# Contents

!!!Caution work in progress!!!

# 1 Introduction

Function optimizes Extraction windows so we have the same number of precursor per window. To do it uses spectral library or nonredundant blib.

# 2 Prerequisites

specL contains a function specL::cdsw.

# 3 Classical Method based on quantile

# moves the windows start and end to regions where no peaks are observed
.makenewfromto <- function( windfrom, empty , isfrom=TRUE){
newfrom <- NULL
for(from in windfrom){
idx <- which.min(abs(from - empty))
startmass <- 0
if(isfrom){
if(empty[idx] < from) {
startmass <- empty[idx]
} else {
startmass <- empty[idx-1]
}
}else{
if(empty[idx] > from) {
startmass <- empty[idx]
} else {
startmass <- empty[idx+1]
}
}
newfrom <- c(newfrom, round(startmass,digits=1))
}
return(newfrom)
}

.cdsw_compute_breaks <-
function(xx, nbins){
q <- quantile(xx, seq(0, 1, length = nbins + 1))
q[1] <- q[1] - 0.5
q[length(q)] <- q[length(q)] + 0.5
q <- round(q)
}

cdsw <-
function(x, massrange = c(300,1250), n = 20, overlap = 1.0, FUN, ...) {
if (class(x) == "psmSet") {
x <- unlist(lapply(x, function(x) {
x\$pepmass
}))
} else if (class(x) == 'specLSet') {
x <- unlist(lapply(x@ionlibrary, function(xx) {
xx@q1
}))
}
# x should be numeric
if (class(x) != "numeric") {
warning("can not compute quantils. 'x' is not numeric.")
return (NULL)
}

x <- x[x > massrange[1] & x < massrange[2]]

q <- FUN(xx=x, nbins=n)

idx <- 1:n
from <- q[idx] - overlap * 0.5
to <- q[idx + 1] + overlap * 0.5
width <- 0.5 * (to - from)
mid <- from + width
h <- hist(x, breaks = q, ...)
data.frame(from, to, mid, width, counts = h\$counts)

}
cdsw(exampledata,
freq=TRUE,
overlap = 0,
main = "peptideStd", xlab='pepmass', FUN=.cdsw_compute_breaks)

##     from   to    mid width counts
## 0%   301  384  342.5  41.5    586
## 5%   384  420  402.0  18.0    591
## 10%  420  449  434.5  14.5    583
## 15%  449  476  462.5  13.5    599
## 20%  476  500  488.0  12.0    565
## 25%  500  524  512.0  12.0    604
## 30%  524  547  535.5  11.5    566
## 35%  547  572  559.5  12.5    598
## 40%  572  598  585.0  13.0    591
## 45%  598  625  611.5  13.5    577
## 50%  625  651  638.0  13.0    603
## 55%  651  682  666.5  15.5    575
## 60%  682  713  697.5  15.5    594
## 65%  713  745  729.0  16.0    574
## 70%  745  783  764.0  19.0    595
## 75%  783  825  804.0  21.0    572
## 80%  825  881  853.0  28.0    592
## 85%  881  948  914.5  33.5    583
## 90%  948 1045  996.5  48.5    592
## 95% 1045 1250 1147.5 102.5    586

# 4 Iterative Distribution Mixing based cdsw

## 4.1 Requirements

• Mass range can be specified (mass_range)
• Maximal window size can be specified (max_window_size). This is because windows should not be to large because of optimal collision energy (personal communication by Bernd R.).
• Minimal window size can be specified (min_window_size).
• target number of windows can be specified (nr_windows).
• boundaries between windows are placed in regions were no precursors are observed.

## 4.2 Contrains and Objective Function

.cdsw_objective <- function(splits, data){
counts <- hist(data, breaks=splits,plot=FALSE)\$counts
nbins<-length(splits)-1
optimumN <- length(data)/(length(splits)-1)
optimumN<-rep(optimumN,nbins)

score2 <-sqrt(sum((counts - optimumN)^2))
score1 <- sum(abs(counts - round(optimumN)))
return(list(score1=score1,score2 = score2, counts=counts, optimumN=round(optimumN)))
}

.cdsw_hardconstrain <- function(splits, minwindow = 5, maxwindow=50){

difsp<-diff(splits)
return(sum(difsp >= minwindow) == length(difsp) & sum(difsp <= maxwindow) == length(difsp))
}

## 4.3 Construction Heuristic

.cdsw_compute_sampling_breaks <- function(xx, nbins=35, maxwindow=150, minwindow = 5, plot=TRUE){
breaks <- nbins+1
#xx <- x

#xx<-xx[xx >=310 & xx<1250]
# TODO(wew): there is something insconsitent with the nbins parameter
qqs <- quantile(xx,probs = seq(0,1,by=1/(nbins)))

plot(1:breaks, qqs, type="b" ,
sub=".cdsw_compute_sampling_breaks")
legend("topleft", legend = c(paste("maxwindow = ", maxwindow),
paste("nbins = ", breaks) ))

# equidistant spaced bins
unif <- seq(min(xx),max(xx),length=(breaks))
lines(1:breaks,unif,col=2,type="b")

if(!.cdsw_hardconstrain(unif,minwindow = 5, maxwindow)){
warning("there is no way to generate bins given minwindow " , minwindow, "maxwindow", maxwindow, " breaks" , breaks, "\n")
}else{
.cdsw_hardconstrain(qqs,minwindow = 5, maxwindow)
}

mixeddata <- xx
it_count <- 0
error <- 0

while(!.cdsw_hardconstrain(qqs,minwindow = 5, maxwindow)){
it_count <- it_count + 1
uniformdata<-runif(round(length(xx)/20), min=min(xx), max=max(xx))
mixeddata<-c(mixeddata,uniformdata)

qqs <- quantile(mixeddata,probs = seq(0,1,by=1/(nbins)))
lines(1:breaks,qqs,type="l", col="#00DD00AA")
error[it_count] <-.cdsw_objective(qqs, xx)\$score1

}

lines(1:breaks,qqs,type="b", col="#FF1111AA")
plot(error, xlab="number of iteration", sub=".cdsw_compute_sampling_breaks")

qqs <- as.numeric(sort(round(qqs)))
qqs[1]  <- qqs[1] - 0.5
qqs[length(qqs)]  <- qqs[length(qqs)] + 0.5

round(qqs, 1)
}

## 4.4 Evaluation

### 4.4.1 Comparizon to Classical Approach

op <- par(mfrow=c(2,2))
par(mfrow=c(3,1))
wind <- cdsw(exampledata,
freq=TRUE,
plot=TRUE,
overlap = 0,
n=35,
massrange = c(350,1250),
sub='sampling based',
main = "peptideStd", xlab='pepmass', FUN=function(...){.cdsw_compute_sampling_breaks(...,maxwindow = 50)})
## Warning in plot.histogram(r, freq = freq1, col = col, border = border,
## angle = angle, : the AREAS in the plot are wrong -- rather use 'freq =
## FALSE'

readjustWindows <- function(wind ,ms1data, breaks=10000, maxbin = 5){
res <- hist(ms1data, breaks=breaks)
abline(v=wind\$from,col=2,lty=2)
abline(v=wind\$to,col=3,lty=2)

empty <- res\$mids[which(res\$counts < maxbin )]
newfrom <- .makenewfromto(wind\$from , empty)
newto <- .makenewfromto(wind\$to , empty , isfrom=FALSE )

plot(res,xlim=c(1060,1065))
abline(v = newfrom,lwd=0.5,col="red")
abline(v = newto , lwd=0.5,col="green")
plot(res,xlim=c(520,550))
abline(v = newfrom,lwd=0.5,col="red")
abline(v = newto , lwd=0.5,col="green")

width <- (newto - newfrom) * 0.5
mid <- (newfrom + newto)*0.5
newCounts <- NULL
for(i in 1:length(newfrom))
{
newCounts <- c(newCounts,sum(ms1data >= newfrom[i] & ms1data <= newto[i]))
}
data.frame(newfrom, newto, mid, width, counts =newCounts)

}

##    newfrom  newto     mid width counts
## 1    349.5  379.1  364.30 14.80    305
## 2    379.0  404.1  391.55 12.55    383
## 3    404.0  424.1  414.05 10.05    338
## 4    424.0  443.1  433.55  9.55    406
## 5    443.0  463.1  453.05 10.05    403
## 6    463.0  481.1  472.05  9.05    433
## 7    481.0  498.1  489.55  8.55    404
## 8    498.0  515.0  506.50  8.50    430
## 9    515.0  532.0  523.50  8.50    418
## 10   531.9  549.0  540.45  8.55    423
## 11   548.9  566.0  557.45  8.55    413
## 12   566.0  583.0  574.50  8.50    408
## 13   582.9  602.0  592.45  9.55    415
## 14   602.0  622.0  612.00 10.00    425
## 15   622.0  639.0  630.50  8.50    393
## 16   639.0  658.0  648.50  9.50    417
## 17   658.0  679.0  668.50 10.50    361
## 18   679.0  698.2  688.60  9.60    412
## 19   698.0  720.0  709.00 11.00    385
## 20   720.0  741.0  730.50 10.50    384
## 21   741.0  762.0  751.50 10.50    372
## 22   762.0  786.0  774.00 12.00    339
## 23   785.9  811.0  798.45 12.55    344
## 24   811.0  838.0  824.50 13.50    343
## 25   837.9  865.0  851.45 13.55    282
## 26   865.0  896.0  880.50 15.50    285
## 27   896.0  927.1  911.55 15.55    281
## 28   927.0  958.1  942.55 15.55    264
## 29   958.0  993.1  975.55 17.55    221
## 30   993.0 1030.0 1011.50 18.50    206
## 31  1030.0 1068.0 1049.00 19.00    193
## 32  1068.0 1109.0 1088.50 20.50    181
## 33  1109.0 1153.0 1131.00 22.00    121
## 34  1153.0 1199.0 1176.00 23.00     98
## 35  1199.0 1249.5 1224.25 25.25     71
cdsw(exampledata,
freq=TRUE,
plot=TRUE,
n=35,
overlap = 0,
sub='quantile based',
main = "peptideStd", xlab='pepmass', FUN=.cdsw_compute_breaks)
## Warning in plot.histogram(r, freq = freq1, col = col, border = border,
## angle = angle, : the AREAS in the plot are wrong -- rather use 'freq =
## FALSE'

##           from   to    mid width counts
## 0%         301  363  332.0  31.0    332
## 2.857143%  363  390  376.5  13.5    343
## 5.714286%  390  410  400.0  10.0    328
## 8.571429%  410  429  419.5   9.5    331
## 11.42857%  429  445  437.0   8.0    339
## 14.28571%  445  462  453.5   8.5    347
## 17.14286%  462  476  469.0   7.0    339
## 20%        476  489  482.5   6.5    315
## 22.85714%  489  503  496.0   7.0    333
## 25.71429%  503  517  510.0   7.0    353
## 28.57143%  517  531  524.0   7.0    338
## 31.42857%  531  544  537.5   6.5    316
## 34.28571%  544  557  550.5   6.5    337
## 37.14286%  557  572  564.5   7.5    341
## 40%        572  586  579.0   7.0    337
## 42.85714%  586  601  593.5   7.5    324
## 45.71429%  601  617  609.0   8.0    350
## 48.57143%  617  632  624.5   7.5    332
## 51.42857%  632  646  639.0   7.0    321
## 54.28571%  646  663  654.5   8.5    342
## 57.14286%  663  682  672.5   9.5    340
## 60%        682  698  690.0   8.0    336
## 62.85714%  698  716  707.0   9.0    323
## 65.71429%  716  736  726.0  10.0    350
## 68.57143%  736  754  745.0   9.0    328
## 71.42857%  754  776  765.0  11.0    335
## 74.28571%  776  800  788.0  12.0    336
## 77.14286%  800  825  812.5  12.5    327
## 80%        825  855  840.0  15.0    344
## 82.85714%  855  891  873.0  18.0    330
## 85.71429%  891  928  909.5  18.5    334
## 88.57143%  928  969  948.5  20.5    340
## 91.42857%  969 1029  999.0  30.0    337
## 94.28571% 1029 1097 1063.0  34.0    332
## 97.14286% 1097 1250 1173.5  76.5    336

### 4.4.2 Comparizon using different MaxWindowSize

op <-par(mfrow=c(4,3))
res <- lapply(c(75,150,300, 800), function(mws){
cdsw(exampledata,
freq=TRUE,
plot=TRUE,
overlap = 0,
main = paste("max window size", mws), xlab='pepmass',
FUN=function(...){
.cdsw_compute_sampling_breaks(...,maxwindow = mws)
})
})