dataesr/scientific-paragraphs-categorization huggingface dataset:
All calculations employed the molecular-meanfield X2C Hamiltonian ( 2 DC M )  [105]  based on the Dirac-Coulomb Hamiltonian. For technical reasons, MP2 and CCSD analytical expectation values were calculated using the RELCCSD  [62, 136]  and ExaCorr  [63]  modules, respectively. The expectation values were calculated using the Lagrangian-based analytical energy derivative technique described in Ref. 62 and references therein. For the CCSD calculations, we used the dyall. aae3z basis sets  [132] [133] [134] , extended with tight functions, as described above. We correlated (n -1)s(n -1)p(n -1)dnsnp electrons, and truncated the virtual space at 100 E h. For MP2 the calibration study indicated that only valence orbitals need to be correlated, so we used the the dyall. acv3z basis. For comparison we carried out DFT calculations using the extended dyall.
aae3z basis sets and functionals from different rungs of the Jacob's ladder of density functional approximations  [137] : LDA (SVWN5)  [138, 139] , BLYP  [140] [141] [142] , and B3LYP  [143] [144] [145] , which is Becke's series, and PBE  [146, 147]  and PBE0  [148, 149] , which is Perdew's series. We also used the long-range correlated functional CAMB3LYP  [150]. 4. Results and discussion. For convenience, we have collected our HF, MP2 and CC results in Table  6  of the Supplemental Material together with previous results  [51, 61, 62]  calculated at the same geometries  [55]. Our outputs are available via the zenodo repository  [151].
Acknowledgement(s) This paper is dedicated to  John F. Stanton , a driving force of coupled cluster theory for 35 years !We would like to thank  David Sanchez (Toulouse) and  Johann Pototschnig ( Vienna ) for a lot of technical support. This work is part of the project molQED funded by the  Agence Nationale de la Recherche  ( ANR, France ). This research used resources of the  Oak Ridge Leadership Computing Facility , which is a  DOE Office of Science User Facility  supported under Contract  DE-AC05-00OR22725. We are thankful to CALMIP ( Calcul en Midi-Pyrénées ) and  LCPQ (Laboratoire de Chimie et Physique Quantiques ) clusters for the additional computation time. We are also thankful to the supercomputer of ACCMS ( Kyoto University ) and  Research Institute for Information Technology, Kyushu University  (General Projects) for test calculations.
Rank-1 lattice rules are used in this paper (higher rank lattices are uncommon in practice). These rules are formally defined as t=1 t=2 ω1 ω2 ω3 ω4 V n = {i • α/n + δ mod 1 ∀ i ∈ 1. n}, where α is a generator vector, and δ is a random point to shift the lattice. Using δ = 0 leads to QMC which is a deterministic sampling technique, whereas RQMC uses δ > 0 to generate a random sample. The quality of the lattice is determined by vector α. We generate α with the software Lattice Builder (L'Ecuyer and Munger 2016), which implements multiple algorithms to build good rank-1 lattice rules. Finally, as demands are integer, a QMC or RQMC sample can contain multiple occurrences of a vector (even if V n is fully projection-regular). Identical vectors are aggregated into a single one by adding their probabilities.
Regarding objective (2), the results show that 50 scenarios sampled with RQMC or QMC lead to good approximations of the two-stage model. Consequently, solving the two-stage model does not require a large computational effort. On the contrary, a good approximation of the multi-stage model requires 3,200 scenarios sampled with RQMC. Therefore, the multi-stage model is harder to solve. However, the two heuristics proposed in this work appear to be very efficient. Table  3  summarizes the approaches evaluated in the experiments and their notations. The methods were implemented with Python and CPLEX 12. 7, and run on an Intel(R) Xeon(R) X5675 3. 07GHz processor. The code is available at https://github. com/StochasticLotSizing/ StochasticMRP. Section 6. 1 introduces the considered instances. The performance of the sampling techniques and optimization approaches for stochastic optimization (objective 1) is shown in Section 6.
g. , the Nasmyth Adaptive Optics System Near-Infrared Imager and Spectrograph (NaCo) on the Very Large Telescope (VLT), the Near Infra Red Camera 2 (NIRC2) on the Keck telescope, the Near-Infrared Coronagraphic Imager (NICI) on the Gemini telescope) was of the order of 10 mas. 1, 18, 19  D dicated procedures were developed for the first dedicated exoplanet imaging instruments SPHERE and GPI to minimize the systematic astrometric error budgets to reach precisions down to ∼1-2 mas not counting the noise contribution. 4, 5   uch precise measurements are more sensitive to previously neglected systematic uncertainties due to biases in the data analysis and/or calibration and our limited knowledge of the thermo-mechanical stability of the instruments. For instance, the astrometric calibration of GPI was recently revised after the correction of issues in the data reduction pipeline and in the data calibration.
20 A homogeneous astrometric strategy is mandatory for precise relative astrometry over time because it minimizes potential systematic uncertainties in the calibration and enables the analysis of its stability over time. A stable astrometric calibration reduces the overhead at the telescope by relaxing the need to take nighttime calibration data close in time to the science observations. Maximizing the observing efficiency and optimizing the data exploitation are important in a context of high pressure on the current 8-10 m class telescopes and the even higher pressure expected for the upcoming extremely large telescopes. The SPHERE consortium was granted with a guaranteed-time program of 230 nights over five years, from which 200 nights are dedicated to the SpHere INfrared survey for Exoplanets (SHINE) program to detect and characterize in the near-infrared (near-IR) the population of young giant planets and brown dwarfs at wide orbits ( 5 au).
3, 21, 22  O e of the major goals of the survey was to measure precisely the orbit of the detected companions. A dedicated and homogeneous strategy for astrometry was designed. A first analysis of the astrometric calibration of SPHERE was performed using data taken in the first two years of operations  23  and showed promising results for the calibration stability. We present in this paper an analysis of SPHERE astrometric data obtained over five years. We derive updated estimates for the astrometric calibration parameters and confirm their stability. We first recall the astrometric strategy defined for SPHERE (Sec. 2). We then describe issues encountered during the course of the survey analysis (Sec. 3). We also present an updated analysis of the SPHERE astrometric data (Sec. 4). Finally, we outline key lessons learned for high-precision relative astrometry with SPHERE for optimizing the preparation of the exploitation of the next generation of exoplanet imaging instruments especially for the Extremely Large Telescope (ELT) being built by the European Southern Observatory (ESO, Sec.
We did not use neutral density filters for the astrometric observations in the SPHERE SHINE survey  1. The use of AO imposes additional constraints on the astrometric fields with the presence of a bright star for guiding (R 13. 5 mag for SPHERE). This strongly limits the selection of fields within stellar clusters. Bright stars are not used for the calibration because they are saturated in the data typically used for catalog positions (e. g. , Hubble Space Telescope, hereafter HST). Finally, the choice of the reference catalog for the stellar positions is important. It should be precise, preferably provide the orbital or proper motions of the individual stars, have a good absolute calibration, and obtained with an instrument with a similar angular resolution to the observations to be calibrated.
Astrometric fields used For calibrating the SPHERE SHINE survey, we selected fields in the globular stellar cluster 47 Tuc and the open stellar cluster NGC3603 as main calibrators (Fig. 3 ). Both catalogs are based on HST data, which are precise and have a good absolute calibration. To mitigate (partially) the poorer angular resolution of the HST compared to the VLT due to the smaller telescope aperture, HST data obtained in the visible were used. The catalog for 47 Tuc contains the proper motions (precision 0. 3 mas/yr, reference epoch 2006. 20; priv. comm. from A. Bellini/STScI, see Ref. 43 for the methodology), but not the catalog for NGC3603. 44 For this reason, we selected 47 Tuc as the reference calibration field. However, NGC3603 is located at a larger distance from the Sun than 47 Tuc (∼9.
5 kpc 45 vs. 4. 45 kpc  46  ) and has a low mass and concentration with respect to typical globular clusters (∼10 4 M vs. ∼10 6 M for 47 Tuc  47, 48  ), hence the internal velocity dispersion is expected to be smaller. Therefore, stellar proper motions should have smaller effects on the precision of the catalog positions. In the future, we envision to use the multi-epoch SPHERE data set obtained on NGC3603 to derive the internal proper motions within this cluster (using the first SPHERE epoch obtained as a reference) and include this information in the catalog. 49 ther calibration fields which were occasionally observed include the θ 1  Ori Trapezium B1-B4 50 and NGC6380 (reference catalog obtained through priv. comm. from E. Noyola/Univ. Texas Austin). For the astrometric calibration derived using the θ 1 Ori Trapezium B1-B4, we accounted for systematic uncertainties of 0.
Observing setup The astrometric fields are mainly observed with a coronagraph in field-tracking mode, where the FoV is stabilized. This makes combining images easier to get more precise measurements, when the calibration stars are faint and/or for measuring the optical distortion. Measuring the optical distortion in pupil-tracking mode is not as straightforward as in field-tracking mode. The image derotator is the first component in the optical train of the instrument, hence the distortion pattern does not rotate in pupil-tracking mode. Thus, pupil-tracking images have to be corrected for the distortion before being realigned and combined. Measuring the optical distortion in such data would require astrometric fields with a large number of stars detected with high signal-to-noise ratios in single short-exposure images.
Verification of the absolute astrometric calibration To verify the absolute astrometric calibration of SPHERE, Ref. 3 compared the relative astrometry for 7 widely-separated ( 5 ) and bright candidate companions observed with SPHERE and present in the Gaia DR2 catalog. A direct comparison to 47 Tuc and NGC3603 is not possible because these fields are typically crowded in Gaia data due to the poorer angular resolution. The Gaia DR2 position offset compared to SPHERE averaged over the sample is -2. 8±1. 5 mas (3. 9 mas rms 2  ) in separation and 0. 06±0. 04 deg (0. 11 deg rms) in position angle. The rms agree well with the expected uncertainties in these quantities in SPHERE data. Ref. 51 performed a similar analysis using the Gaia EDR3 catalog. For 12 physical binary systems and accounting for the relative proper motion between the two components between the Gaia EDR3 and SPHERE epochs, they find an average difference in the separation and position angle between Gaia EDR3 and SPHERE measurements of 1.
5-yr analysis of SPHERE/IRDIS astrometric calibration data Astrometric observations have been obtained regularly since SPHERE has been in operation. SPHERE was commissioned between May and October 2014 and science verification observations took place between December 2014 and March 2015. SPHERE/SHINE observations started in February 2015. SPHERE has been offered to the community since April 2015. Table  1  provides the setup used for the observation of a given field in a given filter. Table  1  Observing setup for observations of astrometric fields with coronagraph. DIT is the Detector Integration Time and Nfr the number of frames. For the Nfr column, the two numbers are the number of frames in a single data cube and the number of data cubes recorded in the sequence, respectively.
Field Filter DIT Nfr (s) 47Tuc DB H23 8 4×16 47Tuc DB K12 4 5×16 47Tuc BB H 5 2×8 NGC3603 DB H23 8 30×3 NGC3603 DB K12 4 40×3 NGC3603 DB J23 4 30×3 NGC3603 BB J 2 80×5 NGC3603 BB Ks 0. 83 80×5 θ 1 Ori B1-B4 DB H23 8 16×2 θ 1 Ori B1-B4 DB K12 4 60×3 NGC6380 DB H23 16 4×16 NGC6380 DB K12 16 4×16 To analyze the astrometric data and derive the calibration, we developed a tool, which requires minimum interactions from the user. 23 It has been subsequently included in the SPHERE Data Center 543 and used to analyze homogeneously all the astrometric data obtained in the SHINE survey and by the ESO Staff as part of the monthly ESO calibration plan (Sec. 4. 5). A calibration table has been produced for the science observations obtained in the SHINE survey and another table for those obtained by open-time programs.
The calibration tables are used by the SPHERE Data Center pipeline to calibrate the data according to the setup used and closeliness in time. Briefly, the astrometric data were reduced with the SPHERE data reduction pipeline  55  either with a custom script or in the SPHERE Data Center. They were subsequently analyzed with custom IDL routines to derive the calibration. For data obtained in field-stabilized mode, the individual frames are first selected based on the flux statistics and combined to enhance the signal-to-noise ratio of the detected stars. Then, the positions of the stars are measured with Gaussian fitting using the mpfit library. 56 We compared the results obtained with Moffat fitting and centroiding through derivative search (using the cntrd routine of the astron library  57  ) and did not find significant systematics.
For θ 1 Ori B1-B4, the uncertainties include in addition systematic uncertainties (Sec. 2. 2. 2). For correcting the optical distortion, two options are available, either measuring the actual distortion (relevant if several tens of stars are detected in the FoV) or applying a generic correction determined from on-sky data taken during the instrument commissioning. The on-sky optical distortion is measured by fitting linear coordinate transformations between the catalog and the SPHERE positions. All angles provided in the following sections are counted positive from North to East. For the IRDIS data, we force the use of the same stars in the left and right dual fields on the detector. Figure  5  compares the measured positions corrected for the optical distortion (Sec. 4. 1) and the catalog positions scaled and translated for the 47 Tuc and NGC3603 fields.
Optical anamorphism The data analysis of the 47 Tuc field observed during the SPHERE commissioning showed that the optical distortion of the images is dominated by the distortion of the optics in SPHERE. 23 aboratory measurements confirmed that the cylindrical mirrors in the SPHERE common path are the main source for the instrument optical distortion. The distortion manifests in the differences in the pixel scale between the horizontal and vertical directions of the IRDIS detector of 0. 60±0. 02%, i. e. 6 mas at 1. This is larger than the SPHERE astrometric requirements (5 mas). To correct the SPHERE data for the optical distortion, we have relied on the on-sky measurements. We did not use the distortion grid data because of issues in the first months of the survey with the data quality (saturation, see below) and with the data reduction recipe and also because the distortion patterns measured on sky and using the internal calibration data are similar.
The SPHERE data reduced at the SPHERE Data Center are corrected for the pixel scale difference (the raw IRDIS images are vertically stretched by a factor 1. 006 on both image sides). Using 47 Tuc data, we measured that the average residual error over the full IRDIS FoV of this first-order correction compared to higher-order corrections is below 1 mas, i. e. 0. 09 pixel. The distortion pattern is not affected by the tracking mode of SPHERE (tracking of the instrument pupil or of the on-sky field) since the instrument image derotator is the first element in the optical train. The distortion is common to all SPHERE science subsystems except for a rotation of their respective FoVs and is stable over time. Using a more extended set of on-sky data taken during the SHINE survey, we reassessed the ratio of the horizontal and vertical pixel scales for the dual-band DB H23 and DB K12 filter configurations with coronagraph.
For this analysis, we used NGC3603 and not 47 Tuc because of the more homogeneous distribution of the stars in the FoV (Fig. 5 ). Based on six NGC3603 data sets taken in 2017-2018 in the DB H23+N ALC YJH S configuration, we find an average pixel scale ratio of 1. 0070±0. 0005, which is larger by ∼1. 9σ than the value derived using the commissioning data. The analysis of five NGC3603 data sets taken in 2017-2018 in the DB K12 filter gives an average pixel scale ratio of 1. 0072±0. 0003. As a cross-check of the on-sky results, we used the systematic reductions of the internal distortion grid data performed by the Quality Control Group at ESO Garching 4. A square grid of transparent dots engraved in a layer of black chrome is located in the calibration unit of SPHERE  58  hence is common to all SPHERE science instruments.
The pitch of the grid is 100. 0±0. 5 µm for a size of the dots of 30 µm. Figure  6  shows a map of the distortion vectors. Distortion grid data are obtained typically once a week for several filter+coronagraph configurations as part of the daytime calibrations. Very few measurements were obtained for the dual-band DB Y23 and DB J23 filters and are not considered in the analysis. All the data obtained starting from May 2015 were used, after a saturation issue was corrected. Only one technical intervention which could have affected the optical distortion was performed since the beginning of the regular monitoring of the optical distortion. A technical intervention on the cylindrical mirrors occurred on 2015 May 22 UT, very close to the beginning of the monitoring. For a given filter and coronagraph configuration, the temporal evolution of the pixel scale ratio with time shows periodic variations of ∼1 yr, with larger values measured during the winter seasons (Fig.
However, these measurement uncertainties would be optimistic if applied to calibrate science data not taken close in time to the calibration data because they would not include variations in the instrumental/ambient conditions in the meantime. The observing runs in the SHINE survey typically last a few days, with the astrometric calibration performed once at the beginning of the run. The uncertainties can vary between measurements on a given stellar cluster field (differences in integration times, observing conditions, S/N, ratio of the point-spread function or PSF width over the S/N). Table  3  compares the statistics on the pixel scale measured in four filters for the 47 Tuc and NGC3603 fields. Table  4  gives the pixel scale estimates for almost all IRDIS filters (except for the BB Y filter, in which no measurements were taken) for the N ALC YJH S apodized pupil Lyot coronagraph.
Dependency of the pixel scale and correction angle to the North with the number of stars Part of the variations observed in the pixel scale and North correction angle for the stellar cluster fields could be due to the use of different numbers of stars from one epoch to another, depending on the data quality. Figure  10  shows the evolution of the pixel scale, standard deviation of the pixel scale, correction angle to the North, and standard deviation of the correction angle to the North as a function of the number of calibration stars for one dataset acquired for 47 Tuc and NGC3603. For   23  All previous measurements were corrected a posteriori (Sec. 3. 1). The dashed horizontal line shows the weighted mean of all the measurements and the dotted lines the 1σ interval. More measurements are shown compared to Fig.
Analysis of the ESO calibration data The pixel scale and correction angle to the North of IRDIS were also monitored in the ESO calibration plan. The same fields as used for the SHINE survey in 47 Tuc, NGC6380, and θ 1 Ori B1-B4 were observed on a monthly basis, mostly without coronagraph in several IRDIS filters: the narrow-band filters DB H23 and DB K12 and the broad-band filters BB Y, BB J, BB H, and BB Ks. In addition, we also analyzed some datasets obtained as part of the technical time program. We analyzed the data with the same methods used for the SHINE survey data. We chose to analyze separately the SHINE and ESO calibration data to assess the impact of not using a coronagraph on the precision achieved for the astrometric calibration. Our analysis revealed that ∼40% of the data obtained in the ESO calibration plan were not suitable for deriving a calibration, mostly because of their lack of depth.
Acknowledgments The authors thank the  ESO Paranal Staff  for support in conducting the observations. A. L. M. acknowledges financial support from the  European Research Council  under the European Union's  Horizon 2020 research and innovation program  (Grant Agreement No. 819155 ). A. V. acknowledges funding from the  European Research Council (ERC)  under the European Union's  Horizon 2020 research and innovation programme  (grant agreement No. 757561 ). This work has made use of the SPHERE Data Center, jointly operated by  OSUG/IPAG (Grenoble), PYTH-EAS/LAM/CeSAM (Marseille) ,  OCA/Lagrange (Nice) ,  Observatoire de Paris/LESIA (Paris) , and  Observatoire de Lyon , also supported by a grant from  Labex OSUG@2020  (Investissements d'avenir - ANR10 LABX56 ). SPHERE is an instrument designed and built by a consortium consisting of  IPAG (Grenoble, France ),  MPIA (Heidelberg, Germany) ,  LAM (Marseille, France), LESIA (Paris, France), Laboratoire Lagrange (Nice, France) ,  INAF -Osservatorio di Padova (Italy) ,  Observatoire de Genève (Switzerland) ,  ETH Zurich (Switzerland) ,  NOVA (Netherlands) ,  ONERA (France) , and  ASTRON (Netherlands) , in collaboration with  ESO.
SPHERE was funded by  ESO , with additional contributions from  CNRS (France) ,  MPIA (Germany) ,  INAF (Italy) ,  FINES (Switzerland) , and  NOVA (Netherlands ). SPHERE received funding from the  European Commission Sixth and Seventh Framework Programs as part of the Optical Infrared Coordination Network for Astronomy (OPTICON)  under grant number  RII3-Ct-2004-001566  for  FP6  ( 2004-2008 ), grant number  226604  for  FP7  ( 2009-2012 ), and grant number  312430  for  FP7  ( 2013-2016 ). Data, Materials, and Code Availability This work is based on observations collected at the  European Organisation for Astronomical Research in the Southern Hemisphere  under  ESO  programmes  095. C-0298 ,  095. C-0309 ,  096. C-0241 ,  097. C-0865 ,  198. C-0209 ,  1100. C-0481 ,  1104. C-0416 ,  60. A-9249 ,  60.
This paper is organized as follows. The next section provides a complete overview of the HDPBL model. The following section describes our implementation of a solver of HDPBL in a program we refer to as AquaVit. AquaVit is a continuation of AquaSol; 31 it is heavily based on the package MG developed by Michael Holst. 32 The next section provides examples of the usefulness of HDPBL for detecting and characterizing binding sites in proteins. We conclude the paper with a discussion on the limitations of HDPBL, of possible improvements that would circumvent those limitations, as well as on possible developments around HDPBL.