Tutorial 3: Imputation scATAC-seq analysis
Here we will use scATAC-seq dataset `Forebrain’ as an example to illustrate how scAGDE performs imputation task in scATAC-seq analysis.
1. Read and preprocess data
We first read ‘.h5ad’ data file using Scanpy package
[4]:
import scanpy as sc
adata = sc.read_h5ad("data/Forebrain.h5ad")
We can use Scanpy to further filter data. In our case, we pass this step because the loaded dataset has been preprocessed. Some codes for filtering are copied below for easy reference:
[5]:
sc.pp.filter_cells(adata, min_genes=100)
min_cells = int(adata.shape[0] * 0.01)
sc.pp.filter_genes(adata, min_cells=min_cells)
[6]:
adata
[6]:
AnnData object with n_obs × n_vars = 2088 × 11285
obs: 'celltype', 'n_genes'
var: 'n_cells'
uns: 'neighbors', 'pca', 'tsne', 'umap'
obsm: 'X_pca', 'X_tsne', 'X_umap'
varm: 'PCs'
obsp: 'connectivities', 'distances'
2. Setup and train scAGDE model
Now we can initialize the trainer with the AnnData object, which will ensure settings for model are in place for training.
We can specify the outdir to the dir path where we want to save the output file (mainly the model weights file).
n_centroids represents the cluster number of dataset. If this information is unknown, we can set n_centroids=None and in this case, scAGDE will apply the estimation strategy to estimate the optimal cluster number for the initialization of its cluster layer. Here, we set n_centroids=8.
We can train scAGDE on specified device by setting gpu. For example, train scAGDE on CPUs by gpu=None and trian it on GPU #0 by gpu="0"
If you are merely interested in learning cell embeddings without consiering any optimization about cell clustering, you can specify cluster_opt=False here. In this case, scAGDE will be run withour any clustering-related module and optimization.
[7]:
import scAGDE
trainer = scAGDE.Trainer(adata,outdir="output",n_centroids=8,gpu="3")
device used: cuda:3
Now we can train scAGDE model in end-to-end style. The whole pipeline behind the function of fit() mainly consists of three stages, as below:
scAGDE first trained an chromatin accessibility-based autoencoder to measure the importance of the peaks and select the key peaks. The number of selected peaks is set to 10,000 in default, or you can change it by setting
top_n. In the meanwhile, the initial cell representations for cell graph construction are stored inadata.obs[embed_init_key], which is"latent_init"in default.scAGDE then constructed cell graph and trains the GCN-based embedded model to extract essential structural information from both count and cell graph data.
scAGDE finally yiels robust and discriminative cell embeddings which are stored in
adata.obsm[embed_key], which is"latent"in default. Also, scAGDE enables imputation task ifimpute_keyis not None and the imputed data will be stored inadata.obsm[impute_key], which is"impute"in default.
scAGDE performs clustering on final embeddings if cluster_key is not None, and the cluster assignments will be in adata.obs[cluster_key], which is "cluster" in default. The cluster number is the value of n_centroids and if estimation is used, the cluster number is the value of estimated cluster number.
You can also explore each step as you wish by following a step-by-step tutorial in Tutorial 2: Step-by-Step scATAC-seq analysis.
[8]:
adata = trainer.fit(topn=10000,impute_key="impute")
print(adata)
Cell number: 2088
Peak number: 11285
n_centroids: 8
## Training CountModel ##
CountModel: 100%|██████████| 5000/5000 [00:31<00:00, 157.84it/s, loss=1687.1017]
## Constructing Cell Graph ##
Cell number: 2088
Peak number: 10000
n_centroids: 8
## Training GraphModel ##
GraphModel-preTrain: 100%|██████████| 1500/1500 [00:14<00:00, 100.03it/s, loss=1804.3624]
GraphModel: 100%|██████████| 4000/4000 [00:50<00:00, 78.97it/s, loss=4249.9907]
R[write to console]: __ __
____ ___ _____/ /_ _______/ /_
/ __ `__ \/ ___/ / / / / ___/ __/
/ / / / / / /__/ / /_/ (__ ) /_
/_/ /_/ /_/\___/_/\__,_/____/\__/ version 6.0.0
Type 'citation("mclust")' for citing this R package in publications.
AnnData object with n_obs × n_vars = 2088 × 11285
obs: 'celltype', 'n_genes', 'cluster'
var: 'n_cells', 'is_selected'
uns: 'neighbors', 'pca', 'tsne', 'umap'
obsm: 'X_pca', 'X_tsne', 'X_umap', 'latent_init', 'impute', 'latent'
varm: 'PCs'
obsp: 'connectivities', 'distances'
3. The imputation visualization
In our study of scAGDE, we evaluated the effectiveness of imputation in multiple ways, like cell clustering and visualization, and explored the impact in downstream analysis. Here we list some key steps for these analysis.
It is worth noting that the main figures presented in our work were produced by R code, and the general idea is shown here.
3.1 Fetch imputed data
We can fetch impued data matrix from adata.obsm[impute_key]. Also we prepare the original data matrix for comparison.
[9]:
# subset the adata with selected features
raw = adata[:,adata.var["is_selected"] == 1].X
imputed = adata.obsm["impute"]
print(imputed.shape)
assert imputed.shape == raw.shape, "shape not identical"
(2088, 10000)
Next let’s binary the imputed data.
[10]:
binary = scAGDE.utils.binarization(imputed,raw)
print(binary.shape)
(2088, 10000)
3.2 t-SNE/UMAP comparison
We can observe the t-SNE or UMAP visualization on raw, imputed and binary imputed data with cell type labels to evaluate the effect of imputation. Besides, we perform Leiden clustering algorithm for further evaluation.
[11]:
import warnings
warnings.filterwarnings('ignore')
[12]:
import anndata
data_raw = anndata.AnnData(raw,obs=adata.obs,var=adata[:,adata.var["is_selected"] == 1].var)
sc.tl.pca(data_raw, svd_solver="arpack")
sc.pp.neighbors(data_raw)
sc.tl.umap(data_raw)
sc.tl.tsne(data_raw)
sc.tl.leiden(
data_raw,
resolution=0.5,
random_state=0,
n_iterations=2,
directed=False,
)
sc.pl.umap(data_raw,color=["celltype","leiden"],title="Raw")
sc.pl.tsne(data_raw,color=["celltype","leiden"],title="Raw")
WARNING: The title list is shorter than the number of panels. Using 'color' value instead for some plots.
WARNING: The title list is shorter than the number of panels. Using 'color' value instead for some plots.
[13]:
data_imputed = anndata.AnnData(imputed,obs=adata.obs,var=adata[:,adata.var["is_selected"] == 1].var)
sc.tl.pca(data_imputed, svd_solver="arpack")
sc.pp.neighbors(data_imputed)
sc.tl.umap(data_imputed)
sc.tl.tsne(data_imputed)
sc.tl.leiden(
data_imputed,
resolution=0.5,
random_state=0,
n_iterations=2,
directed=False,
)
sc.pl.umap(data_imputed,color=["celltype","leiden"],title="Imputed")
sc.pl.tsne(data_imputed,color=["celltype","leiden"],title="Imputed")
WARNING: The title list is shorter than the number of panels. Using 'color' value instead for some plots.
WARNING: The title list is shorter than the number of panels. Using 'color' value instead for some plots.
[14]:
data_binary = anndata.AnnData(binary.A,obs=adata.obs,var=adata[:,adata.var["is_selected"] == 1].var)
sc.tl.pca(data_binary, svd_solver="arpack")
sc.pp.neighbors(data_binary)
sc.tl.tsne(data_binary)
sc.tl.umap(data_binary)
sc.tl.leiden(
data_binary,
resolution=0.5,
random_state=0,
n_iterations=2,
directed=False,
)
sc.pl.umap(data_binary,color=["celltype","leiden"],title="Imputed")
sc.pl.tsne(data_binary,color=["celltype","leiden"],title="Imputed")
WARNING: The title list is shorter than the number of panels. Using 'color' value instead for some plots.
WARNING: The title list is shorter than the number of panels. Using 'color' value instead for some plots.
Finally, we save the AnnData object in .h5ad format, including the binarized imputed data for future use.
[ ]:
#
import os
# Generate Seurat object
outdir = "imputation"
if not os.path.exists(outdir): os.makedirs(outdir)
# We save the binary imputed data into the AnnData object for future use.
adata.obsm["binary"] = binary.A
adata[:,adata.var["is_selected"] == 1].write(os.path.join(outdir,"brain.h5ad"),compression="gzip")
3. Downstream analysis
3.1 Set up the enviornment and data
How to use R code in this notebook?
We have developed several R scripts to perform downstream analyses, and the essential code for key analyses is provided below. To interactively execute the analysis within this notebook, we utilize the rpy2 package, which allows running R code directly. Thus, please ensure that rpy2 is installed. Alternatively, you may extract these R scripts and execute them externally as standalone R scripts.
The code below initializes rpy2. After this setup, you can write and execute R code directly within notebook cells by starting with %%R.
[2]:
import logging
import rpy2.rinterface_lib.callbacks
from rpy2.robjects import pandas2ri
rpy2.rinterface_lib.callbacks.logger.setLevel(logging.ERROR)
pandas2ri.activate()
%load_ext rpy2.ipython
To completely finish the following analysis, you need requires specific R packages listed below (pkgs), and you can verify and install using the code provided below.
The following code will help you install all the required packages:
% Installing with conda solves most of the dependency package installation problems:
conda install r-signac
conda install r-seurat
conda install r-sceasy
conda install bioconductor-tfbstools
% The other packages can be installed just in R:
install.packages(“reticulate”)
install.packages(“dplyr”)
if (!requireNamespace(“BiocManager”, quietly = TRUE)) install.packages(“BiocManager”)
BiocManager::install(“ComplexHeatmap”)
BiocManager::install(“JASPAR2020”)
BiocManager::install(“EnsDb.Mmusculus.v79”)
BiocManager::install(“BSgenome.Mmusculus.UCSC.mm10”)
BiocManager::install(“biovizBase”)
BiocManager::install(“motifmatchr”)
BiocManager::install(“chromVAR”)
[3]:
%%R
pkgs <- c(
"reticulate",
"sceasy",
"Signac",
"Seurat",
"dplyr",
"ComplexHeatmap",
"ggplot2",
"circlize",
"TFBSTools",
"JASPAR2020",
"EnsDb.Mmusculus.v79",
"BSgenome.Mmusculus.UCSC.mm10"
)
######## Install all packages using codes below ########
# if (!requireNamespace("BiocManager", quietly = TRUE))
# install.packages("BiocManager")
# BiocManager::install(pkgs)
suppressWarnings(suppressPackageStartupMessages(lapply(pkgs,library,character.only=TRUE)))
WARNING: The R package "reticulate" only fixed recently
an issue that caused a segfault when used with rpy2:
https://github.com/rstudio/reticulate/pull/1188
Make sure that you use a version of that package that includes
the fix.
[[1]]
[1] "reticulate" "tools" "stats" "graphics" "grDevices"
[6] "utils" "datasets" "methods" "base"
[[2]]
[1] "sceasy" "reticulate" "tools" "stats" "graphics"
[6] "grDevices" "utils" "datasets" "methods" "base"
[[3]]
[1] "Signac" "sceasy" "reticulate" "tools" "stats"
[6] "graphics" "grDevices" "utils" "datasets" "methods"
[11] "base"
[[4]]
[1] "SeuratObject" "Seurat" "Signac" "sceasy" "reticulate"
[6] "tools" "stats" "graphics" "grDevices" "utils"
[11] "datasets" "methods" "base"
[[5]]
[1] "dplyr" "SeuratObject" "Seurat" "Signac" "sceasy"
[6] "reticulate" "tools" "stats" "graphics" "grDevices"
[11] "utils" "datasets" "methods" "base"
[[6]]
[1] "ComplexHeatmap" "grid" "dplyr" "SeuratObject"
[5] "Seurat" "Signac" "sceasy" "reticulate"
[9] "tools" "stats" "graphics" "grDevices"
[13] "utils" "datasets" "methods" "base"
[[7]]
[1] "ggplot2" "ComplexHeatmap" "grid" "dplyr"
[5] "SeuratObject" "Seurat" "Signac" "sceasy"
[9] "reticulate" "tools" "stats" "graphics"
[13] "grDevices" "utils" "datasets" "methods"
[17] "base"
[[8]]
[1] "circlize" "ggplot2" "ComplexHeatmap" "grid"
[5] "dplyr" "SeuratObject" "Seurat" "Signac"
[9] "sceasy" "reticulate" "tools" "stats"
[13] "graphics" "grDevices" "utils" "datasets"
[17] "methods" "base"
[[9]]
[1] "TFBSTools" "circlize" "ggplot2" "ComplexHeatmap"
[5] "grid" "dplyr" "SeuratObject" "Seurat"
[9] "Signac" "sceasy" "reticulate" "tools"
[13] "stats" "graphics" "grDevices" "utils"
[17] "datasets" "methods" "base"
[[10]]
[1] "JASPAR2020" "TFBSTools" "circlize" "ggplot2"
[5] "ComplexHeatmap" "grid" "dplyr" "SeuratObject"
[9] "Seurat" "Signac" "sceasy" "reticulate"
[13] "tools" "stats" "graphics" "grDevices"
[17] "utils" "datasets" "methods" "base"
[[11]]
[1] "EnsDb.Mmusculus.v79" "ensembldb" "AnnotationFilter"
[4] "GenomicFeatures" "AnnotationDbi" "Biobase"
[7] "GenomicRanges" "GenomeInfoDb" "IRanges"
[10] "S4Vectors" "stats4" "BiocGenerics"
[13] "JASPAR2020" "TFBSTools" "circlize"
[16] "ggplot2" "ComplexHeatmap" "grid"
[19] "dplyr" "SeuratObject" "Seurat"
[22] "Signac" "sceasy" "reticulate"
[25] "tools" "stats" "graphics"
[28] "grDevices" "utils" "datasets"
[31] "methods" "base"
[[12]]
[1] "BSgenome.Mmusculus.UCSC.mm10" "BSgenome"
[3] "rtracklayer" "BiocIO"
[5] "Biostrings" "XVector"
[7] "EnsDb.Mmusculus.v79" "ensembldb"
[9] "AnnotationFilter" "GenomicFeatures"
[11] "AnnotationDbi" "Biobase"
[13] "GenomicRanges" "GenomeInfoDb"
[15] "IRanges" "S4Vectors"
[17] "stats4" "BiocGenerics"
[19] "JASPAR2020" "TFBSTools"
[21] "circlize" "ggplot2"
[23] "ComplexHeatmap" "grid"
[25] "dplyr" "SeuratObject"
[27] "Seurat" "Signac"
[29] "sceasy" "reticulate"
[31] "tools" "stats"
[33] "graphics" "grDevices"
[35] "utils" "datasets"
[37] "methods" "base"
How to read AnnData data object in R?
First, we will convert Python objects into data formats required by R. Specifically, we will convert an AnnData object to a Seurat object and save it as an .rds file. Here, we use the sceasy package to perform this task; however, you may opt for any other method you are comfortable with.
[24]:
%%R
sceasy::convertFormat("imputation/brain.h5ad", from = "anndata", to = "seurat", outFile = "imputation/brain.rds", assay="peaks")
An object of class Seurat
10000 features across 2088 samples within 1 assay
Active assay: peaks (10000 features, 0 variable features)
2 layers present: counts, data
7 dimensional reductions calculated: pca, tsne, umap, binary, impute, latent, latent_init
Warning: Feature names cannot have underscores ('_'), replacing with dashes ('-')
Warning: Feature names cannot have underscores ('_'), replacing with dashes ('-')
X -> counts
Next, let we example the correct data object in R.
[34]:
%%R
brain <- readRDS("imputation/brain.rds")
brain
An object of class Seurat
10000 features across 2088 samples within 1 assay
Active assay: peaks (10000 features, 0 variable features)
2 layers present: counts, data
7 dimensional reductions calculated: pca, tsne, umap, binary, impute, latent, latent_init
3.2 Differential accessibility regions (DARs) identification
Next, let’s identify Differential Accessibility Regions following the standard Signac workflow. First, we need to convert the data to the appropriate format. During this process, we will integrate both the imputed and binary imputed data as two ChromatinAssay objects within the same SeuratObject, storing them as different assay.
Prepare data object
[35]:
%%R
library(Signac)
library(EnsDb.Mmusculus.v79)
# Convert our Seurat object to Signac object, saving meta information and cell embeddings.
metadata <- brain@meta.data
latent <- brain@reductions$latent
latent@assay.used <- "peaks"
counts_ <- brain@assays$peaks@counts
impute_ <- t(brain@reductions$impute@cell.embeddings)
rownames(impute_) <- rownames(brain)
binary_ <- t(brain@reductions$binary@cell.embeddings)
rownames(binary_) <- rownames(brain)
chrom_assay <- CreateChromatinAssay(
counts = counts_,
sep = c(":", "-")
)
brain <- CreateSeuratObject(
counts = chrom_assay,
assay = 'peaks',
meta.data = metadata
)
brain[["latent"]] <- latent
brain[["impute"]] <- CreateChromatinAssay(
counts = impute_,
sep = c("-", "-")
)
brain[["binary"]] <- CreateChromatinAssay(
counts = binary_,
sep = c("-", "-")
)
Idents(brain) <- brain$celltype
# Annotation
annotations <- GetGRangesFromEnsDb(ensdb = EnsDb.Mmusculus.v79)
seqlevels(annotations) <- paste0('chr', seqlevels(annotations))
genome(annotations) <- "mm10"
# saveRDS("imputation/annotation.rds",annotations)
# annotations <- readRDS("imputation/annotation.rds")
Annotation(brain[["peaks"]]) <- annotations
Annotation(brain[["impute"]]) <- annotations
Annotation(brain[["binary"]]) <- annotations
rm(counts_,impute_,binary_,annotations,chrom_assay,latent,metadata)
DARs identification
At this stage, we use the FindAllMarkers function to identify differential accessible regions for the raw, imputed, and binary imputed data separately.
[36]:
%%R
markersPeaks.Raw <- FindAllMarkers(brain, only.pos = TRUE, min.pct = 0.15, logfc.threshold = 0.15,assay = "peaks")
markersPeaks.Impute <- FindAllMarkers(brain, only.pos = TRUE, min.pct = 0.15, logfc.threshold = 0.15,assay = "impute")
markersPeaks.Binary <- FindAllMarkers(brain, only.pos = TRUE, min.pct = 0.15, logfc.threshold = 0.15,assay = "binary")
| | 0 % ~calculating |+ | 1 % ~17s |++ | 2 % ~17s |++ | 3 % ~17s |+++ | 4 % ~17s |+++ | 5 % ~17s |++++ | 6 % ~16s |++++ | 7 % ~16s |+++++ | 8 % ~16s |+++++ | 9 % ~16s |++++++ | 10% ~16s |++++++ | 11% ~16s |+++++++ | 12% ~15s |+++++++ | 13% ~15s |++++++++ | 14% ~15s |++++++++ | 15% ~15s |+++++++++ | 16% ~15s |+++++++++ | 17% ~15s |++++++++++ | 18% ~14s |++++++++++ | 19% ~14s |+++++++++++ | 20% ~14s |+++++++++++ | 21% ~14s |++++++++++++ | 22% ~14s |++++++++++++ | 23% ~14s |+++++++++++++ | 24% ~13s |+++++++++++++ | 26% ~13s |++++++++++++++ | 27% ~13s |++++++++++++++ | 28% ~13s |+++++++++++++++ | 29% ~13s |+++++++++++++++ | 30% ~12s |++++++++++++++++ | 31% ~12s |++++++++++++++++ | 32% ~12s |+++++++++++++++++ | 33% ~12s |+++++++++++++++++ | 34% ~12s |++++++++++++++++++ | 35% ~11s |++++++++++++++++++ | 36% ~11s |+++++++++++++++++++ | 37% ~11s |+++++++++++++++++++ | 38% ~11s |++++++++++++++++++++ | 39% ~11s |++++++++++++++++++++ | 40% ~11s |+++++++++++++++++++++ | 41% ~10s |+++++++++++++++++++++ | 42% ~10s |++++++++++++++++++++++ | 43% ~10s |++++++++++++++++++++++ | 44% ~10s |+++++++++++++++++++++++ | 45% ~10s |+++++++++++++++++++++++ | 46% ~09s |++++++++++++++++++++++++ | 47% ~09s |++++++++++++++++++++++++ | 48% ~09s |+++++++++++++++++++++++++ | 49% ~09s |+++++++++++++++++++++++++ | 50% ~09s |++++++++++++++++++++++++++ | 51% ~09s |+++++++++++++++++++++++++++ | 52% ~08s |+++++++++++++++++++++++++++ | 53% ~08s |++++++++++++++++++++++++++++ | 54% ~08s |++++++++++++++++++++++++++++ | 55% ~08s |+++++++++++++++++++++++++++++ | 56% ~08s |+++++++++++++++++++++++++++++ | 57% ~07s |++++++++++++++++++++++++++++++ | 58% ~07s |++++++++++++++++++++++++++++++ | 59% ~07s |+++++++++++++++++++++++++++++++ | 60% ~07s |+++++++++++++++++++++++++++++++ | 61% ~07s |++++++++++++++++++++++++++++++++ | 62% ~07s |++++++++++++++++++++++++++++++++ | 63% ~06s |+++++++++++++++++++++++++++++++++ | 64% ~06s |+++++++++++++++++++++++++++++++++ | 65% ~06s |++++++++++++++++++++++++++++++++++ | 66% ~06s |++++++++++++++++++++++++++++++++++ | 67% ~06s |+++++++++++++++++++++++++++++++++++ | 68% ~06s |+++++++++++++++++++++++++++++++++++ | 69% ~05s |++++++++++++++++++++++++++++++++++++ | 70% ~05s |++++++++++++++++++++++++++++++++++++ | 71% ~05s |+++++++++++++++++++++++++++++++++++++ | 72% ~05s |+++++++++++++++++++++++++++++++++++++ | 73% ~05s |++++++++++++++++++++++++++++++++++++++ | 74% ~04s |++++++++++++++++++++++++++++++++++++++ | 76% ~04s |+++++++++++++++++++++++++++++++++++++++ | 77% ~04s |+++++++++++++++++++++++++++++++++++++++ | 78% ~04s |++++++++++++++++++++++++++++++++++++++++ | 79% ~04s |++++++++++++++++++++++++++++++++++++++++ | 80% ~04s |+++++++++++++++++++++++++++++++++++++++++ | 81% ~03s |+++++++++++++++++++++++++++++++++++++++++ | 82% ~03s |++++++++++++++++++++++++++++++++++++++++++ | 83% ~03s |++++++++++++++++++++++++++++++++++++++++++ | 84% ~03s |+++++++++++++++++++++++++++++++++++++++++++ | 85% ~03s |+++++++++++++++++++++++++++++++++++++++++++ | 86% ~03s |++++++++++++++++++++++++++++++++++++++++++++ | 87% ~02s |++++++++++++++++++++++++++++++++++++++++++++ | 88% ~02s |+++++++++++++++++++++++++++++++++++++++++++++ | 89% ~02s |+++++++++++++++++++++++++++++++++++++++++++++ | 90% ~02s |++++++++++++++++++++++++++++++++++++++++++++++ | 91% ~02s |++++++++++++++++++++++++++++++++++++++++++++++ | 92% ~01s |+++++++++++++++++++++++++++++++++++++++++++++++ | 93% ~01s |+++++++++++++++++++++++++++++++++++++++++++++++ | 94% ~01s |++++++++++++++++++++++++++++++++++++++++++++++++ | 95% ~01s |++++++++++++++++++++++++++++++++++++++++++++++++ | 96% ~01s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 97% ~01s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 98% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 99% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=17s
| | 0 % ~calculating |+ | 1 % ~43s |+ | 2 % ~42s |++ | 3 % ~43s |++ | 4 % ~42s |+++ | 5 % ~42s |+++ | 6 % ~41s |++++ | 7 % ~40s |++++ | 8 % ~40s |+++++ | 9 % ~40s |+++++ | 10% ~39s |++++++ | 11% ~39s |++++++ | 12% ~38s |+++++++ | 13% ~38s |+++++++ | 14% ~37s |++++++++ | 15% ~37s |++++++++ | 16% ~36s |+++++++++ | 17% ~36s |+++++++++ | 18% ~36s |++++++++++ | 19% ~35s |++++++++++ | 20% ~35s |+++++++++++ | 21% ~34s |+++++++++++ | 22% ~34s |++++++++++++ | 23% ~33s |++++++++++++ | 24% ~33s |+++++++++++++ | 25% ~32s |+++++++++++++ | 26% ~32s |++++++++++++++ | 27% ~32s |++++++++++++++ | 28% ~31s |+++++++++++++++ | 29% ~31s |+++++++++++++++ | 30% ~30s |++++++++++++++++ | 31% ~30s |++++++++++++++++ | 32% ~29s |+++++++++++++++++ | 33% ~29s |+++++++++++++++++ | 34% ~29s |++++++++++++++++++ | 35% ~28s |++++++++++++++++++ | 36% ~28s |+++++++++++++++++++ | 37% ~27s |+++++++++++++++++++ | 38% ~27s |++++++++++++++++++++ | 39% ~26s |++++++++++++++++++++ | 40% ~26s |+++++++++++++++++++++ | 41% ~26s |+++++++++++++++++++++ | 42% ~25s |++++++++++++++++++++++ | 43% ~25s |++++++++++++++++++++++ | 44% ~24s |+++++++++++++++++++++++ | 45% ~24s |+++++++++++++++++++++++ | 46% ~23s |++++++++++++++++++++++++ | 47% ~23s |++++++++++++++++++++++++ | 48% ~22s |+++++++++++++++++++++++++ | 49% ~22s |+++++++++++++++++++++++++ | 50% ~22s |++++++++++++++++++++++++++ | 51% ~21s |++++++++++++++++++++++++++ | 52% ~21s |+++++++++++++++++++++++++++ | 53% ~20s |+++++++++++++++++++++++++++ | 54% ~20s |++++++++++++++++++++++++++++ | 55% ~19s |++++++++++++++++++++++++++++ | 56% ~19s |+++++++++++++++++++++++++++++ | 57% ~19s |+++++++++++++++++++++++++++++ | 58% ~18s |++++++++++++++++++++++++++++++ | 59% ~18s |++++++++++++++++++++++++++++++ | 60% ~17s |+++++++++++++++++++++++++++++++ | 61% ~17s |+++++++++++++++++++++++++++++++ | 62% ~16s |++++++++++++++++++++++++++++++++ | 63% ~16s |++++++++++++++++++++++++++++++++ | 64% ~16s |+++++++++++++++++++++++++++++++++ | 65% ~15s |+++++++++++++++++++++++++++++++++ | 66% ~15s |++++++++++++++++++++++++++++++++++ | 67% ~14s |++++++++++++++++++++++++++++++++++ | 68% ~14s |+++++++++++++++++++++++++++++++++++ | 69% ~13s |+++++++++++++++++++++++++++++++++++ | 70% ~13s |++++++++++++++++++++++++++++++++++++ | 71% ~13s |++++++++++++++++++++++++++++++++++++ | 72% ~12s |+++++++++++++++++++++++++++++++++++++ | 73% ~12s |+++++++++++++++++++++++++++++++++++++ | 74% ~11s |++++++++++++++++++++++++++++++++++++++ | 75% ~11s |++++++++++++++++++++++++++++++++++++++ | 76% ~10s |+++++++++++++++++++++++++++++++++++++++ | 77% ~10s |+++++++++++++++++++++++++++++++++++++++ | 78% ~10s |++++++++++++++++++++++++++++++++++++++++ | 79% ~09s |++++++++++++++++++++++++++++++++++++++++ | 80% ~09s |+++++++++++++++++++++++++++++++++++++++++ | 81% ~08s |+++++++++++++++++++++++++++++++++++++++++ | 82% ~08s |++++++++++++++++++++++++++++++++++++++++++ | 83% ~07s |++++++++++++++++++++++++++++++++++++++++++ | 84% ~07s |+++++++++++++++++++++++++++++++++++++++++++ | 85% ~07s |+++++++++++++++++++++++++++++++++++++++++++ | 86% ~06s |++++++++++++++++++++++++++++++++++++++++++++ | 87% ~06s |++++++++++++++++++++++++++++++++++++++++++++ | 88% ~05s |+++++++++++++++++++++++++++++++++++++++++++++ | 89% ~05s |+++++++++++++++++++++++++++++++++++++++++++++ | 90% ~04s |++++++++++++++++++++++++++++++++++++++++++++++ | 91% ~04s |++++++++++++++++++++++++++++++++++++++++++++++ | 92% ~03s |+++++++++++++++++++++++++++++++++++++++++++++++ | 93% ~03s |+++++++++++++++++++++++++++++++++++++++++++++++ | 94% ~03s |++++++++++++++++++++++++++++++++++++++++++++++++ | 95% ~02s |++++++++++++++++++++++++++++++++++++++++++++++++ | 96% ~02s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 97% ~01s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 98% ~01s |++++++++++++++++++++++++++++++++++++++++++++++++++| 99% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=43s
| | 0 % ~calculating |+ | 1 % ~37s |++ | 2 % ~37s |++ | 3 % ~37s |+++ | 4 % ~36s |+++ | 5 % ~36s |++++ | 6 % ~36s |++++ | 7 % ~35s |+++++ | 8 % ~35s |+++++ | 9 % ~34s |++++++ | 10% ~34s |++++++ | 11% ~34s |+++++++ | 12% ~33s |+++++++ | 13% ~33s |++++++++ | 14% ~32s |++++++++ | 15% ~32s |+++++++++ | 16% ~32s |+++++++++ | 17% ~31s |++++++++++ | 18% ~31s |++++++++++ | 19% ~31s |+++++++++++ | 20% ~30s |+++++++++++ | 21% ~30s |++++++++++++ | 22% ~29s |++++++++++++ | 23% ~29s |+++++++++++++ | 24% ~29s |+++++++++++++ | 25% ~28s |++++++++++++++ | 26% ~28s |++++++++++++++ | 27% ~28s |+++++++++++++++ | 28% ~27s |+++++++++++++++ | 29% ~27s |++++++++++++++++ | 30% ~26s |++++++++++++++++ | 31% ~26s |+++++++++++++++++ | 32% ~26s |+++++++++++++++++ | 33% ~25s |++++++++++++++++++ | 34% ~25s |++++++++++++++++++ | 35% ~24s |+++++++++++++++++++ | 36% ~24s |+++++++++++++++++++ | 37% ~24s |++++++++++++++++++++ | 38% ~23s |++++++++++++++++++++ | 39% ~23s |+++++++++++++++++++++ | 40% ~23s |+++++++++++++++++++++ | 41% ~22s |++++++++++++++++++++++ | 42% ~22s |++++++++++++++++++++++ | 43% ~21s |+++++++++++++++++++++++ | 44% ~21s |+++++++++++++++++++++++ | 45% ~21s |++++++++++++++++++++++++ | 46% ~20s |++++++++++++++++++++++++ | 47% ~20s |+++++++++++++++++++++++++ | 48% ~19s |+++++++++++++++++++++++++ | 49% ~19s |++++++++++++++++++++++++++ | 51% ~19s |++++++++++++++++++++++++++ | 52% ~18s |+++++++++++++++++++++++++++ | 53% ~18s |+++++++++++++++++++++++++++ | 54% ~18s |++++++++++++++++++++++++++++ | 55% ~17s |++++++++++++++++++++++++++++ | 56% ~17s |+++++++++++++++++++++++++++++ | 57% ~16s |+++++++++++++++++++++++++++++ | 58% ~16s |++++++++++++++++++++++++++++++ | 59% ~16s |++++++++++++++++++++++++++++++ | 60% ~15s |+++++++++++++++++++++++++++++++ | 61% ~15s |+++++++++++++++++++++++++++++++ | 62% ~15s |++++++++++++++++++++++++++++++++ | 63% ~14s |++++++++++++++++++++++++++++++++ | 64% ~14s |+++++++++++++++++++++++++++++++++ | 65% ~13s |+++++++++++++++++++++++++++++++++ | 66% ~13s |++++++++++++++++++++++++++++++++++ | 67% ~13s |++++++++++++++++++++++++++++++++++ | 68% ~12s |+++++++++++++++++++++++++++++++++++ | 69% ~12s |+++++++++++++++++++++++++++++++++++ | 70% ~11s |++++++++++++++++++++++++++++++++++++ | 71% ~11s |++++++++++++++++++++++++++++++++++++ | 72% ~11s |+++++++++++++++++++++++++++++++++++++ | 73% ~10s |+++++++++++++++++++++++++++++++++++++ | 74% ~10s |++++++++++++++++++++++++++++++++++++++ | 75% ~10s |++++++++++++++++++++++++++++++++++++++ | 76% ~09s |+++++++++++++++++++++++++++++++++++++++ | 77% ~09s |+++++++++++++++++++++++++++++++++++++++ | 78% ~08s |++++++++++++++++++++++++++++++++++++++++ | 79% ~08s |++++++++++++++++++++++++++++++++++++++++ | 80% ~08s |+++++++++++++++++++++++++++++++++++++++++ | 81% ~07s |+++++++++++++++++++++++++++++++++++++++++ | 82% ~07s |++++++++++++++++++++++++++++++++++++++++++ | 83% ~06s |++++++++++++++++++++++++++++++++++++++++++ | 84% ~06s |+++++++++++++++++++++++++++++++++++++++++++ | 85% ~06s |+++++++++++++++++++++++++++++++++++++++++++ | 86% ~05s |++++++++++++++++++++++++++++++++++++++++++++ | 87% ~05s |++++++++++++++++++++++++++++++++++++++++++++ | 88% ~05s |+++++++++++++++++++++++++++++++++++++++++++++ | 89% ~04s |+++++++++++++++++++++++++++++++++++++++++++++ | 90% ~04s |++++++++++++++++++++++++++++++++++++++++++++++ | 91% ~03s |++++++++++++++++++++++++++++++++++++++++++++++ | 92% ~03s |+++++++++++++++++++++++++++++++++++++++++++++++ | 93% ~03s |+++++++++++++++++++++++++++++++++++++++++++++++ | 94% ~02s |++++++++++++++++++++++++++++++++++++++++++++++++ | 95% ~02s |++++++++++++++++++++++++++++++++++++++++++++++++ | 96% ~02s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 97% ~01s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 98% ~01s |++++++++++++++++++++++++++++++++++++++++++++++++++| 99% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=38s
| | 0 % ~calculating |+ | 1 % ~50s |++ | 2 % ~49s |++ | 3 % ~48s |+++ | 4 % ~48s |+++ | 5 % ~47s |++++ | 6 % ~46s |++++ | 7 % ~46s |+++++ | 8 % ~45s |+++++ | 9 % ~45s |++++++ | 10% ~44s |++++++ | 11% ~44s |+++++++ | 12% ~43s |+++++++ | 13% ~43s |++++++++ | 14% ~42s |++++++++ | 15% ~42s |+++++++++ | 16% ~41s |+++++++++ | 17% ~41s |++++++++++ | 18% ~40s |++++++++++ | 19% ~40s |+++++++++++ | 20% ~39s |+++++++++++ | 21% ~39s |++++++++++++ | 22% ~38s |++++++++++++ | 23% ~38s |+++++++++++++ | 24% ~37s |+++++++++++++ | 25% ~37s |++++++++++++++ | 26% ~36s |++++++++++++++ | 27% ~36s |+++++++++++++++ | 28% ~35s |+++++++++++++++ | 29% ~35s |++++++++++++++++ | 30% ~34s |++++++++++++++++ | 31% ~34s |+++++++++++++++++ | 32% ~33s |+++++++++++++++++ | 33% ~33s |++++++++++++++++++ | 34% ~32s |++++++++++++++++++ | 35% ~32s |+++++++++++++++++++ | 36% ~31s |+++++++++++++++++++ | 37% ~31s |++++++++++++++++++++ | 38% ~30s |++++++++++++++++++++ | 39% ~30s |+++++++++++++++++++++ | 40% ~29s |+++++++++++++++++++++ | 41% ~29s |++++++++++++++++++++++ | 42% ~28s |++++++++++++++++++++++ | 43% ~28s |+++++++++++++++++++++++ | 44% ~27s |+++++++++++++++++++++++ | 45% ~27s |++++++++++++++++++++++++ | 46% ~26s |++++++++++++++++++++++++ | 47% ~26s |+++++++++++++++++++++++++ | 48% ~25s |+++++++++++++++++++++++++ | 49% ~25s |++++++++++++++++++++++++++ | 51% ~24s |++++++++++++++++++++++++++ | 52% ~24s |+++++++++++++++++++++++++++ | 53% ~23s |+++++++++++++++++++++++++++ | 54% ~23s |++++++++++++++++++++++++++++ | 55% ~22s |++++++++++++++++++++++++++++ | 56% ~22s |+++++++++++++++++++++++++++++ | 57% ~21s |+++++++++++++++++++++++++++++ | 58% ~21s |++++++++++++++++++++++++++++++ | 59% ~20s |++++++++++++++++++++++++++++++ | 60% ~20s |+++++++++++++++++++++++++++++++ | 61% ~19s |+++++++++++++++++++++++++++++++ | 62% ~19s |++++++++++++++++++++++++++++++++ | 63% ~18s |++++++++++++++++++++++++++++++++ | 64% ~18s |+++++++++++++++++++++++++++++++++ | 65% ~17s |+++++++++++++++++++++++++++++++++ | 66% ~17s |++++++++++++++++++++++++++++++++++ | 67% ~16s |++++++++++++++++++++++++++++++++++ | 68% ~16s |+++++++++++++++++++++++++++++++++++ | 69% ~15s |+++++++++++++++++++++++++++++++++++ | 70% ~15s |++++++++++++++++++++++++++++++++++++ | 71% ~14s |++++++++++++++++++++++++++++++++++++ | 72% ~14s |+++++++++++++++++++++++++++++++++++++ | 73% ~13s |+++++++++++++++++++++++++++++++++++++ | 74% ~13s |++++++++++++++++++++++++++++++++++++++ | 75% ~12s |++++++++++++++++++++++++++++++++++++++ | 76% ~12s |+++++++++++++++++++++++++++++++++++++++ | 77% ~11s |+++++++++++++++++++++++++++++++++++++++ | 78% ~11s |++++++++++++++++++++++++++++++++++++++++ | 79% ~10s |++++++++++++++++++++++++++++++++++++++++ | 80% ~10s |+++++++++++++++++++++++++++++++++++++++++ | 81% ~09s |+++++++++++++++++++++++++++++++++++++++++ | 82% ~09s |++++++++++++++++++++++++++++++++++++++++++ | 83% ~08s |++++++++++++++++++++++++++++++++++++++++++ | 84% ~08s |+++++++++++++++++++++++++++++++++++++++++++ | 85% ~07s |+++++++++++++++++++++++++++++++++++++++++++ | 86% ~07s |++++++++++++++++++++++++++++++++++++++++++++ | 87% ~06s |++++++++++++++++++++++++++++++++++++++++++++ | 88% ~06s |+++++++++++++++++++++++++++++++++++++++++++++ | 89% ~05s |+++++++++++++++++++++++++++++++++++++++++++++ | 90% ~05s |++++++++++++++++++++++++++++++++++++++++++++++ | 91% ~04s |++++++++++++++++++++++++++++++++++++++++++++++ | 92% ~04s |+++++++++++++++++++++++++++++++++++++++++++++++ | 93% ~03s |+++++++++++++++++++++++++++++++++++++++++++++++ | 94% ~03s |++++++++++++++++++++++++++++++++++++++++++++++++ | 95% ~02s |++++++++++++++++++++++++++++++++++++++++++++++++ | 96% ~02s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 97% ~01s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 98% ~01s |++++++++++++++++++++++++++++++++++++++++++++++++++| 99% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=49s
| | 0 % ~calculating |+ | 1 % ~22s |++ | 2 % ~22s |++ | 3 % ~22s |+++ | 4 % ~22s |+++ | 5 % ~21s |++++ | 6 % ~21s |++++ | 7 % ~21s |+++++ | 8 % ~21s |+++++ | 9 % ~20s |++++++ | 10% ~20s |++++++ | 11% ~20s |+++++++ | 12% ~20s |+++++++ | 13% ~20s |++++++++ | 14% ~19s |++++++++ | 15% ~19s |+++++++++ | 16% ~19s |+++++++++ | 17% ~19s |++++++++++ | 18% ~18s |++++++++++ | 19% ~18s |+++++++++++ | 20% ~18s |+++++++++++ | 21% ~18s |++++++++++++ | 22% ~18s |++++++++++++ | 23% ~17s |+++++++++++++ | 24% ~17s |+++++++++++++ | 26% ~17s |++++++++++++++ | 27% ~17s |++++++++++++++ | 28% ~16s |+++++++++++++++ | 29% ~16s |+++++++++++++++ | 30% ~16s |++++++++++++++++ | 31% ~16s |++++++++++++++++ | 32% ~15s |+++++++++++++++++ | 33% ~15s |+++++++++++++++++ | 34% ~15s |++++++++++++++++++ | 35% ~15s |++++++++++++++++++ | 36% ~14s |+++++++++++++++++++ | 37% ~14s |+++++++++++++++++++ | 38% ~14s |++++++++++++++++++++ | 39% ~14s |++++++++++++++++++++ | 40% ~14s |+++++++++++++++++++++ | 41% ~13s |+++++++++++++++++++++ | 42% ~13s |++++++++++++++++++++++ | 43% ~13s |++++++++++++++++++++++ | 44% ~13s |+++++++++++++++++++++++ | 45% ~12s |+++++++++++++++++++++++ | 46% ~12s |++++++++++++++++++++++++ | 47% ~12s |++++++++++++++++++++++++ | 48% ~12s |+++++++++++++++++++++++++ | 49% ~12s |+++++++++++++++++++++++++ | 50% ~11s |++++++++++++++++++++++++++ | 51% ~11s |+++++++++++++++++++++++++++ | 52% ~11s |+++++++++++++++++++++++++++ | 53% ~11s |++++++++++++++++++++++++++++ | 54% ~10s |++++++++++++++++++++++++++++ | 55% ~10s |+++++++++++++++++++++++++++++ | 56% ~10s |+++++++++++++++++++++++++++++ | 57% ~10s |++++++++++++++++++++++++++++++ | 58% ~09s |++++++++++++++++++++++++++++++ | 59% ~09s |+++++++++++++++++++++++++++++++ | 60% ~09s |+++++++++++++++++++++++++++++++ | 61% ~09s |++++++++++++++++++++++++++++++++ | 62% ~09s |++++++++++++++++++++++++++++++++ | 63% ~08s |+++++++++++++++++++++++++++++++++ | 64% ~08s |+++++++++++++++++++++++++++++++++ | 65% ~08s |++++++++++++++++++++++++++++++++++ | 66% ~08s |++++++++++++++++++++++++++++++++++ | 67% ~07s |+++++++++++++++++++++++++++++++++++ | 68% ~07s |+++++++++++++++++++++++++++++++++++ | 69% ~07s |++++++++++++++++++++++++++++++++++++ | 70% ~07s |++++++++++++++++++++++++++++++++++++ | 71% ~06s |+++++++++++++++++++++++++++++++++++++ | 72% ~06s |+++++++++++++++++++++++++++++++++++++ | 73% ~06s |++++++++++++++++++++++++++++++++++++++ | 74% ~06s |++++++++++++++++++++++++++++++++++++++ | 76% ~06s |+++++++++++++++++++++++++++++++++++++++ | 77% ~05s |+++++++++++++++++++++++++++++++++++++++ | 78% ~05s |++++++++++++++++++++++++++++++++++++++++ | 79% ~05s |++++++++++++++++++++++++++++++++++++++++ | 80% ~05s |+++++++++++++++++++++++++++++++++++++++++ | 81% ~04s |+++++++++++++++++++++++++++++++++++++++++ | 82% ~04s |++++++++++++++++++++++++++++++++++++++++++ | 83% ~04s |++++++++++++++++++++++++++++++++++++++++++ | 84% ~04s |+++++++++++++++++++++++++++++++++++++++++++ | 85% ~03s |+++++++++++++++++++++++++++++++++++++++++++ | 86% ~03s |++++++++++++++++++++++++++++++++++++++++++++ | 87% ~03s |++++++++++++++++++++++++++++++++++++++++++++ | 88% ~03s |+++++++++++++++++++++++++++++++++++++++++++++ | 89% ~03s |+++++++++++++++++++++++++++++++++++++++++++++ | 90% ~02s |++++++++++++++++++++++++++++++++++++++++++++++ | 91% ~02s |++++++++++++++++++++++++++++++++++++++++++++++ | 92% ~02s |+++++++++++++++++++++++++++++++++++++++++++++++ | 93% ~02s |+++++++++++++++++++++++++++++++++++++++++++++++ | 94% ~01s |++++++++++++++++++++++++++++++++++++++++++++++++ | 95% ~01s |++++++++++++++++++++++++++++++++++++++++++++++++ | 96% ~01s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 97% ~01s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 98% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 99% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=23s
| | 0 % ~calculating |+ | 1 % ~18s |++ | 2 % ~18s |++ | 3 % ~18s |+++ | 4 % ~17s |+++ | 5 % ~17s |++++ | 6 % ~17s |++++ | 7 % ~17s |+++++ | 8 % ~17s |+++++ | 9 % ~16s |++++++ | 10% ~16s |++++++ | 11% ~16s |+++++++ | 12% ~16s |+++++++ | 13% ~16s |++++++++ | 14% ~16s |++++++++ | 15% ~15s |+++++++++ | 16% ~15s |+++++++++ | 17% ~15s |++++++++++ | 18% ~15s |++++++++++ | 19% ~15s |+++++++++++ | 20% ~14s |+++++++++++ | 21% ~14s |++++++++++++ | 22% ~14s |++++++++++++ | 23% ~14s |+++++++++++++ | 24% ~14s |+++++++++++++ | 25% ~14s |++++++++++++++ | 26% ~13s |++++++++++++++ | 27% ~13s |+++++++++++++++ | 28% ~13s |+++++++++++++++ | 29% ~13s |++++++++++++++++ | 30% ~13s |++++++++++++++++ | 31% ~12s |+++++++++++++++++ | 32% ~12s |+++++++++++++++++ | 33% ~12s |++++++++++++++++++ | 34% ~12s |++++++++++++++++++ | 35% ~12s |+++++++++++++++++++ | 36% ~12s |+++++++++++++++++++ | 37% ~11s |++++++++++++++++++++ | 38% ~11s |++++++++++++++++++++ | 39% ~11s |+++++++++++++++++++++ | 40% ~11s |+++++++++++++++++++++ | 41% ~11s |++++++++++++++++++++++ | 42% ~10s |++++++++++++++++++++++ | 43% ~10s |+++++++++++++++++++++++ | 44% ~10s |+++++++++++++++++++++++ | 45% ~10s |++++++++++++++++++++++++ | 46% ~10s |++++++++++++++++++++++++ | 47% ~10s |+++++++++++++++++++++++++ | 48% ~09s |+++++++++++++++++++++++++ | 49% ~09s |++++++++++++++++++++++++++ | 51% ~09s |++++++++++++++++++++++++++ | 52% ~09s |+++++++++++++++++++++++++++ | 53% ~09s |+++++++++++++++++++++++++++ | 54% ~08s |++++++++++++++++++++++++++++ | 55% ~08s |++++++++++++++++++++++++++++ | 56% ~08s |+++++++++++++++++++++++++++++ | 57% ~08s |+++++++++++++++++++++++++++++ | 58% ~08s |++++++++++++++++++++++++++++++ | 59% ~08s |++++++++++++++++++++++++++++++ | 60% ~07s |+++++++++++++++++++++++++++++++ | 61% ~07s |+++++++++++++++++++++++++++++++ | 62% ~07s |++++++++++++++++++++++++++++++++ | 63% ~07s |++++++++++++++++++++++++++++++++ | 64% ~07s |+++++++++++++++++++++++++++++++++ | 65% ~06s |+++++++++++++++++++++++++++++++++ | 66% ~06s |++++++++++++++++++++++++++++++++++ | 67% ~06s |++++++++++++++++++++++++++++++++++ | 68% ~06s |+++++++++++++++++++++++++++++++++++ | 69% ~06s |+++++++++++++++++++++++++++++++++++ | 70% ~06s |++++++++++++++++++++++++++++++++++++ | 71% ~05s |++++++++++++++++++++++++++++++++++++ | 72% ~05s |+++++++++++++++++++++++++++++++++++++ | 73% ~05s |+++++++++++++++++++++++++++++++++++++ | 74% ~05s |++++++++++++++++++++++++++++++++++++++ | 75% ~05s |++++++++++++++++++++++++++++++++++++++ | 76% ~04s |+++++++++++++++++++++++++++++++++++++++ | 77% ~04s |+++++++++++++++++++++++++++++++++++++++ | 78% ~04s |++++++++++++++++++++++++++++++++++++++++ | 79% ~04s |++++++++++++++++++++++++++++++++++++++++ | 80% ~04s |+++++++++++++++++++++++++++++++++++++++++ | 81% ~03s |+++++++++++++++++++++++++++++++++++++++++ | 82% ~03s |++++++++++++++++++++++++++++++++++++++++++ | 83% ~03s |++++++++++++++++++++++++++++++++++++++++++ | 84% ~03s |+++++++++++++++++++++++++++++++++++++++++++ | 85% ~03s |+++++++++++++++++++++++++++++++++++++++++++ | 86% ~03s |++++++++++++++++++++++++++++++++++++++++++++ | 87% ~02s |++++++++++++++++++++++++++++++++++++++++++++ | 88% ~02s |+++++++++++++++++++++++++++++++++++++++++++++ | 89% ~02s |+++++++++++++++++++++++++++++++++++++++++++++ | 90% ~02s |++++++++++++++++++++++++++++++++++++++++++++++ | 91% ~02s |++++++++++++++++++++++++++++++++++++++++++++++ | 92% ~01s |+++++++++++++++++++++++++++++++++++++++++++++++ | 93% ~01s |+++++++++++++++++++++++++++++++++++++++++++++++ | 94% ~01s |++++++++++++++++++++++++++++++++++++++++++++++++ | 95% ~01s |++++++++++++++++++++++++++++++++++++++++++++++++ | 96% ~01s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 97% ~01s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 98% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 99% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=18s
| | 0 % ~calculating |+ | 1 % ~09s |++ | 2 % ~08s |++ | 3 % ~08s |+++ | 4 % ~08s |+++ | 5 % ~08s |++++ | 6 % ~08s |++++ | 7 % ~08s |+++++ | 8 % ~08s |+++++ | 9 % ~08s |++++++ | 10% ~08s |++++++ | 11% ~08s |+++++++ | 12% ~08s |+++++++ | 13% ~07s |++++++++ | 14% ~07s |++++++++ | 15% ~07s |+++++++++ | 16% ~07s |+++++++++ | 17% ~07s |++++++++++ | 18% ~07s |++++++++++ | 19% ~07s |+++++++++++ | 20% ~07s |+++++++++++ | 21% ~07s |++++++++++++ | 22% ~07s |++++++++++++ | 23% ~07s |+++++++++++++ | 24% ~06s |+++++++++++++ | 25% ~06s |++++++++++++++ | 26% ~06s |++++++++++++++ | 27% ~06s |+++++++++++++++ | 28% ~06s |+++++++++++++++ | 29% ~06s |++++++++++++++++ | 30% ~06s |++++++++++++++++ | 31% ~06s |+++++++++++++++++ | 32% ~06s |+++++++++++++++++ | 33% ~06s |++++++++++++++++++ | 34% ~06s |++++++++++++++++++ | 35% ~06s |+++++++++++++++++++ | 36% ~05s |+++++++++++++++++++ | 37% ~05s |++++++++++++++++++++ | 38% ~05s |++++++++++++++++++++ | 39% ~05s |+++++++++++++++++++++ | 40% ~05s |+++++++++++++++++++++ | 41% ~05s |++++++++++++++++++++++ | 42% ~05s |++++++++++++++++++++++ | 43% ~05s |+++++++++++++++++++++++ | 44% ~05s |+++++++++++++++++++++++ | 45% ~05s |++++++++++++++++++++++++ | 46% ~05s |++++++++++++++++++++++++ | 47% ~05s |+++++++++++++++++++++++++ | 48% ~04s |+++++++++++++++++++++++++ | 49% ~04s |++++++++++++++++++++++++++ | 51% ~04s |++++++++++++++++++++++++++ | 52% ~04s |+++++++++++++++++++++++++++ | 53% ~04s |+++++++++++++++++++++++++++ | 54% ~04s |++++++++++++++++++++++++++++ | 55% ~04s |++++++++++++++++++++++++++++ | 56% ~04s |+++++++++++++++++++++++++++++ | 57% ~04s |+++++++++++++++++++++++++++++ | 58% ~04s |++++++++++++++++++++++++++++++ | 59% ~04s |++++++++++++++++++++++++++++++ | 60% ~03s |+++++++++++++++++++++++++++++++ | 61% ~03s |+++++++++++++++++++++++++++++++ | 62% ~03s |++++++++++++++++++++++++++++++++ | 63% ~03s |++++++++++++++++++++++++++++++++ | 64% ~03s |+++++++++++++++++++++++++++++++++ | 65% ~03s |+++++++++++++++++++++++++++++++++ | 66% ~03s |++++++++++++++++++++++++++++++++++ | 67% ~03s |++++++++++++++++++++++++++++++++++ | 68% ~03s |+++++++++++++++++++++++++++++++++++ | 69% ~03s |+++++++++++++++++++++++++++++++++++ | 70% ~03s |++++++++++++++++++++++++++++++++++++ | 71% ~03s |++++++++++++++++++++++++++++++++++++ | 72% ~02s |+++++++++++++++++++++++++++++++++++++ | 73% ~02s |+++++++++++++++++++++++++++++++++++++ | 74% ~02s |++++++++++++++++++++++++++++++++++++++ | 75% ~02s |++++++++++++++++++++++++++++++++++++++ | 76% ~02s |+++++++++++++++++++++++++++++++++++++++ | 77% ~02s |+++++++++++++++++++++++++++++++++++++++ | 78% ~02s |++++++++++++++++++++++++++++++++++++++++ | 79% ~02s |++++++++++++++++++++++++++++++++++++++++ | 80% ~02s |+++++++++++++++++++++++++++++++++++++++++ | 81% ~02s |+++++++++++++++++++++++++++++++++++++++++ | 82% ~02s |++++++++++++++++++++++++++++++++++++++++++ | 83% ~01s |++++++++++++++++++++++++++++++++++++++++++ | 84% ~01s |+++++++++++++++++++++++++++++++++++++++++++ | 85% ~01s |+++++++++++++++++++++++++++++++++++++++++++ | 86% ~01s |++++++++++++++++++++++++++++++++++++++++++++ | 87% ~01s |++++++++++++++++++++++++++++++++++++++++++++ | 88% ~01s |+++++++++++++++++++++++++++++++++++++++++++++ | 89% ~01s |+++++++++++++++++++++++++++++++++++++++++++++ | 90% ~01s |++++++++++++++++++++++++++++++++++++++++++++++ | 91% ~01s |++++++++++++++++++++++++++++++++++++++++++++++ | 92% ~01s |+++++++++++++++++++++++++++++++++++++++++++++++ | 93% ~01s |+++++++++++++++++++++++++++++++++++++++++++++++ | 94% ~01s |++++++++++++++++++++++++++++++++++++++++++++++++ | 95% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++ | 96% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 97% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 98% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 99% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=08s
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Calculating cluster AC
Calculating cluster EX1
Calculating cluster EX2
Calculating cluster EX3
Calculating cluster IN1
Calculating cluster IN2
Calculating cluster MG
Calculating cluster OC
[4]:
%%R
# saveRDS(object = markersPeaks.Raw,file = "imputation/markersPeaks.Raw.rds")
# saveRDS(object = markersPeaks.Impute,file = "imputation/markersPeaks.Impute.rds")
# saveRDS(object = markersPeaks.Binary,file = "imputation/markersPeaks.Binary.rds")
# markersPeaks.Raw <- readRDS("imputation/markersPeaks.Raw.rds")
# markersPeaks.Impute <- readRDS("imputation/markersPeaks.Impute.rds")
# markersPeaks.Binary <- readRDS("imputation/markersPeaks.Binary.rds")
Select the top 15 most prominent differentially accessible regions for each cluster.
[36]:
%%R
markersPeaks.topn.Raw <- markersPeaks.Raw %>%
group_by(cluster) %>%
top_n(n = 15, wt = avg_log2FC)
markersPeaks.topn.Impute <- markersPeaks.Impute %>%
group_by(cluster) %>%
top_n(n = 15, wt = avg_log2FC)
markersPeaks.topn.Binary <- markersPeaks.Binary %>%
group_by(cluster) %>%
top_n(n = 15, wt = avg_log2FC)
Heatmap visualization
The following code uses the ComplexHeatmap package to plot accessibility heatmaps for the three data matrices across these top DARs.
[49]:
%%R
library(dplyr)
library(ComplexHeatmap)
library(circlize)
solarExtra = c("5"='#3361A5', "7"='#248AF3', "1"='#14B3FF', "8"='#88CEEF', "9"='#C1D5DC', "4"='#EAD397', "3"='#FDB31A',"2"= '#E42A2A', "6"='#A31D1D')
paletteContinuous <- function(
pal,
n = 256,
reverse = FALSE
){
palOut <- colorRampPalette(pal)(n)
return(palOut)
}
.rowZscores <- function(m = NULL, min = -2, max = 2, limit = FALSE){
z <- sweep(m - rowMeans(m), 1, matrixStats::rowSds(m),`/`)
if(limit){
z[z > max] <- max
z[z < min] <- min
}
return(z)
}
hm <- function(mat,sp){
mat <- .rowZscores(mat, limit = FALSE)
limits = c(min(mat), max(mat))
color = paletteContinuous(solarExtra, n = 100)
breaks <- seq(-2,2, length.out = length(color))
color <- circlize::colorRamp2(breaks, color)
top_anno <- HeatmapAnnotation(
cluster = anno_block(gp = gpar(fill = NA,col=NA), # set color
labels = levels(cluster_info),
labels_gp = gpar(cex = 0.5, col ="black",fontsize=25, fontface="bold"))) # set font
Heatmap(
mat,
name = "Z-score",
cluster_rows = FALSE,
cluster_columns = FALSE,
show_column_names = FALSE,
show_row_names = FALSE,
column_split = cluster_info,
row_split = sp,
border = T,
border_gp = gpar(lwd=1,col="#555555"),
# row_split = cluster_info,
top_annotation = top_anno,
# left_annotation = top_anno,
column_title= NULL,
row_title = NULL,
col = color,
heatmap_legend_param = list(
color_bar = "continuous",
legend_direction = "horizontal"
)
)
}
# Fetching data for heatmap plots
cluster_info <- sort(brain$celltype)
mat.raw <- GetAssayData(brain, slot = "data", assay = "peaks")
mat.raw <- as.matrix(mat.raw[markersPeaks.topn.Raw$gene, names(cluster_info)])
mat.impute <- GetAssayData(brain, slot = "data", assay = "impute")
mat.impute <- as.matrix(mat.impute[markersPeaks.topn.Impute$gene, names(cluster_info)])
mat.binary <- GetAssayData(brain, slot = "data", assay = "binary")
mat.binary <- as.matrix(mat.binary[markersPeaks.topn.Binary$gene, names(cluster_info)])
Let’s show the heatmaps for raw, imputed and binary imputed data in that order:
[93]:
%%R
ht_opt$message = FALSE
# pdf("imputation/heatmap_DARs_raw.pdf", width = 8, height = 4.5)
draw(hm(mat.raw,markersPeaks.topn.Raw$cluster),heatmap_legend_side = "bot",)
# dev.off()
[94]:
%%R
# pdf("imputation/heatmap_DARs_impute.pdf", width = 8, height = 4.5)
draw(hm(mat.impute,markersPeaks.topn.Impute$cluster),heatmap_legend_side = "bot")
# dev.off()
[95]:
%%R
# pdf("imputation/heatmap_DARs_binary.pdf", width = 8, height = 4.5)
draw(hm(mat.binary,markersPeaks.topn.Binary$cluster),heatmap_legend_side = "bot")
# dev.off()
Difference sets of DARs
Next, we investigate how imputation enhances the results of DARs analysis, focusing on the set of differential DARs as the starting point.
[98]:
%%R
a <- markersPeaks.Impute %>%
dplyr::filter(avg_log2FC > 1) %>%
arrange(cluster)
b <- markersPeaks.Raw %>%
dplyr::filter(avg_log2FC > 1) %>%
arrange(cluster)
diff.more <- as.data.frame(setdiff(a,b))
diff.more.topn <- diff.more %>%
group_by(cluster) %>%
dplyr::filter(avg_log2FC > 1)
mat.diff <- GetAssayData(brain, slot = "data", assay = "impute")
mat.diff <- as.matrix(mat.diff[diff.more.topn$gene, names(cluster_info)])
mat <- mat.diff
.rowZscores(mat, limit = FALSE)-> mat
Let’s visualize the heatmap on these difference sets of DARs.
[105]:
%%R
color.count = paletteContinuous(solarExtra, n = 100)
breaks <- seq(-2, 2, length.out = length(color.count))
color.count <- circlize::colorRamp2(breaks, color.count)
top_anno <- HeatmapAnnotation(
cluster = anno_block(gp = gpar(fill = c("#E64B35FF","#4DBBD5FF","#00A087FF","#3C5488FF","#F39B7FFF","#8491B4FF","#91D1C2FF","#DC0000FF")), # 设置填充色
labels = levels(cluster_info),
labels_gp = gpar(cex = 0.5, col = "white",fontsize=17,fontface="bold"))) # set font
sp <- subset(diff.more.topn,select=c("gene","cluster"))
sp$gene <- NULL
hm.count <- Heatmap(
mat,
name = "Z-score",
cluster_rows = FALSE,
cluster_columns = FALSE,
show_column_names = FALSE,
show_row_names = FALSE,
column_split = cluster_info,
top_annotation = top_anno,
column_title= NULL,
col = color.count,
split = sp,
row_title = NULL,
row_gap = unit(0, "mm"),
column_gap = unit(0, "mm"),
border = TRUE,
border_gp = gpar(lwd=1),
heatmap_legend_param = list(
color_bar = "continuous",
legend_direction = "horizontal"
)
)
draw(hm.count,gap=unit(0, "points"),heatmap_legend_side = "bot",show_heatmap_legend=F)
3.3 Motif deviation score
To further understand the biological significance behind this increase in cell type-specific peaks post-imputation, we proceeded with enrichment analysis. The analysis revealed that the enhanced cell type-specific peaks after imputation are significantly associated with cell identity, rather than being arbitrary occurrences.
Specifically, we use Signac which has incorporated chromVAR algorithm to calculate the motif activity score for each cell. For a detailed explanation of the method, refer to the Signac or chromVAR paper.
Calculate motif deviation score
[37]:
%%R
library(TFBSTools)
library(JASPAR2020)
library(BSgenome.Mmusculus.UCSC.mm10)
genome <- BSgenome.Mmusculus.UCSC.mm10
pfm <- getMatrixSet(
x = JASPAR2020,
opts = list(species=10090,collection = "CORE", tax_group = 'vertebrates', all_versions = FALSE)
)
brain <- AddMotifs(object = brain,genome = genome,pfm = pfm)
motif.id2name <- lapply(pfm,function(x){x@name})
motif.name2id <- setNames(as.list(names(motif.id2name)), unlist(motif.id2name))
Beyond motif deviation score, we also computed T-SNE embedding based on this score for futher visualization.
[38]:
%%R
brain <- RunChromVAR(
object = brain,
genome = genome,
assay = "peaks",
new.assay.name = "chromvar.peaks",
)
DefaultAssay(brain) <- "chromvar.peaks"
brain <- ScaleData(brain, features = rownames(brain),do.scale=F)
brain <- RunPCA(brain,slot="data", features = rownames(brain),reduction.name = "pca.chromvar.peaks",reduction.key = "pca.chromvar.peaks")
brain <- RunTSNE(brain,slot="data", reduction = "pca.chromvar.peaks", reduction.name = "tsne.chromvar.peaks",reduction.key = "tsne.chromvar.peaks",check_duplicates=F)
[39]:
%%R
brain <- AddMotifs(object = brain,genome = genome,pfm = pfm, assay = "impute")
brain <- RunChromVAR(
object = brain,
genome = genome,
assay = "impute",
new.assay.name = "chromvar.impute",
)
DefaultAssay(brain) <- "chromvar.impute"
brain <- ScaleData(brain, features = rownames(brain),do.scale=F)
brain <- RunPCA(brain,slot="data", features = rownames(brain),reduction.name = "pca.chromvar.impute",reduction.key = "pca.chromvar.impute")
brain <- RunTSNE(brain,slot="data", reduction = "pca.chromvar.impute", reduction.name = "tsne.chromvar.impute",reduction.key = "tsne.chromvar.impute",check_duplicates=F)
Visualize motif deviation scor before and after imputation
[ ]:
%%R
# Ensure the existence of interested motif.
grep("Dlx2",names(motif.name2id),ignore.case=T,value=T)
[1] "Dlx2"
[ ]:
%%R
library(ggplot2)
plotfunction <- function(tf,noTitle=F){
g <- FeaturePlot(
object = brain,
features = as.character(motif.name2id[tf]), # query the corresponding id by motif name.
min.cutoff = 'q5',
max.cutoff = 'q95',
pt.size = 1,
label = T,
reduction = "tsne.chromvar.impute",
# ncol = length(chosen),
col = paletteContinuous(colorRampPalette(
c("1"="#8499cb","2"="white","3"="#ff0000")
)(10), n = 50),
slot = "data"
)+
ggtitle(NULL)+
labs(x = "TSNE1", y = "TSNE2")+
theme(
axis.line = element_line(linewidth=.25,arrow = arrow(type = "closed",length = unit(0.04, "inches"))),
panel.border = element_blank(),
axis.text = element_blank(),
axis.ticks = element_blank(),
axis.title = element_text(hjust = 0, face = "italic"),
plot.margin = margin(0,0,0,0)
)+
NULL
g
}
tf <- "Dlx2"
DefaultAssay(brain) <- "chromvar.impute"
p1 <- plotfunction(tf)
DefaultAssay(brain) <- "chromvar.peaks"
p2 <- plotfunction(tf)
[ ]:
%%R
# `p1` represents the interest feature's expression of imputed data, while 'p2' represents the result of raw data.
p1/p2
Differential testing on motif score
To identify cell type-specific regulatory elements, we can search for differentially-active motifs by performing differential testing on motif score.
[40]:
%%R
markers.dev.peaks <- FindAllMarkers(
object = brain,
only.pos = T,
mean.fxn = rowMeans,
fc.name = "avg_diff",
min.pct = .25, logfc.threshold = .25,
assay = "chromvar.peaks",
slot = "scale.data"
)
markers.dev.peaks$motif.name <- brain[["peaks"]]@motifs@motif.names[markers.dev.peaks$gene]
markers.dev.impute <- FindAllMarkers(
object = brain,
only.pos = T,
mean.fxn = rowMeans,
fc.name = "avg_diff",
min.pct = .25, logfc.threshold = .25,
assay = "chromvar.impute",
slot = "scale.data"
)
markers.dev.impute$motif.name <- brain[["peaks"]]@motifs@motif.names[markers.dev.impute$gene]
| | 0 % ~calculating |+ | 2 % ~00s |++ | 4 % ~00s |+++ | 6 % ~00s |++++ | 8 % ~00s |+++++ | 9 % ~00s |++++++ | 11% ~00s |+++++++ | 13% ~00s |++++++++ | 15% ~00s |+++++++++ | 17% ~00s |++++++++++ | 19% ~00s |+++++++++++ | 21% ~00s |++++++++++++ | 23% ~00s |+++++++++++++ | 25% ~00s |++++++++++++++ | 26% ~00s |+++++++++++++++ | 28% ~00s |++++++++++++++++ | 30% ~00s |+++++++++++++++++ | 32% ~00s |+++++++++++++++++ | 34% ~00s |++++++++++++++++++ | 36% ~00s |+++++++++++++++++++ | 38% ~00s |++++++++++++++++++++ | 40% ~00s |+++++++++++++++++++++ | 42% ~00s |++++++++++++++++++++++ | 43% ~00s |+++++++++++++++++++++++ | 45% ~00s |++++++++++++++++++++++++ | 47% ~00s |+++++++++++++++++++++++++ | 49% ~00s |++++++++++++++++++++++++++ | 51% ~00s |+++++++++++++++++++++++++++ | 53% ~00s |++++++++++++++++++++++++++++ | 55% ~00s |+++++++++++++++++++++++++++++ | 57% ~00s |++++++++++++++++++++++++++++++ | 58% ~00s |+++++++++++++++++++++++++++++++ | 60% ~00s |++++++++++++++++++++++++++++++++ | 62% ~00s |+++++++++++++++++++++++++++++++++ | 64% ~00s |++++++++++++++++++++++++++++++++++ | 66% ~00s |++++++++++++++++++++++++++++++++++ | 68% ~00s |+++++++++++++++++++++++++++++++++++ | 70% ~00s |++++++++++++++++++++++++++++++++++++ | 72% ~00s |+++++++++++++++++++++++++++++++++++++ | 74% ~00s |++++++++++++++++++++++++++++++++++++++ | 75% ~00s |+++++++++++++++++++++++++++++++++++++++ | 77% ~00s |++++++++++++++++++++++++++++++++++++++++ | 79% ~00s |+++++++++++++++++++++++++++++++++++++++++ | 81% ~00s |++++++++++++++++++++++++++++++++++++++++++ | 83% ~00s |+++++++++++++++++++++++++++++++++++++++++++ | 85% ~00s |++++++++++++++++++++++++++++++++++++++++++++ | 87% ~00s |+++++++++++++++++++++++++++++++++++++++++++++ | 89% ~00s |++++++++++++++++++++++++++++++++++++++++++++++ | 91% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++ | 92% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++ | 94% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 96% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 98% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=00s
| | 0 % ~calculating |+ | 2 % ~00s |++ | 4 % ~00s |+++ | 6 % ~00s |++++ | 8 % ~00s |+++++ | 9 % ~00s |++++++ | 11% ~00s |+++++++ | 13% ~00s |++++++++ | 15% ~00s |+++++++++ | 17% ~00s |++++++++++ | 19% ~00s |+++++++++++ | 21% ~00s |++++++++++++ | 23% ~00s |+++++++++++++ | 25% ~00s |++++++++++++++ | 26% ~00s |+++++++++++++++ | 28% ~00s |++++++++++++++++ | 30% ~00s |+++++++++++++++++ | 32% ~00s |+++++++++++++++++ | 34% ~00s |++++++++++++++++++ | 36% ~00s |+++++++++++++++++++ | 38% ~00s |++++++++++++++++++++ | 40% ~00s |+++++++++++++++++++++ | 42% ~00s |++++++++++++++++++++++ | 43% ~00s |+++++++++++++++++++++++ | 45% ~00s |++++++++++++++++++++++++ | 47% ~00s |+++++++++++++++++++++++++ | 49% ~00s |++++++++++++++++++++++++++ | 51% ~00s |+++++++++++++++++++++++++++ | 53% ~00s |++++++++++++++++++++++++++++ | 55% ~00s |+++++++++++++++++++++++++++++ | 57% ~00s |++++++++++++++++++++++++++++++ | 58% ~00s |+++++++++++++++++++++++++++++++ | 60% ~00s |++++++++++++++++++++++++++++++++ | 62% ~00s |+++++++++++++++++++++++++++++++++ | 64% ~00s |++++++++++++++++++++++++++++++++++ | 66% ~00s |++++++++++++++++++++++++++++++++++ | 68% ~00s |+++++++++++++++++++++++++++++++++++ | 70% ~00s |++++++++++++++++++++++++++++++++++++ | 72% ~00s |+++++++++++++++++++++++++++++++++++++ | 74% ~00s |++++++++++++++++++++++++++++++++++++++ | 75% ~00s |+++++++++++++++++++++++++++++++++++++++ | 77% ~00s |++++++++++++++++++++++++++++++++++++++++ | 79% ~00s |+++++++++++++++++++++++++++++++++++++++++ | 81% ~00s |++++++++++++++++++++++++++++++++++++++++++ | 83% ~00s |+++++++++++++++++++++++++++++++++++++++++++ | 85% ~00s |++++++++++++++++++++++++++++++++++++++++++++ | 87% ~00s |+++++++++++++++++++++++++++++++++++++++++++++ | 89% ~00s |++++++++++++++++++++++++++++++++++++++++++++++ | 91% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++ | 92% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++ | 94% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 96% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 98% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=00s
| | 0 % ~calculating |+ | 2 % ~00s |++ | 4 % ~00s |+++ | 6 % ~00s |++++ | 8 % ~00s |+++++ | 9 % ~00s |++++++ | 11% ~00s |+++++++ | 13% ~01s |++++++++ | 15% ~01s |+++++++++ | 17% ~01s |++++++++++ | 19% ~00s |+++++++++++ | 21% ~00s |++++++++++++ | 23% ~00s |+++++++++++++ | 25% ~00s |++++++++++++++ | 26% ~00s |+++++++++++++++ | 28% ~00s |++++++++++++++++ | 30% ~00s |+++++++++++++++++ | 32% ~00s |+++++++++++++++++ | 34% ~00s |++++++++++++++++++ | 36% ~00s |+++++++++++++++++++ | 38% ~00s |++++++++++++++++++++ | 40% ~00s |+++++++++++++++++++++ | 42% ~00s |++++++++++++++++++++++ | 43% ~00s |+++++++++++++++++++++++ | 45% ~00s |++++++++++++++++++++++++ | 47% ~00s |+++++++++++++++++++++++++ | 49% ~00s |++++++++++++++++++++++++++ | 51% ~00s |+++++++++++++++++++++++++++ | 53% ~00s |++++++++++++++++++++++++++++ | 55% ~00s |+++++++++++++++++++++++++++++ | 57% ~00s |++++++++++++++++++++++++++++++ | 58% ~00s |+++++++++++++++++++++++++++++++ | 60% ~00s |++++++++++++++++++++++++++++++++ | 62% ~00s |+++++++++++++++++++++++++++++++++ | 64% ~00s |++++++++++++++++++++++++++++++++++ | 66% ~00s |++++++++++++++++++++++++++++++++++ | 68% ~00s |+++++++++++++++++++++++++++++++++++ | 70% ~00s |++++++++++++++++++++++++++++++++++++ | 72% ~00s |+++++++++++++++++++++++++++++++++++++ | 74% ~00s |++++++++++++++++++++++++++++++++++++++ | 75% ~00s |+++++++++++++++++++++++++++++++++++++++ | 77% ~00s |++++++++++++++++++++++++++++++++++++++++ | 79% ~00s |+++++++++++++++++++++++++++++++++++++++++ | 81% ~00s |++++++++++++++++++++++++++++++++++++++++++ | 83% ~00s |+++++++++++++++++++++++++++++++++++++++++++ | 85% ~00s |++++++++++++++++++++++++++++++++++++++++++++ | 87% ~00s |+++++++++++++++++++++++++++++++++++++++++++++ | 89% ~00s |++++++++++++++++++++++++++++++++++++++++++++++ | 91% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++ | 92% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++ | 94% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 96% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 98% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=00s
| | 0 % ~calculating |+ | 2 % ~00s |++ | 4 % ~00s |+++ | 6 % ~00s |++++ | 8 % ~00s |+++++ | 9 % ~00s |++++++ | 11% ~00s |+++++++ | 13% ~00s |++++++++ | 15% ~00s |+++++++++ | 17% ~00s |++++++++++ | 19% ~00s |+++++++++++ | 21% ~00s |++++++++++++ | 23% ~00s |+++++++++++++ | 25% ~00s |++++++++++++++ | 26% ~00s |+++++++++++++++ | 28% ~00s |++++++++++++++++ | 30% ~00s |+++++++++++++++++ | 32% ~00s |+++++++++++++++++ | 34% ~00s |++++++++++++++++++ | 36% ~00s |+++++++++++++++++++ | 38% ~00s |++++++++++++++++++++ | 40% ~00s |+++++++++++++++++++++ | 42% ~00s |++++++++++++++++++++++ | 43% ~00s |+++++++++++++++++++++++ | 45% ~00s |++++++++++++++++++++++++ | 47% ~00s |+++++++++++++++++++++++++ | 49% ~00s |++++++++++++++++++++++++++ | 51% ~00s |+++++++++++++++++++++++++++ | 53% ~00s |++++++++++++++++++++++++++++ | 55% ~00s |+++++++++++++++++++++++++++++ | 57% ~00s |++++++++++++++++++++++++++++++ | 58% ~00s |+++++++++++++++++++++++++++++++ | 60% ~00s |++++++++++++++++++++++++++++++++ | 62% ~00s |+++++++++++++++++++++++++++++++++ | 64% ~00s |++++++++++++++++++++++++++++++++++ | 66% ~00s |++++++++++++++++++++++++++++++++++ | 68% ~00s |+++++++++++++++++++++++++++++++++++ | 70% ~00s |++++++++++++++++++++++++++++++++++++ | 72% ~00s |+++++++++++++++++++++++++++++++++++++ | 74% ~00s |++++++++++++++++++++++++++++++++++++++ | 75% ~00s |+++++++++++++++++++++++++++++++++++++++ | 77% ~00s |++++++++++++++++++++++++++++++++++++++++ | 79% ~00s |+++++++++++++++++++++++++++++++++++++++++ | 81% ~00s |++++++++++++++++++++++++++++++++++++++++++ | 83% ~00s |+++++++++++++++++++++++++++++++++++++++++++ | 85% ~00s |++++++++++++++++++++++++++++++++++++++++++++ | 87% ~00s |+++++++++++++++++++++++++++++++++++++++++++++ | 89% ~00s |++++++++++++++++++++++++++++++++++++++++++++++ | 91% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++ | 92% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++ | 94% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 96% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 98% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=00s
| | 0 % ~calculating |+ | 2 % ~00s |++ | 4 % ~00s |+++ | 6 % ~00s |++++ | 8 % ~00s |+++++ | 9 % ~00s |++++++ | 11% ~00s |+++++++ | 13% ~00s |++++++++ | 15% ~00s |+++++++++ | 17% ~00s |++++++++++ | 19% ~00s |+++++++++++ | 21% ~00s |++++++++++++ | 23% ~00s |+++++++++++++ | 25% ~00s |++++++++++++++ | 26% ~00s |+++++++++++++++ | 28% ~00s |++++++++++++++++ | 30% ~00s |+++++++++++++++++ | 32% ~00s |+++++++++++++++++ | 34% ~00s |++++++++++++++++++ | 36% ~00s |+++++++++++++++++++ | 38% ~00s |++++++++++++++++++++ | 40% ~00s |+++++++++++++++++++++ | 42% ~00s |++++++++++++++++++++++ | 43% ~00s |+++++++++++++++++++++++ | 45% ~00s |++++++++++++++++++++++++ | 47% ~00s |+++++++++++++++++++++++++ | 49% ~00s |++++++++++++++++++++++++++ | 51% ~00s |+++++++++++++++++++++++++++ | 53% ~00s |++++++++++++++++++++++++++++ | 55% ~00s |+++++++++++++++++++++++++++++ | 57% ~00s |++++++++++++++++++++++++++++++ | 58% ~00s |+++++++++++++++++++++++++++++++ | 60% ~00s |++++++++++++++++++++++++++++++++ | 62% ~00s |+++++++++++++++++++++++++++++++++ | 64% ~00s |++++++++++++++++++++++++++++++++++ | 66% ~00s |++++++++++++++++++++++++++++++++++ | 68% ~00s |+++++++++++++++++++++++++++++++++++ | 70% ~00s |++++++++++++++++++++++++++++++++++++ | 72% ~00s |+++++++++++++++++++++++++++++++++++++ | 74% ~00s |++++++++++++++++++++++++++++++++++++++ | 75% ~00s |+++++++++++++++++++++++++++++++++++++++ | 77% ~00s |++++++++++++++++++++++++++++++++++++++++ | 79% ~00s |+++++++++++++++++++++++++++++++++++++++++ | 81% ~00s |++++++++++++++++++++++++++++++++++++++++++ | 83% ~00s |+++++++++++++++++++++++++++++++++++++++++++ | 85% ~00s |++++++++++++++++++++++++++++++++++++++++++++ | 87% ~00s |+++++++++++++++++++++++++++++++++++++++++++++ | 89% ~00s |++++++++++++++++++++++++++++++++++++++++++++++ | 91% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++ | 92% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++ | 94% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 96% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 98% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=00s
| | 0 % ~calculating |+ | 2 % ~00s |++ | 4 % ~00s |+++ | 6 % ~00s |++++ | 8 % ~00s |+++++ | 9 % ~00s |++++++ | 11% ~00s |+++++++ | 13% ~00s |++++++++ | 15% ~00s |+++++++++ | 17% ~00s |++++++++++ | 19% ~00s |+++++++++++ | 21% ~00s |++++++++++++ | 23% ~00s |+++++++++++++ | 25% ~00s |++++++++++++++ | 26% ~00s |+++++++++++++++ | 28% ~00s |++++++++++++++++ | 30% ~00s |+++++++++++++++++ | 32% ~00s |+++++++++++++++++ | 34% ~00s |++++++++++++++++++ | 36% ~00s |+++++++++++++++++++ | 38% ~00s |++++++++++++++++++++ | 40% ~00s |+++++++++++++++++++++ | 42% ~00s |++++++++++++++++++++++ | 43% ~00s |+++++++++++++++++++++++ | 45% ~00s |++++++++++++++++++++++++ | 47% ~00s |+++++++++++++++++++++++++ | 49% ~00s |++++++++++++++++++++++++++ | 51% ~00s |+++++++++++++++++++++++++++ | 53% ~00s |++++++++++++++++++++++++++++ | 55% ~00s |+++++++++++++++++++++++++++++ | 57% ~00s |++++++++++++++++++++++++++++++ | 58% ~00s |+++++++++++++++++++++++++++++++ | 60% ~00s |++++++++++++++++++++++++++++++++ | 62% ~00s |+++++++++++++++++++++++++++++++++ | 64% ~00s |++++++++++++++++++++++++++++++++++ | 66% ~00s |++++++++++++++++++++++++++++++++++ | 68% ~00s |+++++++++++++++++++++++++++++++++++ | 70% ~00s |++++++++++++++++++++++++++++++++++++ | 72% ~00s |+++++++++++++++++++++++++++++++++++++ | 74% ~00s |++++++++++++++++++++++++++++++++++++++ | 75% ~00s |+++++++++++++++++++++++++++++++++++++++ | 77% ~00s |++++++++++++++++++++++++++++++++++++++++ | 79% ~00s |+++++++++++++++++++++++++++++++++++++++++ | 81% ~00s |++++++++++++++++++++++++++++++++++++++++++ | 83% ~00s |+++++++++++++++++++++++++++++++++++++++++++ | 85% ~00s |++++++++++++++++++++++++++++++++++++++++++++ | 87% ~00s |+++++++++++++++++++++++++++++++++++++++++++++ | 89% ~00s |++++++++++++++++++++++++++++++++++++++++++++++ | 91% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++ | 92% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++ | 94% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 96% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 98% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=00s
| | 0 % ~calculating |+ | 2 % ~00s |++ | 4 % ~00s |+++ | 6 % ~00s |++++ | 8 % ~00s |+++++ | 9 % ~00s |++++++ | 11% ~00s |+++++++ | 13% ~00s |++++++++ | 15% ~00s |+++++++++ | 17% ~00s |++++++++++ | 19% ~00s |+++++++++++ | 21% ~00s |++++++++++++ | 23% ~00s |+++++++++++++ | 25% ~00s |++++++++++++++ | 26% ~00s |+++++++++++++++ | 28% ~00s |++++++++++++++++ | 30% ~00s |+++++++++++++++++ | 32% ~00s |+++++++++++++++++ | 34% ~00s |++++++++++++++++++ | 36% ~00s |+++++++++++++++++++ | 38% ~00s |++++++++++++++++++++ | 40% ~00s |+++++++++++++++++++++ | 42% ~00s |++++++++++++++++++++++ | 43% ~00s |+++++++++++++++++++++++ | 45% ~00s |++++++++++++++++++++++++ | 47% ~00s |+++++++++++++++++++++++++ | 49% ~00s |++++++++++++++++++++++++++ | 51% ~00s |+++++++++++++++++++++++++++ | 53% ~00s |++++++++++++++++++++++++++++ | 55% ~00s |+++++++++++++++++++++++++++++ | 57% ~00s |++++++++++++++++++++++++++++++ | 58% ~00s |+++++++++++++++++++++++++++++++ | 60% ~00s |++++++++++++++++++++++++++++++++ | 62% ~00s |+++++++++++++++++++++++++++++++++ | 64% ~00s |++++++++++++++++++++++++++++++++++ | 66% ~00s |++++++++++++++++++++++++++++++++++ | 68% ~00s |+++++++++++++++++++++++++++++++++++ | 70% ~00s |++++++++++++++++++++++++++++++++++++ | 72% ~00s |+++++++++++++++++++++++++++++++++++++ | 74% ~00s |++++++++++++++++++++++++++++++++++++++ | 75% ~00s |+++++++++++++++++++++++++++++++++++++++ | 77% ~00s |++++++++++++++++++++++++++++++++++++++++ | 79% ~00s |+++++++++++++++++++++++++++++++++++++++++ | 81% ~00s |++++++++++++++++++++++++++++++++++++++++++ | 83% ~00s |+++++++++++++++++++++++++++++++++++++++++++ | 85% ~00s |++++++++++++++++++++++++++++++++++++++++++++ | 87% ~00s |+++++++++++++++++++++++++++++++++++++++++++++ | 89% ~00s |++++++++++++++++++++++++++++++++++++++++++++++ | 91% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++ | 92% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++ | 94% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 96% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 98% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=00s
| | 0 % ~calculating |+ | 2 % ~00s |++ | 4 % ~00s |+++ | 6 % ~00s |++++ | 8 % ~00s |+++++ | 9 % ~00s |++++++ | 11% ~00s |+++++++ | 13% ~00s |++++++++ | 15% ~00s |+++++++++ | 17% ~00s |++++++++++ | 19% ~00s |+++++++++++ | 21% ~00s |++++++++++++ | 23% ~00s |+++++++++++++ | 25% ~00s |++++++++++++++ | 26% ~00s |+++++++++++++++ | 28% ~00s |++++++++++++++++ | 30% ~00s |+++++++++++++++++ | 32% ~00s |+++++++++++++++++ | 34% ~00s |++++++++++++++++++ | 36% ~00s |+++++++++++++++++++ | 38% ~00s |++++++++++++++++++++ | 40% ~00s |+++++++++++++++++++++ | 42% ~00s |++++++++++++++++++++++ | 43% ~00s |+++++++++++++++++++++++ | 45% ~00s |++++++++++++++++++++++++ | 47% ~00s |+++++++++++++++++++++++++ | 49% ~00s |++++++++++++++++++++++++++ | 51% ~00s |+++++++++++++++++++++++++++ | 53% ~00s |++++++++++++++++++++++++++++ | 55% ~00s |+++++++++++++++++++++++++++++ | 57% ~00s |++++++++++++++++++++++++++++++ | 58% ~00s |+++++++++++++++++++++++++++++++ | 60% ~00s |++++++++++++++++++++++++++++++++ | 62% ~00s |+++++++++++++++++++++++++++++++++ | 64% ~00s |++++++++++++++++++++++++++++++++++ | 66% ~00s |++++++++++++++++++++++++++++++++++ | 68% ~00s |+++++++++++++++++++++++++++++++++++ | 70% ~00s |++++++++++++++++++++++++++++++++++++ | 72% ~00s |+++++++++++++++++++++++++++++++++++++ | 74% ~00s |++++++++++++++++++++++++++++++++++++++ | 75% ~00s |+++++++++++++++++++++++++++++++++++++++ | 77% ~00s |++++++++++++++++++++++++++++++++++++++++ | 79% ~00s |+++++++++++++++++++++++++++++++++++++++++ | 81% ~00s |++++++++++++++++++++++++++++++++++++++++++ | 83% ~00s |+++++++++++++++++++++++++++++++++++++++++++ | 85% ~00s |++++++++++++++++++++++++++++++++++++++++++++ | 87% ~00s |+++++++++++++++++++++++++++++++++++++++++++++ | 89% ~00s |++++++++++++++++++++++++++++++++++++++++++++++ | 91% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++ | 92% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++ | 94% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 96% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 98% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=00s
| | 0 % ~calculating |+ | 2 % ~00s |++ | 4 % ~00s |+++ | 6 % ~00s |++++ | 8 % ~00s |+++++ | 9 % ~00s |++++++ | 11% ~00s |+++++++ | 13% ~00s |++++++++ | 15% ~00s |+++++++++ | 17% ~00s |++++++++++ | 19% ~00s |+++++++++++ | 21% ~00s |++++++++++++ | 23% ~00s |+++++++++++++ | 25% ~00s |++++++++++++++ | 26% ~00s |+++++++++++++++ | 28% ~00s |++++++++++++++++ | 30% ~00s |+++++++++++++++++ | 32% ~00s |+++++++++++++++++ | 34% ~00s |++++++++++++++++++ | 36% ~00s |+++++++++++++++++++ | 38% ~00s |++++++++++++++++++++ | 40% ~00s |+++++++++++++++++++++ | 42% ~00s |++++++++++++++++++++++ | 43% ~00s |+++++++++++++++++++++++ | 45% ~00s |++++++++++++++++++++++++ | 47% ~00s |+++++++++++++++++++++++++ | 49% ~00s |++++++++++++++++++++++++++ | 51% ~00s |+++++++++++++++++++++++++++ | 53% ~00s |++++++++++++++++++++++++++++ | 55% ~00s |+++++++++++++++++++++++++++++ | 57% ~00s |++++++++++++++++++++++++++++++ | 58% ~00s |+++++++++++++++++++++++++++++++ | 60% ~00s |++++++++++++++++++++++++++++++++ | 62% ~00s |+++++++++++++++++++++++++++++++++ | 64% ~00s |++++++++++++++++++++++++++++++++++ | 66% ~00s |++++++++++++++++++++++++++++++++++ | 68% ~00s |+++++++++++++++++++++++++++++++++++ | 70% ~00s |++++++++++++++++++++++++++++++++++++ | 72% ~00s |+++++++++++++++++++++++++++++++++++++ | 74% ~00s |++++++++++++++++++++++++++++++++++++++ | 75% ~00s |+++++++++++++++++++++++++++++++++++++++ | 77% ~00s |++++++++++++++++++++++++++++++++++++++++ | 79% ~00s |+++++++++++++++++++++++++++++++++++++++++ | 81% ~00s |++++++++++++++++++++++++++++++++++++++++++ | 83% ~00s |+++++++++++++++++++++++++++++++++++++++++++ | 85% ~00s |++++++++++++++++++++++++++++++++++++++++++++ | 87% ~00s |+++++++++++++++++++++++++++++++++++++++++++++ | 89% ~00s |++++++++++++++++++++++++++++++++++++++++++++++ | 91% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++ | 92% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++ | 94% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 96% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 98% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=00s
| | 0 % ~calculating |+ | 2 % ~00s |++ | 4 % ~00s |+++ | 6 % ~00s |++++ | 8 % ~00s |+++++ | 9 % ~00s |++++++ | 11% ~00s |+++++++ | 13% ~00s |++++++++ | 15% ~00s |+++++++++ | 17% ~00s |++++++++++ | 19% ~00s |+++++++++++ | 21% ~00s |++++++++++++ | 23% ~00s |+++++++++++++ | 25% ~00s |++++++++++++++ | 26% ~00s |+++++++++++++++ | 28% ~00s |++++++++++++++++ | 30% ~00s |+++++++++++++++++ | 32% ~00s |+++++++++++++++++ | 34% ~00s |++++++++++++++++++ | 36% ~00s |+++++++++++++++++++ | 38% ~00s |++++++++++++++++++++ | 40% ~00s |+++++++++++++++++++++ | 42% ~00s |++++++++++++++++++++++ | 43% ~00s |+++++++++++++++++++++++ | 45% ~00s |++++++++++++++++++++++++ | 47% ~00s |+++++++++++++++++++++++++ | 49% ~00s |++++++++++++++++++++++++++ | 51% ~00s |+++++++++++++++++++++++++++ | 53% ~00s |++++++++++++++++++++++++++++ | 55% ~00s |+++++++++++++++++++++++++++++ | 57% ~00s |++++++++++++++++++++++++++++++ | 58% ~00s |+++++++++++++++++++++++++++++++ | 60% ~00s |++++++++++++++++++++++++++++++++ | 62% ~00s |+++++++++++++++++++++++++++++++++ | 64% ~00s |++++++++++++++++++++++++++++++++++ | 66% ~00s |++++++++++++++++++++++++++++++++++ | 68% ~00s |+++++++++++++++++++++++++++++++++++ | 70% ~00s |++++++++++++++++++++++++++++++++++++ | 72% ~00s |+++++++++++++++++++++++++++++++++++++ | 74% ~00s |++++++++++++++++++++++++++++++++++++++ | 75% ~00s |+++++++++++++++++++++++++++++++++++++++ | 77% ~00s |++++++++++++++++++++++++++++++++++++++++ | 79% ~00s |+++++++++++++++++++++++++++++++++++++++++ | 81% ~00s |++++++++++++++++++++++++++++++++++++++++++ | 83% ~00s |+++++++++++++++++++++++++++++++++++++++++++ | 85% ~00s |++++++++++++++++++++++++++++++++++++++++++++ | 87% ~00s |+++++++++++++++++++++++++++++++++++++++++++++ | 89% ~00s |++++++++++++++++++++++++++++++++++++++++++++++ | 91% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++ | 92% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++ | 94% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 96% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 98% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=00s
| | 0 % ~calculating |+ | 2 % ~00s |++ | 4 % ~00s |+++ | 6 % ~00s |++++ | 8 % ~00s |+++++ | 9 % ~00s |++++++ | 11% ~00s |+++++++ | 13% ~00s |++++++++ | 15% ~00s |+++++++++ | 17% ~00s |++++++++++ | 19% ~00s |+++++++++++ | 21% ~00s |++++++++++++ | 23% ~00s |+++++++++++++ | 25% ~00s |++++++++++++++ | 26% ~00s |+++++++++++++++ | 28% ~00s |++++++++++++++++ | 30% ~00s |+++++++++++++++++ | 32% ~00s |+++++++++++++++++ | 34% ~00s |++++++++++++++++++ | 36% ~00s |+++++++++++++++++++ | 38% ~00s |++++++++++++++++++++ | 40% ~00s |+++++++++++++++++++++ | 42% ~00s |++++++++++++++++++++++ | 43% ~00s |+++++++++++++++++++++++ | 45% ~00s |++++++++++++++++++++++++ | 47% ~00s |+++++++++++++++++++++++++ | 49% ~00s |++++++++++++++++++++++++++ | 51% ~00s |+++++++++++++++++++++++++++ | 53% ~00s |++++++++++++++++++++++++++++ | 55% ~00s |+++++++++++++++++++++++++++++ | 57% ~00s |++++++++++++++++++++++++++++++ | 58% ~00s |+++++++++++++++++++++++++++++++ | 60% ~00s |++++++++++++++++++++++++++++++++ | 62% ~00s |+++++++++++++++++++++++++++++++++ | 64% ~00s |++++++++++++++++++++++++++++++++++ | 66% ~00s |++++++++++++++++++++++++++++++++++ | 68% ~00s |+++++++++++++++++++++++++++++++++++ | 70% ~00s |++++++++++++++++++++++++++++++++++++ | 72% ~00s |+++++++++++++++++++++++++++++++++++++ | 74% ~00s |++++++++++++++++++++++++++++++++++++++ | 75% ~00s |+++++++++++++++++++++++++++++++++++++++ | 77% ~00s |++++++++++++++++++++++++++++++++++++++++ | 79% ~00s |+++++++++++++++++++++++++++++++++++++++++ | 81% ~00s |++++++++++++++++++++++++++++++++++++++++++ | 83% ~00s |+++++++++++++++++++++++++++++++++++++++++++ | 85% ~00s |++++++++++++++++++++++++++++++++++++++++++++ | 87% ~00s |+++++++++++++++++++++++++++++++++++++++++++++ | 89% ~00s |++++++++++++++++++++++++++++++++++++++++++++++ | 91% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++ | 92% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++ | 94% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 96% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 98% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=00s
| | 0 % ~calculating |+ | 2 % ~00s |++ | 4 % ~00s |+++ | 6 % ~00s |++++ | 8 % ~00s |+++++ | 9 % ~00s |++++++ | 11% ~00s |+++++++ | 13% ~00s |++++++++ | 15% ~00s |+++++++++ | 17% ~00s |++++++++++ | 19% ~00s |+++++++++++ | 21% ~00s |++++++++++++ | 23% ~00s |+++++++++++++ | 25% ~00s |++++++++++++++ | 26% ~00s |+++++++++++++++ | 28% ~00s |++++++++++++++++ | 30% ~00s |+++++++++++++++++ | 32% ~00s |+++++++++++++++++ | 34% ~00s |++++++++++++++++++ | 36% ~00s |+++++++++++++++++++ | 38% ~00s |++++++++++++++++++++ | 40% ~00s |+++++++++++++++++++++ | 42% ~00s |++++++++++++++++++++++ | 43% ~00s |+++++++++++++++++++++++ | 45% ~00s |++++++++++++++++++++++++ | 47% ~00s |+++++++++++++++++++++++++ | 49% ~00s |++++++++++++++++++++++++++ | 51% ~00s |+++++++++++++++++++++++++++ | 53% ~00s |++++++++++++++++++++++++++++ | 55% ~00s |+++++++++++++++++++++++++++++ | 57% ~00s |++++++++++++++++++++++++++++++ | 58% ~00s |+++++++++++++++++++++++++++++++ | 60% ~00s |++++++++++++++++++++++++++++++++ | 62% ~00s |+++++++++++++++++++++++++++++++++ | 64% ~00s |++++++++++++++++++++++++++++++++++ | 66% ~00s |++++++++++++++++++++++++++++++++++ | 68% ~00s |+++++++++++++++++++++++++++++++++++ | 70% ~00s |++++++++++++++++++++++++++++++++++++ | 72% ~00s |+++++++++++++++++++++++++++++++++++++ | 74% ~00s |++++++++++++++++++++++++++++++++++++++ | 75% ~00s |+++++++++++++++++++++++++++++++++++++++ | 77% ~00s |++++++++++++++++++++++++++++++++++++++++ | 79% ~00s |+++++++++++++++++++++++++++++++++++++++++ | 81% ~00s |++++++++++++++++++++++++++++++++++++++++++ | 83% ~00s |+++++++++++++++++++++++++++++++++++++++++++ | 85% ~00s |++++++++++++++++++++++++++++++++++++++++++++ | 87% ~00s |+++++++++++++++++++++++++++++++++++++++++++++ | 89% ~00s |++++++++++++++++++++++++++++++++++++++++++++++ | 91% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++ | 92% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++ | 94% ~00s |+++++++++++++++++++++++++++++++++++++++++++++++++ | 96% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 98% ~00s |++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=00s
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Select the top 7 most prominent differentially-active motifs for each cluster.
[44]:
%%R
markers.motif.sig.impute <- markers.dev.impute[which(markers.dev.impute$avg_diff>1),]
markers.motif.sig.peaks <- markers.dev.peaks[which(markers.dev.peaks$avg_diff>1),]
markers.motif.sig.impute.topn <- markers.motif.sig.impute%>%
group_by(cluster)%>%
top_n(7,wt = avg_diff)
markers.motif.sig.peaks.topn <- markers.motif.sig.peaks%>%
group_by(cluster)%>%
top_n(7,wt = avg_diff)
The following code uses the ComplexHeatmap package to plot accessibility heatmaps for the three data matrices across these top DARs.
[52]:
%%R
# Fetching data for heatmap plots
mat.dev.impute <- GetAssayData(brain, slot = "data", assay = "chromvar.impute")
mat.dev.impute <- as.matrix(mat.dev.impute[markers.motif.sig.impute.topn$gene, names(cluster_info)])
mat.dev.peaks <- GetAssayData(brain, slot = "data", assay = "chromvar.peaks")
mat.dev.peaks <- as.matrix(mat.dev.peaks[markers.motif.sig.peaks.topn$gene, names(cluster_info)])
top_anno <- HeatmapAnnotation(
cluster = anno_block(gp = gpar(fill = NA,col=NA),
labels = levels(cluster_info),
labels_gp = gpar(cex = 0.5, col = c("#E64B35FF","#4DBBD5FF","#00A087FF","#3C5488FF","#F39B7FFF","#8491B4FF","#91D1C2FF","#DC0000FF"),fontsize=25, fontface="bold"))) # 设置字体
hm.impute <- Heatmap(
mat.dev.impute,
name = "chromVAR deviations of imputed",
cluster_rows = FALSE,
cluster_columns = FALSE,
show_column_names = FALSE,
column_split = cluster_info,
top_annotation = top_anno,
column_title= NULL,
col = paletteContinuous(colorRampPalette(
c("1"="#8499cb","2"="white","3"="#ff0000")
)(10), n = 100),
row_names_rot = 0,
row_names_side = "left",
row_labels = motif.id2name[rownames(mat.dev.impute)],
row_title = NULL,
row_gap = unit(0, "mm"),
column_gap = unit(0, "mm"),
border = F,
border_gp = gpar(lwd=1),
heatmap_legend_param = list(
color_bar = "continuous",
legend_direction = "horizon"
)
)
hm.raw <- Heatmap(
mat.dev.peaks,
name = "chromVAR deviations of raw",
cluster_rows = FALSE,
cluster_columns = FALSE,
show_column_names = FALSE,
column_split = cluster_info,
top_annotation = top_anno,
column_title= NULL,
col = paletteContinuous(colorRampPalette(
c("1"="#8499cb","2"="white","3"="#ff0000")
)(10), n = 100),
row_names_rot = 0,
row_names_side = "left",
row_labels = motif.id2name[rownames(mat.dev.peaks)],
row_title = NULL,
row_gap = unit(0, "mm"),
column_gap = unit(0, "mm"),
border = F,
border_gp = gpar(lwd=1),
heatmap_legend_param = list(
color_bar = "continuous",
legend_direction = "horizon"
)
)
Let’s show the heatmaps for raw, imputed and binary imputed data in that order:
[53]:
%%R
draw(hm.raw,gap=unit(0, "points"),heatmap_legend_side = "left",show_heatmap_legend=F)
[54]:
%%R
draw(hm.impute,gap=unit(0, "points"),heatmap_legend_side = "left",show_heatmap_legend=F)
Obviously, the heatmap of top differentially-active motifs based on imputed data provides clearer cell group distribution.