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

High-Fidelity Control, Detection, and Entanglement of Alkaline-Earth Rydberg Atoms

Trapped neutral atoms have become a prominent platform for quantum science, where entanglement fidelity records have been set using highly excited Rydberg states. However, controlled two-qubit entanglement generation has so far been limited to alkali species, leaving the exploitation of more complex electronic structures as an open frontier that could lead to improved fidelities and fundamentally different applications such as quantum-enhanced optical clocks. Here, we demonstrate a novel approach utilizing the two-valence electron structure of individual alkaline-earth Rydberg atoms. We find fidelities for Rydberg state detection, single-atom Rabi operations and two-atom entanglement that surpass previously published values. Our results pave the way for novel applications, including programmable quantum metrology and hybrid atom–ion systems, and set the stage for alkaline-earth based quantum computing architectures

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

Mechanism of action of VP1-001 in cryAB(R120G)-associated and age-related cataracts

PurposeWe previously identified an oxysterol, VP1-001 (also known as compound 29), that partially restores the transparency of lenses with cataracts. To understand the mechanism of VP1-001, we tested the ability of its enantiomer, ent-VP1-001, to bind and stabilize αB-crystallin (cryAB) in vitro and to produce a similar therapeutic effect in cryAB(R120G) mutant and aged wild-type mice with cataracts. VP1-001 and ent-VP1-001 have identical physicochemical properties. These experiments are designed to critically evaluate whether stereoselective binding to cryAB is required for activity.MethodsWe compared the binding of VP1-001 and ent-VP1-001 to cryAB using in silico docking, differential scanning fluorimetry (DSF), and microscale thermophoresis (MST). Compounds were delivered by six topical administrations to mouse eyes over 2 weeks, and the effects on cataracts and lens refractive measures in vivo were examined. Additionally, lens epithelial and fiber cell morphologies were assessed via transmission electron microscopy.ResultsDocking studies suggested greater binding of VP1-001 into a deep groove in the cryAB dimer compared with ent-VP1-001. Consistent with this prediction, DSF and MST experiments showed that VP1-001 bound cryAB, whereas ent-VP1-001 did not. Accordingly, topical treatment of lenses with ent-VP1-001 had no effect, whereas VP1-001 produced a statistically significant improvement in lens clarity and favorable changes in lens morphology.ConclusionsThe ability of VP1-001 to bind native cryAB dimers is important for its ability to reverse lens opacity in mouse models of cataracts

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

On the Approximability of Dodgson and Young Elections

The voting rules proposed by Dodgson and Young are both designed to nd the alternative closest to being a Condorcet winner, according to two di erent notions of proximity; the score of a given alternative is known to be hard to compute under either rule. In this paper, we put forward two algorithms for ap- proximating the Dodgson score: an LP-based randomized rounding algorithm and a deterministic greedy algorithm, both of which yield an O(logm) approximation ratio, where m is the number of alternatives; we observe that this result is asymptotically optimal, and further prove that our greedy algorithm is optimal up to a factor of 2, unless problems in NP have quasi-polynomial time algorithms. Although the greedy algorithm is computationally superior, we argue that the randomized rounding algorithm has an advantage from a social choice point of view. Further, we demonstrate that computing any reasonable approximation of the ranking produced by Dodgson\u27s rule is NP-hard. This result provides a complexity-theoretic explanation of sharp discrepancies that have been observed in the Social Choice Theory literature when comparing Dodgson elections with simpler voting rules. Finally, we show that the problem of calculating the Young score is NP-hard to approximate by any factor. This leads to an inapproximability result for the Young ranking

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

Precise Stellar Radial Velocities of an M Dwarf with a Michelson Interferometer and a Medium-resolution Near-infrared Spectrograph

Precise near-infrared radial velocimetry enables efficient detection and transit verification of low-mass extrasolar planets orbiting M dwarf hosts, which are faint for visible-wavelength radial velocity surveys. The TripleSpec Exoplanet Discovery Instrument, or TEDI, is the combination of a variable-delay Michelson interferometer and a medium-resolution (R=2700) near-infrared spectrograph on the Palomar 200" Hale Telescope. We used TEDI to monitor GJ 699, a nearby mid-M dwarf, over 11 nights spread across 3 months. Analysis of 106 independent observations reveals a root-mean-square precision of less than 37 m/s for 5 minutes of integration time. This performance is within a factor of 2 of our expected photon-limited precision. We further decompose the residuals into a 33 m/s white noise component, and a 15 m/s systematic noise component, which we identify as likely due to contamination by telluric absorption lines. With further development this technique holds promise for broad implementation on medium-resolution near-infrared spectrographs to search for low-mass exoplanets orbiting M dwarfs, and to verify low-mass transit candidates.Comment: 55 pages and 13 figures in aastex format. Accepted by PAS

Survey Mode Effects on Valuation of Environmental Goods

This article evaluates the effect of the choice of survey recruitment mode on the value of water quality in lakes, rivers, and streams. Four different modes are compared: bringing respondents to one central location after phone recruitment, mall intercepts in two states, national phone-mail survey, and an Internet survey with a national, probability-based panel. The modes differ in terms of the representativeness of the samples, non-response rates, sample selection effects, and consistency of responses. The article also shows that the estimated value of water quality can differ substantially depending on the survey mode. The national Internet panel has the most desirable properties with respect to performance on the four important survey dimensions of interest