lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3)
################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean)/kmin)
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4)
# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
# Degree Distribution
# Professor: Dr. McKinney, Spring 2022
# Noah Schrick - 1492657
library(igraph)
library(igraphdata)
data(yeast)
g <- yeast
g.netname <- "Yeast"
################# Set up Work #################
g.vec <- degree(g)
g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
" Network"))
legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
"Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6",
"#006CD1", "#E66100", "#D35FB7"))
g.mean <- mean(g.vec)
g.seq <- 0:max(g.vec) # x-axis
################# Guessing Alpha #################
alpha.guess <- 1.5
lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1)
################# Poisson #################
g.pois <- dpois(g.seq, g.mean, log=F)
lines(g.seq, g.pois, col="#006CD1", lty=2)
################# Linear model: Least-Squares Fit #################
g.breaks <- g.hist$breaks[-c(1,2,3)] # remove 0
g.probs <- g.hist$density[-1] # make lengths match
# Need to clean up probabilities that are 0
nz.probs.mask <- g.probs!=0
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.breaks[nz.probs.mask]
#plot(log(g.breaks.clean), log(g.probs.clean))
g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
summary(g.fit)
alpha.LM <- coef(g.fit)[2]
lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3)
################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean)/kmin)
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4)
# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
# Degree Distribution
# Professor: Dr. McKinney, Spring 2022
# Noah Schrick - 1492657
library(igraph)
library(igraphdata)
data(yeast)
g <- yeast
g.netname <- "Yeast"
################# Set up Work #################
g.vec <- degree(g)
g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
" Network"))
legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
"Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6",
"#006CD1", "#E66100", "#D35FB7"))
g.mean <- mean(g.vec)
g.seq <- 0:max(g.vec) # x-axis
################# Guessing Alpha #################
alpha.guess <- 1.5
lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1)
################# Poisson #################
g.pois <- dpois(g.seq, g.mean, log=F)
lines(g.seq, g.pois, col="#006CD1", lty=2)
################# Linear model: Least-Squares Fit #################
g.breaks <- g.hist$breaks[-c(1)] # remove 0
g.probs <- g.hist$density[-1] # make lengths match
# Need to clean up probabilities that are 0
nz.probs.mask <- g.probs!=0
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.breaks[nz.probs.mask]
#plot(log(g.breaks.clean), log(g.probs.clean))
g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
summary(g.fit)
alpha.LM <- coef(g.fit)[2]
lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3)
################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean)/kmin)
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4)
# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
# Degree Distribution
# Professor: Dr. McKinney, Spring 2022
# Noah Schrick - 1492657
library(igraph)
library(igraphdata)
data(yeast)
g <- yeast
g.netname <- "Yeast"
################# Set up Work #################
g.vec <- degree(g)
g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
" Network"))
legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
"Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6",
"#006CD1", "#E66100", "#D35FB7"))
g.mean <- mean(g.vec)
g.seq <- 0:max(g.vec) # x-axis
################# Guessing Alpha #################
alpha.guess <- 1.5
lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1)
################# Poisson #################
g.pois <- dpois(g.seq, g.mean, log=F)
lines(g.seq, g.pois, col="#006CD1", lty=2)
################# Linear model: Least-Squares Fit #################
#g.breaks <- g.hist$breaks[-c(1)] # remove 0
g.breaks <- g.hist$breaks # remove 0
g.probs <- g.hist$density[-1] # make lengths match
# Need to clean up probabilities that are 0
nz.probs.mask <- g.probs!=0
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.breaks[nz.probs.mask]
#plot(log(g.breaks.clean), log(g.probs.clean))
g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
summary(g.fit)
alpha.LM <- coef(g.fit)[2]
lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3)
################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean)/kmin)
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4)
# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
# Degree Distribution
# Professor: Dr. McKinney, Spring 2022
# Noah Schrick - 1492657
library(igraph)
library(igraphdata)
data(yeast)
g <- yeast
g.netname <- "Yeast"
################# Set up Work #################
g.vec <- degree(g)
g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
" Network"))
legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
"Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6",
"#006CD1", "#E66100", "#D35FB7"))
g.mean <- mean(g.vec)
g.seq <- 0:max(g.vec) # x-axis
################# Guessing Alpha #################
alpha.guess <- 1.5
lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1)
################# Poisson #################
g.pois <- dpois(g.seq, g.mean, log=F)
lines(g.seq, g.pois, col="#006CD1", lty=2)
################# Linear model: Least-Squares Fit #################
g.breaks <- g.hist$breaks[-c(1)] # remove 0
g.probs <- g.hist$density[-1] # make lengths match
# Need to clean up probabilities that are 0
nz.probs.mask <- g.probs!=0
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.probs[nz.probs.mask]
#plot(log(g.breaks.clean), log(g.probs.clean))
g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
summary(g.fit)
alpha.LM <- coef(g.fit)[2]
lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3)
################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean)/kmin)
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4)
alpha.LM
# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
# Degree Distribution
# Professor: Dr. McKinney, Spring 2022
# Noah Schrick - 1492657
library(igraph)
library(igraphdata)
data(yeast)
g <- yeast
g.netname <- "Yeast"
################# Set up Work #################
g.vec <- degree(g)
g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
" Network"))
legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
"Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6",
"#006CD1", "#E66100", "#D35FB7"))
g.mean <- mean(g.vec)
g.seq <- 0:max(g.vec) # x-axis
################# Guessing Alpha #################
alpha.guess <- 1.5
lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1)
################# Poisson #################
g.pois <- dpois(g.seq, g.mean, log=F)
lines(g.seq, g.pois, col="#006CD1", lty=2)
################# Linear model: Least-Squares Fit #################
g.breaks <- g.hist$breaks[-c(1)] # remove 0
g.probs <- g.hist$density[-1] # make lengths match
# Need to clean up probabilities that are 0
nz.probs.mask <- g.probs!=0
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.probs[nz.probs.mask]
#plot(log(g.breaks.clean), log(g.probs.clean))
g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
summary(g.fit)
alpha.LM <- coef(g.fit)[2]
lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3)
################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean/kmin))
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4)
# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
# Degree Distribution
# Professor: Dr. McKinney, Spring 2022
# Noah Schrick - 1492657
library(igraph)
library(igraphdata)
data(yeast)
g <- yeast
g.netname <- "Yeast"
################# Set up Work #################
g.vec <- degree(g)
g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
" Network"))
legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
"Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6",
"#006CD1", "#E66100", "#D35FB7"))
g.mean <- mean(g.vec)
g.seq <- 0:max(g.vec) # x-axis
################# Guessing Alpha #################
alpha.guess <- 1.5
lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1, lwd=5)
################# Poisson #################
g.pois <- dpois(g.seq, g.mean, log=F)
lines(g.seq, g.pois, col="#006CD1", lty=2)
################# Linear model: Least-Squares Fit #################
g.breaks <- g.hist$breaks[-c(1)] # remove 0
g.probs <- g.hist$density[-1] # make lengths match
# Need to clean up probabilities that are 0
nz.probs.mask <- g.probs!=0
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.probs[nz.probs.mask]
#plot(log(g.breaks.clean), log(g.probs.clean))
g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
summary(g.fit)
alpha.LM <- coef(g.fit)[2]
lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3)
################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean/kmin))
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4)
# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
# Degree Distribution
# Professor: Dr. McKinney, Spring 2022
# Noah Schrick - 1492657
library(igraph)
library(igraphdata)
data(yeast)
g <- yeast
g.netname <- "Yeast"
################# Set up Work #################
g.vec <- degree(g)
g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
" Network"))
legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
"Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6",
"#006CD1", "#E66100", "#D35FB7"))
g.mean <- mean(g.vec)
g.seq <- 0:max(g.vec) # x-axis
################# Guessing Alpha #################
alpha.guess <- 1.5
lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1, lwd=3)
################# Poisson #################
g.pois <- dpois(g.seq, g.mean, log=F)
lines(g.seq, g.pois, col="#006CD1", lty=2)
################# Linear model: Least-Squares Fit #################
g.breaks <- g.hist$breaks[-c(1)] # remove 0
g.probs <- g.hist$density[-1] # make lengths match
# Need to clean up probabilities that are 0
nz.probs.mask <- g.probs!=0
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.probs[nz.probs.mask]
#plot(log(g.breaks.clean), log(g.probs.clean))
g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
summary(g.fit)
alpha.LM <- coef(g.fit)[2]
lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3)
################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean/kmin))
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4)
# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
# Degree Distribution
# Professor: Dr. McKinney, Spring 2022
# Noah Schrick - 1492657
library(igraph)
library(igraphdata)
data(yeast)
g <- yeast
g.netname <- "Yeast"
################# Set up Work #################
g.vec <- degree(g)
g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
" Network"))
legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
"Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6",
"#006CD1", "#E66100", "#D35FB7"))
g.mean <- mean(g.vec)
g.seq <- 0:max(g.vec) # x-axis
################# Guessing Alpha #################
alpha.guess <- 1.5
lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1, lwd=3)
################# Poisson #################
g.pois <- dpois(g.seq, g.mean, log=F)
lines(g.seq, g.pois, col="#006CD1", lty=2, lwd=3)
################# Linear model: Least-Squares Fit #################
g.breaks <- g.hist$breaks[-c(1)] # remove 0
g.probs <- g.hist$density[-1] # make lengths match
# Need to clean up probabilities that are 0
nz.probs.mask <- g.probs!=0
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.probs[nz.probs.mask]
#plot(log(g.breaks.clean), log(g.probs.clean))
g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
summary(g.fit)
alpha.LM <- coef(g.fit)[2]
lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3, lwd=3)
################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean/kmin))
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4, lwd=3)
plot(yeast)
hist(yeast)
hist(g.vec)
g.pois
g.mean
alpha.LM
alpha.ML
degree(g)
sort(degree(g))
sort(degree(g),decreasing=FALSE)
sort(degree(g),decreasing=F)
sort(degree(g),decreasing=false)
sort(degree(g), decreasing = TRUE)
head(sort(degree(g), decreasing = TRUE))
stddev(degree(g))
sd(degree(g))
tail(sort(degree(g), decreasing = TRUE))
plot(log(g.breaks.clean), log(g.probs.clean))
# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
# Degree Distribution
# Professor: Dr. McKinney, Spring 2022
# Noah Schrick - 1492657
library(igraph)
library(igraphdata)
data(yeast)
g <- yeast
g.netname <- "Yeast"
################# Set up Work #################
g.vec <- degree(g)
g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
" Network"))
legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
"Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6",
"#006CD1", "#E66100", "#D35FB7"))
g.mean <- mean(g.vec)
g.seq <- 0:max(g.vec) # x-axis
################# Guessing Alpha #################
alpha.guess <- 1.5
lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1, lwd=3)
################# Poisson #################
g.pois <- dpois(g.seq, g.mean, log=F)
lines(g.seq, g.pois, col="#006CD1", lty=2, lwd=3)
################# Linear model: Least-Squares Fit #################
g.breaks <- g.hist$breaks[-c(1)] # remove 0
g.probs <- g.hist$density[-1] # make lengths match
# Need to clean up probabilities that are 0
nz.probs.mask <- g.probs!=0
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.probs[nz.probs.mask]
plot(log(g.breaks.clean), log(g.probs.clean))
g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
summary(g.fit)
alpha.LM <- coef(g.fit)[2]
lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3, lwd=3)
################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean/kmin))
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4, lwd=3)
plot(log(g.breaks.clean), log(g.probs.clean))
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.probs[nz.probs.mask]
plot(log(g.breaks.clean), log(g.probs.clean))
#### Part B: Loop Recursion Warmup
m <- 3 # row edges
n <- 6 # col edges
path_matrix <- matrix(1, nrow=m+1, ncol=n+1)
for (i in seq(2,m+1)){
for (j in seq(2, n+1)){
path_matrix[i,j] <- path_matrix[i-1,j] + path_matrix[i,j-1]
}
}
path_matrix
path_matrix[m][n]
path_matrix[m]
path_matrix[n]
path_matrix[m,n]
path_matrix[m+1,n+1]
calc.num.paths <- function(n,m){
path_matrix <- matrix(1, nrow=m+1, ncol=n+1)
for (i in seq(2,m+1)){
for (j in seq(2, n+1)){
path_matrix[i,j] <- path_matrix[i-1,j] + path_matrix[i,j-1]
}
}
path_matrix[m+1,n+1]
}
#### Part B: Loop Recursion Warmup
calc.num.paths <- function(n,m){
path_matrix <- matrix(1, nrow=m+1, ncol=n+1)
for (i in seq(2,m+1)){
for (j in seq(2, n+1)){
path_matrix[i,j] <- path_matrix[i-1,j] + path_matrix[i,j-1]
}
}
path_matrix[m+1,n+1]
}
m <- 5 # row edges
n <- 5 # col edges
calc.num.paths(n,m)
m <- 5 # row edges
n <- 6 # col edges
calc.num.paths(n,m)
m <- 10 # row edges
n <- 10 # col edges
calc.num.paths(n,m)
factorial(n+m)/(factorial(n)*factorial(m))
m <- 5 # row edges
n <- 5 # col edges
calc.num.paths(n,m)
factorial(n+m)/(factorial(n)*factorial(m))
m <- 5 # row edges
n <- 6 # col edges
calc.num.paths(n,m)
factorial(n+m)/(factorial(n)*factorial(m))
m <- 10 # row edges
n <- 10 # col edges
calc.num.paths(n,m)
factorial(n+m)/(factorial(n)*factorial(m))
h1n1.Cali
h1n1.Cali.dna.vec <- fasta2vec("FJ969540.1.fasta")
#### Part A: EMBOSS pairwise alignment server and influenza
## Load associated supportive libraries
if (!require("seqinr")) install.packages("seqinr")
library(seqinr)
## Load in the fasta file
fasta2vec <- function(fasta.file){
if (!require("seqinr")) install.packages("seqinr")
library(seqinr)
fasta <- read.fasta(file=fasta.file, as.string= TRUE)
fasta.string <- fasta[[1]][1]
fasta.list <- strsplit(fasta.string,"")
fasta.vec <- unlist(fasta.list)
}
h1n1.Cali.dna.vec <- fasta2vec("FJ969540.1.fasta")
## Set Working Directory to file directory - RStudio approach
setwd(dirname(rstudioapi::getActiveDocumentContext()$path))
h1n1.Cali.dna.vec <- fasta2vec("FJ969540.1.fasta")
h1n1.Cali.dna.vec[1:5]
?count
count(h1n1.Cali.dna.vec[1:5],2)
count(h1n1.Cali.dna.vec[1:5],2)["aa"]
count(h1n1.Cali.dna.vec[1:5],11)
count(h1n1.Cali.dna.vec[1:5],1)
#### Part C: Dinucleotide Signals
calc.sliding.cpg <- function(fastaVec, slideWin){
# allocate memory for odds ratio output
cg_dinuc_oddsRatio <- double()
n<-length(fastaVec)
for (i in 1:(n-slideWin)){
# array slice the vectpr on sliding window size and obtain dinuc appearances
dinucs<-count(fastaVec[i:(i+slideWin)],2)
# retrieve number of times "CG" appeared
cg_dinuc_count <- dinucs["cg"]
# get counts of all nucleotides
nucs<-count(fastaVec[i:(i+slideWin)],1)
# obtain times dinuc pairing appeared per times the indiv nucs appeared
cg_dinuc_oddsRatio[i] <-
cg_dinuc_count/(nucs["c"]*nucs["g"])
}
return(cg_dinuc_oddsRatio) # returns vector
}
apoe.fasta.vec <- fasta2vec("apoe.fasta")
cpg_vec <- calc.sliding.cpg(apoe.fasta.vec,150)
plot(cpg_vec,type="l",main="Observed vs Expected CG",xlab="Base Index", ylab="Obs/Exp")
cpg_vec