dataesr/scientific-paragraphs-categorization huggingface dataset:
BURST PROPERTIES During our follow-up observations, 36 bursts were detected with Effelsberg and none with GBT or AO. The 36 bursts are displayed in Figures  2, 3  and 4  and their inferred properties in Table  4. The figures show the dynamic spectra of the bursts over the 235 MHz frequency band, while the top panels show the pulse profiles after integrating the dynamic spectrum in frequency. Our reported bursts come from four epochs (MJD 58002, 58440, 58720, and 58735) and hinting towards three different values for the dispersion measure of the bursts as a result of S/N optimization. However, given the sub-structure present in some of the bursts, such as bursts B11, B20, and B26, we do not report the dispersion value that yields the highest S/N. Furthermore, we do not attempt to optimize the dispersion value, as our incoherently dedispersed data might not be resolving sub-structure that would otherwise be evident with coherent dedispersion.
The number of components ranges from two components, such as B25, to three components for B11 and B26. Particularly interesting bursts are B10 and B14, displaying a weak trailing emission tail, and B20 and B26 with a characteristic downward drifting pattern. B20 and B21 are the closest spaced bursts of our dataset with a TOA difference of ∼38 milliseconds. Although the majority of the published bursts have separations above 1 second, it is known that few bursts cluster around TOA separations of 20-40 millisecond  (Scholz et al. 2017; Hardy et al. 2017; Gourdji et al. 2019; Caleb et al. 2020 ) and potentially as low as 2. 56 millisecond (see  Gajjar et al. 2018). However, whether this latter case corresponds indeed to two separated events or different components of one burst is ambiguous. B31 is arguably the most interesting burst from the sample.
Short-term TOA periodicity search Given the high number of bursts detected within one single observation, we searched for an underlying periodicity in the arrival times of the bursts detected in the November 2018 dataset. First, we employed an algorithm commonly used to find the periods of bursts from rotating radio transients 5  (McLaughlin et al. 2009). For a range of trial periods, the number of rotations between consecutive bursts is calculated, and the best period is the greatest common denominator that groups the bursts into the narrowest range of pulse phase. We note that this algorithm does not work well if bursts arrive over a wide range of rotational phases or if there are multiple emission windows. B20 and B21 are only separated by ∼38 ms and might be two components of one long burst, so we excluded B21 from our analysis.
Full Effelsberg sample In addition to the set of 36 bursts that we report in Table  4 , we incorporate into the following analysis the published datasets from  Hardy et al. (2017)  and  Houben et al. (2019). Such datasets were acquired with Effelsberg using the identical setup (see Section 2. 1). In total, our sample contains 57 bursts detected in 165 hours of observations in epochs between MJD 57635 to 59006.
Note, our dataset, which totals 34 epochs, is composed of roughly 70% non-detections. This is often not the case, as published data is biased towards detections. Following the formulation presented in VanderPlas (2018), we proceed with the Lomb-Scargle periodogram, which is displayed on the top of Figure  5. First, we subtract the mean value from the time series. This step is important as the Lomb-Scargle model assumes that the data is centered around the mean value of the signal. As seen in Figure  5  the periodogram peaks at a period of 161±5 days, in agreement with the postulate of  Rajwade et al. (2020). The 1- uncertainty is not estimated from the width of the peak, as this is not optimal for time series with long baselines and few data points. Instead, we determine the uncertainty of the peak,   , through (Van-derPlas 2018): 𝜎 𝑙𝑠 = FWHM 2 √︄ 2 N • S/N 2 (3) where N is the number of points in the dataset and FWHM is the full-width at half-maximum of the Gaussian fit to the peak.
This is equivalent to a false-positive rate of 161. /  is the signal-to-noise from the discovery as reported by the pipelines and /  is the value obtained after manual cleaning. Note: 5- confidence upper limits. assumed blackbody temperature, kT, for blackbody model and power-law index for power-law models. days period among 10,000 bootstrap trails. We run the simulation and keep the powers encountered at 161 days. Through this approach, the peak is found to have a significance above 4- level. We do not approach more sophisticated methods to estimate the false alarm rate as it is outside the scope of the paper, but we clearly show that the periodicity reported by  Rajwade et al. (2020)  is also seen in our dataset. In the lower panel of Figure  5 , we see the outcome of assigning a phase to each epoch by folding at a period of 161 days.
The y-axis shows the length of each observation. We take MJD 57057 as reference for phase  = 0. From the outermost observations with detections, we infer an active window of 54%. However, we notice that while the end of the active window is densely sampled (by chance), the start of the active phase is not. Motivated by this, and in order to test how representative the Effelsberg dataset is, we add the published follow-up observations on FRB 121102 at L-band (1-2 GHz). The frequency constraint is driven by fact that simultaneous observations at radio frequencies greater than ∼GHz have mostly not led to simultaneous detections, suggesting that a given activity extends only over a couple of hundreds of Megahertz  (Law et al. 2017). We extend the dataset by including the detections and non-detections reported by  Spitler et al.
(2014 Spitler et al. ( , 2016)) ,  Scholz et al. (2016 Scholz et al. ( , 2017)) ,  Gourdji et al. (2019)  and  Oostrum et al. (2020). We refer hereon to this dataset as the L-band dataset. The L-band dataset is composed of a total of 179 epochs from which 43 are detections and 136 non-detections. The Lomb-Scargle periodogram for this dataset infers a period of 158±3 days, which is consistent with the period deduced independently from the EFF dataset and with  Rajwade et al. (2020). To define a more constraining active phase we proceed with the prediction of 161 days and fold the L-band epochs. By considering the left and right-most observations with detection in the L-band dataset we define an active phase of roughly 60%, which is shown in Figure  5  with the yellow-shadowed region. Based on the inferred periodicity of 161 days and the active phase of 60%, we construct the active windows.
2018) : 𝑃 w (𝛿𝑡, 𝑘, 𝑟) = 1 -𝑒 -( 𝛿𝑡 𝑟 Γ(1+1/𝑘)) 𝑘 ) (4) 𝑃 p 𝛿𝑡, 𝑟 𝑝 = 1 -𝑒 -𝛿𝑡 𝑟 𝑝 (5) in the equations above   and  represents the event rates for Poissonian and Weibull case, respectively,  is the shape parameter and Γ is the incomplete gamma function. and  are taken from the mean value of the two-dimensional posterior probability function. Figure  7  shows the ECDF of the November 2018 dataset alongside the fit from the Weibull and Poisson models. Qualitatively, Weibull's CDF better describes the distribution. To quantify the fit we compute the Kolmogorov-Smirnov statistic (KS test) of the November 2018 sample versus its Weibull distribution fit and versus its Poisson distribution fit. We obtain a p-value of 0. 84 and 0. 12 for the Weibull and Poisson fit respectively, meaning that the null hypothesis -of the November sample drawn from a Weibull or Poisson distribution -cannot be rejected.
82 +0. 1 -0. 09 for the whole 41 bursts (panel c Figure  6 ) and  = 1. 0 +0. 2 -0. 1 for the resultant 39 bursts when excluding events with  < 1 s (panel d Figure  6 ). For this dataset, the exclusion of 2 bursts results in a change to the Poissonian case. Interestingly the sub-set of bursts from our Effelsberg sample from  Houben et al. (2019)  includes two epochs separated by a couple of days before and after the  Gourdji et al. (2019)  detections. The posterior probability for  Houben et al. (2019)  subset gives a  = 1. 0 +0. 4 -0. 2 , which agrees with the  value that we obtained for  Gourdji et al. (2019). We discuss the meaning of the exclusion of events with   < 1 s in Section 4.
DISCUSSION It is long known that detections of FRB 121102 are clustered in time. Much of this clustering likely reflected a not-yet-defined periodicity. Here we investigated whether there is still clustering within a single observation or active phase. We defined active windows for FRB 121102 based on the 161 days period deduced from the 34 total epochs in the Effelsberg dataset but constrain the width of the active phase to be roughly 60% based on the 179 observations from the L-band band dataset. This mixed approach is motivated by the poor coverage of the phases prior to the start of the active phase as seen in Figure  5. This phenomenon is purely by chance as the observations were scheduled mostly based on telescope availability, which led to unevenly sampled epochs and different observation lengths.
Besides observations during the predicted window, where chances to detect bursts are higher, we also recommend unbiased observations through the entire phase to better constrain the activity window. Dataset 𝑟 𝑝 𝑟 𝑘 𝑟 𝑝 𝑟 𝑘 (day -1 ) (day -1 ) (day -1 ) (day -1 ) All 8 ± 3 7 +3 -2 0. 40 +0. 04 -0. 03 8 ± 3 7 +3 -2 0. 43 Regarding the waiting time between consecutive bursts, we first consider all the Effelsberg data -composed of 165 hours of observations and 57 bursts -and ask how clustered the events are. From the two-dimensional posterior probability for k and r and the one-dimensional marginal posterior for k we obtain an event rate of 7 +3 -1 day -1 and k=0. 40 0. 04 0. 03 for a Weibull distribution and a rate of 8 ± 3 day -1 from Poisson. On the other hand, if we acknowledge the presence of a periodic active phase and restrict the observations to the 5 active windows in which the Effelsberg data falls: MJD 57590-57687, 57751-57848, 57912-58009, 58395-58492, and 58717-58814 we determine 18 +5 -4 day -1 and k=0.
50 0. 05 0. 03 for a Weibull distribution and a rate of 18 ± 4 day -1 from Poisson. For both datasets, we also calculate the values after excluding wait times with  < 1 s. All values are listed in Table  6. The rates consider events above a fluence threshold of 0. 15 Jy ms for bursts of 1 ms duration which is imposed by Effelsberg's sensitivity to bursts with S/N > 7. However, the previous results for k and r when restricting the observations to the active window implicitly assume that the event rate is constant across all the active windows and across the full active phase, which may not be the case. If we restrict the analysis to each active window independently, we notice that November 2018 sample is the only one providing sufficient bursts in a single active window to reduce the parameter space of the posterior probability to well-constrained values.
As the November 2018 sample is the only observation falling into the MJD 58395-58492 window, a possible change in the observed rate across the active window is not a concern. Instead, we are exploring possible clustering on time scales of hours. From the waiting times for the November 2018 sample shown in Figure  7 , we see that the peak in  is roughly at ∼200 seconds. This set of 24 bursts during a single continuous 7-hr observation (see Table  1 ) provides the most meaningful constraints out of the 13 observations from the Effelsberg dataset. Something peculiar about this observation is that most of the bursts were detected in the second half of the observation. If the 7-hour session is split into two sections of 3. 5 hours each, the inferred Poisson rates are 27±5 day -1 and 137±12 day -1 for the first and second half, respectively.
A change in the RFI situation during the observation does not explain the higher rate inferred in the second part. From these checks, we conclude that the higher rate toward the end of the observation in November 2018 is likely not an observational bias. We continue to explore the event rate asymmetry beyond Poissonian statistics, and in particular, if the detections of November 2018 are better fit by a Weibull distribution with  < 1. As described in Section 3. 3. 2, the best fit from the two dimensional posterior distribution for  and  predicts  = 0. 62 +0. 10  -0. 09 , while if the one burst with  < 1 s is excluded then  = 0. 73 +0. 12  -0. 10. This strong dependence on the estimation of  with few burst closely spaced is more evident with  Gourdji et al. (2019)  dataset, where the value shifts from  = 0.
3. 3. The scaled rate is in fair agreement with the rate of 14 burst/hr from  Gourdji et al. (2019). Nonetheless, we cannot draw general conclusions on whether the center of the on-window leads to higher rates as we lack information on whether all the active windows have a similar activity behaviour. Regarding the strong clustering reported by  Oppermann et al. (2018)  and recently by  Oostrum et al. (2020) , we infer this was likely a consequence of the unknown periodicity and on-phase. If the analysis is limited to the active windows, despite some indication for small clustering, it is less obvious that it indeed differs from the Poissonian case. It is interesting that the exclusion of one wait time from the November 2018 dataset and two from the  Gourdji et al. (2019)  dataset reduces considerably the parameter space of posterior probability for  and  as seen in the top and bottom panels in Figure  6 , pre and post exclusion respectively.
Telescopes such FAST and Arecibo are crucial to discern this matter. If on the contrary, the events with <1 s are indeed independent bursts generated from the same mechanism as the ones separated by tens-to-hundreds of seconds, such mechanism needs to account for the high energy generation needed on a couple of milliseconds timescale. A high number of bursts on a given on-window is the ideal scenario to test how clustered the events are. To this end, telescopes such as Arecibo and FAST are also key given their sensitivity. We stress that the combination of detections with different instruments can be misleading as the different sensitivities influence the event rate. An interesting study is to compare datasets of different telescopes over the same active window, or for a given telescope to compare the repetition pattern at different active phases to explore whether the event rate is constant or rather higher at given phases, such as the center of the active window.
7±0. 6 from 30 bursts detected with WSRT/Apertif with energies in the range of 7 × 10 38 erg to 6 × 10 39 erg. We show in Figure  9  the previously reported values for  in addition to our measurement (see Section 3). The y-axis errors in both panels represent the 1- uncertainties of. The x-axis bars denote the time span (left panel) and the energy range (right panel) of each dataset used for the gamma determination. Despite marginally agreeing if 3- intervals are considered, converging to  ∼ -1, it is worth investigating the potential reasons for the different values encountered. First, there is a strong dependence of the  value with the completeness limit used. Our measured value after rejecting the bursts below the completeness threshold and above the saturation limit is  = -1. 1 ± 0. 2.
If the completeness threshold is not considered and the slope for all the bursts below the saturation limit is included, the slope flattens and becomes  = -0. 8 ± 0. 1. This is consistent with the  = -0. 6 +0. 2 -0. 3 reported by  Law et al. (2017)  and would misleadingly indicate a  near to the expected values for magnetars. Gourdji et al. (2019)  and  Oostrum et al. (2020)  took into consideration such threshold for Arecibo and WSRT/Apertif respectively when reporting. It would be interesting to explore whether  changes for  Law et al. (2017)  dataset if the completeness limit is considered. Regarding a potential dependence on  with time, as proposed by  Oostrum et al. (2020) , we see in Figure  9  that the bursts considered for the Effelsberg dataset span roughly 3 years. From Figure  8  we see that all the bursts from the dataset are well mixed and follow the same trend, with no indication for different  with time.
The discrepancy of the values reported as of now challenge the universality of the power-law index for the cumulative energy distribution of the bursts and raises the question of whether we are in presence of a much more complex energy distribution (see right panel of Figure  9 ). Given that the energy range span of our dataset lies between the sample of low energy bursts of  Gourdji et al. (2019)  and the more energetic bursts reported by  Law et al. (2017)  and  Oostrum et al. (2020) , one possibility is that a single power-law does not well describe the data over many orders of magnitude. In the right side of Figure  9 , if we exclude the value reported by  Law et al. (2017)  -where the completeness threshold was not considered -we see that the slope of the energy distribution is steep for energies near 10 40 erg and 10 38 erg, while being flatter in the intermediate energy range.
(2017)  for the case where X-ray emission is highly absorbed by material close to the source. We combine our Effelsberg dataset with the published observations carried with identical setup by  Hardy et al. (2017)  and  Houben et al. (2019). The extended sample is composed of roughly 165 hours of observation from MJD 57635 to 59006 and consists of 34 epochs from which roughly 70% are non-detections. Given that the observations were mostly randomly scheduled and that the full set of detections and non-detections are known, we searched for an underlying periodicity through the Lomb-Scargle periodogram. We find a 161±5 days period and an active window of roughly 54%, which broadens to roughly 60% after considering published observations at L-band. These values agree with the finding of  Rajwade et al.
(2020)  on the potential 157 days periodicity for FRB 121102. We continue to investigate how the time interval for consecutive bursts is distributed within the active windows, and particularly whether a Weibull distribution with  < 1 (to allow clustering) describes the data better than the classic time-independent Poissonian statistics. To this end, we use the formalism implemented in  Oppermann et al. (2018)  over all the observations in the Effelsberg dataset lying within an active window. The November 2018 session is the only observation providing a reduced parameter space on the posterior probability for  and , mainly due to the high event rate and observation length. We observe a mild clustering in the sample, however, we find that the Weibull fitting is highly biased towards few events with waiting times shorter than one second.
We test this finding with  Gourdji et al. (2019)  dataset which contains a total of 41 bursts over 3. 2 hours of observation. We conclude that if the few shortly spaced events are removed, then  = 1, meaning that the distribution is indistinguishable from a Poisson distribution. A bimodal distribution of the waiting time has been observed before by  Li et al. (2019)  and  Gourdji et al. (2019)  and could hint towards two mechanisms responsible for the events with  < 1 s of separation and the ones that are hundreds of seconds apart. An alternative scenario is that the events that are tens of milliseconds apart correspond to the main components of broad bursts in which weak, intermediate components are not detectable. This hypothesis is supported by burst B31 detected in November 2018, which with an FWHM of 39±2 ms is the widest burst ever measured for this source.
We conclude that the strong clustering observed by  Oppermann et al. (2018)  and  Oostrum et al. (2020)  was a consequence of the unknown periodicity for FRB 121102. Finally, we study the cumulative energy distribution of the 57 bursts from the Effelsberg dataset. We fit a power law of the form  ∝   through maximum likelihood analysis and find a slope of  = -1. 1 ± 0. 1. This value lies between the  = -0. 6 +0. 2 -0. 3 reported by  Law et al. (2017)  and  = -1. 8 from  Gourdji et al. (2019). Given the different energy regimes covered by the different studies, we suggest that a single power-law might not fit the data over many orders of. In green, the value is shown for the 9 bursts detected with the VLA at 3 GHz  (Law et al. 2017) , in blue for 41 bursts detected with AO at 1. 4 GHz  (Gourdji et al.
2019) , in orange for 30 bursts from WSRT at 1. 4 GHz  (Oostrum et al. 2020)   magnitude or that the instrumental effects, such as completeness threshold and saturation, play an important role in its estimation. We find no indication for an epoch evolving  as proposed by  Oostrum et al. (2020) , as the bursts from the Effelsberg dataset are well mixed and described by a single power-law over the roughly 3 years of the data span. We finalize with key points to be considered after the results of this work: (i) Given the existence of broad bursts with durations of tens of milliseconds, it is advised to future FRB searches to expand the parameter space of the burst widths to at least hundreds of milliseconds. For previously searched data, it is strongly encouraged to re-process the data. (ii) When doing a periodogram search it is important to compute the window transform to discard fake periodicities introduced, for instance, by the observation cadence (see Section 3.
ACKNOWLEDGEMENTS We thank the referee for helpful and insightful comments that improved the quality of the manuscript. We thank  Dr. R. Wharton ,  Dr. N. Porayko , and  L. Houben  for helpful discussions. This publication is based on observations with the 100-m telescope of the  Max-Planck-Institut für Radioastronomie at Effelsberg. We thank  Dr. A. Kraus  for scheduling our observations. This publication has received funding from the  European Union 's  Horizon 2020 research and innovation program  under grant agreement No  730562  [RadioNet]. L. G. S. is a Lise Meitner independent research group leader and acknowledges funding from the  Max Planck Society. J. W. T. H. acknowledges funding from an  NWO   Vici grant  ("AstroFlash"). Partly based on observations with INTEGRAL, an  ESA  project with instruments and science data center funded by ESA member states.
ALMA observations of polarized dust emission in Class 0 protostellar cores In its polarized mode, ALMA produces visibility measurement sets of the three Stokes parameters I, Q, and U , which can be imaged and combined to produce maps of the polarized dust emission. We gathered publicly available ALMA dust polarization observations toward nearby, lowand intermediate-mass Class 0 protostars. Since the statistical tools we use require a large number of statistically independent measurements at the typical scale of the object studied, we selected observations with the most extended polarized dust emission. The regions of interest in these protostellar cores correspond to the inner envelope scales (∼10-2000 au). Therefore, we selected the ALMA datasets whose polarized dust emission was observed with combinations of sensitivity and angular resolution that allow us to detect low levels of polarized emission beyond the peak of continuum emission, at these inner envelopes typical scales.
We present the resulting sample in Table  1. We use the three Stokes maps provided by the authors of the corresponding publications (see Table  1 ) to create the polarized emission maps. In the case of NGC1333 IRAS4A, however, because these data were not yet published at the time we started our investigations, we calibrated and imaged these observations ourselves. We produced the polarized dust continuum images using the task tclean in version 5. 4 of CASA  (McMullin et al. 2007 ). We applied four rounds of consecutive phase-only self-calibration, using the total intensity (Stokes I) solutions as the model, with a Briggs weighting parameter of robust = 1. The three Stokes parameters I, Q, and U were cleaned separately after the last round of self-calibration using an appropriate residual threshold and number of iterations.