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$breaks[-c(1,2)] # remove 0
g.probs <- g.hist$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$breaks[-c(1,2,3)] # remove 0
g.probs <- g.hist$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$density[-1] # make lengths match
# Need to clean up probabilities that are 0
nz.probs.mask <- g.probs!=0
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.probs[nz.probs.mask]
plot(log(g.breaks.clean), log(g.probs.clean))
g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
summary(g.fit)
alpha.LM <- coef(g.fit)[2]
lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3, lwd=3)
################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean/kmin))
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4, lwd=3)
plot(log(g.breaks.clean), log(g.probs.clean))
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.probs[nz.probs.mask]
plot(log(g.breaks.clean), log(g.probs.clean))
# Lab 9 for the University of Tulsa's CS-6643 Bioinformatics Course
# Pairwise Sequence Alignment with Dynamic Programming
# Professor: Dr. McKinney, Fall 2022
# Noah L. Schrick - 1492657
## Set Working Directory to file directory - RStudio approach
setwd(dirname(rstudioapi::getActiveDocumentContext()$path))
#### Part A: Specifying the Input
## Score Rules and Seqs
x_str <- "ATAC"   # side sequence
y_str <- "GTGTAC" # top sequence
match_score <- 3
mismatch_score <- -1
gap_penalty <- -4
## Substitution Matrix
dna.letters<-c("A","C","G","T")
num.letters <- length(dna.letters)
S<-data.frame(matrix(0,nrow=num.letters,ncol=num.letters))  # data frame
rownames(S)<-dna.letters; colnames(S)<-dna.letters
for (i in 1:4){
for (j in 1:4){
if(dna.letters[i]==dna.letters[j]){
S[i,j]<- match_score
}
else{
S[i,j]<- mismatch_score
}
}
}
len(S)
size(S)
nrows(S)
nrow(S)
col(S)
S
S[A][T]
S[A,T]
S
S[A]
S.A
S.at(A)
S[1.1]
S[1,1]
S["A", "T"]
dna.letters("A")
dna.letters
?index()
match("A", dna.letters)
match("T", dna.letters)
S[1,4]