dataesr/scientific-paragraphs-categorization huggingface dataset:
In their analysis of the double cluster system Abell 222 and Abell 223,  Dietrich et al. (2012)  showed evidence for a possible dark matter filament connecting both clusters. Finally, in the COSMOS field  (Scoville et al. 2007 ),  Massey et al. (2007)  uncovered a massive large-scale structure at redshift z ∼ 0. 73 extending over about 1 degree in length. Recently,  Jauzac et al. (2012)  claimed another detection of a large-scale filament connected on one end to the massive cluster MACS J0717+3745, and vanishing into the cosmic web on the other end. They used a model made of a multiscale grid of radial basis functions (RBF) and a Bayesian MCMC optimization algorithm implemented in the lensing software Lenstool to map its mass distribution and measure its size and density. In this paper, we study three methods of lensing map reconstruction, including the method used in  Jauzac et al.
g. Kassiola & Kovner 1993; Kneib et al. 1996; Elíasdóttir et al. 2009)  were giving good results. In our model, we approximate the true convergence field κ with κ(θ) = 1 Σcrit i σ 2 i f ( ||θi -θ ||, si, ti) (27) where the RBFs on grid nodes θi are described by f (R, s, t) = 1 2G r cut t-s 1 √ s 2 +R 2 - 1 √ t 2 +R 2. ( 28 ) 1 The MRLens denoising software is available at the following address: "http://irfu. cea. fr/Ast/mrlens software. php". In the TIMD model, the scaling factor σ 2 i is the velocity dispersion at the centre of the gravitational potential, and radii s and t mark 2 changes in the slope respectively from κ ∝ R 0 to κ ∝ R -1 and κ ∝ R -3 respectively. In a similar manner, we approximate the true shear field with γ1(θ) = σ 2 i Γ1( ||θi -θ ||, si, ti) (29) γ2(θ) = σ 2 i Γ2( ||θi -θ ||, si, ti) (30) where analytical expressions also exist for Γ1 and Γ2 (see Eq A8 in  Elíasdóttir et al.
Bayesian MCMC optimisation In this section, we describe the Bayesian Monte Carlo Markov Chain algorithm used to reconstruct the mass map in  Jauzac et al. (2012). This algorithm called MassInf is also part of the Bayesys package  (Jullo et al. 2007 ), but it is the Parameter q 0 has the strongest impact on the reconstruction result. These reconstructions are without shape noise, and with a multi-scale grid of 575 RBFs. first time we use it in Lenstool 2. It aims at inverting linear systems of equations in a Bayesian manner, i. e. with input priors. Based on our definition of the χ 2 in Eq 34, we define the likelihood of having a set of weights v given the measured ellipticities e as P (v | e) = 1 ZL exp - χ 2 2. ( 39 ) The normalization factor is given by ZL = (2π) 2M det Nee. As a prior, we want the individual weights σ 2 i to be positive, so that the final mass map is positive everywhere.
Reconstructed maps Fig 10 shows the reconstructed convergence maps of MACS J0717 obtained with the three methods. Globally, they all agree on the location of the cluster core, and the presence of an extension to the South-East. In the cluster core where data are missing, both the Lenstool and FLens reconstructions are smooth, whereas the SVD reconstruction is more clumpy. We attribute this difference to the priors assumed in both Lenstool and FLens. We also observe some disagreement on the exact shape of the filament. Lenstool reconstruction suggests MACS J0717 lies into an extended over-dense region. In contrast, FLens reconstruction shows that the cluster is compact and connected to a long filament. In both the FLens and the Lenstool reconstructions, the filament is detected at 95% C. L.
CONCLUSION Systematic errors in lensing map reconstruction, especially due to the reconstruction methods, is a concerning issue. With the current and forthcoming datasets, they start to dominate the error budget over the statistical errors. In this work, we have studied three methods of reconstruction of 10 arc-minutes scale structures, i. e. the environment of galaxy clusters. We limited our study to a toy-model structure in order to focus on the effect of priors. In a forthcoming paper, we will increase the level of complexity by using N-body simulations. The FLens method starts from a pixelated map of shear, with about one galaxy per pixel on average, and filter the noisy reconstructed convergence map by only keeping wavelet scales that contain non Gaussian signal. The Lenstool and the SVD inversion methods share the same underlying multi-scale grid model.
[17] , including determining partition functions and hence thermodynamic data  [18] , and the refinement of theoretical models. Water vapor also plays an important role in characterizing combustion systems  [19]. The first 13 authors of this paper form a Task Group under the auspices of IUPAC (International Union of Pure and Applied Chemistry), with the aim of constructing a database of water transitions from experiment and theory, and with individual tasks described in Table  1  of the first paper in this series  [20] , henceforth referred to as Part I. Since absorption due to electronic excitation requires energies over 50 000 cm À 1 in the case of the water molecule, most of its physical properties are determined by its ground electronic state  [21]. This determines the nature of water spectroscopy  [2] , and thus the present effort concentrates on the pure rotational and rovibrational energy levels of water from within the ground electronic state.
We consider all the corresponding transitions up to the first dissociation limit of the molecule simultaneously and on an equal basis. This paper is the third in a series presenting our evolving methods for collecting and analyzing the experimental (spectroscopic) and quantum chemical information available as well as our validated data recommended for deposition in information systems. In Part I  [20] , we derived labeled energy levels and transition wavenumbers for the water isotopologues H 2 17 O and H 2 18 O. In Part II  [22] , we derived labeled energy levels and transition wavenumbers for the partially deuterated water isotopologues HD 16 O, HD 17 O, and HD 18 O. These analyses were based on the concept of spectroscopic networks  [23, 24]  and were executed using the MARVEL (Measured Active Rotational-Vibrational Energy Levels) protocol of Furtenbacher and Csaszar  [23, [25] [26] [27] , which was considerably refined during the course of the present study  [27]  to allow for the treatment of large datasets.
16 O were already subjected to a comprehensive and systematic study by Tennyson et al. [28]. We note, for example, that the recent release of the HITEMP database  [29]  used the energy levels of Ref. [28]  to generate transition wavenumbers for hot-water spectroscopy. The present study significantly improves on the methodology used previously  [28]  and, given a decade of further collection of experimental data, considerably extends its scope. In this context we note in particular the multiresonance studies of Boyarkin, Rizzo, and co-workers, which have probed the energy levels of water up to  [30] [31] [32] [33] [34]  and even beyond  [35]  the first dissociation limit. These sophisticated experiments have sparked corresponding theoretical studies  [34, 36, 37]. Here we consider all the available experimental spectroscopic transition data linking rotation-vibration levels below the first dissociation limit of H 2 16 O.
Methods, input data, and data treatment The methods employed in this study for collecting and critically evaluating labeled experimental transition wavenumbers and their uncertainties and for inverting the wavenumbers in order to obtain the best possible energy levels with corresponding uncertainties are principally based on the concept of spectroscopic networks  [23, 24]  and on the MARVEL procedure  [23] [24] [25] [26] [27]. During a MARVEL analysis we simultaneously process all the available assigned and labeled experimental lines to give the associated energy levels of the chosen isotopologue. We adopted a reweighting scheme  [51]  where uncertainties for selected line positions are changed (in practice increased) during iterations of the MARVEL procedure  [25]. After removing outliers from the experimental transition data and applying the iterative robust reweighting algorithm, a database is created containing self-consistent and uniquely labeled transitions and related uncertainties.
The procedure is such that the final energy levels and their uncertainties are guaranteed to be compatible with the (adjusted) uncertainties of the experimental line positions. This means that all transitions used in the MARVEL procedure agree, within their revised stated uncertainties, with the MARVEL predictions. This criterion for the error is therefore more stringent than the usual standard deviation used to represent statistical error and will usually lead to the quoted MARVEL errors being systematically larger. The first step in the MARVEL procedure is to split the transition data into components of the spectroscopic network (SN) characterizing the molecule  [24]. Components of SNs contain all interconnected rotational-vibrational energy levels supported by the grand database of the labeled transitions.
These techniques have specific advantages in terms of sensitivity and spectral resolution, which make them particularly suitable for the characterization of spectral regions with weak absorption features. This is why extensive investigations with laser-based methods were mostly limited to transparency windows or to the visible region. The precision of CRDS is limited to about 0. 001 cm À 1. Emission spectra can provide large datasets of line positions. Emission spectra for water are available over a particularly extensive range of temperatures, the hottest being spectra recorded in an oxy-acetylene flame at about 3000 K  [174]. These spectra provide a rich source of information on states both with significant bending excitation  [175] , which are normally not probed in standard absorption spectra, and with high levels of rotational excitation.
Pre-MARVEL validation Similar to Parts I and II, the experimental database assembled based on literature data were first checked for simple transcription errors or other problems in the original data source. Checks were made for formatting incompatibilities, entries with zero uncertainties (not allowed in a MARVEL-type analysis), strongly forbidden (ortho to para) transitions, and transitions with impossible labels. As to invalid labels, the dataset of transitions was searched for cases where the K a þ K c sum, where K a and K c are the usual asymmetric-top rigid-rotor quantum numbers, did not equal J or J þ 1, where J is the rotational quantum number, where either K a or K c were greater than J. A search was performed to identify obvious duplications in the dataset in order to avoid entering the same measurement twice.
A warning was issued if this happened and only the earliest occurrence of the datum was kept (unless the line was reanalyzed in a later study). We also made sure that the dataset of transitions to be analyzed by MARVEL did not contain (a) entries where the two transitions had the same lower-level label but different upper-level labels with transition wavenumber differences less than 0. 05 cm À 1 , and (b) where the transitions had the same lower-and upper-level labels and their wavenumbers differed beyond the related uncertainties. Employing the parities detailed in Table  1  and the associated selection rules, transitions which had incompatible labels were identified and deleted. The rotational parity along with the J values helped in the search for correspondence between the experimental and the variational datasets.
Another pre-MARVEL validation procedure utilized the so-called BT2 linelist  [194]. If the BT2 variational nuclearmotion computations indicated the existence of a degeneracy between an ortho and a para transition within the BT2 linelist to better than 10 À 3 cm À 1 and one of the transitions was missing from the MARVEL input, the missing entry was added by hand and indicated as such in the input by adding the letter ''D'' to the tag of the duplicated transition entry. We added altogether 6589 duplicates to the original database. This step was important to link a number of what otherwise would have been FSNs.
Assignment, labels It is a requirement of the MARVEL protocol that the dataset contains a single unique label for both the lower and the upper states involved in each transition. There is no requirement that labels have any physical significance beyond those needed to give selection rules. Due to the extent of the data for transitions of H 2 16 O, a large number of problems were expected for the approximate vibrational labels. For consistency and to maintain a single set of uniform labels for all levels, we chose to label vibrational states in the usual normal-mode notation, (v 1 v 2 v 3 ). There are strong physical arguments that the higher stretching states of water are better labeled using local modes  [195, 196]. However, there is a one-to-one correspondence between local-and normal-mode labeling schemes  [116] , so the use of normal-mode labels leads to no loss of information.
Hot transitions The high-lying rotational levels probed by hot transitions are hard to validate due to the high density of both predicted and observed transitions. In addition, some of the transitions to a given upper level originate from lower (sometimes unknown) levels belonging to excited vibrational states. The most significant problem with the existing hotwater transition data were their inconsistent labeling. Thus, the labels from these data sources were carefully checked once the MARVEL energy levels, and their labels, were well established based on cold water spectra. As the comments to Table 2 (Section 2. 7) demonstrate, a large number required careful relabeling so that only a small number of assigned transitions were actually omitted during the final MARVEL runs. It must be emphasized again that (a) labels for the hot water transitions may not be physically correct but at least they are unique and consistent as far as the present database is concerned, and Table  3  Validation of the rotational labels of the rovibrational levels determined by the final MARVEL analysis via the rigid rotor decomposition (RRD) protocol  [198, 199]  (b) MARVEL is not able to produce correct labels for assigned transitions; it can only point out inconsistencies within a given dataset.
The sources identified for recalibration include 73CaFlGuAm  [62] , 78KaKaKy  [70] , 80CaFlMa  [74] , 82KaJoHo  [79] , 96PoBuGuZh  [107] , and 99CaJeVaBe  [116]. It was found that no recalibration is needed for the following sources containing FTS data: 94Tothb  [103] , 95PaHo  [105] , and 05HoAnAlPi  [138]. This rms minimization was performed sequentially for all data sources identified as problematic. The multiplicative calibration factors that emerged from these analyses are given in Table  4. For all the sources identified in Table  4 , the experimental data were recalibrated using the calibration factors determined and only the recalibrated transitions were included in the final MARVEL analysis. Recalibrated transitions are distinguished within the dataset by a letter ''R'' attached to the end of the transition entry.
[215]. (2e) 91AmSc  [93]. Spectrum recorded using a millimeterwave spectrometer; details given in Ref. [216]. (2f) 12YuPeDrMa  [164]. Terahertz absorption spectroscopy and far-infrared Fourier-transform emission spectroscopy were employed to measure new rotational and rovibrational transitions and validate some of the lines of existing datasets. (2g) 83HeMeDe  [82]. Frequencies linked to the NIST WWVB radio broadcast time signal. Range of J: 1-10, range of K a : 1-7. The measurements used mm-wave absorption spectroscopy, RF generators harmonically mixed with 50 GHz Klystron radiation signals phase locked to the WWVB signal. Pressure is not indicated in the paper. Uncertainty in line center determination is dominated by the Doppler width, not by frequency accuracy of the radiation source. MARVEL analysis 95PaHo  [105]  177-520 1.
000 048 707 68 was used. The dataset contains transitions up to J max ¼ 24 and K max a ¼ 23. This study was recalibrated to remove systematic differences, see Table  4. (2r) 82KaJoHo  [79]. 65 lines corresponding to 71 transitions. Only positions are given. The goal of the paper was to transfer the high accuracy of the n 1 band of OCS (rms of 3:6 Â 10 À5 cm À1 ) to the pure rotational lines of H 2 16 O. Range of J: 6-14, range of K a : 129. Resolution of the measurements is 0. 0045 cm À 1. The precision of the measurements is high, 7 4 Â 10 À5 cm À1. This study was recalibrated to remove systematic differences, see Table  4. (2s) 05CoBeCaCo  [174]. Emission spectrum recorded on a Bruker IFS 120 M FTS in an oxyacetylene torch at atmospheric pressure. The calibration used water lines from 02TeBeZoSh  [173]  checked using a CO standard.
Variational validation As an independent validation of the experimental transition wavenumbers and the derived MARVEL energy levels and their labels, systematic and mostly automated comparisons were made with the results of state-of-theart variational nuclear motion computations. For this comparison, the so-called BT2 linelist  [194]  was principally used; this linelist was computed using a spectroscopically determined PES  [43] , an ab initio DMS  [47] , and the DVR3D  [227]  nuclear motion program suite. Those measured transitions involving a MARVEL energy level which did not have a matching variational counterpart within 1. 0 cm À 1 , with proper rotational parity (Table  1 ), were investigated individually and the MARVEL process was repeated until all MARVEL levels had variational counterparts within the chosen cut-off value.
A comparison with HITRAN and HITEMP The relevant features of the HITRAN database  [225, 235]  are summarized in the original publication and in Part I; thus, they are not repeated here in detail, just a few remarks are made. For a discussion of comparisons of the results of the present IUPAC-sponsored work (transition wavenumbers and energy levels) with data archived in HITRAN, it is worth recalling the structure of and quantities in the current edition of the HITRAN database  [225]. Table  2  of Ref. [225]  presents the parameters (fields) that are contained in each transition (record) of the HITRAN linelist. The structure is in a text-file format of fixed-length records. The parameters contained in each transition are those that have been deemed necessary for input for calculating high-resolution absorption or radiance spectra through room-temperature gaseous media.
There are 36 550 assigned transitions of H 2  16  O (and an additional 882 unassigned transitions for this isotopologue) in the current edition of the HITRAN database  [225]  from 0 to 25 300 cm À 1. The values for the line positions of different transitions originate from a wide variety of sources which are documented by means of a special reference index. Unlike the MARVEL database, HITRAN contains both experimental and calculated values and also provides only one chosen value for each transition. Table  8  provides statistics on the number of transitions in the MARVEL and HITRAN databases and how many of them are unique for the former set. One can see that there are 4599 assigned transitions in HITRAN that are not present in the MARVEL database or, in other words, have never been measured directly (or at least not published in the refereed works).
This is not surprising because HITRAN contains data that are often calculated using (1) spectroscopic constants that are derived from fitting experimental spectra (for instance data in the 0-500 cm À 1 region originate from Ref. [124] ), and (2) energy differences between empirically determined levels. For instance, there are 4976 transitions in HITRAN that originate from the SISAM database  [229]  which are calculated by the second method. Unlike the case of some other water isotopologues, there are no line positions in HITRAN for the parent isotopologue that are computed variationally using ab initio PESs. One of the most valuable results of this IUPAC effort is that by using validated empirical energy levels, in the present case MARVEL ones, one can generate an extensive database of line positions of all allowed transitions between such levels.
Of course, the number of such transitions is extremely large, and although they are allowed, some of them will be very weak even under extreme thermodynamic conditions and are unlikely to be observed experimentally even in emission. Table  9  compares the database created from MARVEL energy-level differences with HITRAN. In general there is a very good agreement, although some differences exist and they need  to be studied carefully. One should note that there is a problem of correspondence between quantum assignments of energy levels given in the HITRAN and MARVEL lists. This is due to the fact that only the rotational quantum number J and symmetry (cf. Table  1 ) can be unambiguously identified using theoretical approaches. The different experimental works that contributed to HITRAN have used techniques and conventions to aid in the assignments of the observed transitions, which can result in labeling ambiguities.
Therefore, although Table  9  shows that there are 1068 transitions that differ by more than 0. 1 cm À 1 , a few hundred of such transitions are in a category of different assignments and do not necessarily indicate problems in the HITRAN line positions. It is planned to revisit the labeling of energy levels in a future release of HITRAN; this issue is of particular importance since the algorithm used by HITRAN to generate pressurebroadening parameters is based on the quantum numbers  [231]. It is worth noting that the database of transitions generated from MARVEL energy levels can prove extremely useful in updating the HITEMP database  [29]  and the ab initio line positions adopted from the BT2 line list  [194]. In fact, when the HITEMP database was put together, a similar effort had been carried out but the database of transitions generated from experimental energy levels was significantly less complete (by more than a million transitions) and had not undergone a rigorous validation procedure.
saga. iao. ru/ and contains the data forming the basis of this paper. O transition found in HITRAN  [225]  and used in the present compilation for 298 K. O MARVEL-based one-photon absorption transition data and those found in HITRAN  [230]. Total number of transitions generated from MARVEL database of energy levels 5 046 272 Concordant transitions with HITRAN a 36 369 Transitions differing by 4 0:001 cm À1  10 772 Transitions differing by 4 0:01 cm À1 2021 Transitions differing by 4 0:1 cm À1 1068 HITRAN transitions absent in database of transitions generated from MARVEL database of energy levels 181 a Unique transitions which are present both in HITRAN  [225]  and in the present validated IUPAC database.
Acknowledgments We all thank the  International Union of Pure and Applied Chemistry  for funding under Project  2004-035-1-100  (a database of water transitions from experiment and theory). In addition, this work has received partial support from the  UK Natural Environment Research Council , the  Royal Society , the  European Research Council  under Advanced Investigator Project  267219 , the  Scientific Research Fund of Hungary  (Grant  OTKA K77825  and  NK83583 ),  NATO , the  National Science Foundation of the U. S. A. through Grant No. ATM-0803135 , the  Russian Foundation for Basic Research , the  Belgian Federal Science Policy Office  (contracts  EV/35/3A ,  SD/AT/01A ,  PRODEX 1514901NLSFe(IC) ), the  Belgian National Fund for Scientific Research  (FRFC contracts), the  Communautede Belgique  ( Action de Recherche Concertees ),  NASA Earth Observing System (EOS) , under Grant  NAG5-13534 , and the  Programme National LEFE (CHAT)  of  CNRS (INSU).