dataesr/scientific-paragraphs-categorization huggingface dataset:
Gene-based association meta-analyses For the gene-based analyses, we applied two different sets of criteria to select variants, based on coding variant annotation from five prediction algorithms (PolyPhen2 HumDiv and HumVar, LRT, Mutation Taster and SIFT)  42. The mask labeled "broad" included variants with a MAF <0. 05 that are nonsense, stop-loss, splice site, as well as missense variants that are annotated as damaging by at least one program mentioned above. The mask labeled "strict" included only variants with MAF <0. 05 that are nonsense, stop-loss, splice site, as well as missense variants annotated as damaging by all five algorithms. We used two tests for gene-based testing, namely the SKAT  43  and VT  44  tests. Statistical significance for genebased tests was set at a Bonferroni-corrected threshold of P<5×10 -7 (threshold for 25,000 genes and four tests).
In visualizing the analysis, we used affinity propagation clustering  47  to group the most similar reconstituted gene sets based on their gene memberships (see Supplementary Information). Within a "meta-gene set", the best P-value of any member gene set was used as representative for comparison. DEPICT for ExomeChip was written using the Python programming language and the code can be found at https:// github. com/RebeccaFine/height-ec-depict. We also applied the PASCAL pathway analysis tool  16  to association summary statistics for all coding variants. In brief, the method derives gene-based scores (both SUM and MAX statistics) and subsequently tests for the over-representation of high gene scores in predefined biological pathways. We used standard pathway libraries from KEGG, REACTOME and BIOCARTA, and also added dichotomized (Z-score>3) reconstituted gene sets from DEPICT  15.
Following 1 h incubation at 37°C, reactions were terminated by the addition of SDS-PAGE sample buffer supplemented with 25 mM EDTA. Substrate and co-migrating cleavage products were separated by 12% nonreducing SDS-PAGE and visualized by autoradiography using a storage phosphor screen (GE Healthcare) and a Typhoon imaging system (GE Healthcare). Band intensities were quantified using ImageQuant TL 8. 1 software (GE Healthcare). Western blotting-STC2 and covalent complexes between STC2 and PAPP-A were blotted onto PVDF membranes (Millipore) following separation by 3-8% SDS-PAGE. The membranes were blocked with 2% Tween-20, and equilibrated in 50 mM Tris-HCl, 500 mM NaCl, 0. 1% Tween-20, pH 9 (TST). For STC2, the membranes were incubated with goat polyclonal anti-STC2 (R&D systems, AF2830) at 0.
Extended Data Figure  4. Concordance between direct conditional effect sizes using UK Biobank (x-axis) and conditional analysis performed using a combination of imputation-based methodology and approximate conditional analysis (SSimp, y-axis). The Pearson's correlation coefficient is r=0. 85. The dashed line indicates the identity line. The 95% confidence interval is indicated in both directions. Red, SNPs with P cond >0. 05 in the UK Biobank; Green, SNPs with P cond ≤0. 05 in the UK Biobank. Extended Data Figure  5. Heritability estimated for all known height variants in the first release of the UK Biobank dataset. (A) We observed a weak but significant positive trend between minor allele frequency (MAF) and heritability explained (P=0. 012). (B) Average heritability explained per variant when stratifying the analyses by allele frequency or genomic annotation.
The proteoglycan binding pathway was uniquely implicated by coding variants (as opposed to common variants) by both DEPICT and the Pascal method. To visually reduce redundancy and increase clarity, we chose one representative "meta-gene set" for each group of highly correlated gene sets based on affinity propagation clustering (see Methods and Supplementary Information). Heat map intensity and DEPICT p-values correspond to the most significantly enriched gene set within the meta-gene set; meta-gene sets are listed with their database source. Annotations for the genes indicate whether the gene has OMIM annotation as underlying a disorder of skeletal growth (black and grey) and the minor allele frequency of the significant EC variant (shades of blue; if multiple variants, the lowestfrequency variant was kept).
Annotations for the gene sets indicate if the gene set was also found significant for EC by the Pascal method (yellow and grey) and if the gene set was found significant by DEPICT for EC only or for both EC and GWAS (purple and green). Abbreviations: GO: Gene Ontology; KEGG: Kyoto encyclopedia of genes and genomes; MP: mouse phenotype in the Mouse Genetics Initiative; PPI: protein-protein interaction in the InWeb database. Extended Data Figure  8. Heatmaps showing associations of the height variants to other complex traits; -log10(Pvalues) are oriented with beta effect direction for the alternate allele, white are missing values, yellow are non-significant (P>0. 05), green to blue shading for hits with positive beta in the other trait and P-values between 0. 05 and <2×10 -7 and, orange to red shading for hits with negative beta in the other trait and P-values between 0.
Annotations for the genes indicate whether the gene has OMIM annotation as underlying a disorder of skeletal growth (black and grey) and the minor allele frequency of the significant ExomeChip (EC) variant (shades of blue; if multiple variants, the lowest-frequency variant was kept). Annotations for the gene sets indicate if the gene set was also found significant for EC by PASCAL (yellow and grey) and if the gene set was found significant by DEPICT for EC only or for both EC and GWAS (purple and green). Abbreviations: GO: Gene Ontology; MP: mouse phenotype in the Mouse Genetics Initiative; PPI: protein-protein interaction in the In Web database.
Numerical results We focus on this SQG M U model (3. 3). A high-resolution deterministic SQG simulation provides a reference. The MATLAB R codes are available online (http://vressegu. github. io/sqgmu). Numerical results are analyzed in terms of the resolution gains (when a single realization is simulated) and the potential for ensemble forecasting in estimating spatial and spectral reconstruction errors (for an ensemble of realizations).
A MATLAB R code simulating the SQG M U model is available online (http://vressegu. github. io/sqgmu). As a discussion, we can address the problem of uncertainty quantification (UQ) of an unresolved dynamics from an opposite point of view as the usual setting. Instead of specifying a form for the sub-grid velocity, we can wonder what is the optimal form of SPDE for UQ in fluid dynamics. As demonstrated, randomization of initial conditions is far from being sufficient to quantify uncertainty. Therefore, a random forcing is needed to inject randomness at each time step. The simplest choice is a forcing uncorrelated in time. Otherwise, additional stochastic equations need to be simulated to sample a time-correlated process. This is not desirable in high dimension and the correlation time of the process is often small anyway  (Berner et al.
As illustrated in Fig. 1 , chromosome structural organisation can involve nested structures over a large range of scales  [22, 29]. However only the method proposed in  [31]  explicitly includes the possibility to identify chromosome structural domains at diverse scales of observation and the method in  [29]  to hierarchically merge adjacent TADs into metaTADs. Here we propose a novel method to analyse Hi-C data that allows a multi-scale identification of structural domains. Because it does not rely on the specific assembly of the reference genome, this method does not look for structural domains limited to chromosome intervals thereby relaxing our preconception about the nature of structural domains. Moreover, due to polymorphisms within a species or to chromosome rearrangements characteristic of cancer cells  [35] , the assembly of the reference genome does not necessarily corresponds to the true assembly for a cell line under investigation.
Chromatin conformation capture data and topologically associating domains Here we used Hi-C data obtained in different human cell lines: • Embryonic stem cell line H1 (H1 ES) and foetal lung fibroblast cell line IMR90 Hi-C data for which TADs are available  [11] , allowing a direct comparison of our structural communities with what is considered as reference structural domains in the literature. Hi-C matrices at resolution 20 kb and 40 kb for two replicates in each cell lines as well as TADs predictions in these cell lines were downloaded from the GEO database under accession number GSE35156. These data are based on the hg18 assembly version of the human genome. • Myelogenous leukemia cell line K562 and lymphoblastoid cell line GM06990 Hi-C data  [10]  for the analysis of the structural conservation between cell lines.
Hi-C matrices at resolution 100 kb for the two cell lines were downloaded from the GEO database under accession number GSE18199. These matrices are based on the hg18 assembly version of the human genome. • Cervical cancer cell line HeLaS3 Hi-C data  [19]  where the Hi-C experiments were performed on synchronised cells during mitosis and G1 allowing a study of the community structure during the cell cycle. The Hi-C reads alignment files to the human genome (hg19 assembly version) for the two stages of the cell cycle were downloaded from the ArrayExpress database under accession number E-MTAB-1948. Hi-C intra-chromosomal co-localisation frequency matrices for non-overlapping 100 kb loci correspond to the downloaded matrices that were down-sampled to 100 kb when necessary or were constructed from the alignment files (Fig.
1 ). Unexpectedly low and unexpectedly high interacting loci that are likely to introduce noise were removed (Additional file 1: Table  S1 ). The remaining 100 kb loci were concatenated resulting in new masked positions. We compared the structural-communities described in this work to the TADs  [11]  that are considered as a reference for the structural description of Hi-C data. TADs were identified in H1 ES and IMR90 cell lines at both 20 and 40 kb resolutions  [11]. Given our adopted resolution of 100 kb, we used the TADs dataset obtained at the 40 kb resolution, and we assigned each TAD border to the corresponding 100 kb pixel keeping only TADs larger than 200 kb  (3 pixels). This led to a database of 2 993 (resp. 2 263) TADs in H1 ES (resp. IMR90), with 3 905 (resp. 3 096) distincts borders in H1 ES (resp.
IMR90). In this work one focus is to question the existence of a TAD-like structuration of the human genome in the intermediary scale range from the described TAD typical size up to the chromosome length. A second objective is to address the possible conservation of these structural motifs across cell lines. This led us to include the K562 and GM06990 datasets from the original Hi-C study  [10]. These datasets are less resolutive than more recent ones in IMR90 and H1 ES cell lines  [11]  due to a limited sequencing depth and were analysed at best at 100 kb resolution by the original authors. This explains why we chose 100 kb as the resolution for all the analysis presented in our manuscript. However to check whether lower or higher resolution has significant impact on the results, the IMR90 dataset was also analysed at resolutions 40 and 200 kb.
We used the fast implementation of the wavelet-based multi-scale community mining algorithm (Methods and Supplementary text: Graph wavelet transform and community mining in Additional file 1) with η = 200 random Gaussian functions to estimate the distance correlation matrix. For each Hi-C dataset, we considered the 22 autosomes' intra-chromosomal interaction networks constructed for non-overlapping 100 kb loci (Methods). We systematically applied the wavelet-based multi-scale community detection method to all the connected interaction networks scanning 100 scales logarithmically distributed in the range of available scales (Additional file 1: Equation (S13))  [40]. The average total running time per cell line was 5 h 40 mn using Matlab on a linux computing desktop with 8 Xeon CPU at 3. 30 GHz.
H1 ES) for the chromosome 12. When applied to the 6 Hi-C datasets considered (Methods), the methodology presented for human chromosome 12 in H1 ES and IMR90 resulted in few thousands interval-communities per dataset (Table  1 ), except for the mitosis HeLaS3 dataset (discussed below). Interestingly, the length distributions of the intervalcommunities for the IMR90, GM06990, K562 and HeLaS3 G1 datasets are very similar, but they display differences with the one obtained for H1 ES dataset for small interval-communities (Fig. 3b ): there are more intervalcommunities involving only 2-3 nodes (200-300 kb) in the 4 differentiated cell lines datasets and a deficit in interval-communities of length ∼ 500 kb to ∼ 1. 5 Mb relative to H1 ES. A possible interpretation of this excess of interval-communities of size ∼ 1 Mb in H1 ES, compared to differentiated cell lines, is that cell differentiation is accompanied by the merging of the small structural communities in a structural consolidation scenario.
For larger communities, the interval-community size distributions in these 5 Hi-C datasets are almost identical. Indeed, for 2 Mb, they display a power-law behaviour l α with α -1. 3 (Fig. 3b ). Note that if communities of length ∼ l would form a partition of the genome of length L, then the number of communities of this scale would be equal to L/l leading to α = -1 ( -1. 3). This underlines the existence of domains at all scales up to the chromosome length without a characteristic size for genome structuring.
Are interval-communities structural domains? To test the robustness of the wavelet-based community detection method with respect to the possible absence of a community structure over some range of scales, we compared the interval-communities obtained for the Hi-C datasets in synchronised HeLaS3 cells during G1 and M phase, respectively (Methods). The original study  [19]  showed that the highly compartmentalised organisation described before from non synchronous cells  [10, 11, 13, 15, 16, 20, 26, 27]  was restricted to interphase and that during a cell cycle, chromosomes transit from a decondensed and spatially organised state during interphase to a highly condensed and morphologically reproducible metaphase chromosome state. In the former phase, the Hi-C interaction maps display similar plaid patterns of regional enrichment or depletion of long range interactions (as the one shown in Fig.
1 ) while the maps in mitotic cells change and the plaid patterns disappear  [19]. For HeLaS3 G1 (resp. mitosis) dataset, we obtained 6 716 (resp. 1055) non trivial communities and 4 108 (resp. 885) distinct borders (Table  1 ). For the mitosis HeLaS3 Hi-C dataset, we obtained 1 059 communities from which we filtered out 4 resulting in 885 distincts borders (Table  1 ). Consistently with non synchronous cells, G1 cells present a hierarchical structure into intervalcommunities that increase in size across scales (Additional file 1: Figures  S6  and S7 ). Small scale singletons hierarchically group to form large interval-communities at larger scales. As discussed above, the length distribution of the G1 HeLaS3 interval-communities is similar to the interval-communities size distribution obtained in the 3 other differentiated cell line datasets (Fig.
6 in GM06990 and K562, to ∼ 2. 2 in H1 ES and ∼ 3 in IMR90. Over larger distances, the ratio remains rather constant in GM06990 and K562 and decreases to ∼ 1. 5 in H1 ES and IMR90 (Fig. 4 ). This property holds true even for communities larger than 10 Mb. As a comparison, we performed the same analysis for the original TAD datasets in H1 ES and IMR90 (Methods). Over the shared domain length range, the interaction ratio vs distance curves computed for the TAD datasets present very similar shapes as observed for interval-communities (Additional file 1: Figure  S9 ), reaching maximal values ∼ 3 in both H1 ES and IMR90. These results provide evidence that multi-scale interval-communities, very much like TADs, constitute units of 3D genome organisation bordered by structural barriers.
Are TADs interval-communities? We next compared our communities to the TADs previously described in H1 ES and IMR90  [11] , asking to which extent the TADs and TAD borders are recovered in our hierarchical database of interval-communities. The mean best mutual coverage vs TAD length curve (Methods) between TADs and interval-communities is slightly higher in H1 ES as compared to IMR90 for all TAD lengths (Fig. 5a ), ranging from 62% (resp. 52%) at small length (300-500 kb) to 91% (resp. ∼ 89%) at larger length (∼ 1-2 Mb) in H1 ES (resp. IMR90). This suggests a good recovery of the largest TADs by the interval-community classification. Given the 100 kb resolution used in this analysis, it is not surprising to observe lower mutual coverages at small lengths where 1 pixel error results in a dramatic lowering of mutual coverage.
We also observed that the proportion of TADs that have a matching structural community (Methods) increases with the domain length (Fig. 5b ). Only about 1/5 of the smallest TADs ( 500 kb) are recovered consistently with the fact that in this scale range a match has to be exact. For TADs longer than 1 Mb, the proportion of match is relatively high: in IMR90 it increases from 40% for TADs ∼ 1 Mb up to 70% for TADs ≥ 2 Mb and in H1 ES from 70% for TADs ∼ 1 Mb up to 85% for TADs of ∼ 2 Mb (Fig. 5b ). Comparison of TAD borders to interval-community borders shows good concordance for the two datasets (Fig. 5c ). For meaningful comparisons, we restricted the reference domain border set for each species to a subset of borders that at 100 kb resolution (±1 pixel) collectively cover no more than 35% of the genome.
To test the robustness of our methodology with regards to the binning resolution, we reproduced the analysis of the IMR90 data at a finer (40 kb, total running time 8h48mn) and a coarser (200 kb, total running time 31 mn) resolution (Additional file 1: Figure  S10 ). The lengths of interval-communities determined at these 2 resolutions nicely reproduce the distribution obtained at the 100 kb resolution (Additional file 1: Figure  S10A ). Intervalscommunities of size 1 -2 Mb strongly match between these intervals communities datasets (recovery proportion 70 -90%, Additional file 1: Figure  S10B ). For smaller community size, recovery proportion between datasets decreases with community size in the same manner for the 3 resolution pairs. This can be understood when noting that the isolation strength of community borders significantly weakens when decreasing the genomic distance below ∼ 1 Mb (Fig.
4 ). Finally, the proportion of TADs that have a match in the interval-community database is similar at 40 kb resolution than at 100 kb resolution (Additional file 1: Figure  S11 ). This demonstrates that the results do not depend on the choice of the 100 kb resolution and further underlines that the lower structural domain recovery rate generally observed for small domain sizes ( 1 Mb) is likely related to the weaker isolation strength of structural domain borders over short distances  ( 1 Mb).
Conservation of structural communities across cell lines In the pioneering study  [11] , TADs were described to be conserved between cell lines. We observed that interval-communities in different cell lines present similar size distributions (Fig. 3b ). This led us to investigate to which extent they are conserved across cell lines. To compare the communities obtained in different cell lines, we used each of the interval-community database obtained in H1 ES, GM06990, IMR90, K562, as a reference domain set and computed the proportion of matching interval-communities of the 3 other cell lines relative to this reference set (Methods). We observed that small interval-communities ( 600 kb) are not well conserved between different cell lines (Fig. 6 ). This might result from the fact that Hi-C data are average over cell populations and that some regions may present different structural organisations from cell to cell blurring the insulator property of structural domain borders at small scales.
However, when considering interval-communities of larger sizes, higher conservation was observed (Fig. 6 ). More than 60% of intervals-communities of length L 0. 6 Mb in the differentiated cell lines correspond to an interval-community in H1 ES (Fig. 6a ). H1 ES intervalcommunity dataset thus contains a large proportion of the interval-communities observed in the differentiated cell lines above ∼ 600 kb. When using one differentiated cell line interval-community database as reference, we observed a maximal recovery rate that is similar for the 3 other cell lines: 45% for sizes 2 Mb in IMR90, 65% for sizes 1. 5 Mb in GM06990 and 70% for sizes 1. 5 Mb in K562 (Fig. 6b, c  and d ). The observed differences likely reflect the excess of interval-communities in the size range 0. 5-1. 5 Mb observed in H1 ES relative to the differentiated cell lines (Fig.
3b ). As a comparison, we performed the same analysis for the TADs that were claimed to be conserved between H1 ES and IMR90 cell lines  [11]  (Additional file 1: Figure  S12 ). Like for intervalcommunities, the correspondance between TADs in the two cell lines decreases for domain sizes 600 kb. For larger domain sizes, we observed that H1 ES TAD dataset contains more (maximal value ∼ 60%) of the IMR90 TADs than the IMR90 TAD dataset contains H1 ES TADs (∼ 45%). These results corroborate the conservation of structural domains of length ∼1-2 Mb between cell lines in the 45-70% range but also extend this conservation to the largest interval-communities up to length 10 Mb.
Conclusions We introduced a fast multi-scale community mining algorithm based on spectral graph wavelets  [40]  to identify structural motifs from high-throughput chromatin conformation capture data (Hi-C)  [10]. Hi-C data were represented as intra-chromosomal interaction networks and structural motifs were delineated as communities of these networks. The novelty of this approach relies on the combination of a multi-scale procedure and a representation of the data that is independent of the exact assembly of the reference genome over length scales larger than the window size used to construct the interaction network. The proposed methodology has no a priori on the size and on the nature of the structural motifs. The application of this protocol to 6 Hi-C datasets led to a database of several thousands structural communities (Table  1 ).
The database of interval-communities in mitotic HeLaS3 cells that were described not to present a TAD-like structural organisation  [19] , does not contain any intermediary scale structural communities, illustrating the robustness of the proposed methodology with regards to the absence of structural motifs. Consistently with the recent usage of Hi-C data for genome sequence assembly  [47, 48] , we observed that structural-communities in unsynchronised and G1 cells form hierarchies of chromosome intervals of length ranging from the resolution (100 kb) to the chromosome lengths ( 10 Mb) (Fig. 3 ). The prevalence of interval-communities underlines that chromosome folding is mainly driven by interactions between neighbouring loci, at all scales of observation. This constitutes a justification that TAD-like structural motifs indeed correspond to chromosome intervals.
Funding This work was supported by  Centre national de la Recherche Scientifique (CNRS) ,  Ecole Normale Supérieure de Lyon (ENS de Lyon)  and  Agence National de la Recherche  ( ANR-14-CE27-0001  GRAPHSIP). BA acknowledges support from  Science and Technology Commission of Shanghai Municipality  ( 15520711500 ),  Fondation pour la Recherche Médicale  ( DEI20151234404 ) and  Agence National de la Recherche  ( ANR LightComb 2016-2018 ). The funding bodies had no role in the design of the study and collection, analysis, and interpretation of data and in writing the manuscript.