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))
BiocManager::install()
simDats <- createSimulation2(data.type = "discrete", avg.maf = 0.2, sim.type = "mainEffect",
pct.train = 0.5, pct.holdout = 0.5, pct.validation = 0,
main.bias = 0.4, pct.signals = 0.2)
# npdro::createSimulation2() example for gwas simulation
library(npdro)
# npdro::createSimulation2() example for gwas simulation
if (!require("npdro")) install.packages("npdro")
library(npdro)
# npdro::createSimulation2() example for gwas simulation
install_github("insilico/npdro")
# npdro::createSimulation2() example for gwas simulation
if (!require("devtools")) install.packages("devtools")
library(devtools)
install_github("insilico/npdro")
# npdro::createSimulation2() example for gwas simulation
if (!require("devtools")) install.packages("devtools")
#### Part A: Haemodynamic response functions (HRF) and block design
## Plot Basic HRF from 0-20s
hq <- function(t,q=4){
# q=4 or 5, where 5 has more of a delay
return (t^q * exp(-t)/(q^q * exp(-q)))
}
# use seq to create vector time and use hq to create hrf vectors
time <- seq(1,20)
time
# use seq to create vector time and use hq to create hrf vectors
time <- seq(0,20)
hq
# use seq to create vector time and use hq to create hrf vectors
time <- seq(0,20)
hrf1 <- hq(time)
hrf2 <- hq(time, 5)
# plot
plot(time,hrf1,type="l")
lines(time,hrf2,col="red")
## Deconvolve with task onset times
# grabbed from afni c code
# basis_block_hrf4 from 3dDeconvolve.c
HRF <- function(t, d){
if (t<0){
y=0.0
}else{
y = 1/256*exp(4-t)*(-24-24*t-12*t^2-4*t^3-t^4 + exp(min(d,t))*(24+24*(t-min(d,t)) + 12*(t-min(d,t))^2+4*(t-min(d,t))^3+(t-min(d,t))^4))
}
return(y)
}
t=seq(0,360,len=360)
onsets=c(14,174,254)
blocks.model = double()
for (curr_t in t){
summed_hrf=0.0
for (start in onsets){
summed_hrf=summed_hrf+HRF(curr_t-start,20)
}
blocks.model = c(blocks.model,summed_hrf)
}
plot(blocks.model,type="l")
plot(blocks.model, type="l")
lines(time,hrf1,col="red")
pwd
ls
voxel_time <- scan("059_069_025.1D", character(), quote = "\n")
## Set Working Directory to file directory - RStudio approach
setwd(dirname(rstudioapi::getActiveDocumentContext()$path))
voxel_time <- scan("059_069_025.1D", character(), quote = "\n")
voxel_time
plot(blocks.model, type="l")
lines(voxel_time,hrf1,col="red")
voxel_time <- scan("059_069_025.1D", character(), quote = "\n")
t=seq(0,max(voxel_time))
blocks.model = double()
for (curr_t in voxel_time){
summed_hrf=0.0
for (start in onsets){
summed_hrf=summed_hrf+HRF(curr_t-start,20)
}
blocks.model = c(blocks.model,summed_hrf)
}
for (curr_t in t){
summed_hrf=0.0
for (start in onsets){
summed_hrf=summed_hrf+HRF(curr_t-start,20)
}
blocks.model = c(blocks.model,summed_hrf)
}
plot(blocks.model,type="l")
blocks.model = double()
for (curr_t in t){
summed_hrf=0.0
for (start in voxel_time){
summed_hrf=summed_hrf+HRF(curr_t-start,20)
}
blocks.model = c(blocks.model,summed_hrf)
}
voxel_time
onsets
class(onsets)
class(voxel_time)
voxel_time <- as.numeric(scan("059_069_025.1D", character(), quote = "\n"))
t=seq(0,max(voxel_time))
blocks.model = double()
for (curr_t in t){
summed_hrf=0.0
for (start in voxel_time){
summed_hrf=summed_hrf+HRF(curr_t-start,20)
}
blocks.model = c(blocks.model,summed_hrf)
}
plot(blocks.model,type="l")
## Plot voxel time series data and the block design curve
voxel.data <- read.delim("059_069_025.1D")
plot(seq(1,2*dim(voxel.data)[1],by=2),t(voxel.data),
type="l", xlab="time",ylab="intensity")
# normalize the height of the blocks model
blocks.normal <- max(voxel.data)*blocks.model/max(blocks.model)
lines(blocks.normal,type="l",col="red")
# regression
length(blocks.normal) # too long
dim(voxel.data)[1]
# grab elements from blocks.normal to make a vector same as data
blocks.norm.subset <- blocks.normal[seq(1,length(blocks.normal),len=dim(voxel.data)[1])]
length(blocks.norm.subset)
voxel.data.vec <- matrix(unlist(voxel.data),ncol=1)
plot(blocks.norm.subset,voxel.data.vec,
xlab="block model",ylab="voxel data",main="regression fit")
plot(seq(1,2*dim(voxel.data)[1],by=2),t(voxel.data),
type="l", xlab="time",ylab="intensity")
# normalize the height of the blocks model
blocks.normal <- max(voxel.data)*blocks.model/max(blocks.model)
lines(blocks.normal,type="l",col="red")
# regression
length(blocks.normal) # too long
dim(voxel.data)[1]
# grab elements from blocks.normal to make a vector same as data
blocks.norm.subset <- blocks.normal[seq(1,length(blocks.normal),len=dim(voxel.data)[1])]
length(blocks.norm.subset)
voxel.data.vec <- matrix(unlist(voxel.data),ncol=1)
# use lm to create voxel.fit <- lm...
voxel.fit <- lm(voxel.data.vec ~ blocks.norm.subset)
plot(blocks.norm.subset,voxel.data.vec,
xlab="block model",ylab="voxel data",main="regression fit")
# use abline(voxel.fit) to overlay a line with fit coefficients
abline(voxel.fit)
voxel.data.vec <- matrix(unlist(voxel.data),ncol=1)
length(blocks.norm.subset)
voxel.data.vec <- matrix(unlist(voxel.data),ncol=1)
length(voxel.data.vec)
plot(blocks.norm.subset,voxel.data.vec,
xlab="block model",ylab="voxel data",main="regression fit")
plot(blocks.norm.subset,voxel.data.vec,
xlab="block model",ylab="voxel data",main="regression fit")
blocks.norm.subset
voxel.data.vec
voxel.fit <- lm(blocks.norm.subet ~ voxel.data.vec)
voxel.fit <- lm(blocks.norm.subset ~ voxel.data.vec)
# use abline(voxel.fit) to overlay a line with fit coefficients
abline(voxel.fit)
## Plot voxel time series data and the block design curve
voxel.data <- read.delim("059_069_025.1D")
plot(seq(1,2*dim(voxel.data)[1],by=2),t(voxel.data),
type="l", xlab="time",ylab="intensity")
# use lm to create voxel.fit <- lm...
voxel.fit <- lm(voxel.data.vec ~ blocks.norm.subset)
plot(blocks.norm.subset,voxel.data.vec,
xlab="block model",ylab="voxel data",main="regression fit")
# use abline(voxel.fit) to overlay a line with fit coefficients
abline(voxel.fit)
voxel.fitr
voxel.fit
voxel.data
blocks.normal
blocks.model
max(blocks.model)
t=seq(0,360,len=360)
onsets=c(14,174,254)
blocks.model = double()
for (curr_t in t){
summed_hrf=0.0
for (start in onsets){
summed_hrf=summed_hrf+HRF(curr_t-start,20)
}
blocks.model = c(blocks.model,summed_hrf)
}
plot(blocks.model,type="l")
## Plot voxel time series data and the block design curve
voxel.data <- read.delim("059_069_025.1D")
plot(seq(1,2*dim(voxel.data)[1],by=2),t(voxel.data),
type="l", xlab="time",ylab="intensity")
# normalize the height of the blocks model
blocks.normal <- max(voxel.data)*blocks.model/max(blocks.model)
lines(blocks.normal,type="l",col="red")
# regression
length(blocks.normal) # too long
# Lab 11 for the University of Tulsa's CS-6643 Bioinformatics Course
# Introduction to fMRI Analysis and ICA
# Professor: Dr. McKinney, Fall 2022
# Noah L. Schrick - 1492657
## Set Working Directory to file directory - RStudio approach
setwd(dirname(rstudioapi::getActiveDocumentContext()$path))
#### Part A: Haemodynamic response functions (HRF) and block design
## Plot Basic HRF from 0-20s
hq <- function(t,q=4){
# q=4 or 5, where 5 has more of a delay
return (t^q * exp(-t)/(q^q * exp(-q)))
}
# use seq to create vector time and use hq to create hrf vectors
time <- seq(0,20)
hrf1 <- hq(time)
hrf2 <- hq(time, 5)
# plot
plot(time,hrf1,type="l")
lines(time,hrf2,col="red")
## Deconvolve with task onset times
# grabbed from afni c code
# basis_block_hrf4 from 3dDeconvolve.c
HRF <- function(t, d){
if (t<0){
y=0.0
}else{
y = 1/256*exp(4-t)*(-24-24*t-12*t^2-4*t^3-t^4 + exp(min(d,t))*(24+24*(t-min(d,t)) + 12*(t-min(d,t))^2+4*(t-min(d,t))^3+(t-min(d,t))^4))
}
return(y)
}
t=seq(0,360,len=360)
onsets=c(14,174,254)
blocks.model = double()
for (curr_t in t){
summed_hrf=0.0
for (start in onsets){
summed_hrf=summed_hrf+HRF(curr_t-start,20)
}
blocks.model = c(blocks.model,summed_hrf)
}
plot(blocks.model,type="l")
## Plot voxel time series data and the block design curve
voxel.data <- read.delim("059_069_025.1D")
plot(seq(1,2*dim(voxel.data)[1],by=2),t(voxel.data),
type="l", xlab="time",ylab="intensity")
# normalize the height of the blocks model
blocks.normal <- max(voxel.data)*blocks.model/max(blocks.model)
lines(blocks.normal,type="l",col="red")
# regression
length(blocks.normal) # too long
dim(voxel.data)[1]
# grab elements from blocks.normal to make a vector same as data
blocks.norm.subset <- blocks.normal[seq(1,length(blocks.normal),len=dim(voxel.data)[1])]
length(blocks.norm.subset)
voxel.data.vec <- matrix(unlist(voxel.data),ncol=1)
# use lm to create voxel.fit <- lm...
voxel.fit <- lm(voxel.data.vec ~ blocks.norm.subset)
plot(blocks.norm.subset,voxel.data.vec,
xlab="block model",ylab="voxel data",main="regression fit")
# use abline(voxel.fit) to overlay a line with fit coefficients
abline(voxel.fit)
# Lab 11 for the University of Tulsa's CS-6643 Bioinformatics Course
# Introduction to fMRI Analysis and ICA
# Professor: Dr. McKinney, Fall 2022
# Noah L. Schrick - 1492657
## Set Working Directory to file directory - RStudio approach
setwd(dirname(rstudioapi::getActiveDocumentContext()$path))
#### Part A: Haemodynamic response functions (HRF) and block design
## Plot Basic HRF from 0-20s
hq <- function(t,q=4){
# q=4 or 5, where 5 has more of a delay
return (t^q * exp(-t)/(q^q * exp(-q)))
}
# use seq to create vector time and use hq to create hrf vectors
time <- seq(0,20)
hrf1 <- hq(time)
hrf2 <- hq(time, 5)
# plot
plot(time,hrf1,type="l")
lines(time,hrf2,col="red")
## Deconvolve with task onset times
# grabbed from afni c code
# basis_block_hrf4 from 3dDeconvolve.c
HRF <- function(t, d){
if (t<0){
y=0.0
}else{
y = 1/256*exp(4-t)*(-24-24*t-12*t^2-4*t^3-t^4 + exp(min(d,t))*(24+24*(t-min(d,t)) + 12*(t-min(d,t))^2+4*(t-min(d,t))^3+(t-min(d,t))^4))
}
return(y)
}
t=seq(0,360,len=360)
onsets=c(14,174,254)
blocks.model = double()
for (curr_t in t){
summed_hrf=0.0
for (start in onsets){
summed_hrf=summed_hrf+HRF(curr_t-start,20)
}
blocks.model = c(blocks.model,summed_hrf)
}
plot(blocks.model,type="l")
## Plot voxel time series data and the block design curve
voxel.data <- read.delim("059_069_025.1D")
plot(seq(1,2*dim(voxel.data)[1],by=2),t(voxel.data),
type="l", xlab="time",ylab="intensity")
# normalize the height of the blocks model
blocks.normal <- max(voxel.data)*blocks.model/max(blocks.model)
lines(blocks.normal,type="l",col="red")
# regression
length(blocks.normal) # too long
dim(voxel.data)[1]
# grab elements from blocks.normal to make a vector same as data
blocks.norm.subset <- blocks.normal[seq(1,length(blocks.normal),len=dim(voxel.data)[1])]
length(blocks.norm.subset)
voxel.data.vec <- matrix(unlist(voxel.data),ncol=1)
# use lm to create voxel.fit <- lm...
voxel.fit <- lm(voxel.data.vec ~ blocks.norm.subset)
plot(blocks.norm.subset,voxel.data.vec,
xlab="block model",ylab="voxel data",main="regression fit")
# use abline(voxel.fit) to overlay a line with fit coefficients
abline(voxel.fit)
blocks.model
count(blocks.model > 1)
which(blocks.model > 1)
sum(blocks.model < 1)
length(blocks.model)
100* sum(blocks.model < 1)/length(blocks.model)
#### Part B: Resting state fMRI visualization, multidimensional arrays and independent component analysis (ICA).
## example: multi-dimensional array
#                        2 3x4 matrices
multArray <- array(1:24,dim=c(3,4,2))
dim(multArray)
multArray[,,1] # matrix 1
multArray[,,2] # matrix 2
image(multArray[,,1]) # plot slice 1
image(multArray[,,2]) # plot slice 2
dim(multArray)
size(multArray)
length(multArray)
multArray
multArray[,,1] # matrix 1
multArray[,,2] # matrix 2
image(multArray[,,1]) # plot slice 1
image(multArray[,,2]) # plot slice 2
image(multArray[,,1]) # plot slice 1
image(multArray[,,2]) # plot slice 2
## Neuroimaging Informatics Technology Initiative
if (!require("fastICA")) install.packages("fastICA")
if (!require("AnalyzeFMRI")) install.packages("AnalyzeFMRI")
if (!require("fmri")) install.packages("fmri")
#    If this fails, try library(devtools) (install.packages("devtools"))
#    and then install_github(https://github.com/cran/fmri.git)
library(fmri)
## Neuroimaging Informatics Technology Initiative
if (!require("fastICA")) install.packages("fastICA")
if (!require("AnalyzeFMRI")) install.packages("AnalyzeFMRI")
install.packages("R.matlab")
install.packages("Biostrings")
BiocManager::install("Biostrings")
BiocManager::install("Biostrings")
BiocManager::install("AnalyzeFMRI")
BiocManager::install()
if (!require("fmri")) install.packages("fmri")
if (!require("fmri")) install.packages("aws")
if (!require("fmri")) install.packages("gsl")
install.packages("gsl")
install.packages("GSL")
install_github(https://github.com/cran/fmri.git)
install_github("https://github.com/cran/fmri.git")
#    If this fails, try library(devtools) (install.packages("devtools"))
#    and then install_github(https://github.com/cran/fmri.git)
if (!require("devtools")) install.packages("devtools")
library(devtools)
install_github("https://github.com/cran/fmri.git")
install_github("https://github.com/cran/aws.git")
install_github("https://github.com/cran/gsl.git")
#    If this fails, try library(devtools) (insta
install.packages("gsl")
install.packages("fmri")
if (!require("AnalyzeFMRI")) install.packages("AnalyzeFMRI")
if (!require("fastICA")) install.packages("fastICA")
library(fastICA)
# read in 4d nifti
# uses fmri library, takes about 3min to load
img <- read.NIFTI("rest_res2standard.nii")
library(fmri)
# read in 4d nifti
# uses fmri library, takes about 3min to load
img <- read.NIFTI("rest_res2standard.nii")
mask <- img$mask  # Boolean mask for brain voxels
dim(mask)
ttt <- extractData(img) # extract 4d data cube
numScans <- dim(ttt)[4]
# plot a voxel's time series
plot(ttt[30,30,30,],type="l",xlab="time",ylab="activity")
length(ttt)
ttt
dim(ttt)
length(ttt)
numScans
## Plot a 2D Slice
yslice <- 35
scan2dslice <- ttt[,yslice,,50] # grab 2d slice at t=50
image(scan2dslice,main="no masking") # no mask
# mask it off
slice.mask <- mask[,yslice,]
scan2dslice[slice.mask] <- NA # NA's become white
image(scan2dslice,main="masked")
mask
slice.mask
## ICA
t1 <- Sys.time() # for timing purposes
dataMat <- NULL
for(t in seq(1,numScans)){
scan <- ttt[,,,t]
# stretched out the 61x73x61 3d matrix into one row
# apply mask and stack
dataMat <- rbind(dataMat,scan[mask])
}
t2 <- Sys.time()
difftime(t2,t1) # 3 minutes
dim(dataMat)
dataMat
dataMat[1,]
dataMat[99,]
## ICA analysis
# input X: rows observations (voxels) and cols variables (time)
X <- t(dataMat)
m <- 20 # specify number of ICA components
t1<-Sys.time()
f<-fastICA(X,n.comp=m,method="C")
t2<-Sys.time()
difftime(t2,t1) # 1.23min
# S=XKW,
# K is a pre-whitening PCA matrix (components by time)
# S is the matrix of m ICAs (columns of S are spatial signals)
# S has dimensions voxel x components
S<-f$S  # you can find K and W with $
S
dim(S)
dim(f$K)
dim(f$W)
ica.comp <- 5 # look at 5th component
# plot the 5th time ICA
plot(f$K[,ica.comp],type="l",xlab="time",ylab="signal",main="ICA component")
# threshold S matrix
theta <- 2
S[S<=theta] <- NA
# turn S back into 4d multidimensional array
xdim<-dim(ttt)[1]
ydim<-dim(ttt)[2]
zdim<-dim(ttt)[3]
ica.4dArray <- array(matrix(S,ncol=1),dim=c(xdim,ydim,zdim,m))
dim(ica.4dArray) # 61x73x61x10
yslice <- 35
# grab 2d slice at y=yslice and ica 5
ica2dslice <- ica.4dArray[,yslice,,ica.comp]
image(ica2dslice,main="ica component (spatial locations)")