Louisiana State University

mothur aims to be a comprehensive software package that allows users to use a single piece of software to analyze community sequence data. It builds upon previous tools to provide a flexible and powerful software package for analyzing sequencing data. As a case study, we used mothur to trim, screen, and align sequences; calculate distances; assign sequences to operational taxonomic units; and describe the alpha and beta diversity of eight marine samples previously characterized by pyrosequencing of 16S rRNA gene fragments. This analysis of more than 222,000 sequences was completed in less than 2 h with a laptop computer.

The 1000 Genomes Project set out to provide a comprehensive description of common human genetic variation by applying whole-genome sequencing to a diverse set of individuals from multiple populations. Here we report completion of the project, having reconstructed the genomes of 2,504 individuals from 26 populations using a combination of low-coverage whole-genome sequencing, deep exome sequencing, and dense microarray genotyping. We characterized a broad spectrum of genetic variation, in total over 88 million variants (84.7 million single nucleotide polymorphisms (SNPs), 3.6 million short insertions/deletions (indels), and 60,000 structural variants), all phased onto high-quality haplotypes. This resource includes >99% of SNP variants with a frequency of >1% for a variety of ancestries. We describe the distribution of genetic variation across the global sample, and discuss the implications for common disease studies. Results for the final phase of the 1000 Genomes Project are presented including whole-genome sequencing, targeted exome sequencing, and genotyping on high-density SNP arrays for 2,504 individuals across 26 populations, providing a global reference data set to support biomedical genetics. The 1000 Genomes Project has sought to comprehensively catalogue human genetic variation across populations, providing a valuable public genomic resource. The data obtained so far have found applications ranging from association studies and fine mapping studies to the filtering of likely neutral variants in rare-disease cohorts. The authors now report on the final phase of the project, phase 3, which covers previously uncharacterized areas of human genetic diversity in terms of the populations sampled and categories of characterized variation. The sample now includes more than 2,500 individuals from 26 global populations, with low coverage whole-genome and deep exome sequencing, as well as dense microarray genotyping. They find that while most common variants are shared across populations, rarer variants are often restricted to closely related populations. The authors also demonstrate the use of the phase 3 dataset as a reference panel for imputation to improve the resolution in genetic association studies.

We present the first public version (v0.2) of the open-source and community-developed Python package, Astropy. This package provides core astronomy-related functionality to the community, including support for domain-specific file formats such as flexible image transport system (FITS) files, Virtual Observatory (VO) tables, and common ASCII table formats, unit and physical quantity conversions, physical constants specific to astronomy, celestial coordinate and time transformations, world coordinate system (WCS) support, generalized containers for representing gridded as well as tabular data, and a framework for cosmological transformations and conversions. Significant functionality is under activedevelopment, such as a model fitting framework, VO client and server tools, and aperture and point spread function (PSF) photometry tools. The core development team is actively making additions and enhancements to the current code base, and we encourage anyone interested to participate in the development of future Astropy versions.

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160) Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

On August 17, 2017 at 12∶41:04 UTC the Advanced LIGO and Advanced Virgo gravitational-wave detectors made their first observation of a binary neutron star inspiral. The signal, GW170817, was detected with a combined signal-to-noise ratio of 32.4 and a false-alarm-rate estimate of less than one per <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mrow><a:mn>8.0</a:mn><a:mo>×</a:mo><a:msup><a:mrow><a:mn>10</a:mn></a:mrow><a:mrow><a:mn>4</a:mn></a:mrow></a:msup></a:mrow><a:mtext> </a:mtext><a:mtext> </a:mtext><a:mi>years</a:mi></a:mrow></a:math>. We infer the component masses of the binary to be between 0.86 and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mn>2.26</c:mn><c:mtext> </c:mtext><c:mtext> </c:mtext><c:msub><c:mrow><c:mi>M</c:mi></c:mrow><c:mrow><c:mo stretchy="false">⊙</c:mo></c:mrow></c:msub></c:mrow></c:math>, in agreement with masses of known neutron stars. Restricting the component spins to the range inferred in binary neutron stars, we find the component masses to be in the range <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mrow><f:mn>1.17</f:mn><f:mi>–</f:mi><f:mn>1.60</f:mn><f:mtext> </f:mtext><f:mtext> </f:mtext><f:msub><f:mrow><f:mi>M</f:mi></f:mrow><f:mrow><f:mo stretchy="false">⊙</f:mo></f:mrow></f:msub></f:mrow></f:math>, with the total mass of the system <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mn>2.7</i:mn><i:msubsup><i:mrow><i:mn>4</i:mn></i:mrow><i:mrow><i:mo>−</i:mo><i:mn>0.01</i:mn></i:mrow><i:mrow><i:mo>+</i:mo><i:mn>0.04</i:mn></i:mrow></i:msubsup><i:msub><i:mrow><i:mi>M</i:mi></i:mrow><i:mrow><i:mo stretchy="false">⊙</i:mo></i:mrow></i:msub></i:mrow></i:math>. The source was localized within a sky region of <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mrow><l:mn>28</l:mn><l:mtext> </l:mtext><l:mtext> </l:mtext><l:mrow><l:msup><l:mrow><l:mi>deg</l:mi></l:mrow><l:mrow><l:mn>2</l:mn></l:mrow></l:msup></l:mrow></l:mrow></l:math> (90% probability) and had a luminosity distance of <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mrow><n:mrow><n:mn>4</n:mn><n:msubsup><n:mrow><n:mn>0</n:mn></n:mrow><n:mrow><n:mo>−</n:mo><n:mn>14</n:mn></n:mrow><n:mrow><n:mo>+</n:mo><n:mn>8</n:mn></n:mrow></n:msubsup><n:mtext> </n:mtext><n:mtext> </n:mtext></n:mrow><n:mrow><n:mi>Mpc</n:mi></n:mrow></n:mrow></n:math>, the closest and most precisely localized gravitational-wave signal yet. The association with the <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mi>γ</p:mi></p:math>-ray burst GRB 170817A, detected by Fermi-GBM 1.7 s after the coalescence, corroborates the hypothesis of a neutron star merger and provides the first direct evidence of a link between these mergers and short <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>γ</r:mi></r:math>-ray bursts. Subsequent identification of transient counterparts across the electromagnetic spectrum in the same location further supports the interpretation of this event as a neutron star merger. This unprecedented joint gravitational and electromagnetic observation provides insight into astrophysics, dense matter, gravitation, and cosmology. Published by the American Physical Society 2017

By characterizing the geographic and functional spectrum of human genetic variation, the 1000 Genomes Project aims to build a resource to help to understand the genetic contribution to disease. Here we describe the genomes of 1,092 individuals from 14 populations, constructed using a combination of low-coverage whole-genome and exome sequencing. By developing methods to integrate information across several algorithms and diverse data sources, we provide a validated haplotype map of 38 million single nucleotide polymorphisms, 1.4 million short insertions and deletions, and more than 14,000 larger deletions. We show that individuals from different populations carry different profiles of rare and common variants, and that low-frequency variants show substantial geographic differentiation, which is further increased by the action of purifying selection. We show that evolutionary conservation and coding consequence are key determinants of the strength of purifying selection, that rare-variant load varies substantially across biological pathways, and that each individual contains hundreds of rare non-coding variants at conserved sites, such as motif-disrupting changes in transcription-factor-binding sites. This resource, which captures up to 98% of accessible single nucleotide polymorphisms at a frequency of 1% in related populations, enables analysis of common and low-frequency variants in individuals from diverse, including admixed, populations. This report from the 1000 Genomes Project describes the genomes of 1,092 individuals from 14 human populations, providing a resource for common and low-frequency variant analysis in individuals from diverse populations; hundreds of rare non-coding variants at conserved sites, such as motif-disrupting changes in transcription-factor-binding sites, can be found in each individual. This report by the 1000 Genomes Project describes the genomes of 1,092 individuals from 14 human populations, providing a resource for common and low-frequency variant analysis in individuals from diverse populations. Integrative analyses reveal profiles of rare and common variants in different populations. The frequencies of rare variants vary across biological pathways, and hundreds of rare, non-coding variants at conserved sites — such as changes disrupting transcription-factor motifs — can be established for each individual.

The 1000 Genomes Project aims to provide a deep characterization of human genome sequence variation as a foundation for investigating the relationship between genotype and phenotype. Here we present results of the pilot phase of the project, designed to develop and compare different strategies for genome-wide sequencing with high-throughput platforms. We undertook three projects: low-coverage whole-genome sequencing of 179 individuals from four populations; high-coverage sequencing of two mother–father–child trios; and exon-targeted sequencing of 697 individuals from seven populations. We describe the location, allele frequency and local haplotype structure of approximately 15 million single nucleotide polymorphisms, 1 million short insertions and deletions, and 20,000 structural variants, most of which were previously undescribed. We show that, because we have catalogued the vast majority of common variation, over 95% of the currently accessible variants found in any individual are present in this data set. On average, each person is found to carry approximately 250 to 300 loss-of-function variants in annotated genes and 50 to 100 variants previously implicated in inherited disorders. We demonstrate how these results can be used to inform association and functional studies. From the two trios, we directly estimate the rate of de novo germline base substitution mutations to be approximately 10−8 per base pair per generation. We explore the data with regard to signatures of natural selection, and identify a marked reduction of genetic variation in the neighbourhood of genes, due to selection at linked sites. These methods and public data will support the next phase of human genetic research. This issue of Nature contains the first publication from The 1000 Genomes Project, an international collaboration that will produce an extensive public catalogue of human genetic variation. The plan, in fact, is to sequence about 2,000 unidentified individuals from 20 populations around the world. This first paper presents the results from the project's pilot phase, testing three different strategies for genome-wide sequencing with high-throughput platforms: low-coverage whole-genome sequencing of 179 individuals in three population groups, high-coverage sequencing of two mother–father–child trios, and exon-targeted sequencing of 697 individuals from seven populations. The goal of the 1000 Genomes Project is to provide in-depth information on variation in human genome sequences. In the pilot phase reported here, different strategies for genome-wide sequencing, using high-throughput sequencing platforms, were developed and compared. The resulting data set includes more than 95% of the currently accessible variants found in any individual, and can be used to inform association and functional studies.

Abstract The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 2,143 new measurements from 709 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Among the 120 reviews are many that are new or heavily revised, including a new review on Machine Learning, and one on Spectroscopy of Light Meson Resonances. The Review is divided into two volumes. Volume 1 includes the Summary Tables and 97 review articles. Volume 2 consists of the Particle Listings and contains also 23 reviews that address specific aspects of the data presented in the Listings. The complete Review (both volumes) is published online on the website of the Particle Data Group (pdg.lbl.gov) and in a journal. Volume 1 is available in print as the PDG Book. A Particle Physics Booklet with the Summary Tables and essential tables, figures, and equations from selected review articles is available in print, as a web version optimized for use on phones, and as an Android app.

This biennial Review summarizes much of particle physics. Using data from previous editions, plus 2658 new measurements from 644 papers, we list, evaluate, and average measured properties of gauge bosons, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as Higgs bosons, heavy neutrinos, and supersymmetric particles. All the particle properties and search limits are listed in Summary Tables. We also give numerous tables, figures, formulae, and reviews of topics such as the Standard Model, particle detectors, probability, and statistics. Among the 112 reviews are many that are new or heavily revised including those on Heavy-Quark and Soft-Collinear Effective Theory, Neutrino Cross Section Measurements, Monte Carlo Event Generators, Lattice QCD, Heavy Quarkonium Spectroscopy, Top Quark, Dark Matter, ${V}_{\mathit{cb}}$ ${V}_{\mathit{ub}}$, Quantum Chromodynamics, High-Energy Collider Parameters, Astrophysical Constants, Cosmological Parameters, and Dark Matter.A booklet is available containing the Summary Tables and abbreviated versions of some of the other sections of this full Review. All tables, listings, and reviews (and errata) are also available on the Particle Data Group website: http://pdg.lbl.gov/.The 2012 edition of Review of Particle Physics is published for the Particle Data Group as article 010001 in volume 86 of Physical Review D.This edition should be cited as: J. Beringer et al. (Particle Data Group), Phys. Rev. D 86, 010001 (2012).

PART ONE: PARADIGMS AND POLITICS OF RESEARCH Introduction to Mixed Methods and Mixed Model Studies in the Social and Behavioral Sciences Pragmatism and the Choice of Research Strategy Research Design Issues for Mixed Method and Mixed Model Studies PART TWO: METHODS AND STRATEGIES OF RESEARCH Sampling, Measurement, and Quality of Inferences Data Collection Strategies and Research Procedures Alternatives to Traditional Data Analytic Strategies PART THREE: APPLICATIONS, EXAMPLES AND FUTURE DIRECTION OF MIXED MODEL RESEARCH Examples of Mixed Model Designs Extended Examples of Mixed Model Designs Conclusions and Future Directions

Abstract The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 3,324 new measurements from 878 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Among the 120 reviews are many that are new or heavily revised, including a new review on High Energy Soft QCD and Diffraction and one on the Determination of CKM Angles from B Hadrons. The Review is divided into two volumes. Volume 1 includes the Summary Tables and 98 review articles. Volume 2 consists of the Particle Listings and contains also 22 reviews that address specific aspects of the data presented in the Listings. The complete Review (both volumes) is published online on the website of the Particle Data Group (pdg.lbl.gov) and in a journal. Volume 1 is available in print as the PDG Book. A Particle Physics Booklet with the Summary Tables and essential tables, figures, and equations from selected review articles is available in print and as a web version optimized for use on phones as well as an Android app.

We present an analysis of atmospheric neutrino data from a 33.0 kton yr (535-day) exposure of the Super-Kamiokande detector. The data exhibit a zenith angle dependent deficit of muon neutrinos which is inconsistent with expectations based on calculations of the atmospheric neutrino flux. Experimental biases and uncertainties in the prediction of neutrino fluxes and cross sections are unable to explain our observation. The data are consistent, however, with two-flavor ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\leftrightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ oscillations with ${sin}^{2}2\ensuremath{\theta}&gt;0.82$ and $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}&lt;\ensuremath{\Delta}{m}^{2}&lt;6\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}3}\mathrm{eV}{}^{2}$ at 90% confidence level.

Six DNA regions were evaluated as potential DNA barcodes for Fungi, the second largest kingdom of eukaryotic life, by a multinational, multilaboratory consortium. The region of the mitochondrial cytochrome c oxidase subunit 1 used as the animal barcode was excluded as a potential marker, because it is difficult to amplify in fungi, often includes large introns, and can be insufficiently variable. Three subunits from the nuclear ribosomal RNA cistron were compared together with regions of three representative protein-coding genes (largest subunit of RNA polymerase II, second largest subunit of RNA polymerase II, and minichromosome maintenance protein). Although the protein-coding gene regions often had a higher percent of correct identification compared with ribosomal markers, low PCR amplification and sequencing success eliminated them as candidates for a universal fungal barcode. Among the regions of the ribosomal cistron, the internal transcribed spacer (ITS) region has the highest probability of successful identification for the broadest range of fungi, with the most clearly defined barcode gap between inter- and intraspecific variation. The nuclear ribosomal large subunit, a popular phylogenetic marker in certain groups, had superior species resolution in some taxonomic groups, such as the early diverging lineages and the ascomycete yeasts, but was otherwise slightly inferior to the ITS. The nuclear ribosomal small subunit has poor species-level resolution in fungi. ITS will be formally proposed for adoption as the primary fungal barcode marker to the Consortium for the Barcode of Life, with the possibility that supplementary barcodes may be developed for particular narrowly circumscribed taxonomic groups.

BACKGROUND: Weight loss is associated with short-term amelioration and prevention of metabolic and cardiovascular risk, but whether these benefits persist over time is unknown. METHODS: The prospective, controlled Swedish Obese Subjects Study involved obese subjects who underwent gastric surgery and contemporaneously matched, conventionally treated obese control subjects. We now report follow-up data for subjects (mean age, 48 years; mean body-mass index, 41) who had been enrolled for at least 2 years (4047 subjects) or 10 years (1703 subjects) before the analysis (January 1, 2004). The follow-up rate for laboratory examinations was 86.6 percent at 2 years and 74.5 percent at 10 years. RESULTS: After two years, the weight had increased by 0.1 percent in the control group and had decreased by 23.4 percent in the surgery group (P<0.001). After 10 years, the weight had increased by 1.6 percent and decreased by 16.1 percent, respectively (P<0.001). Energy intake was lower and the proportion of physically active subjects higher in the surgery group than in the control group throughout the observation period. Two- and 10-year rates of recovery from diabetes, hypertriglyceridemia, low levels of high-density lipoprotein cholesterol, hypertension, and hyperuricemia were more favorable in the surgery group than in the control group, whereas recovery from hypercholesterolemia did not differ between the groups. The surgery group had lower 2- and 10-year incidence rates of diabetes, hypertriglyceridemia, and hyperuricemia than the control group; differences between the groups in the incidence of hypercholesterolemia and hypertension were undetectable. CONCLUSIONS: As compared with conventional therapy, bariatric surgery appears to be a viable option for the treatment of severe obesity, resulting in long-term weight loss, improved lifestyle, and, except for hypercholesterolemia, amelioration in risk factors that were elevated at baseline.

UBVRI photoelectric observations have been made on the Johnson-Kron-Cousins photometric system of 526 stars centered on the celestial equator. The program stars within a 298 number subset have sufficient measures so that they are capable of providing, for telescopes of intermediate and large size in both hemispheres, an internally consistent homogeneous broadband standard photometric system around the sky. The stars average 29 measures each on 19 nights. The majority of the stars in this paper fall in the magnitude range 11.5-16.0, and in the color range -0.3 to +2.3.

BACKGROUND: In adults, cardiovascular risk factors reinforce each other in their effect on cardiovascular events. However, information is scant on the relation of multiple risk factors to the extent of asymptomatic atherosclerosis in young people. METHODS: We performed autopsies on 204 young persons 2 to 39 years of age, who had died from various causes, principally trauma. Data on antemortem risk factors were available for 93 of these persons, who were the focus of this study. We correlated risk factors with the extent of atherosclerosis in the aorta and coronary arteries. RESULTS: The extent of fatty streaks and fibrous plaques in the aorta and coronary arteries increased with age. The association between fatty streaks and fibrous plaques was much stronger in the coronary arteries (r=0.60, P<0.001) than in the aorta (r=0.23, P=0.03). Among the cardiovascular risk factors, body-mass index, systolic and diastolic blood pressure, and serum concentrations of total cholesterol, triglycerides, low-density lipoprotein cholesterol, and high-density lipoprotein cholesterol, as a group, were strongly associated with the extent of lesions in the aorta and coronary arteries (canonical correlation [a measure of the association between groups of variables]: r=0.70; P<0.001). In addition, cigarette smoking increased the percentage of the intimal surface involved with fibrous plaques in the aorta (1.22 percent in smokers vs. 0.12 percent in nonsmokers, P=0.02) and fatty streaks in the coronary vessels (8.27 percent vs. 2.89 percent, P=0.04). The effect of multiple risk factors on the extent of atherosclerosis was quite evident. Subjects with 0, 1, 2, and 3 or 4 risk factors had, respectively, 19.1 percent, 30.3 percent, 37.9 percent, and 35.0 percent of the intimal surface covered with fatty streaks in the aorta (P for trend=0.01). The comparable figures for the coronary arteries were 1.3 percent, 2.5 percent, 7.9 percent, and 11.0 percent, respectively, for fatty streaks (P for trend=0.01) and 0.6 percent, 0.7 percent, 2.4 percent, and 7.2 percent for collagenous fibrous plaques (P for trend=0.003). CONCLUSIONS: These findings indicate that as the number of cardiovascular risk factors increases, so does the severity of asymptomatic coronary and aortic atherosclerosis in young people.

1. Introduction. 2. Linear Algebra. 3. Linear Systems. 4. H2 and Ha Spaces. 5. Internal Stability. 6. Performance Specifications and Limitations. 7. Balanced Model Reduction. 8. Uncertainty and Robustness. 9. Linear Fractional Transformation. 10. m and m- Synthesis. 11. Controller Parameterization. 12. Algebraic Riccati Equations. 13. H2 Optimal Control. 14. Ha Control. 15. Controller Reduction. 16. Ha Loop Shaping. 17. Gap Metric and ...u- Gap Metric. 18. Miscellaneous Topics. Bibliography. Index.

B-splines are attractive for nonparametric modelling, but choosing the optimal number and positions of knots is a complex task. Equidistant knots can be used, but their small and discrete number allows only limited control over smoothness and fit. We propose to use a relatively large number of knots and a difference penalty on coefficients of adjacent B-splines. We show connections to the familiar spline penalty on the integral of the squared second derivative. A short overview of B-splines, of their construction and of penalized likelihood is presented. We discuss properties of penalized B-splines and propose various criteria for the choice of an optimal penalty parameter. Nonparametric logistic regression, density estimation and scatterplot smoothing are used as examples. Some details of the computations are presented.

We present the results from three gravitational-wave searches for coalescing compact binaries with component masses above <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>1</a:mn><a:mtext> </a:mtext><a:mtext> </a:mtext><a:msub><a:mrow><a:mi>M</a:mi></a:mrow><a:mrow><a:mo stretchy="false">⊙</a:mo></a:mrow></a:msub></a:mrow></a:math> during the first and second observing runs of the advanced gravitational-wave detector network. During the first observing run (<d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>O</d:mi><d:mn>1</d:mn></d:math>), from September 12, 2015 to January 19, 2016, gravitational waves from three binary black hole mergers were detected. The second observing run (<f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>O</f:mi><f:mn>2</f:mn></f:math>), which ran from November 30, 2016 to August 25, 2017, saw the first detection of gravitational waves from a binary neutron star inspiral, in addition to the observation of gravitational waves from a total of seven binary black hole mergers, four of which we report here for the first time: GW170729, GW170809, GW170818, and GW170823. For all significant gravitational-wave events, we provide estimates of the source properties. The detected binary black holes have total masses between <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mrow><h:msubsup><h:mrow><h:mn>18.6</h:mn></h:mrow><h:mrow><h:mo>−</h:mo><h:mn>0.7</h:mn></h:mrow><h:mrow><h:mo>+</h:mo><h:mn>3.2</h:mn></h:mrow></h:msubsup><h:mtext> </h:mtext><h:mtext> </h:mtext><h:msub><h:mrow><h:mi>M</h:mi></h:mrow><h:mrow><h:mo stretchy="false">⊙</h:mo></h:mrow></h:msub></h:mrow></h:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msubsup><k:mn>84.4</k:mn><k:mrow><k:mo>−</k:mo><k:mn>11.1</k:mn></k:mrow><k:mrow><k:mo>+</k:mo><k:mn>15.8</k:mn></k:mrow></k:msubsup><k:mtext> </k:mtext><k:mtext> </k:mtext><k:msub><k:mrow><k:mi>M</k:mi></k:mrow><k:mrow><k:mo stretchy="false">⊙</k:mo></k:mrow></k:msub></k:math> and range in distance between <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msubsup><n:mn>320</n:mn><n:mrow><n:mo>−</n:mo><n:mn>110</n:mn></n:mrow><n:mrow><n:mo>+</n:mo><n:mn>120</n:mn></n:mrow></n:msubsup></n:math> and <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mrow><p:msubsup><p:mrow><p:mn>2840</p:mn></p:mrow><p:mrow><p:mo>−</p:mo><p:mn>1360</p:mn></p:mrow><p:mrow><p:mo>+</p:mo><p:mn>1400</p:mn></p:mrow></p:msubsup><p:mtext> </p:mtext><p:mtext> </p:mtext><p:mi>Mpc</p:mi></p:mrow></p:math>. No neutron star–black hole mergers were detected. In addition to highly significant gravitational-wave events, we also provide a list of marginal event candidates with an estimated false-alarm rate less than 1 per 30 days. From these results over the first two observing runs, which include approximately one gravitational-wave detection per 15 days of data searched, we infer merger rates at the 90% confidence intervals of <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mrow><r:mn>110</r:mn><r:mo>−</r:mo><r:mn>3840</r:mn><r:mtext> </r:mtext><r:mtext> </r:mtext><r:msup><r:mrow><r:mi>Gpc</r:mi></r:mrow><r:mrow><r:mo>−</r:mo><r:mn>3</r:mn></r:mrow></r:msup><r:mtext> </r:mtext><r:msup><r:mrow><r:mi mathvariant="normal">y</r:mi></r:mrow><r:mrow><r:mo>−</r:mo><r:mn>1</r:mn></r:mrow></r:msup></r:mrow></r:math> for binary neutron stars and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mrow><u:mn>9.7</u:mn><u:mo>−</u:mo><u:mn>101</u:mn><u:mtext> </u:mtext><u:mtext> </u:mtext><u:msup><u:mrow><u:mi>Gpc</u:mi></u:mrow><u:mrow><u:mo>−</u:mo><u:mn>3</u:mn></u:mrow></u:msup><u:mtext> </u:mtext><u:msup><u:mrow><u:mi mathvariant="normal">y</u:mi></u:mrow><u:mrow><u:mo>−</u:mo><u:mn>1</u:mn></u:mrow></u:msup></u:mrow></u:math> for binary black holes assuming fixed population distributions and determine a neutron star–black hole merger rate 90% upper limit of <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mrow><x:mn>610</x:mn><x:mtext> </x:mtext><x:mtext> </x:mtext><x:msup><x:mrow><x:mi>Gpc</x:mi></x:mrow><x:mrow><x:mo>−</x:mo><x:mn>3</x:mn></x:mrow></x:msup><x:mtext> </x:mtext><x:msup><x:mrow><x:mi mathvariant="normal">y</x:mi></x:mrow><x:mrow><x:mo>−</x:mo><x:mn>1</x:mn></x:mrow></x:msup></x:mrow></x:math>. Published by the American Physical Society 2019

Abstract On 2017 August 17, the gravitational-wave event GW170817 was observed by the Advanced LIGO and Virgo detectors, and the gamma-ray burst (GRB) GRB 170817A was observed independently by the Fermi Gamma-ray Burst Monitor, and the Anti-Coincidence Shield for the Spectrometer for the International Gamma-Ray Astrophysics Laboratory . The probability of the near-simultaneous temporal and spatial observation of GRB 170817A and GW170817 occurring by chance is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>5.0</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>8</mml:mn> </mml:mrow> </mml:msup> </mml:math> . We therefore confirm binary neutron star mergers as a progenitor of short GRBs. The association of GW170817 and GRB 170817A provides new insight into fundamental physics and the origin of short GRBs. We use the observed time delay of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mo>+</mml:mo> <mml:mn>1.74</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.05</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mspace width="0.25em"/> <mml:mi mathvariant="normal">s</mml:mi> </mml:math> between GRB 170817A and GW170817 to: (i) constrain the difference between the speed of gravity and the speed of light to be between <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>−</mml:mo> <mml:mn>3</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>15</mml:mn> </mml:mrow> </mml:msup> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>+</mml:mo> <mml:mn>7</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>16</mml:mn> </mml:mrow> </mml:msup> </mml:math> times the speed of light, (ii) place new bounds on the violation of Lorentz invariance, (iii) present a new test of the equivalence principle by constraining the Shapiro delay between gravitational and electromagnetic radiation. We also use the time delay to constrain the size and bulk Lorentz factor of the region emitting the gamma-rays. GRB 170817A is the closest short GRB with a known distance, but is between 2 and 6 orders of magnitude less energetic than other bursts with measured redshift. A new generation of gamma-ray detectors, and subthreshold searches in existing detectors, will be essential to detect similar short bursts at greater distances. Finally, we predict a joint detection rate for the Fermi Gamma-ray Burst Monitor and the Advanced LIGO and Virgo detectors of 0.1–1.4 per year during the 2018–2019 observing run and 0.3–1.7 per year at design sensitivity.