dataesr/scientific-paragraphs-categorization huggingface dataset:
Area under the ROC curve (AUROC) On a simulated dataset, the variables that drive the subgroups are known, and it is easy to compute false-positive and true-positive rates. First, variables are ordered by their standard deviation (from the highest to the lowest) computed on the H matrix to highlight the largest differences between the P components and therefore the most contributory to the clusters. To summarize the information of these two quantities, we compute the area under the TPR-FPR curve (AUROC). An AUROC equal to one means that the method selects the variables with no error. An AUROC under 0. 50 means that false-positive variables are selected before the true positive ones.
Simulations on independent datasets (non-correlated blocks) The performance of PIntMF to cluster samples and to select relevant variables was evaluated on simulated data described in  (Pierre-Jean et al. , 2019). The framework of these simulations is composed of three blocks with three different types of distribution (Binary, Beta-like, and Gaussian) to simulate the heterogeneity of the integrative omics data studies. Indeed, a binary distribution could match a mutation (equal to 1 if the gene is mutated and 0 otherwise); a Beta-like distribution could match DNA methylation data, and a Gaussian distribution could match gene expression values. Four unbalanced groups (composed of 25, 20, 5, and 10 individuals) have been simulated (Benchmarks 1 to 5). Datasets with 2, 3, and 4 balanced groups have also been simulated (Benchmarks 6 to 8).
Simulation based on real data (correlated blocks) We evaluate the performance of PIntMF on a simulated framework based on cancer real data and developed by  (Chung and Kang, 2019). Indeed, the previous framework does not simulate any correlation between omics blocks. OmicsSIMLA is a simulation tool for generating multi-omics data with disease status. This tool simulates CpGs with methylation proportions, RNA-seq read counts and normalized protein expression levels. Here, we simulated 50 datasets containing 50 cases (i. e. , short-term survival) and 50 controls (i. e. long-term survival), and three omics blocks (RNAseq, DNA methylation, and proteins). We try to recover the two groups but also the different features that drive overall survival by using DNA methylation, expression, and protein data.
For two of the three blocks (expression and DNA methylation), the variables differentially expressed or methylated between the two groups are known. The simulated data are described in Supplementary Materials (Section 5). In these simulations, we also compare the performance of PIntMF to other methods in terms of clustering and variable selection. First, CIMLR does not give any results on these simulations (the algorithm does not converge). For all the other methods, the ARI is equal to 1 (maximum value) for all 50 datasets. Then, we compare the variable selection performance of PIntMF, intNMF, iClusterPlus, MoCluster, and SGCCA by computing the AUROC on expression and DNA methylation blocks only (the protein block does not contain any variable simulated with differential abundance, more details are given in Supplementary Materials section 5).
DNA Methylation dataset: PintMF and iclusterPlus outperform the others with similar performances but the AUROC of iclusterPlus is significantly higher. Then, the AUROC of PintMF is significantly higher than for MoCluster, SGCCA and intNMF (Fig. 2 ). Expression dataset: PIntMF is the best method with an AUROC significantly higher than the others. However, all methods achieve an AUROC higher than 0. 92. (Fig. 2 ) On these simulations, PIntMF gives similar results to iClusterPlus, but with automatic tuning of parameters. Besides, the algorithm of PIntMF is faster than iClusterPlus.
Stability selection Jackknife was performed to evaluate the stability of variable selection. To perform this technique, we run the model PIntMF on the data without one sample at each step. Therefore, we obtain n datasets containing n -1 individuals on which we apply the method. The stability of the selected variables for Binary, Gaussian, methylation and expression datasets seems to be strong (Fig. S10  in Supplementary Materials). For proteins and for beta-like data, the bootstrap reveals that some selected variables are not stable. The Jackknife method could be used to remove false-positives variables.
Applications In this section, we assess the performance of the PIntMF method on real data by considering two applications. The first one is a dataset from murine liver  (Williams et al. , 2016)  under two different diets already used in two previous comparison articles (  Pierre-Jean et al. , 2019; Tini et al. , 2017) , and the objective is to recover the diets of the mice (fat diet or chow diet). The second one is a glioblastoma dataset from TCGA used in  (Shen et al. , 2012)  and the goal is to find the tumor subtypes.
PIntMF highlights variables linked to phenotypes of samples We analyzed the BXD cohort (composed of 64 samples)  (Williams et al. , 2016) ; the mice were shared into two different environmental conditions of diet: chow diet (CD) (6% kcal of fat) or high-fat diet (HFD) (60% kcal of fat). Measurements have been made in the livers of the entire population at the transcriptome, the proteome, and the metabolome levels. Therefore, we applied PIntMF to this dataset as well as intNMF, MoCluster, SGCCA, iClusterPlus, and CIMLR (Supplementary Materials Table  S2 ). PIntMF produces a perfect classification of the individuals for this real dataset. For this dataset, all criteria for the model selection were computed (Supplementary Material Fig. S6 ), and 2 groups were selected for further analysis. PIntMF highlights interesting variables that seem to have different abundance between the two groups CD and HFD (Fig.
3 ): VITAMIN E (C 2 9H 5 00 2 ), Cholesteryl (C 3 6H 6 2O 5 ), Mustard Oil (C 4 H 5 NS). Saa2 gene that codes for a protein involved in the HDL complex seems to be deferentially expressed between the two groups. Then, the Cidea gene that is involved in the metabolism of lipids and lipoproteins has a slightly different level of expression between the two groups. Finally, Cyp2b9 oxidies steroids, fatty acids, and xenobiotics are less expressed in the high-fat diet group. To conclude, PIntMF succeeds well to recover classification and relevant markers in all datasets.
PIntMF reveals a new classification of non annotated samples on TCGA dataset. Secondly, we analyze a subset of the glioblastoma dataset from the cancer genome atlas (TCGA): the Glioblastoma study (2009) used in  (Shen et al. , 2012). The dataset contains three matrices: copy number variation (1599 regions), Metabolites C37H70O5 C39H72O5 C4H5NS C9H15N3O2S C26H46O6 C29H50O2 C33H64O5 C36H62O5 C24H35O2 C39H60O5 Proteins Srd5a-1 R75370 Ccdc44 Lpsb2 Pcn MTP galectin-1 GstpiB Gst3 Ces6 RNA Cd36 Lcn2 Saa2 Cyp2b9 9030619P08Rik Cyp2a22 Cidea D630002G06Rik AB056442 Cyp2b13 PIntMF Truth DNA methylation (1515 CpG), and mRNA expression (1740 genes) in 55 samples. GBM samples were classified into four subtypes (Classical: CL, Mesenchymal: MES, Neural: NL, and Proneural: PN). Besides, there are samples with no subtype (NA).
Discussion We presented a new model to discover new subgroups of a cohort and potential new markers from several types of omic data. PIntMF is a matrix factorization model with positivity and sparsity constraints (Lasso) on inferred matrices. The method and all scripts of this article are available in an R package named PIntMF. The main advantage of this method is the automatic tuning of the lasso penalties for both variable and sample matrices. To optimize the algorithm at the computational time level (Supplementary Materials Fig. S9 ), we tried several algorithms to infer matrices H k. glmnet is very fast compared to the others (ncvreg, quadrupen, and biglasso), therefore it was retained for all analysis. We also optimized the initialization of the algorithm that is obtained by using the SNF algorithm  (Wang et al.
We re-derived parameters for the stars in the catalog using better quality spectra and/or using the most recent versions of the codes. Moreover, the new SWEET-Cat table can now be more easily combined with the planet properties listed both at the Extrasolar Planets Encyclopedia and at the NASA exoplanet archive to perform statistical analyses of exoplanets. We also made use of the recent GAIA eDR3 parallaxes and respective photometry to derive consistent and accurate surface gravity values for the host stars. Results. We increased the number of stars with homogeneous parameters by more than 40% (from 645 to 928). We reviewed and updated the metallicity distributions of stars hosting planets with different mass regimes comparing the low-mass planets (< 30M ⊕ ) with the high-mass planets. The new data strengthen previous results showing the possible trend in the metallicity-period-mass diagram for low-mass planets.
This work presents a significant upgrade to SWEET-Cat 1. It consists of the addition of 283 new planet hosts, the inclusion of new data relevant for the characterization of the planethost stars, the inclusion of the link to the NASA archive exoplanet database 2  (Akeson et al. 2013) , in addition to the already existing link to the Extrasolar Planets Encyclopedia 3  (Schneider et al. 2011) , and the rederivation of spectroscopic parameters from better quality or recent spectra using the latest updated codes developed by our group. The following sections describe all the work performed for the new version of SWEET-Cat. Section 2 describes the spectroscopic data compilation for the catalog. Section 3 presents how the spectroscopic parameters are derived, and compares the latest parameters with our older results and others in the literature.
Selection of host stars for SWEET-Cat We kept the same constraints of previous catalog versions to include the planet host stars in SWEET-Cat. First, we search for the confirmed planets in the Extrasolar Planets Encyclopedia and selected only the detected by Radial Velocity, Primary Transit, and Astrometry methods. Second, we cross-match their host stars with the stars in SWEET-Cat and include the missing hosts, while removing the stars that no longer had a planet confirmed status. The same procedure is performed with the NASA exoplanet archive to add the confirmed host stars missing in the Extrasolar Planets Encyclopedia. We include the database source in the information of all host stars (see Section 4 for details).
Spectra from public archival data The ESO archive 4 is the main source of reduced spectral public data for SWEET-Cat. We used the astroquery. eso 5 submodule to search for the required data in the ESO archive. We note that a small fraction of the spectra belonging to our UVES programs The compilation of data prioritizes high-resolution and high signal-to-noise ratio (S/N) spectra for each host star. We selected the data from the FEROS, HARPS, and UVES spectrographs, all with R > 40000  6. In most cases we downloaded more than one spectrum per star to achieve a higher S/N by combining them. We avoided very low S/N spectra (S/N<15) due to lowquality individual exposures that could add relatively low signal compared with the noise. We also did not select very high S/N spectra (e. g. , S/N>550 for HARPS, S/N>1000 for UVES 7  ) either due to the likely saturation of the individual exposures.
Moreover, we keep figures S. G. Sousa et al. : SWEET-Cat 2. 0: The Cat just got SWEETer for each final combined spectrum along with the spectra used for its creation. Since this is a significant amount of data the selection of spectra and their combination is an automatic process. However, there is a human validation to certify the quality of the end products. The main problems identified during the validation include the following: i) incorrect identification of the star: some stars are very close in the sky. For example, stars in the Kepler field and close in binaries can be easily mismatched when searching the archival data. We identify mismatches by cross-checking the lists of spectra used for each star. if we find a file used for two or more stars, we discard that spectrum and redo the combination process with the updated list.
ii) data reduction process: some individual spectra in the figures show unexpected flux variations and/or strange behavior in the continuum (e. g. , ripples or strong spikes). These likely indicate a problem with the reduction of the archival spectra. We discard these spectra and redo the combination process. iii) radial velocity correction: some spectra were not properly shifted in radial velocity before the spectral combination by looking at the figures. We identify the files and apply the crosscorrelation function with different parameters to correct the issue. If that fails, we discard the files and redo the combination process. We searched for spectra in other archives for the host stars of SWEET-Cat. In particular, archives where we could do the search and download automatically. We used custom-made python scripts to search for and download spectra from the SO-PHIE 8 , ESPADONS 9 , and HARPS-N 10 spectrographs archival data.
Spectra format The spectra compilation followed the basic procedure described in  Sousa et al. (2018). We store the combined spectra in fits files. In the fits header, in addition to the essential keywords, we added the search parameters, the GAIA DR2 id 11 , the search box area, the date related to the data search, and the respective combinations. Moreover, we include the list with the reduced frames used for the combined spectra and their S/N information from 8 http://atlas. obs-hp. fr/sophie/ 9 http://www. cadc-ccda. hia-iha. nrc-cnrc. gc. ca/en/ cfht/ 10 http://www. not. iac. es/archive/ 11 At the time of the combination of spectra the GAIA DR2 was an identifier in Simbad (http://simbad. u-strasbg. fr/), while the GAIA eDR3 was not. the archives. We plan to provide such spectra in a future update of SWEET-Cat.
Spectroscopic parameters We carried out the spectroscopic analysis with ARES+MOOG for the new spectroscopic data and the legacy data (for details see  Sousa 2014). We re-derived the homogeneous parameters already in SWEET-Cat for several host stars, given that we either collected higher quality data or decided to apply the latest version of the codes described previously. The spectral analysis relies on the excitation and ionization balance of iron abundance. The ARES code 12   (Sousa et al. 2007 (Sousa et al. , 2015a) )  automatically measures the equivalent widths of the absorption lines. The MOOG code  (Sneden 1973 ) is used for the element abundances assuming local thermodynamic equilibrium (LTE) and using a grid of Kurucz ATLAS9 plane-parallel model atmospheres  (Kurucz 1993). We applied this method in our previous spectroscopic studies of planet hosts (e.
Use of GAIA eDR3 We matched the stars listed in SWEET-Cat with the GAIA ID in DR2 and eDR3 using their coordinates and the VizieR catalogs  (Gaia Collaboration et al. 2016 , 2021). We checked the magnitudes and astrometry data to confirm that we selected the correct star. While most stars in SWEET-Cat have the same ID as for GAIA DR2, there are GAIA IDs that appear to change between the data releases. The correct GAIA ID identification was not straightforward in some cases because of the presence of other stars with similar magnitudes in the searched field of view. The GAIA IDs make it easier for SWEET-Cat users to combine the spectroscopic data with the GAIA astrometry. For each target with a GAIA ID, we proceed to the extraction of its parallax from eDR3. Parallax was one of the columns present in the SWEET-Cat table, but not necessarily updated for the whole sample.
,  Hoyer et al. 2021; Leleu et al. 2021). The percentage of stars with spectra and homogeneous parameters increases for bright stars listed in SWEET-Cat. With the work presented in this paper, considering the addition of 283 new stars with homogeneous parameters, we have ∼88% and ∼76% completeness for stars with G<9 and G<12, respectively. Completeness represents the number of host stars with homogeneous spectroscopic parameters relative to the total number of stars listed in SWEET-Cat. We significantly increase the number of homogeneous parameters for planet host stars with this update. However, the continuous increase of new host stars in the catalog keeps the percentage for bright stars almost the same. In Table  1  we can also see that there is still a subset of bright planet-host stars (233 stars, about ∼25% of the bright FGK stars) for which we did not find, at the time of the compilation of this data, high-quality public data at the time of the search for this work.
Link to exoplanet catalogs The match of SWEET-Cat host star parameters with the properties of their exoplanets in online databases is quite useful for the statistical exploration of the data. However, given that we only control the SWEET-Cat table, the continuous match with external databases is not always straightforward. At first SWEET-Cat kept entries for the confirmed planet-hosts in exoplanet. eu exclusively, and we did the matching with the names of the planets that inherit it from the host star. This approach turned out to be problematic: some planets names either changed regularly (Keppler objects of interest to Kepler denominations is a typical example) or were not consistent within the planetary system (e. g. , K2-50 with K2-50b and EPIC201833600 c listed in exoplanet. eu). Therefore, we now rely on the host coordinates obtained from the Simbad database, and we compare them against the coordinates listed in exoplanets.
eu and the NASA exoplanet archive. The updated SWEET-Cat table has the planet coordinates listed in both the exoplanet. eu and the NASA archive exoplanets database to facilitate any matching. By adding the planet coordinates in both databases, we can match the objects even if the coordinates are incorrect (e. g. , due to typos) in the planet databases. We provide a python script example on the website to show the capabilities to explore SWEET-Cat and the properties of the exoplanets statistically.
Stellar mass and planetary mass The relation between the occurrence rate of planets and stellar mass is a statistical result from exoplanetary surveys that enriches our understanding of planet formation (e. g. ,  Fulton & Petigura 2018; Lozovsky et al. 2021; Neil & Rogers 2018; Yang et al. 2020). Because SWEET-Cat is a catalog of host stars only, it is impossible to estimate the occurrence rates of planets and their dependence on stellar parameters. However, SWEET-Cat data can be used to check if the mass distributions of stars hosting different planet types agree with the results related to occurrence rates. We focus these analyses on the hosts with trigonometric surface gravities above 4. 00 dex (dwarf stars) since we rely on the   8 ). The stars with cold and hot HMPs have a mean mass of 1.
We found that stars hosting low-mass planets have a similar distribution to the stars in the solar neighborhood, but that slightly S. G. Sousa et al. : SWEET-Cat 2. 0: The Cat just got SWEETer higher metallicities were favored. We showed the metallicity distributions for massive planets, splitting them between hot and cool according to their period. We found differences between these distributions that are consistent with results in the literature. Finally, we reviewed the metallicity-period-mass correlation for the low-mass planets. The correlation became slightly tighter with the inclusion of new planets, although it is still unclear if the reason behind it is the RV observational bias. We will continue working on SWEET-Cat in the following years to provide the community with a data set relevant for statistical studies of exoplanets.
Acknowledgements. This work was supported by  FCT -Fundacção para a Ciência e Tecnologia  through national funds and by  FEDER  through  COMPETE2020 -Programa Operacional  Competitividade e Internacionalização by these grants:  UID/FIS/04434/2019 ;  UIDB/04434/2020 ;  UIDP/04434/2020; PTDC/FIS-AST/32113/2017 & POCI-01-0145-FEDER-032113; PTDC/FIS-AST/28953/2017 & POCI-01-0145-FEDER-028953; PTDC/FIS-AST/28987/2017 & POCI-01-0145-FEDER-028987; PTDC/FIS-OUT/29048/2017 & IF/00852/2015. S. C. C. B. acknowledges support from  FCT  through contract nr. IF/01312/2014/CP1215/CT0004. S. G. S acknowledges the support from FCT through Investigador FCT contract nr. CEECIND/00826/2018  and  POPH/FSE (EC). V. A. and EDM acknowledges the support from  FCT through Investigador FCT  contract  nrs. IF/00650/2015/CP1273/CT0001  and  IF/00849/2015/CP1273/CT0003.
However, these conclusions were subject to significant uncertainty in the planet masses, making the determination of the compositions less definitive as the uncertainties were still consistent with rocky bodies at the 1 -2σ level. In addition, the masses of all of the planets are highly correlated due to the fact that the dynamical state of all of the planets needs to be solved together and their masses and radii are measured relative to the star, so model comparisons with individual planets are not independent. P T T V = 1 jP -1 i -(j + 1)P -1 i+1 , (1) In this paper we revisit a transit-timing and photometric analysis with the completed Spitzer program using the more extensive transit dataset we now have in hand. The goal of this program is to provide a more precise understanding of the masses, radii, and densities of the planets.
In §2 we summarize the observational data which are analyzed in this paper. In §3 we discuss the nature of transit timing outliers, and the robust likelihood function we use for characterizing the system. This is followed by a description of our N-body transit-timing analysis in §4. With the improved N-body model, we revisit the photometric fit to the Spitzer data using a photodynamical model in §5. The results of these two analyses are combined to obtain the planet bulk properties in §6. In §7 we derive revised parameters for the host star. In §8 we search for an eighth planet with transit-timing. In §9 we interpret the mass-radius measurements for the planets in terms of interior and atmospheric structure models. Discussion and conclusions are given in §10 and §11. We provide Julia, python, and Matlab code for running the Markov chains, creating the figures, and creating the paper PDF in https://github.
com/ericagol/TRAPPIST1_Spitzer. The 3. 5 GB data/ directory in the repository may be found at https://doi. org/10. 5281/zenodo. 4060252. In each figure we embed links to the code (</>) which produced that figure. Since the work described in  Grimm et al. (2018)  based on 284 transits, we have added an additional 163 transit times from a combination of Spitzer ( §2. 1) and ground-based observations ( §2. 2) for a total of 447 transits. With preliminary transit-timing fits, we found evidence for outliers amongst the measured times ( §3), which we account for with a robust likelihood model. Each transit time is measured as a Barycentric Julian Date (BJD TDB ), correcting for the location of the Earth/spacecraft relative to the Solar System barycenter  (Eastman et al. 2010 ) at the time of each transit observation.
Spitzer Observations The dataset used in this work includes the entire photometry database of TRAPPIST-1 observations with Spitzer Space Telescope's Infrared Array Camera (IRAC;  Carey et al. 2004 ) since the discovery of its planetary system. This represents all time series observations gathered within the DDT programs 12126 (PI: M. Gillon), 13175 (PI: L. Delrez) and 14223 (PI: E. Agol). These cover a total of 188 transits observed from Feb 2016 to Oct 2019 and include  64, 47, 23, 18, 16, 13 , and 7 transits of planets b, c, d, e, f, g, and h, respectively  (Ducrot et al. 2020). All of these data can be accessed through the online Spitzer Heritage Archive database 2. Spitzer IRAC Channels 1 (3. 6 µm, 0. 75 µm wide) and 2 (4. 5 µm, 1. 015 µm wide) were used during the Spitzer Warm Mission  (Fazio et al.