dataesr/scientific-paragraphs-categorization huggingface dataset:
QPO is highly persistent The fact that the QPO is detected in the average PDS extracted from data accumulated over a temporal baseline of ≈60 days suggests that the QPO is likely present for a significant fraction of the X-ray monitoring. To further test this we estimated the strength (signal-to-noise ratio) of the QPO as a function of the accumulated exposure. We started with the first 5 ks of exposure, extracted an average PDS, and fit the 224 Hz feature with a Lorentzian. From thereon, for every additional 256-s exposure, we repeated this process of extracting an average PDS, followed by modelling the 224 Hz feature with a Lorentzian. At every point, the QPO strength was calculated as the ratio of the sum of the powers within the width of the best-fit QPO and its errorbar. A normalized QPO strength was also estimated by dividing the QPO strength with the average count rate which itself evolves with the accumulated exposure.
Pulsation search assuming a binary To search for possible orbital periodicities, we used the open source PRESTO software ** to perform an acceleration search over the frequency-frequency derivative plane. The acceleration search scheme assumes that the compact object's acceleration is roughly constant throughout the observation of duration T P orb /10 (62). We ran the search assuming that any possible signal would drift across a maximum of 100 Fourier frequency bins (zmax of 100). Informed by the || Unlike in some past work, we assume that this equilibrium is determined by the balance of accretion spin-up and spin-down from the magnetized wind (the latter enhanced as a result of the larger magnetosphere opened by the fall-back (60)). ** https://github. com/scottransom/presto centroid frequency and width of the QPO (assumed to be the fundamental frequency) reported above, we narrowed the search frequency window to be over 200-260 Hz † †.
7-36. 5 million paired-end reads, and we extracted 8032-107,823 unique contacts per cell (Supplementary Table  1 ). We developed a custom pairtools-based approach termed ORBITA (One Read-Based Interaction Annotation) (Fig. 1b ) to eliminate artificial contacts generated by spontaneous template switches of the Phi29 DNApolymerase  39, 40  (Fig. 1c, d ) during the whole-genome amplification (WGA) step (see "Methods"). In contrast to the hiclib  32, 41  (see "Methods") annotations showing up to 20 contacts per restriction fragment (RF) in a single nucleus, ORBITA detects one or two unique contacts per RF (Fig. 1d , Supplementary Fig. 2b, c ). We tested ORBITA by analyzing previously published snHi-C data from murine oocytes  32  and found that ORBITA allowed us to filter out artificial junctions in this dataset (Supplementary Fig.
3a ). Notably, hiclib and ORBITA detect a similar number of contacts per RF in single-cell Hi-C data obtained without the usage of Phi29 DNA-polymerase  33  (Supplementary Fig. 3b ). Thus, ORBITA efficiently filters out artificial Phi29 DNApolymerase-produced DNA chimeras from snHi-C libraries. We then constructed snHi-C maps with a resolution of up to 10 kb (Fig. 1e ). In single nuclei, the dependence of the contact probability on the genomic distance, P c (s), has a shape comparable to that observed in the bulk BG3 in situ Hi-C regardless of the number of captured contacts (Fig. 1f ), indicating that the key steps of the snHi-C protocol such as fixation, DNA fragmentation, and in situ ligation were performed successfully. To estimate the overall quality of the snHi-C libraries, we first calculated the number of captured contacts per cell.
On average, we extracted 33,291 unique contacts from individual nuclei that represented 5% of the theoretical maximum number of contacts and corresponded to four contacts per 10-kb genomic bin (see "Methods"); in the best cell, 17% of contacts were recovered (Fig. 2a , b, Supplementary Table  1 ). Relying on the number of captured contacts, we then estimated the proportion of the genome available for the downstream analysis. At 10-kb resolution, ~82% of the genome on average was covered with contacts in each individual cell, and 67% of genomic bins established more than 1 contact (Fig. 2c ). Notably, in the previously published mouse snHi-C datasets, ~0. 6% of theoretically possible contacts were detected on average (Fig. 2b ). Because the top-20 mouse snHi-C libraries from Flyamer et al. 32  demonstrated a comparable genome coverage with contacts and a number of contacts per 10-kb genomic bin (Fig.
In individual mammalian cells, TADs frequently overpassed the boundaries identified in the cell population, arguing for a substantial degree of stochasticity in genome folding  32, 35, 44. We used the ORBITA algorithm to reanalyze previously published snHi-C data from murine oocytes  32  and G2 zygote pronuclei  34  and found that 31. 2 and 21% of boundaries were shared on average between any two cells, respectively (Fig. 3e , Supplementary Fig. 9 ). This result is reproduced at 40-kb resolution and persists for a broad range of snHi-C datasets' quality (Supplementary Fig. 10 ). We conclude that, in Drosophila, TADs have more stable boundaries as compared to mammals. This corroborates recent observations of the Cavalli lab  37  and may reflect the differential impact of loop extrusion  18, 19, 34  and internucleosomal contacts  24  on TAD formation  16, 23.
4a ). We analyzed only the haploid X chromosome to avoid combined folding patterns of diploid somatic chromosomes. We assumed that if TADs in individual nuclei are truly hierarchical, then sub-TADs belonging to the same TAD should be demarcated with well-defined boundaries arising from specific folding of the chromatin. To determine whether this is the case, we tested the resistance of sub-TAD boundaries to the data downsampling (two-fold depletion of total number of contacts in the snHi-C maps). In contrast to relatively stable TAD boundaries, sub-TAD boundaries showed a two-fold reduction in the probability of detection in downsampled datasets (Fig. 4b ). Moreover, we found that profiles of sub-TADs were highly different in individual nuclei: only approximately 20% of sub-TAD boundaries in individual cells were shared in pairwise comparisons, similar to the shuffled controls (Supplementary Fig.
Thus, we developed a custom approach for snHi-C data processing termed ORBITA (One Read-Based Interaction Annotation), as described below. Reads mapping. As the first step of the approach, FASTQ files with paired-end sequencing data are mapped to Drosophila reference genome dm3 using Burrows-Wheeler Aligner (BWA-MEM, console version 0. 7. 17-r1188)  76  with default parameters. Notably, this mapping procedure allows independent alignment of chimeric parts of both forward and reverse reads. This step results in BAM files with paired-end mapping information. Annotated pairs retrieval. In the next step, the BAM files are parsed with an adapted version of pairtools (https://github. com/mirnylab/pairtools) with our newly implemented option ORBITA. Among many other utilities for Hi-C data processing, we selected pairtools from the Mirny lab as the basis of our approach, due to the convenience and modular structure of its code.
This version of the tool can be accessed at the GitHub repository https://github. com/agalitsyna/pairtools. ORBITA treats each read in the BAM file independently, regardless of whether it is forward or reverse. Reads that are uniquely mapped to a single location of the genome are marked as type P, meaning that they are part of a standard Hi-C Pair with no DNA breakpoint evidence. Reads that contain precisely two successive regions uniquely mapped to different genomic locations (MAPQ > 1) are selected for further DNA breakpoint annotation. ORBITA takes the genome restriction annotation (provided as a BED file with DpnII restriction fragments positions, produced by cooler digest  77  ) and compares each breakpoint against the list of restriction sites. For each 3′-end of the right chimeric part and 5′-end of the left chimeric part (in other words, ligated ends), both upstream and downstream restriction sites are annotated, and the distance to the closest one is calculated.
Before contact filtration by this rule, we compared the number of restriction fragments with more than four unique contacts according to ORBITA and one previous approach, hiclib for Flyamer et al. 2017. We obtained datasets for mouse nuclei from Flyamer et al. 2017 and Nagano et al. 2017 and mapped with the hiclib and ORBITA pipelines. We found a significant reduction in the number of unique contacts per fragment for snHi-C from Phi29 DNA polymerase datasets (Flyamer  et al. 2017, present work], but not for scHi-C without Phi29 DNA polymerase (Nagano et al. 2017) (Supplementary Figs. 2, 3 ). Thus, we conclude that ORBITA is an effective approach to reduce the number of snHi-C artefactual contacts arising from random template switches of Phi29 DNA polymerase. Cell selection by raw data subsampling.
We obtained filtered contacts for 88 individual nuclei after the initial round of sequencing. Before the second round of sequencing, we assessed the robustness of the number of unique contacts by subsampling of raw datasets (Supplementary Fig. 2a ). For each library, we created a uniform grid of sequencing depth (from 0 to the resulting number of reads with the step of 100,000 reads). We then randomly selected X reads from the full library and calculated the number of unique contacts (as described above) for each number from the grid X. We repeated this procedure ten times and plotted the mean number of unique contacts for each sequencing depth from the grid. We proposed that there are a significant number of cells containing PCR duplicates and that the number of contacts increases slowly depending on the sequencing depth due to the poor efficiency of the snHi-C protocol.
Further sequencing of these cells would result in a relatively small improvement of the detectable number of unique contacts. The number of contacts for other cells increases more rapidly with the number of reads but reaches a plateau once the maximum number of unique contacts is achieved. Thus, additional sequencing of these cells might result in reading duplicated contacts. For other cells, the number of contacts grew slowly with sequencing depth (Supplementary Fig. 2a ). However, for all these cells, the number of unique contacts gradually increased with no plateau signature. We selected the cells displaying the best growth of the number of contacts, indicative of the good quality of the dataset. The top 20 cells by the number of unique contacts were subjected to an additional round of sequencing.
The same mapping and parsing pipeline was used for these datasets. Technical replicates (initial and additional rounds of snHi-C libraries sequencing) were merged at the annotated PAIRS file stage. snHi-C interaction map construction. The resulting pair data were binned at 1 kb, 10 kb. 20-kb, 40-kb, and 100-kb resolutions with cooler version 0. 8. 5  77  and stored in the COOL format. We constructed the merged dataset by summing all snHi-C maps. To exclude self-interacting genomic bins and possible contribution of dangling ends, self-circles  41  , and mirror reads  78  , we removed the first diagonal in both single cells and the merged maps. The HiGlass server was used for data visualization  79. 10-kb resolution was used throughout the paper if another resolution is not specified. Bulk BG3 in situ Hi-C raw data processing.
For bulk BG3 in situ Hi-C (two biological replicates), reads were mapped to Drosophila reference genome dm3 with Burrows-Wheeler Aligner (BWA-MEM, console version 0. 7. 17-r1188)  76  with default parameters. For consistency with the snHi-C analysis, the resulting BAM files were parsed with pairtools v0. 3. 0, (https://github. com/mirnylab/pairtools) using default parameters. The resulting files were sorted by the pairtools module "sort"; replicates were merged by the pairtools module "merge" and duplicates were removed, allowing one mismatch between possible duplicates (pairtools dedup with --max-mismatch 1 and -mark-dups options). The resulting PAIRS file was binned with cooler 77 at the same resolutions as the single-cell datasets. To remove the contribution of possible Hi-C technical artifacts, such as backward ligation, dangling ends, self-circles  41  , and mirror reads  78  , the first two diagonals of Hi-C maps were removed.
For bulk BG3 in situ Hi-C, the P c (s) is assessed by the mean number of contacts for a certain genomic distance  13. However, the same procedure cannot be readily used for snHi-C due to data sparsity and missing data. Thus, to calculate P c (s) for a snHi-C dataset, we counted the number of contacts for a certain genomic distance and normalized by the number of genomic bins that had contact in at least one snHi-C experiment at any distance. Notably, we use the same procedure for the visualization of snHi-C P c (s) dependence on the genomic distance s (Fig. 1f  and Fig. 4e ); the genomic distance step size was set to 1 kb. For snHi-C background models, we used P c (s) genomic distance step size 10 kb. We assessed the region visibility in snHi-C by the marginal distribution of the number of contacts for the region marg i (in other words, the total number of observed intrachromosomal contacts for a genomic region) using maps at a 10-kb resolution.
For each snHi-C map, we calculated P c (s) and the marginal distribution of contacts and shuffled the positions of the contacts for each chromosome, so that the marginal distribution was preserved, and P c (s) was at least approximated (Supplementary Fig. 4a-d ). Note that for 3D modeling, we used more crude shuffling without saving the marginal distribution of contacts. Assessment of percentage of recovered contacts. To compare snHi-C datasets across species (Fig. 2a-c ), we assessed the percentage of recovered contacts out of all possible contacts per nuclei. First, we determined the theoretical size of the pool of restriction fragments for the nucleus of each species and cell type. For Drosophila, we used a diploid male cell line. Thus, the total number of restriction fragments was ~600,000, composed of the double amount of fragments in autosomes (2 × 265,167, as assessed by the dm3 in silico digestion) in addition to the number of fragments on chromosome X (64,108).
2b ); this number is approximately 2. 6% for the best mouse dataset. The mean percentage of recovered contacts is 4. 9% for our dataset and <1% for Flyamer et al. (2017) and Gassler et al. (2017). However, this assessment of the percentage of recovered contacts is not exact for several reasons: (1) we did not perform sorting prior to snHi-C to isolate G1 cells; hence, some regions of the genome might have an increased copy number in S or G2 cells; (2) some regions of the genome might be affected by deletions and copy number variations that were not accounted for in our analysis. However, even in the worst-case scenario, if we imagine that all Drosophila cells are in the G2 phase of the cell cycle, we recovered at least 8% of all possible contacts for the best cells in our analysis, which is still a substantial improvement compared to recovery for the best cells from mammalian studies.
TAD calling in snHi-C and bulk BG3 in situ Hi-C data. We used Hi-C map segmentation with lavaburst (v0. 2. 0) (https://github. com/nvictus/lavaburst) with the modularity scoring function for TAD calling in Hi-C maps at 10-kb resolution  32. All TAD segments smaller or equal to 3 bins (30 kb) were considered to be inter-TADs  24. lavaburst has a gamma (γ) parameter controlling the size and the number of resulting TADs. We varied g from 0 to 375 with a step of 0. 1 for Drosophila datasets. The range and the step were selected to guarantee the comprehensive coverage of both extremes (a small amount of unusually large TADs and a large amount of smallest possible TADs). We observed a sharp decrease in median TAD size and an increase in the number of TADs with the γ increase (Fig. 3b , Supplementary Fig.
5 ). After reaching the peak, the number of TADs starts to drop because many segments fall beyond the minimal allowed TAD size. For large γ, both the number of TADs and mean TAD size reach a plateau at low levels. We considered the point of the maximum number of TADs (γ max ) as the most informative segmentation reachable by the algorithm for a particular dataset. The mean TAD size is ~70 kb on average between cells compared to the expected 120 kb size of Drosophila TADs  24. Thus, we considered this level to be the sub-TADs. To guarantee a uniform γ selection procedure for all the cells, we arbitrarily selected γ max /2 to obtain a resulting TAD segmentation (mean TAD size ~90 kb). For the other resolutions of snHi-C maps, the same protocol of TAD calling was applied, except the inter-TAD size threshold was set to 60 kb (3 bins at 20 kb) for 20 kb and 120 kb (3 bins of 40 kb) for 40 kb.
Robustness of TAD calling. To assess TAD calling robustness and filter out potentially artifactual TAD boundaries, we performed TAD calling on snHi-C maps with random subsampling of the contacts as a control. For each cell, we performed ten iterations of independent subsampling of contacts leaving 95%, 90%, … 5% of the initial number of unique contacts per dataset. For each subsampling, we performed the TAD calling in the same manner as for the full dataset. We then assumed the bins found as TAD boundaries in the full snHi-C maps with no subsampling to be positives and inner TAD bins to be negatives. Based on this definition, we calculated both false positive rates (FPR) and false negative rates (FNR) for each cell and all subsampling levels. As expected, FNR gradually decreased with the percentage of remaining contacts.
FPR reached a maxima at 10-30% subsampling level and then gradually decreased (Supplementary Fig. 6a, b ). We then defined a TAD boundary support for a given subsampling level (X%). TAD boundary support is calculated for each genomic bin as the number of subsampling iterations with the number of contacts equal to or larger than X%, where the bin was annotated as the TAD boundary (allowing a one-bin offset). We used TAD boundary support as a predictor of observed TAD boundaries in each cell (with no subsampling of the snHi-C dataset). We plotted receiver operating characteristic (ROC) curves for each X = (95%, 90%, … 5%) and calculated the ROC area under the curve (AUC) for each case (Supplementary Fig. 6c ). Based on the largest ROC AUC, we selected the best subsampling level predictive of boundaries, X = 90% ROC AUC 0.
All eigenvalues λ i such that R e (λ i ) > r c are isolated, and the corresponding eigenvectors correlate with annotation into the TADs. The position of the spectral edge, determined by the procedure above, has been found to be very close to the edge of the disk for the stochastic block model r c ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d À1 d dÀ1 q , where d is the vector of degrees  83. The typical number of the isolated eigenvalues was around 100 for dense contact matrices and somewhat less for sparser ones. The leading eigenvectors define the coordinates u ðiÞ j ; j ¼ 1; 2; ; N of the nodes (bins) of the network in the space of reduced dimension k << N. At the second step, the clustering of the data was performed using the spherical k-means method, realized in the Python library spherecluster  84.
Regarding the comparison of TAD boundaries with the modularity approach, the mean fraction of conserved modularity boundaries is somewhat less -42% for all pairs of cells in the analyses and 52% for the five densest cells, whereas the number of TADs per chromosome is the same in the two methods (171). Between the two methods, the mean number of matched boundaries for the corresponding cells is 61%. Compartment annotation in snHi-C and bulk BG3 in situ Hi-C. For compartment annotation in bulk BG3 in situ Hi-C, we used eigenvector decomposition of cis-interactions maps for each chromosome, as implemented in cooltools callcompartments tool version 0. 2. 0 (https://github. com/mirnylab/cooltools). We then reversed the sign of eigenvalues based on GC content (positive values corresponding to an A compartment with larger GC content)  26.
We next carried out a saddle plot analysis for each snHi-C dataset based on bulk BG3 in situ Hi-C compartment annotation  32. For this procedure, the bins in raw scHi-C maps were reordered by ascending first eigenvector values and averaged to 5 × 5 saddle plots  32. Epigenetic analysis of TAD boundaries. For the functional annotation of TAD boundaries, we downloaded modENCODE normalized array files 85 : total RNA of ML-DmBG3-c2 cell line assessed by RNA tiling array (modENCODE id 713) and the ChIP-chip for MOF (id 3041), BEAF-32 (id 921), Chriz (275), CP190 (924), CTCF (3280), dmTopo-II (5058), GAF (2651), H1 (3299), HP1a (2666), HP1b (3016), HP1c (942), HP2 (3026), HP4 (4185), ISWI (3030), JIL-1 (3035), mod (mdg4) (324), MRG15 (3045), NURF301 (5063), Pc (325), RNA-polymerase-II (950), Su(Hw) (951), Su(var)3-7 (2671), Su(var)3-9 (952), WDS (5148), H3 (3302), H3K27ac (295), H3K27me3 (297), H3K36me1 (299), H3K36me3 (301), H3K4me1 (2653), H3K4me3 (967), H3K9me2 (310), H3K9me3 (312), H4K16ac (316).
For RNA-Seq coverage, we used the data from ref. 24. The files were binned at 10-kb resolution by summation. We plotted the ChIP-chip signal around different types of boundaries with pybbi utility (https://github. com/nvictus/pybbi. git) based on UCSC tools  86  and constructed six sets of boundaries: boundaries found in the bulk in situ Hi-C, boundaries found in the merged snHi-C dataset, boundaries present in > = 50% of cells (> = 7 cells, stable boundaries), boundaries present in <50% of cells (<7 cells, unstable boundaries), boundaries present in just one single cell, and random boundaries. To obtain randomized boundaries, we shuffled bulk in situ Hi-C boundaries across the Drosophila genome, preserving the number of boundaries per chromosome. We also used the bins from the inner parts of TADs as a control for the epigenetic analysis.
We were not able to split the data using an even grid of percentiles (e. g. , 0-20%, 20-40%) because ~38% of all genomic bins had zero expression in both replicates. The same functional annotation was used later for polymer model coloring. Average loop. For the construction of an average loop of A-compartment regions (Fig. 4f ) and B compartment regions (Fig. 4g ), MSL complex (Fig. 4h ) and Polycomb (Fig. 4i ), we selected the top 1000 genomic regions with the highest abundance of the corresponding genomic annotations as potential looping positions. A and B compartments were assessed by a cis-derived eigenvector of the bulk BG3 Hi-C data. MSL ChIP-Seq was obtained from Ramirez et al. 51  , GEO ID GSE58821). dRING binding data were obtained from modENCODE as a ChIP-chip normalized array file (ID 927  54  ).
We considered the pairs of potential looping positions corresponding to intrachromosomal interactions, at the genomic distances of more than 600 kb, separated by up to 50 other looping positions. The snipping of Hi-C square 600-kb windows, centered on the corresponding looping positions, was done with cooltools (https://github. com/mirnylab/cooltools/tree/master/cooltools). The aggregation was performed by summation. log 10 values were plotted as heatmaps. Assessment of folding hierarchy of TADs. To assess the folding hierarchy at the level of TADs, we used the assumption that the successive sub-TADs that form the same TAD will have more interactions in the observed real snHi-C maps than in the control maps described in the section "snHi-C background model" of these Methods. We calculated the number of contacts directly from snHi-C maps and the control maps.