Query-Efficient Locally Decodable Codes of Subexponential Length

We develop the algebraic theory behind the constructions of Yekhanin (2008) and Efremenko (2009), in an attempt to understand the ``algebraic niceness'' phenomenon in $\mathbb{Z}_m$. We show that every integer $m = pq = 2^t -1$, where $p$, $q$ and $t$ are prime, possesses the same good algebraic property as $m=511$ that allows savings in query complexity. We identify 50 numbers of this form by computer search, which together with 511, are then applied to gain improvements on query complexity via Itoh and Suzuki's composition method. More precisely, we construct a $3^{\lceil r/2\rceil}$-query LDC for every positive integer $r<104$ and a $\left\lfloor (3/4)^{51}\cdot 2^{r}\right\rfloor$-query LDC for every integer $r\geq 104$, both of length $N_{r}$, improving the $2^r$ queries used by Efremenko (2009) and $3\cdot 2^{r-2}$ queries used by Itoh and Suzuki (2010). We also obtain new efficient private information retrieval (PIR) schemes from the new query-efficient LDCs.Comment: to appear in Computational Complexit

A Combined Compton and Coded-aperture Telescope for Medium-energy Gamma-ray Astrophysics

A future mission in medium-energy gamma-ray astrophysics would allow for many scientific advancements, e.g. a possible explanation for the excess positron emission from the Galactic Center, a better understanding of nucleosynthesis and explosion mechanisms in Type Ia supernovae, and a look at the physical forces at play in compact objects such as black holes and neutron stars. Additionally, further observation in this energy regime would significantly extend the search parameter space for low-mass dark matter. In order to achieve these objectives, an instrument with good energy resolution, good angular resolution, and high sensitivity is required. In this paper we present the design and simulation of a Compton telescope consisting of cubic-centimeter Cadmium Zinc Telluride (CdZnTe) detectors as absorbers behind a silicon tracker with the addition of a passive coded mask. The goal of the design was to create a very sensitive instrument that is capable of high angular resolution. The simulated telescope showed achievable energy resolutions of 1.68$\%$ FWHM at 511 keV and 1.11$\%$ at 1809 keV, on-axis angular resolutions in Compton mode of 2.63$^{\circ}$ FWHM at 511 keV and 1.30$^{\circ}$ FWHM at 1809 keV, and is capable of resolving sources to at least 0.2$^{\circ}$ at lower energies with the use of the coded mask. An initial assessment of the instrument in Compton imaging mode yields an effective area of 183 cm$^{2}$ at 511 keV and an anticipated all-sky sensitivity of 3.6 x 10$^{-6}$ photons cm$^{-2}$ s$^{-1}$ for a broadened 511 keV source over a 2-year observation time. Additionally, combining a coded mask with a Compton imager to improve point source localization for positron detection has been demonstrated

The Resolved Asteroid Program - Size, shape, and pole of (52) Europa

With the adaptive optics (AO) system on the 10 m Keck-II telescope, we acquired a high quality set of 84 images at 14 epochs of asteroid (52) Europa on 2005 January 20. The epochs covered its rotation period and, by following its changing shape and orientation on the plane of sky, we obtained its triaxial ellipsoid dimensions and spin pole location. An independent determination from images at three epochs obtained in 2007 is in good agreement with these results. By combining these two data sets, along with a single epoch data set obtained in 2003, we have derived a global fit for (52) Europa of diameters (379x330x249) +/- (16x8x10) km, yielding a volume-equivalent spherical-diameter of 315 +/- 7 km, and a rotational pole within 7 deg of [RA; Dec] = [257,+12] in an Equatorial J2000 reference frame (ECJ2000: 255,+35). Using the average of all mass determinations available forEuropa, we derive a density of 1.5 +/- 0.4, typical of C-type asteroids. Comparing our images with the shape model of Michalowski et al. (A&A 416, 2004), derived from optical lightcurves, illustrates excellent agreement, although several edge features visible in the images are not rendered by the model. We therefore derived a complete 3-D description of Europa's shape using the KOALA algorithm by combining our imaging epochs with 4 stellar occultations and 49 lightcurves. We use this 3-D shape model to assess these departures from ellipsoidal shape. Flat facets (possible giant craters) appear to be less distinct on (52) Europa than on other C-types that have been imaged in detail. We show that fewer giant craters, or smaller craters, is consistent with its expected impact history. Overall, asteroid (52) Europa is still well modeled as a smooth triaxial ellipsoid with dimensions constrained by observations obtained over several apparitions.Comment: Accepted for publication in Icaru

Effectiveness of appropriately trained nurses in preoperative assessment: randomised controlled equivalence/non-inferiority trial

Objective To determine whether preoperative assessments carried out by appropriately trained nurses are inferior in quality to those carried out by preregistration house officers. Design Randomised controlled equivalence/non-inferiority trial. Setting Four NHS hospitals in three trusts. Three of the four were teaching hospitals. Participants All patients attending for assessment before general anaesthesia for general, vascular, urological, or breast surgery between April 1998 and March 1999. Intervention Assessment by one of three appropriately trained nurses or by one of several preregistration house officers. Main outcome measures History taken, physical examination, and investigations ordered. Measures evaluated by a specialist registrar in anaesthetics and placed in four categories: correct, overassessment, underassessment not affecting management, and underassessment possibly affecting management (primary outcome). Results 1907 patients were randomised, and 1874 completed the study; 926 were assessed by house officers and 948 by nurses. Overall 121/948 (13%) assessments carried out by nurses were judged to have possibly affected management compared with 138/926 (15%) of those performed by house officers. Nurses were judged to be non-inferior to house officers in assessment, although there was variation among them in terms of the quality of history taking. The house officers ordered considerably more unnecessary tests than the nurses (218/926 (24%) v 129/948 (14%). Conclusions There is no reason to inhibit the development of nurse led preoperative assessment provided that the nurses involved receive adequate training. However, house officers will continue to require experience in preoperative assessment

Diffuse Galactic antimatter from faint thermonuclear supernovae in old stellar populations

Our Galaxy hosts the annihilation of a few $\times 10^{43}$ low-energy positrons every second. Radioactive isotopes capable of supplying such positrons are synthesised in stars, stellar remnants, and supernovae. For decades, however, there has been no positive identification of a main stellar positron source leading to suggestions that many positrons originate from exotic sources like the Galaxy's central super-massive black hole or dark matter annihilation. %, but such sources would not explain the recently-detected positron signal from the extended Galactic disk. Here we show that a single type of transient source, deriving from stellar populations of age 3-6 Gyr and yielding ~0.03 $M_\odot$ of the positron emitter $^{44}$Ti, can simultaneously explain the strength and morphology of the Galactic positron annihilation signal and the solar system abundance of the $^{44}$Ti decay product $^{44}$Ca. This transient is likely the merger of two low-mass white dwarfs, observed in external galaxies as the sub-luminous, thermonuclear supernova known as SN1991bg-like.Comment: 28 pages main text with 4 figures in preprint style; 26 pages of Supplementary Informatio

Developing a second generation Laue lens prototype: high reflectivity crystals and accurate assembly

Laue lenses are an emerging technology that will enhance gamma-ray telescope sensitivity by one to two orders of magnitude in selected energy bands of the \sim 100 keV to \sim 1.5 MeV range. This optic would be particularly well adapted to the observation of faint gamma ray lines, as required for the study of Supernovae and Galactic positron annihilation. It could also prove very useful for the study of hard X-ray tails from a variety of compact objects, especially making a difference by providing sufficient sensitivity for polarization to be measured by the focal plane detector. Our group has been addressing the two key issues relevant to improve performance with respect to the first generation of Laue lens prototypes: obtaining large numbers of efficient crystals and developing a method to fix them with accurate orientation and dense packing factor onto a substrate. We present preliminary results of an on-going study aiming to enable a large number of crystals suitable for diffraction at energies above 500 keV. In addition, we show the first results of the Laue lens prototype assembled using our beamline at SSL/UC Berkeley, which demonstrates our ability to orient and glue crystals with accuracy of a few arcsec, as required for an efficient Laue lens telescope.Comment: Published in the proceedings of the SPIE conference held in San Diego in August 201