Coursework

                                      1 Simulate Markov Chains

Q 1 Examine the following piece of code which simulates from a simplified version of the Markov Chain. This simplified version only has three states. Also, work the values for a and b in the code below.

set.seed(42) # store a random number using this function 

#Specify the transition probabilities

a <- 0.799 #store the vector a as 0.799 after doing the calculation 1-(0.2+0.001)=0.799
b <- 0.79 # store the vector b as 0.79 after doing the calculation 1-(0.2+0.01)=0.79
n_days <- 400 # store the number of days as 400 days
 # create a 3x3 matrix for the Markov chain 
transition_matrix <- matrix(c(a, 0.2, 0.001,
                          0.2, b, 0.01,
                          0, 0, 1), nrow=3, ncol=3, byrow=TRUE)
print(transition_matrix) # print the transition matrix

##       [,1] [,2]  [,3]
## [1,] 0.799 0.20 0.001
## [2,] 0.200 0.79 0.010
## [3,] 0.000 0.00 1.000

state <- 1 #set state [1]for healthy state [2] sick state[3] dead
patient_record <- rep(0, n_days) # create an empty vector to store (simulated value) the patient's state for each day
#use a for loop to repeat the matrix for each state (simulate it for 400 days) 
for (day in 1:n_days) {
  pr <- transition_matrix[state, ] #select the row of transition probabilities

  state <- sample(c(1:3), size = 1, prob = pr)
  patient_record[day] <- state # store the sampled state
}
# print the simulated sequence
print(pr)

## [1] 0 0 1

print(state)

## [1] 3

plot(1:n_days, patient_record, "l") #Plot the number of days with the state

#Q1 explination ## here we can observe that within the 400 days we have a transition between healthy and sick, the upward shift indicates the transition from healthy to sick and the downward shift indicates the transition from sick to healthy.until it reached dead by around day 250 to have constant line in the dead state.

Q 2 Extend the code above to incorporate the 4th state creating a 4x4 transition matrix, based on the 4 state Markov Chain presented above. Plot the resulting patient record and comment on the plot. We define state 1 as H, state 2 as S0, 3 as state SH and state 4 as D

set.seed(400) # I have changed the random number to have a better vision we can choose any number.

# Specify transition probabilities for the 4-state Markov Chain
z <- 0.799  # Transition probability from H to H   calculation 1-(0.2 + 0.001)=0.799
x <- 0.69  # Transition probability from S0 to S0  calculation 1-(0.2+0.1+0.01)=0.79
c <- 0.5  # Transition probability from SH to SH   calculation 1-(0.1+0.2+0.2)= 0.5

# store the number of days as 400
n_days <- 400

# Create a 4x4 transition matrix

transition_matrix2 <- matrix(c(z, 0.2, 0, 0.001,
                               0.2, x, 0.1, 0.01,
                               0.1, 0.2, c, 0.2,
                               0, 0, 0, 1), nrow = 4, ncol = 4, byrow = TRUE)
print(transition_matrix2) #print the transition matrix

##       [,1] [,2] [,3]  [,4]
## [1,] 0.799 0.20  0.0 0.001
## [2,] 0.200 0.69  0.1 0.010
## [3,] 0.100 0.20  0.5 0.200
## [4,] 0.000 0.00  0.0 1.000

state.new <- 1  # state[1] is set to H

# Create a vector to store the patient's state for each day
patient_record2 <- rep(0, n_days)

# Simulate the 4-state Markov Chain for 'n_days' days
for (day in 1:n_days) {
  pr2 <- transition_matrix2[state.new, ]

  # Sample a new state based on the transition probabilities
  state.new <- sample(c(1:4), size = 1, prob = pr2)
  
  # Record the patient's state for the current day
  patient_record2[day] <- state.new
}

print(pr2)

## [1] 0 0 0 1

print(patient_record2)

##   [1] 1 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 2 2 2 1 1 1 1 1 2 1
##  [38] 1 1 2 1 1 1 1 1 1 2 2 3 3 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
##  [75] 1 1 1 1 1 1 2 2 2 2 1 1 2 2 2 2 2 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1
## [112] 2 2 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [149] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [186] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [223] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [260] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [297] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [334] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [371] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

#plot the number of days with the patient state,Here I wanted to zoom-in to show how the patient state is shifted
plot(1:n_days, patient_record2, "l")

plot(1:n_days, patient_record2,"l",ylim = c(0.5,4.5),xlim = c(0,50))

#Q2 Explination # The plots provide a graphical representation of variations in the patient’s health status over time, showing how the patient moves from one state to another.The enlarged plot provides a better view of the early changes in health states.These defined transition probabilities allow you to view how the patient’s health changes with time.

Q 3 Use your code from Q2 to simulate 1000 patient records. Plot the distribution of the number of days spent in each state. Comment on the results.

set.seed(400) #Set seed for any random number
# Simulate 1000 patient records
n_simulations <- 1000
results <- matrix(0, nrow = n_days, ncol = n_simulations)
#  for loop for each simulation
for (sim in 1:n_simulations) {
  # initial state for the current simulation
  state <- 1
  # Create an empty vector to store the patient's state for each day
  patient_record <- rep(0, n_days)
# Inner loop for each day in the simulation
  for (day in 1:n_days) {
    # transition probabilities for the current state
    pr <- transition_matrix2[state, ]
# Sample a new state based on the transition probabilities
    state <- sample(c(1:4), size = 1, prob = pr)
    # Record the patient's state for the current day
    patient_record[day] <- state
  }
# save the patient record in the results matrix
  results[, sim] <- patient_record

}
# Create a bar plot for the number of days spent in each state
hist(patient_record,breaks = seq(0.5, 4.5, by = 1),col = c("orange", "yellow", "green", "red"),
     main = "Number of Days Spent in Each State",
     xlab = "State", ylab = "Number of Days", border = "black")

#add a describe box of the histogram showing the information of the histogram.

legend("topright", legend = c("State 1", "State 2", "State 3", "State 4"),
       fill = c("orange", "yellow", "green", "red"), border = "black", cex = 0.8)

#Q3 explination. #This bar plot illustrates how the number of days spent in each state varied among all 1000 patient records.Each bar signifies one of the four states (H, S0, SH and D), with its height denoting how many days were spent in that state.The histogram lends a clear picture of the differences in each state’s lifelength across many recorded cases that are randomly generated.Forexmple we can observe that state 4 (Dead) has the hightest number of days.

                                   2 Data Analysis

Q 4 Study the following code example and add comments to describe what it does: #need to add comments.

# ------------- Part 1 -------------

# Load necessary libraries
library(tidyverse)

## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
## ✔ ggplot2 3.3.6      ✔ purrr   0.3.4 
## ✔ tibble  3.1.8      ✔ dplyr   1.0.10
## ✔ tidyr   1.2.1      ✔ stringr 1.4.1 
## ✔ readr   2.1.3      ✔ forcats 0.5.2 
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()

load("assess_data_resit-23 (4).Rdata")
# Transform gene expression data for PCA analysis
pca_x  <- t(log(Y + 1)) # Take the logarithm of each element in the matrix Y and add 1
# Perform Principal Component Analysis (PCA)
pca_res1 <- prcomp(pca_x, scale = TRUE, center = TRUE)
#Create a data frame containing principal component scores, tissue, and patient information.
pca_df1 <- data.frame(
  pca_res1$x,
  tissue = patient_data$tissue,
  patient = patient_data$patient)
# Create a scatter plot using ggplot2 to visualize the PCA results
ggplot(pca_df1, aes(x = PC1, y = PC2, color = tissue)) +
  geom_point(size = 3) +
  theme_bw() +
  labs(x = "PC1", y = "PC2") +
  theme(legend.position = "bottom")

# ------------- Part 2 -------------

library(MASS)

## 
## Attaching package: 'MASS'

## The following object is masked from 'package:dplyr':
## 
##     select

# Set the index for the gene of interest, here we chose gene number 20
idx <- 20

# Specify a subset of columns for analysis from 1 to 20 number of the rows
c_cl <- 1:20

# Extract relevant variables from patient_data
x <- patient_data$tissue[c_cl] #select from the patient_data tissue column for the first 20 rows
z <- patient_data$patient[c_cl]#select from the Patient_data Patient column for the first 20 rows

# Create a data frame for the Poisson regression analysis
tmp <- data.frame(y = Y[idx, c_cl], x = x, z = z, lib_size = colSums(Y[, c_cl]))

# Perform Poisson regression by applying the below equation.

out <- glm(y ~ x + z + lib_size, data = tmp, family = "poisson")

# Extract the p-value for the variable x, so coefficients[2,4] the second row (XTumour)and the fourth column "Pr(>|z|)"
 p_val <- summary(out)$coefficients[2,4] 
print(p_val) #p_val equal to zero for gene expression for gene 20 which indicates the statistical significant

## [1] 0

                           2.1 Principal Component Analysis (PCA)

Q 5 Using the code from Q4 part 1, perform dimensionality reduction using principal components analysis (PCA) for the full data matrix provided.

1)Plot a scatter plot in the first two principal components.

#load libraries
library(tidyverse)

# Transform gene expression data for PCA analysis (full data matrix)
full_pca_x <- t(log(Y + 1))

# Perform Principal Component Analysis (PCA) for the full data matrix
full_pca_result <- prcomp(full_pca_x, scale. = TRUE, center = TRUE)

#access the PCA scores
pca_scores<-full_pca_result$x


# Create a data frame containing principal component scores and patient metadata for the full data matrix
full_pca_df <- data.frame(
  full_pca_result$x,
  tissue = patient_data$tissue,
  patient = patient_data$patient
)

# Create a scatter plot of the first two principal components for the full data matrix
ggplot(full_pca_df, aes(x = PC1, y = PC2, color = tissue)) +
  geom_point(size = 3) +
  theme_bw() +
  labs(x = "PC1", y = "PC2") +
  theme(legend.position = "bottom")

# in this scattered plot of PC1 and PC2 provides insights into the differences between normal and tumor tissues based on gene expression profiles. we can observe that the Normal tissues in red are clustered together which indicates that they are sharing common characteristics. and the tumor tissues in green are scattered away from the normal tissues.

Identify any problematic samples exploring the scatter plot visually.

# identifying the problematic sample by using a colored text.
ggplot(pca_df1, aes(x = PC1, y = PC2, color = tissue)) +
  geom_point(size = 3) + # Plot the points with color representing tissue
  geom_text(data = data.frame(PC1 = -5, PC2 = -30, label = "problamtic sample"),
            aes(label = label), color = "green", size = 3) + # Add text for a specific point
  theme_bw() +
  labs(x = "PC1", y = "PC2") +
  theme(legend.position = "bottom")+
geom_text(data = data.frame(PC1 = -50, PC2 = 51, label = "problamtic sample"),
            aes(label = label), color = "green", size = 3)

#here I identified 2 problematic sample.

Explain briefly why the samples are problematic.

#AS I can observe from the scattered plot that the Normal tissues are clustered together in the positive PC1 which indicates that they are sharing similar characteristic sand the tumor tissues are scattered away in the negative pc1. however one point of the normal tissues is away, similar to the point where all the tumor tissue are close to each other expect the point upward which indicates that this point doesn’t belong to the tumor tissue.

4)Remove problematic sample pairs from further analysis

# Define the threshold
threshold <- 20

# Automatically detect problematic samples based on the threshold
problematic_samples <- pca_df1 %>%
  filter(PC2 < -threshold | PC2 > threshold)

# Display the rows of problematic samples
print(problematic_samples)

##                  PC1       PC2       PC3       PC4       PC5        PC6
## Sample014 -50.922180  51.14770 -31.80735 -2.839778  4.242426   2.254764
## Sample016  -6.794931 -30.90486 -20.67929 11.114778 21.821469 -26.735990
##                  PC7      PC8        PC9      PC10       PC11      PC12
## Sample014 -12.778088 21.95123 -0.6399394 -4.252736  -3.751881  1.284126
## Sample016   1.422906  4.06738  4.0899180 -1.188607 -17.212595 21.971109
##                PC13      PC14       PC15      PC16       PC17       PC18
## Sample014 -11.52586 -2.047688  2.1464452 -3.553092 -0.7716928 -0.2664786
## Sample016 -14.66413 -8.986004 -0.7733178 -2.268979  8.2041625  0.2758526
##                 PC19      PC20      PC21       PC22       PC23        PC24
## Sample014 -0.9311749 -1.874208 -1.086976  0.4610885 -0.0657610 -0.05818136
## Sample016 -4.6299609 -1.021175 -1.426789 -0.1166548 -0.2545733  1.34571170
##                PC25      PC26       PC27      PC28        PC29          PC30
## Sample014  0.577721 -0.935220 -0.7086139 -1.068067 -1.82927863  1.017741e-15
## Sample016 -2.298716  2.352963  0.7459511 -2.798237  0.03914032 -1.894896e-15
##           tissue    patient
## Sample014 Tumour Patient.14
## Sample016 Normal  Patient.1

# Filter out problematic sample pairs
filtered_pca_df <- pca_df1 %>%
  anti_join(problematic_samples, by = "patient")
# Visualize the PCA scatter plot
ggplot(filtered_pca_df, aes(x = PC1, y = PC2, color = tissue)) +
  geom_point(size = 3) +
  theme_bw() +
  labs(x = "PC1", y = "PC2") +
  theme(legend.position = "bottom")

#over-here I removed the problematic sample by setting the threshold at 20 because the first problematic sample is in the positive PC2 above 20 and the the second problematic sample is in the negative PC2 which below -20.

2.2 Expression Analysis

Q 6 Using the code from Q4 part 2, perform a regression-based differential expression analysis between all normal and tumour samples using Poisson regression. Plot the appropriate log10 p-value from your analysis.

# ------------- Q6 -------------
# ------------- Part 1 -------------
#Here I want filter out the problematic samples from the data and then I'll do an expression data analysis. 

library(MASS) # Load the MASS library
filter_samples <- c("Sample014", "Sample016")  # store the sample that I want to filter in a vector

# Filter out problematic sample pairs
filtered_patient_df <- patient_data %>%filter(!sample_id %in% filter_samples) #filter out the samples from the Patient data frame
filter_Y <- Y[, !colnames(Y) %in% c("Sample014","Sample016")] #filter out the samples from Y data frame

library(MASS)
c_cl <- 1:28 #store the number of samples

#number of rows
indx <- nrow(filter_Y) #store all the genes in the Filtered Y data frame
p_val <- rep (0,indx) #store an empty vector for the p value

#for loop for each gene expression to undergo glm

for ( c in 1: indx ) {
  
 # Create a data frame for the Poisson regression analysis
filtered_tmp <- data.frame(y = filter_Y[c, c_cl], s = colSums(filter_Y[, c_cl]))

# Perform Poisson regression
out.new <- glm(y ~ s, data = filtered_tmp, family = "poisson")

# Extract the p-value 
p_val[c] <- summary(out.new)$coefficients[2,4]
}

## Warning in dpois(y, mu, log = TRUE): non-integer x = 798326.500000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 748925.500000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 606693.400000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 1150601.500000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 797200.200000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 871290.200000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 773379.100000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 855243.900000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 513615.700000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 556238.200000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 513463.800000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 1693677.600000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 658086.700000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 538750.300000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 1749774.700000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 733190.400000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 508460.200000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 917148.900000

print(p_val)

##    [1]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##    [6]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##   [11]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##   [16]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##   [21]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##   [26] 1.638531e-223  0.000000e+00  4.846187e-51  0.000000e+00  0.000000e+00
##   [31]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##   [36]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##   [41]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##   [46]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##   [51]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##   [56]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##   [61]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##   [66]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##   [71]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##   [76]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##   [81]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  3.174220e-75
##   [86]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##   [91]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##   [96]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [101]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [106]  0.000000e+00  0.000000e+00  8.908655e-73  0.000000e+00  0.000000e+00
##  [111]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [116]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  3.406543e-67
##  [121]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [126]  0.000000e+00  0.000000e+00  7.173822e-05  0.000000e+00  1.117768e-26
##  [131]  1.158862e-22  0.000000e+00  5.482993e-31  0.000000e+00  0.000000e+00
##  [136]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [141]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [146]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [151] 1.651840e-158  0.000000e+00 3.973230e-179  0.000000e+00  0.000000e+00
##  [156]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [161] 1.722567e-287  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [166]  0.000000e+00  0.000000e+00 2.207046e-142  0.000000e+00  0.000000e+00
##  [171]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [176]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [181]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [186]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [191]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [196]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [201]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [206]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [211]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [216]  0.000000e+00 1.236866e-157  0.000000e+00  0.000000e+00  0.000000e+00
##  [221]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [226]  0.000000e+00  5.605259e-10  0.000000e+00  0.000000e+00  0.000000e+00
##  [231]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [236]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [241]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [246]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [251]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [256]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [261]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [266]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [271]  1.208624e-72  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [276]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [281]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [286]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [291]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [296]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [301]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [306]  0.000000e+00  1.483861e-01  0.000000e+00  0.000000e+00  0.000000e+00
##  [311]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [316]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [321]  0.000000e+00  0.000000e+00  1.847783e-03  0.000000e+00  0.000000e+00
##  [326]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [331]  0.000000e+00  0.000000e+00  0.000000e+00  1.304461e-87  0.000000e+00
##  [336]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [341]  0.000000e+00  0.000000e+00 7.415193e-121  0.000000e+00  0.000000e+00
##  [346] 1.029269e-123  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [351]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [356]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [361]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [366]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [371]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [376]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  9.968785e-50
##  [381]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  4.434390e-50
##  [386]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [391]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [396]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [401]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [406]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [411]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [416]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [421]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  6.821315e-60
##  [426]  0.000000e+00  0.000000e+00  0.000000e+00  2.033663e-44  0.000000e+00
##  [431]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [436]  0.000000e+00  0.000000e+00 1.206607e-175  0.000000e+00  0.000000e+00
##  [441]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [446]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [451]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [456]  0.000000e+00  0.000000e+00  0.000000e+00 5.100235e-209  0.000000e+00
##  [461] 9.235827e-147  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [466]  0.000000e+00 3.454269e-297  0.000000e+00  0.000000e+00  0.000000e+00
##  [471]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [476]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [481]  0.000000e+00  0.000000e+00  0.000000e+00 6.122414e-257  0.000000e+00
##  [486]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [491]  0.000000e+00  1.460054e-18  0.000000e+00 3.403503e-216  0.000000e+00
##  [496]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [501]  0.000000e+00  0.000000e+00 1.274211e-149  0.000000e+00  0.000000e+00
##  [506]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [511]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [516]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [521]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [526]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [531]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [536]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [541]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  8.334103e-86
##  [546]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [551]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [556]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [561]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [566]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [571]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [576]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [581]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [586]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [591]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [596]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [601]  0.000000e+00 3.097293e-209  0.000000e+00  1.740528e-57  0.000000e+00
##  [606]  0.000000e+00  0.000000e+00  0.000000e+00 4.324117e-123  0.000000e+00
##  [611]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [616]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [621]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [626]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [631]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [636]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [641]  1.815894e-01  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [646]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [651]  0.000000e+00  3.654709e-51  0.000000e+00  0.000000e+00 1.970452e-104
##  [656]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [661]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [666]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [671]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 1.517048e-110
##  [676]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [681]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [686]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [691]  0.000000e+00  0.000000e+00 6.866444e-184  7.326463e-79  0.000000e+00
##  [696]  4.517610e-86  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [701]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [706]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [711]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [716]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [721]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [726]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [731] 4.113989e-107  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [736]  4.848912e-52  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [741]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [746] 2.634122e-286  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [751] 4.370484e-293  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [756]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [761]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [766]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [771]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 1.368907e-187
##  [776]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [781]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [786]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [791]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [796] 5.674327e-168  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [801]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [806]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [811]  9.144459e-41  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [816]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [821]  0.000000e+00  0.000000e+00 9.520975e-242  0.000000e+00  0.000000e+00
##  [826]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [831] 3.664121e-153  0.000000e+00  0.000000e+00  0.000000e+00  1.105298e-78
##  [836]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [841]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [846]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [851]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [856]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [861]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [866] 2.062906e-304  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [871]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [876]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 1.114930e-271
##  [881]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [886]  2.376355e-01  0.000000e+00  0.000000e+00  0.000000e+00  3.499014e-04
##  [891]  0.000000e+00  0.000000e+00  0.000000e+00  2.051123e-10  0.000000e+00
##  [896]  0.000000e+00  0.000000e+00  1.511201e-83  0.000000e+00  0.000000e+00
##  [901]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [906]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [911]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [916]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [921]  0.000000e+00  7.062678e-14  0.000000e+00  0.000000e+00  0.000000e+00
##  [926]  0.000000e+00  0.000000e+00  2.999084e-01  0.000000e+00  0.000000e+00
##  [931]  0.000000e+00  0.000000e+00  0.000000e+00  2.172474e-45  0.000000e+00
##  [936]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [941]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [946]  0.000000e+00 3.582064e-291  0.000000e+00  0.000000e+00  0.000000e+00
##  [951]  0.000000e+00  4.276658e-07  0.000000e+00  4.087914e-22  0.000000e+00
##  [956]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [961] 3.622456e-251  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [966]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [971]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [976] 1.439846e-236  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [981]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [986]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##  [991]  0.000000e+00  0.000000e+00  0.000000e+00  1.043451e-66  0.000000e+00
##  [996]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1001]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1006]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1011]  0.000000e+00  0.000000e+00  0.000000e+00  7.982400e-80  0.000000e+00
## [1016]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1021]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1026]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1031]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1036]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1041]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1046]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1051] 1.326056e-182  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1056]  0.000000e+00  3.731570e-10  0.000000e+00  0.000000e+00  0.000000e+00
## [1061]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  5.983535e-07
## [1066]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1071]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1076]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1081]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1086]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1091]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 2.404447e-204
## [1096]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1101]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1106]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 4.501193e-183
## [1111]  0.000000e+00  0.000000e+00 3.070506e-163  0.000000e+00  0.000000e+00
## [1116]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1121]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1126]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1131]  0.000000e+00  0.000000e+00  0.000000e+00  1.423040e-90  0.000000e+00
## [1136]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1141]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1146]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  1.034246e-14
## [1151]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 2.118017e-218
## [1156]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  3.876191e-36
## [1161]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1166]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1171]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1176]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1181]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1186]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1191] 1.845638e-169  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1196]  8.794284e-06  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1201]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1206]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1211]  0.000000e+00  4.889636e-23  0.000000e+00  0.000000e+00  0.000000e+00
## [1216]  0.000000e+00  0.000000e+00 1.568006e-272  0.000000e+00  0.000000e+00
## [1221]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1226]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1231]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1236]  0.000000e+00  0.000000e+00  0.000000e+00  5.537882e-01  0.000000e+00
## [1241]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1246]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1251]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1256]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1261]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1266]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1271]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1276]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1281]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1286]  0.000000e+00  0.000000e+00  0.000000e+00  2.080335e-02  0.000000e+00
## [1291]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1296]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1301]  1.333214e-15  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1306]  0.000000e+00  0.000000e+00  1.293797e-33  0.000000e+00  0.000000e+00
## [1311]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1316]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1321]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1326]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1331]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1336]  0.000000e+00  0.000000e+00 3.440538e-277  0.000000e+00  0.000000e+00
## [1341]  0.000000e+00 4.114487e-176  0.000000e+00  0.000000e+00  0.000000e+00
## [1346]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1351]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1356]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1361]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1366]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1371]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1376]  5.674208e-10  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1381]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  2.062091e-32
## [1386]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1391]  0.000000e+00 1.371283e-149  0.000000e+00  0.000000e+00  0.000000e+00
## [1396]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1401]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  2.027628e-57
## [1406]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1411] 4.251178e-165  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1416]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1421]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1426]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1431]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1436]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1441]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1446]  2.085280e-06 1.007097e-267 1.122939e-145  0.000000e+00  0.000000e+00
## [1451]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1456]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1461]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1466]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1471]  0.000000e+00  0.000000e+00 4.184613e-283  0.000000e+00  0.000000e+00
## [1476]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1481] 2.836668e-138  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1486]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1491]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1496]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1501]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1506]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 1.570128e-115
## [1511]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1516]  0.000000e+00  0.000000e+00  9.537974e-15  0.000000e+00  0.000000e+00
## [1521]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1526]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1531]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1536]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1541]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 4.071351e-132
## [1546]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1551]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1556]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1561]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1566]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1571]  0.000000e+00 2.522472e-122  0.000000e+00  0.000000e+00  0.000000e+00
## [1576]  0.000000e+00  9.562052e-38  0.000000e+00  0.000000e+00  0.000000e+00
## [1581]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1586]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1591]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1596]  0.000000e+00  0.000000e+00 1.716190e-235  0.000000e+00  0.000000e+00
## [1601]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1606]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1611]  0.000000e+00 8.024646e-223  0.000000e+00  0.000000e+00  0.000000e+00
## [1616]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1621]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  5.392425e-95
## [1626]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1631]  0.000000e+00  0.000000e+00  0.000000e+00 2.298513e-166  0.000000e+00
## [1636]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1641]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1646] 2.101382e-180  0.000000e+00  0.000000e+00  0.000000e+00 2.091010e-187
## [1651]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1656]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1661]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1666]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1671]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1676]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1681]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1686]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1691]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 6.710230e-231
## [1696]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1701]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1706]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1711]  0.000000e+00  0.000000e+00  2.854094e-65  0.000000e+00  0.000000e+00
## [1716]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1721]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1726]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1731]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 2.482066e-264
## [1736]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1741]  0.000000e+00  0.000000e+00  0.000000e+00 1.567848e-286  0.000000e+00
## [1746]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1751]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1756]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  3.561103e-69
## [1761]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  9.507828e-35
## [1766]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1771]  1.872705e-01  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1776]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1781]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1786]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1791]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1796]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1801]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1806]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1811]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1816]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1821]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1826]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1831]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1836]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1841]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1846]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1851]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1856]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1861]  0.000000e+00  0.000000e+00 6.225326e-112  8.025881e-01  0.000000e+00
## [1866]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1871]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1876]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1881]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1886]  0.000000e+00  0.000000e+00  0.000000e+00 2.578695e-114  0.000000e+00
## [1891]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1896]  4.630641e-26  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1901]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1906]  0.000000e+00 1.550905e-296  0.000000e+00  0.000000e+00  0.000000e+00
## [1911]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1916]  0.000000e+00  0.000000e+00 3.889662e-104  0.000000e+00  0.000000e+00
## [1921]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1926]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1931]  1.441127e-56  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1936]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1941]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1946]  3.598789e-24  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1951]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1956]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1961]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1966]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1971]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1976]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1981]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1986]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1991]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [1996]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2001]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2006]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2011]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2016]  0.000000e+00 4.119963e-196  0.000000e+00  0.000000e+00  0.000000e+00
## [2021]  0.000000e+00  0.000000e+00  0.000000e+00 1.913894e-115  0.000000e+00
## [2026]  0.000000e+00  0.000000e+00  0.000000e+00 1.091147e-259  0.000000e+00
## [2031]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2036]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2041]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2046]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2051]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2056]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2061]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2066]  0.000000e+00  0.000000e+00  0.000000e+00  8.425181e-01  0.000000e+00
## [2071]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2076]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2081]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2086]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2091]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2096]  0.000000e+00  3.903437e-45  0.000000e+00  0.000000e+00  5.548174e-09
## [2101]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2106]  0.000000e+00  0.000000e+00 1.335557e-208  0.000000e+00  0.000000e+00
## [2111]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2116]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2121]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2126]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2131]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2136]  8.243292e-57  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2141]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2146]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2151] 1.531712e-143  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2156]  0.000000e+00  0.000000e+00  1.916969e-47  0.000000e+00  0.000000e+00
## [2161]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2166]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2171]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2176]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2181]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  5.634084e-21
## [2186]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2191]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2196]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2201]  0.000000e+00  0.000000e+00  3.600841e-50  0.000000e+00  0.000000e+00
## [2206]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2211]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2216]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2221]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2226]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2231]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2236]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2241]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2246]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2251]  0.000000e+00  0.000000e+00 1.808438e-102  0.000000e+00  0.000000e+00
## [2256]  1.565104e-09  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2261]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2266]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  9.672724e-06
## [2271]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2276]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2281]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  4.714913e-43
## [2286]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  1.005295e-26
## [2291]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2296]  0.000000e+00  2.636558e-25  0.000000e+00  0.000000e+00  0.000000e+00
## [2301]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2306] 2.796167e-175  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2311]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2316]  0.000000e+00 2.192560e-218  0.000000e+00  1.400531e-57  0.000000e+00
## [2321]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2326]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2331]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2336]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2341]  0.000000e+00  0.000000e+00  1.992664e-50  0.000000e+00  0.000000e+00
## [2346] 1.745033e-195 1.475456e-192  0.000000e+00  0.000000e+00  0.000000e+00
## [2351]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2356]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2361]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2366]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2371]  0.000000e+00 6.868161e-245  0.000000e+00  0.000000e+00  0.000000e+00
## [2376]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2381]  0.000000e+00  0.000000e+00  0.000000e+00 2.192661e-199  0.000000e+00
## [2386]  0.000000e+00  0.000000e+00  0.000000e+00  1.482917e-95  0.000000e+00
## [2391]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2396]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2401]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2406]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2411]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  2.608087e-49
## [2416]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2421]  0.000000e+00  0.000000e+00 1.102673e-243  1.208661e-21  0.000000e+00
## [2426]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  7.105067e-61
## [2431]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2436]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2441]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2446]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2451]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2456]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  5.124198e-99
## [2461]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2466]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2471]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2476]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 4.256724e-283
## [2481]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2486]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2491]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2496]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2501]  0.000000e+00  0.000000e+00 2.839041e-102  0.000000e+00  0.000000e+00
## [2506]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2511] 2.194170e-216  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2516]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2521]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2526]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2531]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2536]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2541]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2546]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2551]  0.000000e+00  0.000000e+00  0.000000e+00  1.072816e-91  0.000000e+00
## [2556]  0.000000e+00  0.000000e+00  1.784840e-64  0.000000e+00 6.705097e-100
## [2561]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2566]  0.000000e+00  0.000000e+00  4.178271e-03  0.000000e+00  0.000000e+00
## [2571]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2576]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2581]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2586]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2591]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2596]  0.000000e+00  0.000000e+00 1.144766e-307  0.000000e+00  0.000000e+00
## [2601]  4.277207e-37  1.389312e-17  0.000000e+00  0.000000e+00  0.000000e+00
## [2606]  0.000000e+00  0.000000e+00  2.617887e-31  0.000000e+00  0.000000e+00
## [2611]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2616]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2621]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2626]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2631]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2636]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2641]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2646]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2651]  0.000000e+00  0.000000e+00  0.000000e+00 9.843217e-126  0.000000e+00
## [2656]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2661]  0.000000e+00 9.962008e-166  0.000000e+00  0.000000e+00  0.000000e+00
## [2666]  0.000000e+00  0.000000e+00  0.000000e+00 8.920335e-258  0.000000e+00
## [2671]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2676]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2681]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2686]  0.000000e+00  0.000000e+00  0.000000e+00  4.496513e-03  0.000000e+00
## [2691]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2696]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2701]  2.817593e-17  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2706]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2711]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2716]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2721]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2726]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  5.955755e-05
## [2731]  0.000000e+00  0.000000e+00  0.000000e+00 1.864596e-221  0.000000e+00
## [2736]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2741]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2746] 8.537941e-227  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2751]  0.000000e+00  0.000000e+00  0.000000e+00 2.288577e-133  0.000000e+00
## [2756]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2761]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2766]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2771]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2776]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  8.517845e-82
## [2781]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  4.024720e-06
## [2786]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2791]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2796]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2801]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2806]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2811]  3.933021e-19  0.000000e+00  9.254692e-14  0.000000e+00  0.000000e+00
## [2816]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2821]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2826]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2831]  0.000000e+00  0.000000e+00 8.121781e-268  0.000000e+00  0.000000e+00
## [2836]  0.000000e+00 1.075721e-183  0.000000e+00  0.000000e+00  0.000000e+00
## [2841]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2846]  0.000000e+00 5.510486e-273  0.000000e+00  0.000000e+00  0.000000e+00
## [2851]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2856]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2861]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2866]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2871]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2876]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2881]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2886]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2891]  0.000000e+00  0.000000e+00 9.549493e-122  0.000000e+00  0.000000e+00
## [2896]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2901]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2906]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2911]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 3.535116e-268
## [2916]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2921]  0.000000e+00  0.000000e+00  0.000000e+00 1.344573e-182  0.000000e+00
## [2926] 3.217947e-148  0.000000e+00  9.911342e-18  0.000000e+00  0.000000e+00
## [2931]  0.000000e+00  6.397007e-70  0.000000e+00  0.000000e+00  0.000000e+00
## [2936]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  4.435213e-76
## [2941]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2946]  4.690867e-38  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2951]  0.000000e+00  0.000000e+00  0.000000e+00  2.591207e-81  0.000000e+00
## [2956]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2961]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2966]  0.000000e+00  3.493838e-22  0.000000e+00  0.000000e+00  0.000000e+00
## [2971]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2976]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2981]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2986]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [2991]  0.000000e+00  0.000000e+00 2.078265e-246  0.000000e+00  0.000000e+00
## [2996]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3001]  0.000000e+00  8.341685e-21  0.000000e+00  0.000000e+00  0.000000e+00
## [3006]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3011]  3.661901e-01  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3016]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3021]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3026]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3031]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3036]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3041]  0.000000e+00  0.000000e+00  0.000000e+00  6.259339e-36  0.000000e+00
## [3046]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3051]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3056] 2.823897e-143  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3061]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3066]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3071]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3076]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3081]  0.000000e+00  0.000000e+00  0.000000e+00  6.960776e-39  0.000000e+00
## [3086]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3091]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3096]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3101]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3106]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3111]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3116]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3121]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3126]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3131]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3136]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  9.766553e-77
## [3141]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3146]  0.000000e+00  7.702348e-83  0.000000e+00  0.000000e+00  0.000000e+00
## [3151]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3156]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3161]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 4.410507e-139
## [3166] 7.948545e-134  2.870954e-92  0.000000e+00  0.000000e+00  8.280830e-23
## [3171]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3176]  0.000000e+00  0.000000e+00 4.821835e-181  0.000000e+00  4.133886e-85
## [3181]  0.000000e+00  0.000000e+00  3.366840e-01  0.000000e+00  0.000000e+00
## [3186]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3191]  0.000000e+00  0.000000e+00  0.000000e+00  1.492930e-01  0.000000e+00
## [3196]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3201]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3206]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3211]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3216]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3221]  0.000000e+00 9.070093e-180  0.000000e+00  0.000000e+00  0.000000e+00
## [3226]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  1.697322e-10
## [3231]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3236]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3241]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3246]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3251]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3256]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3261]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3266]  0.000000e+00  0.000000e+00  6.307539e-05  0.000000e+00  0.000000e+00
## [3271]  0.000000e+00  0.000000e+00  5.874284e-33  0.000000e+00  0.000000e+00
## [3276]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3281]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  3.963731e-16
## [3286]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3291]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3296]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3301]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3306]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3311]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3316]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3321]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3326]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3331]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3336]  0.000000e+00  0.000000e+00  0.000000e+00 6.279903e-242  0.000000e+00
## [3341]  0.000000e+00 3.751986e-164  0.000000e+00  0.000000e+00  0.000000e+00
## [3346]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3351]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3356]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3361]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3366]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3371]  0.000000e+00  0.000000e+00 4.357817e-307  0.000000e+00  0.000000e+00
## [3376]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3381]  0.000000e+00  0.000000e+00  1.447507e-74  0.000000e+00  0.000000e+00
## [3386]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3391]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3396]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3401]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3406]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3411]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3416]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3421]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 2.592120e-303
## [3426]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3431]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  1.519743e-04
## [3436]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3441]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3446]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3451]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3456]  0.000000e+00  0.000000e+00  0.000000e+00 5.883116e-297  0.000000e+00
## [3461]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3466]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3471]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3476]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3481]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3486] 5.851673e-208  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3491]  4.279608e-14  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3496]  0.000000e+00  0.000000e+00  0.000000e+00 1.627494e-196  0.000000e+00
## [3501] 5.186996e-266  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3506] 7.890515e-109  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3511]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3516]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  3.532222e-28
## [3521]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3526]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3531]  0.000000e+00 1.290299e-278  0.000000e+00  0.000000e+00  0.000000e+00
## [3536]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3541]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3546]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3551]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3556]  0.000000e+00  0.000000e+00  0.000000e+00  1.069451e-39  0.000000e+00
## [3561]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3566]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3571]  0.000000e+00  0.000000e+00 1.371362e-181  0.000000e+00  0.000000e+00
## [3576]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3581]  0.000000e+00 8.187193e-117  0.000000e+00  0.000000e+00  0.000000e+00
## [3586]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3591]  0.000000e+00  0.000000e+00  0.000000e+00 3.341435e-244  0.000000e+00
## [3596]  0.000000e+00  1.390687e-05  0.000000e+00  0.000000e+00  6.965227e-15
## [3601]  0.000000e+00 5.012660e-138  0.000000e+00  0.000000e+00  0.000000e+00
## [3606]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3611]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3616]  0.000000e+00  0.000000e+00  0.000000e+00 4.171767e-220  0.000000e+00
## [3621]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3626] 4.400264e-111  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3631]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3636]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3641]  0.000000e+00  1.363658e-15  0.000000e+00  0.000000e+00  0.000000e+00
## [3646]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3651]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3656]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3661]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3666]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3671]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3676]  1.457269e-09  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3681]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3686]  0.000000e+00  8.110933e-05  0.000000e+00  0.000000e+00  0.000000e+00
## [3691]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3696]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3701]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3706]  0.000000e+00  0.000000e+00 2.337120e-298  0.000000e+00  0.000000e+00
## [3711]  0.000000e+00 3.330628e-237  0.000000e+00 4.506440e-211  0.000000e+00
## [3716]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3721]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3726]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3731]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3736]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3741]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3746]  1.276843e-53  1.024926e-64 3.593367e-139  0.000000e+00  0.000000e+00
## [3751]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3756]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 5.030338e-296
## [3761]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3766]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3771]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3776]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3781]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3786]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3791]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3796]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3801]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3806]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3811]  0.000000e+00  8.145634e-01  0.000000e+00  0.000000e+00  0.000000e+00
## [3816]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3821]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3826]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3831]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3836]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3841]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3846]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3851]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3856]  0.000000e+00  0.000000e+00  0.000000e+00 9.919005e-100  0.000000e+00
## [3861]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3866]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3871]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3876]  0.000000e+00  2.032385e-30  0.000000e+00  0.000000e+00  0.000000e+00
## [3881]  0.000000e+00  2.579679e-71  0.000000e+00  0.000000e+00  0.000000e+00
## [3886] 6.443639e-126  0.000000e+00  3.556189e-36 5.812861e-110  0.000000e+00
## [3891]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3896]  0.000000e+00  0.000000e+00  5.593093e-13  0.000000e+00  0.000000e+00
## [3901]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3906]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3911]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3916]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3921]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3926]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 6.334972e-264
## [3931]  0.000000e+00  0.000000e+00  1.310116e-87  0.000000e+00  0.000000e+00
## [3936]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 1.130051e-228
## [3941]  1.597764e-16  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3946]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3951]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3956]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3961]  0.000000e+00  0.000000e+00  2.156918e-50  0.000000e+00  0.000000e+00
## [3966]  0.000000e+00  0.000000e+00  1.276934e-68  0.000000e+00  0.000000e+00
## [3971]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3976]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3981]  0.000000e+00  0.000000e+00 9.517028e-274  0.000000e+00  0.000000e+00
## [3986]  0.000000e+00  3.111503e-06  0.000000e+00  0.000000e+00  0.000000e+00
## [3991]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [3996]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4001]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4006]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4011] 3.944732e-147  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4016]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4021]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4026]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4031]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4036]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4041]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4046]  0.000000e+00  7.954028e-80  0.000000e+00  0.000000e+00  0.000000e+00
## [4051]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4056]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4061]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4066]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4071]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4076]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4081]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4086]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4091]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4096]  0.000000e+00  0.000000e+00  1.844153e-03  0.000000e+00  0.000000e+00
## [4101]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4106]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  8.769711e-70
## [4111]  0.000000e+00  1.115565e-41  0.000000e+00  0.000000e+00  0.000000e+00
## [4116]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4121] 2.157604e-125  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4126]  0.000000e+00  7.830433e-47  0.000000e+00  0.000000e+00  0.000000e+00
## [4131]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4136]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4141]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4146]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4151]  0.000000e+00  0.000000e+00 9.259235e-248  0.000000e+00  0.000000e+00
## [4156]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4161]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4166]  0.000000e+00  1.855956e-04  0.000000e+00  0.000000e+00  0.000000e+00
## [4171]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4176]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4181]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4186]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4191]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4196]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4201]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4206]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4211]  0.000000e+00  0.000000e+00 2.423013e-294  4.800826e-08  8.068267e-01
## [4216]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4221]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4226]  6.625793e-80  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4231]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4236]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4241]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4246] 1.033838e-112  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4251]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4256]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4261]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 4.213932e-140
## [4266]  0.000000e+00  0.000000e+00 5.688788e-114  0.000000e+00  0.000000e+00
## [4271]  0.000000e+00  3.647126e-54  0.000000e+00 3.199191e-114  0.000000e+00
## [4276]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4281]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4286]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4291]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4296]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4301]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4306]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4311]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4316]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4321]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4326]  0.000000e+00  0.000000e+00  1.887599e-33  0.000000e+00  0.000000e+00
## [4331]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4336]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4341]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4346]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4351]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4356]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4361]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4366]  0.000000e+00  0.000000e+00  0.000000e+00 9.206588e-163 7.545143e-295
## [4371]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 3.417341e-191
## [4376] 3.845309e-143  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4381]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4386]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4391]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4396]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4401]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4406]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4411]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4416]  0.000000e+00  0.000000e+00  0.000000e+00 2.283481e-244  0.000000e+00
## [4421]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4426]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4431]  0.000000e+00  4.915530e-02  0.000000e+00  0.000000e+00  0.000000e+00
## [4436]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4441]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4446]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4451]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4456]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4461]  1.852603e-73  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4466]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4471]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4476]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4481]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4486]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4491]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4496]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4501]  0.000000e+00  0.000000e+00  0.000000e+00  7.806757e-02  0.000000e+00
## [4506]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4511]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 1.910205e-167
## [4516]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4521]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4526]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4531]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4536]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4541]  0.000000e+00  0.000000e+00  4.801784e-81  0.000000e+00  0.000000e+00
## [4546]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4551]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4556]  0.000000e+00  0.000000e+00  3.095892e-38  0.000000e+00  0.000000e+00
## [4561]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## [4566]  0.000000e+00  0.000000e+00  0.000000e+00

#store the resulting p valuses and all the genes in a dataframe
p_val_df <- data.frame(p_val = p_val, idx = 1:indx)
#plot the P-value
ggplot(p_val_df, aes(x = idx, y = p_val)) +
    geom_point(size = 2, col = "green")

#we need to adjust the p value using bonferroni function to avoid any false positive specially we are having a large number of data

adj_p_vals <- p.adjust(p_val, "bonferroni")

  
  adj_val_df <- data.frame(p_val = adj_p_vals, idx = 1:indx)
#plot the adjusted p values
ggplot(adj_val_df, aes(x = idx, y = adj_p_vals)) +
  geom_point(size = 2.5, col = "red") +
  labs(y = "adjusted p-value)")

ggplot(adj_val_df, aes(x = idx, y = log10(adj_p_vals))) +
  geom_point(size = 2.5, col = "dodgerblue1") +
  labs(y = "log10(adjusted p-value)")

#Q6 explination #in analysis of gene expression data,p-values are commonly transformed into log10 values in order to emphasize statistically significant results and make them easier for the eye. A negative log10 transformation is applied to the p-values.The transformation turns small p-values (representing strong evidence against the null hypothesis) into large numeric values.Most useful for visualization, this transformation amplifies differences between p-values and can help identify highly significant results. Like smaller p-values, larger negative log10 values represent more significant results.

Q 7 Perform a regression-based analysis to identify genes differentially expressed between normal and tumour samples including the tissue variable indicating if it is tumour or normal sample. Plot the appropriate log10 p-value from your analysis. Compare the p-values with and without inclusion of the tissue type as a covariate, what do you observe? Which of the covariate has the biggest effect? Explain your answer with supporting plots, tables and further analysis if required.

library(MASS)
library(plyr)

## Warning: package 'plyr' was built under R version 4.2.3

## ------------------------------------------------------------------------------

## You have loaded plyr after dplyr - this is likely to cause problems.
## If you need functions from both plyr and dplyr, please load plyr first, then dplyr:
## library(plyr); library(dplyr)

## ------------------------------------------------------------------------------

## 
## Attaching package: 'plyr'

## The following objects are masked from 'package:dplyr':
## 
##     arrange, count, desc, failwith, id, mutate, rename, summarise,
##     summarize

## The following object is masked from 'package:purrr':
## 
##     compact

library(ggplot2)


# Convert the categorical tissue data into numerical value

filtered_patient_df$tissue <- revalue(filtered_patient_df$tissue, c("Tumour"=1))
filtered_patient_df$tissue <- revalue(filtered_patient_df$tissue, c("Normal"=0))

c_cl <- 1:28

rows <- nrow(filter_Y)
x <- filtered_patient_df$tissue



# Initialize vectors for p-values
p_val_without_tissue <- rep(0, rows)
p_val_with_tissue <- rep(0, rows)

# Go through all the gene expressions
for (c in 1:rows) {
  # Create a dataframe where y indicates each gene expression across 30 samples
  # and s indicates the sum of all the gene expression under each sample
  tmp <- data.frame(y = filter_Y[c, c_cl], s = colSums(filter_Y[, c_cl]), x)
  
  # Perform glm (generalized linear model) without tissue as a covariate
  out_without_tissue <- glm(y ~ s, data = tmp, family = "poisson")
  
  # Extract the p-values from the summary of the glm function
  p_val_without_tissue[c] <- summary(out_without_tissue)$coefficients[2, 4]
  
  # Perform glm with tissue as a covariate
  out_with_tissue <- glm(y ~ s + x, data = tmp, family = "poisson")
  
  # Extract the p-values from the summary of the glm function
  p_val_with_tissue[c] <- summary(out_with_tissue)$coefficients[2, 4]
}

## Warning in dpois(y, mu, log = TRUE): non-integer x = 798326.500000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 748925.500000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 798326.500000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 748925.500000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 606693.400000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 1150601.500000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 797200.200000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 606693.400000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 1150601.500000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 797200.200000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 871290.200000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 871290.200000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 773379.100000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 773379.100000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 855243.900000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 855243.900000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 513615.700000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 513615.700000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 556238.200000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 556238.200000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 513463.800000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 513463.800000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 1693677.600000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 658086.700000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 1693677.600000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 658086.700000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 538750.300000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 538750.300000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 1749774.700000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 1749774.700000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 733190.400000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 733190.400000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 508460.200000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 508460.200000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 917148.900000

## Warning in dpois(y, mu, log = TRUE): non-integer x = 917148.900000

# Adjust the p-values
adj_p_vals_without_tissue <- p.adjust(p_val_without_tissue, "bonferroni")
adj_p_vals_with_tissue <- p.adjust(p_val_with_tissue, "bonferroni")

# Create data frames for ggplot
p_val_df_without_tissue <- data.frame(idx = 1:rows, log_adj_p_val = -log10(adj_p_vals_without_tissue))
p_val_df_with_tissue <- data.frame(idx = 1:rows, log_adj_p_val = -log10(adj_p_vals_with_tissue))

# Plotting
ggplot(p_val_df_without_tissue, aes(x = idx, y = log_adj_p_val)) +
  geom_point(size = 2.5, col = "dodgerblue1") +
  labs(y = "log10(adjusted p-value)", title = "Without Tissue Covariate")

ggplot(p_val_df_with_tissue, aes(x = idx, y = log_adj_p_val)) +
  geom_point(size = 2.5, col = "darkorange") +
  labs(y = "log10(adjusted p-value) for Tissue", title = "With Tissue Covariate")

# Create a data frame for comparison
comparison_df <- data.frame(GLM = adj_p_vals_without_tissue, GLM2 = adj_p_vals_with_tissue)

# Create a scatter plot to compare p-values
ggplot(comparison_df, aes(x = GLM, y = GLM2)) +
  geom_point(size = 2, color = "dodgerblue1") +
  geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "red") +
  labs(x = "P-values (GLM)", y = "P-values (GLM2)",
       title = "Comparison of P-values between GLM and GLM2") +
  theme_minimal()

#Q7 explanation You can see how the addition of the tissue covariate impacts the importance of each gene by contrasting the two separate graphs. Points below the red dashed line in the comparison plot denote genes whose p-value dropped when the tissue covariate was included, whereas points above the line denote genes whose p-value increased. It is possible that taking tissue type into account enhances model fit and yields a more precise evaluation of differential expression if a gene’s p-value falls with tissue covariate inclusion. On the other hand, a higher p-value could mean that tissue type has a different influence.

Coursework

Mona

2023-11-28