dataesr/scientific-paragraphs-categorization huggingface dataset:
g. ,  Peimbert 1971; Rubin 1989; Viegas & Clegg 1994; Cedrés et al. 2013 ). Here we use two different density diagnostics that we consider as lower and upper limits. For both calculations of M ion (Eqs. (  4 ) and (  5 )), we estimate the electron density n e,SII from the R [SII] using the Pyneb package  (Luridiana et al. 2015 ) and assuming T e = 8000 K. The electron density of the ionised gas in our regions is close to the low-density limit. Because of this, we are able to reliably measure it only for a limited sample of ∼20% of regions in which the observed R [SII] falls below the value of 1. 46 10  by at least 3σ (chosen to minimise the bias towards higher densities if R [SII] is underestimated because of the observational uncertainties). To use all the identified regions in the remainder of the analysis, we assume they have in general the same n e as their nearestneighbour H ii regions.
As a consequence of this, the total Hα luminosity (and thus the observed Hα flux) increases as the stellar association mass increases. This is often predicted by photoionisation models (e. g. , in Starburst99 among many others), and this correlation is also observed on the scale of individual H ii regions  (Scheuermann et al. 2023). Meanwhile, our results imply that this correlation is preserved also for the turbulent ionised gas around H ii regions and for superbubbles, whose properties are not necessarily the same as those of normal H ii regions (see  Sect. 4. 5). Given that the mass of the young stars and of the ionised gas (as well as E mech from the stars and E kin of the gas, respectively) are measured from unrelated data in a way independent of each other, we are confident that the correlation between these parameters is real and not a statistical effect.
We also show that the mechanical stellar feedback energy efficiency does not change with metallicity. However, our data are very limited for metallicities Z < 0. 5 Z. A further extension of this analysis to dwarf galaxies will allow us to establish a purely observational constraint on the efficiency of mechanical stellar feedback in various environments, which is a critical ingredient in cosmological simulations. These observations are associated with programme 15654. This research made use of astrodendro, a Python package to compute dendrograms of Astronomical data (http://www. dendrograms. org/). KK, OVE, EJW, JEM-D gratefully acknowledge funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) in the form of an Emmy Noether Research Group (grant number KR4598/2-1, PI Kreckel).
32 × R for various expansion velocities and spatial resolutions 17. We excluded all regions having an axis ratio less than 0. 35 (chosen based on visual inspection of the results obtained with the different parameters). Even if real, such elongated regions may add significant scatter to the further analysis because of the uncertainties of their size measurements. 17 We used sdss5-lvmdatasimulator package (https://github. com/sdss/lvmdatasimulator) for doing this analysis as it allows one to easily construct such toy models with various parameters and numbers of spatial resolution elements across the nebula and obtain the simulated IFU spectra for them. Where possible, we refined the sizes of the elliptical regions identified by astrodendro. We considered the oversampled radial Hα flux distribution for each region.
Acknowledgements. This work was carried out as part of the  PHANGS  collaboration. Based on observations collected at the  European Southern Observatory  under ESO programmes  094. C-0623  (PI:  Kreckel ),  095. C-0473 ,  098. C-0484  (PI:  Blanc ), 1100. B-0651  ( PHANGS-MUSE ; PI: Schinnerer), as well as  094. B-0321  (MAGNUM;  PI: Marconi ),  099. B-0242 ,  0100. B-0116 ,  098. B-0551  (MAD; PI:  Carollo ) and  097. B-0640  (TIMER; PI: Gadotti). This research is based on observations made with the  NASA/ESA Hubble  Space Telescope obtained from the  Space Telescope Science Institute , which is operated by the  Association of Universities for Research in Astronomy, Inc. , under  NASA  contract  NAS 5-26555. A153 , page 21 of 31.
Results: We perform a computational benchmark to assess the impact of experimental parameters and data analysis pipelines on the ability of the cell representation to recapitulate known biological similarities. We run more than ten thousand experiments to systematically study the impact of coverage and number of cells, of the count matrix construction method, of feature selection and normalization, and of the dimension reduction algorithm used. This allows us to identify key experimental parameters and computational choices to obtain a good representation of single-cell HPTM data. We show in particular that the count matrix construction step has a strong influence on the quality of the representation and that using fixed-size bin counts outperforms annotation-based binning. Dimension reduction methods based on latent semantic indexing outperform others, and feature selection is detrimental, while keeping only high-quality cells has little influence on the final representation as long as enough cells are analyzed.
The analysis of more than 10,000 computational experiments allows us to clarify the impact of various experimental choices and data processing factors for scHTPM data and to suggest practical guidelines. To quantify the impact of each of these factors, we use neighbor scores-based on the comparison of epigenomic and transcriptomic embeddings when possible-as well as Adjusted Mutual Information (AMI) or Adjusted Rand Index (ARI) to compare to reference labels. For two single-cell multi-omics datasets, in addition to scHPTM, a second modality is measured for each cell (gene expression or cell surface proteins); in this case, we can assess neighbor score, i. e. , how well the cellto-cell similarity observed with scHPTM data analysis agrees with the one inferred from the co-assay (RNA or protein)  [18, 19].
Going from the mapped read to a vector representation for each cell involves a number a steps that we investigate in this study (Fig. 1A ), including (1) the binning of the mapped reads into genomic regions in order to create a cell×region count matrix to summarize the raw data, (2) various quality control (QC) preprocessing operations to filter out low-quality cells and regions, and (3) an embedding method to build the representation of each cell from the preprocessed count matrix. Each step can be performed in many different ways, and we propose a benchmark to assess the impact of each choice at each step on the final cell representation (Fig. 1 ). In order to evaluate the impact of each decision on the quality of the final representation, we need reference datasets and a way to quantify the quality of that representation.
A standard approach to measure this is to evaluate the performances of clustering algorithms on these representations (such as in  [13] ). This approach requires cell type annotations, which can either be computationally derived or experimental (e. g. , through cell lines or FACS). scHPTM protocols being rather recent, datasets with experimental labels are rare; here, we use the dataset from  [11] , with treated or untreated breast cancer cells as experimental labels. In addition, due to this lack of sufficient ground truth reference datasets for scHPTM analysis, we also rely on two datasets produced with multiomics co-assays (Table  1 ), where two modalities are measured simultaneously in each cell. More precisely, we consider a mouse brain dataset from  [9]  where five histone marks (H3K4m1, H3K4me3, H3K9me3, H3K27ac, and H3K27me3) are assessed by scHPTM jointly with scRNA-seq-based gene expression, and a human peripheral blood mononuclear cell (PBMC) dataset from  [10]  where the same five histone marks are assessed by scHPTM jointly with CITE-seq-based cell surface proteins.
For both datasets, we use a unique representation of the second modality (respectively, scRNAseq and CITE-seq) using a well-established method as a reference (scanpy's  [21]  implementation of PCA) and compare each representation obtained from the scHPTM data to that reference. We compute a neighbor score that assesses to what extent neighbor cells in the scHPTM representation are also found neighbors in the reference representation of the second modality. The neighbor score varies between 0 when both representations disagree completely to 1 when both representations are identical (see Methods and Fig. 1B ). This evaluation has been previously used in  [18, 19]  and is currently the standard for evaluating modality alignment tasks in recent community benchmarks such Fig. 1  Overview of the evaluation protocol.
A We build the count matrix using different bin sizes as well as a GeneTSS annotation and peaks called on the pseudo bulk with both MACS2 and SICER (only for the human PBMC dataset), for the MDA-MB468 dataset we also used author provided annotations. We then simulate in silico different experimental conditions for studying the role of the number of cells in a dataset, and the effect of the coverage per cell, as well as different feature selection strategies. Afterwards, we run 9 different dimension reduction methods to obtain the cell representations. B In order to compute the neighbor score, we start by selecting a cell, we then build the kNN graph for a value of k (5 in the figure), and we then compute the size of the intersection between the neighborhood of the cell in the two embeddings (3 cells in the figure) and divide it by k to obtain the score for one cell and one value of k (score of 0.
6 in the figure). We then compute and average this score over all the cells, to have an neighbor score for a given value of k; that score is then further averaged over different values of k (0. 1%, 0. 3%, 0. 5%, 1%, 3%, 5%, and 10% of the number of cells in the experience) to obtain the final neighbor score as https:// openp roble ms. bio/. We furthermore use the initial labels from authorscomputationally derived-to evaluate representations with ARI and AMI. For each dataset and each histone PTM mark, we systematically vary the choices that we can make in each step of the computational pipeline that goes from the mapped reads to the scHPTM representation of each cell and measure the quality of the final representation with the neighbor score to assess the impact of the choices. More precisely, for the first step that bins mapped reads to regions in order to build a first cell×region count matrix, we consider three different strategies that represent the various approaches used in practice for the analysis of single-cell epigenomic assays: (1) discretizing the whole genome into "bins" of fixed size and trying different sizes following a logarithmic progression between 5 kbp and 1000 kbp, (2) counting the reads into bins based on prior biological knowledge, i.
e. , on genes and transcription start sites annotations (GeneTSS), and (3) counting the reads into a set of peaks, characteristic of each cell population found in the sample (identified from the corresponding pseudo bulk using MACS2  [22] , "MacsPseudoBulk, " or SICER  [23] , "SicerPSeudoBulk"). This last approach was only performed with the human PBMC dataset that is distributed in a format that allows us to build the pseudo bulk and use it for peak calling. With these matrices, we attempt different feature selection approaches to select only a subset of genomic regions to keep for further analysis: (1) selection of highly variable regions using Seurat's  [24]  FindVariableFeatures function (variable features) and (  2 ) selection of regions with the highest coverage (top features). The first feature selection method is the current standard in scRNA-seq, and the second approach is recommended in Signac  [25]  for analyzing scATAC-seq.
TF-IDF-based methods outperform other methods We first focus on the influence of the embedding methods on the quality of the final representation. The nine methods we selected implement a broad range of algorithms that are currently used for the analysis of scATAC-seq and scHPTM data. More precisely, ChromSCape_PCA is a simple use of PCA after count per million (CPM) normalization, which serves as baseline. ChromSCape_LSI and Signac implement two variants of the latent semantic indexing (LSI) algorithm, which consists in transforming the count matrix with TF-IDF and applying PCA on that matrix. They have been used to analyze scHPTM data  [10, 29] , and differ in the fact that ChromSCape_LSI weights the principal components by their eigenvalues, as is standard to do with PCA, while Signac does not and instead whitens the data representation.
They implement variants of the algorithm used in Cusanovich2018  [30] [31] [32] , which was found with SnapATAC and cisTopic to be among the best methods for scATAC-seq data analysis in  [12]. NMF has also been used in combination to TF-IDF to analyze single-cell datasets, in scOpen  [33]. SnapA-TAC computes the Jaccard similarity between all the cells, and runs kernel PCA on this similarity matrix. cisTopic binarizes the count matrix and then applied latent Dirichlet allocation (LDA) on this modified matrix. Finally, SCALE and PeakVI both implement a variational autoencoder (VAE) with a product of Bernoulli likelihood function. They differ in the fact that SCALE uses a mixture of gaussian prior where PeakVI uses a unimodal gaussian prior. Furthermore, PeakVI computes corrections for the size factor of each cell as well as for the accessibility of each DNA region.
We run all methods with their default parameters (see Methods). In particular, we keep the default number of dimensions for all methods; indeed, some methods offer their own heuristics for deciding the number of dimensions, and we did not want to disadvantage them by using a dimension they do not consider optimal. More precisely, PeakVI sets by default the dimension to the square root of the square root of the number of regions, while cisTopic trains model for multiple dimensions and chooses one based on an elbow rule of its evidence lower bound (ELBO). Signac uses a dimension of 50 by default, while SnapATAC, SCALE, NMF, TFIDF-NMF, and ChromSCape have a default dimension of 10. Figures 2A and Additional file 1: Fig. S4  summarize the performance of each embedding method on the different histone PTM marks in the mouse brain and human PBMC datasets, respectively.
In those plots, we summarize the performance of each embedding method by reporting the best performance achieved by each embedding method across all possible matrix construction choices, without performing any additional QC processing such as cell or feature selection. This allows us to quantify the best possible result that each embedding method can reach without setting an arbitrary feature engineering pipeline that could advantage some methods over others. We see that the neighbor scores vary roughly in the range 0. 05∼0. 35 across methods, datasets, and marks. As can be seen in Fig. 2B , where we visualize the embeddings obtained by ChromSCape_LSI on different marks on the mouse brain dataset, this corresponds to a fairly good agreement with scRNA-seq embedding in terms of recovering major cell types, particulary for H3K27ac (score = 0.
302) and H3K4me1 (score = 0. 321). Interestingly, we observe differences in the neighbor scores of different marks across methods in the mouse brain dataset, with H3K4me1 and H3K27ac (score = 0. 291 ± 0. 028 and 0. 273 ± 0. 026 , respectively) generally higher than H3K9me3 and H3K27me3 and H3K4me3 (score = 0. 148 ± 0. 040 , 0. 169 ± 0. 033 , and 0. 112 ± 0. 035 , respectively). Note that this does not necessarily mean that some marks are more informative than others but rather than they are less directly linked to expression than others. A similar trend is visible but weaker on the human PBMC dataset (Additional file 1: Fig. S4 ), where in particular the scores on H3K27ac and H3K4me1 are lower than on the mouse brain dataset (scores=0. 113 ± 0. 031 and 0. 150 ± 0. 021 , respectively). This difference between the mouse brain and human PBMC datasets could be caused by the differences in co-assay, by the relative complexity of the cell types, or by the quality of the experiments.
The performance of each method on each histone PTM mark of the mouse brain datasets is shown in Fig. 2  and Additional file 1: Table  S3. We see that the three best performing methods on the mouse brain datasets are consistently ChromSCape_LSI , TFIDF-NMF, and Signac, which are consistently better than all other methods. They are followed by SnapATAC and PeakVI (except on H3K4me3), then cisTopic, NMF, SCALE, and ChromSCape_PCA. SnapATAC is better than cisTopic and SCALE, while ChromSCape_PCA is worse than all other methods. The top three performing methods (ChromSCape_LSI , TFIDF-NMF, and Signac) implement TF-IDF, suggesting that TF-IDF-based method have an advantage over other approaches. Surprisingly, though, while ChromSCape_LSI and TFIDF-NMF also performs well on the human PBMC dataset, Signac does not (Additional file 1: Fig.
S4 ). This may be due to the lower coverage of the human PBMC dataset than of the mouse brain data, and to the detrimental effect of the whitening operation specific to Signac, as studied in more details in the supplementary text. On the PBMC dataset, ChromSCape_PCA again performs poorly compared to other methods, while the differences between other methods and between marks are overall less pronounced than on the mouse brain dataset. Since the four methods ChromSCape_PCA, ChromSCape_LSI, Signac, and SnapA-TAC all implement a form of PCA after applying to the count data matrix a specific data transformation, the difference in their performance highlights the importance of this Fig. 2  A Best performances of the different representation methods on the mouse brain dataset. B UMAP representation of the different samples in the mouse brain dataset; the first row is the RNA co-assay processed with PCA using the scanpy best practices; the second row is the scHPTM assay processed with ChromSCape_LSI using the matrix construction algorithm with the best neighbor score, both colored by the labels of  [9]  obtained from the scRNA-seq co-assays data transformation choice.
Finally, the more recent VAE-based methods, PeakVI and SCALE, are overall not competitive with the more classical LSI-based ones. As we show below, this may be due to the relatively small size of the datasets used. Using the labels provided by the authors in their papers, obtained computationally on the co-assay, we can also compute supervised evaluations of these representations. By using a clustering algorithm, either k-means or hierarchical clustering (HC) (Additional file 1: Fig. S7 ), we obtain clusters that we can compare to the cell annotations provided by the authors using either the Adjusted Mutual Information (AMI) or Adjusted Rand Index (ARI). AMI and ARI are extremely similar as can be seen in Additional file 1: Fig. S6. The ARI for the mouse brain, human PBMC, and human cell lines datasets are presented in Additional file 1: Fig.
S8 -S10 respectively. According to this metrics, we observe that the best performing methods for Tn5-based methods are still the three TF-IDF-based methods, with PeakVI also becoming competitive. For the MNase-based method, TFIDF-NMF is still the best performing method, but all methods perform well, except for Signac. This might be due to the low complexity of this dataset, and the default use of 50 whitened dimensions, that can introduce noise in the representation.
The count matrix construction strongly influences the quality of the representation We now investigate the influence of the count matrix construction method (i. e. , how the raw reads are mapped to regions) to obtain relevant embeddings of scHTPM datasets. For that purpose, we explore the performance of the different embedding methods as a function of the matrix construction parameter, again without further preprocessing such as cell or feature selection. We show the results in Fig. 3  and Additional file 1: Fig,  S5  for the mouse brain and human PBMC datasets, respectively. We see that matrix construction has overall a strong influence on the quality of the representations. For most methods and marks, the performance first increases when the bin size increases, then decrease after a peak.
This effect is more pronounced on the mouse brain data and in particular for repressive marks (H3K27me3 and H3K9me3, 3). We also observe for repressive marks studied by scChIP-seq the same increase with bin size as can be seen in Additional file 1: Fig,  S10B. In order to quantify this effect, we report the ratios between the best and worst performing matrix construction for each method and mark in Additional file 1: Table  S6  for the mouse brain dataset and in Table  S7  for the human PBMC dataset. In the human PBMC dataset, we can see that the ratio between the best and worst feature engineering can reach up to 10. 76 (TFIDF-NMF on H3K4me1); this is mostly due to the very poor performances of using a Gen-eTSS annotation on this dataset as can be seen in Additional file 1: Fig. S5. In the mouse brain dataset, we can see that this ratio is on average 1.
We see on the mouse brain dataset that performances reach a level close to their maximum for smaller bin sizes for enhancing marks (H3K27ac, H3K4me1 and H3K4me3) than for repressive marks (H3K27me3 and H3K9me3) and that, except for Signac, the range of appropriate bin size is relatively large (e. g. , 50 kbp-1000 kbp for H3K27me3 or 10 kbp-200 kbp for H3K4me1). Furthermore, except for Signac, that range is relatively stable across methods for each bin size. We investigate in more details the reason why Signac behaves so distinctively in the supplementary text (Additional file 1: Fig. S1 ) and Fig. 3  A Neighbor score performances of the 9 dimension reduction algorithms on the 5 marks in the mouse brain dataset, as a function of the matrix construction. B UMAP projection of H3K4me1 and H3K27me3 using ChromsSCape_LSI using bins of 20 kbp and 300 kbp, colored by the labels of  [9]  obtained from the scRNA-seq co-assays show in particular that the fact that it uses a whitening step and a relatively high embedding dimension by default makes it might capture more noise for larger bin sizes.
Feature selection decreases the quality of the embedding Another QC criteria used in single-cell analysis is the selection of features-genomic regions for single-cell epigenomics datasets-prior to dimensionality reduction. Two standard approaches are (i) the selection of regions with the highest coverage or (ii) the selection of regions that have a highly variable enrichment score across cells. Such a selection step is relatively common, but there is currently no consensus for scHPTM analysis on whether such selection is beneficial and which of the two methods is optimal. To address this question, we compare the maximal neighborhood scores for all methods with various feature selection thresholds, when we select features based on variability (HVG) or coverage. The results are shown on Fig.
5. A and Additional file 1: Fig. S11  respectively, for the mouse brain dataset. We observe consistently that feature selection is generally detrimental to the performances, in the sense that for both methods, the more regions we keep the better the performances are. As shown on Fig. 5B  for Signac and ChromSCape_LSI, this trend is in fact not only true when we look at the best performance reached over different bin sizes in the matrix construction step but also when we look at each bin size individually. Feature selection has been shown to increase performances for scRNA-seq in  [13]  and is part of the guidelines for scATAC-seq  [25]. Our results show that, contrary to scRNAseq and scATAC-seq, feature selection is detrimental to the analysis of scHPTM data, and we therefore recommend not to use it.