dataesr/scientific-paragraphs-categorization huggingface dataset:
Summary and conclusions We used approximately 1 800 X-ray-selected AGN from the eFEDS field and more than 17 000 galaxies in the same spatial volume (0. 5 < z < 1. 5), and compared the SFR of the two populations. Both samples have the same photometric coverage. We performed SED fitting using the CIGALE algorithm and the same templates and parametric grid for both datasets. We accounted for the mass completeness of the two catalogues and applied a uniform method to exclude quiescent sources from both samples. These allowed us to compare the SFR of X-ray AGN and non-AGN systems in a uniform manner, minimising systematic effects. Furthermore, our analysis and SED fitting grid are identical to those applied in previous studies  (Mountrichas et al. 2021c (Mountrichas et al. , 2022)) , which used X-ray sources from different fields (COSMOS, Boötes) and spanned different X-ray luminosities.
This allows us to compare and complement our results with theirs and draw a picture regarding the location of X-ray AGN relative to the MS over 2. 5 orders of magnitude in L X (L X,2-10 keV ∼ 10 42. 5-45 erg s -1 ). Our results show that, at low to moderate X-ray luminosities, L X,2-10 keV < 10 44 erg s -1 X-ray AGN have an SFR that is lower than, or at most equal to, that of star-forming galaxies. This is in agreement with the results of  Mountrichas et al. (2022) , who studied X-ray sources in the COSMOS field. Mountrichas et al. (2021c)  used X-ray data from the Boötes field that span high L X , and found indications that the SFR of AGN is higher compared to that of MS galaxies at L X,2-10 keV > 2-3 × 10 44 erg s -1. The eFEDS sample is between two and three times larger at these luminosities compared to the Boötes dataset, enabling us to increase the number of datapoints in this L X regime.
Acknowledgements. G. M. acknowledges support by the  Agencia Estatal de Investigación ,  Unidad de Excelencia María de Maeztu , ref. MDM-2017-0765. The project has received funding from  Excellence Initiative of Aix-Marseille University -AMIDEX , a  French 'Investissements d'Avenir' programme. M. B. gratefully acknowledges support by the  ANID   BASAL  project  FB210003. K. M. is supported by the  Polish National Science Centre  grant  UMO-2018/30/E/ST9/00082.
Patients and data collection. We included all consecutive patients admitted in our ICU department for acute respiratory failure and presented ARDS criteria, according to Berlin definition  26  at the initial phase of ventilatory management (within one hour after intubation). Exclusion criteria were those related to known causes of low-reliability of SpO 2 measurements: (i) low-quality SpO 2 signal assessed on the SpO 2 curve aspect and (ii), patients with nail varnish, methaemoglobinemia or carbon monoxide poisoning  4  and (iii), patients with marked movements leading to SpO 2 signal artefacts  27. ARDS severity was categorized as mild for PaO 2 /FiO 2 ratio between 200 and 300 mmHg, moderate between 100 and 200 mmHg, and severe, under 100 mmHg  26. Data were prospectively collected using a clinical software allowing data management and extraction, Centricity Critical Care (General Electric Healthcare, Massachusetts, United States of America).
Continuous variables were compared using Wilcoxon or paired Student t-tests and Mann-Whitney U-test or Student t-tests. Categorical variables were compared using Chi-2 or Fisherexact tests. We used four different methods to assess the association between SaO 2 and SpO 2 : correlations, agreement, multivariable regression models and concordance. Specifically, correlations were performed using Pearson or Spearman's correlation coefficients, according to data distribution. Agreement between SpO 2 and SaO 2 measurements was assessed with Bland-Altman analysis  33  and intraclass correlation coefficients (ICC), with ICC value > 0. 7 and > 0. 9 indicating satisfactory and excellent agreement respectively  34. Accuracy of SpO 2 measurement was estimated by the bias, calculated as the mean difference between SpO 2 and SaO 2 measurements.
Assuming a correlation coefficient of 0. 69 between SpO 2 and SaO 2  38  and an ICC > 0. 9 with a 95% confidence interval (CI) (0. 84-0. 96), we planned to include at least 50 patients with at least 25 COVID-19 patients. A p value < 0. 05 was considered statistically significant. Statistical analyses were performed using MedCalc 11. 6. 0 software (MedCalc®, Mariakerke, Belgium), and SPSS version 25. 0 (IBM®, Armonk, USA).
Ethics approval and consent to participate. This study was approved by the Comité de Protection des Personnes Ile-de-France X (IDCRB2018-A00050-55, protocol 59-2018) and by the Ethics Committee of the Société de Réanimation de Langue Française (CE SRLF 20-72)  25  , which waived the need for informed consent, following national regulation on standard-of-care data collection. Indeed, this study was performed on data collected in the course of a prospective data collection, without any additional blood sample, as compared to standard of care. As such, only refusal to participate was systematically sought.
We selected sources that had a peak intensity of 25 mJy or higher in the 1 image, resulting in a sample of 46 potential calibrators. The data were then phaseshifted to these sources, creating individual datasets, and self-calibrated. In the direction-dependent self-calibration process we leverage the fact that the dominant remaining effects are the ionosphere and slowly varying effects, such as errors in the primary beam model. A starting model was automatically generated for each source by imaging it before the first iteration started. Subsequent self-calibration is an iterative process where in each iteration calibration solutions are obtained that provide an updated model, which can in turn provide better calibration solutions. Dominated by the ionosphere, we can constrain the "phase-only" self-calibration iterations to calibrate for differential Total Electron Content (dTEC), reducing the degrees of freedom by introducing the known frequency dependence of the ionospheric delay as the functional constraint given by Equation  1.
The remaining 2 sources did not have sufficient compact flux to perform self-calibration on and were thus discarded. Figure  2  shows the progression of self-calibration on three sources of varying complexity and distance from the initial LBCS calibrator. The fact that self-calibration converged for 44 directions across the entire 7. 4 deg 2 area confirms that the density of compact sources is high enough to correct directiondependent effects across the field of view. Furthermore, the fact that a sufficiently accurate skymodel for initiating self-calibration could be created from a direction-independently calibrated dataset indicates that for similar ionospheric conditions a single correction is likely to be approximately valid over the entire field of view. Finally, the solutions were interpolated using radial basis function interpolation into a 2D map of corrections.
A total of approximately 250 000 core hours were required for the data reduction process in order to arrive at the final image. This was split between calibration and imaging as 34% and 76%, respectively. The image covers a 7. 4 deg 2 sky area at an angular resolution of 0. 3 × 0. 4 and a central rms noise level of 32 µJy beam -1 is reached. This equates to a 1. 4 GHz sensitivity of 7 µJy beam -1 , assuming a spectral index of α = -0. 7. This is comparable in depth to the deepest 1. 4 GHz VLA image of the field  [8]. 7143 sources are detected at 6 in the covered area using a single 8 hour observation with an rms noise level of 70 uJy beam -1. Of these 6397 (90%) are unresolved and 746 (10%) are resolved. Of those unresolved sources, 2568 (40%) had a high resolution counterpart detected at a SNR > 5.
293 of these sources are resolved (11%) and the other 2275 remain compact (89%). Our demonstration of wide-field, low-frequency, sub-arcsecond resolution imaging opens up important new scientific parameter space to be explored by the ability to conduct a blind all-sky subarcsecond survey. This resolution is a valuable tool to help, for example, disentangle radio-quiet AGN from star-forming galaxies, which exhibit similar unresolved radio properties and allow the study of radio sources nearby and far in new detail. Low-frequency data is especially important for broadband spectral modelling and at this resolution the ILT is well matched to other telescopes such as e-MERLIN or the VLA. Over the past years the ILT has been conducting the LOFAR Two-Metre Sky Survey (LoTSS), a sensitive 6 survey of the northern sky  [22].
The data recorded for this survey holds incredible legacy value for a future sub-arcsecond survey. Over 75% of the sky has already been observed for LoTSS, using the same duration, bandwidth and averaging as the data presented here. Weighted by integration time, only 3% of this data contains no international stations. 54% has 12 or more international stations per hour of observing time and 84% has 10 or more international stations per hour of observing time. This means that a significant amount of data is already present in the LTA, ready to be processed. Relatively little extra or repeat observing will thus be necessary for a sub-arcsecond counterpart to LoTSS. The work presented here demonstrates a general strategy for widefield low-frequency sub-arcsecond imaging. By combining advanced calibration strategies with new state of the art imaging techniques we have demonstrated complete directiondependent calibration and widefield imaging at sub-arcsecond resolution at frequencies between 120 and 168 MHz.
Calibration and imaging Calibration of the radio data started from the raw data stored in the Long Term Archive (LTA). First the data was processed using the de facto pipelines for calibrating the Dutch stations: prefactor and ddf-pipeline  [5, 23, 25]. Subsequently a suitable infield Long Baseline Calibrator Survey (LBCS) calibrator was selected. From thereon no dedicated pipeline existed. First direction independent calibration of the international stations was carried out. An intermediate resolution image at ∼ 1 was used to select sources for direction-dependent calibration, which were subsequently self-calibrated. Finally the field was split up in "facets" and imaged at the full native resolution.
Direction independent calibration of the DLT The prefactor pipeline consists of two workflows for the calibrator scan and target scan respectively. A detailed overview of the calibration strategy is given by  [5]. A short overview of these workflows will be given next. First the calibrator workflow determined the following corrections for both Dutch and international stations: a phase offset to align XX and YY polarisations (based on the assumption that the calibrator is unpolarised), a bandpass translating correlator units to physical units and a clock offset in nanoseconds to synchronize the clocks of each station to the same reference. These solutions were determined on a 4 s time interval and a 48. 82 kHz frequency intverval. Finally they were transferred to the target dataset and the target workflow determined XX and YY phase solutions for the Dutch stations by calibrating against a skymodel from the TFIR GMRT Sky Survey (TGSS,  [7] ) on an 8 s time interval and a 195.
Direction independent calibration of the ILT To start calibration of the international stations, we followed the strategy as the lofar-vlbi pipeline  [15]. Calibration solutions from prefactor and ddf-pipeline were applied, data was combined into 24 manageable 2 MHz chunks of 32 GB and finally a suitable LBCS calibrator was selected within the international station field of view  [10]. This calibrator source was then split off from the main dataset by phase shifting the visibilities towards this source. After phase shifting, the core stations were all combined into a single "super station", ST001. The dataset was also averaged down to a 16 s time interval and a 195. 28 kHz frequency interval. This heavy averaging causes a ∼ 50% intensity loss due to smearing at a distance of ∼ 4 from the phase centre, which considerably reduces the influence of other sources.
28 kHz frequency interval, for the XX and YY polarisations. The starting model for the first phase-only iteration was a point source, due to the lack of more information, with the flux density taken from the low-resolution 6 image. While such a starting model is likely naive possibly incorrect, after each iteration the model was updated and the self-calibration cycle converged to believable double lobed source structure. These solutions were then applied to the target field dataset as initial direction-independent calibration for the international stations and refined direction-independent calibration solutions for the remote and core stations. The core stations were corrected with the solutions for ST001.
Intermediate resolution imaging and faceting Due to its sheer size, the full field of view could not be covered with a single image at the ILT's native resolution. Therefore the field was split in 25 facets that were imaged separately. To help suppress interference from undeconvolved sources outside of each facet and to determine suitable candidate sources for direction-dependent calibration, an intermediate resolution image at approximately 1 was made by tapering the data with a Gaussian taper. The resulting image was 25000 × 25000 pixels in size and covered the full field of view. In preparation for high-resolution imaging, 25 datasets ("facets") were then split out with their phase centres spread over the field of view in a 5×5 grid, with each facet spanning 0. 55 × 0. 55 deg 2 on the sky, separated by 0.
5 deg. For each facet the intermediate resolution map was subtracted outside this 0. 55 × 0. 55 deg 2 area. The 0. 05 deg on each side ensured some overlap between the facets to not have gaps in the sky coverage. The data were then phase shifted to each of these phase centres and averaged to 4 s and 48. 82 kHz time and frequency resolution. These were the final 25 datasets that would be imaged at high resolution. The data for each facet were about 250 GB in total size.
Direction dependent calibration of the ILT Sources that remain bright and compact at 1 resolution have a better chance of remaining compact down to 0. 3 compared to a selection at 6. From the intermediate resolution image sources with a peak intensity above 25 mJy/beam were selected as candidate DDE calibrators. These were then split off into separate datasets similarly to the LBCS calibrator, but averaged more in time to a 1 min interval. For the brightest sources this balanced well the signal to noise ratio while still retaining the time resolution to correct most of the residual ionospheric distortions properly. The calibration solutions derived on the LBCS calibrator were preapplied and a similar self-calibration routine as for the LBCS calibrator was subsequently used to self calibrate these sources, outlined below.
Final imaging Final high-resolution imaging of the data was done using WSClean in combination with IDG in CPU mode. Since the IDG algorithm can leverage a GPU for the gridding calculations, this amount can likely be significantly reduced  [31]. A 22500 × 22500 image of a similar dataset finished four times faster on a 22-core Intel (R) Xeon(R) Gold 6226 system with an Nvidia Tesla V100 compared to an identical system without one. Each of the facets was imaged separately with robust -1 weighting, a 0. 11 pixel size and a 22700 × 22700 pixel image size. Multiscale multi-frequency synthesis clean was used together with spectral fitting using a second-order polynomial (through -fit-spectral-pol 3). Differential primary beam, dTEC and gain corrections were all applied on the fly during imaging.
The beam corrections were applied every 10 min, dTEC solutions were applied every minute and gain solutions every hour. This could be done efficiently through the use of IDG. The data was imaged using hardware on the Spider platform at surfSARA and the ALICE cluster in Leiden. Imaging took 5 -7 days wall clock time per facet on average using 24 cores on a node with two 12-core Xeon Gold 6126 running at 2. 6GHz and 384 GB of RAM. Effective wall clock time was significantly reduced however due to the availability of many compute nodes, allowing imaging to run in parallel where each compute node imaged a facet independently. From start to finish the entire data reduction procedure consumed approximately 250, 000 core hours.
Acknowledgements We thank the (anonymous) reviewers for their comments. FS would like to thank  SURFsara  for beta access to the Spider platform. This paper is based (in part) on data obtained with the  International LOFAR Telescope (ILT)  under project code  LT10 012. LOFAR (van Haarlem et al. 2013) is the  Low Frequency Array designed  and constructed by  ASTRON. It has observing, data processing, and data storage facilities in several countries, that are owned by various parties (each with their own funding sources), and that are collectively operated by the ILT foundation under a joint scientific policy. The ILT resources have benefitted from the following recent major funding sources:  CNRS-INSU, Observatoire de Paris and Université d'Orléans, France ;  BMBF ,  MIWF-NRW, MPG, Germany ;  Science Foundation Ireland (SFI) ,  Department of Business, Enterprise and Innovation (DBEI) , Ireland; NWO, The Netherlands; The  Science and Technology Facilities Council, UK [7].
Code Availability The various software and pipelines used in this work are publicly available at https://github. com/lofar-astron/prefactor (prefactor), https://github. com/cyriltasse/DDFacet (ddfacet), https://github. com/lmorabit/ lofar-vlbi (lofar-vlbi), https://github. com/ mhardcastle/ddf-pipeline (ddf-pipeline) and https://gitlab. com/astron-idg/idg (IDG). Code from other parts not using these pipelines is 11.
Corollary 5. 2 (Convergence of discrete maps as h → 0). I s,t -I h,s,t → 0 as h → 0. Thus, the computations of I h,s,t , given in §6, are reliable approximations of I l,j. A key point in the computation is the realisation that, for any g ∈ L 2 (Γ s ), I h,s,t g = I h,s,t g h , with g h denoting the L 2 -orthogonal projection of g onto V h (Γ s ). (This is because the finite-element solution of the Helmholtz problem only 'sees' the impedance data through its L 2 moments against the finiteelement basis functions. ) The operator I h,s,t thus acts only on finite-dimensional spaces, and its norm can be computed by solving an appropriate matrix eigenvalue problem. In §6 this is done using the code SLEPc, within the finite-element package FreeFEM++.
Numerical experiments In this section, we verify the theoretical results in Theorems 4. 13 and 4. 16 and Corollaries 4. 8, 4. 14, 4. 15 using the finite-element approximations described in §5. We also perform some extra experiments that provide insight into the performance of the iterative method in situations not covered by the theory. All experiments are on rectangles, the domain is discretized using a uniform triangular mesh with diameter h, and we use the Lagrange conforming element of degree 2. We use mesh diameter h ∼ k -5/4 , which is sufficient to ensure a bounded relative error as k increases  [19, Corollary 5. 2]. The experiments are implemented using the package FreeFEM++  [40].
We introduce a new method of estimating accepted species diversity by adapting mark-recapture methods to comparisons of taxonomic databases. A taxonomic database should become more complete over time, so the error bar on an estimate of its completeness and the known diversity of the taxon it treats will decrease. Independent databases can be correlated, so we use the time course of estimates comparing them to understand the effect of correlation. If a later estimate is significantly larger than an earlier one, the databases are positively correlated, if it is significantly smaller, they are negatively correlated, and if the estimate remains roughly constant, then the correlations have averaged out. We tested this method by estimating how complete MolluscaBase is for accepted names of terrestrial gastropods.
Using random samples of names from an independent database, we determined whether each name led to a name accepted in MolluscaBase. A sample tested in August 2020 found that 16. 7% of tested names were missing; one in July 2021 found 5. 3% missing. MolluscaBase grew by almost 3,000 accepted species during this period, reaching 27,050 species. The estimates ranged from 28,409 ± 365 in 2021 to 29,063 ± 771 in 2020. All estimates had overlapping 95% confidence intervals, indicating that correlations between the databases did not cause significant.
, 2017). Estimates of diversity that take into account abundance and disparity are even more difficult, although mathematical sophistication is rapidly increasing in treating assemblages of taxa in defined areas  (Leinster & Cobbold, 2012; Chao et al. , 2014). We tackle here a simpler question: how to estimate how many species have already been named and are currently accepted. Even in this restricted domain, much uncertainty remains. The Catalogue of Life (2020) aims to attain a complete list of accepted species, by adding together global species databases (GSDs)  (Bisby, 2000; Garnett et al. , 2020). Costello (2020)  stated that it is "about 85% complete", as of 2019 listing 1. 3 million species of 1. 5 million known (based on  Costello, May & Stork (2013) ). Yet the Catalogue of Life website stated on 16 September 2020 that it contained listings of 1,854,034 living species, thought to be "probably just over 80%" of the 2.
2 million species currently known to taxonomists. These estimates, based on the same underlying data, differ by 30%. The Catalogue of Life website no longer estimates completeness, but as of 05 September 2021 it stated that their database contained 2,016,676 species (https://www. catalogueoflife. org/data/taxon/5T6MX), of which 77,977 were "provisionally accepted" (as stated in the website's search interface). We use terrestrial Mollusca as a testbed for developing tools for estimating known species richness. All terrestrial mollusks are gastropods; see Box 1 for a summary of their terminology, classification and habitats. Mollusca is the second most species-rich phylum after the Arthropoda, so techniques that succeed in estimating molluscan diversity should be applicable to overall eukaryote diversity.
We expand here on the methods of  Rosenberg (2014) , who estimated the number of named marine mollusks as 43,600 ± 900 species using the binomial distribution to obtain error bars (standard deviations) for random sampling of the World Register of Marine Species (the parent of MolluscaBase), compared to the collection database for malacology at the Academy of Natural Sciences of Philadelphia (Drexel University). Rosenberg (2014)  did not note that his procedures were analogous to mark-recapture methods. Estimation of the number of species named by a certain date has the same mathematical underpinnings as the Lincoln-Petersen estimator for mark-recapture  (Petersen, 1896; Lincoln, 1930; Seber, 1982) , but a different set of assumptions must be met. One of the key assumptions is that the databases used in the estimate are independent and uncorrelated, in this case, MolluscaBase, and the collection database for Recent Mollusca at the Academy of Natural Sciences of Philadelphia (ANSP).