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BEER: Batch EffEct Remover for single-cell data

Environment: R

BEER's latest version: https://github.com/jumphone/BEER/releases

News:

  • Mar. 2021 ( V0.1.9 ): First version for Seurat 4.0.0

  • Feb. 2021 ( V0.1.8 ): Last version for Seurat 3.0.0

  • Nov. 2019 ( v0.1.7 ): In ".simple_combine(D1, D2, FILL=TRUE)", "FILL" can help users to keep genes that are expressed in only one condition (fill the matrix with “0”). Default "FILL" is FALSE

  • July 2019 ( v0.1.6 ): BEER can automatically adjust "GNUM" when cell number is small in some batch

  • July 2019 ( v0.1.5 ): "ComBat" is used to replace "regression" of "ScaleData" (ComBat is much faster)

  • July 2019 ( v0.1.4 ): Users can provide genes which need to be removed.

  • July 2019 ( v0.1.3 ): Users can use VISA to extract peaks of scATAC-seq.

  • ...

Content:





Workflow:

Latest version

Please see V. Batch-effect Removal Enhancement for details of "Enhancement".



Requirement:

#R >=3.5
install.packages('Seurat') # ==4.0.0 

# Install ComBat:
if (!requireNamespace("BiocManager", quietly = TRUE))
install.packages("BiocManager")
BiocManager::install("sva")
BiocManager::install("limma")

# Users can use "BEER" by directly importing "BEER.R" on the github webpage:

source('https://raw.githubusercontent.com/jumphone/BEER/master/BEER.R')

# Or, download and import it:

source('BEER.R')

For batch-effect removal enhancement, please install BBKNN: https://github.com/Teichlab/bbknn



Vignettes:


Set Python

library(reticulate)
use_python("/home/toolkit/local/bin/python3",required=T)
py_config()

I. Combine Two Batches

Download demo data: https://github.com/jumphone/BEER/raw/master/DATA/demodata.zip

Please do basic quality control before using BEER (e.g. remove low-quality cells & genes).

For QC, please see: https://satijalab.org/seurat/v3.0/pbmc3k_tutorial.html

Step1. Load Data

library(Seurat)

source('https://raw.githubusercontent.com/jumphone/BEER/master/BEER.R')
#source('BEER.R')

#Read 10X data: pbmc.data <- Read10X(data.dir = "../data/pbmc3k/filtered_gene_bc_matrices/hg19/")

#Load Demo Data (subset of GSE70630: MGH53 & MGH54)
#Download: https://github.com/jumphone/BEER/raw/master/DATA/demodata.zip

D1 <- read.table(unz("demodata.zip","DATA1_MAT.txt"), sep='\t', row.names=1, header=T)
D2 <- read.table(unz("demodata.zip","DATA2_MAT.txt"), sep='\t', row.names=1, header=T)

# "D1" & "D2" are UMI matrix (or FPKM, RPKM, TPM, PKM ...; Should not be gene-centric scaled data)
# Rownames of "D1" & "D2" are gene names
# Colnames of "D1" & "D2" are cell names 

# There shouldn't be duplicated colnames in "D1" & "D2":
colnames(D1)=paste0('D1_', colnames(D1))
colnames(D2)=paste0('D2_', colnames(D2))

DATA=.simple_combine(D1,D2)$combine

# Users can use "DATA=.simple_combine(D1,D2, FILL=TRUE)$combine" to keep genes that are expressed in only one condition.

BATCH=rep('D2',ncol(DATA))
BATCH[c(1:ncol(D1))]='D1'

# Simple Quality Control (QC): check the number of sequenced genes
# PosN=apply(DATA,2,.getPos)
# USED=which(PosN>500 & PosN<4000) 
# DATA=DATA[,USED]; BATCH=BATCH[USED] 

Step2. Detect Batch Effect

mybeer=BEER(DATA, BATCH, GNUM=30, PCNUM=50, ROUND=1, GN=2000, SEED=1, COMBAT=TRUE, RMG=NULL)   

# DATA: Expression matrix. Rownames are genes. Colnames are cell names.
# BATCH: A character vector. Length is equal to the "ncol(DATA)".
# GNUM: the number of groups in each batch (default: 30)
# PCNUM: the number of computated PCA subspaces (default: 50)
# ROUND: batch-effect removal strength, positive integer (default: 1)
# GN: the number of variable genes in each batch (default: 2000)
# RMG: genes need to be removed (default: NULL)
# COMBAT: use ComBat to adjust expression value(default: TRUE)    

# Users can use "ReBEER" to adjust GNUM, PCNUM, ROUND, and RMG (it's faster than directly using BEER).
# mybeer <- ReBEER(mybeer, GNUM=30, PCNUM=50, ROUND=1, SEED=1, RMG=NULL) 

# Check selected PCs
PCUSE=mybeer$select
COL=rep('black',length(mybeer$cor))
COL[PCUSE]='red'
plot(mybeer$cor,mybeer$lcor,pch=16,col=COL,
    xlab='Rank Correlation',ylab='Linear Correlation',xlim=c(0,1),ylim=c(0,1))

Users can select PCA subspaces based on the distribution of "Rank Correlation" and "Linear Correlation".

# PCUSE=.selectUSE(mybeer, CUTR=0.7, CUTL=0.7, RR=0.5, RL=0.5)

Step3. Visualization

Keep batch effect:

pbmc_batch=CreateSeuratObject(counts = DATA, min.cells = 0, min.features = 0, project = "ALL") 
[email protected]$batch=BATCH
pbmc_batch=FindVariableFeatures(object = pbmc_batch, selection.method = "vst", nfeatures = 2000)   
VariableFeatures(object = pbmc_batch)
pbmc_batch <- NormalizeData(object = pbmc_batch, normalization.method = "LogNormalize", scale.factor = 10000)
pbmc_batch <- ScaleData(object = pbmc_batch, features = VariableFeatures(object = pbmc_batch))
pbmc_batch <- RunPCA(object = pbmc_batch, seed.use=123, npcs=50, features = VariableFeatures(object = pbmc_batch), ndims.print=1,nfeatures.print=1)
pbmc_batch <- RunUMAP(pbmc_batch, dims = 1:50, seed.use = 123,n.components=2)
DimPlot(pbmc_batch, reduction='umap', group.by='batch', pt.size=0.1) 

Remove batch effect:

pbmc <- mybeer$seurat
PCUSE <- mybeer$select
pbmc <- RunUMAP(object = pbmc, reduction='pca',dims = PCUSE, check_duplicates=FALSE)

DimPlot(pbmc, reduction='umap', group.by='batch', pt.size=0.1) 



II. Combine Multiple Batches

Download demo data: https://sourceforge.net/projects/beergithub/files/

Step1. Load Data

source('https://raw.githubusercontent.com/jumphone/BEER/master/BEER.R')

#Load Demo Data (Oligodendroglioma, GSE70630)
#Download: https://sourceforge.net/projects/beergithub/files/

D1=readRDS('MGH36.RDS')
D2=readRDS('MGH53.RDS')
D3=readRDS('MGH54.RDS')
D4=readRDS('MGH60.RDS')
D5=readRDS('MGH93.RDS')
D6=readRDS('MGH97.RDS')

BATCH=c(rep('D1',ncol(D1)),
        rep('D2',ncol(D2)),
        rep('D3',ncol(D3)),
        rep('D4',ncol(D4)),
        rep('D5',ncol(D5)),
        rep('D6',ncol(D6)) )
        
D12=.simple_combine(D1,D2)$combine
D34=.simple_combine(D3,D4)$combine
D56=.simple_combine(D5,D6)$combine
D1234=.simple_combine(D12,D34)$combine
D123456=.simple_combine(D1234,D56)$combine

DATA=D123456   

rm(D1);rm(D2);rm(D3);rm(D4);rm(D5);rm(D6)
rm(D12);rm(D34);rm(D56);rm(D1234);rm(D123456)

# Simple Quality Control (QC): check the number of sequenced genes
# PosN=apply(DATA,2,.getPos)
# USED=which(PosN>500 & PosN<4000) 
# DATA=DATA[,USED]; BATCH=BATCH[USED] 

Step2. Use BEER to Detect Batch Effect

mybeer=BEER(DATA, BATCH, GNUM=30, PCNUM=50, ROUND=1, GN=2000, SEED=1, COMBAT=TRUE )

# Check selected PCs
PCUSE=mybeer$select
COL=rep('black',length(mybeer$cor))
COL[PCUSE]='red'
plot(mybeer$cor,mybeer$lcor,pch=16,col=COL,
    xlab='Rank Correlation',ylab='Linear Correlation',xlim=c(0,1),ylim=c(0,1))

Step3. Visualization

Keep batch effect:

pbmc_batch=CreateSeuratObject(counts = DATA, min.cells = 0, min.features = 0, project = "ALL") 
[email protected]$batch=BATCH
pbmc_batch=FindVariableFeatures(object = pbmc_batch, selection.method = "vst", nfeatures = 2000)   
VariableFeatures(object = pbmc_batch)
pbmc_batch <- NormalizeData(object = pbmc_batch, normalization.method = "LogNormalize", scale.factor = 10000)
pbmc_batch <- ScaleData(object = pbmc_batch, features = VariableFeatures(object = pbmc_batch))
pbmc_batch <- RunPCA(object = pbmc_batch, seed.use=123, npcs=50, features = VariableFeatures(object = pbmc_batch), ndims.print=1,nfeatures.print=1)
pbmc_batch <- RunUMAP(pbmc_batch, dims = 1:50, seed.use = 123,n.components=2)
DimPlot(pbmc_batch, reduction='umap', group.by='batch', pt.size=0.1) 

Remove batch effect:

pbmc <- mybeer$seurat
PCUSE <- mybeer$select
pbmc <- RunUMAP(object = pbmc, reduction='pca',dims = PCUSE, check_duplicates=FALSE)

DimPlot(pbmc, reduction='umap', group.by='batch', pt.size=0.1)   



III. UMAP-based Clustering

VEC=pbmc@[email protected]

# Here, we use K-means to do the clustering
N=20
set.seed(123)
K=kmeans(VEC,centers=N)

CLUST=K$cluster
[email protected]$clust=as.character(CLUST)
DimPlot(pbmc, reduction='umap', group.by='clust', pt.size=0.5,label=TRUE)

# Or, manually select some cells

ppp=DimPlot(pbmc, reduction='umap', pt.size=0.5)
used.cells <- CellSelector(plot = ppp)

# Press "ESC"

markers <- FindMarkers(pbmc, ident.1=used.cells,only.pos=T)    
head(markers, n=20)


IV. Combine scATAC-seq & scRNA-seq

Please install "Signac": https://satijalab.org/signac/

Download DEMO data: https://sourceforge.net/projects/beer-file/files/ATAC/ & https://satijalab.org/signac/articles/pbmc_vignette.html

Step1. Load Data

source('https://raw.githubusercontent.com/jumphone/BEER/master/BEER.R')
#source('BEER.R')

library(Seurat)
library(Signac)
library(EnsDb.Hsapiens.v75)

counts <- Read10X_h5(filename = "./data/atac_v1_pbmc_10k_filtered_peak_bc_matrix.h5")

metadata <- read.csv(
  file = "./data/atac_v1_pbmc_10k_singlecell.csv",
  header = TRUE,
  row.names = 1
    )

chrom_assay <- CreateChromatinAssay(
    counts = counts,
    sep = c(":", "-"),
    genome = 'hg19',
    fragments = './data/atac_v1_pbmc_10k_fragments.tsv.gz',
    min.cells = 10,
    min.features = 200
   )

pbmc.atac <- CreateSeuratObject(
    counts = chrom_assay,
    assay = "peaks",
    meta.data = metadata
    )

annotations <- GetGRangesFromEnsDb(ensdb = EnsDb.Hsapiens.v75)
seqlevelsStyle(annotations) <- "UCSC"
genome(annotations) <- "hg19"
Annotation(pbmc.atac) <- annotations


gene.activities <- GeneActivity(pbmc.atac)
     
pbmc.rna <- readRDS("./data/pbmc_10k_v3.rds")

D1=as.matrix(gene.activities)
D2=as.matrix(pbmc.rna@assays$RNA@counts)
colnames(D1)=paste0('ATAC_', colnames(D1))
colnames(D2)=paste0('RNA_', colnames(D2))

D1=.check_rep(D1)
D2=.check_rep(D2)

DATA=.simple_combine(D1,D2)$combine
BATCH=rep('RNA',ncol(DATA))
BATCH[c(1:ncol(D1))]='ATAC'

Step2. Use BEER to Detect Batch Effect

mybeer <- BEER(DATA, BATCH, GNUM=30, PCNUM=50, ROUND=1, GN=5000, SEED=1, COMBAT=TRUE)
saveRDS(mybeer, file='mybeer')

# Users can use "ReBEER" to adjust parameters
mybeer <- ReBEER(mybeer, GNUM=100, PCNUM=100, ROUND=3, SEED=1)

PCUSE=mybeer$select
#PCUSE=.selectUSE(mybeer, CUTR=0.8, CUTL=0.8, RR=0.5, RL=0.5)

COL=rep('black',length(mybeer$cor))
COL[PCUSE]='red'
plot(mybeer$cor,mybeer$lcor,pch=16,col=COL,
    xlab='Rank Correlation',ylab='Linear Correlation',xlim=c(0,1),ylim=c(0,1))

Step3. Visualization

Keep batch effect:

pbmc_batch=CreateSeuratObject(counts = DATA, min.cells = 0, min.features = 0, project = "ALL") 
[email protected]$batch=BATCH
pbmc_batch=FindVariableFeatures(object = pbmc_batch, selection.method = "vst", nfeatures = 2000)   
VariableFeatures(object = pbmc_batch)
pbmc_batch <- NormalizeData(object = pbmc_batch, normalization.method = "LogNormalize", scale.factor = 10000)
pbmc_batch <- ScaleData(object = pbmc_batch, features = VariableFeatures(object = pbmc_batch))
pbmc_batch <- RunPCA(object = pbmc_batch, seed.use=123, npcs=50, features = VariableFeatures(object = pbmc_batch), ndims.print=1,nfeatures.print=1)
pbmc_batch <- RunUMAP(pbmc_batch, dims = 1:50, seed.use = 123,n.components=2)
DimPlot(pbmc_batch, reduction='umap', group.by='batch', pt.size=0.1)   

Remove batch effect:

pbmc <- mybeer$seurat  
PCUSE=mybeer$select
pbmc <- RunUMAP(object = pbmc, reduction='pca',dims = PCUSE, check_duplicates=FALSE)

DimPlot(pbmc, reduction='umap', group.by='batch', pt.size=0.1)    

[email protected]$celltype=rep(NA,length([email protected]$batch))
[email protected]$celltype[which([email protected]$batch=='RNA')][email protected]$celltype

DimPlot(pbmc, reduction='umap', group.by='celltype', pt.size=0.1,label=T)

saveRDS(mybeer, file='mybeer.final.RDS')

It's not good enough !

For further enhancement, please see V. Batch-effect Removal Enhancement.



V. Batch-effect Removal Enhancement

Please install BBKNN: https://github.com/Teichlab/bbknn

This DEMO follows IV. Combine scATAC-seq & scRNA-seq

source('https://raw.githubusercontent.com/jumphone/BEER/master/BEER.R')
#source('BEER.R')
mybeer=readRDS('mybeer.final.RDS')
pbmc.rna <- readRDS("./data/pbmc_10k_v3.rds")

Use ComBat & BBKNN without BEER:

pbmc <- mybeer$seurat
PCUSE=c(1:ncol(pbmc@[email protected]))
pbmc=BEER.combat(pbmc) #Adjust PCs using ComBat
umap=BEER.bbknn(pbmc, PCUSE, NB=3, NT=10)
pbmc@[email protected]=umap
DimPlot(pbmc, reduction='umap', group.by='batch', pt.size=0.1,label=F)

Use ComBat & BBKNN with BEER:

pbmc <- mybeer$seurat
PCUSE=mybeer$select   
pbmc=BEER.combat(pbmc) #Adjust PCs using ComBat
umap=BEER.bbknn(pbmc, PCUSE, NB=3, NT=10)
pbmc@[email protected]=umap
DimPlot(pbmc, reduction='umap', group.by='batch', pt.size=0.1,label=F)
 
saveRDS(pbmc, file='seurat.enh.RDS')

[email protected]$celltype=rep(NA,length([email protected]$batch))
[email protected]$celltype[which([email protected]$batch=='RNA')][email protected]$celltype
DimPlot(pbmc, reduction='umap', group.by='celltype', pt.size=0.1,label=T)

Use BBKNN in Python:

Please download beer_bbknn.py.

source('https://raw.githubusercontent.com/jumphone/BEER/master/BEER.R')
#source('BEER.R')
pbmc <- mybeer$seurat
pbmc=BEER.combat(pbmc) #Adjust PCs using ComBat
PCUSE = mybeer$select
used.pca = pbmc@[email protected][,PCUSE]
.writeTable(DATA=used.pca, PATH='used.pca.txt',SEP=',')
.writeTable([email protected]$batch, PATH='batch.txt',SEP=',')

Then, use "beer_bbknn.py" in your command line (please modify parameters in beer_bbknn.py):

python beer_bbknn.py

Finally, load the output of beer_bbknn.py and draw UMAP:

umap=read.table('bbknn_umap.txt',sep='\t',header=FALSE)
umap=as.matrix(umap)
rownames(umap)=rownames(pbmc@[email protected])
colnames(umap)=colnames(pbmc@[email protected])
pbmc@[email protected]=umap
DimPlot(pbmc, reduction='umap', group.by='batch', pt.size=0.1,label=F)

VI. Transfer labels

This DEMO follows V. Batch-effect Removal Enhancement

[email protected]$celltype=rep(NA,length([email protected]$batch))
[email protected]$celltype[which([email protected]$batch=='RNA')][email protected]$celltype
#DimPlot(pbmc, reduction='umap', group.by='celltype', pt.size=0.1,label=T)

#######
VEC=pbmc@[email protected]
set.seed(123)
N=150
K=kmeans(VEC,centers=N)
[email protected]$kclust=K$cluster   
#DimPlot(pbmc, reduction='umap', group.by='kclust', pt.size=0.1,label=T)

[email protected]$transfer=rep(NA, length([email protected]$celltype))
TMP=cbind([email protected]$celltype, [email protected]$kclust)

KC=unique([email protected]$kclust)
i=1
while(i<=length(KC)){
    this_kc=KC[i]
    this_index=which([email protected]$kclust==this_kc)
    this_tb=table([email protected]$celltype[this_index])
    if(length(this_tb)!=0){
        this_ct=names(this_tb)[which(this_tb==max(this_tb))[1]]
        [email protected]$transfer[this_index]=this_ct}
    i=i+1}
    
[email protected][email protected]$celltype
NA.index=which(is.na([email protected]$celltype))
[email protected]$tf.ct[NA.index][email protected]$transfer[NA.index]

######
RNA.cells=colnames(pbmc)[which([email protected]$batch=='RNA')]
ATAC.cells=colnames(pbmc)[which([email protected]$batch=='ATAC')]

library(ggplot2)

plot.all <- DimPlot(pbmc, reduction='umap', group.by='batch', 
    pt.size=0.1,label=F) + labs(title = "Batches")

plot.ct <- DimPlot(pbmc,reduction='umap', group.by='tf.ct', 
    pt.size=0.1,label=T) + labs(title = "CellType")

plot.rna <- DimPlot(pbmc, cells=RNA.cells,reduction='umap', 
    group.by='tf.ct', pt.size=0.1,label=T,plot.title='RNA.transfer') + labs(title = "RNA")

plot.atac <- DimPlot(pbmc, cells=ATAC.cells,reduction='umap', 
    group.by='tf.ct', pt.size=0.1,label=T,plot.title='ATAC.transfer') + labs(title = "ATAC")

CombinePlots(list(all=plot.all, ct=plot.ct, rna=plot.rna, atac=plot.atac))

If you want to visualize peak signals of any given cluster, please go to https://github.com/jumphone/VISA.



VII. Biological Interpretation

Please install "RITANdata" and "RITAN".

RITAN: https://bioconductor.org/packages/devel/bioc/vignettes/RITAN/inst/doc/enrichment.html

This DEMO follows IV. Combine scATAC-seq & scRNA-seq

library(RITANdata)
library(RITAN)

PCUSE <- mybeer$select
PCALL <- c(1:length(mybeer$cor))
PCnotUSE <- PCALL[which(!PCALL %in% PCUSE)]

LD=mybeer$seurat@[email protected]
GNAME=rownames(LD)

N=100
getPosAndNegTop <- function(x){
    O=c(order(x)[1:N],order(x)[(length(x)-(N-1)):length(x)])
    G=GNAME[O]
    return(G)
    }

GMAT=apply(LD,2,getPosAndNegTop)
colnames(GMAT)=paste0(colnames(GMAT),'_R_',round(mybeer$cor,1),"_L_",round(mybeer$lcor,1))
GMAT=toupper(GMAT)

GMAT=GMAT[,PCnotUSE]
#GMAT=GMAT[,PCUSE]

study_set=list()
TAG=colnames(GMAT)
i=1
while(i<=ncol(GMAT)){
     study_set=c(study_set,list(GMAT[,i]))
     i=i+1
     }  
     
names(study_set)=TAG
#names(geneset_list)
resources=c('KEGG_filtered_canonical_pathways','MSigDB_Hallmarks')

e <- term_enrichment_by_subset( study_set, q_value_threshold = 1e-5, 
                            resources = resources,
                            all_symbols = cached_coding_genes )

plot( e, show_values = FALSE, label_size_y = 7, label_size_x = 7, cap=10 )



VIII. QC before using BEER

Download demo data: https://sourceforge.net/projects/beergithub/files/

Step1. Load Data

source('https://raw.githubusercontent.com/jumphone/BEER/master/BEER.R')

#Load Demo Data (Oligodendroglioma, GSE70630)
#Download: https://sourceforge.net/projects/beergithub/files/

D1=readRDS('MGH36.RDS')
D2=readRDS('MGH53.RDS')
D3=readRDS('MGH54.RDS')
D4=readRDS('MGH60.RDS')
D5=readRDS('MGH93.RDS')
D6=readRDS('MGH97.RDS')

BATCH=c(rep('D1',ncol(D1)),
        rep('D2',ncol(D2)),
        rep('D3',ncol(D3)),
        rep('D4',ncol(D4)),
        rep('D5',ncol(D5)),
        rep('D6',ncol(D6)) )
    
D12=.simple_combine(D1,D2)$combine
D34=.simple_combine(D3,D4)$combine
D56=.simple_combine(D5,D6)$combine
D1234=.simple_combine(D12,D34)$combine
D123456=.simple_combine(D1234,D56)$combine

DATA=D123456   

rm(D1);rm(D2);rm(D3);rm(D4);rm(D5);rm(D6)
rm(D12);rm(D34);rm(D56);rm(D1234);rm(D123456)

Step2. QC

pbmc <- CreateSeuratObject(counts = DATA, project = "pbmc3k", min.cells = 0, min.features = 0)
Idents(pbmc)=BATCH
[email protected]$batch=BATCH

pbmc <- subset(pbmc, subset = nFeature_RNA > 200 & nFeature_RNA < 2500 & percent.mt < 5)

Please fllow https://satijalab.org/seurat/v3.1/pbmc3k_tutorial.html to do Quality Control.

[email protected]$batch

DATA=as.matrix(pbmc@assays$RNA@counts[,which(colnames(pbmc@assays$RNA@counts) %in% colnames(pbmc@assays$RNA@data))])

Step3. BEER

Refer to II. Combine Multiple Batches


Reference:

Feng Zhang, Yu Wu, Weidong Tian*; A novel approach to remove the batch effect of single-cell data, Cell Discovery, 2019, https://doi.org/10.1038/s41421-019-0114-x

Differences between the latest version and the manuscript version

Latest version: https://github.com/jumphone/BEER/releases

Manuscript version: https://github.com/jumphone/BEER/archive/0.0.2.zip




More tools & studies: https://fzhang.bioinfo-lab.com/

License

MIT License

Copyright (c) 2019 Zhang, Feng

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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