dataesr/scientific-paragraphs-categorization huggingface dataset:
The agreement of the resulting  In Figs. 11 and 12 we compare the full theory and the leading twist contribution with the lattice data for the NLO and NLO þ NLL DY methods, respectively. For this observable, the uncertainties are large in comparison with the Rp-ITD data, especially at small momentum. While the leading twist and total contributions have considerable FIG. 11. CC correlator data versus Ioffe time ν for the datasets for the full theory as in Eq. (  11 ) (red bands with 1σ uncertainties) and the leading twist contributions (blue bands) for the NLO method. An additive shift of ðz=a -2Þ=8 beyond z ¼ 2a is applied for clarity. 12. Same as Fig. 11 , but for the NLO þ NLL DY method. overlap, notably in the lattice data with a ¼ 0. 094 fm, various features of the data are difficult to capture by using next-to-leading order leading power matching coefficients, and systematic corrections are needed to achieve good agreement with the full set of lattice data.
The valence quark distributions before and after the inclusion of the lattice CC data are shown in Fig. 13  for the NLO and NLO þ NLL DY methods, along with their relative uncertainties. The PDFs themselves are rather stable under the inclusion of the lattice data, suggesting compatibility between these lattice and experimental datasets. Unlike the Rp-ITD data, the CC lattice data have essentially no pull on the central values for the NLO þ NLL DY analysis, indicating that these data have minor impact on the PDFs. The relative uncertainties are very similar in both cases, with a slight increase when including the CC lattice data compared with the experimental-only analysis. Similar behaviors are seen for the sea quark and gluon distributions (not shown here). Despite the small increase in the relative uncertainties of the PDFs, the relative uncertainties on the predictions for the experimental observables using these PDFs do not increase, which is a reflection of the nontrivial interplay between different flavors of PDFs.
The agreement with the lattice data was similar for the two methods; however, the resulting PDFs were affected in the case of the NLO þ NLL DY analysis when including Rp-ITD data. This suggests the need to further investigate possible tensions between the experimental and lattice observables, and the exercise would benefit from new observables being available. Regardless of this, the lattice data, in conjunction with the experimental measurements, consistently prefer an effective exponent β eff ≈ 1. 0-1. 2. The improvement found in the PDF uncertainties with the inclusion of the Rp-ITD lattice data has implications for future global analyses with combined experimental and lattice QCD observables. First, since the p ¼ 1 data have such a limited range of Ioffe time, the Fourier transform and the nature of the inverse problem complicate the determination of an x-space quasi-PDF or pseudo-PDF from the lattice data alone, particularly in the low-x region.
The precise low-ν data from the lattice can provide a significant constraint on the lowest moments of the PDFs, complemented by the experimental range of data in the low-x region. The p ¼ 1 data with Oð0. 1%Þ statistical precision seem necessary for providing a useful constraint on the PDFs, while adding the p ¼ 2 data with Oð1%Þ statistical precision did not dramatically improve the result. This fact suggests that future lattice calculations which aim to complement experimental datasets will require subpercent level precision. These types of constraints can be provided by the lattice data through a factorization method which promotes the use of the low momentum data, such as the pseudo-PDF approach. Through the complementarity of the lattice and experimental data, we were able to quantify the systematic corrections associated with these ensembles and their uncertainties.
ACKNOWLEDGMENTS This work is supported by the  U. S. Department of Energy (DOE)  Contract No. DE-AC05-06OR23177 , under which  Jefferson Science Associates, LLC operates Jefferson Lab , and within the framework of the TMD Collaboration. We acknowledge the facilities of the  USQCD Collaboration  used for this research in part, which are funded by the  Office of Science (OS)  of the  US DOE. This material is based in part upon work supported by a grant from the  Southeastern Universities Research Association (SURA)  under an appropriation from the  Commonwealth of Virginia. This work used the  Extreme Science and Engineering Discovery Environment (XSEDE) , which is supported by  National Science Foundation (NSF)  Grant No. ACI-1548562 [117 ]. This work was performed in part using computing facilities at William and Mary which were provided by contributions from the  NSF  ( MRI Grant  No.
Quantitative and qualitative analyses of ChemCam data From ChemCam spectra, major oxide (i. e. , SiO 2 , TiO 2 , Al 2 O 3 , MgO, CaO, Na 2 O, K 2 O) quantification is made using a large library of spectra acquired on geological standards (>400 samples) and two multivariate analysis algorithms: a partial least squares (PLS,  Clegg et al. (2017) ), and an independent component analysis  (ICA, Forni et al. (2013) ). For iron quantification, we used here a dedicated calibration method described in  David et al. (2020) , more appropriate to highlight the presence of Fe-rich mineral phases in the ChemCam shot-to-shot dataset. The major composition is not normalized to 100 wt. % to take into account volatile concentrations including H and S contents. Indeed, unlike major elements, hydrogen is not yet quantified in granular media, and we used instead the independent component analysis  (Forni et al.
Data selection In this study, we selected the soil targets analyzed by ChemCam from Sol 19 to 194 localized in the Bradbury, Rocknest and Yellowknife Bay area (Figure  1. a). The Chem-Cam Remote Micro-Imager is used to consider only observation points located on gran-ular soils. LIBS spectra with a noise level too high for sulfur peak analyses (i. e. , with total spectral intensity lower than 1. 6x10 14 photons) are removed from our dataset. In the end, the ChemCam dataset used in this study corresponds to 25 soil targets. Chem-Cam analyses are rasters of several observation points, and a burst of laser shots is performed on each of these points. As a result, our 25 soil targets translate into 165 different LIBS observation points and 4790 single-shot LIBS spectra. Finally, we distinguished in our data LIBS shots that probed the dust from the rest of the soil.
-6-manuscript submitted to Geophysical Research Letters ChemCam laser shots reflecting the dust composition are shown in figure  2  (orange squares). The dust fraction of soils contains a significant hydrogen content, consistent with previous ChemCam studies  (Meslin et al. , 2013; Lasue et al. , 2018). However, the hydrated sulfates identified here are not hosted by the eolian dust as seen from the scatter of the ICA H scores. Indeed, we observe that there are LIBS spectra from the bulk soils (∼26. 7% of total number of spectra) that show a higher hydration than the average value of the dust plus uncertainty (i. e. , 0. 045±0. 009). This implies that the dust does not correspond to the hydrated end-member, and that discrete particles of hydrated sulfates coarser than the aeolian dust are present within the soil material itself, or that sulfates are present as rinds or coatings around igneous grains.
Acknowledgments We gratefully acknowledge the  Mars Science Laboratory  scientific and engineering teams for enabling the collection of the datasets used in this study. This research was carried out with financial support from  NASA 's  Mars Exploration Program  in the US and in France with the  Centre National d'Etudes Spatiales (CNES). We thank the  MAHLI and Mastcam teams at Malin Space Science Systems  for processing the images used in this paper.
With this decrease in power requirements comes a desirable decrease in characteristics such as payload mass, size, and cost. All these factors together reduce the cost of manufacturing, launch and operation  [1, 2, 11]. However, an important disadvantage in VLEO is the existence of atmospheric drag, which has a significant negative effect on spacecraft orbits. It leads to premature de-orbiting and a significant shortening of mission lifetime. The drag force can be quantified through the drag coefficient, C d , which is invaluable to determining the drag response of a body in a fluid environment. ADBSat is a new program which determines the C d of any body, both quickly and accurately  [12, 13]. It is a novel implementation of a panel method, in which the equations describing the interaction between the satellite surfaces and the atmospheric particles, known as the gas-surface interaction model (GSIM) equations, are used to calculate the desired outputs  [14].
This program overcomes the difficulty of prohibitively complex GSIM formulae by treating the spacecraft as a set of flat triangular panels. Hence, it reduces the detailed spacecraft geometry to a set of simple shapes, to which the GSIM equations are easily applied. A summation of the plates' contributions provides the results for the body as a whole. A shading algorithm based on 2-dimensional projections of the spacecraft panels is also employed, with the aim of increasing accuracy for concave geometries  [12]. Past applications of the panel method such as DACFREE  [15, 16] , FreeMat  [17]  and FreeMac  [18]  and have suffered from a lack of reproducible and verifiable validation, and thus a limited knowledge of their accuracy. A full, detailed description of the workings and implementation of ADB-Sat is available in an accompanying paper  [12].
ADBSat suffers from known limitations with regard to modeling phenomena such as multiple particle reflections between different components of the spacecraft body. Through validation, we have investigated a range of cases, both simplistic and realistic, and report here our findings with regards to scenarios for which it is particularly suited for analysis. A discussion is also presented of cases which display a significant inaccuracy. Comparison to DSMC constitutes our main method of validation, implemented through the open-source software suite OpenFOAM  [30]  as dsmcFoam  [21, 28]. For simple geometries, cases are also compared to closed-form GSIM equations. Finally, we report the performance of ADBSat as compared to published literature results for real spacecraft. The comparison is complicated by the fact that ADBSat does not give an error margin on its outputs.
It was shown to be at least as good as the other models at reproducing realistic atmospheric conditions  [56]. 2. There is an ongoing effort to maintain and improve the model. Corrections include employing new experimental data to correct the outputs  [57] [58] [59] [60]. 3. It is available as a MATLAB package, and is therefore easy to integrate into ADBSat. The data from the NRLMSISE-00 model can also be found online 1  alongside its source code  2. By utilizing both sources, we maintained consistency between the manually specified DSMC atmospheric conditions, downloaded through the online tool, and the ones accessed by ADBSat through MAT-LAB. Thus, a direct comparison between the two methods of drag analysis was facilitated.
3. These shapes employ details such as angled panels or concavities on the forward-facing surfaces to promote reflection of the particles between faces. We examined shapes in category A at orbital altitudes from 100 km to 400 km, in intervals of 100 km. All other shapes were examined at an altitude of 200 km only. We set AOA and AOS to zero for all shapes. Additionally, we also examined category B shapes a second time at a random selection of small AOA and AOS, ranging from 2. 8 to 12. 1 degrees, as a secondary test of the shading algorithm. Furthermore, these shapes were also discretised into smaller panels than the default CAD geometry, by manually selecting a target face on each shape and subdividing it. Our aim was to ascertain the influence of panel size on the output value of C d. Finally, we identified literature sources that offered drag coefficient data for real satellite missions.
Running multiple simulations, such as those at varying AOA and AOS that are required to obtain the aerodynamic database of a satellite, will compound this difference further. Thus, there is a clear time advantage to using ADBSat over dsmcFoam. Figure  5b  shows a graph of the values of C d obtained from these two methods. Results are consistent for all shapes, at all orbital altitudes except 100 km. For the atmospheric parameters chosen, at an altitude of 100 km, n 0 ∼ 10 17 and K n ∼ 0. 5. Thus, the flow has become transitional, and the equations applied by ADBSat do not reflect the physics involved. However, they perform well at higher altitudes, where strict FMF conditions exist. This is  consistent with existing literature which addresses the comparison of closedform equations to DSMC  [26].
The cause of this is the inherent computational error of MATLAB, caused by the representation of the geometry using floating point values. When panels are at an angle of 90°t o each other and to the flow, the 2D projection employed by the shading algorithm will project the barycenter of the downwind shaded panel exactly on the edge of the upwind shading panel. Thus, the barycenter is neither inside nor outside the shading panel. However, the shading algorithm must still decide which side of the edge it falls on. The small computational error which MATLAB carries will influence such a precise calculation heavily, resulting in an almost random classification of shaded/non-shaded panels. A visualization of this effect is seen in fig. 9. Panels classified by the program as shaded are in orange, with those not shaded in black.
The edges of each panel are not outlined, for clarity. The area containing incorrectly classified panels is outlined in red. Figure  9a  shows shape (e), for which all panels of the central cylindrical section should be shaded. Figure  9b  shows shape (h),      for which the edge panels highlighted should not be shaded. As the shaded panels are effectively removed from the final summation, too few shaded panels lead to an overestimation of C d , while too many shaded panels will lead to underestimation. However, when the flow is at an angle of δ ≥ 0. 1°, the projection of the shaded panel's barycenter is no longer on the edge of the shading panel. Thus, MATLAB's small error is now negligible, and ADBSat yields much more accurate results. In summary, ADBSat can handle the majority of satellite flight scenarios with accurate shading analysis, except those where many large panels are at an angle of δ ≈ 90°to the flow and to each other.
Orion capsule The detailed description of atmospheric and geometric parameters provided by Moss et al. [15]  allowed us to accurately reproduce their simulations. The authors present results obtained with three different codes, two DSMC codes (DAC and DS3V ) and a free-molecular code whose algorithm is not    ADBSat agrees closely with DACFREE for all simulations, even those not in FMF. At approximately 170 km and above, where FMF occurs according to the K n reported by Moss et al. [15] , it also agrees to within 1-3% with both DSMC codes. A better agreement is noted at higher altitudes, where the flow is strictly FMF. To summarize, our results show a good agreement to the C d presented, where the assumption of FMF is valid. Mehta et al. [61]  report the variation in drag coefficient of GRACE over 24 h, both from their own data and from previous sources.
The comparison to DSMC, implemented through dsmcFoam, involved examination of specially designed test objects at a range of atmospheric conditions across VLEO altitudes. These objects included basic shapes, shapes that tested the new shading algorithm, and shapes that promoted multiple reflections of the atmospheric particles between the body panels. Analysis of the basic shapes showed a good agreement to both DSMC and closed-form models for strict FMF, where K n > 10. The shading algorithm shows the desired performance at most incidence angles with respect to the flow. It breaks down if a large number of body panels are parallel to each other and to the flow, due to MATLAB's inherent floating point precision. Despite disregarding multiple particle reflections, ADBSat is shown to be accurate for some detailed shapes, but not for those where deep concavities (such as atmospheric intakes) are present on forward-facing sides of the body.
Aims. The eROSITA Final Equatorial-Depth Survey has been carried out during the performance verification phase of the Spectrum-Roentgen-Gamma/eROSITA telescope and was completed in November 2019. This survey is designed to provide the first eROSITAselected sample of clusters and groups and to test the predictions for the all-sky survey in the context of cosmological studies with clusters of galaxies. Methods. In the area of ∼140 square degrees covered by eFEDS, 542 candidate clusters and groups of galaxies were detected as extended X-ray sources with the eSASS source detection algorithm. We performed imaging and spectral analysis of the 542 cluster candidates with eROSITA X-ray data and studied the properties of the sample. Results. We provide the catalog of candidate galaxy clusters and groups detected by eROSITA in the eFEDS field down to a flux of ∼10 -14 erg s -1 cm -2 in the soft band (0.
Radio properties of the clusters are studied in  Pasini et al. (2022). ICM morphology and X-ray scaling relations based on eROSITA data are studied in  Ghirardini et al. (2022)  and  Bahar et al. (2022) , respectively. Spectroscopic follow-up results will be provided in Ider  Chitham et al. (in prep. ). The catalog of cluster candidates that are misidentified as point sources will be presented in  Bulbul et al. (2022). Moreover, the main eFEDS X-ray source catalog is provided in  Brunner et al. (2022). The eFEDS simulation results are introduced in detail in  Liu et al. (2022). The paper is organized as follows. In Sect. 2 we describe the eROSITA observations of the eFEDS field and the source detection in detail and discuss the potential contamination in the sample. We also summarize in this section the optical confirmation and redshift determination of the clusters on the basis of optical photometric and spectroscopic survey data.
In Sect. 3 we examine the selection function of the cluster sample. In Sect. 4 we provide the details of the X-ray data analysis we performed in this work and of the X-ray observables. In Sect. 5 we compute the X-ray luminosity function of the cluster sample. In Sect. 6 we perform a search for superclusters in the eFEDS field on the basis of the spatial distribution and redshifts of the clusters. Our conclusions are summarized in Sect. 7. Throughout this paper, we adopt the concordance ΛCDM cosmology with Ω Λ = 0. 7, Ω m = 0. 3, and H 0 = 70 km s -1 Mpc -1. Quoted error bars correspond to a 1σ confidence level unless noted otherwise. The accumulate_counts program from the contour binning package  (Sanders & Fabian 2006 ) is used to calculate a map containing the radius around each pixel (including those in masked areas) that encloses at least 36 counts (excluding masked sources).
This map is used to smooth the input image and exposure map with Gaussians, excluding masked areas, where σ is given by the radius in each pixel. The smoothed image and exposure map were divided to create the exposure-corrected image shown here. of the data reduction and calibration are described in Brunner et al. (  2022 ) and  Dennerl et al. (2020). We here provide a short summary of the analysis steps. Pattern recognition and energy calibration are applied for all the seven eROSITA telescope modules (TMs) to produce calibrated event lists. The event lists are then filtered after the determination of good time intervals, dead times, corrupted events and frames, and bad pixels. Using startracker and gyro data, we assign celestial coordinates to the reconstructed X-ray photons, which can then be projected on the sky so that images and exposure maps can be produced.
Optical confirmation and redshift determination The photometric redshifts of the clusters are determined based on the multicomponent matched filter (MCMF) cluster confirmation tool (see  Klein et al. 2018 Klein et al. , 2019 , for more details). The MCMF tool takes optical photometric datasets and searches for A2, page 3 of 25 Redshift Fig. 2. Distribution of the 542 cluster candidates in eFEDS. The color code represents the redshift of the cluster, provided by MCMF  (Klein et al. 2018 (Klein et al. , 2019)). The radius of the circle is equal to R 500 , within which the average density is 500 times the critical density at the cluster redshift. galaxy overdensities along the line of sight at the position of a cluster candidate. To do this, the galaxy cluster richness is measured as a function of redshift using a red-sequence technique and within an aperture defined from the X-ray count rate.
Peaks in richness versus redshift space are fit by specific peak profiles, and redshift and richnesses are recorded for multiple possible counterparts along the line of sight. MCMF is then run on random lines of sight excluding regions around X-ray candidates. MCMF on eFEDS was run on two photometric datasets with different optical filters and depth: DECaLS g, r, z and unWISE W1 bands, and HSC g, r, i, z bands. DECaLS is free from strong calibration issues and provides full coverage of the eFEDS field, but is ∼2 magnitudes shallower than HSC-SSP data. The deep HSC-SSP data in the g, r, i, z bands provide good photometric redshifts out to high redshifts (z ∼ 1. 3), where DECaLS has shallower data and misses the i band. The results of both MCMF runs were then combined to the final catalog. Spectroscopic redshifts, on the other hand, were then derived by cross-matching the clusters with public spectroscopic redshifts including SDSS up to DR16 (Blanton et al.
The source spectra are absorbed by an amount depending on the local Galactic absorption column density. Stellar sources as well as cosmic Xray background and emission from the Galaxy are accounted for using measurements acquired during the calibration and performance verification phases. The SIXTE simulation software  (Dauser et al. 2019 ) is fed with the actual spacecraft attitude file during the eFEDS mapping, hence the simulations faithfully reproduce the exposure variations in the field. The resulting event lists are processed similarly to the true eFEDS event lists, see Sect. 2. 1. In particular, extended sources are identified using identical thresholds in detection and extent likelihood as in the real catalog.
Spectral analysis We extracted spectra and computed ancillary response files (ARFs) and redistribution matrix files (RMFs) from the seven TMs using the eSASS algorithm srctool with the latest version of the calibration database. For the extraction radius that we used for the spectral analysis, we opted for two fixed physical apertures, 300 and 500 kpc. The first was chosen for a fair comparison with similar flux-limited surveys, for instance, the XXL survey  (Pacaud et al. 2016 ). The second is a compromise between the aim to include more photons and the rapidly decreasing signalto-noise ratio (S/N) in the cluster outskirts. In Fig. 8  we verify A2, page 9 of 25 Fig. 7. Luminosity redshift distribution of the clusters with significant luminosity measurements (>2σ) for 300 kpc (upper panel) and 500 kpc (lower panel).