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 Posted: Tue Jun 24, 2003 8:49 am Post subject: Multiple layer perceptron design problem |
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Tom Osborn
Guest
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| Posted: Tue Jun 24, 2003 8:49 am Post subject: Re: Multiple layer perceptron design problem |
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"Newsgroup - Ann" <news_ann@yahoo.com> wrote in message news:3ef752a5$1_1@rcfnews.cs.umass.edu...
| Quote: | Does anybody have any suggestion on classifying the following classes using
multilayer perceptron?
The input data belong to five classes as shown below, each of about the same
size. Classes (0)-(3) occupy the four corners and the (4) occupies the
central round circle. This must be supposed to be very simple. But it took
me some time to try to make it converge it still does not work yet. Do you
have any general idea about how to design a multilayer perceptron? Do not
laugh at me if it's too stupid.
Thanks.
(1) | (3)
------ (4) ------
(0) | (2)
News - Ann
|
Had a few minutes waiting for coffee:
I can get this to converge with 2 input, 3 hidden, 5 output. [97%+, with cross-validation,
doesn't converge every time - re-initialise]. [Classification by maximum score].
2 4 5 is pretty clean. Misclassified points are pretty close to boundaries.
But 2 2 5 doesn't usually get all five classes clean. The number of bits required
to define five classes is > 2, so it makes sense that 2 hidden neurons is not
enough. Adding a weight between input 1 and output 1, and between input 2
and output 1, and just manage it, but the margins are pretty scrappy...
I chose the circle to be radius 0.5, in the centre of a 2*2 square, so the five
classes were about the same size, and generated about 650 data points (about
70..75 points per class).
Maybe "News - Ann" needs to get a bit more experience with learning rates.
[I used eta = 0.02 without relaxation, update after each pattern. Batch update
also ran OK].
If class sizes are unequal, it can get a bit harder. Please read the neural net FAQ.
Cheers, Tom.
--
Dr Tom Osborn
NUIX Pty Ltd
Level 8, 143 York St
Sydney NSW 2000
--
This message is intended for only for the named recipient. If you are not the
intended recipient you are notified that disclosing, copying, distributing or
taking any action in reliance on the content of this information is strictly
prohibited. |
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Andrzej Lewandowski
Guest
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| Posted: Tue Jun 24, 2003 5:45 pm Post subject: Re: Stock forecasting |
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On Mon, 23 Jun 2003 18:32:05 +0200, "Radek" <radekwawa@poczta.fm>
wrote:
| Quote: | Hello
I'm looking for a general NN source code in Pascal or Delphi. Especially
stocks prediction interests me. Where can I find a paper about it?
What kind of NN would be the best for forecasting prices of stocks? How
should I teach that net - with backprop or sth else? I heard backprop is
sufficient. Is this correct?
|
There is a discussion about this topic right now on pl.sci.ai. In
Polish, of course :)
A.L. |
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Andrzej Lewandowski
Guest
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| Posted: Tue Jun 24, 2003 5:46 pm Post subject: Re: Call for Participation: IDA 2003 - 5th Int. Symp. on Int |
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On Tue, 24 Jun 2003 11:29:45 +0200, Andreas Nuernberger
<nuernb@iws.cs.uni-magdeburg.de> wrote:
| Quote: | - Call for Participation -
5th International Symposium on Intelligent Data Analysis - IDA 2003
Berlin, Germany
August 28-30, 2003
(http://ida2003.org)
|
What is "intelligent" data anaysis versus "not intelligent" data
analysis? How to recognize that specific methos is intelligent and
other is not?..
A.L. |
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Zander
Guest
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| Posted: Wed Jun 25, 2003 12:02 am Post subject: Re: resampling technique in variable selection |
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Now, I am finally clear of the bootstrap procedure you are suggesting.
Thanks very much! So for each bootstrap trial, I have a nondesign set
(used as testing) and a design set (used as training). Whatever model
that comes out of the training set will be tested in the nondesign set
in each bootstrap trial. However, for each bootstrap trial, I may end
up with a different model (or say a different set of variables by
appripriate method). Then how can I come up with a final model (i.e.
final set of variables) in the end? and how can I test that final set
of variables? I guess what I really want is at the end of analysis, I
would like to tell people that I have set of variables that when
combined together have good discrimination power, which is the purpose
of doing bootstrap in my situation.
If I take average of the statistics (like F test or t test (I
understand it may not be appropriate)) that I calculate for each
variable in each bootstrap trial, and select variables based on the
averaged statistics, then the nondesign sets from the bootstrap trials
have no use at all in the process?
| Quote: | Next?
I am sorry. This single unsupervised variable reduction step
should precede the bootstrapping trials.
Hope this helps.
Again, original bootstrapping or my version adequately handles
the sampling.
You *really* need to worry about the selection criterion.
|
Yes, I understand with the size of data that i have, this is something
I do have to worry about.
| Quote: |
What you suggested is probably very suboptimal even if you
had 800 cases. |
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Greg Heath
Guest
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| Posted: Wed Jun 25, 2003 1:07 pm Post subject: Re: resampling technique in variable selection |
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arrayprofile@yahoo.com (Zander) wrote in message
news:<d83a0fc3.0306241102.393961e5@posting.google.com>...
| Quote: | Now, I am finally clear of the bootstrap procedure you are suggesting.
Thanks very much! So for each bootstrap trial, I have a nondesign set
(used as testing) and a design set (used as training).
|
Are you using a validation set? I will assume that you are not.
| Quote: | Whatever model
that comes out of the training set will be tested in the nondesign set
in each bootstrap trial. However, for each bootstrap trial, I may end
up with a different model (or say a different set of variables by
appripriate method).
|
You *will* end up with different models. Moreover, the models will
have different numbers of selected variables unless *you* fix the
the number of variables.
| Quote: | Then how can I come up with a final model (i.e.
final set of variables) in the end? and how can I test that final set
of variables?
|
Good question. I don't know the optimal answer or even if there
is a generally accepted practical procedure.
A quick answer would be to rank each model via it's performance
on all of the data. For example, you might use the 0.632 bootstrap
model generalization error estimate eg = 0.368*ed + 0.632*et, a
weighted average of design and test set error (I've read and reread
Efrom's explanation for those weights, however I still don't
understand it). See the bootstrap references in the FAQ (especially
Efrom).
Plot eg vs rank (r=1,...B) and overlay 7 horizontal lines at the
mean +/- j*sigma levels (j=0,1,2,3). Choose the m models worthy
of further consideration. Form a histogram of variables used in
those m models. Then rank the variables. However, you just can't
take the top q variables. Also look at the histograms and rankings
of variable pairs and triplets.
Based on the above info, choose one of the m models.
| Quote: | I guess what I really want is at the end of analysis, I
would like to tell people that I have set of variables that when
combined together have good discrimination power, which is the purpose
of doing bootstrap in my situation.
|
No. The purpose of bootstrap is to squeeze the most information out
of your sparse data set.
| Quote: | If I take average of the statistics (like F test or t test (I
understand it may not be appropriate)) that I calculate for each
variable in each bootstrap trial, and select variables based on the
averaged statistics, then the nondesign sets from the bootstrap trials
have no use at all in the process?
|
You can't rank variables untill you rank models.
| Quote: | You *really* need to worry about the selection criterion.
Yes, I understand with the size of data that i have, this is something
I do have to worry about.
|
I don't think you understand: Even with 10 times as much data
you can still have significant problems. Because of multiple
variable correlations, redundant variables are trickier to
identify than irrelevant variables.
There are 100 models with 1 variable
There are 100 models with 99 variables
There are 100*99/2 = 4950 models with 2 variables
There are 100*99/2 = 4950 models with 98 variables
.. . .
There are 100! / (50! * 50!) models with 50 variables.
See the FAQ and books (statistical regression and pattern
recognition) on input selection.
Hope this helps.
Greg
| Quote: | What you suggested is probably very suboptimal even if you
had 800 cases. |
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Greg Heath
Guest
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| Posted: Wed Jun 25, 2003 1:48 pm Post subject: Re: Multiple layer perceptron design problem |
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"Tom Osborn" <MAPStom@DELETE CAPS.nuix.com.au> wrote in message
news:<3ef7ca62$1_1@news.iprimus.com.au>...
| Quote: | "Newsgroup - Ann" <news ann@yahoo.com> wrote in message
news:3ef752a5$1 1@rcfnews.cs.umass.edu...
Does anybody have any suggestion on classifying the following classes
using multilayer perceptron?
The input data belong to five classes as shown below, each of about
the same
size. Classes (0)-(3) occupy the four corners and the (4) occupies the
central round circle. This must be supposed to be very simple. But it
took
me some time to try to make it converge it still does not work yet. Do
you
have any general idea about how to design a multilayer perceptron? Do
not laugh at me if it's too stupid.
Thanks.
(1) | (3)
------ (4) ------
(0) | (2)
News - Ann
Had a few minutes waiting for coffee:
I can get this to converge with 2 input, 3 hidden, 5 output. [97%+, with
cross-validation,
doesn't converge every time - re-initialise]. [Classification by maximum
score].
2 4 5 is pretty clean. Misclassified points are pretty close to
boundaries. But 2 2 5 doesn't usually get all five classes clean.
|
Usually? I don't see how it can.
The 4 separating lines are easy to visualize for the 2-4-5:
A square contains the circle. The slopes of the sides are
+/- 1.
For the 2-3-5, the circle is contained in a triangle. I'll
leave the details to the reader.
How can you do it with 2-2-5?
| Quote: | The number of bits
required
to define five classes is > 2, so it makes sense that 2 hidden neurons
is not
enough. Adding a weight between input 1 and output 1, and between input
2
and output 1, and just manage it, but the margins are pretty scrappy...
|
Aha. Skip-layer connections.
| Quote: | I chose the circle to be radius 0.5, in the centre of a 2*2 square, so
the five
classes were about the same size, and generated about 650 data points
(about
70..75 points per class)
|
Oh. Good. The classes 0-3 uniformly filled the square outside
of the circle. The original post implied just the corners.
Hope this helps.
Greg
| Quote: | Maybe "News - Ann" needs to get a bit more experience with learning
rates.
[I used eta = 0.02 without relaxation, update after each pattern.
Batch update also ran OK].
If class sizes are unequal, it can get a bit harder. Please read the
neural net FAQ.
Cheers, Tom.
--
Dr Tom Osborn
NUIX Pty Ltd
Level 8, 143 York St
Sydney NSW 2000 |
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Max Xam
Guest
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| Posted: Thu Jun 26, 2003 9:10 am Post subject: Re: Easiest to use / cheapish or free neural network softwar |
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Look at http://www.neuroxl.com
They offer neural network prediction and classification add-ins for Microsoft Excel.
philbrierley@hotmail.com (Phil Brierley) wrote in message news:<4e561a4c.0306211346.652a661b@posting.google.com>...
| Quote: | Hi Jason,
I too would like to promote my own software!
Tiberius will allow you to easily train a neural network. You can then
convert the model to an excel spreadsheet, vb project or web page so
that you can just type or paste in the values and out pops the
modelled value. This convertion tool is found under tools>>development
kit.
I think you'll find the excel spreadsheet exactly what you require.
The price is pretty cheap too - its free to try and $5 to buy!
There is also a newsgroup for Tiberius....
http://groups.yahoo.com/group/TiberiusANN
Tiberius can be downloaded from....
www.philbrierley.com
Hope you find what you want.
Phil
"Jason" <kor@NOOSPAMcomcast.net> wrote in message news:<Mv-dnaDeSuY6G2mjXTWcpg@giganews.com>...
Hi.... been messing around with neural networks now for a few weeks, but I
am having a terrible time of finding software that is easy to use and/or
affordable....
Basically my data has
6 columns, 1000 rows, and once the network has been trained I need to be
able to easily and very quickly add another row, and then the prediction
should be instantly returned.....
Anyone got any software recommendations? (and the stuff I am trying to do is
really far from rocket science, ease of use is the number 1 feature I am
looking for, with the ability of being able to quickly add a new row and get
a response the other important criteria)
thanks! |
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Christos Dimitrakakis
Guest
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| Posted: Mon Jun 30, 2003 6:40 pm Post subject: Re: Resurrecting the dead with A.I. Appeal for workers Londo |
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On Mon, 30 Jun 2003 14:48:18 +0200, ELDRAS wrote:
| Quote: | 1. That human beings exist as physical interactions.
|
Humans always seek physical interaction. However I am not sure they
actually get it.
| Quote: | 2. that those interactions are capable of being mapped and logged by
coming machines, since machines are advancing in complexity capacity
MUCH faster than our bodies are advancing in complexity.
|
I am sorry, but you seem to have simply fallen behind the times. Through
our Artificial Evolution [TM] program we offer advances in complexity
that is exponential to a degree much higher than Moore's law. In fact,
teams of Improbable Geographic [R] scientists have mapped and logged in
meticulous detail not only the known universe, but also parts of the
unknown universes that are guaranteed to lie at the furthest reaches of
the physical laws' probability curves. The acquisition of improbable
universe data is accelerating exponentially.
| Quote: | 3. That at some point in the future machines will arise that can
calculate the exact map of everything that has ever happened on the
palet earth, in every respect. That this will include the nao of each
deceased human, including every thought that they had.
|
One of our research parteners has created a program that not only can
caculate everything that has ever happenned, but that can also predict
everything that is possible to happen. He has also proved that this
calculation much easier than predicting what is actually going to happen.
| Quote: | 4. Thatsuch complex 'Intelligent' machines will then also be able to
reconstitue each passed person.
|
Actually, Thatsuch machines have been around for a long time. However,
while passed persons could be reconstituted, there has always been some
trouble with the bureaucracy. Most countries will simply refuse to assign
hereditary rights to a born-again citizen and even if they did, the
individual's possessions would be heavily taxed. Intelligent Thatsuch
complex machines are now a thing of the past.
| Quote: | 5. That I persoanlly am trying to deliver this with
http://bess.port5.com
|
What about FedEx?
| Quote: | Can you come over to London and join me?
|
I find the weather in London obnoxious and the traffic overwhelming.
| Quote: | please contact the club secretary on the site (below) and not me just
yet.
|
I wish you had a better picture of her.
Christos Dimitrakakis
http://olethros.dmusic.net |
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Guest
|
| Posted: Mon Jun 30, 2003 10:19 pm Post subject: Re: Stock forecasting |
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Dick Penny wrote:
| Quote: |
I'm looking for a general NN source code in Pascal or Delphi. Especially
stocks prediction interests me. Where can I find a paper about it?
There are literally "hundreds" of papers on this subject, and entire
conferences devoted to it. Do a little literature search and you will find
too many. I've been collecting them for ~8 years. Do they work? Ahhha,
there's the rub. Ones that work don't get published, and ones that are
published don't work - BUT, they to point in the right directions.
|
I've been reading these papers recently (got interested in the topic
recently when I interviewed at a place that may want one built).
It appears that heuristic methods have the effect of "game theory" in
stock picking; you can assure that you will do no *worse* than average
in picking stocks, and to the extent that other players make avoidable
mistakes, you may do a trifling bit better than average.
Still and all, there are depths these systems have not yet plumbed, I
think. They've been working strictly with the numerical data and
ignoring news stories about the companies, for example, because the
language problems are much more difficult than just reading numbers.
And they've been concentrating on stock picking because it's such an
obvious way to make money that many heuristic systems have been
trained with stock picking as their sole measure of success.
There may be some substantial treasure in figuring out how, and how
fast, humans react to news stories of various types.
And there may be some substantial treasure in finding newer and
better ways to keep a portfolio diversified properly or finding
ways to profit other than by picking stocks.
And, in general, it probably behooves the developer of a new
system to look at things in ways the other systems don't; you can
assume that patterns in the numbers everybody looks at (stock price
in dollars and volume in shares) will have been found by any heuristic
method that looks for patterns in them. But if you consider things
they don't, such as currency risks (prices relative to gold), news
stories, or volume as a percentage of ownership, it's still possible
to find things they didn't find. In order to find novel patterns,
you have to find new ways of interpreting data.
Bear |
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Rich
Guest
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| Posted: Tue Jul 01, 2003 1:34 am Post subject: Re: Resurrecting the dead with A.I. Appeal for workers Londo |
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On 30 Jun 2003 05:48:18 -0700, ELDRAS wrote:
| Quote: | 1. That human beings exist as physical interactions.
2. that those interactions are capable of being mapped and logged by
coming machines, since machines are advancing in complexity capacity
MUCH faster than our bodies are advancing in complexity.
3. That at some point in the future machines will arise that can
calculate the exact map of everything that has ever happened on the
palet earth, in every respect. That this will include the nao of each
deceased human, including every thought that they had.
4. Thatsuch complex 'Intelligent' machines will then also be able to
reconstitue each passed person.
5. That I persoanlly am trying to deliver this with
http://bess.port5.com
Can you come over to London and join me?
It doesn't matter what degree of knowledge you have in any single
subject; everything is learnable.
Ofcourse i know you wont....but you might if the stakes were high
enough.
please contact the club secretary on the site (below) and not me just
yet.
|
conclusion: Inhaling paint fumes can be very dangerous |
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Koko
Guest
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| Posted: Thu Jul 03, 2003 1:27 am Post subject: Re: Importing data into MATLAB |
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On 2 Jul 2003 12:41:05 -0700, jancse@hotmail.com (janelle) wrote:
| Quote: | Hi,
I need some information on importing data from a text file into
MATLAB. I heard of a command called load but I am unsure of its use.
Thanks.
Jan
help load
|
LOAD Load workspace variables from disk.
LOAD FILENAME retrieves all variables from a file given a full
pathname
or a MATLABPATH relative partial pathname (see PARTIALPATH). If
FILENAME
has no extension LOAD looks for FILENAME and FILENAME.mat and
treats it
as a binary "MAT-file". If FILENAME has an extension other than
..mat, it
is treated as ASCII.
LOAD, by itself, uses the binary "MAT-file" named 'matlab.mat'. It
is
an error if 'matlab.mat' is not found.
LOAD FILENAME X loads only X.
LOAD FILENAME X Y Z ... loads just the specified variables. The
wildcard '*' loads variables that match a pattern (MAT-file only).
LOAD -ASCII FILENAME or LOAD -MAT FILENAME forces LOAD to treat the
file
as either an ASCII file or a MAT file regardless of file extension.
With
-ASCII, LOAD will error if the file is not numeric text. With
-MAT, LOAD
will error if the file is not a MAT file those generated by SAVE
-MAT.
If FILENAME is a MAT file, requested variables from FILENAME are
created
in the workspace. If FILENAME is not a MAT file, a double precision
array
is created with name based on FILENAME. Leading underscores or
digits in
FILENAME are replaced with X. Other non-alpha chars in FILENAME
are
replaced with underscores.
S = LOAD(...) returns the contents of FILENAME in variable S. If
FILENAME is a MAT file, S is a struct containing fields matching
the
variables retrieved. If FILENAME is an ASCII file, S is a double
precision array.
Use the functional form of LOAD, such as LOAD('filename'), when the
file name is stored in a string, when an output argument is
requested,
or if FILENAME contains spaces.
See also SAVE, WHOS, UILOAD, SPCONVERT, PARTIALPATH, IOFUN,
FILEFORMATS.
Overloaded methods
help activex/load.m
Overloaded methods
help activex/load.m |
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ELDRAS
Guest
|
| Posted: Thu Jul 03, 2003 6:52 am Post subject: Re: Resurrecting the dead with A.I. Appeal for workers Londo |
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|
Christos Dimitrakakis <olethrosdc@oohay.com> wrote in message news:<pan.2003.06.30.15.40.38.167963.2065@oohay.com>...
| Quote: | On Mon, 30 Jun 2003 14:48:18 +0200, ELDRAS wrote:
1. That human beings exist as physical interactions.
Humans always seek physical interaction. However I am not sure they
actually get it.
2. that those interactions are capable of being mapped and logged by
coming machines, since machines are advancing in complexity capacity
MUCH faster than our bodies are advancing in complexity.
I am sorry, but you seem to have simply fallen behind the times. Through
our Artificial Evolution [TM] program we offer advances in complexity
that is exponential to a degree much higher than Moore's law. In fact,
teams of Improbable Geographic [R] scientists have mapped and logged in
meticulous detail not only the known universe, but also parts of the
unknown universes that are guaranteed to lie at the furthest reaches of
the physical laws' probability curves. The acquisition of improbable
universe data is accelerating exponentially.
|
| Quote: | I suppose ur joking.
|
if ur not, can you give me a rewf to what may then be similar work?
Cheers.
| Quote: |
3. That at some point in the future machines will arise that can
calculate the exact map of everything that has ever happened on the
palet earth, in every respect. That this will include the nao of each
deceased human, including every thought that they had.
One of our research parteners has created a program that not only can
caculate everything that has ever happenned, but that can also predict
everything that is possible to happen. He has also proved that this
calculation much easier than predicting what is actually going to happen.
4. Thatsuch complex 'Intelligent' machines will then also be able to
reconstitue each passed person.
Actually, Thatsuch machines have been around for a long time. However,
while passed persons could be reconstituted, there has always been some
trouble with the bureaucracy. Most countries will simply refuse to assign
hereditary rights to a born-again citizen and even if they did, the
individual's possessions would be heavily taxed. Intelligent Thatsuch
complex machines are now a thing of the past.
5. That I persoanlly am trying to deliver this with
http://bess.port5.com
What about FedEx?
Can you come over to London and join me?
I find the weather in London obnoxious and the traffic overwhelming.
please contact the club secretary on the site (below) and not me just
yet.
I wish you had a better picture of her.
Christos Dimitrakakis
http://olethros.dmusic.net |
|
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| Back to top |
Greg Heath
Guest
|
| Posted: Thu Jul 03, 2003 11:57 am Post subject: Re: Embarassing AND model convergence question :/ |
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|
"Guillaume Comeau" <gcomeau@secret.com> wrote in message
news:<y3GMa.4700$eF3.559850@news20.bellglobal.com>...
Perhaps. However, I think you meant "stumped".
| Quote: | Problem: A simple model of one neuron doesn't converge. I am starting to
wonder if the problem has to do with lack of understanding of the theory or
a software bug.
|
Probably both, primarily the former.
First think of the geometry.
Obviously, the "optimum" hyperplane goes through
(0.5,1) and (1,0.5):
x2 = -x1 + 1.5
Therefore the corresponding weights are
(wb,w1,w2) = K*(-1.5,1,1)
where K is a positive constant.
| Quote: | Here goes:
Training cases: AND function
(inputs), (outputs)
(0, 0) (.3)
(0, 0) (.3)
(0, 0) (.3)
(0, 0) (.7)
|
Hey! How about some 1s?
x1 x2 y
0 0 0.3
0 1 0.3
1 0 0.3
1 1 0.7
Now think of the geometry again. Are they simultaneously
obtainable outputs or just training targets?
If the latter, what is your definiton of convergence?
| Quote: | Model:
Single 2 input neuron with exponential activation function.
|
Exponential? I think you mean sigmoidal
y = 1/[1+exp(-z)]
z = wb + w1*x1 +w2*x2
y z = -ln[1/y -1]
--- ---------------
0.3 -0.847
0.7 +0.847
Now consider
x1 x2 z = wb + w1*x1 + w2*x2
-- -- ----------------------
0 0 wb = -0.847
0 1 wb + w2 = -0.847
1 0 wb + w1 = -0.847
1 1 wb + w1 +w2 = +0.847
Aha: Four equations but only three unknowns!
Now do you see the problem? Look at the equations
and think of the geometry.
Ignoring the 1st equation yields
w1 = w2 = +2*0.847 = +1.694
wb = -3*0.847 = -2.541
or
(wb,w1,w2) = 1.694*(-1.5,1,1)
| Quote: | Training algorithm:
- starting learning coef : 0.02
- batch mode training.
- if model error increases after training, revert back to old model and use
smaller learning coef.
Initial weights:
w0= -0.2
w1= -0.1
wb= -0.5
The modeling software is home-grown. It is quite possible that there is a
software error. My question to this NG are
1. If a problem is linearly separable as in this case, is there a guarantee
that the model with converge?
2. If the training coefficient is sufficiently small, is there a guarantee
that the error will monotonically decrease?
|
1. State your definition of convergence
2. Choose random bipolar initial weights
3. If you don't converge, restart with new random bipolar weights
4. Post your findings
Hope this helps.
Greg |
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Greg Heath
Guest
|
| Posted: Thu Jul 03, 2003 12:04 pm Post subject: Re: recognizing several subpattern at once |
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|
Matthew Studer <matthias.studer@unibas.ch> wrote in message
news:<3F02E98F.3040307@unibas.ch>...
| Quote: | I'm still new to NN and maybe my question is a bit "stupid"
What would be the best way to recognize different patterns in a *binary*
network input?:
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Use a MLP or RBF. One output for each pattern. If the pattern is
present the training target is 1 otherwise it is 0.
See the FAQ.
Hope this helps.
Greg
| Quote: | We are dealing with chemical mixtures of compounds and would like to
identify all the single substances in a given mixture.
We trained a CPN with all the individual substances we are expecting in
the compounds and it worked very good. But as a next step it should be
possible to identify all the compounds at once - without pre-separation
of the mixture.
Is this possible? And how?
I thought about ABAMs? |
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