dataesr/scientific-paragraphs-categorization huggingface dataset:
Second, data processed by Auto-qPCR does not require any preformatting of the results file to be performed manually. Instead, once the qPCR experiment is complete, our program takes the csv or txt export file directly from the thermocycler so there is no copy/paste or formatting step to be done by the user. Third, Auto-qPCR can manage the data from multiple separate absolute files at once, as well as batch process multiple results files from a relative quantification. The program creates a clean data set (with all technical replicates) and a summary data table. Fourth, unlike the other software mentioned above, Auto-qPCR includes three different models, conceived to support qPCR data generated from absolute and two methods of relative quantification designs. No other program provides the option of choosing between the two relative quantification methods.
However, we also found that GRIN1 and CAMK2A had different levels in the baseline condition (∆CT), thus we observe that information is lost when using a ∆∆CT normalization. For relative quantification using a ∆∆CT normalization we measured a fold change of variation compared to a control condition for a given gene  38  , but information about differences of expression between two genes in control condition were not observed (Fig. 4F ). We have provided both the gold standard method of relative quantification and a method to calculate gene expression without a reference sample, to allow users to quickly determine expression changes without losing information about the level of expression in control conditions. Reprocessing the external dataset highlighted two main advantages of treating qPCR dataset with a program.
Applying such an algorithm to the user's judgement removes variability and potential bias in the resulting normalized gene expression levels. We were able to reprocess external data using Auto-qPCR and acquired the same summary output, reaching the same conclusions as the initial study. We showed that Auto-qPCR can process data from different PCR machines and matched the expected outcome from manual processing without the risk of bias or errors. Using a double rule for data inclusion/exclusion for highly variable signal between technical replicates, the program provides a unique treatment that will considerably reduce the risk of variability and mistakes generated by and between users during manual data processing. The Auto-qPCR program does have has some limitations, but it also has and a number other potential uses not included in this manuscript.
Although the program is able to compute data from independent qPCR plates in single plex (where each plate has a different amplicon), Auto-qPCR has not been adjusted at this stage to manage duplex qPCR (with one endogenous control and one transcript of interest quantified in the same well). Auto-qPCR has also not been equipped to process an inter-plate calibrator, required to cover a sample size of more than one plate, in absolute quantification mode experimental designs. Finally, as most of the primer sets for gene expression are now predesigned and eventually pretested by companies taking in consideration optimal efficiencies of amplification, correction factors for efficiencies have not been added into the Auto-qPCR algorithms. Despite these caveats, we propose that Auto-qPCR could be employed in a variety of molecular biology protocols and many of these features could be added in future iterations.
The Auto-qPCR program was conceived to treat, analyze, and display qPCR data generated using either relative or absolute quantification designs, while limiting errors related to manual processing. Data processing tools cannot replace or supplement appropriate experimental design and statistical power. The conditions included with the design and interpretation of the results still remain in the user's hand. We have provided a tool that will provide easy, reproducible analysis without user errors for unlimited samples. Although, we cannot computationally remove the need for replication and controls, analysis time will no longer be a limitation. Auto-qPCR permits researchers to conduct studies with larger experimental designs while minimizing the risk of mistakes during the data analysis.
Acknowledgements T. M. D. received funding through the  McGill Healthy Brains for Healthy Lives (HBHL) initiative , the  CQDM FACS program , the  Alain and Sandra Bouchard Foundation , the  Ellen Foundation  and the  Mowafaghian Foundation. T. M. D is supported by a project grant from  CIHR  ( PJT-169095 ). R. A. T was funded by a  Healthy Brains  for.
Data availability and reproducibility. All raw csv input files data files and output files used in plots are available at https:// github. com/ neuro eddu/ Auto-qPCR, along with a user guide. The example input (Input Data) and output files (Output Data) are all available and organized by Figure names. The parameters used for each figure can be found in the document "Notes_on_Datasets. docx" and screen shots of the filled web app from for each figure are in the Supplementary Figures. The example output will be replicated identically if the same conditions are entered.
The performance of five variations of CA and standard CA are benchmarked on 10 datasets and compared to glmPCA. CA variations are fast, scalable, and outperform standard CA and glmPCA, to compute embeddings with more performant or comparable clustering accuracy in 8 out of 9 datasets. Of the variations we considered, we found that CA using the Freeman-Tukey chi-squared residual was most performant overall in scRNAseq data. Our analyses also showed that variance stabilizing transformations applied in conjunction with standard CA (using Pearson residuals) and the use of "power deflation" smoothing both improve performance in downstream clustering tasks, as compared to standard CA alone. CA has advantages including visual illustration of associations between genes and cell populations in a "CA biplot," and easy extension to multi-table analysis enabling integrative dimension reduction.
We introduce corralm, a CA-based method for multi-table batch integration of scRNAseq data in shared latent space, and we propose a new approach for assessing batch integration. We implement CA for scRNAseq in the corral R/Bioconductor package (https://www. bioconductor. org/packages/corral) interfaces directly with widely used single cell classes in Bioconductor, allowing for easy integration into scRNAseq pipelines.
Correspondence analysis: Count-based dimension reduction Correspondence analysis (CA) casts scRNAseq read counts in a contingency table analysis framework and in its canonical form can be conceptualized as a two-step procedure (graphically outlined in Figure  1A ; detailed in Methods). The count matrix is transformed to a matrix of Pearson chi-squared residuals, which is then factorized with singular value decomposition (SVD). CA analysis of scRNAseq does not require, but is compatible with, log-transformed read counts (logcounts). PCA, which has been widely used, requires data transformation, and is therefore generally.
Introduction Single cell mRNA sequencing (scRNAseq) simultaneously measures the transcript levels of genes in thousands of individual cells, providing a window into the transcriptional and functional diversity of cells in a tissue or experiment. Because of the size and complexity of the data, the datasets are orders of magnitude greater than those encountered when analyzing "bulk" RNAseq data from tissue samples. While such fine resolution data have the potential to reveal new biological findings, scRNAseq data exhibit sparsity, noisiness, and technical artefacts beyond those seen for bulk RNA samples  (1, 2) , necessitating scRNAseq specific pre-processing and normalization  (3, 4). Typically scRNAseq analysis includes the use of dimension reduction, as it attenuates noise and ensures computational tractability, but the choice of method considerably influences downstream analyses, results, and conclusions  (3, 5).
Selecting an appropriate dimension reduction method is important; an effective method finds a representation of the data that minimizes noise and redundancy and uncovers meaningful signals that reveal latent structures and patterns within the data  (6, 7). When defined from scRNAseq data, reduced dimension embedding representations are most useful when they preserve meaningful, biologically relevant variation; are robust, meaning that the decomposition of new but similar observations consistently yields a similar embedding space; and generalize and transfer to new data, enabling new observations arising from similar biological processes to be projected into the same latent space. Single cell RNAseq counts are generally modeled as multinomially distributed, and are often approximated as negative binomial or Poisson counts  (2) , reflecting the fact that the data are neither continuous nor approximately Gaussian.
We now discuss its application to scRNAseq analysis. Focusing on the issues of log-transforming scRNAseq counts when applying PCA,   (14, 37). However, CA, which can be computed by SVD on the standardized Pearson residuals, may not be the most appropriate approach when there is overdispersion in the contingency table  (41, 42). CA has a rich history and several variations and extensions of CA have been developed for different research contexts across a wide range of fields. We benchmark performance of standard CA with Pearson residuals and three additional CA approaches (with five specific variations) that address the issue of overdispersion, including substitution with an alternative chi-squared statistic that is better adapted to counts data exhibiting high sparsity and overdispersion. We compare the five variations of CA that address data overdispersion with standard CA and glmPCA (2) in scRNAseq analysis.
Because cell clustering and characterization is a key part of most scRNAseq workflows, we set as the goal of the benchmarking task to find embedding representations that facilitate identifying and annotating complex populations of cells. We show that the CA biplot allows a geometric interpretation of features and objects in the same space, which in turn facilitates efficient exploratory data analysis and cluster interpretation. We implemented CA for scRNAseq in corral, an R/Bioconductor package that interfaces directly with Bioconductor classes (such as SingleCellExperiment). The corral package is designed for computational scalability and is fast and performant compared to PCA and other dimension reduction methods, including glmPCA. Because of its design and implementation, switching from PCA to CA with corral is achieved through a simple pipeline substitution, and improves dimension reduction of scRNAseq datasets.
In contrast, CA clearly clustered and separated all groups within two components. Similarly, results in purified PBMCs (Zhengmix4eq benchmarking dataset) demonstrated that CA can be applied directly to counts or to logcounts and still achieve good clustering and separation, whereas PCA on counts produces an "arch" or "horseshoe effect," which arises from the presence of a latent sequential ordering or gradient in the data  (12, 25). PCA on logcounts performed similarly to CA on either counts or logcounts. We quantitatively compared the performance of the four pipeline configurations presented in Figure  1C  (CA and PCA on both counts and logcounts) on six reference benchmark datasets-the three scRNAseq datasets from the SCMixology study that varied the technology for sequencing a known mixture of three cell lines  (38)  and the three Zhengmix PBMC datasets  (39, 40).
(All benchmark datasets are listed in the Benchmarking section of Methods. ) Cluster recovery based on the annotated cell types in the study was assessed using Adjusted Rand Index (ARI), which assesses similarity between two sets of data partitions (Figure  1D ). In all comparisons, CA outperforms or matches PCA's performance (highest ARI per datasets marked with orange circle). Consistent with Figure  1C , CA is robust when applied to either counts or logcounts data, obviating the need for log-transformation and therefore avoiding its associated issues.
Six CA methods (standard CA and five adaptations of CA to address overdispersion) were applied to nine datasets, including the three Zhengmix human PBMC benchmarking datasets, as well as cells from human pancreas, human brain, and Xenopus tail (detailed in Table  1 ). Clustering performance on cell embedding representations generated from each was compared and benchmarked in reference to glmPCA (2) (see Methods -Benchmarking for details). The five adaptations of CA broadly fall into three general approaches (Figure  2A ). The first class of approaches we considered was to explicitly apply a variance stabilizing transformation to the count matrix prior to computing Pearson residuals. Lause et al. (2021)  discussed variance stabilizing transformation as compared to Pearson residual normalization, though in their study did not combine variance stabilization and Pearson residual normalization prior to matrix decomposition.
The second is Anscombe's variance stabilizing count transformation (Row 4 of Figure  2A ), originally proposed in 1948 for use with Poisson, binomial, and negative binomial data  (44). Third, we used the Freeman-Tukey's variance stabilizing count transformation (Row 5 of Figure  2A ), originally proposed in 1950, also for Poisson and other count data  (45). Our results indicate that when variance stabilization is combined with classical CA, performance is superior to CA alone. Variance stabilization of counts prior to computing Pearson residuals provided great gains in downstream clustering with increases in ARI of 0. 4 in two studies (Zhengmix4uneq, Aztekin Xenopus tail); square-root transformation prior to CA increases the ARI in 7 datasets, while transformation to Anscombe counts or Freeman Tukey counts increased the ARI clustering performance in every dataset when compared to standard CA (with no variance stabilization of counts prior to computing Pearson residuals).
Indeed, Anscombe's variance stabilizing count transformation achieves the highest observed ARI in 1 of 9 test datasets (pancreas: Lawlor) and Freeman-Tukey's variance stabilizing count transformation had best overall performance in 3 of 9 datasets (Zhengmix4uneq; pancreas: Muraro, Lawlor). Although the square root count transformation did not outperform the other two transformations in any of the comparisons, its Adjusted Rand Index (ARI) was within 0. 05 of other two transformation in 7 of 9 datasets. Furthermore, in the pancreas datasets, variance stabilizing count transformation coupled with classical CA yielded the highest ARI of tested methods, outperforming glmPCA. The second variation we considered is the use of "power deflation" as a data smoothing method. Power deflation handles extreme outliers in the chi-squared residual matrix by raising all values to a power, a, prior to performing SVD, while preserving sign (Bottom row of Figure  2A ).
Conceptually, this transformation is similar to the Tukey ladder transformation  (46) , and has a smoothing effect on the matrix of chi-squared distances, reducing the impact of outlying values while preserving the ordering of values. The range of a is technically between 0 to 1, where a value of 0. 5 is a square root transformation. To achieve a "soft" smoothing effect, we considered α ∈ [0. 9, 0. 98] (data not shown) and present results for α = 0. 9 in Figure  2. We found that in all nine datasets, this power deflation smoothing approach performed comparably to, or better than, standard CA, although its impact on CA performance was less than variance stabilizing count transformation. Finally, we considered alternative chi-squared statistics that are better-suited to count data with high levels of sparsity and overdispersion.
CA of the Freeman-Tukey residuals (CA-FT) has been applied to archaeological site data, where it exhibited a variance-stabilizing effect and outperformed classical CA (SVD of the Pearson residuals), in the analysis of sparse, over-dispersed artifact data (counts of archeological artifacts by site)  (45, 47, 48). Both Pearson residuals and Freeman-Tukey residuals are members of the Cressie-Read family of power divergence statistics for testing goodness-of-fit in multinomially-distributed count data, and when squared, both residuals are chi-square distributed random variables  (47, 49). We found that CA-FT is well-suited for scRNAseq counts (Row 2 of Figure  2A ) as it outperformed CA of the Pearson residuals in all nine datasets and its performance was comparable to (ARI within 0. 02) or superior to glmPCA in 8 out of 9 benchmarking datasets.
In most datasets CA-FT also had higher or comparable clustering accuracy (ARI) to Pearson residual CA with variance stabilizing transformation. CA-FT achieved the highest ARI overall in 6 out of 9 datasets. Unlike standard CA (Pearson residuals), we observed little benefit to combining CA-FT with variance stabilizing transformation (square root, Anscombe, or Freeman-Tukey) (Figure  S1 ). Variance stabilizing transformation prior to CA-FT actually reduced its performance in 5 out of 9 datasets, and in the Muraro pancreas dataset, decreased the ARI from 0. 75 (CA-FT) to less than 0. 65 (CA-FT with square root transformation). CA-FT with square root transformation only improved downstream clustering of the Darmanis brain dataset from ARI of 0. 65 (CA-FT) to 0. 73 (CA-FT with square root transformation).
In all datasets except for the Darmanis brain, power CA-FT with deflation data smoothing had greater performance that CA-FT with variance stabilizing transformations, however, overall, it provided no or only marginal increases in performance of CA-FT. Results show that while the performance of standard CA of the Pearson residuals improves dramatically with variance stabilizing transformation, CA-FT adjusts for and is appropriate to be used with overdispersed data. In dimension reduction of scRNAseq, component selection can greatly influence downstream cell clustering analysis. Therefore, we considered clustering performance as a function of the number of components selected (Figures  2C, S2 ). The ability to recover "known" clusters (measured with ARI between clustering output and the previously identified and published cell types) was higher for the simpler mixtures of known, purified cell types (i.
e. , Zhengmix datasets) and lower for the complex tissues (i. e. , Brain, Pancreas, and Xenopus tail). We interpret this to mean that the higher order components were capturing variation helpful for separating the larger number of less well-defined cell types. In comparing performance, we found an association between the number of components and the complexity of the clustering task; the inclusion of more components generally increases the ARI in more complex tissue. In contrast, we saw there was little additional gain and for some a reduction in ARI when the number of components was increased for the Zhengmix datasets. The Zhengmix datasets comprise combinations of distinct PBMC cell types that were sorted and purified prior to sequencing. In simple datasets, including additional components beyond those that sufficiently capture the biological variance may add stochastic, technical, or systematic noise in the system.
Benchmarking of methods using the maximum ARI and the ranking of methods was robust to the number of components; CA-FT was consistently the most performant approach whether the first 30 (Figure  S2 ) or first 50 (Figure  2B ) components were included in downstream clustering. CA, CA-FT, and its variations generate a deterministic result that is stably reproduced. In contrast, glmPCA is not deterministic, and therefore results may vary when the method is rerun on the same dataset (Figures  2C, S3 ). For reproducibility, we tested ten random seed initiations of glmPCA (colored in gray; Figure  2C ), which revealed that glmPCA results are consistent for simpler datasets but in other datasets, such as the Xenopus tail dataset, its performance varies dramatically between iterations. In the Lawlor pancreas dataset, one of the tested seeds failed, suggesting that results were somewhat dependent on finding a "lucky seed".
In simpler datasets, such Zhengmix, all methods generated high ARI scores and glmPCA results had consistency between individual runs (Figure  2C ). However, there was greater variance in glmPCA performance with increasing data complexity. For each dataset, we present the average of the maximum ARI achieved in each of 10 runs of glmPCA. CA variations that are adapted for overdispersion are more performant in downstream clustering than standard CA or glmPCA (Figure  2B ). Of the approaches we considered, CA-FT was most performant, and outperformed standard CA with the variance stabilization transformation or related power deflation approach.
The distance from the origin indicates the magnitude of association; the angular rotation distance (cosine similarity) reflects similarity of the objects (or features) to each other, or association between objects and features. To illustrate the power of the CA biplot we performed a standard correspondence analysis of the Zhengmix8 PBMC benchmarking dataset, then plotted the first two dimensions of the resulting cell and gene embeddings (Figure  3 ). The 20 genes with highest weight by L2 norm (Euclidean distance from the origin) in the first two dimensions are colored blue, with a corresponding gene label. Cell populations are colored by cell type. The biplot highlights genes that have strong associations with and may discriminate between particular cell populations. For example, natural killer (NK) cells constitutively express granulysin, encoded by the gene GNLY, and although they are not the only cellular producers of granulysin, GNLY expression in other cells such as cytotoxic T-cell populations is driven by immune activation  (51).
Batch integration with corralm The need to integrate multiple datasets is an important motivator for the development and continued refinement of CA  (10, 35, 58). Our multi-table adaptation of CA, implemented as corralm, operates on the indexed residuals and includes scaling for library size and can align cells from different datasets. We compared corralm's performance with widely used batch integration methods (Figure  4 ), including Harmony and Seurat 3, both of which performed well in a recent benchmarking study examining 14 batcheffect correction methods  (59). Each method was applied to batch integration of the SCMixology dataset, which is a benchmarking dataset comprising scRNAseq profiles from a mixture of three cell lines (H2228, H1975, and HCC827), obtained in three batches using different library preparation platforms (Dropseq, Celseq2, and 10X)  (38).
3 GHz 8-core Intel Core i9; 64 GB memory). However, it should be noted that the SCMixology dataset is relatively small (1,401 cells), but at scale, this difference in run-time would significantly impact the overall speed of a pipeline, thus demonstrating an advantage of corralm and Harmony with corralm. Cluster evaluation measures such as ARI detect whether clusters can be re-identified, but do not directly quantify how well datasets are integrated in their low dimensional embedding representations. We propose a new batch integration metric, scaled variance (SV; scaled_var in the corral package), for quantitatively assessing batch integration when integrating datasets with similar cell populations and distributions across batches, presented in Figure  4B  and described in detail in Methods.