dataesr/scientific-paragraphs-categorization huggingface dataset:
However, application of these potentials for modelling configurations beyond the potential database is rarely discussed. Uncertainty quantification of the Gaussian process regression can provide a qualitative estimate of the potential's accuracy for each atom in a given system. An example of such an estimation was recently demonstrated in ref. 57. The local error is an appropriate measure of the potential reliability; however, its computational cost ascends to M 2 , whereas the MD calculations with GAP scale linearly with the size of the database M. Here we propose a less costly strategy, able to provide a qualitative estimate of the potential's transferability for modelling targeted defects. The method is based on the outlier analysis and performs examination of defect clusters from the potential database and compares them with the defect structures of interest.
2. 5 eV higher than those of SIA dumbbells (Supplementary Fig. 10b ). This yields an impossible formation of C15 in bcc Fe, which is not consistent with the density functional theory (DFT) predictions  58. For the tri-vacancies V 3 , the computed migration energy barrier V max 3 is almost 60% lower than the DFT migration energy (Supplementary Fig. 11b ). Such an error will have an impact on predictions of defect kinetics under irradiation and interpretation of processes during resistivity recovery experiments  59. Besides these two defects, we also examine (iii) 1 2 h111i screw dislocation core and (iv) its saddle point configuration on the top of the Peierls potential. These structures were not explicitly included into the GAP database; however, the potential performs as accurate as ab initio methods for these defects  60.
The ML algorithm that underlays the GAP potential, Gaussian Processes, is non-parametric and can integrate all the information provided by the projection of the database into the descriptor space R D. Most likely, the "failed" configurations (i)-(ii) deviate from the defects in the training database, whereas the dislocation structures (iii)-(iv) are similar to those learned by the potential. To check this assumption, we have examined how the defect clusters (i)-(ii) are related to the defect structures from the potential database. For the dislocations (iii)-(iv), we only employ the detected LAEs of SFs as a training data for the transferability analysis. The latter will allow to estimate if accurate modelling of dislocations can be ensured by the presence of SFs in the potential database. The majority of atoms in the "failed" defect clusters (i)-(ii) (Fig.
7a, b ) are identified as pronounced outliers, characterized by negative SVM distances. Consequently, the GAP potential mainly performs in extrapolation regime for these defects. The predictions in this regime are not necessarily accurate. Hence, it is not surprising that the energy profiles of those defects predicted by GAP do not agree with DFT calculations. In contrast, the dislocation cores (iii)-(iv) (Fig. 7c, d ) do not contain any anomalous instances. Thus, the structural information provided by the SFs was sufficient to ensure good accuracy of the potential for dislocation core structure and its migration barrier. The proposed strategy for transferability analysis (Figs. 6  and 7 ) provides a qualitative estimate of the potential performance. The outlier-based analysis can indicate if the information necessary for modelling certain defects is missing in the potential database.
The same ML technique can be applied for the detection and analysis of dislocations, interstitial atoms, vacancies and other defects. The proposed definition of defects through the distortion score can be used to analyse the output of various numerical methods such as massive atomistic MD (see Supplementary Note 2), Monte Carlo, metadynamics, hyperdynamics and free energy simulations. Moreover, the distortion score can be used to control the degree of precision for the relevant information to be extracted and stored. This metric can serve as a fingerprint for filtering databases with atomic structures to select and/or classify defects. The proposed definition of defects serves to reinforce not only the performance of traditional approaches, but also of modern ML methods in materials science.
Here we have demonstrate how the new concept of defects can be effectively applied for the analysis of kernel ML potentials and their databases. This approach allows optimizing the database content in order to improve the potential accuracy for modelling targeted defects and their properties. This type of potentials is able to approach DFT accuracy and can cope with large systems where the computational cost beyond the scope of ab initio methods. Improvement of these potentials can enable accurate calculations of such important physical properties, as formation and migration energy of large defects, e. g. , straight dislocations and kink pairs, loops, large 3D clusters, etc. In the perspective, similar approaches can be applied to large biological/chemical molecules. The distortion score can be applied for characterization of energy landscapes.
The first step of the analysis (upper panel) implies detection of defects both in the potential database and in the atomic systems to examine using MCD, one-class support vector machine (OCSVM) or any other relevant method. The second step (lower panel) is aimed at transferability analysis of the potential. The detected defect clusters from the potential database form a new training data set with the structures-inliers known by the potential. The new outlier detection model is trained on these configurations using a kernel method, e. g. , OCSVM, with the kernel function identical to that of the tested ML potential. Identification of atoms-outliers within the examined defect cluster implies that these atomic environments are missing in the training database and, therefore, the tested ML potential may provide poor energetic properties for this defect.
The cutoff distance is set to R c = 5. 0 Å. The same form of the SOAP descriptor was used to design the GAP potential  50. The detection of defect clusters in the GAP database  50  is performed on the ca. 100,000 test atomic environments. After performing the outlier detection to isolate structural defects of the database, we consider ca. M def = 17,300 atomic environments as belonging to defects. These M def atomic environments form the training data set (Fig. 6 ) for transferability analysis of the potential. The structural data for analysis of the correlation between statistical distances and energy per atom from GAP potential in Fe (Fig. 2  and figures in the "Methods" section below) is represented with bispectrum SO(4) using R c = 5. 0 Å and j max ¼ 4:5 with all bi-spectral components.
In this work, we employ robust MCD distance d RB (Eq. (  5 )) as a measure of local atomic distortion score to detect and analyse the defect structures. The outlier detection with MCD is performed on the structural data sets (see Representation of the structural data section) with contamination factor ν = 0. 07. It should be noted that MCD is designed for the data with a unimodal distribution. Practically, it means that the model can be directly trained for detection of defects embedded in the structure with unimodal distribution of LAEs, e. g. , in bcc anf fcc cubic metals. In order to train the model on more complex structural data with multimodal distribution of LAEs, calculations of a multidimensional distortion score can be enabled by modal decomposition of the training database. For instance, a multimodal training database D can be decomposed in various unimodal sub-databases D 1 È D 2 È È D n and a statistical distance can be computed with respect to each sub-database D i , providing thus an n-dimensional distortion score.
Supplementary Note 2 provides an example of the training database decomposition and demonstrates the utility of multidimensional distortion score for the analysis of complex structural damage produced by displacement cascades. Statistical distances and their QM-inspired variants. From mathematical point of view, there is a similitude between the formalism that describes the local atomic energy of materials in quantum mechanics (QM) and the statistical distances based on sample covariance matrix. As emphasized in Table  1 , the observables to be evaluated are the energy of the quantum state i ? j i and the statistical distance of the data point jx i ? i in descriptor space. The local orbital basis i j i f g is equivalent to the learning database x m j i f gof the M atomic environments. The eigenelement of the Hamiltonian ϵ m ; m j i f gand λ m ; v m j i f gof the sample covariance matrix have similar meanings, giving the total energy (Eq.
6, Fig. 9 ). One-class support vector machine. One-class support vector machine (OCSVM)  29  is a subclass of widely used support vector machine methods  67. This approach separates inliers from outliers by finding a maximal margin hyperplane between them  29, 67, 68. The vectors that determine the optimal separating hyperplane are called support vectors. OCSVM is similar to binary SVM classification, where the regular training data with the bulk structure (inliers) belongs to the first class, and the defects (outliers) belong to the second class. The proportion of outliers that contaminate the database, ν, is an input parameter. The hyperplane between the two classes is the decision boundary, which can be defined both for linearly separable data and more complex non-linear cases. For linearly separable data, the hyperplane can be described by the classification rule: f x m ð Þ ¼ w; x m h iþb; ð7Þ where w is the normal vector and b is a bias term.
Both parameters w and b are learned from the positive class (bulk) database. For each point x m , the value f(x m ) is determined by evaluating on which side of the hyperplane it falls on (in feature space). The function is positive for the inlier data points (bulk structures) and negative for the outliers (structural defects). The distance d SVM from the origin to a point x along the direction w is given by: d SVM ¼ w T x=ðw T wÞ 1=2 : ð8Þ Similarly to the MCD robust distance d RB , the distance d SVM can be used as the metric of the distortion score for each atom. In order to perform non-linear classification and obtain more complex decision boundaries, the kernel trick can be applied, as was originally proposed by Vapnik  67. In this case, the data are implicitly mapped into a high-dimensional space through a non-linear function Φ(x).
Acknowledgements This work was financially supported by the  Cross-Disciplinary Program on Numerical Simulation of CEA , the  French Alternative Energies and Atomic Energy Commission. A. M. G. , C. L. , J. D. and M. C. M. acknowledge the support from  GENCI -(CINES/CCRT ) computer centre under Grant number  A0070906973. This work has been carried out within the framework of the  EUROfusion Consortium  and has received funding from the  Euratom  research and training programme 2014-2018 and  2019-2020  under grant agreement number  633053. The views and opinions expressed herein do not necessarily reflect those of the  European Commission. This work also received funding from the  Euratom  research and training programme  2019-2020  under grant agreement number  755039. A. M. G. acknowledges  Marie Landeiro dos Reis  for providing simulation cells with dislocations in fcc Al.
Data processing and analyses The LMA was computed from the LDW and La. Leaf N content per area unit (Na) was obtained by multiplying the LMA by the N concentration (Nm). SPAD readings were converted into chlorophyll content per area unit (Chl) using a consensus equation published by  Cerovic et al. (2012) , and the chlorophyll proportion per Na (Chl:Na) was computed. Mean daily PAR T and incident PAR (PAR i ) were calculated as the average values over the last 15 days before photosynthesis measurements and sampling. Leaves were separated into three classes depending on the actual amount of intercepted radiation. In each period, the ten leaves with the highest PAR T were assigned to the high-light group (H), the ten leaves with the lowest values were assigned to the low-light group (L), and the other ten leaves were assigned to the medium-light group (M).
To estimate the effect on individual trees for each crop status, two-way ANOVAs considering tree and light conditions were performed on each date. The effect of the type of shoots (spur or elongated shoots) was tested, and no major significant differences were detected (data not shown). Correlation analyses were conducted to assess the relationships between A net , Na and NSC concentration, between the subvariables involved in Na variation  (LMA, LDW, Nm, La)  and between all NSC forms. These correlation analyses were performed considering the whole dataset or ON and OFF trees separately.
Analysis of relationships between photosynthesis, light harvesting traits and NSC contents When the datasets from both crop statuses were considered together, a negative correlation between A net and starch was observed (Fig. 5A ). Nevertheless, this relationship was not significant for OFF trees. In contrast, the relationship was significant and positive for ON trees. Na and A net were positively but slightly correlated when datasets for both crop statuses were considered together and for ON trees. This relationship was not significant when OFF trees were considered separately (Fig. 5B ). Crop status affected all the variables explaining variations in Na (LDW, LMA, Nm and La) (Fig. 6 ) but had an opposite effect on Na. Indeed, slightly lower La (which increased LMA and Na) and LDW (which decreased LMA and Na) values were observed for ON trees.
ACKNOWLEDGMENTS This study was funded by the  ANR-DFG  " Alternapp" project  ( ANR-14-CE35-0001-01 ). The authors acknowledge  SILVATECH  ( ANR-11-LABX-0002-01 ) from UMR 1434 SILVA, 1136 IAM, 1138 BEF and 4370 EA LERMAB of the research center  INRAE Nancy-Lorraine  for the leaf nitrogen analyses. Dr Marc Saudreau  and  Dr André Lacointe  ( UMR 0547 PIAF ) are thanked for insightful advice regarding light sensor positioning in the field and for useful comments on the manuscript, respectively. Xavier Le Roux  ( Fondation pour la Recherche sur la Biodiversité ) is acknowledged for having initiated questioning the within-tree variability of leaf function at the PIAF unit. Dr Farés Belhassine  is also thanked for providing additional data used to build allometric relationships.
In vitro cell proliferation A total of 20,000 GFP+ sorted cells from Bmpr1a control or Bmpr1a cKO mice were plated in 12-well plates. Each sample was analyzed in duplicate. Cells were then manually counted at d2, d4 and d6 after plating. Growth curve was then generated and area under the curve (AUC) was used to determine cell proliferation using GraphPad Prism (GraphPad Software, Inc. , La Jolla, CA, USA). Genotyping of Bmpr1a mutant cells GFP+ sorted cells from Bmpr1a control or Bmpr1a cKO mice were lysed in NaOH 50mM at 95 C for 10 minutes. The solution was then equilibrated with 23% Tris-HCl. Bmpr1a polymerase chain reaction (PCR) was performed with GoTaq G2 Hot Start Green Master Mix (Promega, San Luis Obispo, CA, USA; ref M7423) using the following primers: Fx2: 5 0 -GCA GCT GCT GCT GCA GCC TCC-3 0 , Fx4: 5 0 -TGG CTA CAA TTT GTC TCA TGC-3 0 , Fx1:5 0 -GGT TTG GAT CTT AAC CTT AGG-3 0 , according to Mishina and colleagues.
Microarray analyses For microarray analyses, datasets from Lu and colleagues  (33)  were reanalyzed. Wild-type fractured hindlimbs between knee and ankle were collected free of skin followed by RNA extraction at day 2 (n = 3) and day 7 (n = 4) and from uninjured limbs (n = 4) using Trizol (Invitrogen, Carlsbad, CA, USA). Microarrays were obtained using Agilent Mouse single-color 4 Â 44 K arrays (Agilent Technologies, Santa Clara, CA, USA). Microarray feature extraction was performed using Agilent's Extraction 9. 1 (Agilent Technologies). (33) Gene set enrichment analysis (GSEA) was performed using all normalized probes on "curated gene set" and "ontology gene set" collections of the Molecular Signatures Database v7 with gene sets between 15 and 5000 genes, 1000 permutations, FDR <0. 25 and p value <0.
Single-cell RNAseq analyses For skeletal muscle-derived muMPs, datasets from Julien and colleagues  (2)  were reanalyzed. Briefly, Prx1-derived skeletal muscle cells were isolated directly by enzymatic and mechanical digestion of skeletal muscles surrounding the tibia from Prx1 Cre ; Rosa mTmG uninjured mice, and at day 3 and day 5 post-tibial fracture. Two mice were used per sample and only skeletal muscles adjacent to the fracture site were dissected. For PC scRNAseq, uninjured cells were isolated from three mice (ie, six uninjured tibias) by explant culture, and d3 post-fracture cells were isolated from five mice (ie, five injured tibias) as described. (10) PCs were then subjected to scRNAseq at passage 0 without further in vitro cell expansion. No specific analysis of the between-animal variance was conducted due to the design of the experiment.
Data analyses Seurat v4. 0. 1 and RStudio v1. 3. 1073 were used for analysis of scRNA-seq data. (34, 35) s described in Julien and colleagues,  (2)  for muMPs, cells expressing between 350 and 8000 genes and expressing less that 20% of mitochondrial genes were retained for analysis, genes expressed in less than three cells were excluded from the analysis. For PCs, cells expressing between 100 and 8000 genes and expressing less that 10% of mitochondrial genes were retained for analysis. Genes expressed in less than three cells were excluded from the analysis. After quality control, 4458 uninjured PCs, 15726 PCs at d3, 4013 uninjured muMPs, 5313 muMPs at d3, and 1449 muMPs at d5 post-fracture were retained for the analysis. Normalization was performed using sctransform pipeline to integrate datasets and raw counts were log normalized and scaled for gene expression.
All datasets were regressed on mitochondrial content. Clustering was performed using the first 20 principal components and a resolution of 0. 6 for muMPs, and the first 25 principal components and a resolution of 0. 5 for PCs. The number of principal components was determined using the ElbowPlot function of Seurat package. Differentially expressed genes were determined using Wilcoxon rank sum test with p value <0. 05. Gene ontology (GO) analyses were done using differentially upregulated genes and implemented in Enrichr interface (https://amp. pharm. mssm. edu/Enrichr/). (36) GO functions including less than five genes and with adjusted p value >0. 05 were excluded. GO functions were classified into manually annotated general functions and the number of GO terms per general function was plotted.
Periosteal cell response to bone injury at single-cell resolution To characterize the cellular response of PCs to fracture, we performed scRNAseq analyses of PCs isolated at d3 post-fracture from Prx1 Cre ;Rosa mTmG mice, and integrated uninjured and d3 post-fracture datasets (Fig. 3A ). In addition to the stem/progenitor, macrophage and osteoclast populations described at steady state (Fig. 2 ), we identified neutrophils expressing Ngp and Elane, fibrochondro progenitors (FCPs) expressing Col2a1 and Postn, and fibroblasts expressing S100a4 and Tpm2 (Figs. 3B-D and S3A,B, Table  S3 ). Prx1-driven GFP expression was mainly detected in the non-hematopoietic populations, ie, stem/progenitor, FCP, and fibroblast populations (Fig. S3C ). We then focused our analysis on these non-hematopoietic populations that form cartilage and bone in the callus.
PC and muMP response to bone injury is mediated by BMP signaling We then assessed the similarities in the molecular programs driving PC and muMP activation. Microarray datasets of uninjured, d2 and d7 post-fracture hindlimbs were reanalyzed. (33) We observed an overrepresentation of signaling pathways related to immune response such as Toll-like receptors (Toll-like R), chemokines, tumor necrosis factor (TNF), and interleukins, as well as Hedgehog (HH), platelet-derived growth factor receptor (PDGFR), epidermal growth factor (EGF), TGF, and BMP pathways at d2 post-fracture compared to uninjured samples (Fig. 5A, B ). This correlated with the enrichment in GO terms related to immune response (Fig. S5A, B ). At d7 post-fracture, GO terms related to immune response and HH, PDGFR, and EGF signaling pathways were downregulated, but not GO terms related to BMP signaling.
In parallel, GO terms related to metabolism, signal transduction, neurotrophin, and Wnt signaling pathways were upregulated (Fig. 5B ). This signature was associated with GO terms related to morphogenesis, skeletal development, and ECM secretion (Fig. S5C, D ). BMP signaling, defined as the mean expression of BMP receptors and effectors, was overexpressed at d2 and d7 post-fracture, suggesting a role in the early stage of repair (Fig. 5C ). In the PC and muMP scRNAseq datasets from Fig. 4 , we observed that BMP signaling was upregulated in FCPs at d3 and in activated muMPs at d3 and d5 post-fracture (Figs. 5D,E and S6). Immunostaining for phoshoSMAD1/5/9 confirmed that the BMP pathway is active in Prx1-derived periosteal and skeletal muscle cells at d3 post-fracture in vivo (Fig. 5F ).
Acknowledgments This work was supported by  Foundation de l'Avenir ,  ANR-18-CE14-0033 ,  NIAMS   R01 AR072707  to CColnot,  INSERM ATIP-Avenir  to MM. AJ and SP were supported by a PhD fellowship from  Paris University. The LabTech Single-Cell@Imagine is supported by the  Paris Region  and the " Investissements d'avenir" program 764  through the  2019 ATF funding -S same Filires PIA  (Grant  N 3877871 ) and the  Agence National de la Recherche  as part of the " Investment for the Future" program  ( Institut Hospitalo-Universitaire Imagine , grant  ANR-10-IAHU-01 ). We thank  C. Alms ,  R. Prota ,  A. Lermant ,  H. Mouigni  and  A. Henry  for technical assistance. Flow cytometry and cell sorting were performed at the  Flow Cytometry platforms of Imagine Institute  and IMRB. Single-cell RNAseq were performed at the  Genomic and Bioinformatic platforms of Imagine Institute.
( Figure legend continued from previous page. ) Left, UMAP projection of uninjured and d3 post-fracture datasets subclusterized for non-hematopoietic cells. Right, Split UMAP visualization of nonhematopoietic cells from uninjured and d3 post-fracture datasets. (F) Feature plot of stem/progenitor, fibrogenic, and chondrogenic lineage scores in the non-hematopoietic cells. (G) Percentage of subpopulations per sample. (H) Left, GO analyses of upregulated genes in FCP subpopulation. Middle, Radar chart of skeletal related functions. Right, signaling pathways enriched in GO analyses. d3 = day 3; FCP = fibrochondro progenitor; Fibro. = fibroblast; GO = gene ontology; Macro. = macrophage; Neutro. = neutrophil; Oc = osteoclast; PC = periosteal cell; SP = stem/progenitor; UMAP = uniform manifold approximation and projection.
To identify the source and to generally evaluate the Middle Eastern NMHC emission patterns, a state-of-the-art atmospheric chemistry model (EMAC, ECHAM5/MESSy for Atmospheric Chemistry)  18, 19  was used to simulate the concentrations along the route. As emission inventory input, we used the most recent version of the Emission Database for Global Atmospheric Research (EDGAR v4. 3. 2)  20, 21  , which was further upgraded to include gas flare emissions and geothermal sources (see the "Methods" section). The observed ethane mixing ratios were reproduced by the model for most of the route (Fig. 1 ), indicating that emission sources and atmospheric processes in the Middle East region are generally well understood. Significant model underestimations (Suez Canal, northern Arabian Gulf) and overestimations (Gulf of Oman) occurred for short periods only during the first leg of the route, suggesting local, small-scale inconsistencies in the emission sources.