From e712a2b843b11d0727e92fb7338646cd5d2918b6 Mon Sep 17 00:00:00 2001 From: 3mmaRand <7593411+3mmaRand@users.noreply.github.com> Date: Tue, 24 Oct 2023 11:48:05 +0000 Subject: [PATCH] =?UTF-8?q?Deploying=20to=20gh-pages=20from=20@=203mmaRand?= =?UTF-8?q?/BIO00088H-data@35bedcb0494188b956d5b2f0e7866b78166d77ad=20?= =?UTF-8?q?=F0=9F=9A=80?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- core/core.html | 2 +- core/week-1/overview.html | 2 +- core/week-1/study_after_workshop.html | 2 +- core/week-1/study_before_workshop.html | 2 +- core/week-1/workshop.html | 2 +- core/week-2/overview.html | 2 +- core/week-2/study_after_workshop.html | 2 +- core/week-2/study_before_workshop.html | 2 +- core/week-2/workshop.html | 54 +- core/week-6/overview.html | 2 +- core/week-6/study_after_workshop.html | 2 +- core/week-6/study_before_workshop.html | 2 +- core/week-6/workshop.html | 2 +- index.html | 2 +- omics/omics.html | 2 +- omics/week-3/overview.html | 2 +- omics/week-3/study_after_workshop.html | 2 +- omics/week-3/study_before_workshop.html | 2 +- omics/week-3/workshop.html | 2 +- omics/week-4/overview.html | 2 +- omics/week-4/study_after_workshop.html | 2 +- omics/week-4/study_before_workshop.html | 2 +- omics/week-4/workshop.html | 2 +- omics/week-5/figures/frog-s30-pca.png | Bin 39429 -> 37338 bytes omics/week-5/figures/prog-hspc-volcano.png | Bin 92842 -> 92184 bytes omics/week-5/figures/prog_hspc-pca.png | Bin 343112 -> 364864 bytes omics/week-5/overview.html | 4 +- omics/week-5/study_after_workshop.html | 2 +- omics/week-5/study_before_workshop.html | 2 +- omics/week-5/workshop.html | 2209 ++++++++++++++--- .../figure-html/unnamed-chunk-24-1.png | Bin 0 -> 28994 bytes .../figure-html/unnamed-chunk-56-1.png | Bin 0 -> 351172 bytes search.json | 39 +- 33 files changed, 1970 insertions(+), 384 deletions(-) create mode 100644 omics/week-5/workshop_files/figure-html/unnamed-chunk-24-1.png create mode 100644 omics/week-5/workshop_files/figure-html/unnamed-chunk-56-1.png diff --git a/core/core.html b/core/core.html index ee62a21..9faa856 100644 --- a/core/core.html +++ b/core/core.html @@ -269,7 +269,7 @@

Core Data Analysis

Published
-

23 October, 2023

+

24 October, 2023

diff --git a/core/week-1/overview.html b/core/week-1/overview.html index 4718dfa..d0bb307 100644 --- a/core/week-1/overview.html +++ b/core/week-1/overview.html @@ -266,7 +266,7 @@

Overview

Published
-

23 October, 2023

+

24 October, 2023

diff --git a/core/week-1/study_after_workshop.html b/core/week-1/study_after_workshop.html index ca12b40..cfb34bf 100644 --- a/core/week-1/study_after_workshop.html +++ b/core/week-1/study_after_workshop.html @@ -266,7 +266,7 @@

Independent Study to consolidate this week

Published
-

23 October, 2023

+

24 October, 2023

diff --git a/core/week-1/study_before_workshop.html b/core/week-1/study_before_workshop.html index 3f40d4c..f32a4b5 100644 --- a/core/week-1/study_before_workshop.html +++ b/core/week-1/study_before_workshop.html @@ -259,7 +259,7 @@

Independent Study to prepare for workshop

Published
-

23 October, 2023

+

24 October, 2023

diff --git a/core/week-1/workshop.html b/core/week-1/workshop.html index a786269..8fdbaed 100644 --- a/core/week-1/workshop.html +++ b/core/week-1/workshop.html @@ -319,7 +319,7 @@

Workshop

Published
-

23 October, 2023

+

24 October, 2023

diff --git a/core/week-2/overview.html b/core/week-2/overview.html index 78b5327..a018dcd 100644 --- a/core/week-2/overview.html +++ b/core/week-2/overview.html @@ -257,7 +257,7 @@

Overview

Published
-

23 October, 2023

+

24 October, 2023

diff --git a/core/week-2/study_after_workshop.html b/core/week-2/study_after_workshop.html index f133cef..7c4c3e5 100644 --- a/core/week-2/study_after_workshop.html +++ b/core/week-2/study_after_workshop.html @@ -257,7 +257,7 @@

Independent Study to consolidate this week

Published
-

23 October, 2023

+

24 October, 2023

diff --git a/core/week-2/study_before_workshop.html b/core/week-2/study_before_workshop.html index f930897..31adbe7 100644 --- a/core/week-2/study_before_workshop.html +++ b/core/week-2/study_before_workshop.html @@ -423,7 +423,7 @@ -

23 October, 2023

+

24 October, 2023

Overview

Overview

diff --git a/omics/week-3/workshop.html b/omics/week-3/workshop.html index 275cb5d..a0db8d3 100644 --- a/omics/week-3/workshop.html +++ b/omics/week-3/workshop.html @@ -359,7 +359,7 @@

Workshop

Published
-

23 October, 2023

+

24 October, 2023

diff --git a/omics/week-4/overview.html b/omics/week-4/overview.html index d1d148a..5a7a56a 100644 --- a/omics/week-4/overview.html +++ b/omics/week-4/overview.html @@ -286,7 +286,7 @@

Overview

Published
-

23 October, 2023

+

24 October, 2023

diff --git a/omics/week-4/study_after_workshop.html b/omics/week-4/study_after_workshop.html index fe3c6e6..90e26f9 100644 --- a/omics/week-4/study_after_workshop.html +++ b/omics/week-4/study_after_workshop.html @@ -259,7 +259,7 @@

Independent Study to consolidate this week

Published
-

23 October, 2023

+

24 October, 2023

diff --git a/omics/week-4/study_before_workshop.html b/omics/week-4/study_before_workshop.html index ea89b8d..b33543e 100644 --- a/omics/week-4/study_before_workshop.html +++ b/omics/week-4/study_before_workshop.html @@ -421,7 +421,7 @@ -

23 October, 2023

+

24 October, 2023

Overview

In these slides we will:

diff --git a/omics/week-4/workshop.html b/omics/week-4/workshop.html index df3be60..123d532 100644 --- a/omics/week-4/workshop.html +++ b/omics/week-4/workshop.html @@ -332,7 +332,7 @@

Workshop

Published
-

23 October, 2023

+

24 October, 2023

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zofGy$0fj|KQ2qhW GtN#Y?GQIQw diff --git a/omics/week-5/overview.html b/omics/week-5/overview.html index 1b22b9a..8465014 100644 --- a/omics/week-5/overview.html +++ b/omics/week-5/overview.html @@ -267,7 +267,7 @@

Overview

Published
-

23 October, 2023

+

24 October, 2023

@@ -277,7 +277,7 @@

Overview

-

This week we cover how to visualise and interpret the results of your differential expression analysis. The independent study will allow you to check you have what you should have following the Omics 2: Statistical Analysis workshop and Consolidation study. It will also summarise the the methods and plots we will go through in the workshop. In the workshop, we will learn how to merge gene information into out results, conduct a Principle Component Analysis (PCA) and plot the results as well as how to create a nicely formatted Volcano plot and heatmap.

+

This week we cover how to visualise and interpret the results of your differential expression analysis. The independent study will allow you to check you have what you should have following the Omics 2: Statistical Analysis workshop and Consolidation study. It will also summarise the the methods and plots we will go through in the workshop. In the workshop, we will learn how to merge gene information into our results, conduct a Principle Component Analysis (PCA) and plot the results as well as how to create a nicely formatted Volcano plot and heatmap.

We suggest you sit together with your group in the workshop.

Learning objectives

diff --git a/omics/week-5/study_after_workshop.html b/omics/week-5/study_after_workshop.html index 8f1039f..95f2f4a 100644 --- a/omics/week-5/study_after_workshop.html +++ b/omics/week-5/study_after_workshop.html @@ -259,7 +259,7 @@

Independent Study to consolidate this week

Published
-

23 October, 2023

+

24 October, 2023

diff --git a/omics/week-5/study_before_workshop.html b/omics/week-5/study_before_workshop.html index 1cbf9bc..13bf93f 100644 --- a/omics/week-5/study_before_workshop.html +++ b/omics/week-5/study_before_workshop.html @@ -421,7 +421,7 @@
-

23 October, 2023

+

24 October, 2023

Overview

In these slides we will:

diff --git a/omics/week-5/workshop.html b/omics/week-5/workshop.html index 6793b5d..f7e0f1b 100644 --- a/omics/week-5/workshop.html +++ b/omics/week-5/workshop.html @@ -291,7 +291,8 @@ 🐸 Analysis

This is where we will save our figure files.

-

🎬 Load tidyverse (Wickham et al. 2019) and conflicted. You most likely have this code at the top of cont-fgf-s30.R or hspc-prog.R already.

+

🎬 Load tidyverse (Wickham et al. 2019) and conflicted (Wickham 2023). You most likely have this code at the top of cont-fgf-s30.R or hspc-prog.R already.

@@ -380,7 +381,9 @@

Workshop

We will carry out several steps

  1. Import data and merge statistical results with normalised values
  2. -
  3. Add gene information from xenbase
  4. +
  5. Add gene information from Xenbase (Fisher et al. 2023) +
  6. +
  7. log2 transform the data
  8. Write the significant genes to file
  9. View the relationship between samples using PCA
  10. Visualise the expression of the most significant genes using a heatmap
  11. @@ -390,123 +393,279 @@

    Workshop

    We need to import both the normalised counts and the statistical results. We will need all of these for the visualisation and interpretation.

    🎬 Import files saved from last week from the results folder: S30_normalised_counts.csv and S30_results.csv. I used the names s30_count_norm and s30_results for the dataframes.

    🎬 Remind yourself what is in the rows and columns and the structure of the dataframes (perhaps using glimpse())

    +
    +
    #---CODING ANSWER---
    +#| include: false
    +glimpse(s30_count_norm)
    +
    +
    Rows: 10,136
    +Columns: 7
    +$ S30_C_5         <dbl> 228.092879, 480.016357, 111.209463, 48.795989, 439.163…
    +$ S30_C_6         <dbl> 222.114104, 498.170204, 81.441838, 45.480507, 551.0545…
    +$ S30_C_A         <dbl> 238.647198, 668.212153, 83.141604, 53.118247, 282.5274…
    +$ S30_F_5         <dbl> 251.794947, 453.047112, 98.328684, 70.759894, 427.3162…
    +$ S30_F_6         <dbl> 239.567397, 481.986786, 81.757127, 44.681221, 539.9773…
    +$ S30_F_A         <dbl> 245.10704, 607.96159, 62.47827, 36.04515, 279.95069, 1…
    +$ xenbase_gene_id <chr> "XB-GENE-1000007", "XB-GENE-1000023", "XB-GENE-1000062…
    +
    +
    + + + + + + + + + +
    +
    #---CODING ANSWER---
    +#| include: false
    +glimpse(s30_results)
    +
    +
    Rows: 10,136
    +Columns: 7
    +$ baseMean        <dbl> 237.553928, 531.565700, 86.392830, 49.813502, 419.9983…
    +$ log2FoldChange  <dbl> 0.096601855, -0.089588528, -0.192811203, -0.008858703,…
    +$ lfcSE           <dbl> 0.2079396, 0.1557384, 0.3253216, 0.4342614, 0.1685420,…
    +$ stat            <dbl> 0.46456683, -0.57525007, -0.59267874, -0.02039947, -0.…
    +$ pvalue          <dbl> 0.64224169, 0.56512218, 0.55339617, 0.98372471, 0.8699…
    +$ padj            <dbl> 0.9998970, 0.9998970, 0.9998970, 0.9998970, 0.9998970,…
    +$ xenbase_gene_id <chr> "XB-GENE-1000007", "XB-GENE-1000023", "XB-GENE-1000062…
    +
    +
    + + + + +

    It is useful to have this information in a single dataframe to which we will add the gene information from xenbase. Having all the information together will make it easier to interpret the results and select genes of interest.

    🎬 Merge the two dataframes:

    -
    # merge the results with the normalised counts
    +
    # merge the results with the normalised counts
     s30_results <- s30_count_norm |>
       left_join(s30_results, by = "xenbase_gene_id")

    This means you have the counts for each sample along with the statistical results for each gene.

    -

Add gene information from xenbase

-

This information comes from the Xenbase information pages

-
-

xenbase Gene Product Information [readme]gzipped gpi (tab separated)

-
-

The xenbase.gpi.gz file contains gene product information for species specific Xenbase genes.

-

If you click on the readme link you can see information telling you that the file is in the Gene Product information 2.1 format and is provided with gzip compression. gene product information for both Xenopus tropicalis (taxon:8364) and Xenopus laevis (taxon:8355)

-

🎬 If you want to

-
gunzip xenbase.gpi.gz
-less xenbase.gpi
-q
+

Add gene information from Xenbase

+ +

If you want to emulate what I did you can use the following commands in the terminal after downloading the file:

+
gunzip xenbase.gpi.gz
+less xenbase.gpi
+q
+

gunzip unzips the file and less allows you to view the file. q quits the viewer. You will see the header lines and that the file contains both Xenopus tropicalis and Xenopus laevis. I read the file in with read_tsv (skipping the first header lines) then filtered out the Xenopus tropicalis entries, dropped some columns and saved the file as an excel file.

+

However, I have already done this for you and saved the file as xenbase_info.xlsx in the meta folder. We will import this file and join it to the results dataframe.

+

🎬 Load the readxl (Wickham and Bryan 2023) package:

+

🎬 Import the Xenbase gene information file:

-
gene_info <- read_excel("meta/xenbase_info.xlsx") 
+
gene_info <- read_excel("meta/xenbase_info.xlsx") 
+

You should view the resulting dataframe to see what information is available. You can use glimpse() or View().

+

🎬 Merge the gene information with the results:

-
# join the gene info with the results
+
# join the gene info with the results
 s30_results <- s30_results |>
   left_join(gene_info, by = "xenbase_gene_id")
+

We will also find it useful to import the metadata that maps the sample names to treatments. This will allow us to label the samples in the visualisations.

+

🎬 Import the metadata that maps the sample names to treatments:

-
# Import metadata that maps the sample names to treatments
+
# Import metadata that maps the sample names to treatments
 meta <- read_table("meta/frog_meta_data.txt")
-row.names(meta) <- meta$sample_id
-
-

We only need the s30

-
-
meta_s30 <- meta |>
+row.names(meta) <- meta$sample_id
+# We only need the s30
+meta_s30 <- meta |>
   dplyr::filter(stage == "stage_30")
-

log2 transformed normalised counts needed for data viz

-

log2 transform the counts in s30_count_norm add a tiny amount to avoid log(0)

+

log2 transform the data

+

We use the normalised counts for data visualisations so that the comparisons are meaningful. Since the fold changes are given is log2 it is useful to log2 transform the normalised counts too. We will add columns to the dataframe with these transformed values. Since we have some counts of 0 we will add a tiny amount to avoid -Inf values.

+

🎬 log2 transform the normalised counts:

-
# log2 transform the counts in s30_count_norm
-# add a tiny amount to avoid log(0)
+
# log2 transform the counts plus a tiny amount to avoid log(0)
 s30_results <- s30_results |>
   mutate(across(starts_with("s30"), 
                 \(x) log2(x + 0.001),
                 .names = "log2_{.col}"))
-

read more about across() and anonymous functions from my posit::conf(2023) workshop

-

We now have datatframe with all the info we need, normalised counts, log2 normalised counts, statistical comparisons with fold changes and p values, information about the gene other than just the id

+

This is a wonderful bit or R wizardy. We are using the across() function to apply a transformation to multiple columns. We have selected all the columns that start with s30. The \(x) is an “anonymous” function that takes the value of the column and adds 0.001 to it before applying the log2() function. The .names = "log2_{.col}" argument tells across() to name the new columns with the prefix log2_ followed by the original column name. You can read more about across() and anonymous functions from my posit::conf(2023) workshop

+

I recommend viewing the dataframe to see the new columns.

+

We now have dataframe with all the information we need: normalised counts, log2 normalised counts, statistical comparisons with fold changes and p values, and information about the gene other than just the id.

Write the significant genes to file

+

We will create dateframe of the signifcant genes and wrte them to file. These are the files you want to examine in more detail along with the visualisations to select your genes of interest.

+

🎬 Create a dataframe of the genes significant at the 0.01 level:

-
s30_results_sig0.01 <- s30_results |> 
-  filter(padj <= 0.01)
-# 59 genes
+
s30_results_sig0.01 <- s30_results |> 
+  filter(padj <= 0.01)
+

🎬 Write the dataframe to file

-
# write to csv file
+
#---CODING ANSWER---
+#| include: false
+# write to csv file
 write_csv(s30_results_sig0.01, 
           file = "results/s30_results_sig0.01.csv")
+

🎬 Create a dataframe of the genes significant at the 0.05 level and write to file:

-
s30_results_sig0.05 <- s30_results |> 
+
#---CODING ANSWER---
+#| include: false
+s30_results_sig0.05 <- s30_results |> 
   filter(padj <= 0.05)
 
-# 117 genes
-
-
-
# write to csv file
+# write to csv file
 write_csv(s30_results_sig0.05, 
           file = "results/s30_results_sig0.05.csv")
+

❓How many genes are significant at the 0.01 and 0.05 levels?

+ + +

View the relationship between samples using PCA

-

we do this on the log2 transformed normalised counts or the regularized the log transformed counts

-

transpose the data we are reducing he number of dimensions from 10136 to 6

+

We have 10,136 genes in our dataset. PCA will allow us to plot our samples in the “gene expression” space so we can see if FGF-treated sample cluster together and control samples cluster together as we would expect. We do this on the log2 transformed normalised counts.

+

Our data have genes in rows and samples in columns which is a common organisation for gene expression data. However, PCA expects samples in rows and genes, the variables, in columns. We can transpose the data to get it in the correct format.

+

🎬 Transpose the log2 transformed normalised counts:

-
s30_log2_trans <- s30_results |> 
+
s30_log2_trans <- s30_results |> 
   select(starts_with("log2_")) |>
   t() |> 
   data.frame()
+

We have used the select() function to select all the columns that start with log2_. We then use the t() function to transpose the dataframe. We then convert the resulting matrix to a dataframe using data.frame(). If you view that dataframe you’ll see it has default column name which we can fix using colnames() to set the column names to the Xenbase gene ids.

+

🎬 Set the column names to the Xenbase gene ids:

-
colnames(s30_log2_trans) <- s30_results$xenbase_gene_id
+
colnames(s30_log2_trans) <- s30_results$xenbase_gene_id
-

perform PCA using standard functions

+

🎬 Perform PCA on the log2 transformed normalised counts:

-
pca <- s30_log2_trans |>
-  prcomp(scale. = TRUE) 
+
pca <- s30_log2_trans |>
+  prcomp(rank. = 4) 
+

The rank. argument tells prcomp() to only calculate the first 4 principal components. This is useful for visualisation as we can only plot in 2 or 3 dimensions. We can see the results of the PCA by viewing the summary() of the pca object.

-
summary(pca)
+
summary(pca)
-
Importance of components:
-                           PC1     PC2     PC3     PC4     PC5       PC6
-Standard deviation     62.3983 45.6748 44.5555 33.3601 32.5295 2.405e-13
-Proportion of Variance  0.3841  0.2058  0.1959  0.1098  0.1044 0.000e+00
-Cumulative Proportion   0.3841  0.5899  0.7858  0.8956  1.0000 1.000e+00
+
Importance of first k=4 (out of 6) components:
+                           PC1     PC2     PC3     PC4
+Standard deviation     64.0124 47.3351 38.4706 31.4111
+Proportion of Variance  0.4243  0.2320  0.1532  0.1022
+Cumulative Proportion   0.4243  0.6562  0.8095  0.9116
-

Importance of components: PC1 PC2 PC3 PC4 PC5 PC6 Standard deviation 57.1519 50.3285 43.8382 35.4644 33.9440 2.403e-13 Proportion of Variance 0.3224 0.2500 0.1897 0.1241 0.1137 0.000e+00 Cumulative Proportion 0.3224 0.5724 0.7621 0.8863 1.0000 1.000e+00

-

remove log2 from row.names(s30_log2_trans) to label the pca results

+

The Proportion of Variance tells us how much of the variance is explained by each component. We can see that the first component explains 0.4243 of the variance, the second 0.2320, and the third 0.1532. Together the first three components explain nearly 81% of the total variance in the data. Plotting PC1 against PC2 will capture about 66% of the variance which is likely much better than we would get plotting any two genes against each other. To plot the PC1 against PC2 we will need to extract the PC1 and PC2 score from the pca object and add labels for the samples.

+

🎬 Remove log2 from the row names:

-
sample_id <- row.names(s30_log2_trans) |> str_remove("log2_")
+
sample_id <- row.names(s30_log2_trans) |> str_remove("log2_")
+

🎬 Create a dataframe of the PC1 and PC2 scores which are in pca$x and add the sample ids:

-
pca_labelled <- data.frame(pca$x,
+
pca_labelled <- data.frame(pca$x,
                            sample_id)
-

merge with metadata so we can label points by treatment and sib group

+

🎬 Merge with the metadata so we can label points by treatment and sibling pair:

-
pca_labelled <- pca_labelled |> 
+
pca_labelled <- pca_labelled |> 
   left_join(meta_s30, 
             by = "sample_id")
+

Since the metadata contained the sample ids, it was especially important to remove the log2_ from the row names so that the join would work. The dataframe should look like this:

+
+
+ ++++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
PC1PC2PC3PC4sample_idstagetreatmentsibling_rep
-76.383910.814699-60.728327-5.820669S30_C_5stage_30controlfive
-67.0257125.66856351.47683528.480254S30_C_6stage_30controlsix
-14.02772-78.47405415.282058-9.213076S30_C_Astage_30controlA
47.6072649.035510-19.28875320.928290S30_F_5stage_30FGFfive
26.0495432.91420120.206072-55.752818S30_F_6stage_30FGFsix
83.78054-29.958919-6.94788421.378020S30_F_Astage_30FGFA
+
+
+

🎬 Plot PC1 against PC2 and colour by sibling pair and shape by treatment:

-
pca <- pca_labelled |> 
+
pca <- pca_labelled |> 
   ggplot(aes(x = PC1, y = PC2, 
              colour = sibling_rep,
              shape = treatment)) +
@@ -517,11 +676,16 @@ 

Workshop

scale_shape_manual(values = c(21, 19), name = NULL, labels = c("Control", "FGF-Treated")) + - theme_classic()
+ theme_classic() +pca
+
+

+
-

There is a bit of separation between treatments on PCA2 not that it isn’t easy to draw strong conclusions on the basis of 3 points

+

There is a good separation between treatments on PCA1. The sibling pairs do not seem to cluster together.

+

🎬 Save the plot to file:

-
ggsave("figures/frog-s30-pca.png",
+
ggsave("figures/frog-s30-pca.png",
        plot = pca,
        height = 3, 
        width = 4,
@@ -531,22 +695,22 @@ 

Workshop

Visualise the expression of the most significant genes using a heatmap

only should do on sig genes. but use the log 2 normalised values

-
mat <- s30_results_sig0.01 |> 
+
mat <- s30_results_sig0.01 |> 
   select(starts_with("log2_")) |>
   as.matrix()
-
rownames(mat) <- s30_results_sig0.01$xenbase_gene_symbol
+
rownames(mat) <- s30_results_sig0.01$xenbase_gene_symbol
-
n_treatment_clusters <- 2
+
n_treatment_clusters <- 2
 n_gene_clusters <- 2
-
heatmaply(mat, 
+
heatmaply(mat, 
           scale = "row",
           hide_colorbar = TRUE,
           k_col = n_treatment_clusters,
@@ -557,23 +721,23 @@ 

Workshop

labRow = rownames(mat), heatmap_layers = theme(axis.line = element_blank()))
-
- +
+

Visualise all the results with a volcano plot

colour the points if padj < 0.05 and log2FoldChange > 1

-
s30_results <- s30_results |> 
+
s30_results <- s30_results |> 
   mutate(log10_padj = -log10(padj),
          sig = padj < 0.05,
          bigfc = abs(log2FoldChange) >= 2) 
-
vol <- s30_results |> 
+
vol <- s30_results |> 
   ggplot(aes(x = log2FoldChange, 
              y = log10_padj, 
              colour = interaction(sig, bigfc))) +
@@ -599,7 +763,7 @@ 

Workshop

theme(legend.position = "none")
-
ggsave("figures/frog-s30-volcano.png",
+
ggsave("figures/frog-s30-volcano.png",
        plot = vol,
        height = 4.5, 
        width = 4.5,
@@ -617,54 +781,1586 @@ 

Workshop

  • Visual all the results with a volcano plot
  • Import

    -

    🎬 Import

    -

    🎬 Combine the two dataframes (minus the gene ids) into one dataframe called prog_hspc:

    +

    We need to import both the normalised counts and the statistical results. We will need all of these for the visualisation and interpretation.

    +

    🎬 Import the normalised counts for the Prog and HSPC cell types. I used the names prog and hspc for the dataframes.

    +

    🎬 Combine the two dataframes (minus one set of gene ids) into one dataframe called prog_hspc:

    -
    # combine into one dataframe dropping one of the gene id columns
    +
    # combine into one dataframe dropping one of the gene id columns
     prog_hspc <- bind_cols(prog, hspc[-1])
    -

    🎬 …

    +

    🎬 Import the statistical results in results/prog_hspc_results.csv. I used the name prog_hspc_results for the dataframe.

    +

    🎬 Remind yourself what is in the rows and columns and the structure of the dataframes (perhaps using glimpse())

    -
    # import the DE results
    -prog_hspc_results <- read_csv("results/prog_hspc_results.csv")
    -
    -

    🎬 …

    +
    #---CODING ANSWER---
    +#| include: false
    +glimpse(prog_hspc)
    +
    +
    Rows: 280
    +Columns: 1,500
    +$ ensembl_gene_id <chr> "ENSMUSG00000004730", "ENSMUSG00000027962", "ENSMUSG00…
    +$ Prog_001        <dbl> 0.000000, 0.000000, 2.447692, 0.000000, 2.447692, 1.07…
    +$ Prog_002        <dbl> 0.0000000, 0.7859542, 9.8669873, 0.0000000, 7.5139828,…
    +$ Prog_003        <dbl> 0.000000, 1.049924, 9.466541, 0.000000, 7.636827, 1.04…
    +$ Prog_004        <dbl> 1.032808, 0.000000, 2.639234, 0.000000, 2.639234, 0.00…
    +$ Prog_006        <dbl> 0.0000000, 0.9376688, 8.9509200, 0.0000000, 0.5437090,…
    +$ Prog_007        <dbl> 0.0000000, 0.7008173, 2.2487025, 0.0000000, 2.0451378,…
    +$ Prog_008        <dbl> 0.0000000, 0.0000000, 9.8216688, 0.0000000, 7.9747826,…
    +$ Prog_009        <dbl> 0.0000000, 0.0000000, 10.3888553, 0.0000000, 4.4437936…
    +$ Prog_010        <dbl> 0.000000, 0.000000, 3.277715, 1.453985, 6.670995, 1.45…
    +$ Prog_011        <dbl> 0.000000, 0.000000, 9.329603, 0.000000, 1.756729, 1.13…
    +$ Prog_012        <dbl> 1.909353, 1.909353, 3.588040, 0.000000, 0.000000, 0.00…
    +$ Prog_013        <dbl> 0.0000000, 1.2104051, 0.7285849, 4.6985794, 7.8677891,…
    +$ Prog_014        <dbl> 0.0000000, 0.0000000, 8.6212214, 0.0000000, 2.4391238,…
    +$ Prog_015        <dbl> 0.0000000, 0.9646149, 1.5375869, 0.0000000, 0.0000000,…
    +$ Prog_016        <dbl> 0.000000, 0.000000, 9.604794, 0.000000, 8.631105, 0.00…
    +$ Prog_017        <dbl> 0.0000000, 0.6852295, 1.4976754, 0.0000000, 5.5232130,…
    +$ Prog_018        <dbl> 0.000000, 0.000000, 8.815843, 0.000000, 1.775663, 0.00…
    +$ Prog_019        <dbl> 0.0000000, 1.2988288, 0.7908933, 0.0000000, 4.5175504,…
    +$ Prog_020        <dbl> 0.000000, 0.000000, 10.912794, 0.000000, 1.588903, 1.0…
    +$ Prog_021        <dbl> 0.000000, 0.000000, 7.638658, 0.000000, 0.000000, 1.08…
    +$ Prog_022        <dbl> 0.000000, 0.000000, 8.671409, 0.000000, 0.000000, 0.00…
    +$ Prog_023        <dbl> 0.0000000, 2.1551569, 1.6194142, 0.0000000, 1.9120124,…
    +$ Prog_024        <dbl> 1.717498, 0.000000, 9.023824, 0.000000, 7.928356, 0.00…
    +$ Prog_025        <dbl> 0.000000, 2.368099, 8.553185, 0.000000, 5.413663, 1.62…
    +$ Prog_026        <dbl> 0.000000, 0.000000, 3.648527, 1.190477, 1.190477, 0.00…
    +$ Prog_027        <dbl> 0.0000000, 0.0000000, 0.8557008, 0.0000000, 1.3891677,…
    +$ Prog_028        <dbl> 0.0000000, 0.0000000, 9.9095248, 0.0000000, 8.1128539,…
    +$ Prog_029        <dbl> 1.152871, 1.152871, 5.870544, 0.000000, 3.060282, 0.00…
    +$ Prog_030        <dbl> 0.000000, 2.598365, 9.181785, 2.127853, 8.651444, 0.00…
    +$ Prog_031        <dbl> 0.0000000, 0.8413201, 9.2314616, 0.8413201, 2.5235954,…
    +$ Prog_032        <dbl> 0.000000, 1.327820, 9.568213, 0.000000, 7.984181, 0.00…
    +$ Prog_033        <dbl> 0.0000000, 1.3828699, 9.7312399, 0.0000000, 1.3828699,…
    +$ Prog_035        <dbl> 0.0000000, 1.3171343, 9.3029109, 0.0000000, 6.4998843,…
    +$ Prog_036        <dbl> 0.000000, 1.499263, 9.081582, 0.000000, 3.054489, 0.00…
    +$ Prog_037        <dbl> 0.000000, 1.042273, 7.977819, 0.000000, 8.941148, 0.00…
    +$ Prog_038        <dbl> 0.000000, 1.602107, 10.272361, 0.000000, 1.012878, 1.0…
    +$ Prog_039        <dbl> 0.0000000, 0.0000000, 8.7123610, 0.0000000, 7.5301015,…
    +$ Prog_040        <dbl> 0.000000, 0.000000, 2.054034, 8.442082, 2.054034, 1.36…
    +$ Prog_042        <dbl> 0.000000, 0.000000, 10.345104, 1.507712, 1.507712, 0.0…
    +$ Prog_043        <dbl> 0.0000000, 0.8515947, 10.7190561, 0.0000000, 1.3834907…
    +$ Prog_044        <dbl> 0.000000, 1.139041, 1.767524, 1.139041, 5.258244, 0.00…
    +$ Prog_045        <dbl> 0.6854953, 0.6854953, 9.9645500, 0.0000000, 8.6240290,…
    +$ Prog_046        <dbl> 0.000000, 0.000000, 9.450093, 0.000000, 1.866185, 0.91…
    +$ Prog_047        <dbl> 0.000000, 8.678573, 2.850378, 1.165030, 3.874419, 1.16…
    +$ Prog_048        <dbl> 0.000000, 0.000000, 2.794052, 0.000000, 1.825335, 1.82…
    +$ Prog_049        <dbl> 0.0000000, 0.6579981, 9.3946513, 0.0000000, 4.7857083,…
    +$ Prog_050        <dbl> 0.0000000, 0.8386825, 2.0543847, 0.0000000, 6.6143445,…
    +$ Prog_051        <dbl> 0.000000, 0.000000, 10.468034, 0.000000, 1.066147, 2.0…
    +$ Prog_052        <dbl> 0.000000, 2.361305, 4.133679, 0.000000, 8.233765, 1.61…
    +$ Prog_053        <dbl> 0.9224419, 0.9224419, 9.2857331, 0.0000000, 1.8820411,…
    +$ Prog_055        <dbl> 0.0000000, 0.0000000, 3.4913807, 0.0000000, 6.6568051,…
    +$ Prog_056        <dbl> 0.000000, 0.000000, 9.725035, 0.000000, 8.116732, 0.00…
    +$ Prog_057        <dbl> 0.5967097, 0.0000000, 2.3499624, 0.0000000, 2.0262980,…
    +$ Prog_058        <dbl> 0.000000, 0.000000, 10.114434, 0.000000, 5.739715, 0.0…
    +$ Prog_059        <dbl> 0.000000, 2.038654, 8.871380, 0.000000, 7.819265, 1.02…
    +$ Prog_060        <dbl> 0.000000, 1.776961, 9.102002, 0.000000, 2.549440, 1.14…
    +$ Prog_061        <dbl> 0.0000000, 0.8198795, 10.4280461, 0.0000000, 1.3394322…
    +$ Prog_062        <dbl> 0.000000, 0.000000, 9.964751, 0.000000, 5.990110, 0.00…
    +$ Prog_063        <dbl> 0.000000, 8.002331, 2.337480, 1.597934, 3.477092, 0.00…
    +$ Prog_064        <dbl> 0.000000, 1.007715, 10.123899, 1.007715, 6.687664, 0.0…
    +$ Prog_065        <dbl> 0.0000000, 0.7570004, 2.1537620, 0.0000000, 8.4055113,…
    +$ Prog_066        <dbl> 0.000000, 0.000000, 6.895361, 0.000000, 2.160890, 0.00…
    +$ Prog_067        <dbl> 0.000000, 0.000000, 9.037415, 0.000000, 1.747210, 2.18…
    +$ Prog_068        <dbl> 0.000000, 0.000000, 1.706107, 0.000000, 7.498985, 0.00…
    +$ Prog_069        <dbl> 0.0000000, 0.0000000, 2.6246170, 0.8962338, 8.5297976,…
    +$ Prog_070        <dbl> 0.000000, 1.475962, 3.022681, 1.475962, 9.416561, 0.00…
    +$ Prog_071        <dbl> 0.000000, 1.028372, 0.000000, 1.028372, 1.622670, 0.00…
    +$ Prog_072        <dbl> 0.000000, 1.478766, 10.580032, 0.000000, 8.863092, 2.1…
    +$ Prog_073        <dbl> 0.0000000, 0.0000000, 3.6520519, 0.0000000, 0.0000000,…
    +$ Prog_074        <dbl> 0.000000, 0.000000, 9.408942, 0.000000, 2.193005, 0.00…
    +$ Prog_075        <dbl> 0.0000000, 0.0000000, 2.2865667, 0.0000000, 1.7343788,…
    +$ Prog_076        <dbl> 0.000000, 0.000000, 9.433579, 0.000000, 6.383341, 1.04…
    +$ Prog_077        <dbl> 0.000000, 1.068131, 9.018616, 1.068131, 5.035832, 2.69…
    +$ Prog_078        <dbl> 0.0000000, 0.0000000, 11.2234617, 0.0000000, 7.5155691…
    +$ Prog_079        <dbl> 0.0000000, 0.0000000, 11.1687105, 0.0000000, 1.2918528…
    +$ Prog_080        <dbl> 0.000000, 6.834183, 4.353284, 0.000000, 8.210067, 1.46…
    +$ Prog_081        <dbl> 0.663083, 0.663083, 9.804585, 0.000000, 1.459635, 0.00…
    +$ Prog_082        <dbl> 0.0000000, 0.0000000, 10.2058437, 0.0000000, 0.9846850…
    +$ Prog_083        <dbl> 0.0000000, 1.4258002, 2.7872699, 0.0000000, 7.7551943,…
    +$ Prog_084        <dbl> 0.000000, 0.000000, 9.331667, 0.000000, 1.701931, 1.08…
    +$ Prog_085        <dbl> 0.0000000, 0.6491118, 9.3288292, 0.0000000, 5.1330763,…
    +$ Prog_087        <dbl> 0.000000, 0.000000, 1.104019, 0.000000, 5.052535, 2.15…
    +$ Prog_088        <dbl> 0.000000, 0.000000, 3.564043, 0.000000, 3.038816, 0.00…
    +$ Prog_089        <dbl> 0.000000, 0.000000, 10.085311, 0.000000, 4.543583, 0.0…
    +$ Prog_090        <dbl> 0.0000000, 0.0000000, 9.2374975, 0.0000000, 1.2838093,…
    +$ Prog_091        <dbl> 0.4305087, 0.7616406, 10.0688175, 0.0000000, 8.2019581…
    +$ Prog_092        <dbl> 0.0000000, 0.9254699, 4.0257506, 0.0000000, 1.8867094,…
    +$ Prog_093        <dbl> 0.9251997, 0.0000000, 6.7901406, 0.0000000, 9.5469428,…
    +$ Prog_094        <dbl> 0.000000, 1.210416, 9.726634, 0.000000, 2.645281, 0.00…
    +$ Prog_095        <dbl> 0.0000000, 0.0000000, 10.3666061, 0.0000000, 9.1749393…
    +$ Prog_096        <dbl> 0.000000, 1.515954, 3.603985, 0.000000, 3.364487, 0.00…
    +$ Prog_097        <dbl> 0.0000000, 0.0000000, 3.3142351, 0.9957312, 1.5792680,…
    +$ Prog_098        <dbl> 0.0000000, 0.0000000, 10.9079028, 0.0000000, 1.6489683…
    +$ Prog_099        <dbl> 0.0000000, 0.0000000, 9.4733082, 0.0000000, 9.2852571,…
    +$ Prog_100        <dbl> 0.0000000, 0.0000000, 10.0645065, 0.0000000, 0.8335261…
    +$ Prog_101        <dbl> 0.0000000, 0.0000000, 3.0554930, 0.0000000, 1.2201851,…
    +$ Prog_102        <dbl> 0.000000, 0.000000, 10.314337, 0.000000, 8.135122, 0.0…
    +$ Prog_103        <dbl> 0.000000, 0.000000, 2.694305, 0.000000, 2.427053, 0.00…
    +$ Prog_105        <dbl> 0.000000, 0.000000, 1.715023, 0.000000, 8.272431, 0.00…
    +$ Prog_106        <dbl> 0.000000, 0.000000, 2.897396, 0.000000, 9.269248, 0.00…
    +$ Prog_107        <dbl> 0.0000000, 0.0000000, 11.2438039, 0.8959356, 8.2190795…
    +$ Prog_108        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 8.187893, 0.00…
    +$ Prog_109        <dbl> 0.000000, 0.000000, 2.847758, 0.000000, 1.798890, 0.00…
    +$ Prog_110        <dbl> 0.0000000, 0.0000000, 7.0447094, 0.0000000, 1.1498271,…
    +$ Prog_111        <dbl> 0.000000, 1.347991, 9.989313, 0.000000, 2.844445, 0.00…
    +$ Prog_112        <dbl> 0.0000000, 0.0000000, 9.7736274, 0.0000000, 0.0000000,…
    +$ Prog_113        <dbl> 0.000000, 0.000000, 3.375645, 0.000000, 4.805584, 0.00…
    +$ Prog_114        <dbl> 0.000000, 0.000000, 5.270999, 0.000000, 9.142589, 0.00…
    +$ Prog_115        <dbl> 0.000000, 0.000000, 9.198819, 0.000000, 7.984094, 0.00…
    +$ Prog_116        <dbl> 0.0000000, 0.8762674, 3.6666065, 0.0000000, 6.3585217,…
    +$ Prog_117        <dbl> 0.0000000, 0.0000000, 1.5843370, 0.0000000, 4.3914238,…
    +$ Prog_118        <dbl> 0.000000, 2.358196, 3.210167, 0.000000, 2.358196, 1.61…
    +$ Prog_119        <dbl> 0.0000000, 0.0000000, 9.5596469, 0.0000000, 5.0827697,…
    +$ Prog_120        <dbl> 0.000000, 0.000000, 9.797611, 1.233285, 6.208574, 1.23…
    +$ Prog_122        <dbl> 0.0000000, 0.0000000, 10.1430231, 0.0000000, 1.5290744…
    +$ Prog_123        <dbl> 0.972353, 3.271775, 1.547981, 0.000000, 0.972353, 0.97…
    +$ Prog_124        <dbl> 0.000000, 1.866390, 1.866390, 0.000000, 7.948926, 1.21…
    +$ Prog_125        <dbl> 0.000000, 0.000000, 10.339672, 0.000000, 1.886583, 0.0…
    +$ Prog_126        <dbl> 0.0000000, 0.9244523, 6.9333965, 0.0000000, 6.5045625,…
    +$ Prog_127        <dbl> 0.0000000, 0.0000000, 1.8946766, 0.9306455, 2.8763501,…
    +$ Prog_128        <dbl> 0.0000000, 0.0000000, 0.9281856, 0.0000000, 7.8305039,…
    +$ Prog_129        <dbl> 0.0000000, 0.4157242, 0.0000000, 0.0000000, 8.6962250,…
    +$ Prog_130        <dbl> 0.0000000, 0.0000000, 0.7728911, 0.0000000, 2.1837890,…
    +$ Prog_131        <dbl> 0.000000, 1.024302, 0.000000, 0.000000, 2.360617, 1.61…
    +$ Prog_132        <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 1.5667490,…
    +$ Prog_133        <dbl> 0.000000, 0.801043, 1.988936, 0.000000, 8.275295, 2.44…
    +$ Prog_134        <dbl> 0.000000, 1.945025, 4.178130, 0.000000, 2.744352, 1.94…
    +$ Prog_135        <dbl> 0.0000000, 0.0000000, 0.9244625, 8.3087390, 1.4833406,…
    +$ Prog_136        <dbl> 0.0000000, 1.3808535, 0.6179955, 0.6179955, 7.6121006,…
    +$ Prog_137        <dbl> 0.0000000, 0.7394643, 0.7394643, 0.7394643, 7.8827291,…
    +$ Prog_138        <dbl> 0.000000, 1.563600, 0.000000, 0.000000, 3.430222, 0.00…
    +$ Prog_139        <dbl> 0.0000000, 1.7812055, 8.3267743, 0.0000000, 1.3921828,…
    +$ Prog_140        <dbl> 0.0000000, 0.7781468, 9.9514318, 0.0000000, 0.7781468,…
    +$ Prog_141        <dbl> 0.0000000, 5.7825012, 0.6970532, 0.0000000, 1.5178150,…
    +$ Prog_142        <dbl> 0.000000, 0.000000, 3.511726, 1.314161, 6.116501, 1.31…
    +$ Prog_143        <dbl> 0.0000000, 0.5895431, 1.5941091, 0.0000000, 2.1805905,…
    +$ Prog_144        <dbl> 0.0000000, 1.7299786, 3.2473969, 0.0000000, 7.0136857,…
    +$ Prog_145        <dbl> 0.0000000, 0.8803065, 2.1253422, 0.0000000, 3.8532234,…
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    +$ Prog_794        <dbl> 0.0000000, 1.2839055, 7.7226264, 1.6564775, 9.9829054,…
    +$ Prog_795        <dbl> 0.0000000, 0.8871069, 2.1367998, 0.0000000, 7.9894805,…
    +$ Prog_796        <dbl> 0.000000, 0.000000, 2.296474, 0.000000, 6.034682, 0.00…
    +$ Prog_797        <dbl> 0.000000, 0.000000, 1.464793, 2.176476, 3.531249, 0.00…
    +$ Prog_798        <dbl> 0.0000000, 0.8285245, 1.7344840, 8.4849731, 2.1671674,…
    +$ Prog_799        <dbl> 0.000000, 4.860757, 0.000000, 0.000000, 7.665351, 1.26…
    +$ Prog_800        <dbl> 0.000000, 8.803266, 2.829021, 0.000000, 2.829021, 0.00…
    +$ Prog_801        <dbl> 0.5808097, 0.0000000, 1.5766449, 3.4480774, 8.7052117,…
    +$ Prog_802        <dbl> 0.000000, 1.898890, 8.412752, 0.000000, 8.778230, 0.00…
    +$ Prog_803        <dbl> 0.000000, 2.543597, 7.878204, 0.000000, 3.708852, 0.00…
    +$ Prog_804        <dbl> 0.000000, 0.000000, 9.348673, 1.233011, 2.954727, 0.00…
    +$ Prog_805        <dbl> 0.000000, 0.000000, 8.315664, 0.000000, 9.369724, 0.00…
    +$ Prog_806        <dbl> 0.000000, 0.935748, 0.935748, 0.935748, 7.896934, 0.00…
    +$ Prog_807        <dbl> 0.0000000, 0.0000000, 8.6811767, 0.0000000, 8.1350692,…
    +$ Prog_808        <dbl> 0.0000000, 0.0000000, 3.0377707, 0.0000000, 1.6615960,…
    +$ Prog_809        <dbl> 0.6287654, 0.0000000, 2.2701368, 0.6287654, 1.6712775,…
    +$ Prog_810        <dbl> 0.0000000, 0.5049969, 1.1746370, 0.0000000, 7.3167564,…
    +$ Prog_811        <dbl> 0.000000, 1.329155, 9.629477, 0.000000, 5.626490, 0.00…
    +$ Prog_812        <dbl> 0.000000, 3.245813, 9.354092, 0.000000, 7.095686, 0.00…
    +$ Prog_813        <dbl> 0.0000000, 0.8803957, 10.2579542, 0.0000000, 5.5099063…
    +$ Prog_814        <dbl> 0.0000000, 0.0000000, 9.3443362, 0.8521854, 2.7304517,…
    +$ Prog_815        <dbl> 0.000000, 0.000000, 9.145702, 0.000000, 1.640454, 1.04…
    +$ Prog_816        <dbl> 0.0000000, 1.5005517, 7.5725424, 0.0000000, 8.4454565,…
    +$ Prog_817        <dbl> 0.000000, 0.617522, 1.876247, 0.000000, 1.876247, 0.61…
    +$ Prog_818        <dbl> 0.000000, 0.000000, 8.817434, 0.000000, 5.110650, 0.00…
    +$ Prog_819        <dbl> 0.0000000, 0.0000000, 9.9789196, 0.0000000, 7.2226335,…
    +$ Prog_820        <dbl> 0.0000000, 0.0000000, 7.8202471, 0.6094958, 6.5794013,…
    +$ Prog_821        <dbl> 0.000000, 0.527402, 9.347671, 0.000000, 7.134023, 0.00…
    +$ Prog_822        <dbl> 0.000000, 0.000000, 10.830559, 0.000000, 5.611126, 0.7…
    +$ Prog_823        <dbl> 0.000000, 2.368033, 6.108218, 0.000000, 3.421181, 0.00…
    +$ Prog_824        <dbl> 0.0000000, 0.0000000, 3.2970935, 0.0000000, 7.2393470,…
    +$ Prog_825        <dbl> 0.614008, 0.000000, 9.102087, 0.000000, 7.067777, 0.61…
    +$ Prog_826        <dbl> 0.0000000, 0.0000000, 10.0184296, 0.0000000, 0.8930072…
    +$ Prog_827        <dbl> 0.000000, 1.153240, 9.651103, 0.000000, 2.224160, 0.00…
    +$ Prog_828        <dbl> 0.0000000, 0.0000000, 1.4730404, 0.0000000, 7.1366525,…
    +$ Prog_829        <dbl> 0.000000, 0.000000, 2.002737, 0.679441, 6.402776, 0.00…
    +$ Prog_830        <dbl> 0.0000000, 0.0000000, 9.9350866, 0.7122405, 2.0675466,…
    +$ Prog_831        <dbl> 0.0000000, 0.7518682, 8.8581337, 0.0000000, 1.2436351,…
    +$ Prog_832        <dbl> 0.0000000, 0.9591086, 1.9382199, 0.0000000, 7.2304444,…
    +$ Prog_833        <dbl> 0.0000000, 0.8376881, 3.0151862, 0.0000000, 3.0151862,…
    +$ Prog_834        <dbl> 0.0000000, 0.0000000, 2.4274006, 0.0000000, 5.4373805,…
    +$ Prog_835        <dbl> 0.0000000, 0.9809832, 10.5344381, 0.0000000, 2.5531271…
    +$ Prog_836        <dbl> 0.0000000, 0.5020465, 1.2967651, 0.5020465, 1.5225555,…
    +$ Prog_837        <dbl> 0.0000000, 0.9850818, 9.8963349, 0.0000000, 0.0000000,…
    +$ Prog_838        <dbl> 0.000000, 0.000000, 9.547417, 0.000000, 1.987452, 1.31…
    +$ Prog_839        <dbl> 0.0000000, 0.0000000, 8.0095143, 0.0000000, 6.1786824,…
    +$ Prog_840        <dbl> 0.0000000, 0.6485416, 2.4700583, 0.0000000, 8.4397289,…
    +$ Prog_841        <dbl> 0.000000, 2.018049, 9.332316, 0.000000, 6.751711, 0.00…
    +$ Prog_842        <dbl> 0.0000000, 0.0000000, 8.9760410, 0.0000000, 6.6732008,…
    +$ Prog_843        <dbl> 0.0000000, 0.0000000, 2.4085725, 0.0000000, 3.5947323,…
    +$ Prog_844        <dbl> 1.153513, 1.153513, 10.215305, 0.000000, 2.832433, 0.0…
    +$ Prog_845        <dbl> 0.0000000, 0.0000000, 1.5265633, 0.0000000, 5.0433788,…
    +$ Prog_846        <dbl> 0.000000, 0.000000, 2.924854, 2.924854, 7.842922, 1.67…
    +$ Prog_847        <dbl> 0.0000000, 0.8935156, 2.1475639, 0.8935156, 8.6586321,…
    +$ Prog_848        <dbl> 0.000000, 0.000000, 9.603595, 0.000000, 3.859249, 0.00…
    +$ Prog_849        <dbl> 1.653308, 2.403562, 4.344108, 0.000000, 2.403562, 1.65…
    +$ Prog_850        <dbl> 0.000000, 0.000000, 9.300996, 0.000000, 7.843614, 0.00…
    +$ Prog_851        <dbl> 0.000000, 1.120675, 9.108092, 0.000000, 7.050312, 1.12…
    +$ Prog_852        <dbl> 0.000000, 0.000000, 9.579540, 0.000000, 3.070503, 0.00…
    +$ HSPC_001        <dbl> 0.0000000, 0.0000000, 0.7390988, 0.7390988, 1.2254389,…
    +$ HSPC_002        <dbl> 0.000000, 0.000000, 2.238601, 0.000000, 2.238601, 0.00…
    +$ HSPC_003        <dbl> 0.0000000, 0.0000000, 0.9929154, 0.9929154, 1.5755086,…
    +$ HSPC_004        <dbl> 0.000000, 0.000000, 2.465632, 0.000000, 8.073635, 0.00…
    +$ HSPC_006        <dbl> 0.000000, 0.000000, 1.941849, 0.000000, 1.941849, 0.00…
    +$ HSPC_008        <dbl> 0.000000, 1.395221, 0.000000, 0.000000, 0.000000, 0.00…
    +$ HSPC_009        <dbl> 0.000000, 1.684562, 2.934193, 0.000000, 5.635680, 0.00…
    +$ HSPC_011        <dbl> 1.237406, 0.000000, 2.685036, 0.000000, 1.237406, 2.34…
    +$ HSPC_012        <dbl> 0.000000, 0.000000, 2.517338, 0.000000, 7.378370, 1.74…
    +$ HSPC_014        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 1.857888, 0.00…
    +$ HSPC_015        <dbl> 0.000000, 2.398869, 0.000000, 7.717134, 4.177566, 2.39…
    +$ HSPC_016        <dbl> 0.0000000, 0.9487581, 2.2390441, 0.0000000, 0.9487581,…
    +$ HSPC_017        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 4.146951, 0.00…
    +$ HSPC_018        <dbl> 0.000000, 1.248476, 2.701241, 0.000000, 8.633940, 1.24…
    +$ HSPC_020        <dbl> 0.000000, 0.000000, 2.277106, 0.000000, 2.277106, 6.73…
    +$ HSPC_021        <dbl> 0.000000, 0.000000, 2.996123, 0.000000, 8.043618, 2.49…
    +$ HSPC_022        <dbl> 0.000000, 1.211071, 1.860045, 1.211071, 7.334868, 8.67…
    +$ HSPC_023        <dbl> 0.000000, 0.000000, 1.539553, 0.000000, 9.321612, 1.53…
    +$ HSPC_024        <dbl> 0.000000, 0.000000, 1.692191, 0.000000, 9.143541, 0.00…
    +$ HSPC_025        <dbl> 1.571690, 0.000000, 3.152201, 8.738315, 1.571690, 0.00…
    +$ HSPC_026        <dbl> 0.000000, 0.000000, 1.384631, 0.000000, 1.384631, 0.00…
    +$ HSPC_027        <dbl> 0.0000000, 0.0000000, 0.0000000, 0.9302884, 7.0772133,…
    +$ HSPC_028        <dbl> 0.0000000, 0.8288203, 0.8288203, 0.0000000, 1.7349575,…
    +$ HSPC_030        <dbl> 0.000000, 1.118674, 1.118674, 0.000000, 5.508301, 0.00…
    +$ HSPC_031        <dbl> 0.0000000, 0.0000000, 2.9918679, 0.0000000, 9.6855069,…
    +$ HSPC_033        <dbl> 0.000000, 0.000000, 1.303195, 0.000000, 1.303195, 0.00…
    +$ HSPC_034        <dbl> 0.0000000, 1.3093499, 2.6262158, 0.7983817, 8.3884282,…
    +$ HSPC_035        <dbl> 0.000000, 2.175011, 0.000000, 0.000000, 2.649348, 0.00…
    +$ HSPC_036        <dbl> 0.0000000, 0.0000000, 2.1381879, 5.5782959, 8.5678887,…
    +$ HSPC_037        <dbl> 0.000000, 1.516975, 2.239950, 0.000000, 3.365905, 0.00…
    +$ HSPC_038        <dbl> 0.000000, 0.000000, 1.364250, 1.364250, 0.000000, 0.00…
    +$ HSPC_040        <dbl> 0.0000000, 1.5383598, 1.9474646, 9.3621654, 8.6231804,…
    +$ HSPC_041        <dbl> 0.000000, 0.000000, 2.579199, 2.579199, 6.743574, 0.00…
    +$ HSPC_042        <dbl> 0.0000000, 1.4051125, 1.7960064, 0.0000000, 0.8672577,…
    +$ HSPC_043        <dbl> 0.000000, 0.000000, 3.553494, 1.341668, 6.491814, 7.93…
    +$ HSPC_044        <dbl> 0.000000, 0.000000, 2.582992, 0.000000, 0.000000, 0.00…
    +$ HSPC_045        <dbl> 0.000000, 0.000000, 1.346994, 0.000000, 0.000000, 2.03…
    +$ HSPC_046        <dbl> 0.0000000, 0.8452114, 1.3746533, 0.0000000, 6.7513398,…
    +$ HSPC_047        <dbl> 0.000000, 8.428296, 4.239537, 0.000000, 3.552610, 2.19…
    +$ HSPC_048        <dbl> 0.000000, 1.108133, 1.727411, 8.235885, 6.865010, 2.98…
    +$ HSPC_049        <dbl> 0.000000, 0.000000, 2.394418, 6.252069, 1.274540, 1.94…
    +$ HSPC_050        <dbl> 0.000000, 0.000000, 3.086078, 0.000000, 6.466053, 0.00…
    +$ HSPC_051        <dbl> 0.0000000, 0.0000000, 1.9634358, 0.0000000, 0.0000000,…
    +$ HSPC_052        <dbl> 0.000000, 7.749301, 2.709016, 1.509063, 1.509063, 0.00…
    +$ HSPC_053        <dbl> 0.0000000, 0.0000000, 2.4796614, 0.0000000, 5.3728144,…
    +$ HSPC_054        <dbl> 0.000000, 0.000000, 1.158501, 0.000000, 2.231666, 1.15…
    +$ HSPC_055        <dbl> 0.000000, 1.797473, 3.075245, 0.000000, 3.446842, 0.00…
    +$ HSPC_056        <dbl> 0.000000, 2.016637, 3.720889, 0.000000, 8.325851, 6.21…
    +$ HSPC_057        <dbl> 0.000000, 0.000000, 1.847003, 0.000000, 8.239896, 7.42…
    +$ HSPC_058        <dbl> 1.398955, 0.000000, 3.199362, 0.000000, 2.916174, 0.00…
    +$ HSPC_060        <dbl> 0.000000, 1.080287, 2.118815, 0.000000, 6.512085, 1.08…
    +$ HSPC_061        <dbl> 0.000000, 1.725558, 2.985726, 0.000000, 1.725558, 2.48…
    +$ HSPC_062        <dbl> 0.000000, 0.000000, 2.211545, 0.000000, 0.000000, 0.00…
    +$ HSPC_063        <dbl> 0.000000, 1.514955, 2.237502, 0.000000, 1.514955, 2.23…
    +$ HSPC_064        <dbl> 0.000000, 0.000000, 1.718347, 0.000000, 8.222925, 1.10…
    +$ HSPC_065        <dbl> 0.0000000, 0.0000000, 0.9703625, 0.0000000, 2.2742114,…
    +$ HSPC_066        <dbl> 0.000000, 0.000000, 2.564196, 5.716981, 9.399772, 1.78…
    +$ HSPC_067        <dbl> 0.000000, 0.000000, 2.147724, 0.000000, 9.138862, 5.93…
    +$ HSPC_068        <dbl> 0.000000, 1.870770, 2.658681, 0.000000, 0.000000, 0.00…
    +$ HSPC_069        <dbl> 0.000000, 1.116169, 1.737865, 7.866496, 3.791268, 8.80…
    +$ HSPC_070        <dbl> 0.0000000, 0.0000000, 1.4430580, 0.8949015, 4.5972951,…
    +$ HSPC_071        <dbl> 0.0000000, 0.9271506, 0.0000000, 0.0000000, 1.8892984,…
    +$ HSPC_072        <dbl> 1.744738, 0.000000, 0.000000, 0.000000, 7.077098, 0.00…
    +$ HSPC_073        <dbl> 0.000000, 0.000000, 4.134335, 0.000000, 3.387315, 0.00…
    +$ HSPC_074        <dbl> 0.000000, 0.000000, 1.703855, 0.000000, 3.326366, 1.70…
    +$ HSPC_075        <dbl> 1.674178, 0.000000, 4.030303, 0.000000, 9.381928, 8.86…
    +$ HSPC_076        <dbl> 0.000000, 0.000000, 2.821284, 0.000000, 6.891389, 1.14…
    +$ HSPC_077        <dbl> 0.000000, 0.000000, 1.114630, 0.000000, 8.460932, 0.00…
    +$ HSPC_078        <dbl> 0.000000, 2.209396, 4.387948, 0.000000, 6.627462, 2.68…
    +$ HSPC_079        <dbl> 0.000000, 0.000000, 4.095390, 0.000000, 2.076810, 0.00…
    +$ HSPC_080        <dbl> 0.000000, 1.012596, 2.828881, 0.000000, 1.012596, 0.00…
    +$ HSPC_081        <dbl> 0.0000000, 1.2652832, 1.2652832, 0.0000000, 5.3328809,…
    +$ HSPC_082        <dbl> 0.000000, 0.000000, 4.421943, 0.000000, 1.970627, 0.00…
    +$ HSPC_083        <dbl> 1.895620, 0.000000, 4.114776, 0.000000, 10.864775, 7.8…
    +$ HSPC_084        <dbl> 0.000000, 0.000000, 3.216417, 0.000000, 4.036024, 0.00…
    +$ HSPC_085        <dbl> 0.000000, 0.000000, 1.934463, 0.000000, 0.000000, 1.93…
    +$ HSPC_087        <dbl> 0.000000, 0.000000, 1.859256, 0.000000, 8.387078, 7.44…
    +$ HSPC_088        <dbl> 0.000000, 0.000000, 2.091761, 1.061818, 1.666812, 0.00…
    +$ HSPC_089        <dbl> 0.000000, 0.000000, 1.542804, 0.000000, 5.429591, 0.00…
    +$ HSPC_090        <dbl> 0.0000000, 0.9583485, 0.0000000, 0.9583485, 7.8106423,…
    +$ HSPC_094        <dbl> 0.000000, 1.001307, 3.002286, 0.000000, 1.001307, 0.00…
    +$ HSPC_095        <dbl> 0.000000, 2.055264, 3.768162, 0.000000, 5.497828, 0.00…
    +$ HSPC_096        <dbl> 0.000000, 0.000000, 3.020317, 0.000000, 4.694719, 0.00…
    +$ HSPC_098        <dbl> 0.000000, 0.000000, 4.033084, 0.000000, 3.353704, 0.00…
    +$ HSPC_099        <dbl> 0.000000, 0.000000, 1.355566, 8.533241, 1.355566, 7.54…
    +$ HSPC_100        <dbl> 0.000000, 1.117108, 2.504994, 0.000000, 1.117108, 0.00…
    +$ HSPC_101        <dbl> 0.000000, 1.007084, 3.182495, 0.000000, 6.058315, 0.00…
    +$ HSPC_102        <dbl> 0.000000, 1.110882, 2.992525, 0.000000, 1.110882, 6.01…
    +$ HSPC_103        <dbl> 0.000000, 0.000000, 3.444022, 3.444022, 3.444022, 6.84…
    +$ HSPC_104        <dbl> 0.000000, 0.000000, 2.720362, 0.000000, 5.326705, 0.00…
    +$ HSPC_105        <dbl> 0.000000, 0.000000, 2.953351, 0.000000, 2.128535, 0.00…
    +$ HSPC_106        <dbl> 0.000000, 0.000000, 2.917053, 8.830809, 10.056331, 0.0…
    +$ HSPC_107        <dbl> 0.000000, 1.539035, 2.266637, 1.539035, 2.266637, 0.00…
    +$ HSPC_108        <dbl> 0.000000, 0.000000, 2.342599, 1.237188, 9.967793, 0.00…
    +$ HSPC_109        <dbl> 0.000000, 1.595174, 3.183524, 1.595174, 6.584986, 0.00…
    +$ HSPC_110        <dbl> 0.000000, 0.000000, 2.667372, 0.000000, 9.520268, 2.66…
    +$ HSPC_111        <dbl> 0.000000, 1.495539, 2.691330, 3.780086, 1.495539, 0.00…
    +$ HSPC_114        <dbl> 0.0000000, 0.0000000, 2.1872025, 0.0000000, 0.9172819,…
    +$ HSPC_115        <dbl> 0.000000, 2.348960, 4.119213, 6.801590, 2.348960, 2.34…
    +$ HSPC_117        <dbl> 0.000000, 0.000000, 2.662801, 0.000000, 2.662801, 0.00…
    +$ HSPC_118        <dbl> 0.000000, 0.000000, 2.731892, 0.000000, 7.192924, 1.26…
    +$ HSPC_119        <dbl> 0.000000, 2.432480, 3.827272, 0.000000, 2.432480, 8.53…
    +$ HSPC_120        <dbl> 0.000000, 0.000000, 1.186672, 0.000000, 1.186672, 9.49…
    +$ HSPC_121        <dbl> 0.000000, 0.000000, 4.264196, 0.000000, 2.822082, 0.00…
    +$ HSPC_122        <dbl> 0.000000, 1.435059, 2.140080, 0.000000, 0.000000, 0.00…
    +$ HSPC_123        <dbl> 0.000000, 0.000000, 2.244368, 0.000000, 6.093587, 0.00…
    +$ HSPC_125        <dbl> 0.000000, 0.000000, 1.285018, 0.000000, 5.553951, 6.70…
    +$ HSPC_126        <dbl> 0.0000000, 0.0000000, 1.5017883, 0.0000000, 2.6995085,…
    +$ HSPC_127        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.822566, 0.00…
    +$ HSPC_130        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 9.443009, 0.00…
    +$ HSPC_131        <dbl> 0.000000, 0.000000, 2.384852, 0.000000, 4.161211, 0.00…
    +$ HSPC_132        <dbl> 0.0000000, 0.7827224, 0.4438051, 0.0000000, 1.6604369,…
    +$ HSPC_133        <dbl> 2.234359, 3.072289, 0.000000, 2.234359, 8.065004, 0.00…
    +$ HSPC_134        <dbl> 0.000000, 2.768568, 0.000000, 0.000000, 6.641594, 0.00…
    +$ HSPC_135        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 3.600652, 8.08…
    +$ HSPC_136        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.962552, 0.00…
    +$ HSPC_138        <dbl> 0.0000000, 0.7062338, 0.7062338, 0.0000000, 1.8180968,…
    +$ HSPC_139        <dbl> 0.000000, 0.000000, 4.345514, 0.000000, 0.000000, 4.09…
    +$ HSPC_140        <dbl> 0.000000, 0.000000, 4.660038, 0.000000, 0.000000, 0.00…
    +$ HSPC_141        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 4.543589, 0.00…
    +$ HSPC_142        <dbl> 0.000000, 0.000000, 2.523431, 0.000000, 0.000000, 0.00…
    +$ HSPC_143        <dbl> 0.000000, 1.958674, 2.760027, 0.000000, 8.379422, 0.00…
    +$ HSPC_144        <dbl> 0.000000, 0.000000, 1.075288, 0.000000, 0.000000, 0.00…
    +$ HSPC_146        <dbl> 0.000000, 2.277948, 2.277948, 3.120975, 1.548407, 0.00…
    +$ HSPC_148        <dbl> 0.000000, 0.000000, 2.428270, 0.000000, 0.000000, 0.00…
    +$ HSPC_149        <dbl> 0.000000, 0.000000, 0.000000, 7.370990, 9.039081, 0.00…
    +$ HSPC_151        <dbl> 0.000000, 0.000000, 1.942220, 0.000000, 6.477871, 0.00…
    +$ HSPC_152        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 8.948497, 0.00…
    +$ HSPC_153        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.00…
    +$ HSPC_154        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 6.567172, 0.00…
    +$ HSPC_155        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 5.981102, 2.73…
    +$ HSPC_156        <dbl> 0.0000000, 0.5544683, 0.5544683, 0.0000000, 1.2665659,…
    +$ HSPC_157        <dbl> 0.000000, 1.992960, 3.313476, 0.000000, 6.056835, 2.79…
    +$ HSPC_158        <dbl> 0.000000, 1.681202, 1.681202, 0.000000, 2.436668, 1.68…
    +$ HSPC_159        <dbl> 0.000000, 0.000000, 0.000000, 4.189894, 9.099914, 9.05…
    +$ HSPC_161        <dbl> 0.000000, 0.000000, 1.701367, 0.000000, 3.323133, 8.08…
    +$ HSPC_162        <dbl> 0.715249, 0.715249, 1.191268, 0.000000, 6.603848, 1.54…
    +$ HSPC_164        <dbl> 0.000000, 1.780116, 4.173269, 0.000000, 3.053739, 0.00…
    +$ HSPC_165        <dbl> 0.000000, 0.000000, 2.521243, 0.000000, 1.752913, 2.52…
    +$ HSPC_166        <dbl> 0.000000, 1.680351, 3.830900, 0.000000, 2.435661, 0.00…
    +$ HSPC_168        <dbl> 0.000000, 0.000000, 2.587724, 0.000000, 1.587172, 0.00…
    +$ HSPC_169        <dbl> 0.000000, 2.231654, 2.231654, 0.000000, 2.840202, 1.15…
    +$ HSPC_170        <dbl> 0.000000, 2.323845, 3.702651, 0.000000, 0.000000, 0.00…
    +$ HSPC_171        <dbl> 0.000000, 2.249267, 0.000000, 0.000000, 6.986101, 0.00…
    +$ HSPC_172        <dbl> 0.0000000, 0.0000000, 1.2663678, 1.6361385, 3.8432543,…
    +$ HSPC_173        <dbl> 0.000000, 0.000000, 2.202687, 0.000000, 2.202687, 0.00…
    +$ HSPC_174        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 1.25…
    +$ HSPC_175        <dbl> 0.000000, 0.000000, 2.214143, 0.000000, 3.959792, 1.49…
    +$ HSPC_176        <dbl> 0.000000, 0.000000, 2.023933, 0.000000, 6.539273, 2.02…
    +$ HSPC_177        <dbl> 0.000000, 1.971046, 1.971046, 0.000000, 3.664721, 0.00…
    +$ HSPC_178        <dbl> 0.000000, 1.002574, 1.002574, 0.000000, 8.129245, 0.00…
    +$ HSPC_179        <dbl> 0.0000000, 0.8360365, 1.7464921, 0.0000000, 2.3003274,…
    +$ HSPC_180        <dbl> 0.000000, 0.000000, 2.753903, 0.000000, 6.624564, 6.08…
    +$ HSPC_181        <dbl> 0.000000, 0.000000, 5.739487, 0.000000, 5.969896, 0.00…
    +$ HSPC_182        <dbl> 0.000000, 0.000000, 3.778793, 0.000000, 3.245451, 3.24…
    +$ HSPC_183        <dbl> 0.000000, 0.000000, 3.206129, 1.020477, 7.802033, 0.00…
    +$ HSPC_185        <dbl> 0.000000, 0.000000, 5.514029, 6.498157, 9.703008, 0.00…
    +$ HSPC_186        <dbl> 0.000000, 1.605849, 9.300294, 0.000000, 3.729280, 0.00…
    +$ HSPC_187        <dbl> 0.000000, 0.000000, 3.016892, 0.000000, 8.206576, 2.18…
    +$ HSPC_189        <dbl> 2.651507, 1.465231, 0.000000, 0.000000, 1.465231, 2.17…
    +$ HSPC_190        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.00…
    +$ HSPC_191        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 1.406826, 0.00…
    +$ HSPC_192        <dbl> 0.000000, 0.000000, 2.111369, 0.000000, 0.000000, 1.41…
    +$ HSPC_193        <dbl> 0.0000000, 2.2721907, 2.9455106, 0.0000000, 9.1712813,…
    +$ HSPC_195        <dbl> 0.0000000, 0.0000000, 2.4446955, 0.0000000, 1.4738612,…
    +$ HSPC_196        <dbl> 0.000000, 1.379440, 2.888830, 0.000000, 0.000000, 0.00…
    +$ HSPC_198        <dbl> 2.155150, 0.000000, 3.506202, 1.105265, 1.105265, 0.00…
    +$ HSPC_199        <dbl> 1.676720, 0.000000, 2.102827, 4.774209, 2.102827, 1.06…
    +$ HSPC_200        <dbl> 1.572132, 2.306518, 0.000000, 0.000000, 2.790837, 1.57…
    +$ HSPC_202        <dbl> 1.3178909, 0.0000000, 0.0000000, 0.0000000, 1.6957804,…
    +$ HSPC_203        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.00…
    +$ HSPC_204        <dbl> 0.000000, 1.342435, 1.342435, 0.000000, 2.487324, 1.34…
    +$ HSPC_205        <dbl> 0.000000, 1.996780, 0.000000, 0.000000, 2.803674, 4.95…
    +$ HSPC_206        <dbl> 1.076411, 0.000000, 1.076411, 0.000000, 1.076411, 0.00…
    +$ HSPC_207        <dbl> 0.000000, 0.000000, 1.482035, 0.000000, 9.592779, 0.00…
    +$ HSPC_208        <dbl> 0.000000, 0.000000, 3.104133, 0.000000, 2.262852, 2.26…
    +$ HSPC_210        <dbl> 0.000000, 1.021329, 1.021329, 0.000000, 1.613332, 1.02…
    +$ HSPC_211        <dbl> 0.000000, 0.000000, 3.567889, 1.351210, 6.755381, 2.03…
    +$ HSPC_212        <dbl> 0.000000, 0.000000, 2.570024, 0.000000, 0.000000, 0.00…
    +$ HSPC_213        <dbl> 0.000000, 1.935211, 1.935211, 0.000000, 1.270332, 1.27…
    +$ HSPC_214        <dbl> 1.4766124, 0.0000000, 1.8775155, 0.0000000, 1.4766124,…
    +$ HSPC_215        <dbl> 0.000000, 0.000000, 3.551326, 0.000000, 2.403099, 6.60…
    +$ HSPC_216        <dbl> 0.0000000, 1.3146495, 0.8021597, 0.8021597, 6.2917837,…
    +$ HSPC_218        <dbl> 0.000000, 2.567330, 3.440186, 0.000000, 3.980149, 0.00…
    +$ HSPC_219        <dbl> 0.000000, 1.620715, 2.040160, 0.000000, 2.364726, 0.00…
    +$ HSPC_220        <dbl> 0.000000, 0.000000, 4.645420, 0.000000, 6.439808, 0.00…
    +$ HSPC_221        <dbl> 0.000000, 1.932925, 3.617433, 1.268520, 8.054842, 1.26…
    +$ HSPC_222        <dbl> 0.000000, 2.630291, 3.270905, 0.000000, 2.157369, 1.44…
    +$ HSPC_223        <dbl> 0.000000, 3.195293, 3.195293, 0.000000, 3.195293, 0.00…
    +$ HSPC_224        <dbl> 0.000000, 0.000000, 3.235910, 0.000000, 2.381448, 3.23…
    +$ HSPC_225        <dbl> 0.000000, 1.892444, 0.000000, 0.000000, 0.000000, 1.89…
    +$ HSPC_227        <dbl> 0.000000, 0.000000, 2.269803, 0.000000, 1.541657, 0.00…
    +$ HSPC_228        <dbl> 0.000000, 0.000000, 2.193480, 0.000000, 2.193480, 3.02…
    +$ HSPC_229        <dbl> 0.000000, 2.483864, 4.276180, 0.000000, 3.348781, 0.00…
    +$ HSPC_230        <dbl> 0.000000, 0.000000, 2.376256, 0.000000, 9.125464, 6.25…
    +$ HSPC_231        <dbl> 0.000000, 2.442191, 3.838346, 0.000000, 10.045009, 2.4…
    +$ HSPC_232        <dbl> 0.000000, 1.868824, 3.834078, 0.000000, 4.080153, 0.00…
    +$ HSPC_233        <dbl> 0.000000, 0.000000, 3.219022, 0.000000, 3.219022, 0.00…
    +$ HSPC_235        <dbl> 0.000000, 0.000000, 6.066406, 0.000000, 3.382760, 0.00…
    +$ HSPC_236        <dbl> 0.000000, 0.000000, 3.747550, 0.000000, 5.733689, 3.08…
    +$ HSPC_237        <dbl> 0.000000, 2.058995, 2.058995, 0.000000, 2.874584, 2.05…
    +$ HSPC_239        <dbl> 0.000000, 2.206777, 3.951001, 0.000000, 3.951001, 0.00…
    +$ HSPC_240        <dbl> 0.0000000, 0.0000000, 1.8347816, 0.0000000, 1.4390643,…
    +$ HSPC_243        <dbl> 0.000000, 1.118272, 0.000000, 0.000000, 1.740598, 0.00…
    +$ HSPC_244        <dbl> 0.7871557, 0.7871557, 0.7871557, 0.0000000, 8.1826024,…
    +$ HSPC_245        <dbl> 0.000000, 1.459488, 0.000000, 0.000000, 1.459488, 0.00…
    +$ HSPC_246        <dbl> 0.000000, 0.000000, 1.629406, 0.000000, 0.000000, 0.00…
    +$ HSPC_247        <dbl> 0.000000, 0.000000, 4.129612, 0.000000, 6.233964, 3.74…
    +$ HSPC_248        <dbl> 0.000000, 0.000000, 3.844645, 0.000000, 0.000000, 1.69…
    +$ HSPC_249        <dbl> 0.000000, 0.000000, 1.595836, 0.000000, 1.595836, 2.33…
    +$ HSPC_250        <dbl> 0.000000, 1.277977, 3.022356, 0.000000, 4.572877, 7.32…
    +$ HSPC_251        <dbl> 0.0000000, 0.0000000, 2.2758529, 0.0000000, 1.9568480,…
    +$ HSPC_253        <dbl> 0.000000, 0.000000, 1.265413, 0.000000, 8.470854, 0.00…
    +$ HSPC_254        <dbl> 0.000000, 2.017054, 2.826829, 2.017054, 5.231539, 0.00…
    +$ HSPC_255        <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 1.8624297,…
    +$ HSPC_256        <dbl> 0.824835, 1.346341, 9.308939, 0.000000, 1.346341, 0.82…
    +$ HSPC_257        <dbl> 0.000000, 0.000000, 1.897882, 0.000000, 6.591455, 0.00…
    +$ HSPC_258        <dbl> 0.0000000, 0.8526372, 0.0000000, 0.0000000, 7.0828772,…
    +$ HSPC_261        <dbl> 0.0000000, 0.9300646, 0.9300646, 0.0000000, 1.4909411,…
    +$ HSPC_263        <dbl> 1.537503, 0.000000, 1.537503, 0.000000, 0.000000, 2.26…
    +$ HSPC_264        <dbl> 0.000000, 1.425741, 1.425741, 0.000000, 0.000000, 8.70…
    +$ HSPC_265        <dbl> 0.000000, 2.672373, 4.308280, 0.000000, 3.554532, 7.62…
    +$ HSPC_266        <dbl> 0.000000, 0.000000, 3.498974, 0.000000, 8.164818, 2.62…
    +$ HSPC_267        <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 1.9510360,…
    +$ HSPC_268        <dbl> 0.0000000, 0.7786889, 3.0278105, 0.0000000, 1.9494543,…
    +$ HSPC_269        <dbl> 0.0000000, 0.0000000, 1.9511222, 0.0000000, 2.5642396,…
    +$ HSPC_270        <dbl> 0.0000000, 0.0000000, 2.2633366, 0.0000000, 6.3366603,…
    +$ HSPC_271        <dbl> 1.351781, 1.351781, 4.404598, 1.351781, 2.037221, 6.96…
    +$ HSPC_274        <dbl> 0.000000, 0.000000, 2.990962, 0.000000, 9.428474, 8.26…
    +$ HSPC_275        <dbl> 0.5251597, 6.3066729, 1.8617796, 0.0000000, 6.2986480,…
    +$ HSPC_276        <dbl> 0.000000, 1.155802, 2.836006, 0.000000, 0.000000, 8.56…
    +$ HSPC_278        <dbl> 0.000000, 1.185387, 2.881903, 0.000000, 2.269850, 3.64…
    +$ HSPC_279        <dbl> 3.563514, 1.487393, 2.204027, 0.000000, 7.109467, 1.48…
    +$ HSPC_280        <dbl> 0.000000, 0.000000, 2.837358, 0.000000, 3.939531, 0.00…
    +$ HSPC_281        <dbl> 3.488013, 0.000000, 3.488013, 0.000000, 3.488013, 0.00…
    +$ HSPC_282        <dbl> 0.0000000, 1.1722813, 2.0476063, 0.0000000, 1.1722813,…
    +$ HSPC_283        <dbl> 0.000000, 3.590649, 4.529495, 1.911441, 1.911441, 0.00…
    +$ HSPC_285        <dbl> 0.0000000, 0.0000000, 3.0705949, 0.0000000, 8.1491892,…
    +$ HSPC_286        <dbl> 0.000000, 0.000000, 2.259352, 0.000000, 2.259352, 0.00…
    +$ HSPC_287        <dbl> 0.000000, 1.048672, 3.408389, 1.649500, 1.649500, 0.00…
    +$ HSPC_288        <dbl> 0.0000000, 1.3879010, 3.0490024, 0.0000000, 8.9178718,…
    +$ HSPC_289        <dbl> 0.000000, 0.000000, 3.641902, 0.000000, 3.940529, 0.00…
    +$ HSPC_290        <dbl> 0.000000, 0.000000, 2.594545, 0.000000, 7.607623, 2.59…
    +$ HSPC_291        <dbl> 0.000000, 1.175842, 1.175842, 0.000000, 9.326333, 0.00…
    +$ HSPC_292        <dbl> 0.000000, 0.000000, 2.804302, 0.000000, 5.422785, 8.43…
    +$ HSPC_293        <dbl> 1.077036, 0.000000, 2.711161, 7.608787, 4.047517, 1.07…
    +$ HSPC_294        <dbl> 0.0000000, 0.0000000, 0.9161348, 0.0000000, 1.8723003,…
    +$ HSPC_295        <dbl> 0.0000000, 1.8799200, 3.0264680, 0.9210673, 4.2380463,…
    +$ HSPC_296        <dbl> 0.000000, 2.157001, 2.157001, 2.157001, 5.287566, 0.00…
    +$ HSPC_297        <dbl> 0.000000, 1.687785, 2.444464, 0.000000, 0.000000, 0.00…
    +$ HSPC_298        <dbl> 0.0000000, 0.7784226, 2.4036840, 0.0000000, 2.4036840,…
    +$ HSPC_299        <dbl> 0.000000, 1.099428, 1.716067, 0.000000, 8.068194, 2.74…
    +$ HSPC_300        <dbl> 0.0000000, 0.0000000, 2.0342975, 0.0000000, 2.0342975,…
    +$ HSPC_301        <dbl> 0.000000, 3.073359, 6.232145, 0.000000, 4.938720, 0.00…
    +$ HSPC_302        <dbl> 3.078836, 0.000000, 4.545226, 0.000000, 3.078836, 3.07…
    +$ HSPC_303        <dbl> 0.000000, 0.000000, 3.009431, 0.000000, 7.544693, 0.00…
    +$ HSPC_304        <dbl> 0.0000000, 1.5484583, 2.7602490, 0.0000000, 5.4055991,…
    +$ HSPC_305        <dbl> 0.000000, 0.000000, 2.558256, 0.000000, 4.669580, 1.15…
    +$ HSPC_306        <dbl> 0.000000, 0.000000, 3.185666, 0.000000, 5.689777, 3.33…
    +$ HSPC_307        <dbl> 0.000000, 1.976472, 4.777034, 0.000000, 3.293648, 2.78…
    +$ HSPC_308        <dbl> 0.000000, 0.000000, 3.975296, 6.548101, 3.526101, 0.00…
    +$ HSPC_309        <dbl> 0.000000, 1.804026, 3.455193, 0.000000, 3.083349, 1.80…
    +$ HSPC_310        <dbl> 1.743404, 0.000000, 2.510071, 0.000000, 2.510071, 1.74…
    +$ HSPC_312        <dbl> 0.0000000, 1.4203264, 1.8133978, 0.0000000, 7.5148795,…
    +$ HSPC_313        <dbl> 0.000000, 1.591589, 4.096808, 1.591589, 2.329876, 0.00…
    +$ HSPC_314        <dbl> 0.000000, 0.000000, 3.527058, 1.634863, 3.236083, 7.90…
    +$ HSPC_315        <dbl> 0.000000, 2.261631, 2.261631, 2.261631, 3.630638, 0.00…
    +$ HSPC_317        <dbl> 0.000000, 2.335038, 3.715556, 0.000000, 2.335038, 0.00…
    +$ HSPC_318        <dbl> 0.000000, 0.000000, 3.357051, 0.000000, 0.000000, 0.00…
    +$ HSPC_320        <dbl> 0.000000, 0.000000, 3.189910, 2.339927, 3.479868, 3.18…
    +$ HSPC_321        <dbl> 0.000000, 1.191188, 1.191188, 0.000000, 2.616741, 1.19…
    +$ HSPC_322        <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 1.9762562,…
    +$ HSPC_323        <dbl> 0.0000000, 0.0000000, 0.9890293, 0.0000000, 2.5666314,…
    +$ HSPC_324        <dbl> 0.000000, 1.088036, 2.728840, 0.000000, 2.728840, 0.00…
    +$ HSPC_325        <dbl> 1.428402, 1.428402, 4.810635, 0.000000, 2.131908, 0.00…
    +$ HSPC_326        <dbl> 0.000000, 0.000000, 5.321205, 0.000000, 6.303048, 0.00…
    +$ HSPC_327        <dbl> 0.0000000, 0.6422346, 2.7240929, 0.0000000, 3.1457469,…
    +$ HSPC_328        <dbl> 0.000000, 0.000000, 3.620927, 0.000000, 2.733670, 1.27…
    +$ HSPC_329        <dbl> 1.954249, 0.000000, 3.800965, 0.000000, 1.954249, 0.00…
    +$ HSPC_330        <dbl> 1.870221, 0.000000, 3.695045, 0.000000, 2.317254, 2.65…
    +$ HSPC_331        <dbl> 0.000000, 0.000000, 2.953080, 0.000000, 2.953080, 0.00…
    +$ HSPC_332        <dbl> 0.000000, 1.044806, 2.883335, 0.000000, 6.444771, 1.04…
    +$ HSPC_333        <dbl> 0.8059525, 1.3199644, 1.3199644, 0.0000000, 1.9975449,…
    +$ HSPC_334        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 1.931089, 0.00…
    +$ HSPC_335        <dbl> 0.000000, 0.000000, 2.751133, 0.000000, 7.599859, 0.00…
    +$ HSPC_336        <dbl> 0.000000, 0.000000, 1.959737, 0.000000, 0.000000, 3.27…
    +$ HSPC_337        <dbl> 0.000000, 0.000000, 5.147478, 0.000000, 4.187618, 0.00…
    +$ HSPC_338        <dbl> 0.0000000, 0.0000000, 10.1024666, 0.0000000, 7.9043216…
    +$ HSPC_339        <dbl> 0.0000000, 0.9599543, 2.5175886, 5.1304754, 7.6196067,…
    +$ HSPC_341        <dbl> 0.0000000, 0.0000000, 2.2497917, 7.5891885, 2.2497917,…
    +$ HSPC_342        <dbl> 0.0000000, 0.7849552, 1.4893359, 0.4452176, 8.7833506,…
    +$ HSPC_343        <dbl> 0.0000000, 0.7869497, 0.7869497, 0.7869497, 1.9640992,…
    +$ HSPC_344        <dbl> 0.000000, 1.425890, 1.425890, 0.000000, 8.886625, 2.59…
    +$ HSPC_345        <dbl> 0.000000, 0.000000, 2.093666, 1.397341, 0.000000, 1.39…
    +$ HSPC_346        <dbl> 0.000000, 0.000000, 1.637347, 0.000000, 1.637347, 1.03…
    +$ HSPC_348        <dbl> 0.000000, 1.733815, 2.768747, 7.794259, 2.166424, 1.73…
    +$ HSPC_349        <dbl> 0.000000, 0.000000, 3.434533, 0.000000, 2.783890, 0.00…
    +$ HSPC_350        <dbl> 0.000000, 0.000000, 4.536066, 5.820193, 0.000000, 0.00…
    +$ HSPC_351        <dbl> 0.000000, 1.910297, 2.704369, 0.000000, 7.827990, 1.91…
    +$ HSPC_352        <dbl> 0.000000, 0.000000, 1.855727, 0.000000, 0.000000, 0.00…
    +$ HSPC_353        <dbl> 0.000000, 0.000000, 0.899194, 0.000000, 0.000000, 0.89…
    +$ HSPC_354        <dbl> 0.000000, 2.331123, 4.869071, 0.000000, 7.191315, 0.00…
    +$ HSPC_356        <dbl> 0.000000, 0.000000, 4.138465, 0.000000, 1.914037, 0.00…
    +$ HSPC_358        <dbl> 0.000000, 1.322769, 3.323190, 1.322769, 3.524842, 0.00…
    +$ HSPC_359        <dbl> 0.0000000, 0.9071742, 1.8584210, 0.0000000, 8.1305324,…
    +$ HSPC_360        <dbl> 0.000000, 0.000000, 2.544055, 0.000000, 9.351724, 0.00…
    +$ HSPC_361        <dbl> 0.000000, 0.000000, 4.073667, 0.000000, 9.554073, 2.05…
    +$ HSPC_362        <dbl> 0.000000, 0.000000, 7.448528, 0.000000, 4.768353, 0.00…
    +$ HSPC_363        <dbl> 0.000000, 0.000000, 2.749745, 8.987973, 7.432788, 7.45…
    +$ HSPC_365        <dbl> 0.000000, 0.000000, 4.965616, 2.594802, 9.358295, 8.09…
    +$ HSPC_367        <dbl> 0.000000, 2.528168, 4.327223, 0.000000, 6.909409, 5.10…
    +$ HSPC_368        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 8.951178, 0.00…
    +$ HSPC_370        <dbl> 0.000000, 0.000000, 1.307598, 0.000000, 0.797134, 0.00…
    +$ HSPC_371        <dbl> 0.000000, 1.257081, 1.257081, 0.000000, 1.257081, 1.25…
    +$ HSPC_372        <dbl> 0.000000, 0.000000, 2.221252, 0.000000, 8.278550, 0.00…
    +$ HSPC_373        <dbl> 0.000000, 0.000000, 4.730281, 2.884763, 3.783634, 6.93…
    +$ HSPC_374        <dbl> 0.000000, 0.000000, 2.862633, 0.000000, 10.146380, 7.7…
    +$ HSPC_376        <dbl> 0.000000, 0.000000, 3.171475, 8.276931, 2.537496, 0.00…
    +$ HSPC_377        <dbl> 0.000000, 0.000000, 3.297929, 0.000000, 8.087149, 1.30…
    +$ HSPC_380        <dbl> 1.219391, 0.000000, 2.934029, 1.219391, 3.165253, 1.21…
    +$ HSPC_382        <dbl> 0.0000000, 0.0000000, 1.5486445, 0.0000000, 9.8626042,…
    +$ HSPC_383        <dbl> 0.000000, 0.000000, 3.684053, 0.000000, 2.521370, 1.75…
    +$ HSPC_386        <dbl> 0.000000, 1.412425, 2.934964, 3.837412, 2.112261, 4.60…
    +$ HSPC_387        <dbl> 0.000000, 0.000000, 2.464120, 0.000000, 2.004298, 2.00…
    +$ HSPC_388        <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 7.0965225,…
    +$ HSPC_389        <dbl> 0.000000, 0.000000, 8.902540, 0.000000, 1.263307, 0.00…
    +$ HSPC_390        <dbl> 0.000000, 1.531571, 3.386125, 7.733304, 3.625976, 0.00…
    +$ HSPC_391        <dbl> 0.000000, 1.423235, 2.125560, 0.000000, 2.125560, 0.00…
    +$ HSPC_392        <dbl> 1.166291, 0.000000, 2.242760, 0.000000, 0.000000, 1.16…
    +$ HSPC_393        <dbl> 0.000000, 1.110847, 8.026679, 0.000000, 7.310363, 1.11…
    +$ HSPC_395        <dbl> 0.000000, 0.000000, 1.923747, 0.000000, 1.923747, 1.26…
    +$ HSPC_396        <dbl> 0.0000000, 0.9279096, 2.8713748, 0.0000000, 8.4108606,…
    +$ HSPC_398        <dbl> 0.000000, 1.052478, 2.405000, 0.000000, 1.654517, 7.24…
    +$ HSPC_399        <dbl> 0.000000, 0.000000, 1.198818, 0.000000, 9.267652, 0.00…
    +$ HSPC_400        <dbl> 0.000000, 0.000000, 2.368347, 0.000000, 1.255700, 0.00…
    +$ HSPC_402        <dbl> 0.000000, 0.000000, 2.004052, 0.000000, 8.950833, 8.75…
    +$ HSPC_403        <dbl> 0.000000, 0.000000, 2.797093, 0.000000, 0.000000, 0.00…
    +$ HSPC_404        <dbl> 0.0000000, 0.0000000, 3.7817437, 0.0000000, 4.2260011,…
    +$ HSPC_405        <dbl> 0.000000, 1.099247, 1.715831, 0.000000, 1.099247, 5.31…
    +$ HSPC_406        <dbl> 0.000000, 0.000000, 2.135083, 1.430987, 3.245124, 0.00…
    +$ HSPC_407        <dbl> 0.0000000, 0.5650490, 1.5448568, 0.0000000, 3.8016573,…
    +$ HSPC_408        <dbl> 0.0000000, 1.5700909, 10.4839578, 0.0000000, 8.0221142…
    +$ HSPC_409        <dbl> 0.000000, 0.000000, 3.044399, 0.000000, 3.044399, 0.00…
    +$ HSPC_410        <dbl> 0.904751, 0.000000, 1.854660, 0.000000, 5.165464, 0.00…
    +$ HSPC_411        <dbl> 0.0000000, 0.0000000, 0.9059253, 0.0000000, 7.5067273,…
    +$ HSPC_412        <dbl> 0.0000000, 0.0000000, 0.6614079, 8.5121379, 7.3252186,…
    +$ HSPC_413        <dbl> 0.000000, 1.169683, 1.807043, 1.169683, 9.674198, 0.00…
    +$ HSPC_415        <dbl> 0.000000, 0.000000, 5.273790, 0.000000, 3.093809, 0.00…
    +$ HSPC_416        <dbl> 0.000000, 1.337731, 3.110643, 0.000000, 0.000000, 0.00…
    +$ HSPC_417        <dbl> 0.0000000, 0.7221578, 1.5601978, 0.0000000, 1.2011916,…
    +$ HSPC_418        <dbl> 0.000000, 0.000000, 2.348200, 0.000000, 1.241207, 0.00…
    +$ HSPC_419        <dbl> 0.000000, 0.000000, 1.158302, 0.692403, 0.000000, 0.69…
    +$ HSPC_420        <dbl> 0.0000000, 0.7442525, 1.5970870, 0.0000000, 1.5970870,…
    +$ HSPC_421        <dbl> 0.000000, 0.000000, 3.682417, 0.000000, 1.985374, 0.00…
    +$ HSPC_422        <dbl> 0.000000, 0.000000, 1.630076, 1.033967, 1.630076, 7.51…
    +$ HSPC_423        <dbl> 0.0000000, 0.0000000, 1.4797402, 0.0000000, 1.1326799,…
    +$ HSPC_424        <dbl> 0.000000, 1.267474, 2.728919, 0.000000, 3.439860, 0.00…
    +$ HSPC_425        <dbl> 0.000000, 0.000000, 1.016015, 0.000000, 6.474436, 0.00…
    +$ HSPC_426        <dbl> 0.000000, 0.000000, 3.133563, 0.000000, 0.000000, 1.55…
    +$ HSPC_427        <dbl> 0.000000, 2.152076, 4.835791, 0.000000, 7.220338, 0.00…
    +$ HSPC_431        <dbl> 0.000000, 2.150174, 3.639547, 1.101833, 5.618926, 2.97…
    +$ HSPC_432        <dbl> 0.000000, 0.000000, 1.949682, 0.000000, 3.261333, 4.18…
    +$ HSPC_435        <dbl> 0.000000, 1.097512, 2.970692, 0.000000, 7.647274, 6.35…
    +$ HSPC_436        <dbl> 0.0000000, 0.0000000, 1.1114827, 0.0000000, 5.7023734,…
    +$ HSPC_440        <dbl> 0.000000, 1.385247, 1.385247, 0.000000, 2.545103, 5.12…
    +$ HSPC_441        <dbl> 0.000000, 0.000000, 1.696075, 1.084126, 8.589432, 1.08…
    +$ HSPC_442        <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 3.6713853,…
    +$ HSPC_443        <dbl> 0.000000, 1.546895, 2.276125, 0.000000, 2.276125, 1.54…
    +$ HSPC_444        <dbl> 1.374089, 0.000000, 0.000000, 0.000000, 1.374089, 0.00…
    +$ HSPC_446        <dbl> 0.000000, 2.439029, 1.683195, 0.000000, 1.683195, 1.68…
    +$ HSPC_447        <dbl> 0.000000, 1.113089, 1.113089, 0.000000, 2.166474, 7.12…
    +$ HSPC_448        <dbl> 0.000000, 1.139444, 0.000000, 0.000000, 9.257634, 0.00…
    +$ HSPC_449        <dbl> 0.000000, 1.344056, 2.489522, 0.000000, 5.057946, 2.02…
    +$ HSPC_450        <dbl> 0.000000, 0.000000, 2.979455, 0.000000, 5.551901, 0.00…
    +$ HSPC_451        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 9.322231, 1.75…
    +$ HSPC_453        <dbl> 0.0000000, 0.0000000, 1.4937200, 0.0000000, 2.4699783,…
    +$ HSPC_454        <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 9.1805553,…
    +$ HSPC_455        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 7.204120, 0.00…
    +$ HSPC_456        <dbl> 0.0000000, 0.0000000, 1.4363752, 0.0000000, 7.5943576,…
    +$ HSPC_457        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 4.535876, 7.75…
    +$ HSPC_459        <dbl> 0.000000, 1.282562, 1.282562, 1.282562, 9.214660, 1.95…
    +$ HSPC_460        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.601133, 0.00…
    +$ HSPC_461        <dbl> 0.000000, 0.000000, 0.000000, 7.294303, 7.224373, 0.00…
    +$ HSPC_462        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 5.732804, 0.00…
    +$ HSPC_463        <dbl> 0.000000, 0.000000, 1.566104, 0.725680, 0.000000, 0.00…
    +$ HSPC_465        <dbl> 0.000000, 4.053991, 0.000000, 3.894882, 2.159925, 0.00…
    +$ HSPC_466        <dbl> 0.000000, 1.163197, 0.000000, 0.000000, 3.274518, 0.00…
    +$ HSPC_467        <dbl> 0.000000, 1.176891, 1.176891, 1.176891, 8.628113, 2.25…
    +$ HSPC_468        <dbl> 0.000000, 1.297938, 1.297938, 0.000000, 10.108305, 0.0…
    +$ HSPC_470        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 3.23…
    +$ HSPC_471        <dbl> 0.000000, 0.000000, 1.535633, 0.000000, 5.948904, 0.00…
    +$ HSPC_472        <dbl> 0.0000000, 0.0000000, 0.0000000, 3.3032627, 0.9896601,…
    +$ HSPC_473        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 6.756343, 6.88…
    +$ HSPC_474        <dbl> 1.040938, 1.040938, 0.000000, 0.000000, 2.386883, 0.00…
    +$ HSPC_475        <dbl> 7.447608, 0.000000, 3.318667, 0.000000, 3.318667, 1.99…
    +$ HSPC_477        <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 1.3981912,…
    +$ HSPC_478        <dbl> 0.000000, 0.000000, 4.083810, 0.000000, 2.884169, 0.00…
    +$ HSPC_479        <dbl> 0.000000, 0.000000, 3.027550, 0.000000, 8.194229, 1.94…
    +$ HSPC_480        <dbl> 0.000000, 1.034469, 3.059791, 0.000000, 2.376690, 1.03…
    +$ HSPC_482        <dbl> 6.620967, 0.000000, 0.000000, 0.000000, 0.000000, 0.00…
    +$ HSPC_483        <dbl> 0.000000, 0.000000, 3.006419, 0.000000, 8.010120, 2.17…
    +$ HSPC_485        <dbl> 0.0000000, 1.0279164, 0.6036333, 0.6036333, 0.6036333,…
    +$ HSPC_486        <dbl> 0.000000, 0.000000, 1.410572, 0.000000, 1.410572, 5.75…
    +$ HSPC_488        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 9.802316, 0.00…
    +$ HSPC_489        <dbl> 0.000000, 1.882197, 0.000000, 0.000000, 0.000000, 0.00…
    +$ HSPC_490        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.790270, 1.30…
    +$ HSPC_491        <dbl> 0.000000, 1.469639, 0.000000, 4.081147, 8.733647, 0.00…
    +$ HSPC_492        <dbl> 1.163132, 0.000000, 0.000000, 0.000000, 9.050494, 0.00…
    +$ HSPC_493        <dbl> 0.000000, 0.000000, 2.223299, 0.000000, 3.586020, 4.73…
    +$ HSPC_494        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 3.680132, 8.44…
    +$ HSPC_495        <dbl> 0.000000, 2.419005, 0.000000, 0.000000, 5.543935, 2.41…
    +$ HSPC_496        <dbl> 0.000000, 0.000000, 0.000000, 1.788287, 1.788287, 10.6…
    +$ HSPC_497        <dbl> 0.000000, 0.000000, 1.945149, 0.000000, 1.945149, 1.94…
    +$ HSPC_498        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 7.967779, 0.00…
    +$ HSPC_499        <dbl> 0.000000, 0.000000, 1.614671, 0.000000, 8.977937, 0.00…
    +$ HSPC_500        <dbl> 0.000000, 1.779610, 1.779610, 0.000000, 7.269594, 2.55…
    +$ HSPC_501        <dbl> 0.000000, 2.304226, 0.000000, 0.000000, 2.304226, 0.00…
    +$ HSPC_502        <dbl> 0.0000000, 0.0000000, 1.4698900, 0.0000000, 7.2171885,…
    +$ HSPC_503        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 7.932863, 8.79…
    +$ HSPC_504        <dbl> 0.000000, 0.000000, 2.201356, 0.000000, 9.317511, 2.20…
    +$ HSPC_505        <dbl> 0.000000, 0.000000, 2.180019, 0.000000, 2.180019, 0.00…
    +$ HSPC_506        <dbl> 0.000000, 0.000000, 1.878328, 0.000000, 2.667432, 0.00…
    +$ HSPC_507        <dbl> 0.000000, 1.878372, 2.667483, 0.000000, 3.549225, 1.87…
    +$ HSPC_508        <dbl> 0.0000000, 0.2296644, 0.2296644, 0.2296644, 4.6628473,…
    +$ HSPC_509        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.942680, 7.82…
    +$ HSPC_510        <dbl> 0.000000, 1.166340, 1.802743, 6.721521, 1.166340, 6.59…
    +$ HSPC_512        <dbl> 0.000000, 0.000000, 1.738345, 0.000000, 0.000000, 1.11…
    +$ HSPC_514        <dbl> 1.237955, 0.000000, 2.962215, 0.000000, 8.674516, 0.00…
    +$ HSPC_515        <dbl> 1.108707, 1.108707, 1.108707, 0.000000, 1.108707, 8.57…
    +$ HSPC_516        <dbl> 0.0000000, 0.0000000, 1.4299322, 0.0000000, 9.6466954,…
    +$ HSPC_518        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.617584, 0.00…
    +$ HSPC_520        <dbl> 0.000000, 0.000000, 1.644413, 0.000000, 8.591871, 0.00…
    +$ HSPC_521        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 9.290520, 0.00…
    +$ HSPC_522        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.182446, 0.00…
    +$ HSPC_523        <dbl> 0.0000000, 0.0000000, 0.7295826, 9.9573376, 1.8610172,…
    +$ HSPC_524        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 3.266931, 0.00…
    +$ HSPC_526        <dbl> 1.301071, 1.301071, 0.000000, 0.000000, 1.301071, 0.00…
    +$ HSPC_527        <dbl> 0.0000000, 0.0000000, 0.0000000, 1.2793196, 7.6901603,…
    +$ HSPC_528        <dbl> 0.000000, 0.000000, 1.669689, 7.592221, 2.423018, 0.00…
    +$ HSPC_530        <dbl> 1.746336, 0.000000, 0.000000, 0.000000, 8.986799, 1.74…
    +$ HSPC_532        <dbl> 0.000000, 0.000000, 0.000000, 1.176792, 10.454235, 0.0…
    +$ HSPC_533        <dbl> 0.0000000, 0.0000000, 0.7536668, 0.0000000, 1.9046925,…
    +$ HSPC_534        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.227399, 0.00…
    +$ HSPC_535        <dbl> 0.000000, 0.000000, 3.918443, 0.000000, 8.372526, 0.00…
    +$ HSPC_537        <dbl> 0.000000, 0.000000, 1.665647, 1.665647, 6.776472, 2.91…
    +$ HSPC_538        <dbl> 0.000000, 0.000000, 2.242435, 0.000000, 2.851982, 8.64…
    +$ HSPC_539        <dbl> 0.000000, 3.354010, 1.725182, 7.588085, 7.535255, 0.00…
    +$ HSPC_540        <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 1.9846071,…
    +$ HSPC_541        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 10.016742, 0.0…
    +$ HSPC_543        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 8.753904, 7.96…
    +$ HSPC_544        <dbl> 0.0000000, 0.0000000, 0.8221823, 0.0000000, 7.1295118,…
    +$ HSPC_545        <dbl> 0.000000, 0.000000, 0.000000, 1.484735, 3.764537, 2.20…
    +$ HSPC_546        <dbl> 0.000000, 2.211853, 3.047085, 0.000000, 0.000000, 0.00…
    +$ HSPC_547        <dbl> 0.000000, 0.000000, 0.000000, 0.654750, 9.253559, 0.65…
    +$ HSPC_548        <dbl> 0.000000, 0.000000, 2.165553, 1.455855, 1.455855, 0.00…
    +$ HSPC_549        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 1.557210, 1.55…
    +$ HSPC_550        <dbl> 1.750214, 0.000000, 1.750214, 0.000000, 3.680372, 0.00…
    +$ HSPC_551        <dbl> 0.000000, 0.000000, 1.287115, 0.000000, 5.908242, 8.49…
    +$ HSPC_552        <dbl> 0.000000, 0.000000, 1.226425, 0.000000, 4.650625, 8.64…
    +$ HSPC_553        <dbl> 0.0000000, 0.4708726, 0.4708726, 0.0000000, 7.2724626,…
    +$ HSPC_554        <dbl> 1.449277, 1.449277, 1.449277, 0.000000, 1.449277, 9.03…
    +$ HSPC_555        <dbl> 0.000000, 0.000000, 1.802172, 0.000000, 0.000000, 0.00…
    +$ HSPC_556        <dbl> 0.0000000, 0.0000000, 0.9369457, 0.0000000, 0.9369457,…
    +$ HSPC_557        <dbl> 1.141542, 0.000000, 1.141542, 0.000000, 1.770759, 0.00…
    +$ HSPC_559        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.411402, 0.00…
    +$ HSPC_560        <dbl> 0.000000, 2.929589, 1.680915, 0.000000, 6.116774, 6.74…
    +$ HSPC_562        <dbl> 0.000000, 0.000000, 2.717569, 0.000000, 0.000000, 8.61…
    +$ HSPC_563        <dbl> 0.000000, 1.199800, 1.845653, 0.000000, 1.845653, 0.00…
    +$ HSPC_566        <dbl> 0.000000, 0.000000, 2.959197, 0.000000, 2.959197, 2.13…
    +$ HSPC_567        <dbl> 0.000000, 0.000000, 1.812523, 0.000000, 1.812523, 6.68…
    +$ HSPC_568        <dbl> 0.000000, 0.000000, 2.956854, 0.000000, 2.131637, 2.95…
    +$ HSPC_569        <dbl> 0.0000000, 1.2707229, 0.7709662, 0.0000000, 1.2707229,…
    +$ HSPC_571        <dbl> 0.000000, 1.041987, 1.041987, 0.000000, 1.041987, 1.64…
    +$ HSPC_573        <dbl> 0.000000, 0.000000, 1.461676, 0.000000, 3.288566, 0.00…
    +$ HSPC_574        <dbl> 0.0000000, 0.7547277, 1.9066029, 0.0000000, 5.9897178,…
    +$ HSPC_575        <dbl> 0.000000, 1.183227, 2.604870, 4.577438, 2.878570, 1.18…
    +$ HSPC_576        <dbl> 0.000000, 0.000000, 2.741129, 0.000000, 10.233110, 6.7…
    +$ HSPC_577        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.834036, 1.60…
    +$ HSPC_578        <dbl> 0.000000, 0.000000, 1.404000, 7.371858, 2.101881, 1.40…
    +$ HSPC_579        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 7.491585, 1.82…
    +$ HSPC_580        <dbl> 0.000000, 0.000000, 1.510090, 0.000000, 1.510090, 0.00…
    +$ HSPC_582        <dbl> 4.342803, 9.749104, 0.000000, 0.000000, 5.826065, 1.65…
    +$ HSPC_584        <dbl> 0.000000, 0.000000, 2.565813, 0.000000, 3.733595, 7.76…
    +$ HSPC_585        <dbl> 0.000000, 0.000000, 1.449121, 0.000000, 1.449121, 5.35…
    +$ HSPC_586        <dbl> 0.0000000, 0.8914714, 1.4383643, 0.0000000, 1.8339836,…
    +$ HSPC_589        <dbl> 0.000000, 1.963326, 2.765365, 0.000000, 7.352066, 0.00…
    +$ HSPC_590        <dbl> 0.000000, 0.000000, 1.835966, 1.192227, 1.192227, 6.95…
    +$ HSPC_592        <dbl> 0.000000, 0.000000, 0.000000, 5.165700, 1.227806, 0.00…
    +$ HSPC_593        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 3.554248, 0.00…
    +$ HSPC_594        <dbl> 1.950098, 0.000000, 1.950098, 0.000000, 4.395615, 5.71…
    +$ HSPC_595        <dbl> 1.756544, 0.000000, 1.756544, 0.000000, 2.796431, 3.54…
    +$ HSPC_596        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.086691, 7.95…
    +$ HSPC_597        <dbl> 0.000000, 0.000000, 1.563392, 0.000000, 0.000000, 2.29…
    +$ HSPC_598        <dbl> 0.000000, 0.000000, 1.220673, 1.220673, 0.000000, 1.22…
    +$ HSPC_599        <dbl> 0.000000, 1.349651, 2.034571, 0.000000, 1.349651, 0.00…
    +$ HSPC_600        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 4.377207, 0.00…
    +$ HSPC_601        <dbl> 0.000000, 0.000000, 2.865429, 0.000000, 2.376203, 1.63…
    +$ HSPC_602        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 3.806407, 2.41…
    +$ HSPC_603        <dbl> 0.000000, 2.004660, 1.589106, 0.000000, 9.490018, 0.00…
    +$ HSPC_604        <dbl> 1.748474, 0.000000, 2.516030, 0.000000, 1.748474, 0.00…
    +$ HSPC_606        <dbl> 0.000000, 0.000000, 1.075087, 0.000000, 2.111214, 0.00…
    +$ HSPC_607        <dbl> 0.000000, 0.000000, 3.717957, 0.000000, 9.191362, 0.00…
    +$ HSPC_608        <dbl> 0.000000, 1.574605, 1.574605, 0.000000, 3.156098, 1.57…
    +$ HSPC_610        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.00…
    +$ HSPC_612        <dbl> 0.000000, 1.356545, 2.043143, 0.000000, 6.275658, 0.00…
    +$ HSPC_613        <dbl> 0.000000, 0.000000, 1.438703, 6.081511, 2.144549, 6.95…
    +$ HSPC_614        <dbl> 0.000000, 1.315161, 3.077500, 0.000000, 4.543775, 1.31…
    +$ HSPC_615        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.450652, 0.00…
    +$ HSPC_617        <dbl> 0.0000000, 1.3847809, 2.3300729, 0.0000000, 0.8525275,…
    +$ HSPC_618        <dbl> 0.000000, 0.000000, 3.542103, 0.000000, 2.885428, 2.39…
    +$ HSPC_620        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.517983, 0.00…
    +$ HSPC_623        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 8.705469, 1.70…
    +$ HSPC_624        <dbl> 0.0000000, 0.7200995, 0.0000000, 0.0000000, 8.9490659,…
    +$ HSPC_625        <dbl> 0.000000, 0.000000, 0.000000, 3.458561, 8.847668, 2.93…
    +$ HSPC_626        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 3.424363, 0.00…
    +$ HSPC_627        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 8.000538, 6.99…
    +$ HSPC_628        <dbl> 0.000000, 1.638219, 0.000000, 0.000000, 1.638219, 0.00…
    +$ HSPC_629        <dbl> 1.196665, 0.000000, 0.000000, 0.000000, 1.841645, 0.00…
    +$ HSPC_630        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.098177, 2.09…
    +$ HSPC_631        <dbl> 0.000000, 1.893172, 1.237108, 0.000000, 9.108643, 1.23…
    +$ HSPC_633        <dbl> 0.000000, 0.000000, 2.731996, 0.000000, 2.731996, 0.00…
    +$ HSPC_634        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 8.501517, 0.00…
    +$ HSPC_635        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.892953, 0.00…
    +$ HSPC_636        <dbl> 0.000000, 1.087599, 1.700617, 1.087599, 6.627788, 0.00…
    +$ HSPC_637        <dbl> 0.0000000, 0.9389313, 2.4816963, 0.0000000, 7.3021856,…
    +$ HSPC_638        <dbl> 0.0000000, 0.0000000, 1.1842890, 0.0000000, 2.5023010,…
    +$ HSPC_639        <dbl> 0.996580, 1.994867, 2.579258, 0.000000, 2.316452, 0.99…
    +$ HSPC_640        <dbl> 0.000000, 1.025432, 2.362406, 0.000000, 2.627103, 1.02…
    +$ HSPC_641        <dbl> 0.000000, 0.000000, 2.000512, 0.000000, 2.000512, 1.00…
    +$ HSPC_643        <dbl> 0.000000, 2.465561, 1.705628, 0.000000, 9.092947, 1.70…
    +$ HSPC_644        <dbl> 0.0000000, 0.4904320, 0.8557752, 0.0000000, 6.1750519,…
    +$ HSPC_645        <dbl> 0.0000000, 0.0000000, 0.7156666, 0.0000000, 2.0742346,…
    +$ HSPC_646        <dbl> 0.0000000, 0.0000000, 0.0000000, 0.9959057, 9.3159931,…
    +$ HSPC_648        <dbl> 0.000000, 2.242718, 0.000000, 0.000000, 3.081640, 1.51…
    +$ HSPC_649        <dbl> 0.0000000, 0.7139349, 0.7139349, 0.0000000, 0.7139349,…
    +$ HSPC_651        <dbl> 0.000000, 2.253619, 7.476806, 0.000000, 6.023902, 2.73…
    +$ HSPC_652        <dbl> 1.352094, 0.000000, 2.500412, 0.000000, 2.037610, 0.00…
    +$ HSPC_654        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 9.886385, 7.53…
    +$ HSPC_656        <dbl> 0.000000, 1.355844, 1.355844, 0.000000, 0.000000, 0.00…
    +$ HSPC_657        <dbl> 0.000000, 2.238724, 3.077173, 0.000000, 6.951322, 3.07…
    +$ HSPC_658        <dbl> 0.000000, 0.000000, 2.796922, 3.846645, 8.942041, 0.00…
    +$ HSPC_660        <dbl> 0.000000, 1.253314, 1.253314, 0.000000, 7.108572, 1.25…
    +$ HSPC_661        <dbl> 0.000000, 1.491329, 3.043680, 1.491329, 9.643608, 0.00…
    +$ HSPC_662        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 1.688146, 4.39…
    +$ HSPC_663        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 6.57…
    +$ HSPC_664        <dbl> 0.0000000, 1.5053124, 0.9406784, 0.0000000, 1.5053124,…
    +$ HSPC_665        <dbl> 0.000000, 1.290390, 1.290390, 0.000000, 6.107672, 1.29…
    +$ HSPC_666        <dbl> 0.000000, 1.130141, 0.000000, 7.631839, 8.362422, 6.31…
    +$ HSPC_667        <dbl> 0.000000, 0.000000, 1.776997, 0.000000, 6.465588, 1.77…
    +$ HSPC_668        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 9.302290, 0.00…
    +$ HSPC_669        <dbl> 0.000000, 0.000000, 2.425594, 0.000000, 1.671860, 0.00…
    +$ HSPC_670        <dbl> 0.000000, 2.337848, 3.718794, 0.000000, 0.000000, 2.33…
    +$ HSPC_671        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.158776, 0.00…
    +$ HSPC_672        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 1.038159, 0.00…
    +$ HSPC_673        <dbl> 0.000000, 1.519487, 1.519487, 0.000000, 8.786551, 5.68…
    +$ HSPC_674        <dbl> 0.000000, 1.235988, 0.000000, 0.000000, 1.891750, 1.89…
    +$ HSPC_676        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 4.975163, 1.74…
    +$ HSPC_678        <dbl> 0.000000, 2.249420, 1.524795, 0.000000, 3.089130, 0.00…
    +$ HSPC_679        <dbl> 2.256522, 2.256522, 0.000000, 1.530665, 2.737162, 1.53…
    +$ HSPC_680        <dbl> 0.000000, 2.323337, 0.000000, 5.359270, 8.465280, 0.00…
    +$ HSPC_681        <dbl> 0.0000000, 1.6627807, 0.0000000, 0.0000000, 1.9591579,…
    +$ HSPC_682        <dbl> 0.000000, 1.043463, 0.000000, 7.477477, 2.064713, 1.04…
    +$ HSPC_683        <dbl> 0.000000, 0.000000, 2.261955, 0.000000, 3.631015, 0.00…
    +$ HSPC_687        <dbl> 0.000000, 0.000000, 3.811941, 9.810273, 3.430744, 2.09…
    +$ HSPC_689        <dbl> 0.000000, 0.000000, 0.000000, 2.085635, 10.065718, 2.0…
    +$ HSPC_690        <dbl> 2.196289, 2.196289, 3.029625, 0.000000, 6.808290, 7.65…
    +$ HSPC_692        <dbl> 2.555176, 0.000000, 4.919547, 0.000000, 5.637318, 2.55…
    +$ HSPC_695        <dbl> 0.0000000, 0.2681148, 1.3971816, 0.2681148, 10.7977224…
    +$ HSPC_696        <dbl> 0.000000, 2.265383, 4.020705, 0.000000, 8.976227, 0.00…
    +$ HSPC_697        <dbl> 0.000000, 1.271303, 3.012385, 0.000000, 0.000000, 7.59…
    +$ HSPC_698        <dbl> 0.000000, 0.000000, 4.694712, 0.000000, 0.000000, 0.00…
    +$ HSPC_699        <dbl> 0.000000, 0.000000, 2.930008, 0.000000, 0.000000, 0.00…
    +$ HSPC_700        <dbl> 0.000000, 0.000000, 1.083768, 0.000000, 1.695606, 0.00…
    +$ HSPC_701        <dbl> 0.000000, 1.156584, 3.066217, 1.156584, 5.095538, 1.79…
    +$ HSPC_702        <dbl> 0.000000, 0.000000, 3.185800, 0.000000, 2.336223, 2.33…
    +$ HSPC_703        <dbl> 0.000000, 3.026458, 2.193467, 4.488271, 7.306130, 6.31…
    +$ HSPC_704        <dbl> 0.000000, 1.708092, 1.708092, 0.000000, 1.708092, 8.37…
    +$ HSPC_705        <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 7.8292660,…
    +$ HSPC_706        <dbl> 0.000000, 1.272727, 0.000000, 1.272727, 6.221902, 7.03…
    +$ HSPC_707        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 3.917498, 1.36…
    +$ HSPC_708        <dbl> 0.000000, 0.000000, 0.000000, 4.944545, 9.429525, 9.22…
    +$ HSPC_709        <dbl> 0.000000, 0.000000, 6.392596, 0.000000, 5.005898, 0.00…
    +$ HSPC_714        <dbl> 0.000000, 0.000000, 3.784587, 0.000000, 2.395136, 1.64…
    +$ HSPC_716        <dbl> 0.000000, 0.000000, 0.000000, 1.311350, 8.040385, 1.31…
    +$ HSPC_717        <dbl> 0.000000, 1.153655, 1.153655, 0.000000, 2.224752, 0.00…
    +$ HSPC_719        <dbl> 0.000000, 0.000000, 3.146515, 6.492252, 4.618557, 0.00…
    +$ HSPC_720        <dbl> 0.0000000, 0.8205612, 1.3403833, 0.0000000, 1.7217133,…
    +$ HSPC_721        <dbl> 0.000000, 2.935568, 3.456262, 0.000000, 0.000000, 2.11…
    +$ HSPC_722        <dbl> 0.000000, 0.000000, 2.268643, 0.000000, 9.095591, 1.18…
    +$ HSPC_723        <dbl> 0.8420975, 0.8420975, 2.5250483, 0.0000000, 4.8843811,…
    +$ HSPC_724        <dbl> 0.0000000, 1.0942930, 1.7093650, 0.0000000, 3.2499204,…
    +$ HSPC_725        <dbl> 1.577147, 0.000000, 3.159495, 0.000000, 2.312545, 2.79…
    +$ HSPC_727        <dbl> 0.000000, 1.576167, 3.894561, 0.000000, 8.810183, 0.00…
    +$ HSPC_729        <dbl> 0.0000000, 0.0000000, 1.9363149, 0.0000000, 7.5873035,…
    +$ HSPC_730        <dbl> 1.134736, 1.761952, 2.197661, 0.000000, 7.311461, 0.00…
    +$ HSPC_731        <dbl> 0.000000, 1.129768, 1.129768, 4.039758, 1.755516, 5.09…
    +$ HSPC_732        <dbl> 0.0000000, 0.6937047, 2.2340688, 0.6937047, 2.0310980,…
    +$ HSPC_733        <dbl> 0.000000, 0.000000, 1.435585, 0.000000, 4.173862, 2.14…
    +$ HSPC_734        <dbl> 0.000000, 1.217180, 1.578880, 0.000000, 9.362294, 1.21…
    +$ HSPC_735        <dbl> 0.000000, 0.000000, 2.048558, 0.000000, 9.326379, 2.04…
    +$ HSPC_736        <dbl> 0.0000000, 0.0000000, 0.6789402, 0.0000000, 2.2034453,…
    +$ HSPC_737        <dbl> 0.0000000, 0.0000000, 0.7110779, 0.0000000, 7.7355892,…
    +$ HSPC_738        <dbl> 0.000000, 2.715943, 0.000000, 0.000000, 3.362289, 8.20…
    +$ HSPC_740        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.620463, 6.54…
    +$ HSPC_742        <dbl> 0.0000000, 0.8436636, 0.8436636, 0.0000000, 1.7586463,…
    +$ HSPC_743        <dbl> 1.122102, 0.000000, 0.000000, 0.000000, 0.000000, 6.91…
    +$ HSPC_744        <dbl> 0.000000, 7.472712, 1.212953, 0.000000, 1.212953, 0.00…
    +$ HSPC_745        <dbl> 0.000000, 0.000000, 0.000000, 2.402561, 2.402561, 0.00…
    +$ HSPC_746        <dbl> 0.000000, 2.183740, 0.000000, 0.000000, 6.837761, 0.00…
    +$ HSPC_747        <dbl> 0.000000, 0.000000, 1.777355, 0.000000, 7.778192, 2.54…
    +$ HSPC_748        <dbl> 0.000000, 2.263816, 0.000000, 0.000000, 3.303450, 0.00…
    +$ HSPC_749        <dbl> 0.000000, 0.000000, 1.443774, 0.000000, 3.501043, 0.00…
    +$ HSPC_750        <dbl> 0.000000, 1.029692, 0.000000, 0.000000, 8.102961, 0.00…
    +$ HSPC_751        <dbl> 0.000000, 0.000000, 3.435201, 0.000000, 3.435201, 7.28…
    +$ HSPC_752        <dbl> 2.227867, 0.000000, 2.227867, 0.000000, 3.065024, 9.23…
    +$ HSPC_753        <dbl> 0.000000, 0.000000, 2.092163, 0.000000, 2.420031, 3.10…
    +$ HSPC_755        <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 5.3881500,…
    +$ HSPC_756        <dbl> 0.000000, 1.730911, 0.000000, 0.000000, 6.980096, 6.68…
    +$ HSPC_757        <dbl> 0.000000, 1.394821, 1.394821, 0.000000, 3.193425, 0.00…
    +$ HSPC_758        <dbl> 0.0000000, 0.8647569, 1.4016663, 0.0000000, 7.1436038,…
    +$ HSPC_759        <dbl> 1.5063802, 0.9414682, 1.9112870, 0.9414682, 2.2271023,…
    +$ HSPC_760        <dbl> 0.000000, 9.073516, 1.653873, 0.000000, 1.051989, 0.00…
    +$ HSPC_761        <dbl> 0.0000000, 2.0270678, 1.5086587, 0.0000000, 2.4076406,…
    +$ HSPC_762        <dbl> 0.000000, 1.935807, 1.935807, 0.000000, 7.772123, 0.00…
    +$ HSPC_764        <dbl> 0.000000, 1.784134, 1.784134, 0.000000, 3.969445, 1.78…
    +$ HSPC_765        <dbl> 0.000000, 2.116018, 2.116018, 0.000000, 11.306195, 2.1…
    +$ HSPC_766        <dbl> 0.0000000, 0.9827582, 0.9827582, 0.0000000, 3.5531934,…
    +$ HSPC_767        <dbl> 0.6646406, 0.0000000, 1.4623246, 0.0000000, 10.4507620…
    +$ HSPC_768        <dbl> 0.000000, 1.703127, 1.703127, 1.703127, 9.992206, 2.46…
    +$ HSPC_769        <dbl> 0.000000, 2.429943, 4.213728, 0.000000, 4.772537, 2.42…
    +$ HSPC_770        <dbl> 0.000000, 1.760248, 1.760248, 1.760248, 6.134208, 2.52…
    +$ HSPC_771        <dbl> 0.000000, 0.000000, 1.818104, 0.000000, 8.774881, 1.81…
    +$ HSPC_772        <dbl> 0.000000, 1.600797, 0.000000, 0.000000, 2.340909, 0.00…
    +$ HSPC_773        <dbl> 0.0000000, 0.9900713, 1.5717090, 0.0000000, 5.2659904,…
    +$ HSPC_774        <dbl> 0.0000000, 0.0000000, 1.5496423, 0.0000000, 2.5406754,…
    +$ HSPC_776        <dbl> 0.000000, 0.000000, 3.691348, 2.314052, 8.369556, 0.00…
    +$ HSPC_777        <dbl> 0.000000, 0.000000, 2.079090, 0.000000, 8.370977, 1.05…
    +$ HSPC_778        <dbl> 0.000000, 0.000000, 3.691686, 1.434589, 4.532296, 0.00…
    +$ HSPC_780        <dbl> 0.000000, 1.178249, 1.818049, 0.000000, 7.874420, 0.00…
    +$ HSPC_781        <dbl> 0.000000, 2.884261, 2.884261, 0.000000, 3.783095, 2.88…
    +$ HSPC_782        <dbl> 0.000000, 0.000000, 2.691145, 0.000000, 7.913867, 0.00…
    +$ HSPC_783        <dbl> 0.000000, 0.000000, 1.775679, 0.000000, 8.938539, 9.20…
    +$ HSPC_784        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.668054, 1.05…
    +$ HSPC_785        <dbl> 0.000000, 0.000000, 2.465903, 0.000000, 3.530782, 1.32…
    +$ HSPC_786        <dbl> 0.000000, 1.148465, 1.779704, 0.000000, 2.552651, 8.42…
    +$ HSPC_787        <dbl> 0.000000, 0.000000, 3.897091, 2.161763, 3.513976, 4.84…
    +$ HSPC_788        <dbl> 0.000000, 0.000000, 3.844884, 0.000000, 1.877270, 6.68…
    +$ HSPC_789        <dbl> 0.000000, 0.000000, 1.822053, 0.000000, 2.264164, 1.18…
    +$ HSPC_790        <dbl> 0.000000, 0.000000, 2.851872, 0.000000, 9.272098, 0.00…
    +$ HSPC_791        <dbl> 1.789964, 0.000000, 4.930584, 0.000000, 6.443477, 2.56…
    +$ HSPC_794        <dbl> 0.000000, 1.112719, 0.000000, 1.112719, 2.498279, 3.78…
    +$ HSPC_795        <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 2.2924736,…
    +$ HSPC_796        <dbl> 0.0000000, 0.7001062, 1.5229964, 1.1694432, 6.1361361,…
    +$ HSPC_797        <dbl> 0.000000, 0.872225, 1.411951, 0.872225, 3.217981, 0.87…
    +$ HSPC_798        <dbl> 0.000000, 1.531160, 0.000000, 2.257120, 4.314828, 0.00…
    +$ HSPC_799        <dbl> 0.000000, 0.000000, 4.059222, 2.637723, 3.516894, 0.00…
    +$ HSPC_800        <dbl> 0.000000, 0.000000, 1.766326, 0.000000, 5.615808, 3.03…
    +$ HSPC_801        <dbl> 0.000000, 1.335456, 0.000000, 0.000000, 1.335456, 0.00…
    +$ HSPC_802        <dbl> 0.000000, 0.000000, 0.000000, 2.881726, 4.081151, 0.00…
    +$ HSPC_803        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 7.326296, 0.00…
    +$ HSPC_804        <dbl> 0.000000, 0.000000, 1.871913, 0.000000, 2.660005, 6.23…
    +$ HSPC_806        <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 4.774769, 0.00…
    +$ HSPC_807        <dbl> 0.0000000, 1.2411117, 0.0000000, 0.0000000, 2.3480676,…
    +$ HSPC_808        <dbl> 0.0000000, 0.0000000, 1.1139506, 2.5001649, 1.1139506,…
    +$ HSPC_809        <dbl> 1.788499, 0.000000, 0.000000, 1.788499, 3.064135, 1.78…
    +$ HSPC_810        <dbl> 0.000000, 0.000000, 1.651345, 0.000000, 3.549216, 0.00…
    +$ HSPC_812        <dbl> 0.0000000, 0.0000000, 2.0668334, 0.0000000, 8.1782380,…
    +$ HSPC_813        <dbl> 0.0000000, 0.0000000, 0.6277581, 4.3663804, 1.8975541,…
    +$ HSPC_814        <dbl> 0.000000, 1.109763, 2.161664, 0.000000, 0.000000, 0.00…
    +$ HSPC_815        <dbl> 0.9630613, 0.9630613, 2.7434401, 0.9630613, 7.9310753,…
    +$ HSPC_816        <dbl> 0.000000, 0.000000, 1.346034, 1.346034, 6.498939, 1.34…
    +$ HSPC_818        <dbl> 0.0000000, 0.0000000, 3.4534483, 0.9967122, 9.8653293,…
    +$ HSPC_819        <dbl> 0.000000, 0.000000, 3.149725, 1.364557, 7.496230, 2.05…
    +$ HSPC_820        <dbl> 0.0000000, 0.8098885, 2.4642646, 0.0000000, 9.0793660,…
    +$ HSPC_821        <dbl> 0.000000, 0.000000, 3.792154, 0.000000, 3.175252, 0.00…
    +$ HSPC_822        <dbl> 0.000000, 1.386534, 3.957031, 0.000000, 2.080316, 0.00…
    +$ HSPC_824        <dbl> 0.000000, 1.236780, 1.236780, 2.342030, 2.342030, 1.23…
    +$ HSPC_825        <dbl> 0.000000, 0.000000, 2.079118, 0.000000, 5.922947, 2.07…
    +$ HSPC_826        <dbl> 0.000000, 2.002994, 2.002994, 0.000000, 4.811203, 0.00…
    +$ HSPC_827        <dbl> 1.746375, 0.000000, 3.381363, 0.000000, 7.353191, 1.74…
    +$ HSPC_828        <dbl> 0.000000, 0.000000, 1.588492, 0.000000, 2.326162, 0.00…
    +$ HSPC_831        <dbl> 0.000000, 1.304384, 0.000000, 0.000000, 6.405611, 6.06…
    +$ HSPC_832        <dbl> 0.000000, 0.000000, 2.376979, 0.000000, 9.076790, 1.03…
    +$ HSPC_833        <dbl> 0.0000000, 0.0000000, 1.8371808, 0.0000000, 0.0000000,…
    +$ HSPC_834        <dbl> 0.0000000, 0.9245023, 1.8852183, 0.0000000, 8.9614736,…
    +$ HSPC_835        <dbl> 0.000000, 0.000000, 2.595404, 0.000000, 6.141626, 6.76…
    +$ HSPC_836        <dbl> 0.000000, 0.000000, 3.994019, 0.000000, 4.386241, 0.00…
    +$ HSPC_837        <dbl> 0.000000, 0.000000, 2.792826, 0.000000, 0.000000, 0.00…
    +$ HSPC_838        <dbl> 0.0000000, 0.0000000, 3.2926469, 0.0000000, 0.9838061,…
    +$ HSPC_839        <dbl> 0.000000, 0.000000, 2.452494, 0.000000, 2.720721, 1.69…
    +$ HSPC_840        <dbl> 0.000000, 0.000000, 3.534585, 0.000000, 1.866730, 5.03…
    +$ HSPC_841        <dbl> 0.000000, 0.000000, 1.438567, 0.000000, 1.438567, 1.43…
    +$ HSPC_842        <dbl> 0.000000, 2.545827, 2.545827, 0.000000, 7.622029, 2.54…
    +$ HSPC_843        <dbl> 1.256817, 0.000000, 1.256817, 0.000000, 1.256817, 0.00…
    +$ HSPC_844        <dbl> 0.000000, 0.000000, 1.584047, 0.000000, 7.433263, 0.00…
    +$ HSPC_845        <dbl> 0.000000, 1.227393, 1.880830, 7.669286, 6.989762, 0.00…
    +$ HSPC_846        <dbl> 0.000000, 1.401354, 1.401354, 0.000000, 2.919525, 7.30…
    +$ HSPC_848        <dbl> 0.000000, 0.000000, 1.391594, 0.000000, 2.553619, 7.94…
    +$ HSPC_849        <dbl> 0.000000, 0.000000, 1.601976, 0.000000, 8.387312, 2.82…
    +$ HSPC_851        <dbl> 0.000000, 0.000000, 3.910752, 0.000000, 6.824279, 7.81…
    +$ HSPC_852        <dbl> 0.000000, 1.658355, 2.409562, 1.658355, 1.658355, 0.00…
    +
    +
    + + +
    +
    #---CODING ANSWER---
    +#| include: false
    +glimpse(prog_hspc_results)
    +
    +
    Rows: 280
    +Columns: 6
    +$ Top             <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,…
    +$ p.value         <dbl> 7.038138e-117, 4.736622e-90, 1.832630e-88, 4.211954e-7…
    +$ FDR             <dbl> 1.970679e-114, 6.631271e-88, 1.710455e-86, 2.948368e-7…
    +$ summary.logFC   <dbl> 1.596910, 3.035165, 3.261056, -2.146491, -3.056730, 3.…
    +$ logFC.hspc      <dbl> 1.596910, 3.035165, 3.261056, -2.146491, -3.056730, 3.…
    +$ ensembl_gene_id <chr> "ENSMUSG00000028639", "ENSMUSG00000024053", "ENSMUSG00…
    +
    +
    + + + + +

    It is useful to have this information in a single dataframe to which we will add the gene information from Ensembl Having all the information together will make it easier to interpret the results and select genes of interest.

    +

    🎬 Merge the two dataframes:

    -
    # merge stats results with normalise values
    +
    # merge stats results with normalise values
     prog_hspc_results <- prog_hspc_results |> 
       left_join(prog_hspc, by = "ensembl_gene_id")
    -

    Add gene information from the NCBI using biomaRt

    -

    add the gene information using biomart

    -

    Ensembl (Birney et al. 2004) is a bioinformatics project to organise all the biological information around the sequences of large genomes. The are a large number of databases but BioMart (smedley2009?) provides a consistent interface to the material. There are web-based tools to use these but the R package biomaRtr (Durinck et al. 2009) enables you to rapidly access and integrate information into your R data structures.

    +

    This means you have the counts for each sample along with the statistical results for each gene.

    +

    Add gene information from Ensembl using biomaRt

    +

    Ensembl (Martin et al. 2023; Birney et al. 2004)is a bioinformatics project to organise all the biological information around the sequences of large genomes. The are a large number of databases but BioMart (Smedley et al. 2009) provides a consistent interface to the material. There are web-based tools to use these but the R package biomaRt (Durinck et al. 2009) gives you programmatic access making it easier to integrate information into R dataframes

    +

    🎬 Load the biomaRt (Durinck et al. 2009) package:

    +

    🎬 Connect to the mouse database and see what information we can retrieve:

    -
    # Connect to the mouse database
    -
    +
    # Connect to the mouse database
     ensembl <- useMart(biomart = "ensembl", 
    -                   dataset = "mmusculus_gene_ensembl")
    -
    -

    See what info we can retrieve:

    -
    -
    listAttributes(mart = ensembl) |> View()
    + dataset = "mmusculus_gene_ensembl") + +# See what information we can retrieve +listAttributes(mart = ensembl) |> View()
    Error in .External2(C_dataviewer, x, title): unable to start data viewer
    -

    We need ensembl_gene_id: because we will need to merge the info external_gene_name: name for gene description: description

    +

    This may take a moment

    +

    We use the getBM() function to retrieve information from the database. The filters argument is used to specified what kind of identifier we are supplying to retrieve information. The attributes argument is used to select the information we want to retrieve. The values argument is used to specify the identifers. The mart argument is used to specify the connection we created.

    +

    🎬 Get the gene information:

    -
    gene_info <- getBM(filters = "ensembl_gene_id",
    +
    gene_info <- getBM(filters = "ensembl_gene_id",
                        attributes = c("ensembl_gene_id",
                                       "external_gene_name",
                                       "description"),
                        values = prog_hspc_results$ensembl_gene_id,
                        mart = ensembl)
    -

    Notice the dataframe returned only has 279 rows, not 280. Which one is missing?

    +

    We are getting the gene name and and a description. We also need to get the id because we will use that to merge the gene_info dataframe with the prog_hspc_results dataframe. Notice the dataframe returned only has 279 rows - one of the ids does not have information.

    +

    🎬 We can find which is missing with:

    -
    prog_hspc_results |> select(ensembl_gene_id) |> 
    +
    prog_hspc_results |> select(ensembl_gene_id) |> 
       filter(!ensembl_gene_id %in% gene_info$ensembl_gene_id)
    Error:
    @@ -677,280 +2373,148 @@ 

    Workshop

    • `conflicts_prefer(plotly::select)`
    +

    Oh, conflicted has flagged a conflict for us.

    +

    🎬 Take the appropriate action to resolve the conflict:

    +

    ❓ What is the id which is missing information?

    + + +

    We might want to look that up - but let’s worry about it later if it turns out to be something important.

    +

    🎬 Merge the gene information with the results:

    -
    prog_hspc_results |> dplyr::select(ensembl_gene_id) |> 
    -  filter(!ensembl_gene_id %in% gene_info$ensembl_gene_id)
    -
    -
    # A tibble: 1 × 1
    -  ensembl_gene_id   
    -  <chr>             
    -1 ENSMUSG00000029386
    -
    -
    -

    We might want to look that up. Google it. Let’s worry about it later if it turns out to be something important.

    -

    merge the gene info with the results

    -
    -
    prog_hspc_results <- prog_hspc_results |> 
    +
    prog_hspc_results <- prog_hspc_results |> 
       left_join(gene_info, by = "ensembl_gene_id")
    -

    We now have datatframe with all the info we need, normalised counts, log2 normalised counts, statistical comparisons with fold changes and p values, information about the gene other than just the id

    +

    I recommend viewing the dataframe to see the new columns. We now have dataframe with all the info we need, normalised counts, log2 normalised counts, statistical comparisons with fold changes and p values, information about the gene other than just the id

    Write the significant genes to file

    -

    save the most sig genes to file

    +

    We will create dateframe of the signifcant genes and write them to file. These are the files you want to examine in more detail along with the visualisations to select your genes of interest.

    +

    🎬 Create a dataframe of the genes significant at the 0.01 level:

    -
    prog_hspc_results_sig0.01 <- prog_hspc_results |> 
    +
    prog_hspc_results_sig0.01 <- prog_hspc_results |> 
       filter(FDR <= 0.01)
    -

    168 genes

    -

    write to csv file

    +

    🎬 Write the dataframe to file

    -
    write_csv(prog_hspc_results_sig0.01, 
    +
    #---CODING ANSWER---
    +#| include: false
    +write_csv(prog_hspc_results_sig0.01, 
               file = "results/prog_hspc_results_sig0.01.csv")
    +

    🎬 Create a dataframe of the genes significant at the 0.05 level and write to file:

    -
    prog_hspc_results_sig0.05 <- prog_hspc_results |> 
    -  filter(FDR <= 0.05)
    -
    -

    182 genes

    -

    write to csv file

    -
    -
    write_csv(prog_hspc_results_sig0.05, 
    +
    #---CODING ANSWER---
    +#| include: false
    +
    +prog_hspc_results_sig0.05 <- prog_hspc_results |> 
    +  filter(FDR <= 0.05)
    +
    +# write to csv file
    +write_csv(prog_hspc_results_sig0.05, 
               file = "results/prog_hspc_results_sig0.05.csv")
    +

    ❓How many genes are significant at the 0.01 and 0.05 levels?

    + + +

    View the relationship between cells using PCA

    -

    we do this on the log2 transformed normalised counts or the regularized the log transformed counts

    -

    transpose the data we are reducing he number of dimensions from 280

    +

    We have 280 genes in our dataset. PCA will allow us to plot our cells in the “gene expression” space so we can see if Prog cells cluster together and HSPC cells cluster together as we would expect. We do this on the log2 transformed normalised counts.

    +

    Our data have genes in rows and samples in columns which is a common organisation for gene expression data. However, PCA expects cells in rows and genes, the variables, in columns. We can transpose the data to get it in the correct format.

    +

    🎬 Transpose the log2 transformed normalised counts:

    -
    prog_hspc_trans <- prog_hspc_results |> 
    +
    prog_hspc_trans <- prog_hspc_results |> 
       dplyr::select(starts_with(c("Prog_", "HSPC_"))) |>
       t() |> 
       data.frame()
    +

    We have used the select() function to select all the columns that start with Prog_ or HSPC_. We then use the t() function to transpose the dataframe. We then convert the resulting matrix to a dataframe using data.frame(). If you view that dataframe you’ll see it has default column name which we can fix using colnames() to set the column names to the gene ids.

    +

    🎬 Set the column names to the gene ids:

    -
    colnames(prog_hspc_trans) <- prog_hspc_results$ensembl_gene_id
    +
    colnames(prog_hspc_trans) <- prog_hspc_results$ensembl_gene_id

    perform PCA using standard functions

    -
    pca <- prog_hspc_trans |>
    -  prcomp(scale. = TRUE) 
    +
    pca <- prog_hspc_trans |>
    +  prcomp(rank. = 15) 
    +

    The rank. argument tells prcomp() to only calculate the first 15 principal components. This is useful for visualisation as we can only plot in 2 or 3 dimensions. We can see the results of the PCA by viewing the summary() of the pca object.

    -
    summary(pca)
    +
    summary(pca)
    -
    Importance of components:
    -                          PC1     PC2     PC3     PC4     PC5     PC6     PC7
    -Standard deviation     4.3892 3.08797 2.25263 2.13943 1.96659 1.76697 1.62753
    -Proportion of Variance 0.0688 0.03406 0.01812 0.01635 0.01381 0.01115 0.00946
    -Cumulative Proportion  0.0688 0.10286 0.12098 0.13733 0.15114 0.16229 0.17175
    -                           PC8     PC9    PC10    PC11    PC12    PC13    PC14
    -Standard deviation     1.47668 1.46595 1.44342 1.42486 1.41429 1.39361 1.37089
    -Proportion of Variance 0.00779 0.00768 0.00744 0.00725 0.00714 0.00694 0.00671
    -Cumulative Proportion  0.17954 0.18721 0.19466 0.20191 0.20905 0.21599 0.22270
    -                          PC15    PC16    PC17    PC18    PC19    PC20    PC21
    -Standard deviation     1.36576 1.33322 1.32697 1.32019 1.31398 1.30389 1.30191
    -Proportion of Variance 0.00666 0.00635 0.00629 0.00622 0.00617 0.00607 0.00605
    -Cumulative Proportion  0.22936 0.23571 0.24200 0.24822 0.25439 0.26046 0.26651
    -                         PC22    PC23    PC24    PC25   PC26    PC27   PC28
    -Standard deviation     1.2962 1.29071 1.28268 1.27844 1.2745 1.26791 1.2634
    -Proportion of Variance 0.0060 0.00595 0.00588 0.00584 0.0058 0.00574 0.0057
    -Cumulative Proportion  0.2725 0.27846 0.28434 0.29018 0.2960 0.30172 0.3074
    -                          PC29    PC30    PC31    PC32    PC33    PC34    PC35
    -Standard deviation     1.25770 1.24910 1.24288 1.23382 1.23236 1.22745 1.22563
    -Proportion of Variance 0.00565 0.00557 0.00552 0.00544 0.00542 0.00538 0.00536
    -Cumulative Proportion  0.31307 0.31864 0.32416 0.32959 0.33502 0.34040 0.34576
    -                         PC36    PC37    PC38    PC39    PC40    PC41    PC42
    -Standard deviation     1.2178 1.21186 1.20980 1.20808 1.20140 1.19771 1.19167
    -Proportion of Variance 0.0053 0.00524 0.00523 0.00521 0.00515 0.00512 0.00507
    -Cumulative Proportion  0.3511 0.35631 0.36153 0.36675 0.37190 0.37702 0.38210
    -                          PC43   PC44    PC45    PC46    PC47    PC48    PC49
    -Standard deviation     1.18693 1.1830 1.17952 1.17629 1.16840 1.16561 1.16494
    -Proportion of Variance 0.00503 0.0050 0.00497 0.00494 0.00488 0.00485 0.00485
    -Cumulative Proportion  0.38713 0.3921 0.39709 0.40204 0.40691 0.41176 0.41661
    -                          PC50   PC51    PC52    PC53    PC54    PC55   PC56
    -Standard deviation     1.16276 1.1597 1.15720 1.15025 1.14323 1.13645 1.1348
    -Proportion of Variance 0.00483 0.0048 0.00478 0.00473 0.00467 0.00461 0.0046
    -Cumulative Proportion  0.42144 0.4262 0.43102 0.43575 0.44042 0.44503 0.4496
    -                          PC57    PC58   PC59    PC60    PC61    PC62    PC63
    -Standard deviation     1.13171 1.12596 1.1226 1.12127 1.11630 1.11416 1.11191
    -Proportion of Variance 0.00457 0.00453 0.0045 0.00449 0.00445 0.00443 0.00442
    -Cumulative Proportion  0.45420 0.45873 0.4632 0.46772 0.47217 0.47661 0.48102
    -                          PC64    PC65    PC66    PC67    PC68    PC69    PC70
    -Standard deviation     1.10848 1.10387 1.09837 1.09610 1.09477 1.08975 1.08839
    -Proportion of Variance 0.00439 0.00435 0.00431 0.00429 0.00428 0.00424 0.00423
    -Cumulative Proportion  0.48541 0.48976 0.49407 0.49836 0.50264 0.50688 0.51111
    -                          PC71    PC72    PC73    PC74    PC75    PC76    PC77
    -Standard deviation     1.08334 1.08041 1.07919 1.07612 1.07293 1.06974 1.06652
    -Proportion of Variance 0.00419 0.00417 0.00416 0.00414 0.00411 0.00409 0.00406
    -Cumulative Proportion  0.51531 0.51947 0.52363 0.52777 0.53188 0.53597 0.54003
    -                          PC78    PC79    PC80    PC81    PC82    PC83   PC84
    -Standard deviation     1.06480 1.06249 1.05454 1.05217 1.04951 1.04646 1.0447
    -Proportion of Variance 0.00405 0.00403 0.00397 0.00395 0.00393 0.00391 0.0039
    -Cumulative Proportion  0.54408 0.54811 0.55208 0.55604 0.55997 0.56388 0.5678
    -                          PC85    PC86    PC87    PC88    PC89    PC90    PC91
    -Standard deviation     1.04048 1.03910 1.03605 1.03344 1.03033 1.02706 1.02398
    -Proportion of Variance 0.00387 0.00386 0.00383 0.00381 0.00379 0.00377 0.00374
    -Cumulative Proportion  0.57165 0.57550 0.57934 0.58315 0.58694 0.59071 0.59445
    -                          PC92   PC93    PC94    PC95    PC96   PC97    PC98
    -Standard deviation     1.02269 1.0178 1.01520 1.01022 1.00512 1.0043 1.00011
    -Proportion of Variance 0.00374 0.0037 0.00368 0.00364 0.00361 0.0036 0.00357
    -Cumulative Proportion  0.59819 0.6019 0.60557 0.60921 0.61282 0.6164 0.62000
    -                          PC99   PC100   PC101  PC102   PC103   PC104   PC105
    -Standard deviation     0.99823 0.99478 0.99302 0.9901 0.98821 0.98275 0.98033
    -Proportion of Variance 0.00356 0.00353 0.00352 0.0035 0.00349 0.00345 0.00343
    -Cumulative Proportion  0.62356 0.62709 0.63061 0.6341 0.63760 0.64105 0.64448
    -                         PC106   PC107   PC108   PC109   PC110   PC111   PC112
    -Standard deviation     0.97805 0.97199 0.96996 0.96693 0.96433 0.96244 0.95904
    -Proportion of Variance 0.00342 0.00337 0.00336 0.00334 0.00332 0.00331 0.00328
    -Cumulative Proportion  0.64790 0.65127 0.65463 0.65797 0.66129 0.66460 0.66789
    -                         PC113   PC114   PC115   PC116  PC117   PC118   PC119
    -Standard deviation     0.95590 0.95299 0.95160 0.94787 0.9468 0.94142 0.94086
    -Proportion of Variance 0.00326 0.00324 0.00323 0.00321 0.0032 0.00317 0.00316
    -Cumulative Proportion  0.67115 0.67439 0.67763 0.68084 0.6840 0.68720 0.69036
    -                         PC120   PC121   PC122   PC123   PC124   PC125   PC126
    -Standard deviation     0.93911 0.93573 0.93081 0.92879 0.92768 0.92383 0.92272
    -Proportion of Variance 0.00315 0.00313 0.00309 0.00308 0.00307 0.00305 0.00304
    -Cumulative Proportion  0.69351 0.69664 0.69973 0.70282 0.70589 0.70894 0.71198
    -                         PC127   PC128   PC129   PC130   PC131   PC132   PC133
    -Standard deviation     0.92121 0.91999 0.91773 0.91295 0.91056 0.90720 0.90358
    -Proportion of Variance 0.00303 0.00302 0.00301 0.00298 0.00296 0.00294 0.00292
    -Cumulative Proportion  0.71501 0.71803 0.72104 0.72402 0.72698 0.72992 0.73283
    -                        PC134   PC135   PC136   PC137   PC138   PC139   PC140
    -Standard deviation     0.9009 0.89932 0.89834 0.89301 0.89167 0.89028 0.88693
    -Proportion of Variance 0.0029 0.00289 0.00288 0.00285 0.00284 0.00283 0.00281
    -Cumulative Proportion  0.7357 0.73862 0.74150 0.74435 0.74719 0.75002 0.75283
    -                         PC141   PC142   PC143   PC144   PC145   PC146   PC147
    -Standard deviation     0.88267 0.88149 0.87828 0.87515 0.87308 0.87031 0.86696
    -Proportion of Variance 0.00278 0.00278 0.00275 0.00274 0.00272 0.00271 0.00268
    -Cumulative Proportion  0.75561 0.75839 0.76114 0.76388 0.76660 0.76931 0.77199
    -                         PC148   PC149   PC150   PC151   PC152  PC153   PC154
    -Standard deviation     0.86536 0.86323 0.86248 0.86061 0.85821 0.8531 0.85071
    -Proportion of Variance 0.00267 0.00266 0.00266 0.00265 0.00263 0.0026 0.00258
    -Cumulative Proportion  0.77466 0.77733 0.77998 0.78263 0.78526 0.7879 0.79044
    -                         PC155   PC156   PC157   PC158   PC159  PC160   PC161
    -Standard deviation     0.84901 0.84521 0.84208 0.84179 0.83835 0.8370 0.83336
    -Proportion of Variance 0.00257 0.00255 0.00253 0.00253 0.00251 0.0025 0.00248
    -Cumulative Proportion  0.79302 0.79557 0.79810 0.80063 0.80314 0.8056 0.80812
    -                         PC162   PC163   PC164   PC165   PC166  PC167   PC168
    -Standard deviation     0.83207 0.82803 0.82685 0.82371 0.82099 0.8189 0.81575
    -Proportion of Variance 0.00247 0.00245 0.00244 0.00242 0.00241 0.0024 0.00238
    -Cumulative Proportion  0.81060 0.81304 0.81549 0.81791 0.82032 0.8227 0.82509
    -                         PC169   PC170   PC171  PC172   PC173   PC174   PC175
    -Standard deviation     0.81407 0.81227 0.80721 0.8026 0.80146 0.79810 0.79633
    -Proportion of Variance 0.00237 0.00236 0.00233 0.0023 0.00229 0.00227 0.00226
    -Cumulative Proportion  0.82745 0.82981 0.83214 0.8344 0.83673 0.83901 0.84127
    -                         PC176   PC177   PC178   PC179   PC180   PC181   PC182
    -Standard deviation     0.79349 0.79025 0.78951 0.78582 0.78058 0.77895 0.77538
    -Proportion of Variance 0.00225 0.00223 0.00223 0.00221 0.00218 0.00217 0.00215
    -Cumulative Proportion  0.84352 0.84575 0.84798 0.85018 0.85236 0.85453 0.85667
    -                         PC183   PC184   PC185  PC186  PC187   PC188   PC189
    -Standard deviation     0.77191 0.77111 0.76859 0.7669 0.7666 0.76160 0.76145
    -Proportion of Variance 0.00213 0.00212 0.00211 0.0021 0.0021 0.00207 0.00207
    -Cumulative Proportion  0.85880 0.86093 0.86303 0.8651 0.8672 0.86931 0.87138
    -                         PC190   PC191   PC192   PC193  PC194   PC195   PC196
    -Standard deviation     0.75890 0.75735 0.75547 0.75079 0.7489 0.74442 0.74130
    -Proportion of Variance 0.00206 0.00205 0.00204 0.00201 0.0020 0.00198 0.00196
    -Cumulative Proportion  0.87343 0.87548 0.87752 0.87953 0.8815 0.88352 0.88548
    -                         PC197   PC198   PC199   PC200  PC201   PC202   PC203
    -Standard deviation     0.73911 0.73641 0.73232 0.73086 0.7299 0.72752 0.72384
    -Proportion of Variance 0.00195 0.00194 0.00192 0.00191 0.0019 0.00189 0.00187
    -Cumulative Proportion  0.88743 0.88937 0.89128 0.89319 0.8951 0.89698 0.89885
    -                         PC204   PC205   PC206   PC207   PC208   PC209   PC210
    -Standard deviation     0.72191 0.72004 0.71646 0.71404 0.71147 0.70617 0.70423
    -Proportion of Variance 0.00186 0.00185 0.00183 0.00182 0.00181 0.00178 0.00177
    -Cumulative Proportion  0.90071 0.90257 0.90440 0.90622 0.90803 0.90981 0.91158
    -                         PC211   PC212   PC213   PC214   PC215   PC216   PC217
    -Standard deviation     0.70298 0.69954 0.69657 0.69582 0.69276 0.69270 0.68833
    -Proportion of Variance 0.00176 0.00175 0.00173 0.00173 0.00171 0.00171 0.00169
    -Cumulative Proportion  0.91335 0.91509 0.91683 0.91856 0.92027 0.92198 0.92368
    -                         PC218   PC219   PC220   PC221   PC222   PC223   PC224
    -Standard deviation     0.68455 0.68008 0.67851 0.67558 0.67106 0.66645 0.66592
    -Proportion of Variance 0.00167 0.00165 0.00164 0.00163 0.00161 0.00159 0.00158
    -Cumulative Proportion  0.92535 0.92700 0.92864 0.93027 0.93188 0.93347 0.93505
    -                         PC225   PC226   PC227   PC228   PC229  PC230   PC231
    -Standard deviation     0.66215 0.65987 0.65570 0.65358 0.65119 0.6488 0.64568
    -Proportion of Variance 0.00157 0.00156 0.00154 0.00153 0.00151 0.0015 0.00149
    -Cumulative Proportion  0.93662 0.93817 0.93971 0.94124 0.94275 0.9443 0.94574
    -                         PC232   PC233   PC234   PC235   PC236   PC237  PC238
    -Standard deviation     0.64343 0.64096 0.63918 0.63427 0.63107 0.62967 0.6260
    -Proportion of Variance 0.00148 0.00147 0.00146 0.00144 0.00142 0.00142 0.0014
    -Cumulative Proportion  0.94722 0.94869 0.95015 0.95158 0.95301 0.95442 0.9558
    -                        PC239   PC240   PC241   PC242   PC243   PC244   PC245
    -Standard deviation     0.6253 0.62063 0.61999 0.61433 0.61119 0.60898 0.60787
    -Proportion of Variance 0.0014 0.00138 0.00137 0.00135 0.00133 0.00132 0.00132
    -Cumulative Proportion  0.9572 0.95859 0.95997 0.96131 0.96265 0.96397 0.96529
    -                        PC246   PC247   PC248   PC249   PC250   PC251  PC252
    -Standard deviation     0.6030 0.60131 0.59776 0.59573 0.59070 0.58844 0.5805
    -Proportion of Variance 0.0013 0.00129 0.00128 0.00127 0.00125 0.00124 0.0012
    -Cumulative Proportion  0.9666 0.96788 0.96916 0.97043 0.97167 0.97291 0.9741
    -                        PC253   PC254   PC255   PC256   PC257   PC258  PC259
    -Standard deviation     0.5791 0.57666 0.57115 0.57036 0.56503 0.56091 0.5561
    -Proportion of Variance 0.0012 0.00119 0.00117 0.00116 0.00114 0.00112 0.0011
    -Cumulative Proportion  0.9753 0.97650 0.97766 0.97882 0.97996 0.98109 0.9822
    -                         PC260   PC261   PC262   PC263   PC264   PC265   PC266
    -Standard deviation     0.55234 0.54999 0.54348 0.53916 0.53751 0.53097 0.52478
    -Proportion of Variance 0.00109 0.00108 0.00105 0.00104 0.00103 0.00101 0.00098
    -Cumulative Proportion  0.98328 0.98436 0.98542 0.98646 0.98749 0.98849 0.98948
    -                         PC267   PC268   PC269  PC270   PC271   PC272   PC273
    -Standard deviation     0.51696 0.51540 0.51156 0.5013 0.48840 0.47896 0.46889
    -Proportion of Variance 0.00095 0.00095 0.00093 0.0009 0.00085 0.00082 0.00079
    -Cumulative Proportion  0.99043 0.99138 0.99232 0.9932 0.99406 0.99488 0.99567
    -                         PC274   PC275   PC276   PC277   PC278   PC279   PC280
    -Standard deviation     0.46518 0.45568 0.43304 0.42194 0.40659 0.36945 0.34821
    -Proportion of Variance 0.00077 0.00074 0.00067 0.00064 0.00059 0.00049 0.00043
    -Cumulative Proportion  0.99644 0.99718 0.99785 0.99849 0.99908 0.99957 1.00000
    -
    -
    -

    Importance of components: PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 Standard deviation 4.3892 3.08797 2.25263 2.13943 1.96659 1.76697 1.62753 1.47668 Proportion of Variance 0.0688 0.03406 0.01812 0.01635 0.01381 0.01115 0.00946 0.00779 Cumulative Proportion 0.0688 0.10286 0.12098 0.13733 0.15114 0.16229 0.17175 0.17954

    +
    Importance of first k=15 (out of 280) components:
    +                           PC1     PC2     PC3     PC4     PC5     PC6     PC7
    +Standard deviation     12.5612 8.36646 5.98988 5.41386 4.55730 4.06142 3.84444
    +Proportion of Variance  0.1099 0.04874 0.02498 0.02041 0.01446 0.01149 0.01029
    +Cumulative Proportion   0.1099 0.15861 0.18359 0.20400 0.21846 0.22995 0.24024
    +                           PC8     PC9   PC10    PC11    PC12    PC13    PC14
    +Standard deviation     3.70848 3.66899 3.5549 3.48508 3.44964 3.42393 3.37882
    +Proportion of Variance 0.00958 0.00937 0.0088 0.00846 0.00829 0.00816 0.00795
    +Cumulative Proportion  0.24982 0.25919 0.2680 0.27645 0.28473 0.29290 0.30085
    +                          PC15
    +Standard deviation     3.33622
    +Proportion of Variance 0.00775
    +Cumulative Proportion  0.30860
    +
    + +

    The Proportion of Variance tells us how much of the variance is explained by each component. We can see that the first component explains 0.1099 of the variance, the second 0.04874, and the third 0.2498. Together the first three components explain 18% of the total variance in the data. Plotting PC1 against PC2 will capture about 16% of the variance. This is not that high but it likely better than we would get plotting any two genes against each other. To plot the PC1 against PC2 we will need to extract the PC1 and PC2 score from the pca object and add labels for the cells.

    +

    🎬 Create a dataframe of the PC1 and PC2 scores which are in pca$x and add the cell ids:

    -
    pca_labelled <- data.frame(pca$x,
    +
    pca_labelled <- data.frame(pca$x,
                                cell_id = row.names(prog_hspc_trans))
    -

    add the cell type information so we can label points split cell_id into cell type and replicate and keep cell_id column

    +

    It will be helpful to add a column for the cell type so we can label points. One way to do this is to extract the information in the cell_id column into two columns.

    +

    🎬 Extract the cell type and cell number from the cell_id column (keeping the cell_id column):

    -
    pca_labelled <- pca_labelled |> 
    +
    pca_labelled <- pca_labelled |> 
       extract(cell_id, 
               remove = FALSE,
               c("cell_type", "cell_number"),
               "([a-zA-Z]{4})_([0-9]{3})")
    +

    "([a-zA-Z]{4})_([0-9]{3})" is a regular expression - or regex. [a-zA-Z] means any lower or upper case letter, {4} means 4 of them, and [0-9] means any number, {3} means 3 of them. The brackets around the two parts of the regex mean we want to extract those parts. The first part goes into cell_type and the second part goes into cell_number. The _ between the two patterns matches the underscore and the fact it isn’t in a bracket means we don’t want to keep it.

    +

    We can now plot the PC1 and PC2 scores.

    +

    🎬 Plot PC1 against PC2 and colour the points by cell type:

    -
    pca <- pca_labelled |> 
    +
    pca <- pca_labelled |> 
       ggplot(aes(x = PC1, y = PC2, 
                  colour = cell_type)) +
       geom_point(alpha = 0.4) +
       scale_colour_viridis_d(end = 0.8, begin = 0.15,
                              name = "Cell type") +
    -  theme_classic()
    + theme_classic() +pca
    +
    +

    +

    Fairly good separation of cell types but plenty of overlap

    +

    🎬 Save the plot to file:

    -
    ggsave("figures/prog_hspc-pca.png",
    +
    ggsave("figures/prog_hspc-pca.png",
            plot = pca,
            height = 3, 
            width = 4,
            units = "in",
            device = "png")
    -

    tSNE ??

    Visualise the expression of the most significant genes using a heatmap

    we will use the most significant genes on a random subset of the cells since ~1500 columns is a lot

    -
    mat <- prog_hspc_results_sig0.01 |> 
    +
    mat <- prog_hspc_results_sig0.01 |> 
       dplyr::select(starts_with(c("Prog", "HSPC"))) |>
       dplyr::select(sample(1:1499, size = 70)) |>
       as.matrix()
    -
    rownames(mat) <- prog_hspc_results_sig0.01$external_gene_name
    +
    rownames(mat) <- prog_hspc_results_sig0.01$external_gene_name
    -
    n_cell_clusters <- 2
    +
    n_cell_clusters <- 2
     n_gene_clusters <- 2
    -
    heatmaply(mat, 
    +
    heatmaply(mat, 
               scale = "row",
               hide_colorbar = TRUE,
               k_col = n_cell_clusters,
    @@ -961,24 +2525,24 @@ 

    Workshop

    labRow = rownames(mat), heatmap_layers = theme(axis.line = element_blank()))
    -
    - +
    +

    will take a few mins to run, and longer to appear in the viewer separation is not as strong as for the frog data run a few times to see different subset

    Visualise all the results with a volcano plot

    colour the points if FDR < 0.05 and prog_hspc_results > 1

    -
    prog_hspc_results <- prog_hspc_results |> 
    +
    prog_hspc_results <- prog_hspc_results |> 
       mutate(log10_FDR = -log10(FDR),
              sig = FDR < 0.05,
              bigfc = abs(summary.logFC) >= 2) 
    -
    vol <- prog_hspc_results |> 
    +
    vol <- prog_hspc_results |> 
       ggplot(aes(x = summary.logFC, 
                  y = log10_FDR, 
                  colour = interaction(sig, bigfc))) +
    @@ -1003,7 +2567,7 @@ 

    Workshop

    theme(legend.position = "none")
    -
    ggsave("figures/prog-hspc-volcano.png",
    +
    ggsave("figures/prog-hspc-volcano.png",
            plot = vol,
            height = 4.5, 
            width = 4.5,
    @@ -1047,15 +2611,30 @@ 

    Workshop

    Durinck, Steffen, Paul T. Spellman, Ewan Birney, and Wolfgang Huber. 2009. “Mapping Identifiers for the Integration of Genomic Datasets with the r/Bioconductor Package biomaRt” 4.
    +
    +Fisher, Malcolm, Christina James-Zorn, Virgilio Ponferrada, Andrew J Bell, Nivitha Sundararaj, Erik Segerdell, Praneet Chaturvedi, et al. 2023. “Xenbase: Key Features and Resources of the Xenopus Model Organism Knowledgebase.” Genetics 224 (1): iyad018. https://doi.org/10.1093/genetics/iyad018. +
    Hester, Jim, Hadley Wickham, and Gábor Csárdi. 2023. “Fs: Cross-Platform File System Operations Based on ’Libuv’.”
    +
    +Martin, Fergal J, M Ridwan Amode, Alisha Aneja, Olanrewaju Austine-Orimoloye, Andrey G Azov, If Barnes, Arne Becker, et al. 2023. “Ensembl 2023.” Nucleic Acids Research 51 (D1): D933–41. https://doi.org/10.1093/nar/gkac958. +
    R Core Team. 2023. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.
    +
    +Smedley, Damian, Syed Haider, Benoit Ballester, Richard Holland, Darin London, Gudmundur Thorisson, and Arek Kasprzyk. 2009. “BioMart Biological Queries Made Easy.” BMC Genomics 10 (1): 22. https://doi.org/10.1186/1471-2164-10-22. +
    +
    +Wickham, Hadley. 2023. “Conflicted: An Alternative Conflict Resolution Strategy.” +
    Wickham, Hadley, Mara Averick, Jennifer Bryan, Winston Chang, Lucy D’Agostino McGowan, Romain François, Garrett Grolemund, et al. 2019. “Welcome to the Tidyverse 4: 1686. https://doi.org/10.21105/joss.01686.
    +
    +Wickham, Hadley, and Jennifer Bryan. 2023. “Readxl: Read Excel Files.” https://CRAN.R-project.org/package=readxl. +
    Xie, Yihui. 2022. “Knitr: A General-Purpose Package for Dynamic Report Generation in r.” https://yihui.org/knitr/.
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