dataesr/scientific-paragraphs-categorization huggingface dataset:
Those representations are further improved using an end-to-end approach to generate structure models with iterative structural refinement. The output of AlphaFold2 is a highly accurate set of structural models with accompanying residue-specific estimates of modeling reliability. This outstanding achievement is not only conceptual, in the sense of the advancement of novel deep learning techniques and protein science, but also practical. It provides the scientific community with a method for fast, reliable, and cheap determination of structural models that can be applied at a large scale. Recently, DeepMind and EMBL-EBI have jointly released the database of AlphaFold2 predictions for the whole human proteome  [5]  and other key organisms (https://alphafold. ebi. ac. uk/). Furthermore, an easy-to-use and fast version of the AlphaFold2 pipeline was introduced by modifying the time-consuming step of multiple sequence alignments generation with almost identical results  [6].
Firstly, we relied on a hand-curated set of proteins with different extensions of experimentally estimated conformational diversity, defined by an apo conformer and the corresponding holo form bound to a biologically relevant ligand. Using this dataset, we studied if AlphaFold2 can reproduce different conformers among their resulting top-scoring models. We also explored how AlphaFold2's performance is affected by the degree of conformational diversity of the protein under study. Additionally, as AlphaFold2's predictions heavily rely on evolutionary information, we used families of homologous proteins with different extensions of conformational diversity among its members to test whether this heterogeneity affects prediction.
Description of the dataset We selected 86 proteins (Supplementary Table  1 ) with different degrees of conformational diversity expressed as the range of pairwise global Cα-RMSD between their conformers in the PDB (Figure  1 ). All the pairs of conformers for each protein are apo-holo pairs selected from the CoDNaS database  [28]  and bibliography. Hand-curation for each protein confirmed that structural deformations were associated with a given biological process based on experimental evidence. This step is essential to ensure that conformational diversity is not associated with artifacts, misalignments, missing regions, or the presence of flexible ends. When more than two conformers are known, we have selected the apo-holo pair showing the maximum Cα-RMSD (maxRMSD). Other considerations were absence of disorder, PDB resolution, absence of mutations, and sequence differences.
AlphaFold2 does not reproduce conformational diversity We have predicted the structure of each protein in the dataset using ColabFold (AlphaFold2. ipynb -Colaboratory) running AlphaFold2 with MMSeq2  [6]  without the use of templates and with the option to obtain relaxed models with Amber force fields  [29] , gathering the first five top models according to plDDT (predicted local Distance Difference Test) scores  [30]. Supplementary Figure  1  shows the distribution of the plDDT scores for all the models. We found that 90% of the models scored higher than 86. 9, reaching 90. 0 if only the best model for each protein is considered, evidencing the good quality of the models obtained. All AlphaFold2 models (five per protein) were structurally aligned to the experimentally resolved apo and holo conformations for each protein in the dataset, and the RMSD value was calculated for each alignment.
53 Pearson correlation coefficient and p-value <0. 001) (Figure  5B ). The model error shows no dependency on the sequence number of the input alignment (-0. 18 Pearson correlation coefficient, p-value >0. 05) and protein length (-0. 25 Pearson correlation coefficient, p-value <0. 05). To study how the error in the model depends on the type of protein movements between the apo and holo forms, we classified the pairs in our dataset in two broad categories  [34] : according to the presence of domains and hinges movements using the DynDom software  [35]  and the presence of flexible loops in just one domain. We found that the error measured as the lowestRMSD is slightly dependent on the type of movement (Wilcoxon rank sum test W= 1128. 5, p-value = 0. 046) with a median of 0. 93 and 1. 6Å for the domain movements group and proteins with loop movements.
To test this hypothesis, we explore families of homologous proteins with experimentally based conformational diversity. These families were obtained from the CoDNaS database using a sequence-based clustering with 40% sequence identity and 70% coverage. Each of the ~29000 protein entries in CoDNaS has an associated maximum Cα-RMSD derived from comparing all the conformers belonging to a given protein. This maxRMSD is taken as the maximum conformational diversity the protein could have. Clusters were further classified into homogeneous or heterogeneous according to the range between the minRMSD and the maxRMSD for each protein in each family (range < 4Å for homogeneous families, or heterogeneous otherwise). Mapping our 86 proteins to these clusters only retrieved 20 proteins distributed in 10 homogeneous and 10 heterogeneous clusters.
RMSF captures the flexibility of the protein per position, as derived from the comparison between apo and holo conformers. To study how the intrinsic flexibility of each conformer relates with the plDDT, we used the profile of the normalized α carbons B-factors obtained by performing normal mode analysis for the apo form of the protein as described in Methods. In this way a similar correlation of -0. 44 (Pearson p-value <0. 001) was obtained. Figure  7 : Distributions of plDDT score as a function of RMSF between apo and holo forms (left for all the positions and right using a window of 15 residues). Models were selected according to their lowest RMSD. Low values of plDDT have been related to the occurrence of disordered regions  [2]. However, according to our results, low-scoring regions could also represent flexible regions connecting ordered conformers, as observed for most of the proteins in our dataset.
In our dataset only 2% of the proteins showed models similar to either the holo or the apo forms with similar error, measured as the best RMSD to a given form (Figure  2 ). For the rest of the proteins, it is not possible to model both the apo and holo forms simultaneously with the same low error as when considering a single conformer (Figure  3 ). Far from disappointing, this observation was expected since a large set of redundant protein structures (conformers) would have been required during the neural network training processes  [5]  in order to predict conformational diversity. We also found that most of the predictions made resemble and are mostly indistinguishable from the holo form of the studied protein (68% of the dataset). This is an exciting result because holo forms of proteins describe the binding capacity to a substrate or any other biologically relevant ligand (see Figure  4 ).
Jumper et al. mentioned that AlphaFold could infer structures when the presence of a ligand is predictable from the sequence  [2]. We thought that this finding could be explained due to a bias in the training process of AlphaFold2. However, exploring the BioLip database to estimate the relative presence of apo and holo forms in PDB shows about 64% of apo forms (a similar proportion observed in CoDNaS, from which our dataset was obtained). We hypothesized that holo forms could have a higher number of inter-residue contacts and that these could have influenced the modeling process in AlphaFold2. However, we did not detect differences in the number of contacts between holo and apo forms (the median number of contacts are equal to 3. 47 and 3. 44 of the apo and holo forms, Wilcoxon p-value >0.
Description of the dataset The set of apo and holo structures was obtained from the database of Conformational Diversity in the Native State of proteins (CoDNaS)  [28]. CoDNaS is a redundant collection of PDB structures for the same sequence that can be taken as snapshots of protein dynamism. The conformational diversity for each protein was estimated as the C⍺-RMSD between apo and holo forms. In order to obtain a well-curated dataset containing protein motions related to a given biological activity we followed several specific quality criteria: (i) Only crystal structures with resolution < 3. 9Å were considered; (ii) structures must not have missing residues; (iii) there must be 100% sequence identity between the conformers; (iv) structural deformations between pairs of conformers were associated with a given biological process based on experimental evidence; (v) no reported mutations; (vi) less than 15% disordered regions according to MobiDB consensus; and (vii) visual inspection was used to confirm an existing conformational diversity (e.
Predictions and comparison of structures Predicted models for each protein in the dataset were obtained using ColabFold (  [6] ) due to its easy access through Google Colab Notebooks. Runs were performed using no templates, automatic alignments and Amber energy minimization. For each run we used the 5 top models derived from the energy minimization. Each model was structurally compared between each other and against the correspondent apo and holo structures. As sequences between conformers and models are identical, the alignments are straightforward. We then quantified the structural similarity using the C⍺ Root Mean Square Deviation (C⍺-RMSD).
Evolutionary information We sequentially clustered the CoDNaS database into homologous families containing sequences with more than 40% sequence identity and 70% coverage using CD-HIT. Each protein in CoDNaS has an associated maximum RMSD (maxRMSD) derived from the pairwise comparison of all its conformers. The maxRMSD is taken as the extent of the protein conformational diversity. A total of 175 well-populated clusters were taken (>8 proteins per cluster). A random protein from each cluster was modeled using ColabFold following the procedure mentioned above. The error of this model estimation was calculated as the lowest RMSD obtained from the comparison of any of the top 5 models with the crystallographic structures of the protein.
Apo-holo characterizations Classification of the 86 proteins in the dataset was done by manual curation following the bibliography. In parallel, the database of biological ligands BioLip  [55]  in its most recent version (October 01, 2021) was used to crosslink all the chains of the PDB (October 2021, total chains 661494) and CoDNaS v3 (March 2021, total chains 430151). If at least one biological ligand is found for a chain, it is assigned in the holo category; otherwise, it is considered as an apo conformer.
Acknowledgements NP, MSF, SFA, and GP are researchers, TS, JM, AJVR are postdoctoral fellows, and  NE  and EG are doctoral fellows from  CONICET. This work was supported by  Universidad Nacional de Quilmes  ( PUNQ 1309/19 ),  ANPCyT  ( PICT-2018-3457 ), and the  European Union 's  Horizon 2020 Research and Innovation Programme  (Grant Agreement No  778247 ). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Code verification is an intricate but crucial part of numerical code development. Due to the complexity of the partial differential equations, an analytical solution might not exist. In those situations and aiming at proving that the code is solving appropriately the governing equations, the method of manufactured solutions (MMS) is a powerful tool. In this method, a source term is derived to enforce the solution to a predetermined function. By performing a mesh refinement study, one can verify if the code is correctly solving the desired equations. In this work, a methodology that allows the automation of the MMS within the OpenFOAM R framework is proposed. The developed computational framework comprises a set of tools prepared, in an open-source environment, for the symbolic computation of the associated source term, and to generate the code required for its implementation as well as appropriate boundary conditions and functions to calculate the error norms.
In the present work, a semi-automatic approach to undertake code verification in OpenFOAM R through the MMS is proposed and illustrated. The approach allows a straightforward extension to different case studies and solvers. It resorts to Sympy  [16]  v1. 8, an open-source symbolic computation module from Python programming language, and OpenFOAM R 'v1912 fvOptions and coded functionality, which allows a high degree of flexibility for a swift, and automatic, computation of source terms and boundary conditions. The remaining paper is organized as follows. Section 2 introduces the MMS and the computation of associated error norms and convergence orders. In Section 3, the semi-automatic approach for implementing the MMS in OpenFOAM R is presented. The subsequent section, Section 4, a number of case studies involving the laplacianFoam  [17]  and simpleFoam  [18]  solvers are carried out, using structured meshes, to demonstrate the application of the proposed semi-automatic approach.
Semi-automatic approach Based on a selected manufactured solution, the implementation of the MMS approach in OpenFOAM R requires the calculation of: (i) the associated distributed source term, (ii) the associated Dirichlet and/or Neumann boundary condition functions, and (iii) the coded functionObject for the computation of the error norms. Given the arbitrary complexity of choosing a non-trivial manufactured solution, the programming of the associated source term and boundary condition functions can become a cumbersome and error-prone task. In that regard, a Python package (referred to as pyMMSFoam) was created to perform the necessary mathematical differentiation based on the Sympy v1. 8 module  [16] , a rich-featured library for symbolic computation written in Python. The package converts the generated mathematical expressions to C syntax so that they can be copied directly into an OpenFOAM R case setup files.
1 and D T = 10 -3 m 2 /s. This will also be used for the case study of the laplacianFoam solver in Section 4. 1. In Step 1 (see Figure  1 ), the manufactured solution has to be defined, and the user can rely on the Sympy's built-in functionality, such as trigonometric and exponential functions. Listing 1 illustrates the code used for the 2D unsteady heat transfer case (Equation (1)), with the above referred parameters. From lines 1 to 3, the pyMMSFoam package is being loaded with the alias mms, the Cartesian space symbolic variables x, y and z, the temporal symbolic variable t, and the cos function from Sympy are being imported from their respective modules. Notice that the symbolic variable z is not required for this specific manufactured solution, but it is shown for the sake of completeness and easy adaptation to other cases.
For this test case study, kinematic viscosity of ν = 0. 01 m 2 s -1 is assumed. In this flow, the velocity satisfies the null divergence condition and, for Re = 5, the resulting velocity and kinematic pressure fields are depicted in Figure  4. The code used to generate the source term, the boundary conditions and the coded functionObjects for the computation of the error norms, is shown in Listing 6. From lines 6 to 11, the Reynolds number and the manufactured solution for the velocity components and pressure fields are defined. In lines 13 and 18, the velocity vector and stress tensor are calculated, respectively, and, in line 20, the momentum source term is computed. The advantages of using the pyMMSFoam package are clearly evidenced in such a convoluted manufactured solution, since it allows to avoid lengthy handmade and error-prone calculations.
Finally, from lines 23 to 36, the fvOptions dictionary, boundary condition functions and coded functionObject are generated the OpenFOAM R test case study. For this test case study, Dirichlet boundary conditions are prescribed for the velocity on the left, top and bottom patches of the domain, and for the pressure on the right patch. Moreover, Neumann boundary conditions are prescribed for the velocity on the right patch of the domain and for the pressure on left, top and bottom patches. The code required to setup these features in this case study are automatically generated by pyMMSFoam. The temporal and spatial discretization schemes considered in this case study are presented in Table  3. Table  3. Temporal and spatial discretization schemes for the verification of the sim-pleFoam solver (fvSchemes dictionary).
In that regard, assessing that the computed solution error converges with some order to the underlying exact solution, as the mesh characteristic size and/or time-step size decreases, is a necessary condition. In the general case, finding analytic solutions for such a verification process can be a cumbersome task, especially for complex geometries and/or mathematical models. For the more demanding cases, the method of manufactured solutions provides a practical, simple and versatile framework for the verification procedure of numerical codes (discretization schemes, solution methods, boundary conditions, material models, etc. ). In the present work, a semi-automatic approach was proposed based on the method of manufactured solutions for the verification of solvers in OpenFOAM R. For this aim, a Python package, pyMMSFoam, was developed to support the calculation of source terms, boundary conditions and functions to calculate the errors associated with the numerical method implemented to solve a prescribed mathematical model.
Moreover, pyMMSFoam automatically generates the associated C code and case setup dictionaries, as well as coded functionObjects to compute the errors in different norms, allowing a less invasive, less error-prone and more flexible methodology for code verification. The application of the proposed approach was illustrated for the verification of the laplacianFoam and simpleFoam solvers of OpenFOAM R , with different test case studies, consisting of 1D and 2D, steady-state and unsteady problems, employing structured meshes. The approach proved to be very practical to apply and provides a simple and versatile means to assess the convergence orders of a numerical code. It is important to notice that consecutive lower residual tolerances for the solution method should be used in the calculations until confirming that the computed solution is influenced only by the discretization schemes, and not by the algorithm that solves the system of linear equations.
Acknowledgements This work is funded by  FEDER  funds through the  COMPETE 2020 Programme  and  National Funds through FCT (Portuguese Foundation for Science and Technology)  under the PhD Grant  2020. 07424. BD, projects  UID-B/05256/ 2020  and  UID-P/05256/2020  and from the  European High-Performance Computing Joint Undertaking (JU)  under grant agreement No  956416 , in the framework of the exaFOAM project.
Consequently, multi-leg MC generators that combine multiple exclusive jet emissions with the highest possible perturbative accuracy in the strong and electroweak couplings are preferred. In recent years, the statistical precision of V + jets MC samples has become an increasingly limiting factor for a broad array of ATLAS data analyses. This is primarily due to the long event-generation time of multi-leg MC predictions with high perturbative accuracy that is demanded by the ATLAS physics programme. The relatively large V + jets production cross-section and the rapidly growing integrated luminosity of the proton-proton collision dataset require MC event generators to provide enormous simulated samples, which results in a significant computational challenge for experiments. Current analyses exploring high cross-section regions of phase space already rely on simulated samples that contain many billions of events.
The computational resources required for large-scale production of any multi-jet merged MC prediction that meets the mentioned theoretical demands is significant. Furthermore, the techniques used to populate the low cross-section regions of phase space can significantly exacerbate the problem. In the Sherpa 2. 2. 1 configuration, a discrete phase-space slicing technique was used, which resulted in artificial features in the distribution of event weights that adversely impacted the statistical precision of the sample. In addition, the relatively large fraction of MC events with negative weights in the high cross-section regions of phase space, coupled with the long event-generation time, made it difficult to provide a simulated dataset with enough generated luminosity to match the collected data.
Impact on computing resources The inclusive V + jets cross-section is sufficiently large that the computing resources required to match the dataset's integrated luminosity are significant and difficult to achieve across the wide range of phase space required for physics analyses. Moreover, as the LHC physics programme advances it continues to explore extreme regions of phase space often requiring computationally expensive higher-order strong and electroweak corrections. As shown in the previous section, this higher accuracy requires additional resources but these can be reduced through well-motivated approximations with minimal impact on the physics modelling. In this section, the computing resources for the Sherpa 2. 2. 11 and 2. 2. 1 configurations are compared in order to quantify the combined effect of the various improvements described in this paper.
Generated effective luminosity The effective luminosity of a generated MC dataset can be used as a metric to quantify the MC sample size and compare the performance of the different configurations. It is defined to be: L eff (x b ) = N (x b ) eff σ(x b ) , where x b is the center of bin b of a generic observable, σ(x b ) is the total cross-section in bin b, and N (x b ) eff is the effective number of events in bin b. The effective number of events is computed from weighted events and defined to be: N (x b ) eff = ( i w i ) 2 i w 2 i , - 32 -.
The sum of all the slices are then normalized to 200 M for comparison with the continuous enhancement samples. The effective luminosity in each generated MC sample as a function of the boson transverse momentum and the total sum of jet transverse momenta (H T ) are shown in figure  15. The Sherpa 2. 2. 11 configuration provides an effective luminosity similar to that from the sliced Sherpa 2. 2. 1 set-up across a wide range of phase spaces, and exceeds the ATLAS Run 2 dataset's integrated luminosity for intermediate to high p V T and H T selections. When comparing the effective luminosity of the 2. 2. 11 and 2. 2. 1 set-ups in the low p V T and H T regions, the two configurations have comparable performance overall, with maximum differences of 30%. For high p V T and H T selections, the spread of weights and the negative-weight fraction are slightly higher in the Sherpa 2.
2. 11 set-up than in 2. 2. 1, which is reflected by the reduced effective luminosity in the tails of the Sherpa 2. 2. 11 set-up. However, both set-ups already exceed the dataset's integrated luminosity by over an order of magnitude. On the other hand, the extremely large spread of weights present in the differential enhancement Sherpa 2. 2. 11 configuration has a detrimental effect on the effective luminosity, which can be over two orders of magnitude lower than that of the Sherpa 2. 2. 11 configuration when using the analytic enhancement scheme. The differential enhancement configuration fails to reach the Run 2 dataset's integrated luminosity across the most of the phase space. Besides providing comparable performance to the 2. 2. 1 setup the effective luminosity of the 2. 2. 11 set-up is more uniform than in the 2.