José López | 11 Jan 23:22 2013
Picon

Re: vsn preprocess with oligo package

Ooops. Sorry for the question. I use to check CEL images and to  
further analyze quality with arrayQualityMetrics but yes, I didn't  
realize that the GeneFeatureSet was indicating the total number of  
probes in the array.

Thank you again for your kind help,

Best,

  Jose

El ene 11, 2013, a las 6:46 p.m., James W. MacDonald escribió:

> Hi Jose,
>
> On 1/11/2013 12:05 PM, José LÓPEZ wrote:
>> Hi,
>>
>> I have one more question. The GeneFeatureSet has 1102500 features  
>> while the vsn2 is done on 899636 features no matter whether target  
>> in pm is "core" (default method) or "probeset". Why vsn2 does not  
>> use all the features? Is that correct/normal? After sumarization,  
>> as expected, I have 35556 features. It is possible that the  
>> normalization on only part of the features can introduce some kind  
>> of bias in the summarization process (899636 in stead of 1102500)?
>
> I think you misunderstand a basic tenet of Affymetrix arrays. Not  
> all features on an Affy array are used to measure expression of  
> transcript. There are for instance thousands of features that go all  
> the way around the outside of the array (the oligo-dT features) that  
> are there only to help the scanner align itself to the chip. There  
> are also two big blocks of features in the middle that are not  
> measuring transcript either.
>
> You can see this if you do something like
>
> tmp <- log2(as.numeric(exprs(raw([,1]))))
> geom <- geometry(getPD(raw))
> ## convert back to a matrix
> tmp <- matrix(tmp, ncol = geom[1], nrow = geom[2])
> ## reorder because image() is weird
> tmp <- as.matrix(rev(as.data.frame(tmp)))
> image(tmp[1:100,1:100])
>
> This shows the (still transposed) top left corner of the chip. The  
> checkerboard in the corner, and all the features along the top and  
> side are oligo-dT probes used to align. The chip name is made up of  
> oligo-dT features (and blanks) as well and there primarily I suppose  
> to look cool.
>
> If you just do image(tmp), you will see the big blocks in the middle  
> of the array.
>
> Does that help?
>
> Best,
>
> Jim
>
>
>
>
>>
>> I think the alternative to this option is i.e. make the CDF file  
>> and environment (to avoid the unofficial CDF) and make vsnrma in  
>> affy but, since oligo was designed ad hoc (to analyze Gene and Exon  
>> affymetrix arrays), I though it makes sense to try to find your  
>> help to combine vsn and oligo.
>>
>> Thank you for your answer,
>>
>> Jose
>>
>> El ene 11, 2013, a las 5:42 p.m., José LÓPEZ escribió:
>>
>>> Yes, the exprs() did the job and it is allowing me to combine vsn  
>>> with oligo and Gene ST arrays.
>>>
>>> Thank you again for your kind help,
>>>
>>> Best,
>>>
>>> Jose
>>>
>>>
>>> > library(limma)
>>> > library(oligo)
>>> > Data=read.celfiles(list.celfiles())
>>> Loading required package: pd.mogene.1.0.st.v1
>>> Loading required package: RSQLite
>>> Loading required package: DBI
>>> Platform design info loaded.
>>> Reading in : ABRNA1.CEL
>>> Reading in : ABRNA2.CEL
>>> Reading in : ABRNA3.CEL
>>> Reading in : ABRNA4.CEL
>>> Reading in : ABRNA5.CEL
>>> Reading in : ABRNA6.CEL
>>> > Data
>>> GeneFeatureSet (storageMode: lockedEnvironment)
>>> assayData: 1102500 features, 6 samples
>>>  element names: exprs
>>> protocolData
>>>  rowNames: ABRNA1.CEL ABRNA2.CEL ... ABRNA6.CEL (6 total)
>>>  varLabels: exprs dates
>>>  varMetadata: labelDescription channel
>>> phenoData
>>>  rowNames: ABRNA1.CEL ABRNA2.CEL ... ABRNA6.CEL (6 total)
>>>  varLabels: index
>>>  varMetadata: labelDescription channel
>>> featureData: none
>>> experimentData: use 'experimentData(object)'
>>> Annotation: pd.mogene.1.0.st.v1
>>> > class(Data)
>>> [1] "GeneFeatureSet"
>>> attr(,"package")
>>> [1] "oligoClasses"
>>> > raw=backgroundCorrect(Data,"rma")
>>> Background correcting... OK
>>> > pms=pm(raw)
>>> > head(pms)
>>>     ABRNA1.CEL ABRNA2.CEL ABRNA3.CEL ABRNA4.CEL ABRNA5.CEL  
>>> ABRNA6.CEL
>>> 2106   7.853059   7.635413   5.221570   5.160448   5.978796    
>>> 5.767533
>>> 2107   5.990083   4.764031   4.659925   5.160448   7.067603    
>>> 5.903628
>>> 2108   4.867173   4.587342   5.023095   4.762256   5.978796    
>>> 6.045105
>>> 2109  10.657556   8.827158   7.679404   6.124607  11.523816    
>>> 6.045105
>>> 2110  12.538396  13.906774   6.147958   5.860049  38.764281    
>>> 6.843026
>>> 2111  10.241785   6.356910   4.836138   5.160448   7.067603    
>>> 7.405633
>>> > class(pms)
>>> [1] "matrix"
>>> > pmsVSN=vsn::vsnMatrix(pms)
>>> vsn2: 899636 x 6 matrix (1 stratum). Please use 'meanSdPlot' to  
>>> verify the fit.
>>> > class(pmsVSN)
>>> [1] "vsn"
>>> attr(,"package")
>>> [1] "vsn"
>>> > pmsVSN
>>> vsn object for n=899636 features and d=6 samples.
>>> sigsq=0.1
>>> hx: 899636 x 6 matrix.
>>> > pm(raw) <- exprs(pmsVSN)
>>> > rm(pms, pmsVSN)
>>> > ls()
>>> [1] "Data" "raw"
>>> > raw
>>> GeneFeatureSet (storageMode: lockedEnvironment)
>>> assayData: 1102500 features, 6 samples
>>>  element names: exprs
>>> protocolData
>>>  rowNames: ABRNA1.CEL ABRNA2.CEL ... ABRNA6.CEL (6 total)
>>>  varLabels: exprs dates
>>>  varMetadata: labelDescription channel
>>> phenoData
>>>  rowNames: ABRNA1.CEL ABRNA2.CEL ... ABRNA6.CEL (6 total)
>>>  varLabels: index
>>>  varMetadata: labelDescription channel
>>> featureData: none
>>> experimentData: use 'experimentData(object)'
>>> Annotation: pd.mogene.1.0.st.v1
>>> > eset=rma(raw, background=FALSE,normalize=FALSE)
>>> Calculating Expression
>>> > eset
>>> ExpressionSet (storageMode: lockedEnvironment)
>>> assayData: 35556 features, 6 samples
>>>  element names: exprs
>>> protocolData
>>>  rowNames: ABRNA1.CEL ABRNA2.CEL ... ABRNA6.CEL (6 total)
>>>  varLabels: exprs dates
>>>  varMetadata: labelDescription channel
>>> phenoData
>>>  rowNames: ABRNA1.CEL ABRNA2.CEL ... ABRNA6.CEL (6 total)
>>>  varLabels: index
>>>  varMetadata: labelDescription channel
>>> featureData: none
>>> experimentData: use 'experimentData(object)'
>>> Annotation: pd.mogene.1.0.st.v1
>>>
>>> El ene 11, 2013, a las 5:07 p.m., James W. MacDonald escribió:
>>>
>>>> Hi Jose,
>>>>
>>>> On 1/11/2013 10:31 AM, José LÓPEZ wrote:
>>>>> Dear Jim,
>>>>>
>>>>> Thank you for the advise on the background correction step.
>>>>> I already tryed before the whole Benilton's code but it doesn't  
>>>>> work at the following step.
>>>>>
>>>>>> pm(raw)<- pmVSN
>>>>> Error: object 'pmVSN' not found
>>>>>
>>>>> May I ask you what this step is doing? Does it replace the pm  
>>>>> matrix in the raw ExpressionFeatureSet by the normalized one?
>>>>
>>>> Exactly. But the 'pm <-'  function expects to be fed a matrix,  
>>>> and the pmsVSN isn't a matrix. Instead, it is a 'vsn' object,  
>>>> which is related to an ExpressionSet object. So you can extract  
>>>> the matrix of normalized data as usual, with exprs():
>>>>
>>>> pm(raw) <- exprs(pmsVSN)
>>>>
>>>> and there was another error in my code, as summarize() won't work  
>>>> on a GeneFeatureSet object. Instead, you want to use rma():
>>>>
>>>> eset <- rma(raw, normalize = FALSE, background = FALSE)
>>>>
>>>> Best,
>>>>
>>>> Jim
>>>>
>>>>
>>>>
>>>>>
>>>>> Thank you in advance for your time and your kind help,
>>>>>
>>>>> Jose
>>>>>
>>>>>> library(limma)
>>>>>> library(oligo)
>>>>>> Data=read.celfiles(list.celfiles())
>>>>> Loading required package: pd.mogene.1.0.st.v1
>>>>> Loading required package: RSQLite
>>>>> Loading required package: DBI
>>>>> Platform design info loaded.
>>>>> Reading in : ABRNA1.CEL
>>>>> Reading in : ABRNA2.CEL
>>>>> Reading in : ABRNA3.CEL
>>>>> Reading in : ABRNA4.CEL
>>>>> Reading in : ABRNA5.CEL
>>>>> Reading in : ABRNA6.CEL
>>>>>> pms=pm(Data)
>>>>>> raw=backgroundCorrect(Data,"rma")
>>>>> Background correcting... OK
>>>>>> pms=pm(raw)
>>>>>> pmsVSN=vsn::vsnMatrix(pms)
>>>>> vsn2: 899636 x 6 matrix (1 stratum). Please use 'meanSdPlot' to  
>>>>> verify the fit.
>>>>>> pm(raw)<- pmVSN
>>>>> Error: object 'pmVSN' not found
>>>>>> pm(raw)<- pmsVSN
>>>>> Error in function (classes, fdef, mtable)  :
>>>>>  unable to find an inherited method for function ‘pm<-’ for  
>>>>> signature ‘"GeneFeatureSet", "missing", "missing", "vsn"’
>>>>>> pmsVSN
>>>>> vsn object for n=899636 features and d=6 samples.
>>>>> sigsq=0.1
>>>>> hx: 899636 x 6 matrix.
>>>>>> head(pms)
>>>>>     ABRNA1.CEL ABRNA2.CEL ABRNA3.CEL ABRNA4.CEL ABRNA5.CEL  
>>>>> ABRNA6.CEL
>>>>> 2106   7.853059   7.635413   5.221570   5.160448   5.978796    
>>>>> 5.767533
>>>>> 2107   5.990083   4.764031   4.659925   5.160448   7.067603    
>>>>> 5.903628
>>>>> 2108   4.867173   4.587342   5.023095   4.762256   5.978796    
>>>>> 6.045105
>>>>> 2109  10.657556   8.827158   7.679404   6.124607  11.523816    
>>>>> 6.045105
>>>>> 2110  12.538396  13.906774   6.147958   5.860049  38.764281    
>>>>> 6.843026
>>>>> 2111  10.241785   6.356910   4.836138   5.160448   7.067603    
>>>>> 7.405633
>>>>>> class(pms)
>>>>> [1] "matrix"
>>>>>> ls()
>>>>> [1] "Data"   "pms"    "pmsVSN" "raw"
>>>>>
>>>>>> sessionInfo()
>>>>> R version 2.15.2 (2012-10-26)
>>>>> Platform: x86_64-apple-darwin9.8.0/x86_64 (64-bit)
>>>>>
>>>>> locale:
>>>>> [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
>>>>>
>>>>> attached base packages:
>>>>> [1] stats     graphics  grDevices utils     datasets  methods    
>>>>> base
>>>>>
>>>>> other attached packages:
>>>>> [1] pd.mogene.1.0.st.v1_3.8.0 RSQLite_0.11.2             
>>>>> DBI_0.2-5                 oligo_1.22.0
>>>>> [5] Biobase_2.18.0            oligoClasses_1.20.0        
>>>>> BiocGenerics_0.4.0        limma_3.14.3
>>>>>
>>>>> loaded via a namespace (and not attached):
>>>>> [1] affxparser_1.30.0     affy_1.36.0            
>>>>> affyio_1.26.0         BiocInstaller_1.8.3   Biostrings_2.26.2
>>>>> [6] bit_1.1-9             codetools_0.2-8        
>>>>> ff_2.2-10             foreach_1.4.0         GenomicRanges_1.10.5
>>>>> [11] grid_2.15.2           IRanges_1.16.4         
>>>>> iterators_1.0.6       lattice_0.20-10       parallel_2.15.2
>>>>> [16] preprocessCore_1.20.0 splines_2.15.2         
>>>>> stats4_2.15.2         vsn_3.26.0            zlibbioc_1.4.0
>>>>>
>>>>>
>>>>> *****************************************************
>>>>> José P. LÓPEZ-ATAYALA
>>>>> Instituto de Neurociencias
>>>>> CSIC - UMH
>>>>> Avda. D. Santiago Ramón y Cajal, S/N
>>>>> E-03550, Sant Joan d'Alacant
>>>>> Alicante, Spain
>>>>> jose.lopez@... <mailto:jose.lopez@...>
>>>>> http://in.umh.es/grupos-detalle.aspx?grupo=30
>>>>> (34) 965 919 531
>>>>>
>>>>> El ene 11, 2013, a las 3:59 p.m., James W. MacDonald escribió:
>>>>>
>>>>>> Hi Jose,
>>>>>>
>>>>>> Let's say you followed Benilton's code from https://stat.ethz.ch/pipermail/bioconductor/2010-June/033936.html
>>>>>>
>>>>>> library(oligo)
>>>>>> cels = list.celfiles()
>>>>>> raw = read.celfiles(cels)
>>>>>> raw = backgroundCorrect(raw, "rma") ## I added this - you might  
>>>>>> want BG correction
>>>>>> pms = pm(raw)
>>>>>> pmsVSN = vsn::vsnMatrix(pms)
>>>>>> pm(raw)<- pmVSN
>>>>>> rm(pms, pmsVSN)
>>>>>>
>>>>>> you now have an ExpressionFeatureSet with normalized data that  
>>>>>> you want to summarize. You can then
>>>>>>
>>>>>> eset<- summarize(raw, method = "medianpolish")
>>>>>>
>>>>>> See
>>>>>>
>>>>>> ?summarizationMethods
>>>>>>
>>>>>> for more information.
>>>>>>
>>>>>> Best,
>>>>>>
>>>>>> Jim
>>>>>>
>>>>>>
>>>>>> On 1/11/2013 6:17 AM, José LÓPEZ wrote:
>>>>>>> Dear Benilton,
>>>>>>>
>>>>>>> I am using oligo for Mouse Gene 1.0ST arrays. In addition to  
>>>>>>> RMA, I would also like to pre-process with vsn. I have seen  
>>>>>>> previous threads related to this question in the past,
(https://stat.ethz.ch/pipermail/bioconductor/2010-January/031100.html 
>>>>>>> , https://stat.ethz.ch/pipermail/bioconductor/2010-June/033936.html) 
>>>>>>> , but unfortunately, I am not bioinformatician and, although I  
>>>>>>> read oligo and vsn manuals, it is not easy to me to follow up  
>>>>>>> to summarize the vsn object.
>>>>>>> May you (or someone else) please, give me some additional clue  
>>>>>>> to sumarize the vsn object using the oligo package.
>>>>>>>
>>>>>>> Thank you very much in advance for your time and your kind help,
>>>>>>>
>>>>>>> Jose LOPEZ
>>>>>>>
>>>>>>> **************************
>>>>>>>
>>>>>>>> list.files()
>>>>>>> [1] "ABRNA1.CEL"                           
>>>>>>> "ABRNA2.CEL"                          "ABRNA3.CEL"
>>>>>>> [4] "ABRNA4.CEL"                           
>>>>>>> "ABRNA5.CEL"                          "ABRNA6.CEL"
>>>>>>> [7] "Limma_FilterBefore_H2BGFP_jla_vsn.R"
>>>>>>>> library(limma)
>>>>>>>> library(oligo)
>>>>>>> Loading required package: BiocGenerics
>>>>>>>
>>>>>>> Attaching package: ‘BiocGenerics’
>>>>>>>
>>>>>>> The following object(s) are masked from ‘package:stats’:
>>>>>>>
>>>>>>>    xtabs
>>>>>>>
>>>>>>> The following object(s) are masked from ‘package:base’:
>>>>>>>
>>>>>>>    anyDuplicated, cbind, colnames, duplicated, eval, Filter,  
>>>>>>> Find, get, intersect, lapply, Map, mapply,
>>>>>>>    mget, order, paste, pmax, pmax.int, pmin, pmin.int,  
>>>>>>> Position, rbind, Reduce, rep.int, rownames, sapply,
>>>>>>>    setdiff, table, tapply, union, unique
>>>>>>>
>>>>>>> Loading required package: oligoClasses
>>>>>>> Loading package bit 1.1-9
>>>>>>> package:bit (c) 2008-2012 Jens Oehlschlaegel (GPL-2)
>>>>>>> creators: bit bitwhich
>>>>>>> coercion: as.logical as.integer as.bit as.bitwhich which
>>>>>>> operator: !&   | xor != ==
>>>>>>> querying: print length any all min max range sum summary
>>>>>>> bit access: length<- [ [<- [[ [[<-
>>>>>>> for more help type ?bit
>>>>>>> Loading package ff2.2-10
>>>>>>> - getOption("fftempdir")=="/var/folders/U+/U 
>>>>>>> +SFMmqcEbKkSysJQ3OYbk+++TQ/-Tmp-//RtmpKgQzWD"
>>>>>>>
>>>>>>> - getOption("ffextension")=="ff"
>>>>>>>
>>>>>>> - getOption("ffdrop")==TRUE
>>>>>>>
>>>>>>> - getOption("fffinonexit")==TRUE
>>>>>>>
>>>>>>> - getOption("ffpagesize")==65536
>>>>>>>
>>>>>>> - getOption("ffcaching")=="mmnoflush"  -- consider  
>>>>>>> "ffeachflush" if your system stalls on large writes
>>>>>>>
>>>>>>> - getOption("ffbatchbytes")==16777216 -- consider a different  
>>>>>>> value for tuning your system
>>>>>>>
>>>>>>> - getOption("ffmaxbytes")==536870912 -- consider a different  
>>>>>>> value for tuning your system
>>>>>>>
>>>>>>> Welcome to oligoClasses version 1.20.0
>>>>>>> Loading required package: Biobase
>>>>>>> Welcome to Bioconductor
>>>>>>>
>>>>>>>    Vignettes contain introductory material; view with  
>>>>>>> 'browseVignettes()'. To cite Bioconductor, see
>>>>>>>    'citation("Biobase")', and for packages  
>>>>>>> 'citation("pkgname")'.
>>>>>>>
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>>>>>>> ================================================================
>>>>>>> Welcome to oligo version 1.22.0
>>>>>>> = 
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>>>>>>> ================================================================
>>>>>>>
>>>>>>> Attaching package: ‘oligo’
>>>>>>>
>>>>>>> The following object(s) are masked from ‘package:limma’:
>>>>>>>
>>>>>>>    backgroundCorrect
>>>>>>>
>>>>>>>> Data=read.celfiles(list.celfiles())
>>>>>>> Loading required package: pd.mogene.1.0.st.v1
>>>>>>> Loading required package: RSQLite
>>>>>>> Loading required package: DBI
>>>>>>> Platform design info loaded.
>>>>>>> Reading in : ABRNA1.CEL
>>>>>>> Reading in : ABRNA2.CEL
>>>>>>> Reading in : ABRNA3.CEL
>>>>>>> Reading in : ABRNA4.CEL
>>>>>>> Reading in : ABRNA5.CEL
>>>>>>> Reading in : ABRNA6.CEL
>>>>>>>> pms=pm(Data)
>>>>>>>> class(pms)
>>>>>>> [1] "matrix"
>>>>>>>> head(pms)
>>>>>>>     ABRNA1.CEL ABRNA2.CEL ABRNA3.CEL ABRNA4.CEL ABRNA5.CEL  
>>>>>>> ABRNA6.CEL
>>>>>>> 2106         46         43         36         36          
>>>>>>> 37         33
>>>>>>> 2107         38         32         33         36          
>>>>>>> 43         34
>>>>>>> 2108         31         31         35         34          
>>>>>>> 37         35
>>>>>>> 2109         54         46         45         40          
>>>>>>> 58         35
>>>>>>> 2110         58         55         40         39          
>>>>>>> 94         40
>>>>>>> 2111         53         39         34         36          
>>>>>>> 43         43
>>>>>>>> pmsVSN=vsn::vsnMatrix(pms)
>>>>>>> vsn2: 899636 x 6 matrix (1 stratum). Please use 'meanSdPlot'  
>>>>>>> to verify the fit.
>>>>>>>> class(pmsVSN)
>>>>>>> [1] "vsn"
>>>>>>> attr(,"package")
>>>>>>> [1] "vsn"
>>>>>>>> pmsVSN
>>>>>>> vsn object for n=899636 features and d=6 samples.
>>>>>>> sigsq=0.026
>>>>>>> hx: 899636 x 6 matrix.
>>>>>>>> eset=rma(pmsVSN, background=FALSE,normalize=FALSE)
>>>>>>> Error in function (classes, fdef, mtable)  :
>>>>>>>  unable to find an inherited method for function ‘rma’ for  
>>>>>>> signature ‘"vsn"’
>>>>>>>
>>>>>>>> library(vsn)
>>>>>>>> meanSdPlot(pmsVSN)
>>>>>>> KernSmooth 2.23 loaded
>>>>>>> Copyright M. P. Wand 1997-2009
>>>>>>>
>>>>>>>> sessionInfo()
>>>>>>> R version 2.15.2 (2012-10-26)
>>>>>>> Platform: i386-apple-darwin9.8.0/i386 (32-bit)
>>>>>>>
>>>>>>> locale:
>>>>>>> [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/ 
>>>>>>> en_US.UTF-8
>>>>>>>
>>>>>>> attached base packages:
>>>>>>> [1] stats     graphics  grDevices utils     datasets   
>>>>>>> methods   base
>>>>>>>
>>>>>>> other attached packages:
>>>>>>> [1] vsn_3.26.0                pd.mogene.1.0.st.v1_3.8.0  
>>>>>>> RSQLite_0.11.2            DBI_0.2-5
>>>>>>> [5] oligo_1.22.0              Biobase_2.18.0             
>>>>>>> oligoClasses_1.20.0       BiocGenerics_0.4.0
>>>>>>> [9] limma_3.14.3
>>>>>>>
>>>>>>> loaded via a namespace (and not attached):
>>>>>>> [1] affxparser_1.30.0     affy_1.36.0            
>>>>>>> affyio_1.26.0         BiocInstaller_1.8.3   Biostrings_2.26.2
>>>>>>> [6] bit_1.1-9             codetools_0.2-8        
>>>>>>> ff_2.2-10             foreach_1.4.0         GenomicRanges_1.10.5
>>>>>>> [11] grid_2.15.2           IRanges_1.16.4         
>>>>>>> iterators_1.0.6       KernSmooth_2.23-8     lattice_0.20-10
>>>>>>> [16] parallel_2.15.2       preprocessCore_1.20.0  
>>>>>>> splines_2.15.2        stats4_2.15.2         tools_2.15.2
>>>>>>> [21] zlibbioc_1.4.0
>>>>>>>
>>>>>>>
>>>>>>> [[alternative HTML version deleted]]
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> _______________________________________________
>>>>>>> Bioconductor mailing list
>>>>>>> Bioconductor@... <mailto:Bioconductor@...>
>>>>>>> https://stat.ethz.ch/mailman/listinfo/bioconductor
>>>>>>> Search the archives: http://news.gmane.org/gmane.science.biology.informatics.conductor
>>>>>> -- 
>>>>>> James W. MacDonald, M.S.
>>>>>> Biostatistician
>>>>>> University of Washington
>>>>>> Environmental and Occupational Health Sciences
>>>>>> 4225 Roosevelt Way NE, # 100
>>>>>> Seattle WA 98105-6099
>>>>>>
>>>>
>>>> -- 
>>>> James W. MacDonald, M.S.
>>>> Biostatistician
>>>> University of Washington
>>>> Environmental and Occupational Health Sciences
>>>> 4225 Roosevelt Way NE, # 100
>>>> Seattle WA 98105-6099
>>>>
>>>
>>
>
> -- 
> James W. MacDonald, M.S.
> Biostatistician
> University of Washington
> Environmental and Occupational Health Sciences
> 4225 Roosevelt Way NE, # 100
> Seattle WA 98105-6099
>

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