We present a catalog of 1,172,157 quasar candidates selected from the photometric imaging data of the Sloan Digital Sky Survey (SDSS). The objects are all point sources to a limiting magnitude of i = 21.3 from 8417 deg 2 of imaging from SDSS Data Release 6 (DR6). This sample extends our previous catalog by using the latest SDSS public release data and probing both UV-excess and high-redshift quasars. While the addition of high-redshift candidates reduces the overall efficiency (quasars:quasar candidates) of the catalog to ∼ 80%, it is expected to contain no fewer than 850,000 bona fide quasars -∼ 8 times the number of our previous sample, and ∼ 10 times the size of the largest spectroscopic quasar catalog. Cross-matching between our photometric catalog and spectroscopic quasar catalogs from both the SDSS and 2dF Surveys, yields 88,879 -2spectroscopically confirmed quasars. For judicious selection of the most robust UV-excess sources (∼ 500, 000 objects in all), the efficiency is nearly 97%more than sufficient for detailed statistical analyses. The catalog's completeness to type 1 (broad-line) quasars is expected to be no worse than 70%, with most missing objects occurring at z < 0.7 and 2.5 < z < 3.0. In addition to classification information, we provide photometric redshift estimates (typically good to ∆z ± 0.3 [2σ]) and cross-matching with radio, X-ray, and proper motion catalogs. Finally, we consider the catalog's utility for determining the optical luminosity function of quasars and are able to confirm the flattening of the bright-end slope of the quasar luminosity function at z ∼ 4 as compared to z ∼ 2.

We identify 885,503 type 1 quasar candidates to i 22  using the combination of optical and mid-IR photometry. Optical photometry is taken from the Sloan Digital Sky Survey-III: Baryon Oscillation Spectroscopic Survey (SDSS-III/BOSS), while mid-IR photometry comes from a combination of data from the Wide-field Infrared Survey Explorer (WISE) "AllWISE" data release and several large-area Spitzer Space Telescope fields. Selection is based on a Bayesian kernel density algorithm with a training sample of 157,701 spectroscopically confirmed type1 quasars with both optical and mid-IR data. Of the quasar candidates, 733,713 lack spectroscopic confirmation (and 305,623 are objects that we have not previously classified as photometric quasar candidates). These candidates include 7874 objects targeted as high-probability potential quasars with z 3.5 5 < < (of which 6779 are new photometric candidates). Our algorithm is more complete to z 3.5 > than the traditional mid-IR selection "wedges" and to z 2.2 3.5 < < quasars than the SDSS-III/BOSS project. Number counts and luminosity function analysis suggestthat the resulting catalog is relatively complete to known quasars and is identifying new high-z quasars at z 3 >. This catalog paves the way for luminosity-dependent clustering investigations of large numbers of faint, high-redshift quasars and for further machine-learning quasar selection using Spitzer and WISE data combined with other large-area optical imaging surveys.

We conduct a pilot investigation to determine the optimal combination of color and variability information to identify quasars in current and future multi-epoch optical surveys. We use a Bayesian quasar selection algorithm to identify 35,820 type 1 quasar candidates in a 239 deg 2 field of the Sloan Digital Sky Survey (SDSS) Stripe 82, using a combination of optical photometry and variability. Color analysis is performed on 5-band single-and multi-epoch SDSS optical photometry to a depth of r 22.4.From these data, variability parameters are calculated by fitting the structure function of each object in each band with a power-law model using 10 to 100 > observations over timescales from ∼1 day to ∼8 years. Selection was based on a training sample of 13,221 spectroscopically confirmed type-1 quasars, largely from the SDSS. Using variability alone, colors alone, and combining variability and colors we achieve 91%, 93%, and 97% quasar completeness and 98%, 98%, and 97% efficiency, respectively, with particular improvement in the selection of quasars at z 2.7 3.5 < < where quasars and stars have similar optical colors. The 22,867 quasar candidates that are not spectroscopically confirmed reach a depth of i 22.0; 21,876 (95.7%) are dimmer than coadded i-band magnitude of 19.9, the cutoff for spectroscopic follow-up for SDSS on Stripe 82. Brighter than 19.9, we find 5.7% more quasar candidates without confirming spectra in sky regions otherwise considered complete. The resulting quasar sample has sufficient purity (and statistically correctable incompleteness) to produce a luminosity function comparable to those determined by spectroscopic investigations. We discuss improvements that can be made to the process in preparation for performing similar photometric selection and science on data from post-SDSS sky surveys.

Knowledge base question answering (KBQA) is an important task in Natural Language Processing. Existing approaches face significant challenges including complex question understanding, necessity for reasoning, and lack of large end-to-end training datasets. In this work, we propose Neuro-Symbolic Question Answering (NSQA), a modular KBQA system, that leverages (1) Abstract Meaning Representation (AMR) parses for task-independent question understanding; (2) a simple yet effective graph transformation approach to convert AMR parses into candidate logical queries that are aligned to the KB; (3) a pipeline-based approach which integrates multiple, reusable modules that are trained specifically for their individual tasks (semantic parser, entity and relationship linkers, and neuro-symbolic reasoner) and do not require end-to-end training data. NSQA achieves state-of-the-art performance on two prominent KBQA datasets based on DBpedia (QALD-9 and LC-QuAD 1.0). Furthermore, our analysis emphasizes that AMR is a powerful tool for KBQA systems.

Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of such systems. For the first time, we give a sound and complete axiomatization for a broad class containing all the common real-valued logics. This axiomatization allows us to derive exactly what information can be inferred about the combinations of real values of a collection of formulas given information about the combinations of real values of several other collections of formulas. We then extend the axiomatization to deal with weighted subformulas. Finally, we give a decision procedure based on linear programming for deciding, under certain natural assumptions, whether a set of our sentences logically implies another of our sentences.Preprint. Under review.