An Analysis of Non-Comparison Based Sorting Algorithms

Sorting algorithms put elements of a list into an order (e.g., numerical, alphabetical). Sorting is an important problem because a nontrivial percentage of all computing resources are devoted to sorting all kinds of lists. For our project, we implemented two non-comparison based sorting algorithms from pseudocode and compared them to various comparison based sorting algorithms. The two algorithms have their advantages and disadvantages as well as their unique features. We found that Radix Sort (which is a modified version of Counting Sort) was the most efficient of them all

An Analysis of Comparison-based Sorting Algorithms

Our names are Edgar Aponte and Jacob Gomez and we are Applied Mathematics students at City Tech. Our mentor is Prof. Isaacson and we conducted an analysis of comparison-based sorting algorithms, meaning that they can sort items of any type for which a “less-than” relation is defined. We implemented 24 comparison-based sorting algorithms and elaborated on 6 for our poster. We analyzed the running times of these sorting algorithms with various sets of unsorted data and found that introspective sort and timsort were the fastest and most efficient, with introspective sort being the very fastest

Two Transiting Earth-size Planets Near Resonance Orbiting a Nearby Cool Star

Discoveries from the prime Kepler mission demonstrated that small planets (< 3 Earth-radii) are common outcomes of planet formation. While Kepler detected many such planets, all but a handful orbit faint, distant stars and are not amenable to precise follow up measurements. Here, we report the discovery of two small planets transiting K2-21, a bright (K = 9.4) M0 dwarf located 65$\pm$6 pc from Earth. We detected the transiting planets in photometry collected during Campaign 3 of NASA's K2 mission. Analysis of transit light curves reveals that the planets have small radii compared to their host star, 2.60 $\pm$ 0.14% and 3.15 $\pm$ 0.20%, respectively. We obtained follow up NIR spectroscopy of K2-21 to constrain host star properties, which imply planet sizes of 1.59 $\pm$ 0.43 Earth-radii and 1.92 $\pm$ 0.53 Earth-radii, respectively, straddling the boundary between high-density, rocky planets and low-density planets with thick gaseous envelopes. The planets have orbital periods of 9.32414 days and 15.50120 days, respectively, and have a period ratio of 1.6624, very near to the 5:3 mean motion resonance, which may be a record of the system's formation history. Transit timing variations (TTVs) due to gravitational interactions between the planets may be detectable using ground-based telescopes. Finally, this system offers a convenient laboratory for studying the bulk composition and atmospheric properties of small planets with low equilibrium temperatures.Comment: Updated to ApJ accepted version; photometry available alongside LaTeX source; 10 pages, 7 figure

Two transiting low density sub-Saturns from K2

We report the discovery and confirmation of K2-24 b and c, two sub-Saturn planets orbiting a bright (V = 11.3), metal-rich ([Fe/H] = 0.42 ± 0.04 dex) G3 dwarf in the K2 Campaign 2 field. The planets are 5.68 ± 0.56 R⊕ and 7.82 ± 0.72 R⊕ and have orbital periods of 20.8851 ± 0.0003 days and 42.3633 ± 0.0006 days, near the 2:1 mean-motion resonance. We obtained 32 radial velocities with Keck/HIRES and detected the reflex motion due to K2-24 b and c. These planets have masses of 21.0 ± 5.4 M⊕ and 27.0 ± 6.9 M⊕, respectively. With low densities of 0.63 ± 0.25 g cm-3 and 0.31 ± 0.12 g cm-3, respectively, the planets require thick envelopes of H/He to explain their large sizes and low masses. Interior structure models predict that the planets have fairly massive cores of 17.6 ± 4.3 M⊕ and 16.1, ± 4.2 M⊕, respectively. They may have formed exterior to their present locations, accreted their H/He envelopes at large orbital distances, and migrated in as a resonant pair. The proximity to resonance, large transit depths, and host star brightness offers rich opportunities for TTV follow-up. Finally, the low surface gravities of the K2-24 planets make them favorable targets for transmission spectroscopy by Hubble Space Telescope, Spitzer, and James Webb Space Telescope

A Randomized Feasibility Trial of a Novel, Integrative, and Intensive Virtual Rehabilitation Program for Service Members Post-Acquired Brain Injury.

INTRODUCTION: Acquired Brain Injury, whether resulting from Traumatic brain injury (TBI) or Cerebral Vascular Accident (CVA), represent major health concerns for the Department of Defense and the nation. TBI has been referred to as the signature injury of recent U.S. military conflicts in Iraq and Afghanistan - affecting approximately 380,000 service members from 2000 to 2017; whereas CVA has been estimated to effect 795,000 individuals each year in the United States. TBI and CVA often present with similar motor, cognitive, and emotional deficits; therefore the treatment interventions for both often overlap. The Defense Health Agency and Veterans Health Administration would benefit from enhanced rehabilitation solutions to treat deficits resulting from acquired brain injuries (ABI), including both TBI and CVA. The purpose of this study was to evaluate the feasibility of implementing a novel, integrative, and intensive virtual rehabilitation system for treating symptoms of ABI in an outpatient clinic. The secondary aim was to evaluate the system\u27s clinical effectiveness. MATERIALS AND METHODS: Military healthcare beneficiaries with ABI diagnoses completed a 6-week randomized feasibility study of the BrightBrainer Virtual Rehabilitation (BBVR) system in an outpatient military hospital clinic. Twenty-six candidates were screened, consented and randomized, 21 of whom completed the study. The BBVR system is an experimental adjunct ABI therapy program which utilizes virtual reality and repetitive bilateral upper extremity training. Four self-report questionnaires measured participant and provider acceptance of the system. Seven clinical outcomes included the Fugl-Meyer Assessment of Upper Extremity, Box and Blocks Test, Jebsen-Taylor Hand Function Test, Automated Neuropsychological Assessment Metrics, Neurobehavioral Symptom Inventory, Quick Inventory of Depressive Symptomatology-Self-Report, and Post Traumatic Stress Disorder Checklist- Civilian Version. The statistical analyses used bootstrapping, non-parametric statistics, and multilevel/hierarchical modeling as appropriate. This research was approved by the Walter Reed National Military Medical Center and Uniformed Services University of the Health Sciences Institutional Review Boards. RESULTS: All of the participants and providers reported moderate to high levels of utility, ease of use and satisfaction with the BBVR system (x- = 73-86%). Adjunct therapy with the BBVR system trended towards statistical significance for the measure of cognitive function (ANAM [x- = -1.07, 95% CI -2.27 to 0.13, p = 0.074]); however, none of the other effects approached significance. CONCLUSION: This research provides evidence for the feasibility of implementing the BBVR system into an outpatient military setting for treatment of ABI symptoms. It is believed these data justify conducting a larger, randomized trial of the clinical effectiveness of the BBVR system

K2-66b and K2-106b: Two Extremely Hot Sub-Neptune-size Planets with High Densities

We report precise mass and density measurements of two extremely hot sub-Neptune-size planets from the K2 mission using radial velocities, K2 photometry, and adaptive optics imaging. K2-66 harbors a close-in sub-Neptune-sized (2.49_(-0.24)^(+0.34)R_⊕) planet (K2-66b) with a mass of 21.3 ± 3.6 M_⊕. Because the star is evolving up the subgiant branch, K2-66b receives a high level of irradiation, roughly twice the main-sequence value. K2-66b may reside within the so-called "photoevaporation desert," a domain of planet size and incident flux that is almost completely devoid of planets. Its mass and radius imply that K2-66b has, at most, a meager envelope fraction (<5%) and perhaps no envelope at all, making it one of the largest planets without a significant envelope. K2-106 hosts an ultra-short-period planet (P = 13.7 hr) that is one of the hottest sub-Neptune-size planets discovered to date. Its radius (1.82_(-0.14)^(+0.20) R_⊕) and mass (9.0 ± 1.6 M_⊕) are consistent with a rocky composition, as are all other small ultra-short-period planets with well-measured masses. K2-106 also hosts a larger, longer-period planet (R_p = 2.77_(-0.23^(+0.37)R_⊕, P = 13.3 days) with a mass less than 24.4 M_⊕ at 99.7% confidence. K2-66b and K2-106b probe planetary physics in extreme radiation environments. Their high densities reflect the challenge of retaining a substantial gas envelope in such extreme environments

Eleven multiplanet systems from K2 campaigns 1 and 2 and the masses of two hot super-Earths

We present a catalog of 11 multiplanet systems from Campaigns 1 and 2 of the K2 mission. We report the sizes and orbits of 26 planets split between seven two-planet systems and four three-planet systems. These planets stem from a systematic search of the K2 photometry for all dwarf stars observed by K2 in these fields. We precisely characterized the host stars with adaptive optics imaging and analysis of high-resolution optical spectra from Keck/HIRES and medium-resolution spectra from IRTF/SpeX. We confirm two planet candidates by mass detection and validate the remaining 24 candidates to &gt;99% confidence. Thirteen planets were previously validated or confirmed by other studies, and 24 were previously identified as planet candidates. The planets are mostly smaller than Neptune (21/26 planets), as in the Kepler mission, and all have short periods (P &lt; 50 days) due to the duration of the K2 photometry. The host stars are relatively bright (most have Kp &lt; 12.5 mag) and are amenable to follow-up characterization. For K2-38, we measured precise radial velocities using Keck/HIRES and provide initial estimates of the planet masses. K2-38b is a short-period super-Earth with a radius of R ⊕, a mass of M ⊕, and a high density consistent with an iron-rich composition. The outer planet K2-38c is a lower-density sub-Neptune-size planet with a radius of R ⊕ and a mass of M ⊕ that likely has a substantial envelope. This new planet sample demonstrates the capability of K2 to discover numerous planetary systems around bright stars

Eleven Multiplanet Systems from K2 Campaigns 1 and 2 and the Masses of Two Hot Super-Earths

We present a catalog of 11 multiplanet systems from Campaigns 1 and 2 of the K2 mission. We report the sizes and orbits of 26 planets split between seven two-planet systems and four three-planet systems. These planets stem from a systematic search of the K2 photometry for all dwarf stars observed by K2 in these fields. We precisely characterized the host stars with adaptive optics imaging and analysis of high-resolution optical spectra from Keck/HIRES and medium-resolution spectra from IRTF/SpeX. We confirm two planet candidates by mass detection and validate the remaining 24 candidates to >99% confidence. Thirteen planets were previously validated or confirmed by other studies, and 24 were previously identified as planet candidates. The planets are mostly smaller than Neptune (21/26 planets), as in the Kepler mission, and all have short periods (P < 50 days) due to the duration of the K2 photometry. The host stars are relatively bright (most have Kp < 12.5 mag) and are amenable to follow-up characterization. For K2-38, we measured precise radial velocities using Keck/HIRES and provide initial estimates of the planet masses. K2-38b is a short-period super-Earth with a radius of 1.55 ± 0.16 R⊕, a mass of 12.0 ± 2.9 M⊕, and a high density consistent with an iron-rich composition. The outer planet K2-38c is a lower-density sub-Neptune-size planet with a radius of 2.42 ± 0.29 R⊕ and a mass of 9.9 ± 4.6 M⊕ that likely has a substantial envelope. This new planet sample demonstrates the capability of K2 to discover numerous planetary systems around bright stars

The LCES HIRES/Keck Precision Radial Velocity Exoplanet Survey

This document is the Accepted Manuscript version of the following article: R. Paul Butler, et al, The LCES HIRES/Keck Precision Radial Velocity Exoplanet Survey, The Astronomical Journal, Vol 153 (5), 19 pp., published 13 April 2017. The Version of Record is available online at doi: https://doi.org/10.3847/1538-3881/aa66ca. Paper data available at: http://home.dtm.ciw.edu/ebps/data/. © 2017. The American Astronomical Society. All rights reserved.We describe a 20-year survey carried out by the Lick-Carnegie Exoplanet Survey Team (LCES), using precision radial velocities from HIRES on the Keck-I telescope to find and characterize extrasolar planetary systems orbiting nearby F, G, K, and M dwarf stars. We provide here 60,949 precision radial velocities for 1,624 stars contained in that survey. We tabulate a list of 357 significant periodic signals that are of constant period and phase, and not coincident in period and/or phase with stellar activity indices. These signals are thus strongly suggestive of barycentric reflex motion of the star induced by one or more candidate exoplanets in Keplerian motion about the host star. Of these signals, 225 have already been published as planet claims, 60 are classified as significant unpublished planet candidates that await photometric follow-up to rule out activity-related causes, and 54 are also unpublished, but are classified as "significant" signals that require confirmation by additional data before rising to classification as planet candidates. Of particular interest is our detection of a candidate planet with a minimum mass of 3.9 Earth masses and an orbital period of 9.9 days orbiting Lalande 21185, the fourth-closest main sequence star to the Sun. For each of our exoplanetary candidate signals, we provide the period and semi-amplitude of the Keplerian orbital fit, and a likelihood ratio estimate of its statistical significance. We also tabulate 18 Keplerian-like signals that we classify as likely arising from stellar activity.Peer reviewedFinal Accepted Versio

Mass Constraints of the WASP-47 Planetary System from Radial Velocities

We report precise radial velocity (RV) measurements of WASP-47, a G star that hosts three transiting planets in close proximity (a hot Jupiter, a super-Earth, and a Neptune-sized planet) and a non-transiting planet at 1.4 au. Through a joint analysis of previously published RVs and our own Keck-HIRES RVs, we significantly improve the planet mass and bulk density measurements. For the super-Earth WASP-47e (P = 0.79 days), we measure a mass of 9.11 ± 1.17 M_⊕, and a bulk density of 7.63 ± 1.90 g cm^(−3), consistent with a rocky composition. For the hot Jupiter WASP-47b (P = 4.2 days), we measure a mass of 356 ± 12 M_⊕ (1.12 ± 0.04 M_(Jup)) and constrain its eccentricity to $\lt 0.021$ at 3σ confidence. For the Neptune-size planet WASP-47d (P = 9.0 days), we measure a mass of 12.75 ± 2.70 M_⊕ and a bulk density of 1.36 ± 0.42 g cm^(−3), suggesting that it has a thick H/He envelope. For the outer non-transiting planet, we measure a minimum mass of 411 ± 18 M_⊕ (1.29 ± 0.06 M_(Jup)), an orbital period of 595.7 ± 5.0 days, and an orbital eccentricity of 0.27 ± 0.04. Our new measurements are consistent with but two to four times more precise than previous mass measurements