dataesr/scientific-paragraphs-categorization huggingface dataset:
Upon inspection of figure  11 , it can be noted that the house of card type configuration of graphene oxide flakes from transmission electron microscopy (a), which are in the scale of a few micrometers is similar to layers of clay in soils, which are in the scale of a few metres. Following image treatment with Matlab (b), one can export the house of cards geometry in SimSonic and simulate the propagation of a seismic signal upon change of scale by a factor 10 6. The house of cards configuration in figure  10(a ) can be exploited to build an effective porous diffusion model for drug diffusion through a graphene oxide membrane as achieved in  [3]  using mathematical analogies with diffusion models in porous soils, reminiscent of asymptotic techniques used in thin-walled domains, such as acoustic metamaterials  [53, 54] , if one replaces propagating waves by evanescent pseudo-waves.
5 Hz. On the other hand, in panel (a) concrete masses do not match the fundamental mode of the bridge and thus do not prevent its swaying. Indeed, the Millenium bridge was closed down after walk of pedestrians happened to excite one of its fundamental eigenfrequencies  [60]. If we assume a time harmonic dependence e -iωt in (1. 3) and (1. 4), with ω the angular wave frequency (rad • s -1 ), a spectral analysis can be performed for so-called Floquet-Bloch waves (ν 1 , ν 2 ) of the form ν j (x 1 + d, x 2 ) = ν j (x 1 , x 2 ) exp (ikd), j = 1, 2 propagating in a bridge which can be considered as a periodic structure with periodicity d along x 1. A closed form representation of the Green's function corresponding to the upper deck of the bridge as in figure  13 (a) provides dispersion curves for flexural waves like in panel (c), which are computed here using the commercial finite element package COMSOL Multiphysics.
Acknowledgments R Aznavourian ,  S Guenneau  and  T M Puvirajesinghe  acknowledge the A* MIDEX project  (no  ANR-11-IDEX-0001-02 ) funded by the  Investissements d'Avenir French Government program , managed by the  French National Research Agency (ANR)  with  Aix Marseille Université (TMP ,  A_M-AAP-ID-14-15-140314-09. 45-GUENNEAU-PUVIRAJESINGHE-HLS_SAT ). S Guenneau also acknowledges European funding through  ERC   Starting Grant  ANAMORPHISM.
Related works on tropical Gröbner bases We refer to the book of  Maclagan and Sturmfels [MS15]  for an introduction to computational tropical algebraic geometry. The computation of tropical varieties over Q with trivial valuation is available in the Gfan package by Anders Jensen (see  [Gfan] ), by using standard Gröbner bases computations. Yet, for computation of tropical varieties over general fields, with non-trivial valuation, such techniques are not readily available. Then Chan and Maclagan have developed in  [CM13]  a way to extend the theory of Gröbner bases to take into account the valuation and allow tropical computations. Their theory of tropical Gröbner bases is effective and allows, with a suitable division algorithm, a Buchberger algorithm. Following their work, a Matrix-F5 algorithm has been proposed in  [V15].
Implementation and numerical results A toy implementation of our algorithms in Sagemath  [Sage]  is available on https://gist. github. com/TristanVaccon. Remark 7. 1. It is possible to apply Algorithm 1 to compute a tropical Gröbner basis of I given by F = (P 1 ,. , P s ) by performing complete computation succesively for (P 1 ), (P 1 , P 2 ), (P 1 , P 2 , P 3 ),. adding a polynomial at a time playing the part f 1 played in the rest of the article. As we only deal with homogeneous polynomials, it is also possible to do the global computation degree by degree, and at a given degree iteratively on the initial polynomials. By indexing accordingly the signatures, as in  [F02] , the algorithm can be adapted straightforwardly. This is what has been chosen in the implementation we have achieved. We have gathered some numerical results in the following array.
Biological small-angle X-ray scattering (SAXS) is an increasingly popular technique used to obtain nanoscale structural information on macromolecules in solution. However, radiation damage to the samples limits the amount of useful data that can be collected from a single sample. In contrast to the extensive analytical resources available for macromolecular crystallography (MX), there are relatively few tools to quantitate radiation damage for SAXS, some of which require a significant level of manual characterization, with the potential of leading to conflicting results from different studies. Here, computational tools have been developed to automate and standardize radiation damage analysis for SAXS data. RADDOSE-3D, a dose calculation software utility originally written for MX experiments, has been extended to account for the cylindrical geometry of the capillary tube, the liquid composition of the sample and the attenuation of the beam by the capillary material to allow doses to be calculated for many SAXS experiments.
The 2 statistic, which describes the global goodness-of-fit of a model  (Franke et al. , 2012) , and the SAXS Merge method, which employs Gaussian process regression  (Spill et al. , 2014) , have previously been used to determine the similarity of scattering profiles. The CorMap test  (Franke et al. , 2015)  is the most recent method developed to assess the similarity of frames. Its advantage is that it does not use the errors on the experimental intensities, which are generally incorrectly estimated due to inaccurate propagation through the data processing pipeline. For experiments by different researchers to be intercomparable, the progression of radiation damage is most usefully tracked as a function of the dose absorbed by the sample. RADDOSE-3D is a free and open source software program used to calculate the time-and space-resolved threedimensional distribution of the dose absorbed by a protein crystal in an MX experiment  (Zeldin et al.
, 2013a). However, there is no equivalent software available for SAXS. Radiation damage studies in SAXS thus currently require the experimenters to correctly parameterize the experiment and manually calculate a single estimate of the dose within the sample  (Hopkins & Thorne, 2016; Jeffries et al. , 2015; Meisburger et al. , 2013). Here, extensions to RADDOSE-3D are presented, which enable the convenient calculation of doses for SAXS experiments, reducing the burden of manually performing the calculation. The three-dimensional geometry of the experiment is also taken into account. Furthermore, a new Python library has been developed to provide visual analysis of the results of scattering curve similarity tests from applying the CorMap test. Using this, it was possible to define a simple metric for significant radiation damage onset.
Data collection Data collection was performed at the ESRF BioSAXS beamline BM29  (Blanchet et al. , 2015; Brennich et al. , 2016; Materlik et al. , 2015; Pernot et al. , 2013). The photon energy used throughout was 12. 5 keV and the photon flux was estimated from the beamline diode readings which were recorded for every frame using the conversion formula flux ¼ 5:72293 þ 2:72295 Â 10 15 Â d c ; ð1Þ where d c is the reading of the diode mounted within the backstop. The flux obtained using this formula was calibrated as described by  Owen et al. (2009) , here using an OSD1-0 photodiode purchased from Optoelectronics, which was a 500 mm-thick silicon diode with a 1 mm 2 active area. The data were recorded using a Pilatus 1M detector from Dectris. 15 ml of each sample was loaded into a 1. 8 mm external diameter quartz capillary (1.
7 mm internal diameter, thus the wall thickness is 50 mm) held at 20 C using the BioSAXS Sample Changer described by  Round et al. (2015). For every additive, data were collected at each of the concentrations stated in x2. 1, and each of these individual data collection runs was repeated three times (i. e. three datasets per radioprotectant per concentration). The exposure time for each frame was 1 s, and a total of 120 frames were collected for each repeat (i. e. 120 s total exposure for each dataset) with the sample kept static. After data collection on a sample, the capillary was washed with cleaning solution (2% Hellmanex, 10% ethanol and 88% distilled water), rinsed with distilled water and dried with dry air, a procedure also described by  Round et al. (2015). For each radioprotecant concentration, a single dataset was collected with only the buffer (no protein) and the radioprotectant, so that a suitable buffer correction (subtraction) could be applied during data analysis.
Data processing Azimuthal integration of diffraction frames was performed as described in the corresponding section (x3. 1) of  Brennich et al. (2016). A custom script was written in Python to average the frames from the datasets collected with only the buffer with each radioprotectant added. These averaged frames were then subtracted from the frames collected with both the buffer and protein sample. Finally, the frames were cropped at both the lowest and highest scattering angles using the same Python script. The cropped scattering angles were the same for all datasets, and the choice of angles was determined by visual inspection to remove the regions with a higher level of noise. 2. 4. Extending RADDOSE-3D for SAXS 2. 4. 1. Cylindrical sample geometry. In many SAXS experiments, liquid samples are contained in, or flowed through, a cylindrical capillary during the X-ray exposure, so it is necessary to model cylindrical sample shapes.
S2  of the supporting information). To calculate a full two-dimensional beam profile from these aperture scans, a computational rectangular grid was constructed with the edges of the measurement positions used as the boundaries of the grid. The flux at and beyond the grid boundaries was assumed to be zero. The diode measurements from the vertical aperture scans were placed in their corresponding positions on the grid and interpolation between these values was performed using the 'RectBivariateSpline' function in the SciPy package in the Python programming language  (Jones et al. , 2001). The same procedure was performed for the data in the horizontal direction. The interpolated two-dimensional beams were then averaged to obtain the final two-dimensional beam profile which was used in the RADDOSE-3D simulation (Fig.
Radiation damage onset using the CorMap test The program DATCMP, distributed as part of the ATSAS suite of programs for processing SAXS data  (Petoukhov et al. , 2012) , was used to perform the one-dimensional scatter curve similarity analysis. DATCMP implements the CorMap test for assessing frame similarity  (Franke et al. , 2015). This test performs a pairwise correlation between one-dimensional scattering curves derived from the diffraction frames, which involves taking the difference between the scattering curves. If the two curves are similar, and hence come from the same distribution, then the chance of observing a positive or negative value is 50%, which is the same chance as observing a head or tail when an unbiased coin is tossed. The Schilling distribution quantifies the likelihood of observing C number of heads/tails in a row, and this is extended to observing a given number of positive or negative values in the pairwise correlation map.
Furthermore, the visualization library developed for this work was able to highlight why DTT performed poorly, and show that performing all pairwise comparisons could result in more consistent frame-merging methods. Despite the extensions described above, the SAXS data collection model in RADDOSE-3D makes some implicit assumptions. For instance, with regard to the capillary, the atomic composition is assumed to be uniform throughout, and the thickness to be constant around the entire sample volume. The advantage of these assumptions is that the attenuation by  Heat map of all possible pairwise frame comparisons for the first repeat with 10 mM concentration DTT added to the GI sample. The y-axis represents the reference frame to which all other frames on the x-axis are compared. Blue: P(> C) = 1.
Acknowledgements We thank the  ESRF  for beam time under the auspices of the  Radiation Damage BAG  and the staff of beamline  BM29 ,  Martha Brennich  and  Petra Pernot , for their support. We gratefully acknowledge the  UK Engineering and Physical Sciences Research Council  for studentship funding in the  Systems Biology Programme of the University of Oxford Doctoral Training Centre (JBB  and  CSB , grant number  EP/ G03706X/1 ), and studentship funding from the  Wellcome Trust  (HMG, studentship number  075491/04 ). We also thank the referees for their insightful comments.
Over the last couple of years, IRSN has established an important experimental validation database using a set of 76 samples of radiochemical assay data and decay heat measurements  [2]  for a wide variety of reactor and fuel types (PWR, VVER, MOX, UO 2 , UO 2 -Gd 2 O 3 fuel). The results of the calculations are definetely influenced by the underlying nuclear data library  [3]. We will further illustrate this aspect in this paper by comparing the results for the decay heat measurements from the VESTA experimental validation database using four nuclear data libraries, namely JEFF-3. 1, JEFF3. 2, JEFF-3. 3T1 and ENDF/B-VII. 0. The experiments that have been selected for this work are PWR assembly decay heat measurements performed by the Swedish Central Interim Storage Facility (CLAB) located in Oskarshamm (Sweden)  [4].
Overview of experimental data The CLAB measurements were performed on a total of 39 BWR assemblies and 34 PWR assemblies from various reactors in Sweden. The PWR assembly measurements come from the Ringhals 2 unit (23 measurements for 18 15 × 15 assemblies) and the Ringhals 3 unit ND2016 (20 measurements for 16 17 × 17 assemblies). All assemblies are UO 2 assemblies covering a 235 U enrichment range of 2. 1 to 3. 4%, burn up range of 20 to 51 MWd•kgHM -1 for cooling times from 13 to 23 years. These CLAB measurements were performed using a pool calorimeter located underwater in the spent fuel storage pool. It is 4. 6 m long and consists of two concentric carbon steel pipes separated by urethane foam insulation to reduce heat loss to the pool. A so called static mode is the measurement method in which the water temperature increase in the vessel is measured.
Nuclear data libraries All nuclear data files used by VESTA (and the underlying transport codes such as MCNP) have been produced using the NJOY nuclear data processing system  [6]  through the GAIA software  [7]. GAIA is a computer software developed at IRSN to minimise the effort on the generation of nuclear data libraries using NJOY and provide additional quality assurance. The library files produced consist of ACE files (which will only be used by MCNP or MCNPX) and PENDF files (which will only be used by VESTA). GAIA not only automates the entire NJOY processing path, but it will also perform a number of additional operations to verify the produced files and add any missing data required for the applications in question. The software generates a tailormade NJOY input file for each nuclide without intervention of the user using data found in the nuclide's ENDF file (such as the initial temperature of the ENDF file, whether or not the nuclide is fissile, whether or not it has unresolved resonances, etc.
). When the library files have been generated, GAIA will also process the output from NJOY and extract all messages and warnings from NJOY that are deemed important. A print out including a short explanation of the messages in question is then printed to the listing (the user can, if needed, override this setting to extract all messages and errors regardless of their importance). The most important test provided by the software is the verification of the unresolved resonance probability tables. GAIA will check for the presence of any negative cross section values in the tables. If such negative values are detected, GAIA will rerun NJOY but omit the generation of the unresolved resonance probability tables (no selfshielding calculations using probability tables in the unresolved resonance range can thus be performed).
For 4-kb and 5-kb mate-pair libraries, SOLiD adaptors were ligated and sequenced on a SOLiD 5500xl Sequencer. Library construction for PacBio sequencing was carried out using the manufacturer's protocols. Genomic DNA was sheared using a Megaruptor, followed by damage repair, end repair, hairpin ligation, and size selection using BluePippin. After primer annealing and polymerase binding, the DNA templates were sequenced on a PacBio RSII sequencer using P4/C2 chemistry and 120-min video time and later using P6/C4 chemistry and 360-min movie time. Contigs were assembled from 454 sequencing data using Newbler with large genome parameter settings. The accuracy of the contigs was improved using the Pilon software with Illumina paired-end sequences. Scaffolding was done using the Illumina and SOLiD mate-pair libraries and SSPACE 2 in a hierarchical manner; first the 2 kb library was mapped to the contigs, then contigs were scaffolded accordingly.
3  and 4 ). A separate PacBio assembly was carried out for the mitochondrial genome using a modified Newbler assembler (Supplementary Note and Supplementary Figs. 5  and 6 ). Linkage mapping. For linkage mapping, low-coverage whole-genome sequencing data from 63 individuals were mapped to the genome using BWA-mem, and genotype posterior probabilities were calculated by the Lep-MAP3 pipeline using the output from samtools mpileup. The relatedness of individuals was checked using the IBD module of Lep-MAP3, and then the parental genotypes for each potential marker were estimated, providing the final data set for linkage mapping. Markers segregating identically on each contig were joined and collapsed into linkage groups separately for markers informative only paternally, maternally, or both.
During the scaffold placement, super-scaffolds showing signs of possible chimeric assembly were split from the regions between markers and placed in their respective linkage groups. Assembly validation. The quality of the assembly was monitored during all stages and using several independent validation methods. Contig assembly was first tested using Scarpa software and the 2-kb Illumina mate-pair library and then validated by mapping a set of high-quality ESTs to the contigs using Exonerate. The completeness of the scaffold-level assembly was tested by mapping the unassembled Illumina reads against the scaffolds and by mapping Trinity de novo assembled RNA-sequencing transcripts to the assembly with PASA, as well as through CEGMA. An independent validation of the scaffold-level assembly quality was gap-filling with long Pacbio reads.
Gene annotation. A modular gene annotation framework was established to estimate gene models by combining evidence from ab initio gene predictors based on Hidden Markov Models, spliced transcript evidence from RNAseq and EST data, protein evidence from orthologous proteins obtained from closely related and model plant species, and manually curated gene sequences. Gene prediction was carried out in two phases. The first phase (Supplementary Fig. 9 ) involved generation of an initial set of automated predictions, followed by manual curation of genes from select gene families to provide verified gene models for the second phase of predictions. RNA-seq transcripts generated using Trinity were splice aligned against the unmasked birch genome using PASA in a strand-specific manner to generate long ORFs.
Augustus, SNAP and GlimmerHMM were run on the masked birch genome using the optimized parameters, whereas GeneMark-ES was executed on the unmasked genome. Orthologous protein sequences from A. thaliana, Populus trichocarpa, and Prunus persica were splice-aligned against the unmasked birch genome using exonerate to obtain spliced protein evidence. EVidence Modeler was used to generate a single high-confidence gene model set, using ab initio gene predictions, spliced protein alignments, and spliced transcript alignments as inputs. Finally, UTR addition was carried out by running PASA with the RNA-seq and EST data. Manual annotation was carried out using the WebApollo software (see Supplementary Table  6 ) for the list of manually annotated genes. For the second phase of the training, ORF generation using PASA was followed by filtering for complete ORFs and combining with core eukaryotic genes from CEGMA plus manually annotated genes to generate a nonredundant training set for the gene predictors (Supplementary Fig.
10 ). Gene predictors were trained as in the first phase and by passing the new parameters. Finally, UTR addition using PASA was re-executed. The manually curated genes and automated annotations were compared for overlaps using the overlap software. Annotations not having any overlap with the manual annotations were extracted and merged with the manually curated genes, thereby creating a single nonredundant set of merged annotations (Supplementary Table  6 ). Protein functional analysis. Protein functional analysis was carried out using Interproscan. Descriptions for the gene models were generated using AHRD with a custom database of A. thaliana and SWISS-PROT proteins. Finally, gene model predictions of 200 conserved single-copy genes were verified manually in CoGe by comparing orthologous birch gene models against A.
Population data analysis. A phylogeny for nine representatives of different birch species was estimated using SNPs called with GATK and hard filtering criteria. Only SNPs within 2 kb from coding regions and at neutrally evolving sites within coding regions were used. Phylogeny was estimated using SNPhylo, with SNPs having minor allele frequency >0. 1. For ancestral state estimation, Illumina resequencing reads mapped against the birch reference genome were used to call consensus sequences using a combination of SAMtools, bcftools, and vcfutils. The consensus FASTA files were read into R, and the ancestral states estimated using the Phangorn package with maximum likelihood estimation and the GTR model of molecular evolution, where edge lengths were estimated separately for each contig. Marginal reconstruction of the ancestral character states was carried out using a maximum a posteriori estimate.
ANGSD was run to obtain the site frequency spectrum, heterozygosity (Supplementary Fig. 17 ) and sitewise estimates of allele frequency statistics following the protocols recommended by the software authors. The analysis was restricted to the set of 60 non-admixed B. individuals with accurate information on their sampling origin. A custom R script was developed to calculate population genetic descriptive statistics for each gene (Supplementary Table  17 ). To filter out loci with low coverage and low numbers of called SNPs, only regions with >50 called nucleotides were used for computing the gene-wise statistics. The site frequency spectrum from ANGSD was used to estimate the population history with Stairway plots using 200 bootstrap iterations, and a range of 0. 7, 1. 0, and 2. 0 × 10 -9 as the mutation rate, and 10, 20 and 40 years as the generation time (Supplementary Note and Supplementary Fig.
20 ). Selective sweeps were estimated with SweepFinder2. To prepare the input files for Sweepfinder, ANGSD was used to call allele frequencies for each position, given the ancestral states estimated earlier. Sweepfinder2 was run for each contig having mapping data from all individuals, with a grid size of 200 bp. For processing the composite likelihood ratio (CLR) scores into putative sweep regions, a custom R script was developed to carry out several filtering steps. First, the first three CLR scores in contig ends were set to 0. Then, to smoothe the fluctuations of CLR scores in neighboring sites, the scores were filtered with median filtering using a window size of 5. Then, CLR scores were merged into sweep regions if the neighboring scores exceeded the top 1% of CLR scores (CLR > 26). Regions where only one 200-bp site exceeded this threshold were removed from the analysis.