dataesr/scientific-paragraphs-categorization huggingface dataset:
The added information brought by the analysis of SI time series has been also demonstrated here. The time varying sensitivities of the input parameters was clearly demonstrated, from the dominance of the snow/ice ones in frozen conditions, to the relative contribution of the other ones for free water according to lake depth, that is, larger sensitivity of lake depth and light extinction coefficient for shallow lakes whereas water albedo and thermocline relaxation constant are more influential for deeper lakes. The analysis was limited to LWST and surface turbulent fluxes because these are the main variables seen by the atmosphere in a climate model. It has been fully informative to better understand the functioning of FLake model, its parameters and interactions. It allows us to start its implementation in ORCHIDEE with confidence and to identify the databases that will be used for its calibration.
IV. APPLICATIONS OF THE SDP HIERARCHY We implemented a version of this hierarchy (and the variant described in Appendix B) in MATLAB, exploiting the SDP interface YALMIP  [29] , and our code is freely available  [30]. Our implementation can handle arbitrary contextuality scenarios, restrictions to pure or projective quantum models or to classical (commuting) models, and solve either the feasibility SDP of Proposition 6 or maximise a linear functional of the correlations p(b|x, y) subject to linear constraints on the probabilities. In solving large SDP problems that would otherwise be numerically intractable, it can make use of RepLAB  [31, 32]  (a recently developed tool for manipulating finite groups with an emphasis on SDP applications) to exploit symmetries in noncontextuality inequalities, a capability we exploit in obtaining some of the results presented below.
B. Mixed states as resources for quantum contextuality In many forms of nonclassicality, such as Bell nonlocality, steering and quantum dimension witnessing, the strongest quantum correlations are necessarily obtained with pure states. In the former two, this stems from the fact that any mixed state can be purified in a larger Hilbert space. In the 5 The precise lists of moments used in this and all subsequent examples can be found along with our implementation of the SDP hierarchy, where the code generating these results is available  [30]. In all these examples we take the monomial lists L and O for the localising matrices to be the same (simply because this was sufficient to obtain the presented results), although one could indeed take these to be different if desired. latter, it follows from the possibility to realise a mixed state as a convex combination of pure states of the same dimension.
These, e. g. , further impose that γ ρxσE 2|2 E 1|1 = γ ρxσE 1|1 -γ ρxσE 1|2 E 1|1 , γ ρxσE 2|2 E 2|1 = γ ρxσ -γ ρxσE 1|2 -γ ρxσE 1|1 + γ ρxσE 1|2 E 1|1 , etc. The other blocks of Γ can be reduced and related in similar ways by applying similar simplifications. In practice, our code (which is freely accessible [30]), works by applying reductions to every element of the moment matrix to reduce it to a canonical form, before identifying the unique elements. The completeness relations can then be applied to further reduce the number of variables in the optimisation problem. We note, however, that when projective measurements are considered it is generally not actually necessary to apply the constraints arising from the completeness relation. Although one obtains a potentially weaker set of necessary conditions, in practice we rarely see any difference in the power of the hierarchy under this relaxation.
ACKNOWLEDGMENTS The authors thank  Jean-Daniel Bancal  for helpful discussions on the efficient implementation of SDP hierarchies and, in particular, on the use of RepLAB to exploit symmetries in such implementations, as well as the anonymous referees for comments that helped to significantly improve this paper. This work was supported by the  Swiss National Science Foundation  (Starting grant DIAQ,  NCCR-SwissMAP ,  Early Mobility Fellowship   P2GEP2 194800  and  Mobility Fellowship   P2GEP2 188276 ).
We demonstrate that this technique yields an improvement of WISDOM vertical resolution by a factor of 3 while well preserving the time of arrival and amplitude of the detected echoes. We validate the BWE technique on synthetic data before applying it to experimental observations acquired both in controlled and natural environments. The resulting super-resolved radargrams greatly improve our understanding of the investigated terrains with a better separation of echoes from underground reflectors, and demonstrate the value of implementing the BWE technique in the WISDOM data processing pipeline which will ultimately provide images of the Martian subsurface down to a few meters depth with a vertical resolution of ~2 cm in typical soils.
WISDOM has been designed by the LATMOS (Laboratoire Atmosph eres, Milieux, Observations Spatiales, France), the TUD (Tecnische Universt€ at Dresden, Germany) and the LAB (Laboratoire d'Astrophysique de Bordeaux, France) to unveil the structure and dielectric properties of the Martian subsurface below the ExoMars rover down to a likely maximum depth of ~3 m in a lithic environment with a vertical resolution of a few centimeters. In the context of searching for a drilling place to collect 3-cm long samples  (Vago et al. , 2017) , this latter parameter is key. However, the range resolution of a radar is limited by the instrument bandwidth (2. 5 GHz in the case of WISDOM). In this paper, we describe how to expand the nominal bandwidth of WISDOM and therefore to improve the instrument resolution, by implementing in the data processing chain a super-resolution method called the Bandwidth Extrapolation (BWE) technique.
The BWE technique was proposed by the Radar Imaging Technique group of the Lincoln laboratory. The concept was introduced by S. B. Bowling (1977)  and then further developed by K. M. Cuomo (1992)  who applied it to radar data. Moore et al. (1997)  then applied it to SAR imaging. More recently, the technique has been used to enhance resolution in planetary radar imaging, for example to improve the bathymetric capabilities of the Cassini Radar instrument  (Mastrogiuseppe et al. , 2014)  and the stratigraphic analysis of the Martian polar ice sheets using SHARAD/MRO dataset  (Raguso et al. , 2018). Following such promising results, we have adapted and applied the BWE technique to WISDOM data. In this paper, we briefly introduce the instrument and its performances in term of range resolution. Then, we present the BWE technique, and its integration to the WISDOM data processing chain.
WISDOM vertical resolution As previously mentioned, WISDOM is in charge of providing information that will help the mission's scientific team to identify the very layer where to take a sample. In order to achieve this goal, the instrument requires a vertical resolution commensurate with the 3-cm length of the sample. The range resolution is defined as the shortest distance between two echoes that can be discriminated. In a horizontally layered subsurface, it corresponds to the smallest thickness that can be resolved by the instrument. As previously mentioned, WISDOM is operating in the frequency-domain over a frequency bandwidth B ¼ 2. 5 GHz and an Inverse Fourier Transform (IFT) is applied to the data to reconstruct the response in time-domain. A radar range resolution δr is limited by the width of the synthetic pulse obtained after IFT, which is inversely proportional to the effective bandwidth of the instrument.
b) Therefore, for a frequency spectrum of N samples and a given order p for the model, the total energy E p of the residual has to be minimized in order to determine the coefficients of the model: E p ¼ 1 2 X N n ¼ pþ1 e p f À n Á 2 þ e p b À n Á 2 (6) This process is known as the "Maximum Entropy Method"  (Burg, 1967). It can be implemented using several algorithms, but only the Burg algorithm is considered in this study, as it has proved to guaranty the stability of the model, and performs better on experimental data than the others  (Raguso, 2018). For the best model's order, a value of p ¼ N=3 has been experimentally found to yield the best results  (Cuomo, 1992; Raguso, 2018)  and is commonly used in literature. We will show in section 4. 2 that this also applies to the WISDOM dataset.
The idea of the Bandwidth Extrapolation technique is to use the model previously obtained from the available data (i. e. , the order p and a i coefficient values) to extrapolate the spectrum to frequency values outside the initial frequency range. Considering an initial frequency spectrum made of N samples, the ðN þ 1)-th sample can be estimated in the forward direction: b s f nþ1 ¼ À X p i¼1 a i s NÀiþ1 for frequency ν Nþ1 ¼ ν max þ ν (7) The same process can be performed in the backward direction, b s 0 b ¼ À X p i¼1 a i * s i for frequency ν 0 ¼ ν min À ν leading to negative indices for extrapolation to even lower frequency b s b À1 ¼ À X p i¼1 a * i s iÀp for frequency ν À1 ¼ ν min À 2ν (8) Further estimates are obtained based on the initial dataset gradually extrapolated. The Burg method  (Burg, 1967)  is a recursive algorithm which minimizes the value of E p for increasing values of p.
Fig. 2  a displays the resulting synthetic radargram (obtained with a Hamming window, zero padding but without BWE). It shows constructive and destructive interference features between the two echoes (that are also observed on the corresponding experimental radargram, Fig. 10 ). The instrument is unable to resolve the echoes when the distance between the reflectors is less than ~11 cm in vacuum, which is consistent with equation (2) for ε r ¼ 1. Fig. 2  b displays the radargram that is obtained with the same dataset after BWE to a bandwidth 3 times larger than the original one. As expected, the resolution is improved by a factor 3 therefore reaching ~4 cm (see section 4. 3). We will describe in the following how this result has been obtained. In frequency domain, the accuracy of the BWE applied to this synthetic dataset can also be appreciated.
Determination of the order of the model To generate the radargram enhanced by BWE shown in Fig. 2 b , we have applied the method described in section 3. The first step of the method is to choose the value for the order p of the autoregressive model. To do that, we limit all the initial spectra to one third of their bandwidth by symmetrically removing frequencies on both sides. Then, we apply the BWE technique to reconstruct the initial dataset for different orders values p ranging from 1 to N. For each p value, the reconstructed radargram is compared to the original one to identify the best order for the BWE algorithm. The correlation between both radargrams is computed, which provides a quantitative analysis of the reliability of the extrapolation. This process is repeated for 1000 noise realisations (Monte Carlo approach).
Effect of the BWE on the resolution With the same dataset, it is possible, from the time delays measured at the peaks of the two echoes (when resolved), to obtain an estimate of the distance between the two reflectors and to compare this estimate b d to the known distance d in order to test the ability of BWE to improve the resolution of the soundings. In Fig. 5 , the mean value of the error b d À d, with its standard deviation computed on 1000 realisations (Monte Carlo approach) a randomised phase for the first echo is displayed as a function of d. Without BWE, the simulated echoes obtained with d < 11 cm cannot be separated, while with BWE this limit is brought to 3. 75 cm with an error that remains well below the expected resolution. It can be also noted that, with or without BWE, the error oscillates, depending on the phase between the two echoes.
Effect of the BWE on the precision Having studied the effect of the BWE on the resolution with the generated synthetic dataset, it is also important to verify that this technique does not alter the positions of the reflectors. In other words, that the precision of the super-resolved radargrams remain barely changed after application of the BWE. For each echo, the error on the estimation of its position is measured for each value of d before and after application of the BWE. In Fig. 6  displays the error on the position of both echoes as a function of d. It can be observed that the absolute error on the position stays below 1 cm as it oscillates. It is even lower than 0. 5 cm for d > 5 cm. This worst case result (i. e. , in vacuum) demonstrate the ability of the BWE to increase the resolution of the WISDOM soundings without impairing their precision.
Effect of the BWE on the echo amplitude An advantage of the BWE, when compared to other super-resolution techniques (MUSIC, ESPRIT), is the conservation of the amplitude of each echo in the enhanced radargram  (Cuomo, 1992). This advantage is essential because, in experimental data, the echo amplitude will ultimately be used to infer information about the reflecting structures (starting with the permittivity value in a case of a smooth interface). The ability to obtain a satisfactory estimate of the amplitude has been tested on the previously described synthetic dataset for which the amplitude of both echoes has been set to 1. When these latter ones are resolved by BWE (i. e. , for d > 3. 75 cm after BWE), the ratio between the first echo amplitude and the second echo one is computed. Fig.
Distance estimation after application of the BWE A peak detection can easily be applied to the different soundings performed without and with BWE to measure the time delay between the two echoes coming from the metallic plates and therefore the distance between these plates, as performed in Section 4 on synthetic soundings. Fig. 12  shows the error on the estimated distance as extracted both from the synthetic and the experimental datasets and before and after BWE. As previously mentioned, for the synthetic data, each sounding has been generated with 1000 cases of noise, with a SNR ¼ 30 dB. Mean values of the distance error with associated standard deviations are displayed in Fig. 12  as a function of the distance between the reflectors. For the experimental data, only one measurement is performed for a given distance d which has been measured with an uncertainty of about 0.
Application of the Bandwidth Extrapolation technique to WISDOM field test data Between 2010 and 2019, several field campaigns have been organised in order to evaluate WISDOM performances on different environments, some of them potentially analogs to the Martian subsurface. These field tests have been performed with various models of the instrument, the first ones with prototypes and the most recent ones with models similar to the instrument flight model. The result is a large dataset of radargrams to which BWE can be applied. We have selected four campaigns, during which structures of interest were detected in the subsurface, and for which the application of the BWE proved to be very helpful for radargram legibility and interpretation. For some campaigns, no free-space or no calibration measurements are available.
Conclusions and perspectives In the present study we have adapted and applied for the first time to WISDOM data the super-resolution method known as "Bandwidth Extrapolation technique". While the technique has already been successfully applied to observations from planetary orbital radar sounders (MARSIS/Mars Express, SHARAD/MRO, Cassini radar), this is, to our knowledge, its first application to planetary surface GPR soundings. The BWE technique is now implemented in the WISDOM processing pipeline described in Herv e et al. (2020). As the WISDOM instrument is set to arrive on Mars only in 2023, the BWE has been methodologically tested on synthetic, experimental and    Once on Mars, the improvement in vertical resolution of WISDOM radargrams, and therefore the improved separation of echoes from underground reflectors, will indeed be essential to ensure the drill safety by avoiding buried rocks as well as to investigate of the geological history of the ExoMars landing site, Oxia Planum.
Acknowledgements Development of the WISDOM instrument and preparation of the data processing and interpretation have been funded and supported by  CNES  ( Centre National d'Etudes Spatiales, France)  and  DLR (Deutsches Zentrum für Luft-und Raumfahrt, Germany). Nicolas Oudart 's PhD fellowship is funded by  CNES  and  UVSQ (Universit e de Versailles Saint-Quentin ).
Results The Porites australiensis Genome Because P. australiensis is gonochoric, in order to isolate highquality P. australiensis genomic DNA, we collected sperm from a male colony (fig. 1B ). We obtained about 39 Gigabase pairs (Gbp) of genome sequencing data (supplementary table 1, Supplementary Material online), assembled the data, and then created a P. australiensis draft genome assembly of 576 Mbp with a 554-kb N50 size and 4,983 scaffold sequences (table 1). We confirmed that 99% of the shotgun sequences mapped back to the assembled genome, and among uniquely mapped pairs (mapping quality >10), 99. 3% of all pairs were properly mapped on the same scaffold. Estimation of the haploid genome size, based on.
kmer coverage of the shotgun sequencing data using GenomeScope  (Vurture et al. 2017) , was close to the assembled genome size (560 Mbp, kmer length 29; supplementary fig. 1 , Supplementary Material online). We predicted 30,301 protein coding genes from the assembled genome. Although genome assembly statistics for P. lutea  (Robbins et al. 2019)  are slightly better than these for P. australiensis, the number of predicted genes was comparable between the two genomes (table 1;  Robbins et al. 2019). Benchmarking Universal Single-Copy Orthologs (BUSCO) analyses  (Simao et al. 2015; Waterhouse et al. 2017) , which assess whether universal single-copy orthologous genes observed in more than 90% of metazoan species (from the OrthoDB database of orthologs) (www. orthodb. org; version 9) are recovered in a genome/transcriptome assembly, yielded completeness scores for the P.
australiensis genome assembly and gene models of about 91% and 94% (average of Complete BUSCO %), respectively, indicating that the genome assembly and gene models are of reasonable quality and comparable to those of previously reported coral genomes, including P. lutea (table  1 ). Among the 30,301 predicted genes, 20,418 exhibited similarities with genes in the Uniprot/Swissprot database, whereas 20,447 were related to entries in the Pfam conserved protein domains database (supplementary table 2, Supplementary Material online). We also obtained the complete sequence of the P. australiensis mitochondrial genome (18,647 bp, accession number: LC605627), which is >99. 7% identical to the Porites lobata mitochondrial genome (KU761954. 1, 18,604/18,647 bp identity, no gaps). In addition to the P.
Porites-Specific Gene Expansions Include Environmental Stress Response Genes Gene duplication is a major driving force of genome evolution and facilitates acquisition of novel gene functions  (Ohno 1970). Therefore, genes supporting unique characters of Porites, such as stress tolerance, may have been duplicated during evolution of the Porites lineage. To eliminate the potential impact of genome assembly and gene prediction errors, we considered HOGs for which gene numbers in both P. australiensis and P. lutea are larger than other coral or anthozoan genomes. We identified 31 HOGs specifically expanded in the Porites lineage (fig. 3A ). Among those, 25 HOGs exhibit similarities to proteins in the SwissProt protein database. The 31 expanded HOGs show significantly more Swiss-Prot protein database hits (83%, 257 out of 309 genes) than P.
Purple indicates Acropora-specific SC-HOGs that were differentially expressed. (B) Gene expression changes of SC-HOGs differentially expressed in both Porites and Acropora, but in which expression patterns were opposite. Putative gene names are based on the Uniprot/ Swissprot database. Pink shading denotes SC-HOG gene pairs that were significantly upregulated in Porites and downregulated in Acropora. Brown shading indicates SC-HOGs that were significantly downregulated in Porites and upregulated in Acropora. Gene expression changes compared with control conditions are shown in a colored heatmap. (C) Maximum likelihood analysis of anthozoan fluorescent protein (FP)-like genes using 215 aligned translated amino acids. Bootstrap values more than 80% are shown. Porites australiensis genes are shown with circles and Acropora digitifera genes are shown with triangles.
1. 19 (Li et al. 2009). Estimation of the haploid genome size using shotgun sequencing data was performed using GenomeScope  (Vurture et al. 2017 ) with a kmer length of 29 and max kmer coverage of 10,000. We assessed genome assembly completeness with BUSCO ver. 3. 0. 2 (Simao et al. 2015; Waterhouse et al. 2017)  using the Metazoa set (978 genes). To reconstruct the complete P. australiensis mitochondrial genome, we BLAST-searched raw Newbler assembled scaffolds using Porites mitochondrial genomes as queries and identified the best candidate sequence. Then the sequence was annotated using GeSeq  (Tillich et al. 2017).
In order to remove gene models that sometimes originate from different haplotypes, the predicted proteome was clustered using CDHIT (98% sequence identity)  (Li and Godzik 2006) , and proteins shorter than 30 amino acids were excluded from subsequent analyses. Predicted gene models were BLASTed against the Uniprot/ Swissprot (UniProt Consortium 2018) database and were analyzed with InterProScan 5 with e-value cutoff of 1e À5  (Jones et al. 2014).
Clustering of Orthologous Genes and Molecular Phylogenetic Analysis We used publicly available gene models of the two anemones, N. vectensis  (Putnam et al. 2007 ) and E. pallida  (Baumgarten et al. 2015) , two corallimorpharians, A. fenestrafer and Discosoma spp. (Wang et al. 2017) , and three scleractinians from the "robust" clade, S. pistillata  (Voolstra et al. 2017) , P. damicornis  (Cunning et al. 2018) , and O. faveolata  (Prada et al. 2016). Five Acropora corals, A. awi, A. cytherea, A. digitifera, A. tenuis  (Shinzato et al. 2021), and A. millepora (Ying et al. 2019 ), representing the "complex" clade, were also included in our analyses. For the A. millepora, S. pistillata, O. faveolata, and E. pallida genomes, we downloaded data from the NCBI RefSeq database. Then, using OrthoFinder version 2.
For MS and MS/MS, analyses were performed using an Ultimate 3000 Rapid Separation Liquid Chromatographic (RSLC) system (Thermo Fisher Scientific) online with a hybrid LTQ-Orbitrap-Velos mass spectrometer (Thermo Fisher Scientific). All technical details are provided in  Immel et al. (2016). Database searches were carried out using Mascot version 2. 4 and 2. 5 (MatrixScience, London, UK) on gene models of P. australiensis. The false discovery rate (FDR) was set to 0. 05. Proteins were treated as identified SOMPs and further analyzed when more than two unique peptides or more than ten total peptides were detected (supplementary table 5, Supplementary Material online). In order to find functional domains in SOMPs, amino acid sequences were analyzed using InterProScan 5. 3  (Jones et al. 2014).
Signal peptides were predicted with SignalP 4. 1  (Petersen et al. 2011). Transmembrane domains were assessed with TMHMM 2. 0 software  (Krogh et al. 2001). Theoretical molecular weights and isoelectric points of SOMP sequences without signal peptides were calculated using IPC 1. 0  (Kozlowski 2016). All programs were run using default settings and thresholds. Sequence similarities between SOMPs of P. australiensis and other corals, including A. digitifera  (Takeuchi et al. 2016 ), A. millepora (Ramos-Silva et al. 2013) , and S. pistillata  (Drake et al. 2013) , were evaluated using BLASTP with a threshold of e À5. We also BLASTPsearched all protein models encoded in the A. digitifera genome  (Shinzato et al. 2011 ) to find homologous gene candidates of P. australiensis SOMPs. A. digitifera protein-coding gene(s) significantly (cutoff e À5 ) similar to P.