dataesr/scientific-paragraphs-categorization huggingface dataset:
Using the step-index MMF geometry as an example, it was shown that the GQ approach scales linearly or at most quadratically (as opposed with the third or fourth power) with the number of guided modes. Moreover, the method easily permits to take into account mode profile dispersion. The GQ method was shown to be superior to methods based on evaluating the nonlinear polarization by summing mode overlap integrals whenever more than six guided modes are involved, and when mode profile dispersion is important. In 2018, Wright et al. introduced a parallel numerical solution method for the system of MM-GNLSEs  15. This numerical solver is freely available for download from the internet, implemented in MATLAB, and includes a number of multimode fiber analysis tools. It features a significant parallel computing speed-up on modern graphical processing units, translating to orders-of-magnitude speed-up over the conventionally-used split-step Fourier method.
ACKNOWLEDGMENTS This work was supported by the  European Research Council (ERC)  under the European Union's  Horizon 2020 research and innovation programme (Advanced research  grant No. 740355 ); the  Russian Ministry of Science and Education  (Grant  14. Y26. 31. 0017 ); the  Institut Universitaire de France ; the  french Investissements d'Avenir program , project  ISITE-BFC  (contract  ANR-15-IDEX-0003 ); XLIM has received funding from  Agence Nationale de la Recherche (ANR)  ( TRAFIC  project :  ANR-18-CE080016-01 ), and from  CILAS Company (ArianeGroup)  by means of the shared X-LAS laboratory.
3(b) and 3(c) corresponding to the samples annealed at 500 ○ C and 600 ○ C. These rings were not pointed out in order to simplify the figures. The HZO spots are very fine and less intense due to the layer thickness and grain width. The monoclinic and orthorhombic phases of HZO were indicated in SAED and FFT patterns as a result of the measurements; the distance between the shown spot and the central spot was measured and the corresponding interplanar distance calculated. In order to determine the correct phase and space group of the material, the obtained result is compared with the database. The main difference between the monoclinic and orthorhombic phase is made by the m(11-1) (with d = 3. 14 Å) and o(111) (with d = 2. 96 Å) lines. The difference between these lines (0. 18 Å) can be easily evidenced in SAED and FFT patterns and confusion between these phases cannot be made.
The seismic facies (SF) identified are summarized in Figure  4. We interpret the morphologic elements found in the 3D data and compare these to morphologies observed in present day river systems  (Posamentier, 2000). To accomplish the later, we utilized our second primary data set, satellite images and digital elevation models (DEMs) from the present day surface of the Amazonian Basin. We have used public satellite images and airborne radar (https://uavsar. jpl. nasa. gov), as well as digital elevation models from the NASA Shuttle Radar Topography Mission (SRTM) (https://www2. jpl. nasa. gov/srtm/). Geomorphological features such as channels (Figure  5 ) have been quantified following the scheme developed by previous workers on quantitative seismic geomorphology of fluvial features (e. g. Miall 2002; Wood, 2007; Ethridge and Schumm, 2007).
ACKNOWLEDGEMENTS GC would like to thank  PeruPetro  for allowing this work being published. Financial support from  Institut-Carnot IsiFor  ( Agence National de la Recherche ) is appreciated. Thanks to  IHS-Kingdom, dGB Earth Sciences OpendTect and GeoTeric , for their academic software donations and support. Palaeocurrent diagram were produced using freeware Rose 2. 1. 0(Todd Thompson Software). Many thanks to  A. Hartley  ( University of Aberdeen ) and  S. Leleu  ( ENSEGID -IPBordeaux ) for earlier discussion and perspectives on fluvial sedimentary systems. Thanks to C.
This is the case for negative interactions such as exploitative competition (e. g. for nutrient resources), or for positive interactions such as cross-feeding or syntrophy  (Coyte and Rakoff-Nahoum, 2019 ) that we will refer to with the generic term of cooperation. In order to unravel such interactions between species, it is necessary to go beyond functional annotation of individual genomes and connect metagenomic data to metabolic modelling. The main challenges impeding mathematical and computational analysis and simulation of metabolism in microbiomes are the scale of metagenomic datasets and the incompleteness of their data. Genome-scale metabolic networks (GSMNs) integrate all the expected metabolic reactions of an organism. Thiele and Palsson (2010) defined a precise protocol for their reconstruction, associating the use of automatic methods and thorough curation based on expertise, literature and mathematical analyses.
There now exist a variety of GSMN reconstruction implementations: all-in-one platforms such as Pathway Tools  (Karp et al. , 2016) , CarveMe  (Machado et al. , 2018)  or KBase that provides narratives from metagenomic datasets analysis up to GSMN reconstruction with ModelSEED  (Henry et al. , 2010a; Seaver et al. , 2020). In addition, a variety of toolboxes  (Aite et al. , 2018; Wang et al. , 2018; Schellenberger et al. , 2011) , or individual tools perform targeted refinements and analyses on GSMNs  (Prigent et al. , 2017; Thiele et al. , 2014; Vitkin and Shlomi, 2012). Reconstructed GSMNs are a resource to analyse the metabolic complementarity between species, which can be seen as a representation of the putative cooperation within communities  (Opatovsky et al. , 2018). SMETANA (Zelezniak et al.
, 2020). In addition, current methods require GSMNs of high-quality in order to produce accurate mathematical predictions and quantitative simulations. Reaching this level of quality entails manual modifications to the models using human expertise, which is not feasible at a large scale in metagenomics. Automatic reconstruction of GSMNs scales to metagenomic datasets, but it comes with the cost of possible missing reactions and inacurate stoichiometry that impede the use of constraint-based modelling  (Bernstein et al. , 2019). Therefore, development of tools tailored to the analysis of large communities is needed. Here we describe Metage2Metabo (M2M), a software system for the characterisation of metabolic complementarity starting from annotated individual genomes. M2M capitalises on the parallel reconstruction of GSMNs and a relevant metabolic modelling formalism to scale to large microbiotas.
It comprises a pipeline for the individual and collective analysis of GSMNs and the identification of communities and key species ensuring the producibility of metabolic compounds of interest. M2M automates the systematic reconstruction of GSMNs using Pathway Tools or relies on GSMNs provided by the user. The software system uses the algorithm of network expansion  (Ebenhöh et al. , 2004)  to capture the set of producible metabolites in a GSMN. This choice answers the needs for stoichiometry inaccuracy handling and the robustness of the algorithm was demonstrated by the stability of the set of reachable metabolites despite missing reactions  (Handorf et al. , 2005; Kruse and Ebenhöh, 2008). Consequently, M2M scales metabolic modelling to metagenomics and large collections of (metagenome-assembled) genomes.
Cooperation potential Metabolic cooperation enables the activation of more reactions in GSMNs than what can be expected when networks are considered in isolation. By taking into account the complementarity between GSMNs in each dataset, it is possible to capture the putative benefit of metabolic cooperation on the diversity of producible metabolites. Running m2m cscope predicted 156 new metabolites as producible by the gut collection of GSMNs if cooperation is allowed. We analysed the composition of the 156 newly producible metabolites for the gut dataset using the ontology provided for metabolic compounds in the MetaCyc database. 80. 1% of them could be grouped into 6 categories: amino acids and derivatives (5 metabolites), aromatic compounds (11), carboxy acids (14), coenzyme A (CoA) derivatives (10), lipids (28), sugar derivatives (58).
Comparison of M2M applications to MAGs and draft reference genomes In order to compare the effect of genome quality on M2M predictions, we performed analyses on a collection of 913 MAGs binned from cow rumen metagenomes  (Stewart et al. , 2018). These MAGs were predicted to be > 80% complete and < 10% contaminated. The complete M2M workflow ran in 81 minutes on a cluster with 72 CPUs and 144 Gb of memory. Results of the GSMN reconstruction are presented in Table  2. GSMNs of the cow rumen MAGs dataset consisted in average of 1,155 (± 199) reactions and 1,422 (± 212) metabolites. 73. 8% of the reactions could be associated to genes. We compared these numbers with those obtained for the collection of draft reference genomes from the human gut microbiota of the previous subsection. Appendix 1 displays the distributions of the numbers of reactions, pathways, metabolites and genes for both datasets.
Altogether, these distributions are very similar for both datasets although the initial number of genes in the whole genomes varies a lot (Appendix 1 g), a difference that is expected between MAGs and reference genomes. Interestingly, the average number of reactions per GSMN is slightly higher for the MAGs of the rumen than for the reference genomes of the gut. This could be explained by the higher phylogenetic diversity observed in MAGs compared to culturable bacteria, or a higher potential for contaminated genomes, or a difference in average genome size. However, the smallest GSMN size is observed in the rumen (340 reactions vs 617 for the smallest GSMN of the gut dataset). The similarity in the characteristics displayed by both datasets suggests a level of quality of the rumen MAGs close to the one of the gut reference genomes regarding the genes associated to metabolism.
This indicates that each equivalent minimal community for these compounds would consist in the same 20 GSMNs, associated to 24 others selected within the 107 alternative species, thereby reaching a total of 44 GSMNs. Results are displayed in Supplementary File 1 (Table  4 ), together with those of an equivalent analysis (default settings of M2M with cooperation potential as targets) for the gut reference genomes. M2M robustly identifies key species, even with degraded genomes A recurring concern in metagenomics is the completeness of reconstructed MAGs due to the possible loss of functions during the genome assembly process  (Parks et al. , 2015). Misidentified genes can impede GSMN reconstruction and consequently the contents of the scopes and cooperation potential. To assess the impact of MAG completeness, we altered the rumen MAGs dataset by randomly removing genes.
We created four altered datasets by removing: i) 2% of genes in all genomes, ii) 5% of genes in 80% of the genomes, iii) 5% of genes in all genomes and iv) 10% of genes in 70% of the genomes. We analysed these degraded datasets with the same M2M bioinformatic workflow, using a community selection with the metabolic cooperation potential as a community objective. The metabolic cooperation potential, the global set of reachable metabolites in the community and the key species (essential and alternative symbionts) were computed and compared between the four altered datasets and the original one. Results are depicted in Figure  2. The global set of producible metabolites in the community and the contents of the metabolic cooperation potential remain stable between datasets. In both we observe a single subset of 36 metabolites that is only reachable by the original dataset.
It consists in a variety of metabolites mostly from secondary metabolism. Discrepancies appear between datasets when studying key species with respect to the original dataset, with an overall stability of the datasets to 2% degradation and to 5% degradation in 80% of genomes. The main discrepancies are observed for alternative symbionts with an additional small set of symbionts that are selected in altered datasets but not in the original one. For the most degraded genomes (10% degradation in 70% of MAGs), key species composition is altered compared to original genomes: a set of 31 key species is no longer identified. However, producibility analyses and community selections performed by M2M are stable to small genome degradations of up to 2% of random gene loss in all genomes or 5% in 80% of the genomes.
, 2016)  mapped to OTUs at the species level as described in Diener et al. (2020). 778 MGS were retrieved from the dataset and used to build GSMNs (Table  2 ), whereas when using the mapping of OTUs to existing curated GSMNs, only 289 GSMNs were used. The distribution of phyla in the two cases is illustrated in Appendix 2 (Figure  2 ). We first focus on the results obtained with the MGS-based protocol. In average, communities were composed of 108 (± 29) GSMNs. The median community size was 111 (Supplementary File 1 -Table  20 ). Diversity and richness analyses are available in Appendix 2 The effect of the cohort (MHD, SWE) was strong in the analyses performed with MGS, impacting community sizes, size and composition (in families of metabolites) of the set of metabolites producible by the community, as well as the cooperation potential.
Results are depicted in Appendix 2(Figure  3 ). A classification experiment using the composition of the community scope or the composition of the cooperation potential can efficiently determine the cohort of the samples (Appendix 2 figure 3 panels c and g). Similar differences between cohorts were also observed in  (Diener et al. , 2020)  and in  (Forslund et al. , 2015)  based on functional or taxonomic annotations, likely driven by the different sampling protocols used in the two datasets  (Forslund et al. , 2015). This indicates that the commonly observed cohort effect in metagenomics is also reflected at the metabolic modelling scale, which could be explained by the observed GSMN redundancies shared within phyla.
The putative producibility of some families of metabolites (alcohols, esters, carbohydrates, amino-acids, acids) in the community scopes also differed between metabolic communities derived from diseased and healthy individuals (anova p < 0. 05), whereas other metabolic families like lipids remained stable between cohorts. This can be at least partly explained by the number of metabolites matching these categories according to the Metacyc database (e. g. 191 metabolites tagged "All-carbohydrates" in average in community scopes, and only 10 tagged "Lipids" as the remaining of them are scattered in other categories). No clear difference appears between the three statuses (Figure  4  e) in terms of community scope composition. Regarding the cooperation potential, two groups tend to appear, separated due to diverse secondary metabolites, but they are not driven by the disease status of the individual (Figure  4  f).
Focus on short chain fatty acids production Given the importance of short chain fatty acids (SCFAs) in human health  (Baxter et al. , 2019) , we focused on the production of butyrate, propionate and acetate in communities for each sample of the dataset. A small number of MGS (N = 11) GSMNs were predicted to be able to individually produce butyrate from the nutrients. All 778 MGS were capable to ferment acetate and most of them propionate (N = 515). The putative production of butyrate in the 170 communities when allowing cooperation between GSMNs was systematic. As expected  (Rivière et al. , 2016) , a majority (54. 1%) of the unique MGS predicted as possible butyrate producers in communities (GSMNs comprising a reaction producing butyrate that could be activated in a community) belonged to the Firmicutes phylum.
Discussion Metage2Metabo is a new software system for the functional analysis of metagenomic datasets at the metabolic level. M2M can be used as an all-in-one pipeline or as independent steps to depict an initial picture of metabolic complementarity within a community. controlling the communities for a complex alga, the inoculated algae exhibited a significant increase in growth and metabolic profiles that at least partially aligned with the predictions, demonstrating the versatility in application fields of our methods. There are limitations associated to the software solution described in this paper. One challenge in applying our tool is to accurately estimate the nutrients available in a given environment (seeds), on which the computation of network expansion relies. The algorithm provides a snapshot of producible metabolites, representing the sub-network that can be activated under given nutritional conditions.
Conclusion Metage2Metabo (M2M) allows metabolic modelling of large-scale communities, based on reference genomes or de novo constructed MAGs, inferring metabolic complementarity found within communities. M2M is a flexible framework that automates GSMN reconstruction, individually and collectively analyse GSMNs, and performs community selection for targeted functions. The large combinatorics of minimal communities due to functional redundancy in microbiotas is addressed by providing key species associated to metabolic end-products. This could allow targeting specific members of the community through pro-or prebiotics, to model the metabolites the human host will be exposed to. We validated the flexibility of the software and the range of analyses it can offer with several datasets, corresponding to multiple use-cases in the microbiome field.
Material and Methods Metage2Metabo (M2M) is a Python package. It can be used on a workstation or on a cluster using Docker or Singularity. M2M's source code is available on github. com/AuReMe/metage2metabo, and the package is available though the Python Package Index at pypi. org/project/Metage2Metabo/. A detailed documentation is available on metage2metabo. readthedocs. io. We detail below the characteristics of M2M through a description of its main steps.
Individual metabolic capabilities The m2m iscope command predicts the set of reachable metabolites for each GSMN using the network expansion algorithm and the given nutrients as seeds. The content of each scope is exported to a json file. A summary is also provided to the user comprising the intersection (metabolites reachable by all GSMNs) and the union of all scopes, as well as the average size of the scopes, the minimal size and the maximal size of all. This command extends core functions implemented in Menetools 2 , a Python package that was previously used in Aite et al. (2018).
M2M was run using version 23. 0 of Pathway Tools. The cow rumen dataset of MAGs was not functionally annotated. Therefore, as a preliminary step of analysis, we annotated the genomic contigs using Prokka (v. 1. 13. 4)  (Seemann, 2014). M2M was run using version 23. 0 of Pathway Tools. The nutritional environment for modelling experiments consisted in basic nutrients: 26 metabolites including inorganic compounds, carbon dioxide, glucose and cellobiose and a small number of currency metabolites (Supplementary File 1 -Table  2 ). The rumen MAGs were artificially degraded to assess the robustness of M2M with respect to incomplete MAGs. This was done by randomly removing genes in all or a fraction of genomes. Four degradation scenarios were tested: removal of 2% of genes in all MAGs, removal of 5% of genes in 80% of the genomes, removal of 5% of genes in all genomes and removal of 10% of genes in 70% of the genomes.
Shotgun metagenomic analysis of individuals Metagenomic shotgun data from samples previously studied in Diener et al. (2020)  from 186 Danish and Swedish individuals  (Forslund et al. , 2015)  were used in this paper. Genomes were de novo reconstructed from the dataset using the MATAFILER pipeline described in Hildebrand et al. (2019). Briefly, metagenomic samples were quality-filtered using sdm  (Hildebrand et al. , 2014) , assembled using MEGAHIT  (Li et al. , 2015) , genes were predicted using Prodigal  (Hyatt et al. , 2010) , and a non-redundant gene catalogue was constructed across all samples using MMseqs2 (Steinegger and Söding, 2017). MAGs were predicted from metagenomic assemblies using MetaBAT2  (Kang et al. , 2019)  and dereplicated into species level metagenomic species (MGS), using a combination of shared genes among MetaBAT2 bins, canopy clustering  (Nielsen et al.
, 2014)  and custom R scripts  (Hildebrand et al. , 2019). Abundance of MGS was estimated across samples by using the average coverage of 40 conserved, single copy marker genes associated to each MGS  (Mende et al. , 2013). This abundance matrix was further populated with specI species from the proGenomes database  (Mende et al. , 2019) , that were not represented by MGS and are high quality genomes from cultured bacteria. This pipeline is described in further detail in Hildebrand et al. (2019). Samples for which the global estimated abundance of MGS was lower than 1,000 in accumulated coverage of all species were removed. This corresponds to a low number of reads passing the upstream quality checks for these samples (< 9. 10e6). 170 samples were kept for analysis. The initial bacterial community of each sample was determined using the estimated abundance matrix provided by the MATAFILER pipeline, following a boolean rule of presence/absence of MGS and specI species in samples.
Genomes consisted in MGS obtained with MATAFILER as well as SpecI genomes from the Progenomes database  (Mende et al. , 2019)  that were identified in the samples. For the latter case, we downloaded the genes and proteins of the corresponding representative genome from the database (SpecI v3). Functional annotation of genes from both specI genomes and MGS core genomes was performed using EggNOG-mapper v2. 0. 0  (Huerta-Cepas et al. , 2017)  based on eggNOG orthology data  (Huerta-Cepas et al. , 2019). Sequence searches were performed using Diamond v0. 9. 24. 125 (Buchfink et al. , 2014). Treatment of EggNOG-mapper annotation and creation of M2M Genbank inputs was done with the package Emapper2gbk 6  that we developed for the project. Seeds describing the nutritional environment were compounds of the western diet as presented in the study by Diener et al.
(2020). These metabolites were translated into identifiers from the Metacyc database  (Caspi et al. , 2019) , to which were added a small number of currency metabolites. The seeds are available on the Github repository of M2M. M2M was run for each sample and community selection was performed with different sets of targets (short-chain fatty acids, cooperation potential in each community). The cohort and disease status of each sample was known, enabling the comparison of scopes and cooperation potentials contents between statuses. M2M was also run using the approach presented in MICOM  (Diener et al. , 2020)  building sample communities, as presented in the paper and associated data repository, through the attribution of curated GSMN  (Magnúsdóttir et al. , 2016)  to operational taxonomic units (OTUs) identified in samples.
We reused the mapping at species-level provided in the MICOM paper to build the communities. Downstream analyses were performed in R (Team, 2017) and Python. Figures were produced using the package ggplot2  (Wickham, 2009)  and diversity measures were computed with the vegan R package (v2. 5-6). Classifications of disease statuses or cohorts using sets of predicted producible  metabolites were made using the Python package Scikit-learn (v0. 23. 1)  (Pedregosa et al. , 2011). Briefly, redundancy between features were removed with a Multidimensional scaling (MDS), Support Vector Machine (SVM) classifications with Stratified K-Folds cross-validations were performed using the MDS results. Finally, receiver operating characteristic curve (ROC-AUC) were computed and visualised with tools from the package.