dataesr/scientific-paragraphs-categorization huggingface dataset:
Database Dependency Analysis In this section, we present the results of the database dependency analysis performed on DirectMap. As it's mentioned in section 2. 1, the database contains 101 simulations. To assess the database dependency, we suggest selecting subsets from the original dataset using the geodesic distance between stimulation sites as a selection criterion. In fact, we first compute the geodesic distances between all the stimulation sites corresponding to the 101 simulations. Then, we select the simulations whose distance between stimulation sites is above a fixed threshold. Using this approach, we succeed to select 9 subsets containing, respectively, 100,  85, 63, 50, 32, 25, 18, 16, 12, 10 , and 8 simulations corresponding to a minimal distance between stimulation sites equal to 0.
2, 1. 2, 2. 2, 3. 2, 4. 2, 5. 2, 6. 2, 7. 2, 8. 2, 9. 2, and 10. 2 mm, respectively. The subsets have been constructed by computing the minimal (min dist ) and maximal (max dist ) inter pacing sites distances, discretizing the interval [min dist , max dist ] by 1mm, finding the subsets corresponding to each discretization step and removing the subsets containing <8 cases. This approach characterizes the spatial sparsity of each training data with its inter pacing site distance. Figure  2  shows the evolution of mean and standard deviation of absolute activation time error and correlation coefficient over the testing subset with respect to dataset size. Each row corresponds to the results obtained using, respectively (from top to bottom) 5, 10, 100, 1000, 2000, and 8000 neurons per hidden layer in the neural network.
To select the most appropriate model, we refer to the study conducted by  Duchateau et al. (2019) , where mean absolute error between invasive and noninvasive estimated activation times is equal to 20. 04 ms. Considering the fact that this study is performed using in-silico data, we use a threshold in terms of absolute error equal to 15 ms represented in the Figure  2  by the dashed line. Another important selection criterion is the standard deviation. In fact, a high standard deviation means that results fluctuate between the folds and thus the model is not stable and vice versa. By taking into account all these criteria, we observe that the model using 1000 neurons per hidden layer is the most stable for all the dataset sizes. We observe also that absolute activation time errors and correlation coefficients improve by increasing the dataset size.
Cardiac Activation Mapping Results In this section, we detail the results of the 3 methods and compare their performances based on the point-wise absolute activation time error and correlation coefficient. To do so, we choose the best model, in the sense of validation, from the 4 built models using the k-fold cross validation approach for DirectMap and SATDNN-AT. Figure  3  shows the absolute activation time error and correlation coefficient for every simulation of the training, validation and testing datasets using the methods DirectMap, SATDNN-AT and FEM-L1. If we concentrate on the testing results, we observe that DirectMap performs better than FEM-L1 and SATDNN-AT in terms of absolute errors and correlation coefficients. In fact, the average and standard deviation of the absolute errors and correlation coefficients are, respectively, equal to 7.
Pacing Site Localization Results To assess the pacing site localization performance, we use the geodesic distance between exact and reconstructed pacing sites as an evaluation metric. According to the observed results, there is an exception where we reconstruct the pacing site differently. In the case where the minimum value of activation times is shared by multiple nodes, as shown in Figure  5 , we choose to take the gravity center of the nodes having the minimal AT value as the reconstructed pacing site. In Figure  6 , we show the simulations of the testing dataset with the reconstructed pacing sites and the geodesic errors. We observe that in average, geodesic distances using FEM-L1, SATDNN-AT and DirectMap are, respectively, 9. 5 mm ± 8. 1, 13. 2 mm ± 5. 7, and 7. 6 mm ± 4. 2. We conclude that DirectMap outperforms the two other methods in terms of pacing site localization.
Robustness Against Added Gaussian Noise to the Testing Data To assess and compare the robustness of the three methods against additive Gaussian noise, we represent in this section their results in terms of absolute activation time errors and correlation coefficients after adding to ECGs different noise levels in the range between 5 and 50% of the maximum signal amplitude. These tests are performed only on the testing data. Tables  3, 4  show that DirectMap is insensitive to noise addition in terms of both absolute error and correlation coefficient. Besides, SATDNN-AT is more robust than FEM-L1 against additive noise. Considering that the 3 methods behave the same way for all the simulations, Figure  7  represents results of a simulation of the testing dataset that confirms the previous deductions.
DISCUSSION AND CONCLUSION This study addresses two different issues: First, it studies the DirectMap generalization performance with respect to dataset size and the neural network architecture. Then, it compares DirectMap with two methods of the stateof-the-art cardiac activation mapping. The results confirm that the larger the dataset, the greater the performance. According to  Duchateau et al. (2019) , mean activation time absolute error using non-invasive cardiac activation mapping methods assessed on clinical data is equal to 20. 04 ms. So, by fixing a threshold equal to 15 ms we deduce that using 32 simulations as a training dataset provides a great generalization performance. Based on these results, a comparison study is conducted between DirectMap, SATDNN-AT and FEM-L1. It shows that DirectMap outperforms the two other methods.
Second, DirectMap performance was assessed when trained and tested using noisy data. As expected, the study shows that the performance deteriorates proportionally to the added amount of noise but it is still under the fixed threshold even when the noise added to activation maps ranges between -20 and 20 ms. Geometric uncertainties were also considered by inflating the torso geometry by a 1. 2 factor. Testing the different approaches with these data shows a decline in the evaluation metrics. Nevertheless, DirectMap still achieves the best performance compared to FEM-L1 and SATDNN-AT. Although DirectMap has promising results compared to SATDNN-AT and FEM-L1, many limitations are still to be addressed in future works. First, we have to admit that the built model has a basic neural network architecture which can be improved to meet the complexity of the problem.
We have to notice that the size of the database has been optimized on the basis of DirectMap performance results and used later to evaluate the performance of the two other methods. This doesn't affect the FEM-L1 results. However, this choice might not be optimal for SATDNN-AT. Then, as we mentioned in  Karoui et al. (2019a) , tests are performed using perfect data with the same heart-torso geometry which is not compatible with real cases. So, geometry standardization would be one step forward in data-driven cardiac activation mapping. We also have to notice that using intrinsic deflection time as the computation method of activation time from the inverse solution computed with SATDNN-AT and FEM-L1 may not be optimal to compare these two methods to DirectMap. Besides, we observe that low-pass filtering of the inverse solutions EGMs improved the reconstruction of the activation maps.
Means and standard deviations of absolute errors and correlation coefficients of the inflated testing dataset with respect to noise added to activation maps. After proving the feasibility and applicability of DirectMap, this work attests that it outperforms at least two of state-of-the-art methods: SATDNN-AT and FEM-L1. In summary, this study is encouraging and suggests that DirectMap technique needs further investigation and may have potential to become a useful noninvasive cardiac activation mapping tool.
Image processing and data analysis Software. All image processing and data analyses were performed using ImageJ 1. 52t or Matlab 2015a either separately or together using the MIJ plugin (D. Sage, D. Prodanov, C. Ortiz, and J. Y. Tivenez, retrieved from http://bigwww. epfl. ch/sage/soft/mij). The graphics were produced using OriginPro 9. 0 and exported to Adobe Illustrator CS6 for final figure layout. Live 3D segmentation and tracking procedure. To monitor the position of the chromatid clusters within the oocyte, we developed an automatic 3D segmentation and tracking procedure coded in Matlab and ImageJ. This method, based on gray levels thresholding, enabled us to extract the DNA clusters and the cell outlines in H2B-mCherry-injected oocytes. Briefly, we filtered the images using Gaussian blurs to smoothen the edges and applied adaptive thresholding to account for the overall brightness reduction in the deeper part of the Z-stacks.
(6) The t i rotation, which was defined as the time when the spindle reaches 5% of its total fitted rotation. To fit the rotation, we manually selected the time points corresponding to the actual rotation and fitted the results using a 5-parameter logistic model implemented in Matlab (G. Cardillo, retrieved from https://github. com/dnafinder/logistic5). Cortical F-actin and myosin-II levels and distance to DNA clusters. During this study, we repeatedly assessed the cortical F-actin and myosin-II (pMLC2) levels and eventually correlated them to the distance separating the cortex and the DNA clusters (see Figs  3C, 3D, 4B,  and 4C ). To do so, we first segmented the oocyte, using the procedure described above, and defined a 10-to 20-pixel-wide line selection following the cell outline. We next generated Euclidean distance maps (EDM commands in Matlab and ImageJ) centered on the centroid of the DNA clusters.
These maps use grayscales to encode the distances between a previously defined point (for instance, DNA cluster centroid) and the rest of the image pixels. Finally, we extracted the values along the line selections for the F-actin, myosin-II, and EDM channels. In Particle image velocimetry (PIV). To measure the flow of cytoplasmic materials in oocytes, we devised a Matlab routine built on the PIVlab implementation of PIV  [57]. We eliminated the vectors outside the oocyte using a mask and smoothed the vector field in space and time with custom filters based on running averages. In Figs  1C, 2H, 5E, 6F,  and S1E Fig,  we used an interrogation window of 80 × 80 pixels for the first pass and 40 × 40 pixels for the second pass. We smoothed the vector field using a 3 × 3 vectors kernel in space and a 9-time point kernel in time.
In single-cell RNA-sequencing (scRNA-seq), gene expression is assessed individually for each cell, allowing the investigation of developmental processes, such as embryogenesis and cellular differentiation and regeneration, at unprecedented resolutions. In such dynamic biological systems, grouping cells into discrete groups is not reflective of the biology. Cellular states rather form a continuum, e. g. , for the differentiation of stem cells into mature cell types. This process is often represented via a trajectory in a reduced-dimensional representation of the scRNA-seq dataset. While many methods have been suggested for trajectory inference, it is often unclear how to handle multiple biological groups or conditions, e. g. , inferring and comparing the differentiation trajectories of wild-type and knock-out stem cell populations.
In this manuscript, we present a method for the estimation and downstream interpretation of cell trajectories across multiple conditions. Our framework allows the interpretation of differences between conditions at the trajectory, cell population, and gene expression levels. We start by integrating datasets from multiple conditions into a single trajectory. By comparing the conditions along the trajectory's path, we can detect large-scale changes, indicative of differential progression. We also demonstrate how to detect subtler changes by finding genes that exhibit different behaviors between these conditions along a differentiation path.
The emergence of RNA sequencing at the single-cell level (scRNA-Seq) has enabled a new degree of resolution in the study of cellular processes. The ability to consider biological processes as continuous phenomena instead of individual discrete stages has permitted a finer and more comprehensive understanding of dynamic processes such as embryogenesis and cellular differentiation. Trajectory inference was one of the first applications that leveraged this continuum  [1]  and a consequential number of methods have been proposed since then  [2] [3] [4]. Saelens et al. [5]  offer an extensive overview and comparison of such methods. Analysis of scRNA-Seq datasets using a curated database reveals that about half of all datasets were used for trajectory inference (TI)  [6]. At its core, TI represents a dynamic process as a directed graph.
The pseudotime values represent how far a cell has progressed along each lineage, while the weights represent how likely it is that a cell belongs to each lineage. The gene expression model will be described below. Using this notation, we can properly define a trajectory inference (TI) method as a function that takes as input Y -and potentially other arguments -and returns estimates of L c , T, W, and eventually T c. Step 1 -Differential Topology: Should we fit a common trajectory? The first question to ask in our workflow is: Should we fit a common trajectory to all cells regardless of their condition? Or are the developmental trajectories too dissimilar between conditions? To demonstrate what this means, consider two extremes. For a dataset that consists of a mix of bone marrow stem cells and epithelial stem cells, using tissue as our condition, it is obvious that the developmental trajectories of the two conditions are not identical and should be estimated separately.
On the other hand, if we consider a dataset where only a few genes are differentially expressed between conditions, the impact on the developmental process will be minimal and it is sensible to estimate a single common trajectory. Indeed, we favor fitting a common trajectory for several reasons. Firstly, fitting a common trajectory is a more stable procedure since more cells are used to infer the trajectory. Secondly, our workflow still The examples are all built on a similar wild-type backbone, i. e. , two lineages that slowly diverge in the absence of knocking out. Cells either originate from a wild-type (WT, blue) or a knock-out (KO, orange) condition. In (b. ), the knock-out has no effect, all three tests fail to reject their null hypothesis. In (c. ), the knock-out partly blocks differentiation along Lineage 2, meaning that fewer cells develop along that lineage.
Following the tradeSeq manuscript by Van den Berge et al. [8] , we consider a general and flexible model for gene expression, where the gene expression measure Y ji for gene j in cell i is modeled with the negative binomial generalized additive model (NB-GAM) described in Equation  (13). We extend the tradeSeq model by additionally estimating condition-specific average gene expression profiles for each gene. We therefore rely on lineage-specific, gene-specific, and condition-specific smoothers, s jlc. With this notation, we can introduce the conditionTest, which, for a given gene j, tests the null hypothesis that these smoothers are identical across conditions: H 0 : s jlc1 = s jlc2 , ∀(c 1 , c 2 ), ∀l. (7) As in tradeSeq, we rely on the Wald test to test H 0 in terms of the smoothers' regression coefficients.
Simulations We generate multiple trajectories using the simulation framework provided by Cannoodt et al. [22]. Within this framework, it is possible to knock out a specific gene. Here, we knock out a master regulator that drives differentiation into the second lineage. The strength of this knock-out can be controlled via a multiplier parameter m. If m = 0, the knock-out is total. If 0 < m < 1, we have partial knock-out. If m > 1, the master regulator is over-expressed and cells differentiate much faster along the second lineage. Three types of datasets are generated: Simple branching trajectories (two lineages, e. g. , Fig. 2a ) of 3, 500 cells, with equal parts wild-type and knock-out; trajectories with two consecutive branchings (and thus three lineages, e. g. , Fig. 2b ) of 3, 500 cells, with equal parts wild-type and knock-out; and branching Figure  2 : Simulation results.
Three types of datasets are generated, with respectively two, three, and two lineages, and two, two, and three conditions. Reduced-dimensional representations of these datasets, for a multiplier value of m =. 5, are presented in (a. ), (b. ), and (c. ), respectively. After generating multiple versions of the datasets for a range of values of m, we compare the performance of the progressionTest and differentiationTest with that of DAseq  [17]  and milo  [16] , when controlling the false discovery rate at nominal levels 1% and 5% using the Benjamini-Hochberg  [21]  procedure. In (d. ), each cell represents the performance measure associated with one test on one dataset for one nominal FDR level. Cells are also colored according to the performance. Overall, with two conditions, the progressionTest ranks first, followed by DAseq and the differentiationTest.
These methods returns multiple tests per dataset (i. e. , one per neighborhood), so we adjustfor multiple hypothesis testing using the Benjamini-Hochberg procedure  [21]. By applying milo, DAseq, and condiments on the simulated datasets, we can compare the results of the tests versus the values of m: We count a true positive when a test rejects the null and m = 1, and a true negative if the test fails to reject the null and m = 1. We compare the methods' ability to detect correct differences between conditions using five metrics: The true negative rate (TNR), positive predictive value (PPV), true positive rate (TPR), negative predictive value (NPV), and F1-score, when controlling the FDR at two nominal levels of 1% and 5%. More details on the simulation scenarios and metrics can be found in the Methods section.
Results are displayed in Fig. 2d. On all simulations, all methods display excellent results for the TNR and PPV (except for the differentiationTest with level 1% on the branching dataset). However, the performances for the TPR (power), NPV, and F1-rate vary quite widely. On the two types of datasets with two conditions, the ranking is uniform over all metrics and levels: progressionTest, DAseq, differentiationTest, and milo. On the third simulation setting with three conditions, we cannot benchmark DAseq since its testing framework is restricted to two conditions. Here, also, the ranking is uniform but the differentiationTest outperforms the progressionTest. Looking more closely at the results, we can see (Fig  S2 ) that this mostly stems from increased power for the differentiationTest when m is close to 1.
TGFB dataset McFaline-Figueroa et al. [9]  studied the epithelial-to-mesenchymal transition (EMT), where cells migrate from the epithelium (inner part of the tissue culture dish) to the mesenchyme (outer part of the tissue culture dish) during development. The developmental process therefore is both temporal and spatial. As cells differentiate, gene expression changes. Moreover, the authors studied this system under two settings: a mock (control) condition and a condition under activation of transforming growth factor β (TGFB). After pre-processing, normalization, and integration (see details in the supplementary methods), we have a dataset of 9, 268 cells, of which 5, 207 are mock and 4, 241 are TGFB-activated. The dataset is represented in reduced dimension using UMAP  [24]  (Fig. 3a ). Adding the spatial label of the cells (Fig.
Plotting the per-condition kernel density estimates of pseudotimes in Fig. 3e  reveals a strong treatment effect. The pseudotime distribution for the mock cells is trimodal, likely reflecting initial, intermediary, and terminal states. However, the first mode is not present in the TGFB condition, and the second is skewed towards higher pseudotime values. This is Figure  3 : TGFB dataset: Differential topology and differential progression. After normalization and projection on a reduced-dimensional space (using UMAP), the cells can be colored either by treatment label (a. ) or spatial origin (b. ). Using the treatment label and the reduced-dimensional coordinates, an imbalance score is computed and displayed (c. ). The topologyTest fails to reject the null hypothesis of no differential topology and a common trajectory is therefore fitted (d.
TCDD dataset Nault et al. [10]  collected a dataset of 16, 015 single nuclei to assess the hepatic effects of 2,3,7,8tetrachlorodibenzo-p-dioxin or TCDD. In particular, they focused on the effect of TCDD on the 9, 951 hepatocytes cells along the central-portal axis. This dataset is not a developmental dataset per se but still exhibits continuous changes along a spatial axis, demonstrating the versatility of the trajectory inference framework in general, and of the condiments workflow in particular. Fig. S3a  shows a reduced-dimensional representation of the dataset, with cells labelled according to treatment/control condition, while Fig. S3b  shows the same plot colored by cell type, as derived by the authors of the original publication. The cells are aligned in a continuum, from central to mid-central and then mid-portal and portal.
KRAS dataset Xue et al. [23]  studied the impact of KRAS(G12C) inhibitors at the single-cell level on three models of KRAS(G12C) lung cancers. Specifically, they examined how various cell populations react to these inhibitors and how some cells can return in proliferation mode shortly after the end of the treatment. Here, we want to investigate how the three cancer models (H358, H2122, and SW1573) differ in their response to the KRAS(G12C) inhibitors. We use the reduced-dimensional representation from the original paper to display the 10, 177 cells Note that this does not necessarily imply that the trajectory of reaction to the KRAS(G12C) inhibitors is different between cancer types. Indeed, this may also reflect strong batch effects between conditions, which the normalization scheme was unable to fully remove when integrating the three cancer types in one common reduced-dimensional representation.
This is evident in the three case studies presented in the manuscript. Indeed, in the first case study we have a developmental system under treatment and control conditions, while in the second case study the continuum does not represent a developmental process but spatial separation. In the third case study, the conditions do not reflect different treatments but instead different cancer models. This shows that condiments can be used to analyze a wide range of datasets. Often, the different conditions also represent different batches. Indeed, some interventions cannot be delivered on a cell-by-cell basis and this creates unavoidable confounding between batches and conditions. Normalization and integration of the datasets must therefore be done without eliminating the underlying biological signal.