-- CristinaAnaMantillaSuarez - 2015-02-23
We are interested on how is the top quark mass m_{t} related to the kinematics of the leptons in the final state. The idea is that is this analysis the measurement won't be affected by the jet energy scale JES uncertainty.
This is the theory article from which the idea is based on: http://inspirehep.net/record/1305642
Slides: https://indico.cern.ch/event/301787/session/3/contribution/17/material/slides/0.pdf
Label | Observable |
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Unfolding can be defined as correcting data for detector effects. Due to the finite resolution of real world particle detectors, any measurement conducted in experimental high energy physics is contaminated by stochastic smearing. The observations recorded with any real world particle detector are always subject to undesired experimental effects, such as limited detector resolution and detection inefficiencies. The observation of such distorted collision events instead of the desired true events is called smearing or folding of the data and often results in broadening of the physical spectra measured by the LHC experiments.
Unfolding then refers to using the smeared observations to infer the true physical distribution of the events. It refers to the problem of estimating the particle level distribution of some physical quantity of interest on the basis of observations smeared by an imperfect measurement device.
There are three main reasons when unfolding is desirable:
In our case, we apply an unfolding technique because we want to compare our results with the theoretical predictions from our theory paper of reference. The measured distributions are distorted from the true underlying distributions by the limited acceptance of our detector and by bin-to-bin smearing due to a finite resolution of the variables. We perform our unfolding using TUnfold package, which consists on a matrix inversion based on a least square fit with Tikhonov regularisation. Similar (but not identical) to the SVD method. Some documentation can be found here:
http://www.desy.de/~sschmitt/tunfoldv16docu.html http://www.desy.de/~sschmitt/TUnfold/tunfold_manual_v17.3.pdf
Also we will try to follow TOP group general recomendations related to unfolding for top signatures.
https://twiki.cern.ch/twiki/bin/viewauth/CMS/TopUnfolding
Actually, the unfolding code we use is based in the code spinnet in this page:
https://twiki.cern.ch/twiki/bin/view/CMS/TopUnfoldingExampleCodes
For more information about TUnfold algorithm, have a look at:
The class TUnfold can be used to unfold measured data spectra and obtain the underlying "true" distribution. The unfolding method is summarized here: *The measured spectrum can be expressed by the true spectrum multiplied by a smearing matrix S, that accounts for migration of an event from one bin into another bin due to resolution effects as well as for different acceptances for the different bins:
= S
By performing a regularized inversion of the matrix S, TUnfold gives an estimate for the true spectrum and accounts for the above mentioned effects. In addition TUnfold can also take care of the proper subtraction of background contributions with a proper handling of the uncertainties on the background estimation. We use TUnfoldSys which provides methods to do systematic error propagation and to do unfolding with background subtraction.
TUnfoldSys uses a regularization parameter , giving the strength of regularization. Will be roughly on the order of 1e-4. We use this value suggested but in principle you can determine this value by performing unfolding with many different values, maybe between 1e-3 and 1e-7 or such, and choosing the value of tau that minimizes tunfold.GetRhoAvg().
After correcting the binning, we found that the distributions still contained a high number of events the first and last bin. We corrected this by not counting the overflow and underflow bin in the migration matrix, i.e. when generating plots with runPlotter.py we add the option:
python scripts/runPlotter.py -j test/topss2014/mass_scan_samples.json -o quantiles/mc/ptpos/166/plots quantiles/mc/ptpos/166 --cutUnderOverFlow
Besides, we found a bug while calculating Mellin moments from the unfolded distribution. We were working with the unfolded distribution divided by the bin width, and this was causing a displacement on the mean value from 52 to 44 approx. This mean value we use to calculate the first and second moments.
After correcting this two bugs, we obtained the final plots. However we still observe a difference between the moments calculated from the unfolded and generated level kinematic distributions.
The plots for each of the kinematic variables are here:
For kinematic distribution plots at reconstructed and generated level, and also for the unfolded distribution, I attach here only the results for 171 mass sample. The other mass samples distributions look quite similar (look at the comparison plot between rec and gen).
Distribution comparison at reconstructed level | Distribution comparison at generated level |
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Unfolded vs Generated | Unfolded vs Generated |
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Unfolded vs Top Mass | Unfolded vs Top Mass |
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Generated level | Reconstructed level | Reconstructed level Bin-corrected |
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Unfolded | Efficiency, Purity and Stability |
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Distribution comparison at reconstructed level | Distribution comparison at generated level |
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Unfolded vs Generated | Unfolded vs Generated |
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Unfolded vs Top Mass | Unfolded vs Top Mass |
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Generated level | Reconstructed level | Reconstructed level Bin-corrected |
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Unfolded | Efficiency, Purity and Stability |
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Distribution comparison at reconstructed level | Distribution comparison at generated level |
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Unfolded vs Generated | Unfolded vs Generated |
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Unfolded vs Top Mass | Unfolded vs Top Mass |
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Generated level | Reconstructed level | Reconstructed level Bin-corrected |
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Unfolded | Efficiency, Purity and Stability | |
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/> |
Distribution comparison at reconstructed level | Distribution comparison at generated level |
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Unfolded vs Generated | Unfolded vs Generated |
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Unfolded vs Top Mass | Unfolded vs Top Mass |
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Generated level | Reconstructed level | Reconstructed level Bin-corrected |
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Unfolded | Efficiency, Purity and Stability |
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Distribution comparison at reconstructed level | Distribution comparison at generated level |
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Unfolded vs Generated | Unfolded vs Generated |
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Unfolded vs Top Mass | Unfolded vs Top Mass |
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Generated level | Reconstructed level | Reconstructed level Bin-corrected |
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Unfolded | Efficiency, Purity and Stability |
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I obtained the stability, purity and efficiency of the binning as a closure test.
*Purity :
The purity p denotes the number of events that are generated and correctly reconstructed in a given bin i relative to the number of events that are reconstructed in bin i but generated anywhere.
*Stability
(notice this is basically the diagonal of the matrix after normalizing it) The stability s denotes the number of events that are generated and correctly reconstructed in a given bin i relative to the number of events that are generated in bin i but reconstructed anywhere
That is, the number of events reconstructed in a given bin which are matched at generator level divided by the total number of events which have been matched at generator level
Efficiency, Purity and Stability |
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Also, I found a bug in my unfolding procedure, where I was subtracting background although I was not taking it into account. I corrected this and summarized my results in this slides:
Now I am having problems to define a correct binning to unfold, since the last bin and the first bin contain also the overflow and underflow bins respectively. So I am doing several tests with the binning, and using just one of the variables to test:
At the end I compare the unfolded distributions obtained for each of the cases. And I compare the purity, stability and efficiency and also the
Here I describe how do I choose the bins:
The purpose of using quantiles is to choose these bins in such a way that all bins in the histograms contain the same numbers of events. This will increase the stability of the method. Depending on the case, flattening the truth spectrum after selection might be better than before selection. You have to use a finer binning in the measured variable as compared to the truth variable. As a rule of thumb, we should use at least twice the number of bins for the measured variable.
bins_gen = [22.72,25.45,28.18,30.92,33.67,36.42,39.17,42.01,44.89,47.77,50.94,55.06,59.19,63.63,68.15,74.76,83.59,95,115.65]
bins_rec = [20,21.36,22.73,24.09,25.45,26.82,28.18,29.55,30.92,32.29,33.67,35.04,36.41,37.79,39.17,40.57,42.01,43.45,44.89,46.33,47.77,49.21,50.93,53,55.06,57.12,59.18,61.37,63.63,65.89,68.15,70.73,74.76,78.74,83.59,88.75,95,102.85,115.65,138.46,250]
The bold bins are the extra bins in the reconstructed level.
Generated level | Reconstructed level | Reconstructed level Bin-corrected |
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Unfolded | Efficiency, Purity and Stability |
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For all the mass samples:
Distribution comparison | First Mellin Moment Unfolded vs Generated | Second Mellin Moment Unfolded vs Generated |
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u1 Unfolded vs Top Mass | u2 Unfolded vs Top Mass |
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The new version of the binning flattens out the distribution, so it is okay. And also now the bins at reconstructed level are the double than at generated level, so the unfolding procedure is working.
Still there are some things to work in. When we compare the unfolded and the generated plots versus top mass they don't give exactly the same. They are both linear but the scale is somehow different.
I have put the plots for the other distributions here:
http://cmsdoc.cern.ch/~cmantill/top/
Distribution comparison at reconstructed level | Distribution comparison at generated level |
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Distribution comparison at reconstructed level | Distribution comparison at generated level |
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Distribution comparison at reconstructed level | Distribution comparison at generated level |
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Distribution comparison at reconstructed level | Distribution comparison at generated level |
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Distribution comparison at reconstructed level | Distribution comparison at generated level |
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All of the variables show a similar (but fairly weak) dependence on the top mass
Given an observable O (e.g. one of the listed in the table), the Mellin moments are given by:
( Mean )
I obtained the first plots, as a test, using just information from reconstructed and generated level. The unfolding procedure is not working, we think it is due to a binning problem.
First Mellin Moment Reconstructed vs Generated | Second Mellin Moment Reconstructed vs Generated |
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u1 Generated level vs Top Mass | u1 Reconstructed level vs Top Mass |
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u2 Generated level vs Top Mass | u2 Reconstructed level vs Top Mass |
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We will start to work with mass samples from here, corresponding to m_{t} = [166.5,169.5,171.5,173.5,175.5,178.5] GeV.
The mass samples are located in
/store/cmst3/group/top/summer2015/treedir_bbbcb36/ttbar/mass_scan/
for ttbar they are named as MC8TeV_TTJets_MSDecays_*.root where * is the mass. In addition, given tW/tbarW is the main background I will also use:
/store/cmst3/group/top/summer2015/bbbcb36/mass_scan/MC8TeV_SingleTbar_tW_*.root /store/cmst3/group/top/summer2015/bbbcb36/mass_scan/MC8TeV_SingleT_tW_*.root
I have to reproduce the distribution plots for all the samples and for each of the kinematic variables. I have to unfold this distributions using MC only, and then calculate the Mellin moments such as at the end I will obtain a calibration curve of the moments values vs the top mass.
The migration matrix we use to unfold the distributions of each of the mass samples, is the one from the nominal sample MC8TeV_TTJets_MSDecays_172v5.root
To check the binning array I was using, I got the quantiles separately and then round those numbers a bit so I have the same bin size for a long range and then a bit bigger bins towards the end.Then I just hardcode them by adding that array into my code. At the end I got this:
Generated level | Reconstructed level | Reconstructed level Bin-corrected |
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In some cases there are events in the 0 pt bin. Could be that there are some events with only one lepton.
I checked the event selection, and there is indeed a cut on abs(EvCat) to be either 11*11, 11*13, or 13*13. But there are some events in the MC samples which have events in the 0 pt bin, we impose the condition:
if not isData: if tree.GenLpPt == 0 or tree.GenLmPt == 0: continue
Now the plots look like this:
Generated level | Reconstructed level | Reconstructed level Bin-corrected |
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I found a bug in the way that I was calculating the quantiles, so now the distributions look like this for ptpos:
Generated level | Reconstructed level | Reconstructed level Bin-corrected |
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It looks like all the bins except the first and last are ok (they have more or less the same number of entries), but those two are wrong. I added one more quantil, by adding the 1.0 into my array
Generated level | Reconstructed level | Reconstructed level Bin-corrected |
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We have started to study the unfolding procedure.
We are going to define the binning scheme for our histograms, such that we get flat distributions to unfold.
This is the idea: GetQuantiles ROOT Function gets you the values of x which divide the distribution in the quantiles you define.
You can use it to re-define the binning of the distribution, such that now you now that the statistics will be distributed according to your pre-defined quantiles.
i.e.
Generated level | Reconstructed level | Reconstructed level Bin-corrected |
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I extended the bin range, but I am just increasing the range to 200 without changing the binning, so I just make one big bin from 100 to 200, which will contain all the events there.
Generated level | Reconstructed level | Reconstructed level Bin-corrected |
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wget -q -O - --no-check-certificate https://raw.github.com/stiegerb/TopMassSecVtx/master/TAGS.txt | sh git clone git@github.com:stiegerb/TopMassSecVtx.git UserCode/TopMassSecVtx git status cp ~/.gitconfig ~/.gitconfig.orig cp /afs/cern.ch/user/s/stiegerb/public/forCarlotta/.gitconfig ~/ git df git br git remote -v git remote add cmantill git@github.com:cmantill/TopMassSecVtx.git git remote -v git checkout -b mtdilepton git add scripts/runDileptonUnfolding.py git add scripts/utils.py git commit -m'Cristinas first commit' git l git push cmantill mtdilepton
history | grep git > githistory
Getting CERN Kerberos ticket in my laptop I connected my computer with lxplus using OpenAFS. In order to access your CERN AFS account you'll need to obtain an AFS token from the CERN server. I had already installed Kerberos packages but I followed instructions from this sites:
http://linux.web.cern.ch/linux/docs/kerberos-access.shtml
https://gist.github.com/KFubuki/10728230 - Also here I found some CERN very useful hacks
https://wiki.chipp.ch/twiki/bin/view/CmsTier3/HowToWorkInCmsEnv
After installing and setting it up, you should create a ticket and log on:
kinit username@CERN.CH aklog
You can also test your access with:
klist ls /afs/cern.ch/ ls /afs/cern.ch/user/c/cmantill/
Now you can work directly from your computer.
Request Workspace at Lxplus Locally at CERN, the personal working area on CERN's LXPLUS cluster isn't big enough to handle the output files, you'll need to write them to a larger-capacity area.
To ask for "AFS workspace" (up to 100 GB, backed up), login to the Cern account web page and go to "List Services", take the "AFS Workspaces" and then "Settings".
There you can ask for "workspace" in AFS, as well as extend the quota for your backed-up home (up to 10 GB). Please note the different AFS path to your workspace: /afs/cern.ch/work/initial/username where initial is the first letter of your username, i.e. the workspace is not hanging from your home.
Workspace path: /afs/cern.ch/work/c/cmantill
Turns out I was submitting 0 jobs before because the input directory should be this one:
input directory with the files: /store/cmst3/group/top/summer2015/treedir_bbbcb36/ttbar
I got the plots for the other four distributions. I modified scripts/runDileptonUnfolding.py and got a new version. Here I attach some plots:
The notation I use in my code is the following:
Generated level | Reconstructed level | Reconstructed level Bin-corrected |
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Observed normalization | |
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Generated level | Reconstructed level | Reconstructed level Bin-corrected |
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Observed normalization | |
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Generated level | Reconstructed level | Reconstructed level Bin-corrected |
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Observed normalization | |
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Generated level | Reconstructed level | Reconstructed level Bin-corrected |
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Observed normalization | |
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The twiki page: https://twiki.cern.ch/twiki/bin/viewauth/CMS/CMGTopStudents2015
Working directory: /afs/cern.ch/user/c/cmantill/private/top/CMSSW_5_3_22/src/UserCode/TopMassSecVtx
./scripts/runPlotter.py --rereadXsecWeights /store/cmst3/group/top/summer2015/bbbcb36/ -j test/topss2014/samples.json
...Processing all MC8TeV and Data8TeV ... >>> Produced xsec weights and wrote to cache (.xsecweights.pck)
The normalization is computed as a weight where is the theoretical cross section of a process and is the number of generated events. The luminosity is the ratio of the number of events detected in a certain time interval to the interaction cross-section . With this definition, the number of expected events after acquiring a given integrated luminosity , is given by where is the number of selected events in the analysis.
python scripts/runDileptonUnfolding.py -i /store/cmst3/group/top/summer2015/treedir_bbbcb36/ -o unfoldResults/ --jobs 8
input directory with the files: /store/cmst3/group/top/summer2015/treedir_bbbcb36/
-------------------------------------------------------------------------------- Creating ROOT file with migration matrices, data and background distributions from /store/cmst3/group/top/summer2015/treedir_bbbcb36/singlet/ Discarded 0 files duplicated in cmsLs output Submitting jobs in 8 threads Histograms saved in unfoldResults/Data8TeV_SingleElectron2012C.root ... --------------------------------------------------------------------------------
I obtained the distributions at generated and reconstructed level for %$p_T (l^{+})$ (ptpos).
Simple counting | Bin-corrected |
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I can subtract the background from the data, and unfold the result by running
python scripts/runDileptonUnfolding.py -r unfoldResults/plots/plotter.root -v ptpos -o unfoldResults
Observed normalization | |
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eoscms ls -l /eos/cms/store/cmst3/group/top/summer2015
TFile::Open("root://eoscms.cern.ch//eos/cms/store/cmst3/group/top/summer2015/ttbar/treedir_bbbcb36/ttbar/MC8TeV_ZZ.root")
I | Attachment | History | Action | Size | Date | Who | Comment |
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png | EposEm171_gen.png | r1 | manage | 20.9 K | 2015-07-24 - 12:23 | CristinaAnaMantillaSuarez | EposEm distribbutions |
png | EposEm171_pur_stab_eff.png | r1 | manage | 12.4 K | 2015-07-24 - 12:23 | CristinaAnaMantillaSuarez | EposEm distributions |
png | EposEm171_rec.png | r1 | manage | 18.6 K | 2015-07-24 - 12:23 | CristinaAnaMantillaSuarez | EposEm distributions |
png | EposEm171_rec_wgt.png | r1 | manage | 20.1 K | 2015-07-24 - 12:23 | CristinaAnaMantillaSuarez | EposEm distributions |
png | EposEm171_unfolded.png | r1 | manage | 24.0 K | 2015-07-24 - 12:23 | CristinaAnaMantillaSuarez | EposEm distributions |
png | EposEm_gen_comparisonNorm_2.png | r1 | manage | 24.3 K | 2015-07-24 - 12:23 | CristinaAnaMantillaSuarez | EposEm distributions |
png | EposEm_rec_comparisonNorm_2.png | r1 | manage | 28.0 K | 2015-07-24 - 12:23 | CristinaAnaMantillaSuarez | EposEm distributions |
png | mll171_gen.png | r1 | manage | 21.0 K | 2015-07-24 - 12:06 | CristinaAnaMantillaSuarez | Mll distributions |
png | mll171_pur_stab_eff.png | r1 | manage | 11.9 K | 2015-07-24 - 12:05 | CristinaAnaMantillaSuarez | Mll distributions |
png | mll171_rec.png | r1 | manage | 17.8 K | 2015-07-24 - 12:05 | CristinaAnaMantillaSuarez | Mll distributions |
png | mll171_rec_wgt.png | r1 | manage | 18.1 K | 2015-07-24 - 12:05 | CristinaAnaMantillaSuarez | Mll distributions |
png | mll171_unfolded.png | r1 | manage | 24.1 K | 2015-07-24 - 12:05 | CristinaAnaMantillaSuarez | Mll distributions |
png | mll_gen_comparisonNorm_2.png | r1 | manage | 24.9 K | 2015-07-24 - 12:05 | CristinaAnaMantillaSuarez | Mll distributions |
png | mll_rec_comparisonNorm_2.png | r1 | manage | 27.6 K | 2015-07-24 - 12:05 | CristinaAnaMantillaSuarez | Mll distributions |
png | ptll171_gen.png | r1 | manage | 20.1 K | 2015-07-24 - 12:03 | CristinaAnaMantillaSuarez | Ptll distributions |
png | ptll171_pur_stab_eff.png | r1 | manage | 12.2 K | 2015-07-24 - 12:02 | CristinaAnaMantillaSuarez | Ptll distributions |
png | ptll171_rec.png | r1 | manage | 17.5 K | 2015-07-24 - 12:02 | CristinaAnaMantillaSuarez | Ptll distributions |
png | ptll171_rec_wgt.png | r1 | manage | 19.0 K | 2015-07-24 - 12:02 | CristinaAnaMantillaSuarez | Ptll distributions |
png | ptll171_unfolded.png | r1 | manage | 23.7 K | 2015-07-24 - 12:02 | CristinaAnaMantillaSuarez | Ptll distributions |
png | ptll_gen_comparisonNorm_2.png | r1 | manage | 24.6 K | 2015-07-24 - 12:02 | CristinaAnaMantillaSuarez | Ptll distributions |
png | ptll_rec_comparisonNorm_2.png | r1 | manage | 28.1 K | 2015-07-24 - 12:02 | CristinaAnaMantillaSuarez | Ptll distributions |
png | ptpos171_gen.png | r1 | manage | 20.0 K | 2015-07-24 - 11:58 | CristinaAnaMantillaSuarez | Ptpos distributions |
png | ptpos171_pur_stab_eff.png | r1 | manage | 12.0 K | 2015-07-24 - 11:58 | CristinaAnaMantillaSuarez | Ptpos distributions |
png | ptpos171_rec.png | r1 | manage | 17.1 K | 2015-07-24 - 11:58 | CristinaAnaMantillaSuarez | Ptpos distributions |
png | ptpos171_rec_wgt.png | r1 | manage | 17.7 K | 2015-07-24 - 11:58 | CristinaAnaMantillaSuarez | Ptpos distributions |
png | ptpos171_unfolded.png | r1 | manage | 24.5 K | 2015-07-24 - 11:58 | CristinaAnaMantillaSuarez | Ptpos distributions |
png | ptpos_gen_comparisonNorm_2.png | r1 | manage | 22.8 K | 2015-07-24 - 11:58 | CristinaAnaMantillaSuarez | Ptpos distributions |
png | ptpos_rec_comparisonNorm_2.png | r1 | manage | 25.8 K | 2015-07-24 - 11:58 | CristinaAnaMantillaSuarez | Ptpos distributions |
png | ptposptm173_gen.png | r1 | manage | 21.5 K | 2015-07-24 - 12:34 | CristinaAnaMantillaSuarez | Ptposptm distributions |
png | ptposptm173_pur_stab_eff.png | r1 | manage | 12.4 K | 2015-07-24 - 12:33 | CristinaAnaMantillaSuarez | Ptposptm distributions |
png | ptposptm173_rec.png | r1 | manage | 18.1 K | 2015-07-24 - 12:33 | CristinaAnaMantillaSuarez | Ptposptm distributions |
ptposptm173_rec_wgt.pdf | r1 | manage | 14.7 K | 2015-07-24 - 12:33 | CristinaAnaMantillaSuarez | Ptposptm distributions | |
png | ptposptm173_unfolded.png | r1 | manage | 25.0 K | 2015-07-24 - 12:33 | CristinaAnaMantillaSuarez | Ptposptm distributions |
png | ptposptm_gen_comparisonNorm_2.png | r1 | manage | 23.7 K | 2015-07-24 - 12:33 | CristinaAnaMantillaSuarez | Ptposptm distributions |
png | ptposptm_rec_comparisonNorm_2.png | r1 | manage | 26.3 K | 2015-07-24 - 12:33 | CristinaAnaMantillaSuarez | Ptposptm distributions |
png | u1_EposEm_2.png | r1 | manage | 17.5 K | 2015-07-24 - 12:23 | CristinaAnaMantillaSuarez | EposEm distributions |
png | u1_EposEm_unf_2.png | r1 | manage | 12.8 K | 2015-07-24 - 12:23 | CristinaAnaMantillaSuarez | EposEm distributions |
png | u1_mll_2.png | r1 | manage | 16.3 K | 2015-07-24 - 12:05 | CristinaAnaMantillaSuarez | Mll distributions |
png | u1_mll_unf_2.png | r1 | manage | 13.6 K | 2015-07-24 - 12:05 | CristinaAnaMantillaSuarez | Mll distributions |
png | u1_ptll_2.png | r1 | manage | 15.9 K | 2015-07-24 - 12:02 | CristinaAnaMantillaSuarez | Ptll distributions |
png | u1_ptll_unf_2.png | r1 | manage | 13.6 K | 2015-07-24 - 12:02 | CristinaAnaMantillaSuarez | Ptll distributions |
png | u1_ptpos_2.png | r1 | manage | 17.3 K | 2015-07-24 - 11:58 | CristinaAnaMantillaSuarez | Ptpos distributions |
png | u1_ptpos_unf_2.png | r1 | manage | 13.8 K | 2015-07-24 - 11:58 | CristinaAnaMantillaSuarez | Ptpos distributions |
png | u1_ptposptm_2.png | r1 | manage | 17.0 K | 2015-07-24 - 12:33 | CristinaAnaMantillaSuarez | Ptposptm distributions |
png | u1_ptposptm_unf_2.png | r1 | manage | 14.3 K | 2015-07-24 - 12:33 | CristinaAnaMantillaSuarez | Ptposptm distributions |
png | u2_EposEm_2.png | r1 | manage | 19.4 K | 2015-07-24 - 12:23 | CristinaAnaMantillaSuarez | EposEm distributions |
png | u2_EposEm_unf_2.png | r1 | manage | 17.0 K | 2015-07-24 - 12:23 | CristinaAnaMantillaSuarez | EposEm distributions |
png | u2_mll_2.png | r1 | manage | 17.0 K | 2015-07-24 - 12:33 | CristinaAnaMantillaSuarez | Mll distributions |
png | u2_mll_unf_2.png | r1 | manage | 15.1 K | 2015-07-24 - 12:26 | CristinaAnaMantillaSuarez | Mll distributions |
png | u2_ptll_2.png | r1 | manage | 17.9 K | 2015-07-24 - 12:02 | CristinaAnaMantillaSuarez | Ptll distributions |
png | u2_ptll_unf_2.png | r1 | manage | 15.4 K | 2015-07-24 - 12:02 | CristinaAnaMantillaSuarez | Ptll distributions |
png | u2_ptpos_2.png | r1 | manage | 19.5 K | 2015-07-24 - 11:58 | CristinaAnaMantillaSuarez | Ptpos distributions |
png | u2_ptpos_unf_2.png | r1 | manage | 15.8 K | 2015-07-24 - 11:58 | CristinaAnaMantillaSuarez | Ptpos distributions |
png | u2_ptposptm_2.png | r1 | manage | 16.8 K | 2015-07-24 - 12:33 | CristinaAnaMantillaSuarez | Ptposptm distributions |
png | u2_ptposptm_unf_2.png | r1 | manage | 14.9 K | 2015-07-24 - 12:33 | CristinaAnaMantillaSuarez | Ptposptm distributions |