Constraining the False Positive Rate for Kepler Planet Candidates with Multi-Color Photometry from the GTC

Using the OSIRIS instrument installed on the 10.4-m Gran Telescopio Canarias (GTC) we acquired multi-color transit photometry of four small (Rp < 5 R_Earth) short-period (P < 6 days) planet candidates recently identified by the Kepler space mission. These observations are part of a program to constrain the false positive rate for small, short-period Kepler planet candidates. Since planetary transits should be largely achromatic when observed at different wavelengths (excluding the small color changes due to stellar limb darkening), we use the observed transit color to identify candidates as either false positives (e.g., a blend with a stellar eclipsing binary either in the background/foreground or bound to the target star) or validated planets. Our results include the identification of KOI 225.01 and KOI 1187.01 as false positives and the tentative validation of KOI 420.01 and KOI 526.01 as planets. The probability of identifying two false positives out of a sample of four targets is less than 1%, assuming an overall false positive rate for Kepler planet candidates of 10% (as estimated by Morton & Johnson 2011). Therefore, these results suggest a higher false positive rate for the small, short-period Kepler planet candidates than has been theoretically predicted by other studies which consider the Kepler planet candidate sample as a whole. Furthermore, our results are consistent with a recent Doppler study of short-period giant Kepler planet candidates (Santerne et al. 2012). We also investigate how the false positive rate for our sample varies with different planetary and stellar properties. Our results suggest that the false positive rate varies significantly with orbital period and is largest at the shortest orbital periods (P < 3 days), where there is a corresponding rise in the number of detached eclipsing binary stars... (truncated)Comment: 13 pages, 12 figures, 3 tables; revised for MNRA

High-Spatial-Resolution K-Band Imaging of Select K2 Campaign Fields

NASA's K2 mission began observing fields along the ecliptic plane in 2014. Each observing campaign lasts approximately 80 days, during which high-precision optical photometry of select astrophysical targets is collected by the Kepler spacecraft. Due to the 4 arcsec pixel scale of the Kepler photometer, significant blending between the observed targets can occur (especially in dense fields close to the Galactic plane). We undertook a program to use the Wide Field Camera (WFCAM) on the 3.8 m United Kingdom InfraRed Telescope (UKIRT) to collect high-spatial-resolution near-infrared images of targets in select K2 campaign fields, which we report here. These 0.4 arcsec resolution K-band images offer the opportunity to perform a variety of science, including vetting exoplanet candidates by identifying nearby stars blended with the target star and estimating the size, color, and type of galaxies observed by K2.Comment: 2 pages, Published by Research Notes of the American Astronomical Societ

Stochastic Invariants for Probabilistic Termination

Termination is one of the basic liveness properties, and we study the termination problem for probabilistic programs with real-valued variables. Previous works focused on the qualitative problem that asks whether an input program terminates with probability~1 (almost-sure termination). A powerful approach for this qualitative problem is the notion of ranking supermartingales with respect to a given set of invariants. The quantitative problem (probabilistic termination) asks for bounds on the termination probability. A fundamental and conceptual drawback of the existing approaches to address probabilistic termination is that even though the supermartingales consider the probabilistic behavior of the programs, the invariants are obtained completely ignoring the probabilistic aspect. In this work we address the probabilistic termination problem for linear-arithmetic probabilistic programs with nondeterminism. We define the notion of {\em stochastic invariants}, which are constraints along with a probability bound that the constraints hold. We introduce a concept of {\em repulsing supermartingales}. First, we show that repulsing supermartingales can be used to obtain bounds on the probability of the stochastic invariants. Second, we show the effectiveness of repulsing supermartingales in the following three ways: (1)~With a combination of ranking and repulsing supermartingales we can compute lower bounds on the probability of termination; (2)~repulsing supermartingales provide witnesses for refutation of almost-sure termination; and (3)~with a combination of ranking and repulsing supermartingales we can establish persistence properties of probabilistic programs. We also present results on related computational problems and an experimental evaluation of our approach on academic examples.Comment: Full version of a paper published at POPL 2017. 20 page

Synthesis for Polynomial Lasso Programs

We present a method for the synthesis of polynomial lasso programs. These programs consist of a program stem, a set of transitions, and an exit condition, all in the form of algebraic assertions (conjunctions of polynomial equalities). Central to this approach is the discovery of non-linear (algebraic) loop invariants. We extend Sankaranarayanan, Sipma, and Manna's template-based approach and prove a completeness criterion. We perform program synthesis by generating a constraint whose solution is a synthesized program together with a loop invariant that proves the program's correctness. This constraint is non-linear and is passed to an SMT solver. Moreover, we can enforce the termination of the synthesized program with the support of test cases.Comment: Paper at VMCAI'14, including appendi

Curating for Accessibility

Accessibility of research data to disabled users has received scant attention in literature and practice. In this paper we briefly survey the current state of accessibility for research data and suggest some first steps that repositories should take to make their holdings more accessible. We then describe in depth how those steps were implemented at the Qualitative Data Repository (QDR), a domain repository for qualitative social-science data. The paper discusses accessibility testing and improvements on the repository and its underlying software, changes to the curation process to improve accessibility, as well as efforts to retroactively improve the accessibility of existing collections. We conclude by describing key lessons learned during this process as well as next steps

Refinement Type Inference via Horn Constraint Optimization

We propose a novel method for inferring refinement types of higher-order functional programs. The main advantage of the proposed method is that it can infer maximally preferred (i.e., Pareto optimal) refinement types with respect to a user-specified preference order. The flexible optimization of refinement types enabled by the proposed method paves the way for interesting applications, such as inferring most-general characterization of inputs for which a given program satisfies (or violates) a given safety (or termination) property. Our method reduces such a type optimization problem to a Horn constraint optimization problem by using a new refinement type system that can flexibly reason about non-determinism in programs. Our method then solves the constraint optimization problem by repeatedly improving a current solution until convergence via template-based invariant generation. We have implemented a prototype inference system based on our method, and obtained promising results in preliminary experiments.Comment: 19 page