Analyzing Group ID Redundancy Across Rank 35 Components
Analysis
2025-11-02
Overview
This analysis examines whether the same group_id (orthogroup) appears across multiple components with the same GO BP terms, which would indicate redundancy in the cross-component frequency counts.
Load Libraries
library(tidyverse)
library(ggplot2)
library(RColorBrewer)
library(knitr)Define Paths
# Input directory
input_dir <- "/Users/sr320/Documents/GitHub/timeseries_molecular/M-multi-species/output/22-Visualizing-Rank-outs"
# Output directory
output_dir <- "/Users/sr320/Documents/GitHub/timeseries_molecular/M-multi-species/output/23-visualizing-rank35"
# Create output directory if it doesn't exist
dir.create(output_dir, showWarnings = FALSE, recursive = TRUE)Load All Data
# Get all rank_35 top100 annotation files
files <- list.files(input_dir,
pattern = "rank_35_comp.*_top100_annotation\\.csv$",
full.names = TRUE)
# Sort files by component number
file_df <- data.frame(
path = files,
component = str_extract(basename(files), "comp\\d+")
) %>%
mutate(comp_num = as.numeric(str_extract(component, "\\d+"))) %>%
arrange(comp_num)
cat(sprintf("Loading data from %d files...\n", nrow(file_df)))## Loading data from 35 files...# Read all files and combine
all_data <- map2_df(file_df$path, file_df$component, function(path, comp) {
read_csv(path, show_col_types = FALSE) %>%
mutate(component = comp)
})
cat(sprintf("Total rows loaded: %d\n", nrow(all_data)))## Total rows loaded: 3501cat(sprintf("Unique group_ids: %d\n", n_distinct(all_data$group_id)))## Unique group_ids: 475Parse GO BP Terms with Group ID Tracking
# Function to expand GO BP terms while maintaining group_id
expand_go_bp_terms <- function(data) {
data %>%
filter(!is.na(go_bp) & go_bp != "") %>%
select(group_id, component, go_bp) %>%
mutate(
# Split GO terms by semicolon
go_terms = str_split(go_bp, ";")
) %>%
unnest(go_terms) %>%
mutate(
# Clean up the term (remove GO:XXXXX part)
go_term_clean = str_trim(go_terms),
go_term_clean = str_replace(go_term_clean, "\\s*\\[GO:.*\\]", "")
) %>%
filter(go_term_clean != "") %>%
select(group_id, component, go_term = go_term_clean)
}
# Expand all GO terms with group_id tracking
go_expanded <- expand_go_bp_terms(all_data)
cat(sprintf("Total GO term occurrences: %d\n", nrow(go_expanded)))## Total GO term occurrences: 10831cat(sprintf("Unique GO terms: %d\n", n_distinct(go_expanded$go_term)))## Unique GO terms: 1116Analyze Redundancy
# For each GO term, count:
# 1. Total occurrences across all components
# 2. Number of unique group_ids
# 3. Number of components it appears in
# 4. How many times the same group_id appears in multiple components
go_term_analysis <- go_expanded %>%
group_by(go_term) %>%
summarise(
total_occurrences = n(),
unique_group_ids = n_distinct(group_id),
n_components = n_distinct(component),
# Calculate redundancy: if a group_id appears in 3 components, that's 2 redundant occurrences
redundant_occurrences = total_occurrences - unique_group_ids
) %>%
mutate(
# Percentage of occurrences that are redundant (same group_id in multiple components)
redundancy_pct = (redundant_occurrences / total_occurrences) * 100,
# Average times each unique group_id appears
avg_times_per_group = total_occurrences / unique_group_ids
) %>%
arrange(desc(total_occurrences))
# Display top terms
cat("\n### Top 30 GO Terms with Redundancy Analysis\n\n")##
## ### Top 30 GO Terms with Redundancy Analysisprint(kable(head(go_term_analysis, 30), digits = 2))##
##
## |go_term | total_occurrences| unique_group_ids| n_components| redundant_occurrences| redundancy_pct| avg_times_per_group|
## |:---------------------------------------------------------------------------------|-----------------:|----------------:|------------:|---------------------:|--------------:|-------------------:|
## |proteolysis | 94| 11| 35| 83| 88.30| 8.55|
## |positive regulation of transcription by RNA polymerase II | 91| 10| 33| 81| 89.01| 9.10|
## |innate immune response | 88| 5| 35| 83| 94.32| 17.60|
## |positive regulation of gene expression | 86| 10| 33| 76| 88.37| 8.60|
## |defense response to Gram-negative bacterium | 81| 5| 35| 76| 93.83| 16.20|
## |signal transduction | 79| 6| 35| 73| 92.41| 13.17|
## |adenylate cyclase-activating G protein-coupled receptor signaling pathway | 71| 4| 35| 67| 94.37| 17.75|
## |visual perception | 68| 6| 35| 62| 91.18| 11.33|
## |gene expression | 67| 6| 32| 61| 91.04| 11.17|
## |cell surface receptor signaling pathway | 66| 3| 35| 63| 95.45| 22.00|
## |negative regulation of transcription by RNA polymerase II | 66| 9| 34| 57| 86.36| 7.33|
## |negative regulation of apoptotic process | 62| 7| 32| 55| 88.71| 8.86|
## |positive regulation of reactive oxygen species biosynthetic process | 58| 2| 35| 56| 96.55| 29.00|
## |response to lipopolysaccharide | 57| 4| 28| 53| 92.98| 14.25|
## |response to bacterium | 56| 4| 29| 52| 92.86| 14.00|
## |cell adhesion | 53| 6| 35| 47| 88.68| 8.83|
## |cilium assembly | 51| 8| 31| 43| 84.31| 6.38|
## |flagellated sperm motility | 49| 7| 35| 42| 85.71| 7.00|
## |regulation of transcription by RNA polymerase II | 48| 10| 24| 38| 79.17| 4.80|
## |toll-like receptor signaling pathway | 48| 2| 30| 46| 95.83| 24.00|
## |basement membrane organization | 46| 4| 27| 42| 91.30| 11.50|
## |cell division | 45| 8| 30| 37| 82.22| 5.62|
## |mRNA processing | 44| 6| 27| 38| 86.36| 7.33|
## |negative regulation of tumor necrosis factor production | 44| 2| 28| 42| 95.45| 22.00|
## |actin cytoskeleton organization | 42| 3| 27| 39| 92.86| 14.00|
## |negative regulation of cell population proliferation | 41| 4| 35| 37| 90.24| 10.25|
## |negative regulation of transforming growth factor beta receptor signaling pathway | 41| 3| 34| 38| 92.68| 13.67|
## |muscle organ development | 40| 3| 35| 37| 92.50| 13.33|
## |in utero embryonic development | 39| 6| 27| 33| 84.62| 6.50|
## |negative regulation of angiogenesis | 39| 2| 35| 37| 94.87| 19.50|Detailed Analysis: Top Terms
# Focus on top 30 terms from previous analysis
top_30_terms <- head(go_term_analysis$go_term, 30)
# For each top term, show which group_ids appear in multiple components
redundancy_details <- go_expanded %>%
filter(go_term %in% top_30_terms) %>%
group_by(go_term, group_id) %>%
summarise(
n_components = n_distinct(component),
components = paste(sort(unique(component)), collapse = ", "),
.groups = "drop"
) %>%
filter(n_components > 1) %>%
arrange(go_term, desc(n_components))
cat(sprintf("\nFound %d group_ids that appear in multiple components\n", nrow(redundancy_details)))##
## Found 123 group_ids that appear in multiple componentscat(sprintf("Across the top 30 GO terms\n\n"))## Across the top 30 GO terms# Show examples
if (nrow(redundancy_details) > 0) {
cat("### Examples of Group IDs Appearing in Multiple Components\n\n")
print(kable(head(redundancy_details, 20)))
}## ### Examples of Group IDs Appearing in Multiple Components
##
##
##
## |go_term |group_id | n_components|components |
## |:-------------------------------------------------------------------------|:--------|------------:|:-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
## |actin cytoskeleton organization |OG_01645 | 26|comp1, comp11, comp13, comp14, comp15, comp16, comp18, comp2, comp20, comp21, comp22, comp24, comp25, comp26, comp27, comp28, comp3, comp30, comp31, comp32, comp34, comp4, comp6, comp7, comp8, comp9 |
## |actin cytoskeleton organization |OG_08222 | 15|comp1, comp11, comp13, comp15, comp16, comp2, comp22, comp25, comp27, comp3, comp31, comp4, comp6, comp7, comp8 |
## |adenylate cyclase-activating G protein-coupled receptor signaling pathway |OG_02537 | 35|comp1, comp10, comp11, comp12, comp13, comp14, comp15, comp16, comp17, comp18, comp19, comp2, comp20, comp21, comp22, comp23, comp24, comp25, comp26, comp27, comp28, comp29, comp3, comp30, comp31, comp32, comp33, comp34, comp35, comp4, comp5, comp6, comp7, comp8, comp9 |
## |adenylate cyclase-activating G protein-coupled receptor signaling pathway |OG_02927 | 29|comp1, comp10, comp11, comp13, comp14, comp15, comp16, comp18, comp2, comp20, comp21, comp22, comp23, comp24, comp25, comp26, comp27, comp28, comp29, comp30, comp31, comp32, comp33, comp34, comp4, comp6, comp7, comp8, comp9 |
## |adenylate cyclase-activating G protein-coupled receptor signaling pathway |OG_07351 | 6|comp12, comp16, comp17, comp3, comp30, comp34 |
## |basement membrane organization |OG_01645 | 26|comp1, comp11, comp13, comp14, comp15, comp16, comp18, comp2, comp20, comp21, comp22, comp24, comp25, comp26, comp27, comp28, comp3, comp30, comp31, comp32, comp34, comp4, comp6, comp7, comp8, comp9 |
## |basement membrane organization |OG_02338 | 15|comp11, comp13, comp15, comp16, comp2, comp20, comp21, comp28, comp30, comp34, comp4, comp6, comp7, comp8, comp9 |
## |basement membrane organization |OG_03906 | 4|comp16, comp17, comp22, comp34 |
## |cell adhesion |OG_02537 | 35|comp1, comp10, comp11, comp12, comp13, comp14, comp15, comp16, comp17, comp18, comp19, comp2, comp20, comp21, comp22, comp23, comp24, comp25, comp26, comp27, comp28, comp29, comp3, comp30, comp31, comp32, comp33, comp34, comp35, comp4, comp5, comp6, comp7, comp8, comp9 |
## |cell adhesion |OG_08313 | 7|comp11, comp15, comp16, comp2, comp22, comp28, comp4 |
## |cell adhesion |OG_04601 | 6|comp11, comp15, comp16, comp2, comp22, comp4 |
## |cell adhesion |OG_06280 | 2|comp29, comp35 |
## |cell adhesion |OG_09347 | 2|comp17, comp30 |
## |cell division |OG_01645 | 26|comp1, comp11, comp13, comp14, comp15, comp16, comp18, comp2, comp20, comp21, comp22, comp24, comp25, comp26, comp27, comp28, comp3, comp30, comp31, comp32, comp34, comp4, comp6, comp7, comp8, comp9 |
## |cell division |OG_08313 | 7|comp11, comp15, comp16, comp2, comp22, comp28, comp4 |
## |cell division |OG_04601 | 6|comp11, comp15, comp16, comp2, comp22, comp4 |
## |cell division |OG_07762 | 2|comp12, comp17 |
## |cell surface receptor signaling pathway |OG_02537 | 35|comp1, comp10, comp11, comp12, comp13, comp14, comp15, comp16, comp17, comp18, comp19, comp2, comp20, comp21, comp22, comp23, comp24, comp25, comp26, comp27, comp28, comp29, comp3, comp30, comp31, comp32, comp33, comp34, comp35, comp4, comp5, comp6, comp7, comp8, comp9 |
## |cell surface receptor signaling pathway |OG_02927 | 29|comp1, comp10, comp11, comp13, comp14, comp15, comp16, comp18, comp2, comp20, comp21, comp22, comp23, comp24, comp25, comp26, comp27, comp28, comp29, comp30, comp31, comp32, comp33, comp34, comp4, comp6, comp7, comp8, comp9 |
## |cell surface receptor signaling pathway |OG_09347 | 2|comp17, comp30 |Summary Statistics
# Overall statistics
overall_stats <- data.frame(
Metric = c(
"Total GO term occurrences",
"Unique GO terms",
"Unique group_ids with GO terms",
"Redundant occurrences (same group_id in multiple components)",
"Overall redundancy percentage"
),
Value = c(
nrow(go_expanded),
n_distinct(go_expanded$go_term),
n_distinct(go_expanded$group_id),
sum(go_term_analysis$redundant_occurrences),
round(sum(go_term_analysis$redundant_occurrences) / nrow(go_expanded) * 100, 2)
)
)
cat("\n### Overall Statistics\n\n")##
## ### Overall Statisticsprint(kable(overall_stats))##
##
## |Metric | Value|
## |:------------------------------------------------------------|--------:|
## |Total GO term occurrences | 10831.00|
## |Unique GO terms | 1116.00|
## |Unique group_ids with GO terms | 168.00|
## |Redundant occurrences (same group_id in multiple components) | 9324.00|
## |Overall redundancy percentage | 86.09|# Stats for top 30 terms
top_30_stats <- go_term_analysis %>%
slice_head(n = 30) %>%
summarise(
total_occurrences = sum(total_occurrences),
redundant_occurrences = sum(redundant_occurrences),
avg_redundancy_pct = mean(redundancy_pct)
)
cat("\n### Top 30 Terms Statistics\n\n")##
## ### Top 30 Terms Statisticscat(sprintf("Total occurrences: %d\n", top_30_stats$total_occurrences))## Total occurrences: 1760cat(sprintf("Redundant occurrences: %d\n", top_30_stats$redundant_occurrences))## Redundant occurrences: 1594cat(sprintf("Redundancy percentage: %.2f%%\n", (top_30_stats$redundant_occurrences / top_30_stats$total_occurrences * 100)))## Redundancy percentage: 90.57%cat(sprintf("Average redundancy per term: %.2f%%\n", top_30_stats$avg_redundancy_pct))## Average redundancy per term: 90.42%Visualization: Redundancy Analysis
# Plot for top 30 terms
plot_data <- go_term_analysis %>%
slice_head(n = 30) %>%
mutate(
go_term = factor(go_term, levels = rev(go_term))
) %>%
pivot_longer(
cols = c(unique_group_ids, redundant_occurrences),
names_to = "type",
values_to = "count"
) %>%
mutate(
type = case_when(
type == "unique_group_ids" ~ "Unique group_ids",
type == "redundant_occurrences" ~ "Redundant (same group_id)"
)
)
p1 <- ggplot(plot_data, aes(x = go_term, y = count, fill = type)) +
geom_bar(stat = "identity", position = "stack") +
coord_flip() +
scale_fill_manual(
values = c("Unique group_ids" = "steelblue",
"Redundant (same group_id)" = "orange"),
name = "Occurrence Type"
) +
labs(
title = "Redundancy Analysis: Top 30 GO BP Terms",
subtitle = "Blue = unique group_ids, Orange = redundant occurrences (same group_id in multiple components)",
x = "GO Biological Process Term",
y = "Count"
) +
theme_minimal(base_size = 12) +
theme(
plot.title = element_text(size = 16, face = "bold"),
plot.subtitle = element_text(size = 11, color = "gray40"),
axis.text.y = element_text(size = 10),
legend.position = "bottom"
)
print(p1)
ggsave(
filename = file.path(output_dir, "rank35_GO_redundancy_analysis.png"),
plot = p1,
width = 14,
height = 10,
dpi = 300
)Redundancy Percentage Plot
p2 <- go_term_analysis %>%
slice_head(n = 30) %>%
mutate(go_term = factor(go_term, levels = rev(go_term))) %>%
ggplot(aes(x = go_term, y = redundancy_pct)) +
geom_bar(stat = "identity", fill = "coral", alpha = 0.8) +
geom_text(aes(label = sprintf("%.1f%%", redundancy_pct)),
hjust = -0.1, size = 3) +
coord_flip() +
labs(
title = "Redundancy Percentage: Top 30 GO BP Terms",
subtitle = "Percentage of occurrences due to same group_id appearing in multiple components",
x = "GO Biological Process Term",
y = "Redundancy Percentage (%)"
) +
theme_minimal(base_size = 12) +
theme(
plot.title = element_text(size = 16, face = "bold"),
plot.subtitle = element_text(size = 11, color = "gray40"),
axis.text.y = element_text(size = 10),
panel.grid.major.y = element_blank()
)
print(p2)
ggsave(
filename = file.path(output_dir, "rank35_GO_redundancy_percentage.png"),
plot = p2,
width = 14,
height = 10,
dpi = 300
)Group IDs Appearing in Most Components
# Which group_ids appear in the most components?
group_id_frequency <- go_expanded %>%
group_by(group_id) %>%
summarise(
n_components = n_distinct(component),
n_go_terms = n_distinct(go_term),
go_terms_sample = paste(head(unique(go_term), 3), collapse = "; ")
) %>%
arrange(desc(n_components)) %>%
head(50)
cat("\n### Top 50 Group IDs by Component Frequency\n\n")##
## ### Top 50 Group IDs by Component Frequencyprint(kable(head(group_id_frequency, 50)))##
##
## |group_id | n_components| n_go_terms|go_terms_sample |
## |:--------|------------:|----------:|:-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
## |OG_00264 | 35| 1|flagellated sperm motility |
## |OG_01620 | 35| 4|retinoid metabolic process; retinol metabolic process; steroid metabolic process |
## |OG_02537 | 35| 22|adenylate cyclase-activating G protein-coupled receptor signaling pathway; apoptotic cell clearance; axonogenesis |
## |OG_01636 | 34| 3|negative regulation of activin receptor signaling pathway; negative regulation of BMP signaling pathway; negative regulation of transforming growth factor beta receptor signaling pathway |
## |OG_01919 | 31| 6|diacylglycerol catabolic process; phosphatidylcholine catabolic process; phosphatidylethanolamine catabolic process |
## |OG_02927 | 29| 5|adenylate cyclase-activating G protein-coupled receptor signaling pathway; cell surface receptor signaling pathway; circadian behavior |
## |OG_03269 | 29| 1|proteolysis |
## |OG_07218 | 27| 4|Notch signaling pathway; protein ubiquitination; regulation of postsynaptic neurotransmitter receptor internalization |
## |OG_08311 | 27| 11|cilium assembly; determination of heart left/right asymmetry; notochord morphogenesis |
## |OG_01645 | 26| 7|actin cytoskeleton organization; basement membrane organization; cell division |
## |OG_02341 | 26| 7|cellular response to stress; G protein-coupled glutamate receptor signaling pathway; gene expression |
## |OG_02998 | 25| 5|intracellular signal transduction; negative regulation of apoptotic process; positive regulation of transcription by RNA polymerase II |
## |OG_02929 | 24| 8|atrial cardiac muscle cell development; heart trabecula formation; negative regulation of apoptotic process |
## |OG_03335 | 23| 1|negative regulation of epidermal growth factor receptor signaling pathway |
## |OG_04437 | 23| 31|activation of NF-kappaB-inducing kinase activity; cellular response to amyloid-beta; cellular response to diacyl bacterial lipopeptide |
## |OG_04516 | 23| 1|protein localization to nucleus |
## |OG_00643 | 22| 1|proteolysis |
## |OG_08098 | 21| 54|cell population proliferation; cellular response to angiotensin; cellular response to cadmium ion |
## |OG_06663 | 19| 26|adherens junction maintenance; cell-matrix adhesion; focal adhesion assembly |
## |OG_00622 | 18| 8|blastocyst development; columnar/cuboidal epithelial cell differentiation; defense response to Gram-negative bacterium |
## |OG_03122 | 18| 4|chloride transport; regulation of cardiac muscle contraction by regulation of the release of sequestered calcium ion; regulation of release of sequestered calcium ion into cytosol by sarcoplasmic reticulum |
## |OG_01101 | 16| 2|microtubule bundle formation; protein modification process |
## |OG_02936 | 16| 2|CDP biosynthetic process; UDP biosynthetic process |
## |OG_04538 | 16| 2|antibacterial innate immune response; defense response to Gram-negative bacterium |
## |OG_05198 | 16| 23|antiviral innate immune response; cellular response to exogenous dsRNA; cytoplasmic pattern recognition receptor signaling pathway |
## |OG_02338 | 15| 78|antigen processing and presentation; axon guidance; basement membrane organization |
## |OG_08222 | 15| 2|actin cytoskeleton organization; actin nucleation |
## |OG_07129 | 14| 8|inner ear development; intracellular triglyceride homeostasis; negative regulation of mitochondrial calcium ion concentration |
## |OG_08842 | 14| 1|sensory perception of sound |
## |OG_07963 | 13| 3|bradykinin catabolic process; negative regulation of programmed cell death; proteolysis |
## |OG_00225 | 12| 9|citrate metabolic process; intestinal absorption; intracellular iron ion homeostasis |
## |OG_06323 | 12| 5|DNA double-strand break processing; double-strand break repair; double-strand break repair via homologous recombination |
## |OG_06909 | 12| 6|apoptotic process; chitin catabolic process; immune system process |
## |OG_06279 | 11| 8|blastocyst development; columnar/cuboidal epithelial cell differentiation; defense response to Gram-negative bacterium |
## |OG_08952 | 11| 7|auditory receptor cell stereocilium organization; cilium assembly; determination of left/right symmetry |
## |OG_07947 | 10| 8|cellular response to glucose stimulus; cellular response to tumor necrosis factor; gluconeogenesis |
## |OG_01210 | 9| 12|blood circulation; defense response to bacterium; immune system process |
## |OG_04857 | 9| 49|adult heart development; apoptotic process involved in heart morphogenesis; atrial cardiac muscle tissue development |
## |OG_04999 | 9| 8|camera-type eye development; circadian regulation of gene expression; embryonic retina morphogenesis in camera-type eye |
## |OG_05636 | 9| 2|cellular response to nerve growth factor stimulus; endocytic recycling |
## |OG_07887 | 9| 9|innate immune response; pattern recognition receptor signaling pathway; positive regulation of inflammatory response |
## |OG_08392 | 9| 5|cartilage development; cell differentiation; ossification |
## |OG_10182 | 9| 1|regulation of dendrite development |
## |OG_00797 | 8| 1|tight junction assembly |
## |OG_07103 | 8| 1|unsaturated fatty acid biosynthetic process |
## |OG_07200 | 8| 4|heart development; mRNA processing; regulation of translation |
## |OG_10186 | 8| 8|epidermis development; gene expression; lymph circulation |
## |OG_01396 | 7| 8|chaperone cofactor-dependent protein refolding; clathrin coat disassembly; mRNA processing |
## |OG_08313 | 7| 15|cell adhesion; cell division; cell migration |
## |OG_09440 | 7| 7|cell differentiation; hematopoietic stem cell proliferation; mesenchymal cell apoptotic process |# Plot
p3 <- group_id_frequency %>%
head(30) %>%
mutate(group_id = factor(group_id, levels = rev(group_id))) %>%
ggplot(aes(x = group_id, y = n_components)) +
geom_bar(stat = "identity", fill = "darkgreen", alpha = 0.7) +
geom_text(aes(label = n_components), hjust = -0.2, size = 3) +
coord_flip() +
labs(
title = "Top 30 Group IDs by Number of Components",
subtitle = "Group IDs that appear in the most components",
x = "Group ID",
y = "Number of Components"
) +
theme_minimal(base_size = 12) +
theme(
plot.title = element_text(size = 14, face = "bold"),
axis.text.y = element_text(size = 9),
panel.grid.major.y = element_blank()
)
print(p3)
ggsave(
filename = file.path(output_dir, "rank35_most_frequent_group_ids.png"),
plot = p3,
width = 12,
height = 8,
dpi = 300
)Export Detailed Results
# Export full redundancy analysis
write_csv(
go_term_analysis,
file.path(output_dir, "rank35_GO_redundancy_full_analysis.csv")
)
# Export group IDs appearing in multiple components
write_csv(
redundancy_details,
file.path(output_dir, "rank35_redundant_group_ids_details.csv")
)
# Export group ID frequency
write_csv(
group_id_frequency,
file.path(output_dir, "rank35_group_id_component_frequency.csv")
)
cat("\nExported detailed results to CSV files\n")##
## Exported detailed results to CSV filesSession Info
sessionInfo()## R version 4.3.2 (2023-10-31)
## Platform: aarch64-apple-darwin20 (64-bit)
## Running under: macOS Sonoma 14.7.6
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRlapack.dylib; LAPACK version 3.11.0
##
## locale:
## [1] C
##
## time zone: America/Los_Angeles
## tzcode source: internal
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] knitr_1.48 RColorBrewer_1.1-3 lubridate_1.9.3 forcats_1.0.0
## [5] stringr_1.5.1 dplyr_1.1.4 purrr_1.0.2 readr_2.1.5
## [9] tidyr_1.3.1 tibble_3.2.1 ggplot2_3.5.1 tidyverse_2.0.0
##
## loaded via a namespace (and not attached):
## [1] sass_0.4.9 utf8_1.2.4 generics_0.1.3 stringi_1.8.4
## [5] hms_1.1.3 digest_0.6.37 magrittr_2.0.3 evaluate_1.0.0
## [9] grid_4.3.2 timechange_0.3.0 fastmap_1.2.0 jsonlite_1.8.9
## [13] fansi_1.0.6 scales_1.3.0 textshaping_0.4.0 jquerylib_0.1.4
## [17] cli_3.6.3 rlang_1.1.4 crayon_1.5.3 bit64_4.5.2
## [21] munsell_0.5.1 withr_3.0.1 cachem_1.1.0 yaml_2.3.10
## [25] tools_4.3.2 parallel_4.3.2 tzdb_0.4.0 colorspace_2.1-1
## [29] vctrs_0.6.5 R6_2.5.1 lifecycle_1.0.4 bit_4.5.0
## [33] vroom_1.6.5 ragg_1.3.3 pkgconfig_2.0.3 pillar_1.9.0
## [37] bslib_0.8.0 gtable_0.3.6 glue_1.8.0 systemfonts_1.1.0
## [41] highr_0.11 xfun_0.48 tidyselect_1.2.1 farver_2.1.2
## [45] htmltools_0.5.8.1 rmarkdown_2.28 labeling_0.4.3 compiler_4.3.2