fastest way to keep score when reduce Granges data
1
0
Entering edit mode
Ou, Jianhong ★ 1.2k
@ou-jianhong-4539
Last seen 10 weeks ago
United States
Hi ALL, I want to reduce a GRanges data by fixed window size and keep scores after reduce. My code is .dat <- GRanges("chr1", Iranges(start=1:50, width=2), strand="+", score=Sample(1:50, 50)) windowSize <- 10 Grwin <- GRanges("chr1", IRanges(start=(0:5)*windowSize+scale[1]-1, width=windowSize), strand="+") ol <- findOverlaps(.dat, GRwin) ol <- as.data.frame(ol) ol <- ol[!duplicated(ol[,1]),] .dat <- split(.dat, ol[,2]) reduceValue <- function(.datReduce){ .datReduceM <- reduce(.datReduce, with.mapping=TRUE) wid <- width(.datReduce) .datReduceScore <- .datReduce$value .datReduceM$score <- sapply(.datReduceM$mapping, function(.idx){ round(sum(.datReduceScore[.idx]*wid[.idx])/sum(wid[.idx])) }) .datReduceM$mapping <- NULL .datReduceM } .dat <- lapply(.dat, reduceValue) .dat <- unlist(GRangesList(.dat)) But the efficiency is very low. What is the best way to keep scores when reduce GRanges data by fixed window size? Thanks for your help. Yours sincerely, Jianhong Ou LRB 670A Program in Gene Function and Expression 364 Plantation Street Worcester, MA 01605 [[alternative HTML version deleted]]
• 1.5k views
ADD COMMENT
0
Entering edit mode
@herve-pages-1542
Last seen 3 days ago
Seattle, WA, United States
Hi Jianhong, It would help enormously if you could send code that we can actually run. Thanks! H. On 02/24/2014 07:53 AM, Ou, Jianhong wrote: > Hi ALL, > > I want to reduce a GRanges data by fixed window size and keep scores after reduce. My code is > > .dat <- GRanges("chr1", Iranges(start=1:50, width=2), strand="+", score=Sample(1:50, 50)) > windowSize <- 10 > Grwin <- GRanges("chr1", IRanges(start=(0:5)*windowSize+scale[1]-1, > width=windowSize), strand="+") > ol <- findOverlaps(.dat, GRwin) > ol <- as.data.frame(ol) > ol <- ol[!duplicated(ol[,1]),] > .dat <- split(.dat, ol[,2]) > reduceValue <- function(.datReduce){ > .datReduceM <- reduce(.datReduce, with.mapping=TRUE) > wid <- width(.datReduce) > .datReduceScore <- .datReduce$value > .datReduceM$score <- sapply(.datReduceM$mapping, function(.idx){ > round(sum(.datReduceScore[.idx]*wid[.idx])/sum(wid[.idx])) > }) > .datReduceM$mapping <- NULL > .datReduceM > } > .dat <- lapply(.dat, reduceValue) > .dat <- unlist(GRangesList(.dat)) > > But the efficiency is very low. What is the best way to keep scores when reduce GRanges data by fixed window size? Thanks for your help. > > Yours sincerely, > > Jianhong Ou > > LRB 670A > Program in Gene Function and Expression > 364 Plantation Street Worcester, > MA 01605 > > [[alternative HTML version deleted]] > > _______________________________________________ > Bioconductor mailing list > Bioconductor at r-project.org > https://stat.ethz.ch/mailman/listinfo/bioconductor > Search the archives: http://news.gmane.org/gmane.science.biology.informatics.conductor > -- Hervé Pagès Program in Computational Biology Division of Public Health Sciences Fred Hutchinson Cancer Research Center 1100 Fairview Ave. N, M1-B514 P.O. Box 19024 Seattle, WA 98109-1024 E-mail: hpages at fhcrc.org Phone: (206) 667-5791 Fax: (206) 667-1319
ADD COMMENT
0
Entering edit mode
Hi Herve, I am not mean I have the code. As I asked, I want the high efficient one. What I am doing now is that something like this (much faster than last codes) size <- 50000 FUN <- sum .dat <- GRanges("chr1", IRanges(start=1:size, width=2), strand="+", score=sample(1:size, size)) windowSize <- 10 GRwin <- GRanges("chr1", IRanges(start=(0:(size/windowSize))*windowSize+scale[1]-1, width=windowSize), strand="+") ##new codes, rename seqnames and reduce system.time({ ##split by strand NO NEED ol <- as.data.frame(findOverlaps(.dat, GRwin)) ol <- ol[!duplicated(ol[,1]), 2] ##change the seqnames by windows. new.seqname <- paste(seqnames(.dat), "__gp", ol, sep="") .newData <- GRanges(new.seqname, IRanges(start(.dat), end(.dat), names=names(.dat)), strand=strand(.dat)) mcols(.newData) <- mcols(.dat) .datR <- reduce(.newData, with.mapping=TRUE) .datR$score <- sapply(.datR$mapping, function(.idx) FUN(.dat$score[.idx])) .datReduceWithScore <- GRanges(gsub("__gp\\d+$", "", seqnames(.datR)), IRanges(start(.datR), end(.datR)), strand=strand(.datR), score=score(.datR)) }) ##user system elapsed ##1.469 0.022 1.492 ##old codes, split and reduce system.time({ ol <- findOverlaps(.dat, GRwin) ol <- as.data.frame(ol) ol <- ol[!duplicated(ol[,1]),] .datS <- split(.dat, ol[,2]) reduceValue <- function(.datReduce){ .datReduceM <- reduce(.datReduce, with.mapping=TRUE) wid <- width(.datReduce) .datReduceScore <- .datReduce$score .datReduceM$score <- sapply(.datReduceM$mapping, function(.idx){ FUN(.datReduceScore[.idx]) }) .datReduceM$mapping <- NULL .datReduceM } .datReduceWithScore2 <- lapply(.datS, reduceValue) .datReduceWithScore2 <- unlist(GRangesList(.datReduceWithScore2)) }) ## user system elapsed ##300.591 3.833 310.751 .datReduceWithScore <- .datReduceWithScore[order(as.character(seqnames(.datReduceWithScore)), start(.datReduceWithScore))] names(.datReduceWithScore2) <- NULL identical(.datReduceWithScore, .datReduceWithScore2) ##TRUE Yours Sincerely, Jianhong Ou LRB 670A Program in Gene Function and Expression 364 Plantation Street Worcester, MA 01605 On 2/25/14 8:21 PM, "Hervé Pagès" <hpages at="" fhcrc.org=""> wrote: >Hi Jianhong, > >It would help enormously if you could send code that we can actually >run. Thanks! > >H. > > >On 02/24/2014 07:53 AM, Ou, Jianhong wrote: >> Hi ALL, >> >> I want to reduce a GRanges data by fixed window size and keep scores >>after reduce. My code is >> >> .dat <- GRanges("chr1", Iranges(start=1:50, width=2), strand="+", >>score=Sample(1:50, 50)) >> windowSize <- 10 >> Grwin <- GRanges("chr1", IRanges(start=(0:5)*windowSize+scale[1]-1, >> width=windowSize), >>strand="+") >> ol <- findOverlaps(.dat, GRwin) >> ol <- as.data.frame(ol) >> ol <- ol[!duplicated(ol[,1]),] >> .dat <- split(.dat, ol[,2]) >> reduceValue <- function(.datReduce){ >> .datReduceM <- reduce(.datReduce, with.mapping=TRUE) >> wid <- width(.datReduce) >> .datReduceScore <- .datReduce$value >> .datReduceM$score <- sapply(.datReduceM$mapping, >>function(.idx){ >> >>round(sum(.datReduceScore[.idx]*wid[.idx])/sum(wid[.idx])) >> }) >> .datReduceM$mapping <- NULL >> .datReduceM >> } >> .dat <- lapply(.dat, reduceValue) >> .dat <- unlist(GRangesList(.dat)) >> >> But the efficiency is very low. What is the best way to keep scores >>when reduce GRanges data by fixed window size? Thanks for your help. >> >> Yours sincerely, >> >> Jianhong Ou >> >> LRB 670A >> Program in Gene Function and Expression >> 364 Plantation Street Worcester, >> MA 01605 >> >> [[alternative HTML version deleted]] >> >> _______________________________________________ >> Bioconductor mailing list >> Bioconductor at r-project.org >> https://stat.ethz.ch/mailman/listinfo/bioconductor >> Search the archives: >>http://news.gmane.org/gmane.science.biology.informatics.conductor >> > >-- >Hervé Pagès > >Program in Computational Biology >Division of Public Health Sciences >Fred Hutchinson Cancer Research Center >1100 Fairview Ave. N, M1-B514 >P.O. Box 19024 >Seattle, WA 98109-1024 > >E-mail: hpages at fhcrc.org >Phone: (206) 667-5791 >Fax: (206) 667-1319
ADD REPLY
0
Entering edit mode
Hi Jianhong, Thanks for the new code. Still didn't work out of the box for me but I managed to run it after some minor edit. Please understand that before we can show you the "high efficient code", we need to understand exactly what you're trying to do. And since you didn't give much details, the "slow code" is the only thing we have. So what you're trying to do looks like a common use case to me: you have a numeric variable defined a along the genome (the score in your case), and you want to summarize it on tiling windows (often fixed- size windows but they don't need to be). It's a classic problem in digital signal processing, called resampling. Note that you cannot just "keep" the score, you need to summarize in a way or another. In your case, you choose to sum the scores associated with the ranges that overlap with a given tiling window. This topic is covered in the examples section of the tileGenome() function in the GenomicRanges package. Note that the approach described there uses the "weighted coverage" of the variable to solve the problem, no findOverlaps() or reduce() is needed: score <- coverage(.dat, weight="score") This puts the score in an RleList object so now there is a score associated to each genomic position. Note that when the input object has overlapping ranges (which is the case for your input object '.dat'), the score associated to a given genomic position is the sum of the scores associated to the original ranges that cover that position. Then to summarize 'score' on your fixed-size tiling windows, you need a summarizing function like the binnedAverage() function shown in ?tileGenome. binnedAverage() computes the average on each window but it's easy to write a summarizing function that computes the sum: binnedSum <- function(bins, numvar, mcolname) { stopifnot(is(bins, "GRanges")) stopifnot(is(numvar, "RleList")) stopifnot(identical(seqlevels(bins), names(numvar))) bins_per_chrom <- split(ranges(bins), seqnames(bins)) sums_list <- lapply(names(numvar), function(seqname) { views <- Views(numvar[[seqname]], bins_per_chrom[[seqname]]) viewSums(views) }) new_mcol <- unsplit(sums_list, as.factor(seqnames(bins))) mcols(bins)[[mcolname]] <- new_mcol bins } Then: GRwin2 <- binnedSum(GRwin, score, "binned_score") This will not give you the same result as what you get with your "slow code" below because of how you deal with original ranges spanning more than one tiling window (you arbitrary assign the range to one tiling window), and also because the contribution of the original score values to our final "binned score" here is weighted by the width of the original range (but since all the ranges in your '.dat' object have width=2, you can easily adjust this). Hope this helps, H. On 02/26/2014 08:40 AM, Ou, Jianhong wrote: > Hi Herve, > > I am not mean I have the code. As I asked, I want the high efficient one. > What I am doing now is that something like this (much faster than last > codes) > > size <- 50000 > FUN <- sum > > .dat <- GRanges("chr1", IRanges(start=1:size, width=2), strand="+", > score=sample(1:size, size)) > windowSize <- 10 > GRwin <- GRanges("chr1", > IRanges(start=(0:(size/windowSize))*windowSize+scale[1]-1, > width=windowSize), strand="+") > ##new codes, rename seqnames and reduce > system.time({ > ##split by strand NO NEED > ol <- as.data.frame(findOverlaps(.dat, GRwin)) > ol <- ol[!duplicated(ol[,1]), 2] > ##change the seqnames by windows. > new.seqname <- paste(seqnames(.dat), "__gp", ol, sep="") > .newData <- GRanges(new.seqname, IRanges(start(.dat), end(.dat), > names=names(.dat)), strand=strand(.dat)) > mcols(.newData) <- mcols(.dat) > .datR <- reduce(.newData, with.mapping=TRUE) > .datR$score <- sapply(.datR$mapping, function(.idx) FUN(.dat$score[.idx])) > .datReduceWithScore <- GRanges(gsub("__gp\\d+$", "", seqnames(.datR)), > IRanges(start(.datR), end(.datR)), strand=strand(.datR), > score=score(.datR)) > }) > > ##user system elapsed > ##1.469 0.022 1.492 > ##old codes, split and reduce > system.time({ > ol <- findOverlaps(.dat, GRwin) > ol <- as.data.frame(ol) > ol <- ol[!duplicated(ol[,1]),] > .datS <- split(.dat, ol[,2]) > reduceValue <- function(.datReduce){ > .datReduceM <- reduce(.datReduce, with.mapping=TRUE) > wid <- width(.datReduce) > .datReduceScore <- .datReduce$score > .datReduceM$score <- sapply(.datReduceM$mapping, > function(.idx){ > FUN(.datReduceScore[.idx]) > }) > .datReduceM$mapping <- NULL > .datReduceM > } > .datReduceWithScore2 <- lapply(.datS, reduceValue) > .datReduceWithScore2 <- unlist(GRangesList(.datReduceWithScore2)) > }) > > ## user system elapsed > ##300.591 3.833 310.751 > .datReduceWithScore <- > .datReduceWithScore[order(as.character(seqnames(.datReduceWithScore)), > start(.datReduceWithScore))] > names(.datReduceWithScore2) <- NULL > identical(.datReduceWithScore, .datReduceWithScore2) > ##TRUE > > Yours Sincerely, > > Jianhong Ou > > LRB 670A > Program in Gene Function and Expression > 364 Plantation Street Worcester, > MA 01605 > > > > > On 2/25/14 8:21 PM, "Hervé Pagès" <hpages at="" fhcrc.org=""> wrote: > >> Hi Jianhong, >> >> It would help enormously if you could send code that we can actually >> run. Thanks! >> >> H. >> >> >> On 02/24/2014 07:53 AM, Ou, Jianhong wrote: >>> Hi ALL, >>> >>> I want to reduce a GRanges data by fixed window size and keep scores >>> after reduce. My code is >>> >>> .dat <- GRanges("chr1", Iranges(start=1:50, width=2), strand="+", >>> score=Sample(1:50, 50)) >>> windowSize <- 10 >>> Grwin <- GRanges("chr1", IRanges(start=(0:5)*windowSize+scale[1]-1, >>> width=windowSize), >>> strand="+") >>> ol <- findOverlaps(.dat, GRwin) >>> ol <- as.data.frame(ol) >>> ol <- ol[!duplicated(ol[,1]),] >>> .dat <- split(.dat, ol[,2]) >>> reduceValue <- function(.datReduce){ >>> .datReduceM <- reduce(.datReduce, with.mapping=TRUE) >>> wid <- width(.datReduce) >>> .datReduceScore <- .datReduce$value >>> .datReduceM$score <- sapply(.datReduceM$mapping, >>> function(.idx){ >>> >>> round(sum(.datReduceScore[.idx]*wid[.idx])/sum(wid[.idx])) >>> }) >>> .datReduceM$mapping <- NULL >>> .datReduceM >>> } >>> .dat <- lapply(.dat, reduceValue) >>> .dat <- unlist(GRangesList(.dat)) >>> >>> But the efficiency is very low. What is the best way to keep scores >>> when reduce GRanges data by fixed window size? Thanks for your help. >>> >>> Yours sincerely, >>> >>> Jianhong Ou >>> >>> LRB 670A >>> Program in Gene Function and Expression >>> 364 Plantation Street Worcester, >>> MA 01605 >>> >>> [[alternative HTML version deleted]] >>> >>> _______________________________________________ >>> Bioconductor mailing list >>> Bioconductor at r-project.org >>> https://stat.ethz.ch/mailman/listinfo/bioconductor >>> Search the archives: >>> http://news.gmane.org/gmane.science.biology.informatics.conductor >>> >> >> -- >> Hervé Pagès >> >> Program in Computational Biology >> Division of Public Health Sciences >> Fred Hutchinson Cancer Research Center >> 1100 Fairview Ave. N, M1-B514 >> P.O. Box 19024 >> Seattle, WA 98109-1024 >> >> E-mail: hpages at fhcrc.org >> Phone: (206) 667-5791 >> Fax: (206) 667-1319 > -- Hervé Pagès Program in Computational Biology Division of Public Health Sciences Fred Hutchinson Cancer Research Center 1100 Fairview Ave. N, M1-B514 P.O. Box 19024 Seattle, WA 98109-1024 E-mail: hpages at fhcrc.org Phone: (206) 667-5791 Fax: (206) 667-1319
ADD REPLY
0
Entering edit mode
Cool code. Yes, it is resampling (sorry I don't know this name). Your idea is do coverage first and then use view-summarization methods to resample the data. In the sample code we use fixed-size tiling windows. After resampling, the signal will be averaged by the window size. If I want to remove the affection of 0 points, I could just use viewApply and write a function to filter the 0 points. I got it. Thank you a lot. Yours Sincerely, Jianhong Ou LRB 670A Program in Gene Function and Expression 364 Plantation Street Worcester, MA 01605 On 2/26/14 2:58 PM, "Hervé Pagès" <hpages at="" fhcrc.org=""> wrote: >Hi Jianhong, > >Thanks for the new code. Still didn't work out of the box for me but I >managed to run it after some minor edit. Please understand that before >we can show you the "high efficient code", we need to understand exactly >what you're trying to do. And since you didn't give much details, the >"slow code" is the only thing we have. > >So what you're trying to do looks like a common use case to me: you >have a numeric variable defined a along the genome (the score in your >case), and you want to summarize it on tiling windows (often fixed- size >windows but they don't need to be). It's a classic problem in digital >signal processing, called resampling. Note that you cannot just "keep" >the score, you need to summarize in a way or another. In your case, >you choose to sum the scores associated with the ranges that overlap >with a given tiling window. > >This topic is covered in the examples section of the tileGenome() >function in the GenomicRanges package. Note that the approach described >there uses the "weighted coverage" of the variable to solve the problem, >no findOverlaps() or reduce() is needed: > > score <- coverage(.dat, weight="score") > >This puts the score in an RleList object so now there is a score >associated to each genomic position. Note that when the input >object has overlapping ranges (which is the case for your input >object '.dat'), the score associated to a given genomic position is >the sum of the scores associated to the original ranges that cover >that position. > >Then to summarize 'score' on your fixed-size tiling windows, you need >a summarizing function like the binnedAverage() function shown in >?tileGenome. binnedAverage() computes the average on each window but >it's easy to write a summarizing function that computes the sum: > > binnedSum <- function(bins, numvar, mcolname) > { > stopifnot(is(bins, "GRanges")) > stopifnot(is(numvar, "RleList")) > stopifnot(identical(seqlevels(bins), names(numvar))) > bins_per_chrom <- split(ranges(bins), seqnames(bins)) > sums_list <- lapply(names(numvar), > function(seqname) { > views <- Views(numvar[[seqname]], > bins_per_chrom[[seqname]]) > viewSums(views) > }) > new_mcol <- unsplit(sums_list, as.factor(seqnames(bins))) > mcols(bins)[[mcolname]] <- new_mcol > bins > } > >Then: > > GRwin2 <- binnedSum(GRwin, score, "binned_score") > >This will not give you the same result as what you get with your >"slow code" below because of how you deal with original ranges >spanning more than one tiling window (you arbitrary assign the range >to one tiling window), and also because the contribution of the >original score values to our final "binned score" here is weighted >by the width of the original range (but since all the ranges in your >'.dat' object have width=2, you can easily adjust this). > >Hope this helps, >H. > > >On 02/26/2014 08:40 AM, Ou, Jianhong wrote: >> Hi Herve, >> >> I am not mean I have the code. As I asked, I want the high efficient >>one. >> What I am doing now is that something like this (much faster than last >> codes) >> >> size <- 50000 >> FUN <- sum >> >> .dat <- GRanges("chr1", IRanges(start=1:size, width=2), strand="+", >> score=sample(1:size, size)) >> windowSize <- 10 >> GRwin <- GRanges("chr1", >> IRanges(start=(0:(size/windowSize))*windowSize+scale[1]-1, >> width=windowSize), >>strand="+") >> ##new codes, rename seqnames and reduce >> system.time({ >> ##split by strand NO NEED >> ol <- as.data.frame(findOverlaps(.dat, GRwin)) >> ol <- ol[!duplicated(ol[,1]), 2] >> ##change the seqnames by windows. >> new.seqname <- paste(seqnames(.dat), "__gp", ol, sep="") >> .newData <- GRanges(new.seqname, IRanges(start(.dat), end(.dat), >> names=names(.dat)), strand=strand(.dat)) >> mcols(.newData) <- mcols(.dat) >> .datR <- reduce(.newData, with.mapping=TRUE) >> .datR$score <- sapply(.datR$mapping, function(.idx) >>FUN(.dat$score[.idx])) >> .datReduceWithScore <- GRanges(gsub("__gp\\d+$", "", seqnames(.datR)), >> IRanges(start(.datR), end(.datR)), strand=strand(.datR), >> score=score(.datR)) >> }) >> >> ##user system elapsed >> ##1.469 0.022 1.492 >> ##old codes, split and reduce >> system.time({ >> ol <- findOverlaps(.dat, GRwin) >> ol <- as.data.frame(ol) >> ol <- ol[!duplicated(ol[,1]),] >> .datS <- split(.dat, ol[,2]) >> reduceValue <- function(.datReduce){ >> .datReduceM <- reduce(.datReduce, with.mapping=TRUE) >> wid <- width(.datReduce) >> .datReduceScore <- .datReduce$score >> .datReduceM$score <- sapply(.datReduceM$mapping, >> function(.idx){ >> FUN(.datReduceScore[.idx]) >> }) >> .datReduceM$mapping <- NULL >> .datReduceM >> } >> .datReduceWithScore2 <- lapply(.datS, reduceValue) >> .datReduceWithScore2 <- unlist(GRangesList(.datReduceWithScore2)) >> }) >> >> ## user system elapsed >> ##300.591 3.833 310.751 >> .datReduceWithScore <- >> .datReduceWithScore[order(as.character(seqnames(.datReduceWithScore)), >> start(.datReduceWithScore))] >> names(.datReduceWithScore2) <- NULL >> identical(.datReduceWithScore, .datReduceWithScore2) >> ##TRUE >> >> Yours Sincerely, >> >> Jianhong Ou >> >> LRB 670A >> Program in Gene Function and Expression >> 364 Plantation Street Worcester, >> MA 01605 >> >> >> >> >> On 2/25/14 8:21 PM, "Hervé Pagès" <hpages at="" fhcrc.org=""> wrote: >> >>> Hi Jianhong, >>> >>> It would help enormously if you could send code that we can actually >>> run. Thanks! >>> >>> H. >>> >>> >>> On 02/24/2014 07:53 AM, Ou, Jianhong wrote: >>>> Hi ALL, >>>> >>>> I want to reduce a GRanges data by fixed window size and keep scores >>>> after reduce. My code is >>>> >>>> .dat <- GRanges("chr1", Iranges(start=1:50, width=2), strand="+", >>>> score=Sample(1:50, 50)) >>>> windowSize <- 10 >>>> Grwin <- GRanges("chr1", IRanges(start=(0:5)*windowSize+scale[1]-1, >>>> width=windowSize), >>>> strand="+") >>>> ol <- findOverlaps(.dat, GRwin) >>>> ol <- as.data.frame(ol) >>>> ol <- ol[!duplicated(ol[,1]),] >>>> .dat <- split(.dat, ol[,2]) >>>> reduceValue <- function(.datReduce){ >>>> .datReduceM <- reduce(.datReduce, with.mapping=TRUE) >>>> wid <- width(.datReduce) >>>> .datReduceScore <- .datReduce$value >>>> .datReduceM$score <- sapply(.datReduceM$mapping, >>>> function(.idx){ >>>> >>>> round(sum(.datReduceScore[.idx]*wid[.idx])/sum(wid[.idx])) >>>> }) >>>> .datReduceM$mapping <- NULL >>>> .datReduceM >>>> } >>>> .dat <- lapply(.dat, reduceValue) >>>> .dat <- unlist(GRangesList(.dat)) >>>> >>>> But the efficiency is very low. What is the best way to keep scores >>>> when reduce GRanges data by fixed window size? Thanks for your help. >>>> >>>> Yours sincerely, >>>> >>>> Jianhong Ou >>>> >>>> LRB 670A >>>> Program in Gene Function and Expression >>>> 364 Plantation Street Worcester, >>>> MA 01605 >>>> >>>> [[alternative HTML version deleted]] >>>> >>>> _______________________________________________ >>>> Bioconductor mailing list >>>> Bioconductor at r-project.org >>>> https://stat.ethz.ch/mailman/listinfo/bioconductor >>>> Search the archives: >>>> http://news.gmane.org/gmane.science.biology.informatics.conductor >>>> >>> >>> -- >>> Hervé Pagès >>> >>> Program in Computational Biology >>> Division of Public Health Sciences >>> Fred Hutchinson Cancer Research Center >>> 1100 Fairview Ave. N, M1-B514 >>> P.O. Box 19024 >>> Seattle, WA 98109-1024 >>> >>> E-mail: hpages at fhcrc.org >>> Phone: (206) 667-5791 >>> Fax: (206) 667-1319 >> > >-- >Hervé Pagès > >Program in Computational Biology >Division of Public Health Sciences >Fred Hutchinson Cancer Research Center >1100 Fairview Ave. N, M1-B514 >P.O. Box 19024 >Seattle, WA 98109-1024 > >E-mail: hpages at fhcrc.org >Phone: (206) 667-5791 >Fax: (206) 667-1319
ADD REPLY

Login before adding your answer.

Traffic: 162 users visited in the last hour
Help About
FAQ
Access RSS
API
Stats

Use of this site constitutes acceptance of our User Agreement and Privacy Policy.

Powered by the version 2.3.6