dataesr/scientific-paragraphs-categorization huggingface dataset:
, 2005). For one single spectrum, one can use simulation algorithm (see for instance  Faisal et al. , 2020). For large datasets, simplest ideas would be to scrutinize average spectra, or potential band depth distribution. Unfortunately, in the case of low signal-to-noise ratio (SNR, defined as signal / standard deviation of noise), such methods fail (as will be illustrated in the toy example). Analyzing residuals after modeling is a good method but it requires a lot of work. Several statistical tools with various approaches have been proposed, such as the Principal Component Analysis (PCA)  (Penttilä et al. , 2018; Geminale et al. , 2015) , or Independent Component Analysis (ICA)  (Shashilov et al. , 2006; Erard et al. , 2009) , but most of them require a human operator to pick endmembers and trends since those methods are nothing more than a change of representation.
Furthermore, none of these methods guarantees positivity of the component (which are sometimes also called source), which can be problematic during the interpretation. Recently, advanced machine learning methods based on non-negative matrix factorization have been proposed  (Lee and Seung, 1999; Moussaoui et al. , 2008; Dobigeon et al. , 2009; Schmidt et al. , 2010; Gillis and Glineur, 2012; Hinrich and Mørup, 2018). This approach is completely different from PCA/ICA: each source is positive and represents an endmember / a trend. A source is not one spectrum extracted from the dataset but a statistical reconstruction. By using this approach, the human operator doesn't have to identify endmembers/trends anymore, since they are automatically picked by the algorithm in form of source. Furthermore when there are statistical / spectral correlations between sources PCA/ICA fails because it assumes orthogonality / independence, which is not the case for non-negative matrix factorization.
Based on this new approach, we propose a tool: • to give an overview and quickly summarize a large and complex spectroscopic dataset with simple variables • to detect potential new spectroscopic features (unexpected minor species, new absorption lines,. ) • to be performed in a fully blind way (without prior information on neither the spectra, nor the abundances). The target observation type of this study is solar occultation. This measurement principle has been proposed as early as 1900, an interesting review was published by  Smith and Hunten (1990). Several recent instruments used this technique to investigate the composition of the Earth's (SCIAMACHY/  ENVISAT Bovensmann et al. 1999) , Mars' (SPICAM  Bertaux et al. , 2000)  or Venus' atmospheres (SPICAV  Bertaux et al. , 2007). Here we will focus on the recent NOMAD instrument  (Vandaele et al.
Dataset We propose here to focus on the Nadir and Occultation for MArs Discovery (NOMAD) instrument onboard ESA's ExoMars Trace Gas Orbiter and especially the Solar Occultation (SO) channel  (Vandaele et al. , 2015). NOMAD is a compact, high-resolution, dual channel IR spectrometer (SO and LNO) coupled with a highly miniaturized UV-visible spectrometer (UVIS), capable of operating in different observation modes: solar occultation, nadir and limb. The SO channel operates at wavenumbers from 2320 cm -1 to 4550 cm -1 (wavelength 2. 2 to 4. 3 µm), using an echelle grating with a groove density of 4 lines/mm in a Littrow configuration in combination with an Acousto-Optic Tunable Filter (AOTF) for spectral order selection. The width of the selected spectral ranges is recorded by 320 spectels (spectral element) and varies from 20 to 35 cm -1 depending on the selected diffraction order.
The detector is an actively cooled HgCdTe Focal Plane Array. SO achieves an instrument line profile resolution of 0. 15 cm -1 , corresponding to a resolving power λ/Δλ of approximately 25000. All details of the instrument are available in  Neefs et al. 2015 and Vandaele et al. 2018. The orders with the maximum sensitivity to CH 4 are: 119, 134 and 136. We will use the data from the beginning of the mission in April 2018 until 15 January 2020, in calibration version 1p0a. Due to temperature change, the spectral registration varies, producing a shift up to ∼10 spectels. We corrected it by aligning the full dataset to a reference spectra (arbitrarily choosen with the maximum band depth of water) by crosscorrelation. No sub-spectel resampling has been performed but a simple shift. When the calibration will be improved, this step will most probably be replaced by a routine correction.
One approach to reduce the computation time is to select only relevant spectra out of the dataset  (Moussaoui et al. , 2008) , but then the statistics may be biased  (Schmidt et al. , 2010). Thanks to the advances of computer capabilities, we propose to treat the full dataset. This kind of algorithm is very slow but since the formulation is Bayesian, it converge toward an unique solution. psNMF. In order to regularize the problem of eq. 6, one can add an extra penalization term to enforce sparsity on A (only few non zeros elements in A)  (Kim and Park, 2007)  : F = X -S. A 2 + λ A 1 (7) With. 1 , the L 1 norm. The first term is called data attachment term (the usual squared difference). The second is called regularization term. The problem with this approach, is that hyperparameter λ is not known and has to be tuned manually.
A recent approach has been proposed to solve this problem in the Bayesian framework  (Hinrich and Mørup, 2018). The main idea is to encompass all variables and hyperparameters in a unique problem that is estimated with variational update principle. We will refer this algorithm to probability sparse NMF (psNMF). This algorithm has the advantage to have a reduced computation time and no hyperparameter tuning. It also has a regularization term to avoid strong dependence of the initialization on the final solution. In order to estimate the precision of the reconstruction, we used the Root Mean Square Difference RM SD: RM SD = X -Ṡ. Ȧ 2 X (8) With. , the mean. Once the sources are estimated, we quantify their relevance for the global dataset. From the total reconstruction Ẋkj = Ṡki. Ȧij , for all i, we can estimate the contribution of source i , that is to say: Ẋi kj = Ṡki.
Ȧi j. Thus, the relevance of source i is defined as: R i = Ẋi -Ẋ Ẋ (9) This definition is convenient since the sum of all R i is one (this property is only present when sources and abundances are positive) and we can easily estimate the % contribution of each source in the final reconstruction. One has to note that relevance is not a measure of presence or not of a minor specie (for instance CH 4 ) but a measure of how important is the source over the dataset. Major species, should always have a larger relevance than minor species. In the following, we plot all sources results by decreasing order of relevance.
Synthetic tests We simulated several synthetic observations in different conditions, to mimic the case of NOMAD-SO. The first section describes a simple toy model example and the second one presents extensive tests of this toy model with various cases. By hidden spectra, hidden compounds and hidden CH 4 , we always refer to a spectral dataset with a dominant major component (here water) and a minor specie (here CH 4 ). The goal of the proposed approach is to pick up a source, containing CH 4 only.
Synthetic dataset In order to demonstrate the usefulness of our method, we propose here a toy example in a very difficult case. We will see that usual method fails detection but our method is able to detect the hidden compounds. For this toy example, we simulate a linear mixture of N O = 10 4 observations spanned over N ν = 320 spectels (see fig. 1 ) similar to order 136 of NOMAD-SO. Each spectrum is a mixture of a spectra of water vapor S H2O (coming from one actual source estimated from real data using psNMF) and theoretical methane S CH4 from  Villanueva et al. (2018) , with corresponding abundances A H2O , A CH4 : X = S H2O. A H2O + S CH4. A CH4 + n (11) The noise n is assumed to be a Gaussian process with a standard deviation of σ=0. 001 and no bias: n = G (0, σ). All spectra contain pure water vapor with a coefficient following A H2O = 5/6.
β(1, 10) + 1/6. U(0, 1), a mixture of beta (β) distribution for 5/6 of the sample and an uniform (U) distribution for 1/6 of the sample. This process mimics well the water vapor band depth distribution (BD, see definition in section 3. 3) of the real dataset (see Fig. 2 ). As the baseline of S H2O is not zero, we also mimic baseline correction errors. In addition 100 spectra out of 10000 contain methane with A CH4 = 1, such that the band depth of S CH4 is at 3-σ level. Please note that the model to generate the data is not fulfilling the sum-to-one constraint, but fully fulfilling the positivity constraint. Given the defined noise and signal level, the RM SD expected for a perfect reconstruction of the signal (and not the noise) is 0. 16. The final synthetic dataset is represented in Fig. 1.
Results By plotting the 10000 samples of the dataset, one is able to identify easily the H 2 O bands. Nevertheless, we cannot observe the target CH 4 in the average The second simple tool for detection would be the analysis of the band depth. represents the 100 spectra with the maximum CH 4 BD at 3067. 2 cm 1. Again, no particular elements can be used to argue for detection. Figure  4  represents the results from the non-negative matrix factorization using psNMF algorithm. One can clearly identify both H 2 O and CH 4 sources. Since those 2 chemical compounds are not correlated in abundance, (A H2O and A CH4 are independent), two different source spectra are identified. Please note that the relevance of source 4 is very low (0. 4%), meaning that only 0. 4% of the variability in the dataset is due to CH 4 , a very low value, as expected for minor species.
Convergence and computation time We set the MU algorithm convergence to relative difference of the cost function < 10 8 and a maximum running time of 1000 seconds. For psNMF, we set the relative difference of the cost function to < 10 7 and a maximum iteration to 2000. For BPSS2, we compute a minimum burn in of 1000 iterations and after that when the long term statistics (1000 last iterations) of the Markov Chain is close to the short term statistics (100 last iterations), convergence is considered to be reached. Then another 1000 iterations are computed to estimate the final solution statistics. We run the 3 identified tools 10 times on the same dataset with different noise realization, and compute mean and standard deviation from these 10 experiments. Results are presented in Table  1. One can clearly see that the even if the convergence is set, there is a high variability in MU results, due to the 9 spectrum, even at 3-σ level, because it is lost in the baseline changes.
The second simple tool for detection would be the analysis of the band depth. Figure  3  (left) shows the histogram of the main CH 4 band that exhibits no sign of the presence of CH 4 (no asymmetry in the positive part). Figure  3  (right) represents the 100 spectra with the maximum CH 4 BD at 3067. 2 cm -1. Again, no particular elements can be used to argue for detection. Figure  4  represents the results from the non-negative matrix factorization using psNMF algorithm. One can clearly identify both H 2 O and CH 4 sources. Since those 2 chemical compounds are not correlated in abundance, (A H2O and A CH4 are independent), two different source spectra are identified. Please note that the relevance of source 4 is very low (0. 4%), meaning that only 0. 4% of the variability in the dataset is due to CH 4 , a very low value, as expected for minor species.
Convergence and computation time We set the MU algorithm convergence to relative difference of the cost function < 10 -8 and a maximum running time of 1000 seconds. For psNMF, we set the relative difference of the cost function to < 10 -7 and a maximum iteration to 2000. For BPSS2, we compute a minimum burn in of 1000 iterations and after that when the long term statistics (1000 last iterations) of the Markov Chain is close to the short term statistics (100 last iterations), convergence is considered to be reached. Then another 1000 iterations are computed to estimate the final solution statistics. We run the 3 identified tools 10 times on the same dataset with different noise realization, and compute mean and standard deviation from these 10 experiments. Results are presented in if the convergence is set, there is a high variability in MU results, due to the lack of regularization.
Simulation dataset This second dataset has been generated with the most precise direct model, taking into account the full non-linear radiative transfer and instrumental effects to produce synthetic transmittance, highly comparable with actual observations. Synthetic transmittances were made for real NOMAD-SO observation files using the relevant geometry and instrument parameters to attempt to include the variability inherent in the true measurements. Model atmospheres for each occultation were developed from the GEM-Mars general circulation model  (Neary and Daerden, 2018; Daerden et al. , 2019). The output of the model were provided for 1 Martian day every 10 solar longitude, and 48 timesteps per Martian day. Atmospheric profiles were developed for each occultation by interpolating the model temperature and pressure to the solar longitude, local solar time, latitude, longitude, and tangent altitude relative to the areoid.
When dust is optically thick, then non-linearity may appear that are out of the scope of this simulation. The simulation dataset consist of 12486 spectra, simulating observations of order 136 in the same configuration as the 106 solar occultations actually observed from May to December 2018. We add to the dataset a random noise with standard deviation of 0. 001 and 0. 0001 in order to simulate the instrumental noise (corresponding to SNR of 100 and 1000 approximately). We hide spectra containing CH 4 in a fraction of the total number of spectra from 1% to 100% in a random manner. In real observation, CH 4 may be spatially / temporally coherent but the number of scenarios is infinite. We feel that the random case is interesting enough to be tested. One has to note that contrarily to the previous toy model of section 4, here abundance are quantitative abundance in the atmosphere.
This is because CH 4 is a minor specie (as expected from the conditions of our simulation), its absorption band generally follows the air-mass, as H 2 O does. So there is no particular source for CH 4 only. When more than two lines are detected, we can consider it as a detection. This limit is reached for CH 4 ≥ 500 ppt for 10 and 100 ppm of H 2 O. Nevertheless, the detection limits lies between 100 and 500 ppt in the case of 10 ppm of H 2 O vapor since the detection is perfect (100% of the 4 main CH 4 peaks detected) occurs for a fraction of CH 4 5 to 50%. Interestingly, the optimum detection is not when 100% of the spectra contains CH 4 , but more between 5-50 %. This behavior is due to the statistics that is richer when also CH 4 is lacking in certain spectra. When 100% of spectra contain CH 4 , the statistical variability of the dataset is mainly due to airmass (atmosphere is assumed to be well mixed).
Real data analysis In this section, we report the results of actual NOMAD data, focusing on diffraction orders with potential CH be well mixed). So both CH 4 and H 2 O are varying together and there is less statistics to base the detection on. Noise level does not affect first the fraction of the 4 main CH 4 peaks but increases the spectral shift of the band center. In addition, it clearly affects the abundance and thus the band depth. In conclusion, from this simulation analysis, one could expect detection limits of CH 4 in the range 100-500 ppt when operating in favorable conditions.
These lines has been also detected in the ACS instrument data and attributed to CO 2 magnetic dipole transition  (Trokhimovskiy et al. , 2020). Further analysis shall be done to compare both NOMAD AND ACS data. Solar lines are never appearing in the sources. They are self-corrected by the calibration since we don't use a reference solar spectra but the solar observation during the transit when the tangent altitude is so high that there is no martian atmosphere (typically > 200 km). None of the analyzed orders presents sources related to CH 4.
Solar Figure  9 : Results of the psNMF algorithm for the diffraction order 134 for N S = 5. The source 1 is identified to the background level (continuum misestimation), the sources 3, 4 and 5 are identified to H 2 O. The sources 2 present unmodeled lines that are not present in the spectroscopic database. These lines has been first detected in the ACS instrument data and attributed to CO 2 magnetic dipole transition  (Trokhimovskiy et al. , 2020). No source seems to be related to CH 4.
19 Figure  9 : Results of the psNMF algorithm for the diffraction order 134 for N S = 5. The source 1 is identified to the background level (continuum misestimation), the sources 3, 4 and 5 are identified to H 2 O. The sources 2 present unmodeled lines that are not present in the spectroscopic database. These lines has been first detected in the ACS instrument data and attributed to CO 2 magnetic dipole transition  (Trokhimovskiy et al. , 2020). No source seems to be related to CH 4. We illustrate the approach for typical atmospheric spectroscopy. We first put forward a synthetic test, based on simple linear mixing to give a toy example and to identify the best promising algorithm. The psNMF clearly outperformed MU and BPSS2. Then we proposed a simulation, based on realistic radiative transfer and instrumental effects, applied on NOMAD-SO spectra.
The detection limits goes below 500 ppt in favorable conditions, with reduced H 2 O and low noise level. The same range of detection limits is reach with usual approach of model fitting at a much higher computation cost and analysis effort. Given the simplicity of use, this tool may be relevant to handle large and complex datasets at first glance. As a perspective, analysis of residuals after the non-linear retrieval of the data may lower the detection limits. One can then test if the residuals are simply Gaussian noise, or if they may contain interesting features. Interestingly, a molecular specie not well mixed in the atmosphere can be most easily detected with our approach. The last section presented the results of the application on real NOMAD-SO data, using orders 119, 134 and 136, selected as they are representative of the baseline strategy of measurements in NOMAD, allowing characterization of H 2 O and potential detection of CH 4.
The outcome is that no CH 4 has been identified, but H 2 O and CO 2 are detected. Interestingly a new set of spectral lines has been discovered in the NOMAD data. These lines has been first detected in the ACS instrument data and attributed to CO 2 magnetic dipole transition  (Trokhimovskiy et al. , 2020). We thus confirm their presence with our current analysis. One way to go back to the data is to pick the real data with the highest source contribution Ȧ. Our quicklook analysis is thus only a starting point of a more complete scientific analysis. This second step will require much more prior information (chemical compounds, fundamental spectroscopic constants, radiative transfer model,. ). Future work should apply the proposed approach to other datasets, such as other NOMAD-SO orders, or other spectroscopic datasets (including hyperspectral images) from laboratory measurements, ground based telescopes or space-born spectrometers.
The approach is generic enough to treat datasets that can be at first order approximated to a linear mixture. grants PGC2018-101836-B-I00 and ESP2017-87143-R (MINECO/FEDER), as well as by UK Space Agency through grants ST/R005761/1, ST/P001262/1, ST/R001405/1 and ST/R001405/1 and Italian Space Agency through grant 2018-2-HH. 0. This work was supported by the Belgian Fonds de la Recherche Scientifique -FNRS under grant number 30442502 (ET-HOME). The IAA/CSIC team acknowledges financial support from the State Agency for Research of the Spanish MCIU through the Center of Excellence Severo Ochoa award for the Instituto de Astrofísica de Andalucía (SEV-2017-0709). US investigators were supported by the National Aeronautics and Space Administration. Canadian investigators were supported by the Canadian Space Agency.
One can clearly see that the evenFigure 3: (left) Histogram of Band Depth at 3067. 2 cm 1 from the dataset containing 100 CH 4 at 3-level out of 10 4 spectra. (right) 100 spectra with the maximum Band Depth at 3067. 2 cm 1 specific of CH 4. Signal is dominated by water and by noise. No specific signature of CH 4 is visible. Histogram of Band Depth at 3067. 2 cm -1 from the dataset containing 100 CH 4 at 3-σ level out of 10 4 spectra. (right) 100 spectra with the maximum Band Depth at 3067. 2 cm -1 specific of CH 4. Signal is dominated by water and by noise. No specific signature of CH 4 is visible.
Acknowledgements We acknowledge support from the  "Institut National des Sciences de l'Univers" (INSU) , the  "Centre National de la Recherche Scientifique" (CNRS)  and " Centre National d'Etudes Spatiales" (CNES)  through the " Programme National de Planétologie " and the ExoMars TGO programs. The NOMAD experiment is led by the  Royal Belgian Institute for Space Aeronomy (BIRA-IASB ), assisted by Co-PI teams from  Spain (IAA-CSIC), Italy (INAF-IAPS) , and the  United Kingdom (Open University ). This project acknowledges funding by the  Belgian Science Policy Office (BELSPO) , with the financial and contractual coordination by the  ESA Prodex Office  ( PEA 4000103401 ,  4000121493 ), by  Spanish Ministry of Science and Innovation (MCIU)  and by  European funds  under.
Fluorescence polarisation assay. To determine the dissociation constant (Kd) of the fluorescent probes (TAMRA-NNG-SHWTIDI and TAMRA-NNG-SHW(Tle)(Chg)DI), solutions of increasing concentrations of syntenin PDZ1-2 in 25 mM HEPES, 0. 15 M NaCl, 1 mM β-mercaptoethanol, pH 7. 4 were prepared. The protein solutions were diluted with 200 nM TAMRA-NNG-SHWTIDI or TAMRA NNG-SHW(Tle)(Chg)DI , in black flat bottom low-binding 384-well plates (Corning), to generate a final fluorescent probe concentration of 100 nM. The samples were incubated for 5 min at room temperature. The fluorescent polarisation was read on a Tecan Safire 2 platereader at excitation/emission of 530/585 nm. The data was fitted to a non-linear one-site saturation binding curve in Prism 6 to determine the Kd value. To resolve the affinities for the unlabelled peptides, 100 nM syntenin PDZ12, 100 nM TAMRA-NNG-SHWTIDI or TAMRA-NNG-SHW(Tle)(Chg)DI and increasing concentrations of cold peptide was prepared in black flat bottom low-binding 384-well plates.
The fluorescent polarisation was determined as describe for the saturation binding experiments. Data was fitted to a sigmoidal dose-response curve in Prism 6 by using the equation Y = Bottom + (Top-Bottom)/(1+10 (logIC50-X)-Hill Slope ), where X is the cold ligand concentration in log units. The generated IC50 values was converted to Ki values, as previously described (30). Surface plasmon resonance (SPR). KSL-128018 was biotin labelled on the N-terminal and immobilised on a streptavidin sensor chip. Increasing concentrations of syntenin-1 PDZ1-2 and syntenin-2 PDZ1-2 were freshly prepared and analysed on a BIAcore T200. Sensorgrams were collected and the Kd values were determined based on the ratio of the association and dissociation rate constants, as previously described  45. High-throughput screening of the human PDZome.