The Capacity of Linear Computation Broadcast

The two-user computation broadcast problem is introduced as the setting where user 1 wants message W1 and has side information W0 1 , user 2 wants message W2 and has side information W0 2, and (W1;W0 1 ;W2;W0 2) may have arbitrary dependencies. The goal is to minimize the entropy H(S) of the broadcast information S that simultaneously satisfies both users' demands. It is shown that H(S) H(W1jW0 1) + H(W2jW0 2) min I(W1;W2;W0 2jW0 1 ); I(W2;W1;W0 1jW0 2 ) . Furthermore, for the linear computation broadcast problem, where W1;W0 1;W2;W0 2 are comprised of arbitrary linear combinations of a basis set of independent symbols, the bound is shown to be tight

Extreme weights in Steinhaus triangles

Let {0=w0<w1<w2<…<wm0=w0<w1<w2<…<wm} be the set of weights of binary Steinhaus triangles of size n , and let Wibe the set of sequences in F2n that generate triangles of weight wi. In this paper we obtain the values of wi and the corresponding sets Wi for i¿{2,3,m}i¿{2,3,m}, and partial results for i=m-1i=m-1.Peer ReviewedPostprint (author's final draft

Characterizing AGB stars in Wide-field Infrared Survey Explorer (WISE) bands

Since asymptotic giant branch (AGB) stars are bright and extended infrared objects, most Galactic AGB stars saturate the Wide-field Infrared Survey Explorer (WISE) detectors and therefore the WISE magnitudes that are restored by applying point-spread-function fitting need to be verified. Statistical properties of circumstellar envelopes around AGB stars are discussed on the basis of a WISE AGB catalog verified in this way. We cross-matched an AGB star sample with the WISE All-Sky Source Catalog and the Two Mircon All Sky Survey catalog. Infrared Space Observatory (ISO) spectra of a subsample of WISE AGB stars were also exploited. The dust radiation transfer code DUSTY was used to help predict the magnitudes in the W1 and W2 bands, the two WISE bands most affected by saturation, for calibration purpose, and to provide physical parameters of the AGB sample stars for analysis. DUSTY is verified against the ISO spectra to be a good tool to reproduce the spectral energy distributions of these AGB stars. Systematic magnitude-dependent offsets have been identified in WISE W1 and W2 magnitudes of the saturated AGB stars, and empirical calibration formulas are obtained for them on the basis of 1877 (W1) and 1558 (W2) AGB stars that are successfully fit with DUSTY. According to the calibration formulae, the corrections for W1 at 5 mag and W2 at 4 mag are $-0.383$ and 0.217 mag, respectively. In total, we calibrated the W1/W2 magnitudes of 2390/2021 AGB stars. The model parameters from the DUSTY and the calibrated WISE W1 and W2 magnitudes are used to discuss the behavior of the WISE color-color diagrams of AGB stars. The model parameters also reveal that O-rich AGB stars with opaque circumstellar envelopes are much rarer than opaque C-rich AGB stars toward the anti-Galactic center direction, which we attribute to the metallicity gradient of our Galaxy.Comment: 9 pages in two column format, 7 figures, accepted for publication in A&

Optical Spectroscopic Survey of High-latitude WISE-selected Sources

We report on the results of an optical spectroscopic survey at high Galactic latitude (|b| ≥ 30°) of a sample of WISE-selected targets, grouped by WISE W1 (λ_eff = 3.4 μm) flux, which we use to characterize the sources WISE detected. We observed 762 targets in 10 disjoint fields centered on ultraluminous infrared galaxy candidates using DEIMOS on Keck II. We find 0.30 ± 0.02 galaxies arcmin–2 with a median redshift of z = 0.33 ± 0.01 for the sample with W1 ≥ 120 μJy. The foreground stellar densities in our survey range from 0.23 ± 0.07 arcmin–2 to 1.1 ± 0.1 arcmin–2 for the same sample. We obtained spectra that produced science grade redshifts for ≥90% of our targets for sources with W1 flux ≥120 μJy that also had an i-band flux gsim 18 μJy. We used this for targeting very preliminary data reductions available to the team in 2010 August. Our results therefore present a conservative estimate of what is possible to achieve using WISE's Preliminary Data Release for the study of field galaxies

Full-depth Coadds of the WISE and First-year NEOWISE-Reactivation Images

The Near Earth Object Wide-field Infrared Survey Explorer (NEOWISE) Reactivation mission released data from its first full year of observations in 2015. This data set includes ~2.5 million exposures in each of W1 and W2, effectively doubling the amount of WISE imaging available at 3.4 and 4.6 microns relative to the AllWISE release. We have created the first ever full-sky set of coadds combining all publicly available W1 and W2 exposures from both the AllWISE and NEOWISE-Reactivation (NEOWISER) mission phases. We employ an adaptation of the unWISE image coaddition framework (Lang 2014), which preserves the native WISE angular resolution and is optimized for forced photometry. By incorporating two additional scans of the entire sky, we not only improve the W1/W2 depths, but also largely eliminate time-dependent artifacts such as off-axis scattered moonlight. We anticipate that our new coadds will have a broad range of applications, including target selection for upcoming spectroscopic cosmology surveys, identification of distant/massive galaxy clusters, and discovery of high-redshift quasars. In particular, our full-depth AllWISE+NEOWISER coadds will be an important input for the Dark Energy Spectroscopic Instrument (DESI) selection of luminous red galaxy and quasar targets. Our full-depth W1/W2 coadds are already in use within the DECam Legacy Survey (DECaLS) and Mayall z-band Legacy Survey (MzLS) reduction pipelines. Much more work still remains in order to fully leverage NEOWISER imaging for astrophysical applications beyond the solar system.Comment: coadds available at http://unwise.me, zoomable full-sky rendering at http://legacysurvey.org/viewe

Optical Spectroscopic Survey of High Latitude WISE Selected Sources

We report on the results of an optical spectroscopic survey at high Galactic latitude (b\geq30{\deg}) of a sample of WISE-selected targets, grouped by WISE W1 ({\lambda}_eff = 3.4 \mum) flux, which we use to characterize the sources WISE detected. We observed 762 targets in 10 disjoint fields centered on ultra-luminous infrared galaxy (ULIRG) candidates using the DEIMOS spectrograph on Keck II. We find 0.30 \pm 0.02 galaxies arcmin^-2 with a median redshift of z=0.33 \pm 0.01 for the sample with W1 \geq 120 \muJy. The foreground stellar densities in our survey range from 0.23 \pm 0.07 arcmin^(-2) to 1.1 \pm 0.1 arcmin^(-2) for the same sample. We obtained spectra that produced science grade redshifts for \geq 90% of our targets for sources with W1 flux \geq 120 \muJy that also had i-band flux \geq 18 \muJy. We used for targeting very preliminary data reductions available to the team in August of 2010. Our results therefore present a conservative estimate of what is possible to achieve using WISE's Preliminary Data Release for the study of field galaxies.Comment: 29 pages, 10 figures, 8 table