[Bioc-devel] mapping between original and reduced ranges
Hervé Pagès
hpages at fhcrc.org
Fri Mar 16 06:07:22 CET 2012
On 03/15/2012 04:13 PM, Hahne, Florian wrote:
> Would such a solution also allow to keep the original elementMetadata in
> the respective list representation?
Let see if I understand your question correctly.
IIUC Michael is proposing to store the "reverse mapping" (i.e. the
mapping from the reduced ranges to the original ranges) in the
elementMetadata slot of the reduced object. Note that, unlike the
"direct mapping" (i.e. the mapping from the original ranges to the
reduced ranges), which is a many-to-1 relationship, the "reverse
mapping is 1-to-many, hence the need to use an IntegerList to represent
it. The good thing about this IntegerList is that it has the length of
the reduced object so it fits naturally in its elementMetadata slot:
> ir
IRanges of length 5
start end width
[1] 24 28 5
[2] 27 31 5
[3] 1 5 5
[4] 6 10 5
[5] 12 16 5
> ir2 <- reduce(ir)
> ir2
IRanges of length 3
start end width
[1] 1 10 10
[2] 12 16 5
[3] 24 31 8
> hits <- findOverlaps(ir, ir2)
> rmap <- IntegerList(split(queryHits(hits), subjectHits(hits)))
> rmap
CompressedIntegerList of length 3
[["1"]] 3 4
[["2"]] 5
[["3"]] 1 2
The "direct mapping" is a simpler object (just an integer vector) but it
has the length of the original object so it cannot be stored in the
elementMetadata of the reduced object. It has to go somewhere else
(attribute or metadata). A good thing about storing the "reverse
mapping" in the elementMetadata slot is that there is no risk of
"getting in the way" (i.e. clash with other stuff in that slot)
because reduce() drops the original elementMetadata anyway. It also
plays nice with subsetting the reduced object and with the vectorized
behaviour of the "reduce" method for GRangesList.
The only small con I see is that, like in the use case you show in your
original post, the user might actually need the direct mapping, not the
reverse one. However it's not too hard to reverse a mapping. There is
actually a function in Biobase for doing this on a regular list:
> as.integer(reverseSplit(as.list(rmap)))
[1] 3 3 1 1 2
> findOverlaps(ir, reduce(ir), select="first")
[1] 3 3 1 1 2
There is also revmap() in AnnotationDbi that does the same on Bimap
objects. It also works on a regular list:
> as.integer(revmap(as.list(rmap)))
[1] 3 3 1 1 2
We could move the revmap() generic from AnnotationDbi to IRanges (or
to BiocGenerics) and add a method for IntegerList objects.
I think this is actually my preferred solution so far.
Back to your question:
Would such a solution also allow to keep the original elementMetadata
in the respective list representation?
Something like "folding" the original elementMetadata in a way that
makes it fit in the elementMetadata of the reduced object? The original
elementMetadata (a DataFrame) could actually be split in a
SplitDataFrameList (i.e. conceptually a list of DataFrame's that all
have the same columns), and this SplitDataFrameList stored in the
elementMetadata of the reduced object. It would be stored as a single
column though since elementMetadata must be DataFrame, it cannot
be a SplitDataFrameList. That solution feels "heavy" to me i.e. it
involves complex data structures that are not so easy to manipulate.
I still like Michael's proposal better, it's much lighter.
Cheers,
H.
> I assume that creates about the same
> overhead as keeping the index?
>
>
> Florian Hahne
> Novartis Institute For Biomedical Research
> Translational Sciences / Preclinical Safety / PCS Informatics
> Expert Data Integration and Modeling Bioinformatics
> CHBS, WKL-135.2.26
> Novartis Institute For Biomedical Research, Werk Klybeck
> Klybeckstrasse 141
> CH-4057 Basel
> Switzerland
> Phone: +41 61 6967127
> Email : florian.hahne at novartis.com
>
>
>
>
>
>
>
> On 3/15/12 11:58 PM, "Michael Lawrence"<lawrence.michael at gene.com> wrote:
>
>> I would be in favor of either the attribute or metadata solution. I could
>> see having an IntegerList element in the element metadata that indicates
>> the original ranges that were reduced into the returned range, or a Hits
>> object in the top-level metadata. A plus and minus of the metadata
>> approach
>> is that it is more familiar to the users than hiding stuff in attributes,
>> which is pretty low-level. However, using the metadata will increase the
>> probabilty of "getting in the way". The user does need to explicitly
>> request it though.
>>
>> Michael
>>
>> On Thu, Mar 15, 2012 at 3:26 PM, Hervé Pagès<hpages at fhcrc.org> wrote:
>>
>>> On 03/15/2012 02:40 PM, Kasper Daniel Hansen wrote:
>>>
>>>> I'll vote against the attribute solution and for a solution where the
>>>> type of return object gets changed, for example into a list.
>>>>
>>>
>>> Thanks for voting!
>>>
>>> Problem with this is how you handle 'with.mapping=TRUE' when the input
>>> is GRangesList. Do you return
>>>
>>> (1) a list of the same length as the input 'x', where the i-th
>>> top-level element is itself the 2-element list returned
>>> by reduce(x[[i]], with.mapping=TRUE)
>>>
>>> (2) or a 2-element list where 1 element is the reduced GRangesList
>>> and the other element is an IntegerList representing the
>>> list of mappings?
>>>
>>> (1) would be very inefficient because the returned object would need
>>> to be populated with hundreds of thousands of S4 instances.
>>>
>>> (2) disrupts too much how reduce() is expected to behave on a
>>> GRangesList object i.e. it's expected to operate in a "vectorized"
>>> fashion, that is, each top-level element in the input is reduced
>>> independently of the others and all the results are stored in a
>>> list-like object of the *same length* as the input. So we have nice
>>> properties like
>>>
>>> reduce(x, ...)[[i]] is identical to reduce(x[[i]], ...)
>>>
>>> Here that would not be the case anymore :-/
>>>
>>> More generally speaking, I would not give up on the "endomorphism"
>>> nature of reduce() so easily. It gives us good things like for
>>> example its behaviour on a GRangesList object can be explained
>>> as easily as with
>>>
>>> endoapply(x, reduce, ....)
>>>
>>> *whatever* arguments/parameters/toggles are passed to it. This
>>> makes the documentation *much* easier to write and also it makes
>>> writing unit test much easier.
>>>
>>> So if we really want to go for the list solution, I would suggest
>>> that this is done outside reduce() e.g. in reduceAndMap() or
>>> something like that.
>>>
>>> Cheers,
>>>
>>> H.
>>>
>>>
>>>> Kasper
>>>>
>>>> 2012/3/15 Hervé Pagès<hpages at fhcrc.org>:
>>>>
>>>>> On 03/15/2012 12:45 PM, Cook, Malcolm wrote:
>>>>>
>>>>>>
>>>>>> Hi Herve,
>>>>>>
>>>>>> I've not used attributes to return values before.
>>>>>>
>>>>>> I guess it would work, and I won't object further if you do it this
>>>>>> way,
>>>>>> but, since you asked
>>>>>>
>>>>>> Again, it "feels wrong" in violating functional
>>>>>>
>>>>>> I suspect there may be issues with memory management. When does the
>>>>>> attribute get gc-ed? When the object does? If so, then, retaining
>>>>>> the
>>>>>> attribute in memory when not needed _could_ be a burden, no?
>>>>>>
>>>>>> Back in my lisp days, this is when I would use `values` and
>>>>>> `multiple-value-bind` (and friends) when I wanted a function to
>>>>>> (optionally)
>>>>>> return multiple values.
>>>>>>
>>>>>> But this is R.
>>>>>>
>>>>>> Would you consider returning instead a list of values, keyed by
>>>>>> `value`
>>>>>> and `hits`, but only when with.hits
>>>>>>
>>>>>> BTW: with.inframe.attrib is documented as 'For internal use'. What
>>>>>> does
>>>>>> it return in the attr?
>>>>>>
>>>>>
>>>>>
>>>>> AFAIK, it's only supported by the "reduce" methods for IRanges
>>>>> objects.
>>>>>
>>>>> The "inframe" attribute contains an IRanges object of the same length
>>>>> as
>>>>> the input. For each range in the input it tells you the position of
>>>>> that range with respect to the "frame" i.e. the space obtained by
>>>>> pasting together the ranges in the reduce object:
>>>>>
>>>>>
>>>>> > ir
>>>>> IRanges of length 5
>>>>> start end width
>>>>> [1] 24 28 5
>>>>> [2] 27 31 5
>>>>> [3] 1 5 5
>>>>> [4] 6 10 5
>>>>> [5] 12 16 5
>>>>>
>>>>> > ir2<- reduce(ir, with.inframe.attrib=TRUE)
>>>>> > ir2
>>>>> IRanges of length 3
>>>>> start end width
>>>>> [1] 1 10 10
>>>>> [2] 12 16 5
>>>>> [3] 24 31 8
>>>>> > attr(ir2, "inframe")
>>>>> IRanges of length 5
>>>>> start end width
>>>>> [1] 16 20 5
>>>>> [2] 19 23 5
>>>>> [3] 1 5 5
>>>>> [4] 6 10 5
>>>>> [5] 11 15 5
>>>>>
>>>>>
>>>>> 1 1 2 2 3
>>>>> 1...5....0....5....0....5....**0.<- standard coordinate system
>>>>> ir[1] xxxxx
>>>>> ir[2] xxxxx
>>>>> ir[3] xxxxx
>>>>> ir[4] xxxxx
>>>>> ir[5] xxxxx
>>>>>
>>>>> ir2: xxxxxxxxxx xxxxx xxxxxxxx
>>>>>
>>>>> 1...5....1 ....1 ....2...<- "frame" coordinate system
>>>>> 0 5 0
>>>>>
>>>>> I'll document this.
>>>>>
>>>>> H.
>>>>>
>>>>>
>>>>>
>>>>>> Thanks for listening!
>>>>>>
>>>>>> ~Malcolm
>>>>>>
>>>>>>
>>>>>> -----Original Message-----
>>>>>>> From:
>>>>>>> bioc-devel-bounces at r-project.**org<bioc-devel-bounces at r-project.org>[
>>>>>>> mailto:
>>>>>>> bioc-devel-bounces at r-
>>>>>>> project.org] On Behalf Of Hervé Pagès
>>>>>>> Sent: Thursday, March 15, 2012 1:55 PM
>>>>>>> To: Kasper Daniel Hansen
>>>>>>> Cc: bioc-devel at r-project.org
>>>>>>> Subject: Re: [Bioc-devel] mapping between original and reduced
>>>>>>> ranges
>>>>>>>
>>>>>>> Hi reducers,
>>>>>>>
>>>>>>> I agree it "feels wrong" to use findOverlaps() to extract the
>>>>>>> mapping
>>>>>>> from original to reduced ranges. Even if it can be computed very
>>>>>>> easily
>>>>>>> with:
>>>>>>>
>>>>>>> findOverlaps(gr, reduce(gr), select="first")
>>>>>>>
>>>>>>> (Note that using 'queryHits(findOverlaps(**reduce(gr), gr))' only
>>>>>>> produces
>>>>>>> the correct result if 'gr' is already sorted by increasing order.)
>>>>>>>
>>>>>>> I think it would be easy for reduce() internal code to produce this
>>>>>>> mapping. The question is: how do we give it back to the user?
>>>>>>>
>>>>>>> Is it OK to use an attribute for this? reduce() already uses this
>>>>>>> for returning some extra information about the reduction:
>>>>>>>
>>>>>>> > ir
>>>>>>> IRanges of length 5
>>>>>>> start end width
>>>>>>> [1] 1 5 5
>>>>>>> [2] 6 10 5
>>>>>>> [3] 12 16 5
>>>>>>> [4] 24 28 5
>>>>>>> [5] 27 31 5
>>>>>>> > ir2<- reduce(ir, with.inframe.attrib=TRUE)
>>>>>>> > ir2
>>>>>>> IRanges of length 3
>>>>>>> start end width
>>>>>>> [1] 1 10 10
>>>>>>> [2] 12 16 5
>>>>>>> [3] 24 31 8
>>>>>>> > attr(ir2, "inframe")
>>>>>>> IRanges of length 5
>>>>>>> start end width
>>>>>>> [1] 1 5 5
>>>>>>> [2] 6 10 5
>>>>>>> [3] 11 15 5
>>>>>>> [4] 16 20 5
>>>>>>> [5] 19 23 5
>>>>>>>
>>>>>>> We could to the same thing for the mapping from original to reduced
>>>>>>> ranges with e.g. an argument called 'with.mapping.attrib'.
>>>>>>> Would that work?
>>>>>>>
>>>>>>> Cheers,
>>>>>>> H.
>>>>>>>
>>>>>>>
>>>>>>> On 03/15/2012 05:44 AM, Kasper Daniel Hansen wrote:
>>>>>>>
>>>>>>>>
>>>>>>>> So the key question is to what extent keeping track of where the
>>>>>>>> ranges comes from would slow down the reduce operation. I am not
>>>>>>>> familiar enough with the algorithm to know this, but given how fast
>>>>>>>> IRanges is in general, I am not one for guessing on this.
>>>>>>>>
>>>>>>>> I agree with Florian that this is a very typical use case.
>>>>>>>>
>>>>>>>> Kasper
>>>>>>>>
>>>>>>>> On Thu, Mar 15, 2012 at 5:02 AM, Hahne, Florian
>>>>>>>> <florian.hahne at novartis.com> wrote:
>>>>>>>>
>>>>>>>>>
>>>>>>>>> Hi all,
>>>>>>>>> It is true that this is not terribly slow when you deal with
>>>>>>>>> fairly
>>>>>>>>> large
>>>>>>>>> range objects:
>>>>>>>>>
>>>>>>>>> foo<- GRanges(seqnames=sample(1:4, 1e6, TRUE),
>>>>>>>>> ranges=IRanges(start=as.**integer(runif(min=1, max=1e7, n=1e6)),
>>>>>>>>>
>>>>>>>>
>>>>>>> width=50))
>>>>>>>
>>>>>>>>
>>>>>>>>> system.time(bar<- reduce(foo))
>>>>>>>>> user system elapsed
>>>>>>>>> 0.918 0.174 1.091
>>>>>>>>>
>>>>>>>>> system.time(foobar<- findOverlaps(foo, bar))
>>>>>>>>> user system elapsed
>>>>>>>>> 2.051 0.402 2.453
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> However the whole process does take about 3x the time of just the
>>>>>>>>>
>>>>>>>>
>>>>>>> reduce
>>>>>>>
>>>>>>>>
>>>>>>>>> operation, and in my use case I want this to happen interactively,
>>>>>>>>> where
>>>>>>>>> waiting 3 seconds compared to 1 makes a huge difference...
>>>>>>>>>
>>>>>>>>> I wouldn't push this high up on the development agenda, but it
>>>>>>>>> seems
>>>>>>>>> to
>>>>>>>>>
>>>>>>>>
>>>>>>> be
>>>>>>>
>>>>>>>>
>>>>>>>>> something that is already 95% existing and could easily be added.
>>>>>>>>> But
>>>>>>>>> maybe I am wrong...
>>>>>>>>>
>>>>>>>>> Florian
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Florian Hahne
>>>>>>>>> Novartis Institute For Biomedical Research
>>>>>>>>> Translational Sciences / Preclinical Safety / PCS Informatics
>>>>>>>>> Expert Data Integration and Modeling Bioinformatics
>>>>>>>>> CHBS, WKL-135.2.26
>>>>>>>>> Novartis Institute For Biomedical Research, Werk Klybeck
>>>>>>>>> Klybeckstrasse 141
>>>>>>>>> CH-4057 Basel
>>>>>>>>> Switzerland
>>>>>>>>> Phone: +41 61 6967127
>>>>>>>>> Email : florian.hahne at novartis.com
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> On 3/14/12 9:40 PM, "Kasper Daniel
>>>>>>>>>
>>>>>>>>
>>>>>>> Hansen"<kasperdanielhansen@**gmail.com
>>>>>>> <kasperdanielhansen at gmail.com>>
>>>>>>>
>>>>>>>>
>>>>>>>>> wrote:
>>>>>>>>>
>>>>>>>>> We have discussed this a couple of times. I routinely uses the
>>>>>>>>>> reduce
>>>>>>>>>> followed by findOverlaps paradigm. As Malcolm says it feels
>>>>>>>>>> wrong,
>>>>>>>>>> but from a practical point of view it is pretty fast, so I
>>>>>>>>>> stopped
>>>>>>>>>> worrying about it. I only think there is a reason to do this,
>>>>>>>>>> if it
>>>>>>>>>> is substantially faster.
>>>>>>>>>>
>>>>>>>>>> Kasper
>>>>>>>>>>
>>>>>>>>>> On Wed, Mar 14, 2012 at 3:46 PM, Cook, Malcolm<MEC at stowers.org>
>>>>>>>>>>
>>>>>>>>>
>>>>>>> wrote:
>>>>>>>
>>>>>>>>
>>>>>>>>>>> Chiming in....
>>>>>>>>>>>
>>>>>>>>>>> on a similar note....
>>>>>>>>>>>
>>>>>>>>>>> A version of `disjoin` which returns a Hits/RangesMapping
>>>>>>>>>>> additional
>>>>>>>>>>> to
>>>>>>>>>>> the GRanges result would be most useful and probably not
>>>>>>>>>>> require
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>> much
>>>>>>>
>>>>>>>>
>>>>>>>>>>> additional effort (assuming `disjoin` computes this internally)
>>>>>>>>>>>
>>>>>>>>>>> Of course, it is easy to live without since I can just perform
>>>>>>>>>>> the
>>>>>>>>>>> findOverlaps myself after the disjoin.... it just "feels wrong"
>>>>>>>>>>> (tm)
>>>>>>>>>>>
>>>>>>>>>>> Ahoy!
>>>>>>>>>>>
>>>>>>>>>>> ~Malcolm
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> -----Original Message-----
>>>>>>>>>>>> From:
>>>>>>>>>>>> bioc-devel-bounces at r-project.**org<bioc-devel-bounces at r-project.
>>>>>>>>>>>> org>[mailto:
>>>>>>>>>>>> bioc-devel-
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>> bounces at r-
>>>>>>>
>>>>>>>>
>>>>>>>>>>>> project.org] On Behalf Of Hahne, Florian
>>>>>>>>>>>> Sent: Wednesday, March 14, 2012 2:22 PM
>>>>>>>>>>>> To: bioc-devel at r-project.org
>>>>>>>>>>>> Subject: [Bioc-devel] mapping between original and reduced
>>>>>>>>>>>> ranges
>>>>>>>>>>>>
>>>>>>>>>>>> This bounced before, guess the mailing list does not like HTML
>>>>>>>>>>>> mails.
>>>>>>>>>>>> So
>>>>>>>>>>>> one more try:
>>>>>>>>>>>>
>>>>>>>>>>>> I had the following offline discussion with Michael about how
>>>>>>>>>>>> one
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>> could
>>>>>>>
>>>>>>>>
>>>>>>>>>>>> retain a mapping of the ranges in a GRanges object before and
>>>>>>>>>>>> after
>>>>>>>>>>>> reduce. He suggested to take it to the list. Is that something
>>>>>>>>>>>> that
>>>>>>>>>>>> could
>>>>>>>>>>>> be added to GenomicRanges/IRanges?
>>>>>>>>>>>> Florian
>>>>>>>>>>>>
>>>>>>>>>>>> I have a slightly tricky application for which I need to
>>>>>>>>>>>> reduce a
>>>>>>>>>>>> GRanges
>>>>>>>>>>>> object, but I would like to be able to process some of the
>>>>>>>>>>>> original
>>>>>>>>>>>> elementMetadata of the merged ranges later. The only way I was
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>> able to
>>>>>>>
>>>>>>>>
>>>>>>>>>>>> figure out which of the original ranges correspond to the
>>>>>>>>>>>> merged
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>> ranges
>>>>>>>
>>>>>>>>
>>>>>>>>>>>> was to perform a findOverlaps operation, but of course that is
>>>>>>>>>>>> rather
>>>>>>>>>>>> costly. Is there a way to get the merge information out of the
>>>>>>>>>>>> original
>>>>>>>>>>>> reduce call?
>>>>>>>>>>>> Here is a brief example:
>>>>>>>>>>>>
>>>>>>>>>>>> gr<- GRanges(seqnames="chr1",
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>> ranges=IRanges(start=c(1,6,12,**24,27),
>>>>>>>
>>>>>>>>
>>>>>>>>>>>> width=5), foo=1:5, bar=letters[1:5])
>>>>>>>>>>>> gr2<- reduce(gr, min.gapwidth=1)
>>>>>>>>>>>> ind<- queryHits(findOverlaps(gr2, gr))
>>>>>>>>>>>> split(values(gr), ind)
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Unfortunately, this is the idiom. I could see an improvement
>>>>>>>>>>>> where
>>>>>>>>>>>> reduce
>>>>>>>>>>>> or a similarly named function would return a Hits object (in
>>>>>>>>>>>> addition
>>>>>>>>>>>> to
>>>>>>>>>>>> the actual reduce result) that would indicate the mapping
>>>>>>>>>>>> between
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>> the
>>>>>>>
>>>>>>>>
>>>>>>>>>>>> input and reduced ranges. The RangesMapping structure would be
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>> really
>>>>>>>
>>>>>>>>
>>>>>>>>>>>> close to what we would need.
>>>>>>>>>>>>
>>>>>>>>>>>> Michael
>>>>>>>>>>>>
>>>>>>>>>>>> ______________________________**_________________
>>>>>>>>>>>> Bioc-devel at r-project.org mailing list
>>>>>>>>>>>>
>>>>>>>>>>>> https://stat.ethz.ch/mailman/**listinfo/bioc-devel<https://stat.
>>>>>>>>>>>> ethz.ch/mailman/listinfo/bioc-devel>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> ______________________________**_________________
>>>>>>>>>>> Bioc-devel at r-project.org mailing list
>>>>>>>>>>>
>>>>>>>>>>> https://stat.ethz.ch/mailman/**listinfo/bioc-devel<https://stat.e
>>>>>>>>>>> thz.ch/mailman/listinfo/bioc-devel>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>> ______________________________**_________________
>>>>>>>> Bioc-devel at r-project.org mailing list
>>>>>>>>
>>>>>>>> https://stat.ethz.ch/mailman/**listinfo/bioc-devel<https://stat.ethz
>>>>>>>> .ch/mailman/listinfo/bioc-devel>
>>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> --
>>>>>>> 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
>>>>>>>
>>>>>>> ______________________________**_________________
>>>>>>> Bioc-devel at r-project.org mailing list
>>>>>>>
>>>>>>> https://stat.ethz.ch/mailman/**listinfo/bioc-devel<https://stat.ethz.
>>>>>>> ch/mailman/listinfo/bioc-devel>
>>>>>>>
>>>>>>
>>>>>
>>>>>
>>>>> --
>>>>> 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
>>>
>>> ______________________________**_________________
>>> Bioc-devel at r-project.org mailing list
>>>
>>> https://stat.ethz.ch/mailman/**listinfo/bioc-devel<https://stat.ethz.ch/m
>>> ailman/listinfo/bioc-devel>
>>>
>>
>> [[alternative HTML version deleted]]
>>
>> _______________________________________________
>> Bioc-devel at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/bioc-devel
>
--
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
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