[Eeglablist] ICA preprocessing and bipolar montage configuration
Makoto Miyakoshi
mmiyakoshi at ucsd.edu
Thu Jun 23 18:16:39 PDT 2022
Dear Jason,
If we have 20 bipolar-referenced pairs of electrodes, there are only 10
time-series data. Are you saying you can recover 20-channel scalp topos,
after ICA, by building the proposed M matrix from the practically
10-channel data? Here, the issue is not invertibility per se, but whether
we can make a unipolar-reference-like scalp topos using
bipolar-referenced data that are not chain-referenced as A-B, B-C, C-D,
D-E, E-F but non-overlapping separated pairs as A-B, C-D, E-F.
I want to put it in a Wiki page for future reference. Please advise.
Makoto
On Tue, Jun 21, 2022 at 10:53 AM Jason Palmer <japalmer29 at gmail.com> wrote:
> Yes it is possible in this case too. For example, the following for 6
> channels defines 3 bipolar and 3 average channels:
>
> M =
>
> 1.0000 -1.0000 0 0 0 0
> 0 0 1.0000 -1.0000 0 0
> 0 0 0 0 1.0000 -1.0000
> 0.5000 0.5000 0 0 0 0
> 0 0 0.5000 0.5000 0 0
> 0 0 0 0 0.5000 0.5000
>
> Then the inverse is:
>
> >> inv(M)
>
> ans =
>
> 0.5000 0 0 1.0000 0 0
> -0.5000 0 0 1.0000 0 0
> 0 0.5000 0 0 1.0000 0
> 0 -0.5000 0 0 1.0000 0
> 0 0 0.5000 0 0 1.0000
> 0 0 -0.5000 0 0 1.0000
>
> -Jason
>
>
> On Tue, Jun 21, 2022 at 10:49 AM Makoto Miyakoshi <mmiyakoshi at ucsd.edu>
> wrote:
>
>> Dear Jason,
>>
>> Thank you for your reply.
>> Again, please pay attention to this realistic condition: ...when the
>> bipolar pairs are not redundantly connected to each other?
>>
>> To repeat, the realistic bipolar reference does not connect all the
>> electrodes like a chain, but it is more like a collection of isolated
>> pairs. It'll be like this:
>>
>> M =
>> 1 -1 0 0 0 0
>> 0 0 1 -1 0 0
>> 0 0 0 0 -1 1
>>
>> rather than
>>
>> M =
>> 1 -1 0 0 0 0
>> 0 1 -1 0 0 0
>> 0 0 1 -1 0 0
>> ...
>>
>> Do you see the difference?
>>
>> In words, an electrode is connected to only one electrode, no more than
>> two. In your case, one electrode is connected to two other electrodes. This
>> is what I call a redundant connection which EEG researches do not do.
>>
>> The bipolar reference users' question is, in the former instance, NOT the
>> latter one, is there a way to 'use' ICA meaningfully.
>>
>> Makoto
>>
>> On Tue, Jun 21, 2022 at 10:37 AM Jason Palmer <japalmer29 at gmail.com>
>> wrote:
>>
>>> Makoto,
>>>
>>> Yes it is possible. The bipolar matrix defines up to nchan-1 bipolar
>>> pairs, and the remaining rows are defined so as to make the matrix
>>> invertible. For example if we have 5 channels, you can define the bipolar
>>> matrix as:
>>>
>>> M =
>>>
>>> 1.0000 -1.0000 0 0 0
>>> 0 1.0000 -1.0000 0 0
>>> 0 0 1.0000 -1.0000 0
>>> 0 0 0 1.0000 -1.0000
>>> -0.2500 -0.2500 -0.2500 -0.2500 0.7500
>>>
>>> Here the last channel is 1/(nchan-1) times itself minus the average of
>>> the other channels. (It could also be [0 0 0 0 1]). Then the inverse is:
>>>
>>> >> inv(M)
>>>
>>> ans =
>>>
>>> 0 -1 -2 -3 -4
>>> -1 -1 -2 -3 -4
>>> -1 -2 -2 -3 -4
>>> -1 -2 -3 -3 -4
>>> -1 -2 -3 -4 -4
>>>
>>> Then you can run ICA on M * EEG.data. And then look at component maps
>>> inv(M) * EEG.icawinv.
>>>
>>> Best,
>>> Jason
>>>
>>>
>>>
>>> On Tue, Jun 21, 2022 at 10:26 AM Makoto Miyakoshi <mmiyakoshi at ucsd.edu>
>>> wrote:
>>>
>>>> Dear Jason,
>>>>
>>>> Sorry for the late reply. There was a big conference we hosted and I
>>>> got interrupted.
>>>>
>>>> So, is it possible to run ICA meaningfully on bipolar-referenced data
>>>> when the bipolar pairs are not redundantly connected to each other? I'm
>>>> still not convinced and believe it is impossible.
>>>>
>>>> Once we reach a clear conclusion, I'll summarize my understanding and
>>>> add it to SCCN Wiki page. Please help me.
>>>>
>>>> Makoto
>>>>
>>>> On Thu, Jun 2, 2022 at 1:37 AM Jason Palmer <japalmer29 at gmail.com>
>>>> wrote:
>>>>
>>>>> Sorry, I realized the last row should be [-0.25 -0.25 -0.25 1-0.25]
>>>>> for avg reference of the last channel, and this makes the matrix rank
>>>>> deficient again.
>>>>>
>>>>>
>>>>>
>>>>> So I think the matrix should just be something like:
>>>>>
>>>>>
>>>>>
>>>>> M = [1 -1 0 0 ;
>>>>>
>>>>> 0 1 -1 0 ;
>>>>>
>>>>> 0 0 1 -1 ;
>>>>>
>>>>> 0 0 0 1 ];
>>>>>
>>>>>
>>>>>
>>>>> The last channel would probably result in a 50 or 60 Hz line noise
>>>>> component after ICA since the bipolar channels will have the common line
>>>>> noise largely attenuated.
>>>>>
>>>>>
>>>>>
>>>>> Jason
>>>>>
>>>>>
>>>>>
>>>>> *From:* Jason Palmer [mailto:japalmer29 at gmail.com]
>>>>> *Sent:* Wednesday, June 1, 2022 9:27 PM
>>>>> *To:* 'Makoto Miyakoshi' <mmiyakoshi at ucsd.edu>
>>>>> *Cc:* 'Scott Makeig' <smakeig at gmail.com>; 'EEGLAB List' <
>>>>> eeglablist at sccn.ucsd.edu>
>>>>> *Subject:* RE: [Eeglablist] ICA preprocessing and bipolar montage
>>>>> configuration
>>>>>
>>>>>
>>>>>
>>>>> Actually it would probably be better to replace the last row with
>>>>> -ones(1,nbchan)/nbchan. So, e.g.,
>>>>>
>>>>>
>>>>>
>>>>> M = [1 -1 0 0 ;
>>>>>
>>>>> 0 1 -1 0 ;
>>>>>
>>>>> 0 0 1 -1 ;
>>>>>
>>>>> -0.25 -0.25 -0.25 -0.25 ];
>>>>>
>>>>>
>>>>>
>>>>> This way the non-bipolar channel becomes an average referenced version
>>>>> of itself. This is still invertible.
>>>>>
>>>>>
>>>>>
>>>>> *From:* Jason Palmer [mailto:japalmer29 at gmail.com
>>>>> <japalmer29 at gmail.com>]
>>>>> *Sent:* Wednesday, June 1, 2022 8:57 PM
>>>>> *To:* 'Makoto Miyakoshi' <mmiyakoshi at ucsd.edu>
>>>>> *Cc:* 'Scott Makeig' <smakeig at gmail.com>; 'EEGLAB List' <
>>>>> eeglablist at sccn.ucsd.edu>
>>>>> *Subject:* RE: [Eeglablist] ICA preprocessing and bipolar montage
>>>>> configuration
>>>>>
>>>>>
>>>>>
>>>>> Makoto,
>>>>>
>>>>>
>>>>>
>>>>> You are right, if the M matrix has only 1 -1 pairs in rows, then it is
>>>>> not full rank. However, if you use 1 -1 pairs for all but one, channel, e.g.
>>>>>
>>>>>
>>>>>
>>>>> M = [1 -1 0 0 ;
>>>>>
>>>>> 0 1 -1 0 ;
>>>>>
>>>>> 0 0 1 -1 ;
>>>>>
>>>>> 0 0 0 1 ];
>>>>>
>>>>>
>>>>>
>>>>> This has 3 pairs and leaves one channel unchanged, and it is full rank
>>>>> and invertible. It is not necessary for the bipolar matrix to have all 1 -1
>>>>> pairs, just the ones that are relevant.
>>>>>
>>>>>
>>>>>
>>>>> Jason
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> *From:* Makoto Miyakoshi [mailto:mmiyakoshi at ucsd.edu
>>>>> <mmiyakoshi at ucsd.edu>]
>>>>> *Sent:* Wednesday, June 1, 2022 8:13 PM
>>>>> *To:* Jason Palmer <japalmer29 at gmail.com>
>>>>> *Cc:* Scott Makeig <smakeig at gmail.com>; EEGLAB List <
>>>>> eeglablist at sccn.ucsd.edu>
>>>>> *Subject:* Re: [Eeglablist] ICA preprocessing and bipolar montage
>>>>> configuration
>>>>>
>>>>>
>>>>>
>>>>> Jason, your example uses redundant bipolar referencing, which is A-B,
>>>>> B-C, C-D as I explained above. This can be confirmed in your example below
>>>>> (I changed your B to M because I use A B C D for electrode indices)
>>>>>
>>>>>
>>>>>
>>>>> > A bipolar channel matrix looks like:
>>>>> >
>>>>> > M = [ 1 -1 0 0 0 0 0 …. ;
>>>>> >
>>>>> > 0 1 -1 0 0 0 0 …. ;
>>>>> >
>>>>> > 0 0 1 -1 0 0 0 … ;
>>>>>
>>>>>
>>>>>
>>>>> Note the rank of this data is nbchan-1, which is the same as the
>>>>> unipolar recorded EEG data including the initial reference. In other words,
>>>>> your example does not differ from unipolarly recorded data!
>>>>>
>>>>>
>>>>>
>>>>> But I'm talking about the case in which only A-B and C-D pairs are
>>>>> available without B-C. The reason why I assume this is because this is the
>>>>> reality of bipolar reference. In this case, M is
>>>>>
>>>>>
>>>>>
>>>>> M = [ 1 -1 0 0 0 0 0 …. ;
>>>>> 0 0 1 -1 0 0 0 … ;
>>>>>
>>>>> 0 0 0 0 1 -1 0 ...;
>>>>>
>>>>>
>>>>>
>>>>> M is not invertible.
>>>>>
>>>>>
>>>>>
>>>>> > It should be possible to define a square, invertible bipolar matrix
>>>>> (which I called B, but is called M here).
>>>>>
>>>>>
>>>>>
>>>>> I want to first confirm if your explanation is still valid for my
>>>>> 'realistic bipolar reference M' scenario.
>>>>>
>>>>>
>>>>>
>>>>> Makoto
>>>>>
>>>>>
>>>>>
>>>>> On Wed, Jun 1, 2022 at 7:13 PM Jason Palmer <japalmer29 at gmail.com>
>>>>> wrote:
>>>>>
>>>>> Hi Makoto,
>>>>>
>>>>>
>>>>>
>>>>> It should be possible to define a square, invertible bipolar matrix
>>>>> (which I called B, but is called M here). Then I don’t think there needs to
>>>>> be a caveat about the interpretation.
>>>>>
>>>>>
>>>>>
>>>>> Jason
>>>>>
>>>>>
>>>>>
>>>>> *From:* Makoto Miyakoshi [mailto:mmiyakoshi at ucsd.edu]
>>>>> *Sent:* Wednesday, June 1, 2022 11:12 AM
>>>>> *To:* Scott Makeig <smakeig at gmail.com>; Jason Palmer <
>>>>> japalmer29 at gmail.com>
>>>>> *Cc:* EEGLAB List <eeglablist at sccn.ucsd.edu>
>>>>> *Subject:* Re: [Eeglablist] ICA preprocessing and bipolar montage
>>>>> configuration
>>>>>
>>>>>
>>>>>
>>>>> Dear Scott and Jason,
>>>>>
>>>>>
>>>>>
>>>>> See this comment from one of the discussions on the list from 2017,
>>>>> particularly the last highlighted part.
>>>>>
>>>>> Scott, we discussed this issue during tea time. Did you reach a
>>>>> different conclusion? Do we want to correct this conclusion?
>>>>>
>>>>>
>>>>>
>>>>> Makoto
>>>>>
>>>>>
>>>>>
>>>>> %%%%%%%%%%%%%%%%%
>>>>>
>>>>> https://sccn.ucsd.edu/pipermail/eeglablist/2017/012597.html
>>>>>
>>>>>
>>>>>
>>>>> [Eeglablist] convert EEG montage from bipolar to unipolar
>>>>> Makoto Miyakoshi mmiyakoshi at ucsd.eduThu May 25 12:35:12 PDT 2017
>>>>>
>>>>>
>>>>>
>>>>> Dear colleagues,
>>>>>
>>>>> Update--
>>>>>
>>>>> I discussed this method with the colleague who taught me about this trick
>>>>>
>>>>> because I got an inquiry about it off the list.
>>>>>
>>>>> He said that he would use it only to draw a scalp topography, and
>>>>>
>>>>> performing signal processing using the 'recovered' full-channel signal is
>>>>>
>>>>> not recommended.
>>>>>
>>>>>
>>>>>
>>>>> Again, let X be the (single-channel referenced) original EEG data and Xb
>>>>>
>>>>> the bipolar-montage version of it.
>>>>>
>>>>> Using a bipolar-referencing transform matrix M, the relation of X and Xb
>>>>>
>>>>> can be written as
>>>>>
>>>>>
>>>>>
>>>>> Xb = M * X
>>>>>
>>>>>
>>>>>
>>>>> Suppose X has 6 channels F1, F2, C1, C2, P1, P2, and bipolar-referencing
>>>>>
>>>>> was done with F1-F2, C1-C2, P1-P2.
>>>>>
>>>>> Then, Xb is 3*t, M is 3*6, and X is 6*t (t is time).
>>>>>
>>>>> The matrix M is
>>>>>
>>>>>
>>>>>
>>>>> 1 -1 0 0 0 0
>>>>>
>>>>> 0 0 1 -1 0 0
>>>>>
>>>>> 0 0 0 0 1 -1
>>>>>
>>>>>
>>>>>
>>>>> (sorry but I don't have code)
>>>>>
>>>>> To compute M^-1, one should use pinv() (i.e. pseudo-inverse) and the
>>>>>
>>>>> recovered full-channel data are NOT full-ranked (and this is NOT the only
>>>>>
>>>>> solution)
>>>>>
>>>>> To recover full channel data, you also need to have something like F1-C1,
>>>>>
>>>>> C2-P1, P2-F2 so that the matrix is full-ranked and square, but such data
>>>>>
>>>>> are not usually available (as far as I know, Paul Sajda presented such a
>>>>>
>>>>> complicated reference system to address high-amplitude artifact in
>>>>>
>>>>> simultaneous fMRI-EEG recording).
>>>>>
>>>>>
>>>>>
>>>>> So the recommended use of this solution is just to draw scalp topography
>>>>>
>>>>> for convenience.
>>>>>
>>>>>
>>>>>
>>>>> Accordingly, let me correct my previous statement.
>>>>>
>>>>>
>>>>>
>>>>> >* Thus, by multiplying the inverse matrix of the known bipolar-referencing*
>>>>>
>>>>> transform matrix M, you obtain the original signal.
>>>>>
>>>>>
>>>>>
>>>>> This is true ONLY IF you have redundantly referenced channels (which is
>>>>>
>>>>> very rare). Otherwise, it does NOT properly convert standard bipolar
>>>>>
>>>>> montage to a single-referenced data (because M is not square), therefore
>>>>>
>>>>> analyzing the 'recovered' data should be limited to specific purposes only.
>>>>>
>>>>>
>>>>>
>>>>> Sorry if my previous writing was misleading.
>>>>>
>>>>>
>>>>>
>>>>> Makoto
>>>>>
>>>>>
>>>>>
>>>>> On Wed, Jun 1, 2022 at 10:29 AM Scott Makeig <smakeig at gmail.com>
>>>>> wrote:
>>>>>
>>>>> Jason -
>>>>>
>>>>> Thanks - exact, as usual for you ... I am looking to try it - then put
>>>>> it
>>>>> into EEGLAB.
>>>>>
>>>>> Scott
>>>>>
>>>>> On Wed, Jun 1, 2022 at 1:13 PM Jason Palmer <japalmer29 at gmail.com>
>>>>> wrote:
>>>>>
>>>>> > ICA will try to produce independent sources (the s below) regardless
>>>>> of
>>>>> > how they are linearly mixed.
>>>>> >
>>>>> >
>>>>> >
>>>>> > A bipolar channel matrix looks like:
>>>>> >
>>>>> >
>>>>> >
>>>>> > B = [ 1 -1 0 0 0 0 0 …. ;
>>>>> >
>>>>> > 0 1 -1 0 0 0 0 …. ;
>>>>> >
>>>>> > 0 0 1 -1 0 0 0 … ;
>>>>> >
>>>>> > ...
>>>>> >
>>>>> > ];
>>>>> >
>>>>> >
>>>>> >
>>>>> > Or similar, depending on how you define the bipolar channels.
>>>>> >
>>>>> >
>>>>> >
>>>>> > And the raw data x, after bipolar channel extraction is B*x = B*A*s,
>>>>> where
>>>>> > A is mixing matrix topo maps, and s is the source vector. If you run
>>>>> ICA on
>>>>> > B*x, then you get a decomposition with a mixing matrix M. This is not
>>>>> > necessarily interpretable with topoplot. To get the actual topo
>>>>> maps, you
>>>>> > need to invert the bipolar matrix:
>>>>> >
>>>>> >
>>>>> >
>>>>> > B*A = M => A = pinv(B)*M
>>>>> >
>>>>> >
>>>>> >
>>>>> > where again, B is the custom bipolar channel difference matrix, and
>>>>> M is
>>>>> > the EEG.icawinv after running ICA on B*x (where x is EEG.data). The
>>>>> columns
>>>>> > of this A matrix should be as usual. Using the bipolar differences
>>>>> might
>>>>> > remove more far field noise and components vs usual raw channels.
>>>>> >
>>>>> >
>>>>> >
>>>>> > Jason
>>>>> >
>>>>> >
>>>>> >
>>>>> > *From:* Scott Makeig [mailto:smakeig at gmail.com]
>>>>> > *Sent:* Wednesday, June 1, 2022 10:01 AM
>>>>> > *To:* Jason Palmer <japalmer29 at gmail.com>
>>>>> > *Cc:* Velu Prabhakar Kumaravel <velu.kumaravel at unitn.it>; EEGLAB
>>>>> List <
>>>>> > eeglablist at sccn.ucsd.edu>
>>>>> > *Subject:* Re: [Eeglablist] ICA preprocessing and bipolar montage
>>>>> > configuration
>>>>> >
>>>>> >
>>>>> >
>>>>> > Jason - But the mapping problem remains, no? Will ICA make the IC
>>>>> maps
>>>>> > (including somehow the bipolar channel) smooth even when the data
>>>>> contains
>>>>> > a bipolar channel? What about this argument: Making such a dataset
>>>>> > zero-mean does not necessarily mean that the difference between the
>>>>> common
>>>>> > reference and each electrode in the bipolar channel is 0. If the
>>>>> sources
>>>>> > were [equally everywhere], then this might be the case, but in
>>>>> actual fact,
>>>>> > is it?
>>>>> >
>>>>> >
>>>>> >
>>>>> > Scott
>>>>> >
>>>>> >
>>>>> >
>>>>> > On Wed, Jun 1, 2022 at 12:07 PM Jason Palmer <japalmer29 at gmail.com>
>>>>> wrote:
>>>>> >
>>>>> > A bipolar montage is basically just a linear transformation, and
>>>>> assuming
>>>>> > you use at most nbchan number of bipolar channels, it is invertible.
>>>>> >
>>>>> > x = A*s
>>>>> > B*x = B*A*s = M*s
>>>>> > A = inv(B) * M
>>>>> >
>>>>> > Where B is the bipolar montage with 1 -1 in the columns
>>>>> corresponding to
>>>>> > the
>>>>> > bipolar difference for each row, and M is the EEG.icawinv after
>>>>> running ica
>>>>> > on the bipolar transformed data.
>>>>> >
>>>>> > Jason
>>>>> >
>>>>> > -----Original Message-----
>>>>> > From: eeglablist [mailto:eeglablist-bounces at sccn.ucsd.edu] On
>>>>> Behalf Of
>>>>> > Scott Makeig
>>>>> > Sent: Wednesday, June 1, 2022 8:52 AM
>>>>> > To: Velu Prabhakar Kumaravel <velu.kumaravel at unitn.it>
>>>>> > Cc: EEGLAB List <eeglablist at sccn.ucsd.edu>
>>>>> > Subject: Re: [Eeglablist] ICA preprocessing and bipolar montage
>>>>> > configuration
>>>>> >
>>>>> > Velu -
>>>>> >
>>>>> > ICA is a linear decomposition, so should be able to decompose
>>>>> bipolar and
>>>>> > common-reference channels in the same session together. However, the
>>>>> > bipolar
>>>>> > channels will be 'floating' with respect to the common-reference
>>>>> channels.
>>>>> > This might interfere with the decomposition (I have no practical
>>>>> experience
>>>>> > here) - but even if not it will mean that the ICA scalp maps should
>>>>> not be
>>>>> > plotted to include the bipolar channels. Here I imagine you might
>>>>> try to
>>>>> > find fixed offsets representing a 'standing difference'
>>>>> > between each bipolar channel and the common reference channel that
>>>>> would
>>>>> > produce max smooth IC maps -- but are these differences reliably
>>>>> > stationary? I'd be interested to see a result of attempting this ...
>>>>> >
>>>>> > Scott Makeig
>>>>> >
>>>>> > On Wed, Jun 1, 2022 at 11:42 AM Velu Prabhakar Kumaravel <
>>>>> > velu.kumaravel at unitn.it> wrote:
>>>>> >
>>>>> > > Dear EEGLABers,
>>>>> > >
>>>>> > > Does anyone know the effects of ICA preprocessing on EEG acquired
>>>>> > > using bipolar configuration?
>>>>> > > I tried on a few datasets and it looks like the decomposition is
>>>>> not
>>>>> > > effective. Classifying using ICLabel results in more number of
>>>>> "Other"
>>>>> > > category.
>>>>> > >
>>>>> > > Could someone provide insights on this?
>>>>> > >
>>>>> > > Best regards,
>>>>> > >
>>>>> > > Velu Prabhakar Kumaravel, Ph.D. Student Center for Mind/Brain
>>>>> > > Sciences, University of Trento, Italy
>>>>> > > _______________________________________________
>>>>> > > Eeglablist page: http://sccn.ucsd.edu/eeglab/eeglabmail.html
>>>>> > > To unsubscribe, send an empty email to
>>>>> > > eeglablist-unsubscribe at sccn.ucsd.edu
>>>>> > > For digest mode, send an email with the subject "set digest mime"
>>>>> to
>>>>> > > eeglablist-request at sccn.ucsd.edu
>>>>> > >
>>>>> >
>>>>> >
>>>>> > --
>>>>> > Scott Makeig, Research Scientist and Director, Swartz Center for
>>>>> > Computational Neuroscience, Institute for Neural Computation,
>>>>> University of
>>>>> > California San Diego, La Jolla CA 92093-0559,
>>>>> http://sccn.ucsd.edu/~scott
>>>>> > _______________________________________________
>>>>> > Eeglablist page: http://sccn.ucsd.edu/eeglab/eeglabmail.html
>>>>> > To unsubscribe, send an empty email to
>>>>> > eeglablist-unsubscribe at sccn.ucsd.edu
>>>>> > For digest mode, send an email with the subject "set digest mime" to
>>>>> > eeglablist-request at sccn.ucsd.edu
>>>>> >
>>>>> >
>>>>> >
>>>>> >
>>>>> > --
>>>>> >
>>>>> > Scott Makeig, Research Scientist and Director, Swartz Center for
>>>>> > Computational Neuroscience, Institute for Neural Computation,
>>>>> University of
>>>>> > California San Diego, La Jolla CA 92093-0559,
>>>>> http://sccn.ucsd.edu/~scott
>>>>> >
>>>>>
>>>>>
>>>>> --
>>>>> Scott Makeig, Research Scientist and Director, Swartz Center for
>>>>> Computational Neuroscience, Institute for Neural Computation,
>>>>> University of
>>>>> California San Diego, La Jolla CA 92093-0559,
>>>>> http://sccn.ucsd.edu/~scott
>>>>> _______________________________________________
>>>>> Eeglablist page: http://sccn.ucsd.edu/eeglab/eeglabmail.html
>>>>> To unsubscribe, send an empty email to
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>>>>>
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