anglemania is a feature selection package that extracts genes from multi-batch scRNA-seq
experiments for downstream dataset integration.
The goal is to select genes that carry high biological information and low
technical noise between the batches. Those genes are extracted from gene pairs
that have an invariant and extremely narrow or wide angle between their expression vectors.
Conventionally, highly-variable genes (HVGs) or sometimes all genes are used
for integration tasks (https://www.nature.com/articles/s41592-021-01336-8).
While HVGs are a great and easy way to reduce the noise and
dimensionality of the data, we hypothesize that there are better ways to select genes
specifically for integration tasks. HVGs are sensitive to batch effects because the
variance is a function of both the technical and biological variance.
anglemania improves conventional usage of HVGs for integration tasks,
especially when the transcriptional difference between cell types or cell states
is subtle (showcased here using simulated data generated using splatter
with de.facLoc
and de.facScale
set to 0.1, which results in mild differences between
“Groups”).
The package can be used on top of SingleCellExperiment or
Seurat objects.
Under the hood, anglemania works with file-backed big matrices (FBMs) from the bigstatsr package for fast and memory efficient computation.
suppressPackageStartupMessages({
library(anglemania)
library(dplyr)
library(Seurat)
options(Seurat.object.assay.version = "v5")
library(splatter)
library(SingleCellExperiment)
library(scater)
library(scran)
library(bluster)
library(batchelor)
library(UpSetR)
})
We simulate a scRNA-seq dataset using Splatter with 4 batches and 3 cell types with subtle differences between cell types and rather big batch effects.
batch.facLoc <- 0.3
de.facLoc <- 0.1
nBatches <- 4
nGroups <- 3
nGenes <- 5000
groupCells <- 300
sce_raw <- splatSimulate(
batchCells = rep(groupCells * nGroups, nBatches),
batch.facLoc = batch.facLoc,
group.prob = rep(1 / nGroups, nGroups),
nGenes = nGenes,
batch.facScale = 0.1,
method = "groups",
verbose = FALSE,
out.prob = 0.001,
de.prob = 0.1, # mild
de.facLoc = de.facLoc,
de.facScale = 0.1,
bcv.common = 0.1,
seed = 42
)
sce <- sce_raw
assays(sce)
## List of length 6
## names(6): BatchCellMeans BaseCellMeans BCV CellMeans TrueCounts counts
Here we perform a standard workflow on the unintegrated data. When we perform clustering on the unintegrated data and visualize it in a UMAP, we can see that the clusters are driven by batch effects rather than cell types.
sce_unintegrated <- sce
# Normalization.
sce_unintegrated <- logNormCounts(sce_unintegrated)
# Feature selection.
dec <- modelGeneVar(sce_unintegrated)
hvg <- getTopHVGs(dec, prop = 0.1)
# PCA.
set.seed(1234)
sce_unintegrated <- scater::runPCA(
sce_unintegrated,
ncomponents = 50,
subset_row = hvg
)
# Clustering.
colLabels(sce_unintegrated) <- clusterCells(sce_unintegrated,
use.dimred = "PCA",
BLUSPARAM = NNGraphParam(cluster.fun = "louvain")
)
# Visualization.
sce_unintegrated <- scater::runUMAP(sce_unintegrated, dimred = "PCA")
patchwork::wrap_plots(
plotUMAP(sce_unintegrated, colour_by = "Batch") +
ggtitle("Unintegrated data, colored by Batch"),
plotUMAP(sce_unintegrated, colour_by = "Group") +
ggtitle("Unintegrated data, colored by Group")
)
Figure 1: UMAPs of unintegrated data, colored by Batch and Group
The clusters are driven by batch effects.
anglemania works on a SingleCellExperiment object.
The function has a few important arguments:
- batch_key
: the column in the metadata of the SingleCellExperiment
object that indicates which batch the cells belong to. This is required to
distinguish between batches, because we compute the angle between gene pairs
for each batch.
- method
: either cosine, spearman or diem
- this is the method by which the relationship of the gene pairs is measured.
Default is cosine, which is the cosine similarity between the expression
vectors of the gene pairs.
- zscore_mean_threshold
: We compute a mean of the zscore of the relationship
between a gene pair, and then we set a minimal cutoff for the (absolute)
mean zscore. A cutoff of 2 means that the filtered gene pairs have a
relationship, e.g. cosine similarity, that is 2 standard deviations away
from the mean of all cosine similarities from this dataset.
A higher value means a more stringent cutoff.
- zscore_sn_threshold
: The SNR or signal-to-noise ratio measures the
invariance of the relationship of the relationship between the gene pair.
A high SN ratio means that the relationship is constant over multiple batches.
- max_n_genes
: you can specify a maximum number of extracted genes. They are
sorted by decreasing mean zscore after passing the thresholds.
head(colData(sce))
## DataFrame with 6 rows and 4 columns
## Cell Batch Group ExpLibSize
## <character> <character> <factor> <numeric>
## Cell1 Cell1 Batch1 Group1 46898.1
## Cell2 Cell2 Batch1 Group1 54688.2
## Cell3 Cell3 Batch1 Group2 52027.9
## Cell4 Cell4 Batch1 Group1 52319.5
## Cell5 Cell5 Batch1 Group3 37774.7
## Cell6 Cell6 Batch1 Group3 58112.3
batch_key <- "Batch"
sce <- anglemania(
sce,
batch_key = batch_key,
zscore_mean_threshold = 2,
zscore_sn_threshold = 2
)
anglemania_genes <- get_anglemania_genes(sce)
head(anglemania_genes)
## [1] "Gene394" "Gene3527" "Gene71" "Gene5000" "Gene1055" "Gene4201"
length(anglemania_genes)
## [1] 1496
once anglemania was run on the SCE, you can adjust the initial zscore
mean and zscore SNR thresholds by using the select_genes()
function
# If you think the number of selected genes is
# too high or low you can adjust the thresholds:
sce <- select_genes(sce,
zscore_mean_threshold = 2.5,
zscore_sn_threshold = 2.5
)
# Inspect the anglemania genes
anglemania_genes <- get_anglemania_genes(sce)
head(anglemania_genes)
## [1] "Gene394" "Gene3527" "Gene71" "Gene5000" "Gene1055" "Gene4201"
length(anglemania_genes) # 306 genes are selected with these thresholds
## [1] 306
The anglemania genes can now be used for downstream integration algorithms such as MNN. We compare the integration results using the anglemania genes with the results using 300 and the standard 2000 HVGs. ## HVGs ### 300 HVGs
hvg_300 <- sce %>%
scater::logNormCounts() %>%
modelGeneVar(block = colData(sce)[[batch_key]]) %>%
getTopHVGs(n = 300)
barcodes_by_batch <- split(rownames(colData(sce)), colData(sce)[[batch_key]])
sce_list <- lapply(barcodes_by_batch, function(x) sce[, x])
sce_mnn <- sce %>%
scater::logNormCounts()
sce_mnn <- batchelor::fastMNN(
sce_mnn,
subset.row = hvg_300,
k = 20,
batch = factor(colData(sce_mnn)[[batch_key]]),
d = 50
)
reducedDim(sce, "MNN_hvg_300") <- reducedDim(sce_mnn, "corrected")
sce <- scater::runUMAP(sce, dimred = "MNN_hvg_300", name = "umap_MNN_hvg_300")
# k is the number of nearest neighbours to consider when identifying MNNs
hvg_2000 <- sce %>%
scater::logNormCounts() %>%
modelGeneVar(block = colData(sce)[[batch_key]]) %>%
getTopHVGs(n = 2000)
barcodes_by_batch <- split(rownames(colData(sce)), colData(sce)[[batch_key]])
sce_list <- lapply(barcodes_by_batch, function(x) sce[, x])
sce_mnn <- sce %>%
scater::logNormCounts()
sce_mnn <- batchelor::fastMNN(
sce_mnn,
subset.row = hvg_2000,
k = 20,
batch = factor(colData(sce_mnn)[[batch_key]]),
d = 50
)
reducedDim(sce, "MNN_hvg_2000") <- reducedDim(sce_mnn, "corrected")
sce <- scater::runUMAP(sce, dimred = "MNN_hvg_2000", name = "umap_MNN_hvg_2000")
sce_mnn <- sce %>%
scater::logNormCounts()
sce_mnn <- batchelor::fastMNN(
sce_mnn,
subset.row = anglemania_genes,
k = 20,
batch = factor(colData(sce_mnn)[[batch_key]]),
d = 50
)
reducedDim(sce, "MNN_anglemania") <- reducedDim(sce_mnn, "corrected")
sce <- scater::runUMAP(
sce,
dimred = "MNN_anglemania",
name = "umap_MNN_anglemania"
)
We can see from the UMAPs that anglemania genes yield the best integration in terms of clustering by cell type and mixing the batches. The goal of an integration and subsequent clustering should be to have low intra cluster variance and high inter cluster variance. This is at least true for most downstream scRNA-seq analyses where the goal is to e.g. differentiate between cell types or cell states and annotate these.
# Use wrap_plots
patchwork::wrap_plots(
plotReducedDim(sce, colour_by = "Batch", dimred = "umap_MNN_anglemania") +
ggtitle("MNN integration using anglemania genes, colored by Batch"),
plotReducedDim(sce, colour_by = "Group", dimred = "umap_MNN_anglemania") +
ggtitle("MNN integration using anglemania genes, colored by Group"),
plotReducedDim(sce, colour_by = "Batch", dimred = "umap_MNN_hvg_300") +
ggtitle("MNN integration using top 300 HVGs, colored by Batch"),
plotReducedDim(sce, colour_by = "Group", dimred = "umap_MNN_hvg_300") +
ggtitle("MNN integration using top 300 HVGs, colored by Group"),
plotReducedDim(sce, colour_by = "Batch", dimred = "umap_MNN_hvg_2000") +
ggtitle("MNN integration using top 2000 HVGs, colored by Batch"),
plotReducedDim(sce, colour_by = "Group", dimred = "umap_MNN_hvg_2000") +
ggtitle("MNN integration using top 2000 HVGs, colored by Group"),
ncol = 2
)
Figure 2: UMAPs of MNN integrated data
Comparison of UMAP embeddings of integrated data using anglemania genes, top 300 HVGs and top 2000 HVGs.
upsetr_df <- fromList(
list(
anglemania = anglemania_genes,
hvg_300 = hvg_300,
hvg_2000 = hvg_2000
)
)
upset(upsetr_df, text.scale = 2)
Figure 3: Overlap of selected genes
Additionally, we check the overlap of the anglemania genes with the HVGs. About 33 of the 306 anglemania genes are also found in the top 300 HVGs, and about 179 of the 306 anglemania genes are also found in the top 2000 HVGs.
Now you can just use the anglemania genes for other integration algorithms. When using Seurat, the easiest approach is to create an SCE from the counts and metadata of the SeuratObject, then run anglemania on it and save those genes as the VariableFeatures of the SeuratObject.
se <- CreateSeuratObject(
counts = counts(sce_raw),
meta.data = as.data.frame(colData(sce_raw))
)
se
## An object of class Seurat
## 5000 features across 3600 samples within 1 assay
## Active assay: RNA (5000 features, 0 variable features)
## 1 layer present: counts
anglemania_genes <- se |>
as.SingleCellExperiment(assay = "RNA") |>
anglemania(
batch_key = "Batch",
zscore_mean_threshold = 2,
zscore_sn_threshold = 2
) |>
get_anglemania_genes()
In Seurat v5 you split the layers of an assay by batch and then run the normal
Seurat workflow. To use anglemania genes for integration, you need to assign them
to the VariableFeatures slot of the SeuratObject. After that, you integrate the layers
using the anglemania genes as the features
argument.
# Split by batch
se[["RNA"]] <- split(se[["RNA"]], f = se$Batch)
# Standard preprocessing but use anglemania genes as "VariableFeatures"
se <- NormalizeData(se, verbose = FALSE)
VariableFeatures(se) <- anglemania_genes
se <- se |>
ScaleData(verbose = FALSE) |>
RunPCA(verbose = FALSE)
# Integrate
se <- IntegrateLayers(
object = se,
method = CCAIntegration,
orig.reduction = "pca",
new.reduction = "integrated.cca",
features = anglemania_genes,
verbose = FALSE
)
se <- RunUMAP(se, dims = 1:30, reduction = "integrated.cca", verbose = FALSE)
se
## An object of class Seurat
## 5000 features across 3600 samples within 1 assay
## Active assay: RNA (5000 features, 1496 variable features)
## 9 layers present: counts.Batch1, counts.Batch2, counts.Batch3, counts.Batch4, data.Batch1, data.Batch2, data.Batch3, data.Batch4, scale.data
## 3 dimensional reductions calculated: pca, integrated.cca, umap
patchwork::wrap_plots(
DimPlot(se, reduction = "umap", group.by = "Batch") +
ggtitle("Seurat integration using\nanglemania genes\ncolored by Batch"),
DimPlot(se, reduction = "umap", group.by = "Group") +
ggtitle("Seurat integration using\nanglemania genes\ncolored by Group"),
ncol = 2
)
Figure 4: UMAPs of Seurat integrated data
Here we show that we can use the anglemania genes for integration of a SeuratObject.
sce_raw <- sce_example()
sce <- sce_raw
batch_key <- "batch"
sce <- anglemania(sce, batch_key = batch_key, verbose = FALSE)
anglemania
is run on the SCE object and it basically calls three functions:
factorise
:
get_list_stats
mean_zscore
and the signal-to-noise ratio matrix
sn_zscore
. These are stored in the metadata of the SCE object.select_genes
mean_zscore
and sn_zscore
matrices
(SN ratio, i.e. the mean divided by the standard deviation).barcodes_by_batch <- split(rownames(colData(sce)), colData(sce)[[batch_key]])
counts_by_batch <- lapply(barcodes_by_batch, function(x) {
counts(sce[, x]) %>% sparse_to_fbm()
})
counts_by_batch[[1]][1:10, 1:6]
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 8 5 5 2 4 2
## [2,] 9 5 4 1 4 9
## [3,] 4 2 7 4 6 1
## [4,] 7 4 4 1 3 8
## [5,] 6 8 5 5 7 4
## [6,] 5 8 5 9 8 6
## [7,] 6 4 7 4 7 5
## [8,] 3 3 3 3 5 4
## [9,] 6 4 5 5 3 1
## [10,] 6 4 5 2 6 4
# we are working on FBMs (file-backed matrices
# implemented in the bigstatsr package)
class(counts_by_batch[[1]])
## [1] "FBM"
## attr(,"package")
## [1] "bigstatsr"
# factorise produces the correlation matrices transformed to z-scores
factorised <- lapply(counts_by_batch, factorise)
factorised[[1]][1:10, 1:6]
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.00000000 -1.74668209 -0.79613304 1.1776966 0.8601212 0.50193905
## [2,] -1.73785984 0.00000000 0.59661885 2.5115045 0.5348975 1.43483620
## [3,] -0.85963025 0.53988067 0.00000000 0.2901283 -1.5767324 -0.06260101
## [4,] 1.13658651 2.45514150 0.33158301 0.0000000 -0.3715653 -0.57325460
## [5,] 0.92122274 0.57796947 -1.62420449 -0.3961608 0.0000000 -0.26750572
## [6,] 0.52925575 1.57028828 -0.02415793 -0.6582967 -0.2979901 0.00000000
## [7,] -0.41325531 -0.10548957 -1.16180200 0.0055108 0.3444741 1.41598180
## [8,] 0.10001406 -1.38192310 -1.29577006 -0.2524730 -0.7968541 -1.56575595
## [9,] 0.51996703 0.05963883 -0.37002326 -0.2927571 -0.9185203 -0.12159157
## [10,] 0.06970488 -0.33637803 1.57056534 0.3728527 0.5142178 1.01784989
The “list stats” are computed by get_list_stats
and take the z-score transformed
correlation matrices from factorise
as input.
The outputs are the mean zscore matrix mean_zscore
and the
signal-to-noise ratio matrix sn_zscore
. These are stored in the metadata of
the SCE object.
matrix_list <- metadata(sce)$anglemania$matrix_list
weights <- setNames(
metadata(sce)$anglemania$weights$weight,
metadata(sce)$anglemania$weights$batch
)
list_stats <- get_list_stats(
matrix_list = matrix_list,
weights = weights,
verbose = FALSE
)
names(list_stats)
## [1] "mean_zscore" "sds_zscore" "sn_zscore"
class(list_stats)
## [1] "list"
list_stats$mean_zscore[1:10, 1:6]
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.00000000 -1.4773877 -0.6690115 0.80957395 0.21191114 0.3065459
## [2,] -1.43297508 0.0000000 0.8094372 1.79591873 0.87491750 0.0903189
## [3,] -0.70975605 0.8090174 0.0000000 -0.90002758 -0.14215190 0.4217798
## [4,] 0.81025807 1.7916458 -0.8103351 0.00000000 -0.29386285 -0.2877692
## [5,] 0.26228504 0.8796571 -0.2190412 -0.31429554 0.00000000 -0.7944232
## [6,] 0.34210706 0.1727196 0.4235970 -0.32724467 -0.79625202 0.0000000
## [7,] 0.60813294 0.4576137 -1.4403958 -0.03807431 0.35694728 0.5394522
## [8,] -0.03868058 -1.0958225 -0.7680151 -0.62207485 -1.42724690 -0.8197054
## [9,] 1.26715940 0.3486664 -0.5030029 -0.76152650 -0.66668260 -0.4825756
## [10,] 0.49115807 1.1467226 0.7976727 -0.27013900 0.03028304 0.8112288
list_stats$sn_zscore[1:10, 1:6]
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] NA 3.87928890 3.7213414 1.5550667 0.23116551 1.1093569
## [2,] 3.3234406 NA 2.6894229 1.7746389 1.81948152 0.0475004
## [3,] 3.3486305 2.12554305 NA 0.5347330 0.07006687 0.6157208
## [4,] 1.7557127 1.90940919 0.5017815 NA 2.67420836 0.7127632
## [5,] 0.2814584 2.06177351 0.1102260 2.7147101 NA 1.0660911
## [6,] 1.2925884 0.08738832 0.6689559 0.6989744 1.12999842 NA
## [7,] 0.4210103 0.57464016 3.6559091 0.6177018 20.23533063 0.4351825
## [8,] 0.1972052 2.70836022 1.0290168 1.1901274 1.60093202 0.7769169
## [9,] 1.1991785 0.85301337 2.6746701 1.1487110 1.87190277 0.9452842
## [10,] 0.8240564 0.54672981 0.7297777 0.2970755 0.04424840 2.7762187
# Or we can access them directly from the SCE object
# after running anglemania
metadata(sce)$anglemania$list_stats$mean_zscore[1:10, 1:6]
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.00000000 -1.4773877 -0.6690115 0.80957395 0.21191114 0.3065459
## [2,] -1.43297508 0.0000000 0.8094372 1.79591873 0.87491750 0.0903189
## [3,] -0.70975605 0.8090174 0.0000000 -0.90002758 -0.14215190 0.4217798
## [4,] 0.81025807 1.7916458 -0.8103351 0.00000000 -0.29386285 -0.2877692
## [5,] 0.26228504 0.8796571 -0.2190412 -0.31429554 0.00000000 -0.7944232
## [6,] 0.34210706 0.1727196 0.4235970 -0.32724467 -0.79625202 0.0000000
## [7,] 0.60813294 0.4576137 -1.4403958 -0.03807431 0.35694728 0.5394522
## [8,] -0.03868058 -1.0958225 -0.7680151 -0.62207485 -1.42724690 -0.8197054
## [9,] 1.26715940 0.3486664 -0.5030029 -0.76152650 -0.66668260 -0.4825756
## [10,] 0.49115807 1.1467226 0.7976727 -0.27013900 0.03028304 0.8112288
metadata(sce)$anglemania$list_stats$sn_zscore[1:10, 1:6]
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] NA 3.87928890 3.7213414 1.5550667 0.23116551 1.1093569
## [2,] 3.3234406 NA 2.6894229 1.7746389 1.81948152 0.0475004
## [3,] 3.3486305 2.12554305 NA 0.5347330 0.07006687 0.6157208
## [4,] 1.7557127 1.90940919 0.5017815 NA 2.67420836 0.7127632
## [5,] 0.2814584 2.06177351 0.1102260 2.7147101 NA 1.0660911
## [6,] 1.2925884 0.08738832 0.6689559 0.6989744 1.12999842 NA
## [7,] 0.4210103 0.57464016 3.6559091 0.6177018 20.23533063 0.4351825
## [8,] 0.1972052 2.70836022 1.0290168 1.1901274 1.60093202 0.7769169
## [9,] 1.1991785 0.85301337 2.6746701 1.1487110 1.87190277 0.9452842
## [10,] 0.8240564 0.54672981 0.7297777 0.2970755 0.04424840 2.7762187
anglemania
calls select_genes
with the default thresholds
zscore_mean_threshold = 2.5
, zscore_sn_threshold = 2.5
select_genes
to change the thresholds without having to run anglemania againprevious_genes <- get_anglemania_genes(sce)
sce <- select_genes(
sce,
zscore_mean_threshold = 2,
zscore_sn_threshold = 2,
verbose = FALSE
)
# Inspect the anglemania genes
new_genes <- get_anglemania_genes(sce)
length(previous_genes)
## [1] 25
length(new_genes)
## [1] 194
sessionInfo()
## R version 4.5.1 Patched (2025-08-23 r88802)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 24.04.3 LTS
##
## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.22-bioc/R/lib/libRblas.so
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.12.0 LAPACK version 3.12.0
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_GB LC_COLLATE=C
## [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
## [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
## [9] LC_ADDRESS=C LC_TELEPHONE=C
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
##
## time zone: America/New_York
## tzcode source: system (glibc)
##
## attached base packages:
## [1] stats4 stats graphics grDevices utils datasets methods
## [8] base
##
## other attached packages:
## [1] future_1.67.0 UpSetR_1.4.0
## [3] batchelor_1.25.0 bluster_1.19.0
## [5] scran_1.37.0 scater_1.37.0
## [7] ggplot2_4.0.0 scuttle_1.19.0
## [9] splatter_1.33.1 SingleCellExperiment_1.31.1
## [11] SummarizedExperiment_1.39.2 Biobase_2.69.1
## [13] GenomicRanges_1.61.5 Seqinfo_0.99.2
## [15] IRanges_2.43.4 S4Vectors_0.47.4
## [17] BiocGenerics_0.55.1 generics_0.1.4
## [19] MatrixGenerics_1.21.0 matrixStats_1.5.0
## [21] Seurat_5.3.0 SeuratObject_5.2.0
## [23] sp_2.2-0 dplyr_1.1.4
## [25] anglemania_0.99.6 BiocStyle_2.37.1
##
## loaded via a namespace (and not attached):
## [1] RcppAnnoy_0.0.22 splines_4.5.1
## [3] later_1.4.4 tibble_3.3.0
## [5] polyclip_1.10-7 fastDummies_1.7.5
## [7] lifecycle_1.0.4 edgeR_4.7.5
## [9] doParallel_1.0.17 globals_0.18.0
## [11] lattice_0.22-7 MASS_7.3-65
## [13] backports_1.5.0 magrittr_2.0.4
## [15] limma_3.65.4 plotly_4.11.0
## [17] sass_0.4.10 rmarkdown_2.30
## [19] jquerylib_0.1.4 yaml_2.3.10
## [21] bigparallelr_0.3.2 metapod_1.17.0
## [23] httpuv_1.6.16 sctransform_0.4.2
## [25] spam_2.11-1 spatstat.sparse_3.1-0
## [27] reticulate_1.43.0 cowplot_1.2.0
## [29] pbapply_1.7-4 RColorBrewer_1.1-3
## [31] ResidualMatrix_1.19.0 abind_1.4-8
## [33] Rtsne_0.17 purrr_1.1.0
## [35] bigassertr_0.1.7 ggrepel_0.9.6
## [37] irlba_2.3.5.1 listenv_0.9.1
## [39] spatstat.utils_3.2-0 goftest_1.2-3
## [41] RSpectra_0.16-2 dqrng_0.4.1
## [43] spatstat.random_3.4-2 fitdistrplus_1.2-4
## [45] parallelly_1.45.1 DelayedMatrixStats_1.31.0
## [47] codetools_0.2-20 DelayedArray_0.35.3
## [49] tidyselect_1.2.1 farver_2.1.2
## [51] ScaledMatrix_1.17.0 bigstatsr_1.6.2
## [53] viridis_0.6.5 spatstat.explore_3.5-3
## [55] flock_0.7 jsonlite_2.0.0
## [57] BiocNeighbors_2.3.1 progressr_0.16.0
## [59] ggridges_0.5.7 survival_3.8-3
## [61] iterators_1.0.14 foreach_1.5.2
## [63] tools_4.5.1 ica_1.0-3
## [65] Rcpp_1.1.0 glue_1.8.0
## [67] gridExtra_2.3 SparseArray_1.9.1
## [69] xfun_0.53 withr_3.0.2
## [71] BiocManager_1.30.26 fastmap_1.2.0
## [73] digest_0.6.37 rsvd_1.0.5
## [75] R6_2.6.1 mime_0.13
## [77] scattermore_1.2 tensor_1.5.1
## [79] dichromat_2.0-0.1 spatstat.data_3.1-8
## [81] tidyr_1.3.1 data.table_1.17.8
## [83] FNN_1.1.4.1 httr_1.4.7
## [85] htmlwidgets_1.6.4 S4Arrays_1.9.1
## [87] uwot_0.2.3 pkgconfig_2.0.3
## [89] gtable_0.3.6 lmtest_0.9-40
## [91] S7_0.2.0 XVector_0.49.1
## [93] htmltools_0.5.8.1 dotCall64_1.2
## [95] bookdown_0.44 scales_1.4.0
## [97] png_0.1-8 spatstat.univar_3.1-4
## [99] knitr_1.50 reshape2_1.4.4
## [101] checkmate_2.3.3 nlme_3.1-168
## [103] cachem_1.1.0 zoo_1.8-14
## [105] stringr_1.5.2 rmio_0.4.0
## [107] KernSmooth_2.23-26 parallel_4.5.1
## [109] miniUI_0.1.2 vipor_0.4.7
## [111] pillar_1.11.1 grid_4.5.1
## [113] vctrs_0.6.5 RANN_2.6.2
## [115] promises_1.3.3 BiocSingular_1.25.0
## [117] ff_4.5.2 beachmat_2.25.5
## [119] xtable_1.8-4 cluster_2.1.8.1
## [121] beeswarm_0.4.0 evaluate_1.0.5
## [123] magick_2.9.0 tinytex_0.57
## [125] cli_3.6.5 locfit_1.5-9.12
## [127] compiler_4.5.1 rlang_1.1.6
## [129] crayon_1.5.3 future.apply_1.20.0
## [131] labeling_0.4.3 ps_1.9.1
## [133] plyr_1.8.9 ggbeeswarm_0.7.2
## [135] stringi_1.8.7 viridisLite_0.4.2
## [137] deldir_2.0-4 BiocParallel_1.43.4
## [139] lazyeval_0.2.2 spatstat.geom_3.6-0
## [141] Matrix_1.7-4 RcppHNSW_0.6.0
## [143] patchwork_1.3.2 sparseMatrixStats_1.21.0
## [145] statmod_1.5.0 shiny_1.11.1
## [147] ROCR_1.0-11 igraph_2.1.4
## [149] bslib_0.9.0 bit_4.6.0