dataesr/scientific-paragraphs-categorization huggingface dataset:
Comparison with FSS We compare our symmetric quadrangulation results with the stateof-the-art method of Fields on Symmetric Surfaces (FSS) by  Panozzo et al. [2012]. In all of the following experiments, for computing the FSS results we used the cross eld output data provided by the authors. For generating our cross eld, we used as input the symmetry-map generated by their intrinsic symmetry computation method (using code provided by the authors), which results in a vertex-to-point in face mapping, and used the full hat basis unless otherwise noted. For both methods, we generated a quad mesh from the cross eld using MIQ and QEx, using the same parameters for both approaches. Behavior near the symmetry line. As discussed in Proposition 6 in  [Panozzo et al. 2012] , at the symmetry line the cross eld should either have a singularity, be aligned with the symmetry line, or form π /4 angle with the symmetry line.
Pushforward error evaluation. When given a pair of shapes with the same connectivity, we can provide a more accurate measurement of the consistency error related to our computed cross elds. To this end, we facilitate a decimated version (752 vertices) of the SCAPE dataset  [Anguelov et al. 2005 ]. We compute cross elds 1 and 2 on the template pose paired with each of the rst 50 poses. Then, using the ground-truth map di erential, we push the associated x 1 to M 2 In this example, we demonstrate the robustness of our method in the presence of imperfect correspondences. We compared the quad meshes we obtain when using maps with deteriorating quality (le to right) in the full basis (top row) and reduced basis (bo om row). While we achieve very good results with the exact mapping (top le ), the quad meshes produced with the noisy maps display only quasi-symmetry (top middle and top right).
Specically, we used the seamless mapping method  [Aigerman et al. 2015 ], and we generated approximately consistent quad meshes using the full basis (left) and the reduced basis (right). Notice that the resulting quadrangulations are qualitatively similar being slightly more consistent for the full map case. 16. We design consistent cross fields x 1 and x 2 , on pairs of shapes from the SCAPE dataset (α c =. 1, α l = 0), and we measure the pointwise L 2 error of the computed x 2 compared to dϕ (x 1 ) which is the pushforward of x 1 using the ground-truth map di erential. In the above plot, we show the distribution of the error for all of the pairs. Notice that in most of the cases, 80% of the points have an error of at most 10 -5. Genus 1 examples. In Fig. 1  (left), we show an example on a genus 1 model with intrinsic symmetry.
Notice that since the tail is attached to the head of the kitten, it is unclear in this model where exactly the symmetry line goes through, which makes it a stress test for many mapping techniques. Nevertheless, we were able to compute a high quality functional map, which allows us to generate an approximately consistent quad mesh which mostly respects the underlying symmetry. In addition, we tried a similar experiment on a pair of meshes from the FAUST dataset, where we "glued" the hands of one of the persons. Using a reduced functional map of size k = 50, we obtain compatible quad meshes, as can be seen in Fig. 18. Notice that the right leg is somewhat less consistent and it is due to the map which is only approximate. We show in the zoomed-in gures that the same singularity structure is maintained on both meshes, but it is twisted on the left person.
B A PRACTICAL OPTIMIZATION APPROACH In what follows, we re-formulate our minimization problem (7) as a standard quadratic programming optimization problem. Our analysis shows that the involved Hessian is composed of sparse term and a dense component, which is the product of a matrix and its transpose. Thus, we can facilitate MATLAB's quadprog with the trust-region-reflective method, allowing to solve a large and dense problem as long as its Hessian is structured. As the derivation for the case of a pair of shapes closely follows the single shape scenario, we omit the discussion of re-formulating the problem given in Eq. (  11 ). Recalling the smoothness and alignment terms, Eqs. (  1 ) and (  2 ), respectively, we observe that their associated Hessian matrices, H s and H l are extremely sparse.
Background: Skeletal muscle satellite (stem) cells are quiescent in adult mice and can undergo multiple rounds of proliferation and self-renewal following muscle injury. Several labs have profiled transcripts of myogenic cells during the developmental and adult myogenesis with the aim of identifying quiescent markers. Here, we focused on the quiescent cell state and generated new transcriptome profiles that include subfractionations of adult satellite cell populations, and an artificially induced prenatal quiescent state, to identify core signatures for quiescent and proliferating. Methods: Comparison of available data offered challenges related to the inherent diversity of datasets and biological conditions. We developed a standardized workflow to homogenize the normalization, filtering, and quality control steps for the analysis of gene expression profiles allowing the identification up-and down-regulated genes and the subsequent gene set enrichment analysis.
To share the analytical pipeline of this work, we developed Sherpa, an interactive Shiny server that allows multi-scale comparisons for extraction of desired gene sets from the analyzed datasets. This tool is adaptable to cell populations in other contexts and tissues. Results: A multi-scale analysis comprising eight datasets of quiescent satellite cells had 207 and 542 genes commonly up-and down-regulated, respectively. Shared up-regulated gene sets include an over-representation of the TNFα pathway via NFKβ signaling, Il6-Jak-Stat3 signaling, and the apical surface processes, while shared down-regulated gene sets exhibited an over-representation of Myc and E2F targets and genes associated to the G2M checkpoint and oxidative phosphorylation. However, virtually all datasets contained genes that are associated with activation or cell cycle entry, such as the immediate early stress response genes Fos and Jun.
An empirical examination of fixed and isolated satellite cells showed that these and other genes were absent in vivo, but activated during procedural isolation of cells. Conclusions: Through the systematic comparison and individual analysis of diverse transcriptomic profiles, we identified genes that were consistently differentially expressed among the different datasets and shared underlying biological processes key to the quiescent cell state. Our findings provide impetus to define and distinguish transcripts associated with true in vivo quiescence from those that are first responding genes due to disruption of the stem cell niche.
To address this issue, it is necessary to generate comprehensive catalogs of gene expression data of myogenic cells across distinct states and in different conditions. Soon after their introduction two decades ago, highthroughput microarray studies started to be compiled into common repositories that provide the community access to the data. Several gene expression repositories for specific diseases, such as the Cancer Genome Atlas (TCGA)  [5] , the Parkinson's disease expression database ParkDB  [6] , or for specific tissues, such the Allen Human and Mouse Brain Atlases  [7, 8]  among many, have been crucial in allowing scientists the comparison of datasets, the application of novel methods to existing datasets, and thus a more global view of these biological systems. In this work, we generated transcriptome datasets of satellite cells in different conditions and performed comparisons with published datasets.
Due to the diversity of platforms and formats of published datasets, this was not readily achievable. For this reason, we developed an interactive tool called Sherpa (SHiny ExploRation tool for transcriPtomic Analysis) to provide comprehensive access to the individual datasets analyzed in a homogeneous manner. This web server allows users to (i) identify differentially expressed genes of the individual datasets, (ii) identify the enriched gene sets of the individual datasets, and (iii) effectively compare the chosen datasets. Sherpa is adaptable and serves as a repository for the integration and analysis of future transcriptomic data. It has a generic design that makes it applicable to the analysis of other transcriptome datasets generated in a variety of conditions and tissues. We analyzed gene expression profiles (GEPs) of activated and quiescent states of mouse satellite cells derived from three new experimental setups and six publicly available microarray datasets to define a consensus molecular signature of the quiescent state.
Gene expression profiles The microarray data compared activated satellite cells (ASCs) and quiescent satellite cells (QSCs) from different experiments. Table  1  describes the public datasets that were taken into account for the analysis with the GEO  [15]  (Gene Expression Omnibus) identifications, references, and sample distribution. The new mouse microarray datasets include the following comparisons: young adult Quiescent(adult)/Activated (postnatal day 8) and Quiescent [high/low]/D3Activated [high/low], and Fetal_-NICD [E17. 5/E14. 5]. Table  1  presents all sample details.
Specific primers for each gene were designed, using the Pri-mer3Plus online software, to work under the same cycling conditions. For each reaction, standard curves for reference genes were constructed based on six fourfold serial dilutions of cDNA. All samples were run in triplicate. The relative amounts of gene expression were calculated with RLP13 expression as an internal standard (calibrator). RT-qPCR primers used appear in Additional file 6: Table  S2.
Normalization, quality control, and filtering of GEPs Gene expression profiles (GEPs) were processed using standard quality control tools to obtain normalized, probeset-level expression data. For all raw datasets derived from affymetrix chips, Robust Multi-Array Average expression measure (rma) was used as normalization method using the affy and the oligo R packages  [20, 21]. All analyses were preferentially conducted at the probeset level. Probesets were annotated to gene symbol and gene ENTREZ using chip-specific annotations. For gene level results, the probeset with the highest expression variability was selected to represent the corresponding gene. Quality controls were performed on raw data using relative log expression (RLE) and Normalized Unscaled Standard Errors (NUSE) plots from the affyPLM R package  [22].
Sample distribution was examined using hierarchical clustering of the Euclidean distance and principal component analysis from the stats  [23]  and FactoMineR R packages  [24]  (see Additional file 1: Figure  S1  for the resulting plots for dataset Quiescent [high/ low]/D3Activated [high/low]). The resulting plots of the remaining datasets are not shown, but they presented similar trends, which can be explored through the interactive web server Sherpa.
Differential expression analysis Each dataset was individually analyzed to identify genes showing significant differential expression (DEGs) between the ASC and the QSC (gene level analysis in Fig. 1 ; differential analysis in Fig. 2 ). This analysis was performed using the linear model method implemented in the Limma R package  [25]. The basic statistic was the moderated t-statistic with a Benjamini and Hochberg's multiple testing correction to control the false discovery rate (FDR)  [26].
Gene set enrichment analysis on individual sets Each dataset was tested for gene set enrichment independently, using the CAMERA competitive test implemented in the Limma R package  [27]  and three gene set collections from the mouse version of the Molecular Signatures Database MSigDB v6  [28, 29] : (1) Hallmark gene sets (H), which summarize and represent specific well-defined biological states or processes displaying a coordinate gene expression; (2) Kyoto Encyclopedia of Genes and Genomes (KEGG) canonical pathways (C2 CP:KEGG), derived from the Kyoto Encyclopedia of Genes and Genomes  [30] ; and (3) Reactome canonical pathways (C2 CP:Reactome) from the curated and peer reviewed pathway database  [31]  (gene set analysis in Figs. 1  and 2 ).
Multiple set analysis: determination of the quiescent signature The combinatorial landscape of datasets was explored using the SuperExactTest  [32]  and the UpSetR  [33]  R packages to test and visualize the intersection of the datasets. Additionally, the Jaccard index  [34]  of similarity was calculated to assess the extent of similarity between statistically differentially expressed genes (DEGs) of each pair of datasets. A significance ranking, based on several criteria, was calculated for each individual dataset to determine its presence or absence in the final dataset ensemble, which was used for determining the gene signature. Once the dataset ensemble was defined, the overlapping differentially up-and down-regulated genes Fig. 1  General framework of the analysis: an individual dataset analysis followed by a multi-set analysis.
The individual dataset analysis consisted of (i) the analysis of gene expression profiles (GEPs) of each dataset, including normalization, filtering and quality control check of each raw dataset, and the differential analysis to identify dataset-specific differentially expressed genes (DEGs), (ii) the Gene Set Enrichment Analysis (GSEA) performed in the gene set space. The GSEA consisted in identifying enriched pathways from three gene sets of the MSigDB collection  [29]  (Hallmark gene sets, CP: KEGG gene sets and CP: Reactome gene sets); (iii) the multi-set analysis to assemble a study-independent gene signature, i. e. , a list of genes specific to the quiescence state (DEGs, as defined by the adjusted P value ≤ 0. 05) were used to build the quiescent signature.
Gene set enrichment analysis on the quiescent signature An over-representation analysis (ORA)  [35]  was applied to the quiescent signature using the previously described gene collection (Hallmark, Kegg, Reactome). For this purpose, commonly up-regulated or down-regulated genes were used in a one-sided Fisher's exact test implemented in R script with a Benjamini and Hochberg's multiple testing correction of the P value to determine the enriched gene sets and the direction of such enrichment.
Results This study involves an individual dataset analysis followed by a multi-set analysis (Fig. 1 ). First, each raw dataset was normalized, filtered, and subjected to the same quality controls and checks. Gene-level differential analysis and gene set enrichment analysis were then performed (Fig. 2 ). Finally, a multi-set analysis assembled a platformindependent list of genes specific to the quiescent state. When analyzing multiple microarray GEPs, however, several issues needed to be addressed regarding the experimental setup, the microarray platforms and the laboratory conditions  [37]. First, the individual studies, even if related, had different aims, experimental designs, and cell populations of interests (e. g. , developmental stage and gender of mice). Second, the different microarray platforms contained different probes and probesets with specific locations and alternative splicing that might produce different expression results  [38].
Finally, sample preparation, protocols, and dates of extractions might have influenced array hybridization and introduced bias [39]. This experimental heterogeneity required critical data processing to ensure statistically meaningful assumptions to drive biological interpretation and compile gene signatures. For this, we used a standardized workflow to reduce the technical variations between datasets. Specifically, this workflow applied (i) the same normalization method for the experiments having the same microarray chips, (ii) the same quality control criteria to discard poor-quality samples, (iii) the same aggregation method for summarizing probesets into single genes, and (iv) the same filtering in all datasets. The filtering of the datasets was based on the same significance criteria which included a minimum number of differentially expressed genes, the presence of genes known to be differentially expressed between quiescent and activated states from previous studies, and a similarity measure among the datasets.
Statistically, differentially expressed genes (DEGs) were identified between the ASC and the QSC groups using the linear model implemented by the Limma R package  [10]. Gene set enrichment analysis was based on three gene set collections from the mouse version of the Molecular Signatures Database MSigDB v6. 0  [12, 13] : (1) Hallmark, which summarizes and represents specific well-defined biological states or processes displaying a coordinate gene expression; (2) KEGG canonical pathways, derived from the Kyoto Encyclopedia of Genes and Genomes  [14] ; and (3) Reactome canonical pathways from the curated and peer-reviewed pathway database  [15]. To test for the enrichment of these gene sets, the competitive gene set test CAMERA  [16]  was used this study, as well as the technical differences present in the datasets.
Three new sets of microarrays of quiescent versus activated satellite cell are reported here (see Table  1 ). The first one is part of a developmental and postnatal series that was reported previously  [16]  (E12. 5 vs. E17. 5), and here, P8 (postnatal day 8, in vivo proliferating) and 4-5 week old (quiescent) mice were compared. The second one is based on previously reported differences in quiescent and proliferating cell states in subpopulations of satellite cells (quiescent: dormant, top 10% GFP+ cells vs. primed, bottom 10% GFP+ cells isolated from Tg:Pax7-nGFP mice; proliferating: 3 days postinjury  [3] ). The third dataset is based on previous observations that the Notch intracellular domain (NICD) when expressed constitutively (Myf5 Cre : R26 stop-NICD ) in prenatal muscle progenitors leads to cell-autonomous expansion of the myogenic progenitor population (Pax7+/Myod-) and the absence of differentiation, followed by premature quiescence at late fetal stages (E17.
5) [16]. Here, E17. 5 (quiescent) and E14. 5 (proliferating) prenatal progenitors were compared. Except for our datasets Quiescent(adult)/Activated(P8) and Fetal_NICD[E17. 5/E14. 5], all the studies were conducted on adult mice (male and female) with ages ranging from 8 weeks to 6 months. While all datasets shared similar cell states (quiescent (QSC) and activated (ASC) satellite cells), the experimental procedures varied between studies. Activation of cells, for instance, was achieved in different ways: (i) in vitro, by culturing freshly isolated satellite cells for several days and (ii) in vivo, by extracting ASCs from an injured muscle. Furthermore, for in vivo activation, several techniques were used to induce the injuries-BaCl 2 , or the snake venoms cardiotoxin or notexin. Cell extraction protocols also varied among the different studies: (i) using transgenic mice expressing a reporter gene that marks satellite cells (several alleles) or (ii) using a combination of antibodies targeting surface cell antigens specific to satellite cells (several combinations, see Table  1 ).
The number of differentially expressed genes varies significantly among different datasets A total of 32 samples from ASCs and 34 samples from QSCs from the nine datasets were analyzed. After the quality control, one sample from the GSE38870 dataset was considered to be an outlier and was not included in the final analysis. The number of significantly up-and down-regulated genes (DEGs) resulting from the differential expression analysis of the quiescent with respect to the activated states were calculated (Additional file 5: Table  S1 ). DEGs were identified as having |logFC| ≥ 1 and a false discovery rate FDR ≤ 0. 05. The statistical analysis was performed at the probeset level, and only those probesets matching to genes are reported. On average, the datasets exhibited 1548 up-regulated genes with a standard deviation of 1173 genes.
The number of down-regulated genes corresponded to 2122, with a standard deviation of 1658 genes. The lowest number of DEGs belonged to the Fetal_NICD[E17. 5/E14. 5] dataset (39 up, 136 down), while the highest number of DEGs belonged to the GSE70376 dataset (4367 up, 6346 down). Additionally, an analysis of the distribution of the logFC across the datasets revealed that there were significant differences among the ranges and shapes of such distributions for each dataset (Additional file 2: Figure  S2 ).
Gene set level analysis reveals common underlying biological processes across the datasets Despite the great difference among the number of DEGs for the different sets, clear trends among the significantly enriched pathways were found (Fig. 3a ). This heatmap shows each dataset as a column and each enriched gene set as a row. The gene set collection that was tested for enrichment corresponds to the Hallmark gene set collection from MSigDB  [40]. Enriched gene sets corresponding to overexpressed genes are shown in red, while enriched gene sets that were generally abundant in under-expressed genes are shown in blue. Out of the 11 datasets, GSE38870 stood as an outlier for both over-and under-represented gene sets compared to the rest. For the other ten datasets, most of them showed an enrichment in the quiescent state for the TNFA_SIGNALING_VIA_NFKB pathway (nine datasets), while eight datasets were enriched in UV_RESPONSE_DN, IL6_JAK_STAT3_SIGNALING, APICAL_SURFACE, and KRAS-SIGNALING_DN pathways.
Similarly, the ten datasets shared similar trends for under-expressed genes in the pathways MYC_TARGETS_V1, E2F_TARGETS, G2M_ CHECKPOINT, and OXYDATIVE_PHOSPORYLATION, all of which are expected to be absent in the quiescent state. In total, two subnetworks corresponding to 8 under-and 15 over-expressed enriched gene sets could be distinguished (Fig. 3b ). A network representation of the top 3 most commonly found enriched gene sets (nodes, thickoutlined circles) is shown in Fig. 3b  for the over-expressed (TNFA_SIGNALING_VIA_NFKB, UV_RESPONSE_DN, I L6_JAK_STAT3_SIGNALING) and under-expressed (MY C_TARGETS_V1, E2F_TARGETS, G2M_CHECKPOINT) categories. The size of each node corresponds to the total number of times that the gene set was enriched in all the datasets, and the thickness of the interconnecting lines is proportional to the number of genes shared between connected nodes.
Determining a quiescent transcriptional signature among all datasets To determine a consensus quiescent signature from the datasets, we compared the genes found to be differentially expressed within each dataset, in order to identify genes commonly up-or down-regulated in the quiescent state. Although the aforementioned technical and experimental heterogeneity could introduce noise in this analysis, such variation was distinguishable from the more stable, underlying common quiescent signature. Given that the distribution and ranges of the logFCs varied so drastically between datasets (Additional file 2: Figure  S2 ), a single FC (fold change) threshold could not be chosen to be used for all datasets. Thus, for the combinatorial analysis approach, we set out to maximize the number of differentially expressed genes common to all the datasets that were considered, where only the adjusted P value was used as a threshold to define DEGs.
However, even in this low constrained scenario, combining all the datasets together resulted in very few overlapping genes: 12 up (Arntl, Atf3, Atp1a2, Cdh13, Dnajb1, Enpp2, Ier2, Jun, Nfkbiz, Rgs4, Usp2, Zfp36) and 1 down (Igfbp2). Alternatively, when certain datasets were excluded from the analysis, the number of DEGs increased (Fig. 4a ).