill the remaining fibers with previously confirmed and new color-magnitude selected candidate OSFC members. Radial velocity measurements from APOGEE-1 and new APOGEE-2 observations taken in the survey's first year indicate that ~90% of the uniformly selected targets have radial velocities consistent with Orion membership.The APOGEE-2 Orion survey will include >1100 bona fide YSOs whose uniform selection function will provide a robust sample for comparative analyses of the stellar populations and properties across all sub-regions of Orion.Comment: Accepted for publication in ApJ

Why are rapidly rotating M dwarfs in the Pleiades so (infra)red? New period measurements confirm rotation-dependent color offsets from the cluster sequence

Stellar rotation periods (P_(rot)) measured in open clusters have proved to be extremely useful for studying stars' angular momentum content and rotationally driven magnetic activity, which are both age- and mass-dependent processes. While P rot measurements have been obtained for hundreds of solar-mass members of the Pleiades, measurements exist for only a few low-mass (<0.5 M_⊙) members of this key laboratory for stellar evolution theory. To fill this gap, we report P_(rot) for 132 low-mass Pleiades members (including nearly 100 with M ≤ 0.45 M_⊙), measured from photometric monitoring of the cluster conducted by the Palomar Transient Factory in late 2011 and early 2012. These periods extend the portrait of stellar rotation at 125 Myr to the lowest-mass stars and re-establish the Pleiades as a key benchmark for models of the transport and evolution of stellar angular momentum. Combining our new P_(rot) with precise BVIJHK photometry reported by Stauffer et al. and Kamai et al., we investigate known anomalies in the photometric properties of K and M Pleiades members. We confirm the correlation detected by Kamai et al. between a star's P_(rot) and position relative to the main sequence in the cluster's color–magnitude diagram. We find that rapid rotators have redder (V − K) colors than slower rotators at the same V, indicating that rapid and slow rotators have different binary frequencies and/or photospheric properties. We find no difference in the photometric amplitudes of rapid and slow rotators, indicating that asymmetries in the longitudinal distribution of starspots do not scale grossly with rotation rate

An Activity–Rotation Relationship and Kinematic Analysis of Nearby Mid-to-Late-Type M Dwarfs

Using spectroscopic observations and photometric light curves of 238 nearby M dwarfs from the MEarth exoplanet transit survey, we examine the relationships between magnetic activity (quantified by Hα emission), rotation period, and stellar age. Previous attempts to investigate the relationship between magnetic activity and rotation in these stars were hampered by the limited number of M dwarfs with measured rotation periods (and the fact that v sin i measurements probe only rapid rotation). However, the photometric data from MEarth allows us to probe a wide range of rotation periods for hundreds of M dwarf stars (from shorter than one to longer than 100 days). Over all M spectral types that we probe, we find that the presence of magnetic activity is tied to rotation, including for late-type, fully convective M dwarfs. We also find evidence that the fraction of late-type M dwarfs that are active may be higher at longer rotation periods compared to their early-type counterparts, with several active, late-type, slowly rotating stars present in our sample. Additionally, we find that all M dwarfs with rotation periods shorter than 26 days (early-type; M1–M4) and 86 days (late-type; M5–M8) are magnetically active. This potential mismatch suggests that the physical mechanisms that connect stellar rotation to chromospheric heating may be different in fully convective stars. A kinematic analysis suggests that the magnetically active, rapidly rotating stars are consistent with a kinematically young population, while slow-rotators are less active or inactive and appear to belong to an older, dynamically heated stellar population

LSST Science Book, Version 2.0

A survey that can cover the sky in optical bands over wide fields to faint magnitudes with a fast cadence will enable many of the exciting science opportunities of the next decade. The Large Synoptic Survey Telescope (LSST) will have an effective aperture of 6.7 meters and an imaging camera with field of view of 9.6 deg^2, and will be devoted to a ten-year imaging survey over 20,000 deg^2 south of +15 deg. Each pointing will be imaged 2000 times with fifteen second exposures in six broad bands from 0.35 to 1.1 microns, to a total point-source depth of r~27.5. The LSST Science Book describes the basic parameters of the LSST hardware, software, and observing plans. The book discusses educational and outreach opportunities, then goes on to describe a broad range of science that LSST will revolutionize: mapping the inner and outer Solar System, stellar populations in the Milky Way and nearby galaxies, the structure of the Milky Way disk and halo and other objects in the Local Volume, transient and variable objects both at low and high redshift, and the properties of normal and active galaxies at low and high redshift. It then turns to far-field cosmological topics, exploring properties of supernovae to z~1, strong and weak lensing, the large-scale distribution of galaxies and baryon oscillations, and how these different probes may be combined to constrain cosmological models and the physics of dark energy.Comment: 596 pages. Also available at full resolution at http://www.lsst.org/lsst/sciboo