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  1. Abstract We search NANOGrav’s 12.5 yr data set for evidence of a gravitational-wave background (GWB) with all the spatial correlations allowed by general metric theories of gravity. We find no substantial evidence in favor of the existence of such correlations in our data. We find that scalar-transverse (ST) correlations yield signal-to-noise ratios and Bayes factors that are higher than quadrupolar (tensor-transverse, TT) correlations. Specifically, we find ST correlations with a signal-to-noise ratio of 2.8 that are preferred over TT correlations (Hellings and Downs correlations) with Bayesian odds of about 20:1. However, the significance of ST correlations is reduced dramatically when we include modeling of the solar system ephemeris systematics and/or remove pulsar J0030+0451 entirely from consideration. Even taking the nominal signal-to-noise ratios at face value, analyses of simulated data sets show that such values are not extremely unlikely to be observed in cases where only the usual TT modes are present in the GWB. In the absence of a detection of any polarization mode of gravity, we place upper limits on their amplitudes for a spectral index of γ = 5 and a reference frequency of f yr = 1 yr −1 . Among the upper limits for eight general families of metric theories of gravity, we find the values of A TT 95 % = ( 9.7 ± 0.4 ) × 10 − 16 and A ST 95 % = ( 1.4 ± 0.03 ) × 10 − 15 for the family of metric spacetime theories that contain both TT and ST modes. 
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  2. Abstract We present an analysis of a densely repeating sample of bursts from the first repeating fast radio burst, FRB 121102. We reanalyzed the data used by Gourdji et al. and detected 93 additional bursts using our single-pulse search pipeline. In total, we detected 133 bursts in three hours of data at a center frequency of 1.4 GHz using the Arecibo telescope, and develop robust modeling strategies to constrain the spectro-temporal properties of all of the bursts in the sample. Most of the burst profiles show a scattering tail, and burst spectra are well modeled by a Gaussian with a median width of 230 MHz. We find a lack of emission below 1300 MHz, consistent with previous studies of FRB 121102. We also find that the peak of the log-normal distribution of wait times decreases from 207 to 75 s using our larger sample of bursts, as compared to that of Gourdji et al. Our observations do not favor either Poissonian or Weibull distributions for the burst rate distribution. We searched for periodicity in the bursts using multiple techniques, but did not detect any significant period. The cumulative burst energy distribution exhibits a broken power-law shape, with the lower- and higher-energy slopes of −0.4 ± 0.1 and −1.8 ± 0.2, with the break at (2.3 ± 0.2) × 10 37 erg. We provide our burst fitting routines as a Python package burstfit 4 4 that can be used to model the spectrogram of any complex fast radio burst or pulsar pulse using robust fitting techniques. All of the other analysis scripts and results are publicly available. 5 5 
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