dataesr/scientific-paragraphs-categorization huggingface dataset:
Automated Qyscore® imaging markers All QyScore® imaging markers (GM, WM, HP, AM, and WMH volumes) are widely employed in the imaging field as markers of brain atrophy  [21] [22] [23] [24]  and white matter hyperintensities  [24]. The algorithms used for volume calculation are based on existing segmentation methods, as described in detail below. Fifteen minutes are needed for the segmentation of all structures (less than 10 min for T1-weighted MRI images only). Whole GM and WM volumes were quantified using the Statistical Parametric Mapping software v12 (SPM12). SPM is a software highly used for GM and WM segmentation both in research and in clinical data  [25]. Hippocampus and AM volumes were measured using an improved version of SACHA (Segmentation Automatique Compétitive de l'Hippocampe et de l'Amygdale), a fast and fully automatic hybrid segmentation tool previously described in detail  [26, 27].
Grey matter, white matter, hippocampus, and amygdala volumes Three expert neuroradiologists manually edited and corrected the segmentation of GM and WM (rater's initials: C. S. , N. P. , S. S. ). First, GM and WM segmentations were performed using Freesurfer  [29]. Then, GM and WM segmentations were corrected using the software ITK-SNAP according to their experience. Since no protocols were found in the literature, we asked clinicians to check the segmentation automatically performed to identify important segmentation errors, mainly at the cortex level. Three expert neuroradiologists manually delineated HP and AM according to the anatomical constraints described by Chupin and colleagues  [26]. For each marker considered (GM, WM, HP, and AM), we established a consensus from the corrections/segmentations obtained from the expert tracers by the Simultaneous Truth and Performance Level Estimation (STAPLE) algorithm.
White matter hyperintensity volume Some of the data used for the validation of WHASA are publicly available (N = 30)  [17]. We used the consensus derived from the WMH manual segmentation of three anonymous expert raters reported in the manuscript of Lesjak and colleagues  [16]. On the remaining data (N = 100), segmentations were first initiated using the Lesion Segmentation Toolbox (LST)  [31] , then three expert neuroradiologists (rater's initials: C. D. , D. H. , N. P. ) manually corrected the WMH segmentation. The consensus among raters was obtained using the STAPLE algorithm.
For RVD and AVE (the lower, the better), the null hypothesis was that the metrics were equal to/above the threshold, and the alternative hypothesis is that the metrics were lower. The upper bound of the 97. 5% confidence interval was compared to the threshold, indicating that the RVD and AVE obtained using QyScore® were significantly inferior to the RVD and AVE reported in the literature for similar segmentation methods. Furthermore, we compared volumes obtained from the automated QyScore® imaging markers with the consensus obtained by three experts using regression analysis and Bland-Altmann plots. We used the following library in Python to perform statistical analysis: Scikit-learn (http:// scikit-learn. org/ stable/), version 0. 19. 1; Scipy (https:// www. scipy. org/), version 0. 17. 0; NumPy (http:// www.
Conclusions QyScore® provides reliable automatic segmentation of brain structures compared to the experts' consensus and other semi-automatic and automatic software described in the literature. Our results support the implementation of medical devices, such as QyScore® using neuroimaging methods, in clinical routine for supporting the diagnosis and monitoring of brain disorders. QyScore® markers could also be implemented in clinical trials to test the efficacy of new drugs for neurological diseases. Reliable measures of brain atrophy and white matter hyperintensities, such as the ones provided by QyScore®, will help us move into more personalized and evidence-based medicine for neurological diseases. Further retrospective and prospective validation studies, as well as test-retest reliability studies, are currently ongoing on real-world data to demonstrate the diagnostic performance and the clinical impact of using QyScore® in neurological disorders.
The type of manufacturers used for the acquisition of the MRI images was distributed among GM and WM database (2 GE, 9 Philips, 19 Siemens), HP and AM database (4 GE, 13 Philips, 33 Siemens), WMH database (30 GE, 26 Philips, 74 Siemens). Consensus results and the contribution of each expert neuroradiologist EW reported in Table4.
In the simplest form, this leads to a limit cycle trajectory, composed by linear segments in logarithmic coordinates describing some extensive (depending on system size) cell properties. We prove a theorem connecting the effective embedding dimensionality of the cell cycle trajectory with the number of its linear segments. We also develop a simplified kinetic model with piecewiseconstant kinetic rates describing the dynamics of lumps of genes involved in S-phase and G2/M phases. We show how the developed cell cycle models can be applied to analyze the available single cell datasets and simulate certain properties of the observed cell cycle trajectories. Based on our model, we can predict with good accuracy the cell line doubling time from the length of cell cycle trajectory.
, 2020) , which suggests that the transcriptomic cell cycle trajectory represents a spiral, or, after neglecting the relatively slow drift unrelated to cell cycle progression, a shape close to "a flat circle". This type of trajectories was indeed phenomenologically observed in the HeLa cell line profiled with scRNASeq technology, after deconvoluting the transcriptomic dynamics connected to the cell cycle from other sources of transcriptional heterogeneity. In particular, the absence of cell cycle-related transcriptional epochs was deduced from this model. In the current study, we suggest an extended and different point of view on the properties of transcriptomic cell cycle trajectory which, in our opinion, in some cases better matches its observed properties in various cellular systems, when sufficiently good quality data can be collected.
The type of models discussed here was partly introduced by Shkolnik (a pseudonym for a collective authorship), including authors of this manuscript  (Shkolnik, 1989). Here, we significantly extend the previous effort and adapt it to the description of the cell cycle trajectory in single cell datasets. In order to connect the geometric properties of cell cycle trajectory to interpretable mechanistic parameters, we extended the model of piecewise linear growth in logarithmic coordinates, to a simple kinetic model with rates depending on time as piecewise constant functions. In this case, some of the segments of the trajectory become nonlinear but remain smooth and do not deviate from linearity too far. Therefore, the suggested model is conceptually similar to previously suggested hybrid discretecontinuous models, but conceptualizes them, addresses the transcriptional dynamics and can be fit to multiple available scRNASeq datasets  (Singhania et al.
Single Cell Data Used in This Study We made a screening of available single cell sequencing of cancer cell lines in order to identify datasets with sufficient number of good quality single cell transcriptomic profiles and in which the principal source of transcriptomic heterogeneity would be progression through the cell cycle. We identified publicly available scRNASeq data on CHLA9 Ewing sarcoma cell line, produced with 10x Genomics sequencing technology  (Miller et al. , 2020) , which contained more than 4,000 cells with total number of unique molecular identifiers (UMIs) varying from 10 ,000 to 50 ,000 per cell, after applying the standard quality criteria and filtering cells containing a large fraction (>20%) of reads in mitochondrial genes. For this dataset, we reanalyzed the raw sequencing data using Kallisto mapper  (Bray et al.
, 2016)  resulting in a loom file that could be used for obtaining the gene expression levels and for quantifying RNA velocity vectors (La  Manno et al. , 2018). In addition, we used a recently published collection of 200 scRNASeq profiles of cancer cell lines from Cancer Cell Line Encyclopedia (CCLE) collection  (Kinker et al. , 2020). We also analyzed several scRNASeq datasets by downloading them directly from Gene Expression Omnibus (GEO). The estimation of cell line doubling times, when available were obtained from Cellosaurus database  (Bairoch, 2018).
Definition of Cell Cycle Genes We systematically tested several existing definitions of cell cycle gene sets and verified that our results remain qualitatively invariant even if the choice of cell cycle gene set can vary. In our experiments, we used the following cell cycle gene set definitions: • Standard "Regev's set": markers of S-and G2/M cell cycle phases used in scanpy tutorials  (Tirosh et al. , 2016 ) • Set of cell cycle genes annotated in Reactome pathway database  (Jassal et al. , 2020)  • Set of top-contributing genes, extracted from application of independent component analysis (ICA) to the dataset under study, from those components whose top-contributing genes were strongly associated with the cell cycle. In particular, similar to our previous work  (Aynaud et al. , 2020) , two independent components were significantly enriched with the markers of S-and G2/M cell cycle phases in all single cell cell line datasets we analyzed.
Therefore, library size normalization was required but not at the global cell population level. We hypothesized that the total number of reads should increase in the course of cell cycle progression on average such that the cells characterized by similar value of pseudotime along the cell cycle trajectory could be normalized to the same local library size. As usual, this poses a chicken-or-egg problem because for reconstructing the cell cycle trajectory one needs normalized data, and for normalization of the library size one needs a reconstructed trajectory. This problem is similar to those approaches which use normalization locally conditioned on clusters in single cell datasets  (Azizi et al. , 2018). We used a simplified two-stage approach for library size normalization which preserved both the geometric structure of CCT and the trend of increasing the total number of reads along CCT.
1. The row count data have been normalized to the global median number of counts and ln(x+1)-transformed, using standard functions of scanpy. 10,000 most variable genes have been selected, the dimensionality was reduced to 30 by PCA. In the reduced space, a kNN graph has been computed using the standard Euclidean distance for k 10. This graph was used for pooling reads from neighbor cells as described above. 2. For such initially normalized dataset, we computed closed cell cycle trajectory in the subspace of cell cycle genes, by fitting a principal closed curve, using the Python implementation of ElPiGraph  (Albergante et al. , 2020). The data points were partitioned according to the proximity to the nodes of the elastic principal curve. 3. In each partition, we analyzed the distribution of the total number of reads across cells.
5. Each cell's library size was normalized to the smoothed local median value of the total number of reads. 6. The newly normalized pseudocount data matrix passed through the same pre-processing as described in 1), namely a) Pooling reads from neighbour cells using the kNN graph obtained with trajectory-based normalized data, b) ln(x+1) transformation, selecting most variable 10 ,000 genes. The cell cycle trajectory-based normalization procedure is illustrated in the Jupyter notebook at https://github. com/ auranic/CellCycleTrajectory_SegmentModel, which can be easily reused for other cell lines.
Computing the Cell Cycle Trajectory and Quantifying Pseudotime We used the ElPiGraph Python package to fit elastic principal curves or closed elastic principal curves (principal circles) to single cell data distributions  (Albergante et al. , 2020). ElPiGraph was applied in the data space defined by the set of 10 ,000 most variable genes or by the cell cycle-related genes, after dimensionality reduction by PCA (first 30 principal components were retained). In order to compute open elastic principal curve with q nodes, first a closed curve was fit with q/2 nodes, then a node with the least number of data points projected onto it was removed from the principal graph, and this configuration was used as an initialization to compute the elastic principal graph without branching and having q nodes.
Estimating the Effective Dimensionality of a Set of Vectors In order to estimate the effective dimensionality of CCT, we used scikit-dimension Python package  (Bac et al. , 2021). We used linear estimators of global intrinsic dimensionality, based on application of PCA and various approaches to select the significant number of eigenvalues from the scree plot. In order to compute the effective rank of a rectangular matrix, we looked at the distribution of its singular values, and selected such a number of them that the ratio between the largest and the smallest number would not exceed 10, such that the reduced matrix is well-conditioned.
Example of a Cell Cycle Trajectory Extracted From Single Cell Data The current study is motivated by the observation that after appropriate pre-processing of single cell RNA-Seq data (see Methods), one can observe the cell cycle trajectory (Figure  1 ) which can be approximated by a piecewise linear curve, with a gap between the beginning and the end of the trajectory corresponding to the cell division moment. Here we use the example of Ewing sarcoma cell line CHLA9 sequenced at single cell level using the Chromium 10x technology  (Miller et al. , 2020). The distinguishing feature of this dataset was that it contained a significant number of proliferating cells with single cell transcriptomes of good quality (more than 4,000 cells with the total number of Unique Molecular Identifiers (UMIs) between 10 ,000 and 50 ,000).
Also, the proliferation signal in this dataset seems to explain the largest fraction of transcriptomic heterogeneity, since in the plane of the first two principal components one can clearly observe the cyclic trajectory. In other cell line single cell datasets, the proliferative signal can be masked by other sources of transcriptomic heterogeneity, requiring special procedures of data treatment to reveal it  (Aynaud et al. , 2020; Liang et al. , 2020; Schwabe et al. , 2020). The scRNA-Seq data have been normalized in order to preserve the pattern of dynamics of the total number of counts (UMIs) along the CCT, see Methods section. The normalized gene expression levels are represented at the logarithmic scale, following the standard practice. The multidimensional distribution of single cell transcriptomic profiles projected into the space of the first 30 principal components has been approximated by a principal curve (see Methods).
Model of Cell Cycle as a Trajectory of Allometric Growth With Switches and Divisions Based on the observations of the properties of the cell cycle trajectory in several scRNASeq datasets, we hypothesized that it can be recapitulated by a formal model of linear growth in logarithmic coordinates with switches and a cell division event. The suggested model is hybrid in nature, similar to some previously published models  (Singhania et al. , 2011; Noël et al. , 2013). Namely, we distinguish the extrinsic observable cell state, characterized by continuous variables, and the intrinsic hidden cell state, characterized by discrete variables. The intrinsic state of a cell determines the parameters of the extrinsic dynamic process as in  (Singhania et al. , 2011). Let the extrinsic state of a proliferating cell be determined by n substances quantified by their amounts, not their concentrations.
Therefore, we put S max x (C) S , M max x (D) M , M e x (E) M. Instead of using directly the B point, we will use the position of the non-proliferating cell with the maximum sum of the coordinates in the S, M plane, and we designate it as x B′ S , x B′ M (other choices are also possible). Then c min x (B′) S + x (B′) M. Then we define rates: k v 2 x C ( ) v -x B′ ( ) v x C -x B′ , k S 1 x C ( ) S -x D ( ) S x C -x D , k M 1 x E ( ) M -x D ( ) M x E ( ) -x D ( ) , k v 0 x B′ ( ) v -x 0 ( ) v x 0 ( ) -x B′ The resulting steady state cell cycle trajectory is shown in Figure  3. We denote the linear segments of the trajectory shown in Figure  3  as T1, Ts, T2, Tm, assuming that they have significant overlap with G1, S, G2 and M phases correspondingly. The suggested model describes 2D dynamics of the signals S, M which are empirically shown to explain most of the variance of all cell cycle genes in scRNASeq data (see below).
The curvature analysis suggests the existence of five segments for the cell cycle trajectory reconstructed in the subspace of 30 first principal components of the complete dataset. However, some of these components might correspond to the variance not related to the progression through the cell cycle. In order to diminish the possible role of this variance, we considered a reduced version of the dataset confined to cell cycle-related genes only. We estimated the global intrinsic dimensionality, using six different linear ID estimators from scikit-dimension Python package  (Bac et al. , 2021) , and it varied from 2 to 7, with average value 4. 0. The scree plot shows existence of two dominant eigenvalues explaining 83% of total variance, indicating that the trajectory is relatively flat and located close to a 2D linear manifold.
Thus, assuming that the duration of mitosis is by order of magnitude faster than the T1s epoch, for CHLA9 cell line one estimates the ratio between transcriptional epochs T2s and T1s close to 1. 0 and the value of transcriptional boost of G2/M genes in T2s epoch close to 2. 5-fold (Figure  6C ). The determined values of all other parameters can be found in the Jupyter notebook at https://github. com/auranic/ CellCycleTrajectory_SegmentModel.
One can estimate the position of these points from the analysis of observed cell cycle trajectory curvature ((s 0 , m 0 ), (s 1 , m 1 ), (s max , m s ), (s m , m max ), (s t , m t ), shown by red points in Figure  6D )) by requiring that the model trajectory should pass as close as possible to them. This defines an optimization problem which can be easily solved numerically by iterations, using the simplest fixed-point algorithm. The details of parameter fitting are provided in the Jupyter notebook at https://github. com/ auranic/CellCycleTrajectory_SegmentModel. We note that this optimization does not allow us to determine all the model parameters uniquely, since they enter in the aforementioned optimization functional as certain combinations (as simple rational functions), namely, k S t k S,2 d , k M t k M,2 d , k S d T 1 , k M d T 1 , k S,2 d T 1s , k M,2 d T 1s , k S,2 d T 2s , k M,2 d T 2s , k S,2 d T m , k M,2 d T m.
Simulating Cell Cycle Trajectories With Various Durations of Temporal Transcriptional Epochs After fitting the kinetic parameters for an observable in the S-phase vs G2/M score plane cell cycle trajectory, one can perturb the parameters and investigate how the trajectory geometry depends on them. In real life scRNASeq datasets, we observe that CCT geometry can appear very different in various biological systems. When projecting onto the plane of standard scores of S-phase and G2/M phase genes, scRNASeq datasets might not always reveal the circular nature of CCT. In some cases, the circular structure is not at all detectable via this projection, (Figure  7 ), and the two scores might be connected via a strong positive or negative correlation. Also, in some systems we observed co-existence of several CCT shapes, like it is the case in the U2OS cell line dataset (GSE146773).
The univariate histograms of two score distributions might be characterized by bi-or uni-modal character. Quite strikingly, we were able to reproduce these patterns qualitatively by fitting the kinetic parameters to the CHLA9 scRNASeq dataset, and then by manipulating the durations of T1, T1s and T2s transcriptional epochs and producing computersimulated trajectory examples. Thus, significant reduction in the duration of both T1 and T1s epochs led to the negative correlation pattern between S-phase and G2/M scores. This could be interpreted as drastic reduction of the G1 cell cycle phase. In real life datasets, such pattern has been observed in human embryonic stem cells (dataset GSE85917). If both T1 and T2s were shortened then this led to the increase of the positive correlation between two scores, (Figure  7 ).
Predicting Cell Line Doubling Time From the Geometrical Properties of Cell Cycle Trajectory The developed simple kinetic model leads to a simple prediction which can be validated: the total length of the transcriptomic cell cycle trajectory must diminish in rapidly dividing cells. This can be interpreted as a consequence of the fact that in a rapid proliferation process, during the post-mitotic G1 phase (T1 transcriptional epoch), there is not enough time to degrade all mitotic transcripts produced before the cell division moment, so they are reused in the consequent cell cycle phases, shortening the subsequent G1 phase. We verified this prediction in a relatively large collection of cell line scRNASeq datasets. Using the data from Cellosaurus database, we identified those few ones for which the cell line doubling time has been estimated, and for which the number of available good quality single cell profiles exceeded 300.
We used the total length of the principal circle fit in the 2D plane of the scaled to maximum equals 1 cell cycle phase scores, as a proxy to quantify the level of CCT contraction (see Methods). This measure was correlated with cell line doubling time in hours. Two cell lines CHLA10 and SCC25 appeared to be strong outliers from otherwise significant positive regression line (Pearson correlation 0. 931, p-value 10 -5 ) (Figure  8 ). When this regression line was used as a predictor, CHLA10 cell line was predicted to have doubling time around 64 h (instead of determined by database search of around 32 h) and for SCC25 around 78 instead of 50 h. It is known that cell line doubling time can vary depending on the growth conditions, so we hypothezised that this variability could explain the appearance of two outliers.
DISCUSSION This paper provides a framework for analyzing the cell cycle trajectories using single cell omics measurements such as scRNASeq data. Unlike the previously suggested model of the trajectory as a flat circle, we provide arguments that at least in some conditions the piecewise-linear in logarithmic coordinates approximation appears to fit the single cell transcriptomic data and to be biologically tractable. In particular, it allows us to delineate transcriptional epochs of cell cycle at which the corresponding segment of the trajectory remains close to linear in logarithmic coordinates which corresponds to locally allometric changes of the transcriptome. We suggest two modeling formalisms to recapitulate the cell cycle transcriptomic dynamics as a sequence of switches. The first one is purely phenomenological and describes the dynamics as a change of states of a hidden automaton, leading to the switches of parameters of allometric growth, followed by a shift representing the cell division event.