Uniquely and 2-Uniquely Hamiltonian Graphs

In graph theory a Hamilton cycle is a walk around the vertices of a graph in which each vertex is visited exactly once, and then it returns to the starting vertex. The problem of determining whether a graph contains a Hamilton cycle has been studied extensively and is determined to belong to the so-called NP-complete family of problems for arbitrary graphs. Due to the difficulty in solving such a problem for an arbitrary graph, we set our sights on a family of graphs described by graph theorist John Sheehan. A maximum uniquely Hamiltonian graph contains the greatest number of edges possible while maintaining a single Hamilton cycle. Sheehan shows that for a graph with n nodes (for n \u3e= 4), the maximum number of edges it can contain is equal to (n^2/4) + 1. We will describe an algorithm that finds the Hamilton cycle for any such graph or any of its subgraphs in polynomial time. This algorithm shows that these graphs do not suffer the same complexity issues as do arbitrary graphs for a Hamilton cycle problem. For any graph containing a single Hamilton cycle, that cycle can be revealed in polynomial time

Badger: Complexity Analysis with Fuzzing and Symbolic Execution

Hybrid testing approaches that involve fuzz testing and symbolic execution have shown promising results in achieving high code coverage, uncovering subtle errors and vulnerabilities in a variety of software applications. In this paper we describe Badger - a new hybrid approach for complexity analysis, with the goal of discovering vulnerabilities which occur when the worst-case time or space complexity of an application is significantly higher than the average case. Badger uses fuzz testing to generate a diverse set of inputs that aim to increase not only coverage but also a resource-related cost associated with each path. Since fuzzing may fail to execute deep program paths due to its limited knowledge about the conditions that influence these paths, we complement the analysis with a symbolic execution, which is also customized to search for paths that increase the resource-related cost. Symbolic execution is particularly good at generating inputs that satisfy various program conditions but by itself suffers from path explosion. Therefore, Badger uses fuzzing and symbolic execution in tandem, to leverage their benefits and overcome their weaknesses. We implemented our approach for the analysis of Java programs, based on Kelinci and Symbolic PathFinder. We evaluated Badger on Java applications, showing that our approach is significantly faster in generating worst-case executions compared to fuzzing or symbolic execution on their own

Coz: Finding Code that Counts with Causal Profiling

Improving performance is a central concern for software developers. To locate optimization opportunities, developers rely on software profilers. However, these profilers only report where programs spent their time: optimizing that code may have no impact on performance. Past profilers thus both waste developer time and make it difficult for them to uncover significant optimization opportunities. This paper introduces causal profiling. Unlike past profiling approaches, causal profiling indicates exactly where programmers should focus their optimization efforts, and quantifies their potential impact. Causal profiling works by running performance experiments during program execution. Each experiment calculates the impact of any potential optimization by virtually speeding up code: inserting pauses that slow down all other code running concurrently. The key insight is that this slowdown has the same relative effect as running that line faster, thus "virtually" speeding it up. We present Coz, a causal profiler, which we evaluate on a range of highly-tuned applications: Memcached, SQLite, and the PARSEC benchmark suite. Coz identifies previously unknown optimization opportunities that are both significant and targeted. Guided by Coz, we improve the performance of Memcached by 9%, SQLite by 25%, and accelerate six PARSEC applications by as much as 68%; in most cases, these optimizations involve modifying under 10 lines of code.Comment: Published at SOSP 2015 (Best Paper Award

Spatially Resolved Stellar Populations of Eight GOODS-South Active Galactic Nuclei at z ~ 1

We present a pilot study of the stellar populations of eight active galactic nucleus (AGN) hosts at z ~ 1 and compare with (1) lower redshift samples and (2) a sample of nonactive galaxies of similar redshift. We utilize K' images in the Great Observatories Origins Deep Survey South field obtained with the laser guide star adaptive optics system at Keck Observatory. We combine these K' data with B, V, i, and z imaging from the Advanced Camera for Surveys on Hubble Space Telescope to give multicolor photometry at a matched spatial resolution better than 100 mas in all bands. The hosts harbor AGNs as inferred from their high X-ray luminosities (LX > 10^42 erg s^–1) or mid-IR colors. We find a correlation between the presence of younger stellar populations and the strength of the AGN, as measured with [O III] line luminosity or X-ray (2-10 keV) luminosity. This finding is consistent with similar studies at lower redshift. Of the three Type II galaxies, two are disk galaxies and one is of irregular type, while in the Type I sample there are only one disk-like source and four sources with smooth, elliptical/spheroidal morphologies. In addition, the mid-IR spectral energy distributions of the strong Type II AGNs indicate that they are excited to Luminous InfraRed Galaxy (LIRG) status via galactic starbursting, while the strong Type I AGNs are excited to LIRG status via hot dust surrounding the central AGN. This supports the notion that the obscured nature of Type II AGNs at z ~ 1 is connected with global starbursting and that they may be extincted by kpc-scale dusty features that are by-products of this starbursting

The Asymptotic Giant Branch and the Tip of the Red Giant Branch as Probes of Star Formation History: The Nearby Dwarf Irregular Galaxy KKH 98

We investigate the utility of the asymptotic giant branch (AGB) and the red giant branch (RGB) as probes of the star formation history (SFH) of the nearby (D=2.5 Mpc) dwarf irregular galaxy, KKH 98. Near-infrared (IR) Keck Laser Guide Star Adaptive Optics (AO) images resolve 592 IR bright stars reaching over 1 magnitude below the Tip of the Red Giant Branch. Significantly deeper optical (F475W and F814W) Hubble Space Telescope images of the same field contain over 2500 stars, reaching to the Red Clump and the Main Sequence turn-off for 0.5 Gyr old populations. Compared to the optical color magnitude diagram (CMD), the near-IR CMD shows significantly tighter AGB sequences, providing a good probe of the intermediate age (0.5 - 5 Gyr) populations. We match observed CMDs with stellar evolution models to recover the SFH of KKH 98. On average, the galaxy has experienced relatively constant low-level star formation (5 x 10^-4 Mo yr^-1) for much of cosmic time. Except for the youngest main sequence populations (age < 0.1 Gyr), which are typically fainter than the AO data flux limit, the SFH estimated from the the 592 IR bright stars is a reasonable match to that derived from the much larger optical data set. Differences between the optical and IR derived SFHs for 0.1 - 1 Gyr populations suggest that current stellar evolution models may be over-producing the AGB by as much as a factor of three in this galaxy. At the depth of the AO data, the IR luminous stars are not crowded. Therefore these techniques can potentially be used to determine the stellar populations of galaxies at significantly further distances.Comment: 15 pages, 14 figs, accepted for publication in Ap

Integrated Laboratory Demonstrations of Multi-Object Adaptive Optics on a Simulated 10-Meter Telescope at Visible Wavelengths

One important frontier for astronomical adaptive optics (AO) involves methods such as Multi-Object AO and Multi-Conjugate AO that have the potential to give a significantly larger field of view than conventional AO techniques. A second key emphasis over the next decade will be to push astronomical AO to visible wavelengths. We have conducted the first laboratory simulations of wide-field, laser guide star adaptive optics at visible wavelengths on a 10-meter-class telescope. These experiments, utilizing the UCO/Lick Observatory's Multi-Object / Laser Tomography Adaptive Optics (MOAO/LTAO) testbed, demonstrate new techniques in wavefront sensing and control that are crucial to future on-sky MOAO systems. We (1) test and confirm the feasibility of highly accurate atmospheric tomography with laser guide stars, (2) demonstrate key innovations allowing open-loop operation of Shack-Hartmann wavefront sensors (with errors of ~30 nm) as will be needed for MOAO, and (3) build a complete error budget model describing system performance. The AO system maintains a performance of 32.4% Strehl on-axis, with 24.5% and 22.6% at 10" and 15", respectively, at a science wavelength of 710 nm (R-band) over the equivalent of 0.8 seconds of simulation. The MOAO-corrected field of view is ~25 times larger in area than that limited by anisoplanatism at R-band. Our error budget is composed of terms verified through independent, empirical experiments. Error terms arising from calibration inaccuracies and optical drift are comparable in magnitude to traditional terms like fitting error and tomographic error. This makes a strong case for implementing additional calibration facilities in future AO systems, including accelerometers on powered optics, 3D turbulators, telescope and LGS simulators, and external calibration ports for deformable mirrors.Comment: 29 pages, 11 figures, submitted to PAS

First Frontier Field Constraints on the Cosmic Star-Formation Rate Density at z~10 - The Impact of Lensing Shear on Completeness of High-Redshift Galaxy Samples

We search the complete Hubble Frontier Field dataset of Abell 2744 and its parallel field for z~10 sources to further refine the evolution of the cosmic star-formation rate density (SFRD) at z>8. We independently confirm two images of the recently discovered triply-imaged z~9.8 source by Zitrin et al. (2014) and set an upper limit for similar z~10 galaxies with red colors of J_125-H_160>1.2 in the parallel field of Abell 2744. We utilize extensive simulations to derive the effective selection volume of Lyman-break galaxies at z~10, both in the lensed cluster field and in the adjacent parallel field. Particular care is taken to include position-dependent lensing shear to accurately account for the expected sizes and morphologies of highly-magnified sources. We show that both source blending and shear reduce the completeness at a given observed magnitude in the cluster, particularly near the critical curves. These effects have a significant, but largely overlooked, impact on the detectability of high-redshift sources behind clusters, and substantially reduce the expected number of highly-magnified sources. The detections and limits from both pointings result in a SFRD which is higher by 0.4+-0.4 dex than previous estimates at z~10 from blank fields. Nevertheless, the combination of these new results with all other estimates remain consistent with a rapidly declining SFRD in the 170 Myr from z~8 to z~10 as predicted by cosmological simulations and dark-matter halo evolution in LambdaCDM. Once biases introduced by magnification-dependent completeness are accounted for, the full six cluster and parallel Frontier Field program will be an extremely powerful new dataset to probe the evolution of the galaxy population at z>8 before the advent of the JWST.Comment: 10 pages, 7 figures, changed to match accepted version to appear in Ap

CATS: CfAO Treasury Survey of distant galaxies, supernovae, and AGN's

The NSF Science and Technology Center for Adaptive Optics (CfAO) is supporting a major scientific legacy project called the CfAO Treasury Survey (CATS). CATS is obtaining near-infrared AO data in deep HST survey fields, such as GEMS, GOODS-N, & EGS. Besides summarizing the main objectives of CATS, we highlight some recent imaging work on the study of distant field galaxies, AGNs, and a redshift z = 1.32 supernova. CATS plans the first data release to the community in early 2007 (check http://www.astro.ucla.edu/~irlab/cats/index.shtml for more details on CATS and latest updates).Comment: 2 pages. Proceedings of the IAU Symposium 235, "Galaxy Evolution across the Hubble Time", F. Combes & J. Palous (eds.

Identifying Very Metal-Rich Stars with Low-Resolution Spectra: Finding Planet-Search Targets

We present empirical calibrations that estimate stellar metallicity, effective temperature and surface gravity as a function of Lick/IDS indices. These calibrations have been derived from a training set of 261 stars for which (1) high-precision measurements of [Fe/H], T_eff and log g have been made using spectral-synthesis analysis of HIRES spectra, and (2) Lick indices have also been measured. Our [Fe/H] calibration, which has precision 0.07 dex, has identified a number of bright (V < 9) metal-rich stars which are now being screened for hot Jupiter-type planets. Using the Yonsei-Yale stellar models, we show that the calibrations provide distance estimates accurate to 20% for nearby stars. This paper outlines the second tier of the screening of planet-search targets by the N2K Consortium, a project designed to identify the stars most likely to harbor extrasolar planets. Discoveries by the N2K Consortium include the transiting hot Saturn HD 149026 b (Sato et al. 2005, astro-ph/0507009) and HD 88133 b (Fischer et al. 2005). See Ammons et al. (2005, In Press) for a description of the first tier of N2K metallicity screening, calibrations using broadband photometry.Comment: Accepted for publication in the Astrophysical Journa