dataesr/scientific-paragraphs-categorization huggingface dataset:
Simulated ICOD TM average is about half that of observations, but IQRs are very similar meaning larger dispersion of modelled values with respect to MODIS. Figure  11b    As described in Section 2, WRF-CHIMERE includes also the glaciation indirect effect through the processes of heterogeneous and homogeneous ice nucleation starting from aerosol predicted by chemical modules. Unfortunately, no available in situ measurements allow the evaluation of the ice particle concentration. The simulated ice cloud optical depth (ICOD) was compared to that observed by MODIS, including the precipitating hydrometeors and suspended ice cloud. Although in this section we have focused on the relationship among aerosol size distribution, hygroscopicity, CDNC, and COD, the uncertainties in simulating cloud optical properties may be also related to model setup used.
The data sample used in this analysis corresponds to integrated luminosities of 35. 9 fb -1 collected in 2016 and 41. 5 fb -1 collected in 2017 during Run 2 of the CERN LHC at a center-ofmass energy of 13 TeV. These results are combined with results obtained earlier from the data collected at center-of-mass energies of 7 TeV (in 2011), 8 TeV (in 2012),  and 13 TeV (in 2015) , corresponding to integrated luminosities of 5. 1, 19. 7, and 2. 7 fb -1 , respectively  [25, 27]. The increase in either energy and integrated luminosity leads to substantial improvement in the precision of the width measurement using the off-shell technique, either under the assumption of SM couplings or with BSM effects. This analysis follows closely the general H → 4 (leptons = e or µ) selection and reconstruction documented in Ref.
[60]. The JHUGEN 7. 0. 2 [47, 50, 54, 59 ] Monte Carlo (MC) program is used to simulate anomalous couplings in the H boson production and H → ZZ / Zγ * / γ * γ * → 4 decay. The gluon fusion production is simulated with the POWHEG 2  [61] [62] [63] [64] [65]  event generator at next-to-leading order (NLO) in QCD, and simulation with the MINLO  [66]  program at NLO in QCD is used for evaluation of systematic uncertainties related to modeling of two associated jets. The kinematics of events produced in gluon fusion with two associated jets are also modified by anomalous Hgg couplings. These effects are studied using JHUGEN, and it is found that the kinematic distributions relevant for this analysis are not affected significantly. The production of the H boson through VBF, in association with a W or Z boson, or with a tt pair, is simulated using both JHUGEN at LO in QCD and POWHEG at NLO in QCD.
Production in association with a bb pair is simulated only at LO in QCD via JHUGEN. In the VBF, VH, and ttH production modes, the JHUGEN and POWHEG simulations are explicitly compared after parton showering in the SM case, and no significant differences are found in kinematic observables. Therefore, the JHUGEN simulation is adopted to describe kinematics in the VBF, VH, and ttH production modes with anomalous couplings in the on-shell region, with expected yields taken from the POWHEG simulation. The POWHEG program is used to simulate wide resonances at masses ranging from 115 GeV to 3 TeV, produced in gluon fusion, VBF, or VH. The events from the POWHEG simulation are later reweighted using the package for the matrix element likelihood approach (MELA)  [9, 47, 50, 54, 59]  to model off-shell H boson production distributions, as discussed below.
The gg → ZZ/Zγ * → 4 background process is simulated with MCFM 7. 0. 1  [18, [67] [68] [69]. The vector boson scattering and triple-gauge-boson (VVV) backgrounds are obtained by reweighting the POWHEG simulation with the matrix elements provided by the MELA package using the MCFM and JHUGEN matrix elements, and the reweighted simulation is checked against the predictions of the PHANTOM 1. 3  [70]  simulation. Both the MCFM and PHANTOM generators allow one to model the H boson signal, background, and their interference in the off-shell production. However, they do not allow modeling of the anomalous interactions considered in this analysis. Therefore, a combined program has been developed for both gluon fusion and VBF with triple-gauge-boson production based on the modeling of signal and background scattering amplitudes from MCFM and anomalous contributions in the signal scattering amplitude from JHUGEN.
This program is included within the JHUGEN and MELA packages, as detailed in Ref. [22]. A large number of MC events with anomalous couplings in the signal and their interference with background have been generated with these packages. The simulated events also include alternative weights to model various anomalous couplings in the signal. In the gluon fusion process, the factorization and renormalization scales are chosen to be running as m 4 /2. In order to include higher-order QCD corrections, LO, NLO, and next-to-NLO (NNLO) signal cross-section calculations are performed using the MCFM and HNNLO 2 programs  [71] [72] [73]  for a wide range of masses using a narrow width approximation. The ratios between the NNLO and LO values (NNLO K factors) are used to reweight  [22]  the m 4 distributions from the MCFM and JHUGEN simulation at LO in QCD, and a uniform factor of 1.
We therefore multiply the background and interference contributions by the same NNLO K factor and uniform N 3 LO correction, both calculated for signal and including associated uncertainties, and introduce an additional unit factor with a 10% uncertainty for the background and the square root of this factor for the interference. The MELA package contains a library of matrix elements from JHUGEN and MCFM for the signal, and MCFM for the background, and is used to apply weights to events in any MC sample to model any other set of anomalous or SM couplings in either on-shell or off-shell production. This matrix element library also allows reweighting of the signal POWHEG simulation of the wide resonances at NLO in QCD in either gluon fusion, VBF, or triple-gauge-boson production to model the signal, background, or their interference.
The trigger efficiency is measured in data using a sample of 4 events collected by the single-lepton triggers and is found to be consistent with the expectation from simulation. Event reconstruction is based on the particle-flow (PF) algorithm  [84] , which exploits information from all the CMS subdetectors to identify and reconstruct individual particles in the event. The PF candidates are classified as charged hadrons, neutral hadrons, photons, electrons, or muons, and they are then used to build higher-level objects such as jets and lepton isolation quantities. Electrons (muons) are reconstructed within the geometrical acceptance defined by a requirement on the pseudorapidity |η| < 2. 5 (2. 4) for transverse momentum p T > 7  (5)  GeV with an algorithm that combines information from the ECAL (muon system) and the tracker.
The kinematic discriminants used in this study are computed using the same MELA package that is utilized in simulation. The signal includes both the four-lepton decay kinematics in the processes H → ZZ / Zγ * / γ * γ * → 4 , and kinematics of associated particles in production H+jet, H+2jets, VBF, WH, ZH, ttH, tqH, or bbH. The background includes gg or qq → ZZ / Zγ * / γ * γ * / Z → 4 processes, and VBF or associated production with a V boson of the ZZ system. Analytical algorithms are available for the cross-checks of the four-lepton kinematics in H decay and VH associated production within the MELA framework and were adopted in the previous CMS analyses  [9, 10, 23]. Kinematic distributions of particles produced in the H boson decay or in association with H boson production are sensitive to the quantum numbers and anomalous couplings of the H boson.
The "int" label represents the interference between the two model contributions. The probabilities P are calculated from the matrix elements provided by the MELA package and are normalized to give the same integrated cross sections in the relevant phase space of each process. Such normalization leads to a balanced distribution of events in the range between 0 and 1 of the D alt discriminants, and between -1 and 1 of D int. One can apply the Neyman-Pearson lemma to prove that the two discriminants in Eqs. (  7 ) and (  8 ) become the minimal and complete set of optimal observables for the purpose of separating the two processes "sig" and "alt" while including their interference as well  [54, 59]. The selected events are split into three categories: VBF-tagged, VH-tagged, and untagged. A set of discriminants D 2jet is constructed, following Eq.
The uncertainty on the modeling of this misidentification as a function of p T and η, combined with the Z + 1 control region statistical uncertainty, leads to a +20 -12 % to +30 -27 % variation in the 4e channel, ±(10 -20)% variation in the m 4 shape in the 2e2µ channel, and ±4% to +14 -17 % variation in the 4µ channel. Uncertainties in the Z + X background in the 2016 data set are only slightly larger. The normalization of the background processes derived from the MC simulation is affected by the uncertainties in the integrated luminosity of 2. 5%  [94]  and 2. 3%  [95]  in the 2016 and 2017 data sets, respectively. The integrated luminosity is measured using data from the CMS silicon pixel detector, drift tubes, and the forward hadron calorimeters, or from the fast beam conditions monitor and pixel luminosity telescope.
The off-shell region is analyzed using only 2016 and 2017 data because no such analysis of the three anomalous couplings has been performed with the Run 1 or 2015 data in this region. The one-parameter likelihood scans of f ai cos (φ ai ) combining all such available on-shell and off-shell events is shown for two cases in Fig. 6 , either with Γ H unconstrained in the fit or with the constraint Γ H = Γ SM H. The corresponding 68 and 95% CL constraints are summarized in Table  6. The full two-parameter likelihood scans of f ai cos (φ ai ) and Γ H are likewise shown in Fig. 6. Using the transformation in Eq. (  5 ), the f ai cos (φ ai ) results can be interpreted for the coupling parameters used in Eq. (  2 ), as shown in Table  7. Limits on Γ H are set by combining events from the on-shell and off-shell regions.
Acknowledgments We thank  Markus Schulze  for optimizing the  JHUGEN Monte Carlo simulation program  and matrix element library for this analysis. We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at  CERN  and at other  CMS institutes  for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. We also acknowledge the  Maryland Advanced Research Computing Center (MARCC)  for providing computing resources essential for this analysis. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies:  BMBWF  and  FWF (Austria) ;  FNRS  and  FWO (Belgium) ;  CNPq ,  CAPES ,  FAPERJ ,  FAPERGS , and  FAPESP (Brazil) ;  MES (Bulgaria) ;  CERN ;  CAS, MoST , and  NSFC (China) ;  COLCIENCIAS (Colombia) ;  MSES  and  CSF (Croatia) ;  RPF (Cyprus) ;  SENESCYT (Ecuador) ;  MoER ,  ERC IUT , and  ERDF (Estonia) ;  Academy of Finland ,  MEC , and  HIP (Finland) ;  CEA  and  CNRS/IN2P3  (France);  BMBF ,  DFG , and  HGF (Germany) ;  GSRT (Greece) ;  NK-FIA (Hungary) ;  DAE  and  DST (India) ;  IPM (Iran) ;  SFI (Ireland) ;  INFN (Italy) ;  MSIP  and  NRF (Republic of Korea) ;  MES (Latvia) ;  LAS (Lithuania) ;  MOE  and  UM (Malaysia) ;  BUAP ,  CIN-VESTAV ,  CONACYT ,  LNS ,  SEP , and  UASLP-FAI (Mexico) ;  MOS (Montenegro) ;  MBIE (New Zealand );  PAEC (Pakistan) ;  MSHE  and  NSC (Poland) ;  FCT (Portugal) ;  JINR (Dubna) ;  MON, RosAtom ,  RAS ,  RFBR , and  NRC KI (Russia) ;  MESTD (Serbia) ;  SEIDI, CPAN, PCTI , and  FEDER (Spain) ;  MOSTR (Sri Lanka) ;  Swiss Funding Agencies (Switzerland) ;  MST (Taipei) ; ThEPCenter, IPST, STAR, and  NSTDA (Thailand) ;  TUBITAK  and  TAEK (Turkey) ;  NASU  and  SFFR (Ukraine) ;  STFC  ( United Kingdom );  DOE  and  NSF (USA).
GENA In addition to the above sampling algorithms, which seek to reconstruct a posterior distribution, we also employ an optimization procedure for comparing GRMHD simulations to data in Section 6. The optimization code, GENA  (Fromm et al. 2019) , is a genetic algorithm written in Python and parallelized using MPI. GENA minimizes a χ 2 statistic on visibility amplitudes and closure phases, using the gain calibration procedures in the eht-imaging  (Chael et al. 2016 (Chael et al. , 2018 (Chael et al. , 2019a) )  Python package to solve for the gain amplitudes. GENA implements the Non-dominated Sorting Genetic Algorithm II (NSGA-II;  Deb et al. 2002)  for parameter exploration and the differential evolution algorithm from  Storn & Price (1997)  for constrained optimization.
Geometric Modeling As detailed in Paper IV, images reconstructed from the M87 data show a prominent and asymmetric ring ("crescent") structure. In this section we use the techniques described in Section 4 to fit the M87 data sets with a specific class of geometric crescent models. We first quantify the preference for crescent structure in Figure  2 , which summarizes the results of fitting a series of increasingly complex geometric models to the M87 data. We Figure  2. Relative log-likelihood values for different geometric models fit to the M87 data as a function of nominal model complexity; the number of parameters is given in parenthesis for each model. April 5 is shown here, and all days and bands show the same trend. The models shown in this figure are strict subsets of the "generalized crescent model" (labeled here as model "n"; see Section 5.
Calibrating the Crescent Diameter to a Physical Scale Using GRMHD Simulations Though the GC models have been constructed to fit the M87 data well, the geometric parameters describing these models do not directly correspond to any physical quantities governing the underlying emission. Our primary physical parameter of interest is Contours enclose 68% and 95% of the posterior probability. Note that recovery of the total compact flux density ĈF is not possible for the dynesty-based fits, which only make use of closure quantities. the angular size corresponding to one gravitational radius, q = ( ) GM c D. 2 6 g 2 The gravitational radius sets the physical length scale of the emission region. Most of the observed 230 GHz emission is expected to originate near the photon ring (see, e. g. ,  Dexter et al.
Direct Comparison with GRMHD Models EHT data have the power to directly constrain GRMHD simulation based models of M87 and to estimate the physical properties of the black hole and emitting plasma. Such a direct comparison is challenging due to stochastic structure in the models. The EHT 2017 data span a very short time frame for the M87 source structure. Its characteristic variability timescale at 230 GHz is ;50 days  (Bower et al. 2015) , much longer than our observing run. Thus, although the entire ensemble of model snapshots taken from a given simulation captures both the persistent structure as well as the statistics of the stochastic components, we do not yet have enough time coverage for M87 itself to measure its structural variations. Model images from GRMHD simulations show a dominant, compact, asymmetric ring structure resulting from strong gravitational lensing and relativistic gas motions (Paper V).
The various uncertainty components are described in Appendix D. 2. We quote median values for all measurements and the associated 68% confidence intervals for the different categories of uncertainty. GRMHD fitting to mm-VLBI data of Sgr A * (e. g. ,  Dexter et al. 2010; Kim et al. 2016). We further develop and apply a method for testing the consistency of the M87 data with the simulation models (Section 6. 4) and find that the majority of the simulation library models is consistent with the data. We use the results to estimate physical parameters, including the black hole angular radius GM Dc 2 (Section 6. 5). The implications of our results for the physical properties of the emission region are discussed in more detail in Paper V. From EHT data alone it is difficult to rule out many of the broad range of possible models for the black hole and plasma properties.
Fitting Single Snapshots to EHT Data For both model selection and parameter estimation, the first step is fitting an SSM model to the EHT data set described in detail in Section 2. 1. The only difference here is that intra-site baselines are excluded. These probe angular scales between 0 1 and 10″, at which unmodeled large-scale features, e. g. , HST-1, contribute substantially (see Section4 of Paper IV). We verify after the fact that the reconstructed compact flux estimates are consistent with the upper limits necessarily implied by these baselines. The fitting process is complicated by large structural variations between snapshots resulting from turbulence in the simulations (see Section 6. 4). We employ two independent methods to fit SSMs to the EHT data sets. Both employ the likelihoods constructed as described in Section 4.
Model Selection and Average Image Scoring (AIS) Quantitatively assessing the quality of SSM fits presents unique challenges because of the presence of stochastic image features due to turbulence in the underlying GRMHD simulations that produce large variations in image structure. The structural variability leads to changes in EHT observables that are much larger than the observational errors. It is therefore not feasible to generate a sufficient number of images from existing GRMHD simulations to have a significant probability of finding a formally adequate (i. e. , χ 2 ≈1) fit to the data (see the discussion in Paper V). Nevertheless, the ensemble of snapshots from a given simulation provides a natural way to characterize the impact of these stochastic features on the inferred SSM parameters.
Finally, the average snapshot image is compared to the EHT data, and the resulting χ 2 is assessed. Thus, THEMIS-AIS is effectively determining if the EHT data are consistent with being drawn from the GRMHD simulation. The result is characterized by a simulation p-value, which we call p AIS. Because of the significant variations in data quality and baseline coverage across days, this procedure must be repeated independently for each day. It is possible for a model to be ruled out by the AIS procedure both by the average image SSM having a χ 2 that is too high (the data is "further" from the average snapshot image than typical for the simulation) and by the average image SSM having a χ 2 that is too low (the data is "closer" to the average snapshot image than typical for the simulation, usually a consequence of too much variability in the GRMHD model).
Ensemble-based Parameter Estimation The posteriors for the SSM parameters for a given GRMHD model are estimated using both the observational errors in the EHT data and the stochastic fluctuations in the snapshot images themselves; among these "noise" terms, the latter significantly dominates. This is evidenced by the variations among SSM fit parameters from snapshots within a GRMHD model, which typically exceed the formal fit errors from the SSM fit alone (see Appendix G). Some care must be taken in extracting and interpreting parameter estimates from these. Only SSM fits with likelihoods among the highest 10% within each model are used for parameter estimation. The results for θ g are insensitive to the precise value of this fit-quality cut after it passes 50%. The measured values are consistent over the range of GRMHD models explored (see Figure  10  for five examples).
All of the simulations shown are deemed acceptable by AIS (p AIS >0. 01; see Section 6. 4 for details). simply summing the posteriors obtained for each acceptable GRMHD model. In principle, it is possible for the posteriors constructed in this fashion to suffer from biases induced by the treatment of the high values of χ 2 found when including only observational errors. We have attempted to estimate this bias using a large number of mock analyses. In those, simulated data were generated from a snapshot within a GRMHD model. Posteriors were then generated for that model given the simulated data and compared to their known SSM parameters; no significant biases were found. We have further conducted two posterior mock analyses for the full suite of GRMHD models, independently for the THEMIS and GENA pipelines.
In these the impact of including "incorrect" GRMHD models was a key difference with the previous tests. See Appendix G for more details. The results of both of these experiments only hold if the GRMHD models used as synthetic data provide a good description of M87. As multiple observation epochs become available, it will be possible to explicitly measure the statistics of the stochastic fluctuations, empirically addressing this assumption. It will also enable direct ensemble-to-ensemble comparison like that described in  Kim et al. (2016). A promising, alternative approach would be to perform a principal component analysis (PCA) decomposition of the snapshots within each model  (  Medeiros et al. 2018) , and fit images generated by varying the weights of the PCA components to the data to mimic the set of possible realizations of the turbulence.
Lensed Emission Around the Black Hole Shadow The results of fitting analytic models (Section 5) and GRMHD image snapshots (Section 6) to visibility domain data, as well as image reconstructions (Paper IV, Section 7) strongly favor an asymmetric ring (crescent) source morphology with a deep central brightness depression. This morphology is robust among the different analysis methods and is consistent with characteristic features in the interferometric visibilities (Section 3). Fitting geometric models to the data and extracting feature parameters in the image domain both allow us to quantify the following properties of the crescents: (i) a compact flux density Figure  18. Distributions of fractional spreads in the inferred diameters of the M87 images measured along different orientations, for images reconstructed using two methods for the April 5 data set.
All of the individual θ g estimates use the GRMHD simulation library, either through directly fitting GRMHD snapshots to the data (Section 6) or through calibration of diameters resulting from geometric models or reconstructed images (Sections 5 and 7). A degree of caution is therefore warranted. The measurements rely on images generated from GRMHD simulations and should be understood within that context (see also Paper V). We have also used only a small subset of 100 such randomly chosen frames (with randomly assigned SSM parameters) out of a much larger library. A simple (but poorly motivated) alternative to the full calibration presented here would be to assign the mean emission diameter to the size of the photon ring itself (α;9. 6-10. 4 for all methods). That would give a nearly identical θ g result for the image domain estimates and only a ;10% increase for the geometric models, within its current systematic uncertainty.
Conclusions The horizon-scale emission of M87 at 1. 3 mm exhibits a robust crescent-like structure. This is seen in image reconstructions (Paper IV) and supported by features in the visibility data from the 2017 EHT campaign (Paper III). Geometric crescent models are overwhelmingly preferred to similarly complex models that we have explored that do not have a central flux depression. The crescent structure is well defined, with a rapid decline to a dark interior with a brightness 10× lower than the average of that in the annular region. The average diameter of the crescent is well constrained by multiple methods with a combined range of 42 ± 3 μas. This is consistent among all observation days and bands. Based on geometric models, GRMHD simulations, and image domain feature extraction, the angular size of the gravitational radius is θ g =3.