dataesr/scientific-paragraphs-categorization huggingface dataset:
| Genetic assignment of the trees phenotyped for SI group and assessment of genetic diversity To determine how our sampling represented the genetic diversity and the geographic structure of the Mediterranean olive tree, SSR alleles were scored in a single analysis (Tables  S1  and S5 ) and combined with previous data obtained from the complete OWGB collection  (El Bakkali et al. , 2013). The number of alleles per locus (Na), the observed (Ho) heterozygosity and expected (He) heterozygosity  (Nei, 1987)  were estimated using the Excel Microsatellite Toolkit v3. 1  (Park, 2001). Principal coordinate analysis (PCoA), implemented in the DARWIN v. 5. 0. 137 program  (Perrier, Flori, & Bonnot, 2003) , was carried out using a simple matching coefficient. 2007) ). For each selected K value, each accession was assigned to its respective cluster with a posterior membership coefficient (Q > 0.
8). We tested whether the allelic diversity observed in the 89 genotypes representing a subsample of the core collection was significantly lower than that of the overall OWGB collection using a Mann-Whitney U-test (p-value >. 01 one-tailed test) after standardization of the dataset using the rarefaction method according to ADZE  (Szpiech, Jakobsson, & Rosenberg, 2008). F M Oit26 G1 Oit28 G2 Oit26 G1 Oit28 G2 (a) (b) (c) (d) | 873 SAUMITA-SAPSADE DEI Sl.
ACKNOWLEDGEMENTS We warmly thank  Drs. Vincent Castric ,  Isabelle De Cauwer , and  Lynda Delph  for scientific discussions and helpful comments on the manuscript. We thank  Sylvia Lochon-Menseau  for collecting pollen from the  French germplasm collection in Porquerolles Island , and  Sylvain Santoni ,  Pierre Mournet , and  Ronan Rivallan  for their technical support of molecular analysis in genotyping platform (UMR AGAP, Montpellier).
Funding information This research was supported by the  Project OLEA -Genomics and Breeding of Olive , funded by  MiPAAF, Italy , D. M. 27011/7643/10 , by the Project " BeFOre -Bioresources for Oliviculture ," 2015-2019,  H2020-MSCA-RISE-Marie Skłodowska-Curie Research and Innovation Staff Exchange , Grant Agreement N. 645595, by the  French National Research Agency  through the project " TRANS"  ( ANR-11-BSV7-013-03 ), by  French-Moroccan scientific cooperation PRAD   14-03 , and by  Agropolis Fondation "OliveMed "  N° 1202-066  through the  "Investissements d'avenir" / Labex Agro   ANR-10-Labex-0001-01. , managed by  French National Research Agency.
Context of this work. All the work described in this paper was done using the Coq proof assistant  [19]. This system provides a library describing the basic definition of real analysis, known as the standard Coq library for reals, where the existence of the type of real numbers as an ordered, archimedian, and complete field with decidable comparison is assumed. This choice of foundation makes that mathematics based on this library is inherently classical, and real numbers are abstract values which cannot be exploited in the programming language that comes in Coq's type theory. The standard Coq library for reals provides notions like convergent sequences, series, power series, integrals, and derivatives. In particular, the sine and cosine functions are defined as power series, π is defined as twice the first positive root of the cosine function, and the library provides a first approximation of π 2 as being between 7 8 and 7  4.
Note that this is a partial correctness statement. A program that always returns None also satisfies this statement. If we look at the actual program, it is clear that one can precompute a p that fulfills the first two tests, the equality test is another story. A long sequence of 0 (or F) may require a very high precision. This program is executable but almost useless since it is based on a Peano representation of the natural numbers. Our next step was to derive an equivalent program using a more efficient representation of natural numbers, provided by the type BigN  [24]. This code also receives some optimizations to implement faster operations of multiplications and divisions by powers of 2 and fast modular exponentiations. Computing within Coq that 2 is the millionth decimal in hexadecimal of π with a precision of 28 bits (27 are required for the first two tests and 28 for the equality test) takes less than 2 minutes.
In practice, this does not provide all the tools we need, because we actually want to restrict the concept of uniform convergence to subsets of the whole type. In this case the structure of UniformSpace is still appropriate, but the concept of NormedModule is not, because two functions that differ outside the considered subset may have distance 0 when only considering their values inside the subset. The alternative is provided by a treatment of uniform convergence that was developed in Coq's standard library of real numbers at the end of the 1990's, with a notion denoted CVU f g c r, where f is a sequence of functions from R to R, g is a function from R to R, c is a number in R and r is a positive real number. The meaning is that the sequence of function f converges uniformly towards g inside the ball centered in c of radius r.
Given a function like x → 1/ (x 2 + a 2 )(x 2 + b 2 ), the Coquelicot library provides automatic tools (mainly a tactic called auto derive) to show that this function is differentiable under conditions that are explicitly computed. For this to work, the tool needs to rely on a database of facts concerning all functions involved. In this case, the database must of course contain facts about exponentiation, square roots, and the inverse function. As a result, the tactic auto derive produces conditions, expressing that (x 2 + a 2 )(x 2 + b 2 ) must be positive and the whole square root expression must be non zero. The tactic auto derive is used more than 40 times in our development, mostly because there is no automatic tool to show the continuity of functions and we rely on a theorem that states that any differentiable function is continuous, so that we often prove derivability only to prove continuity.
When proving that the functions a n and b n are differentiable, we need to rely on a more elementary proof tool, called auto derive fun. When given a function to derive, which contains functions that are not known in the database, it builds an extra hypothesis, which says that the whole expression is differentiable as soon as the unknown functions are differentiable. This is especially useful in this case, because the proof that b n is differentiable is done recursively, so that there is no pre-existing theorem stating that a n and b n are differentiable when studying the derivative of b n+1. For instance, we can call the following tactic: Another place where automation provides valuable help is when we wish to find good approximations or bounds for values. The interval tactic  [34]  works on goals consisting of such comparisons and solves them right away, as long as it knows about all the functions involved.
Compute (Z. sqrt (2 * (2 ^29) ^2)). = 759250124%Z : Z This approach of computing integer values for numerators of rational numbers with a fixed denominator is the one we are going to exploit to compute the first million digits of π, using three advantages provided by the Coq system: 1. The Coq system provides an implementation of big integers, which can withstand computations of the order of 10 10 12. 2. The big integers library already contains an efficient implementation of integer square roots. 3. The Coq system provides a computation methodology where code is compiled into OCaml and then into binary format for fast computation.
This evaluation strategy relies on compiling the executed code in OCaml and then on relying on the most efficient variant of the OCaml compiler to produce a code that is executed and whose results are integrated in the memory of the Coq system  [10]. This strategy relies on the OCaml compiler and the operating system linker in ways that are more demanding than traditional uses of Coq. Still it is the same compiler that is being used as the one used to compile the Coq system, so that the trusted base is not changed drastically in this new approach. When it comes to time constraints, all scaling factors are not as efficient. In conventional computer arithmetics, it is well-known that multiplications by powers of 2 are less costly, because they can simply be implemented by shifts on the binary representation of numbers.
This property is also true for Coq's implementation of big integers. If we compare the computation of √ 2 when the scaling factor is 10 10 6 or 2 3321929 , we get a performance ratio of 1. 5, the latter setting is faster even though the scaling factor and the intermediate values are slightly larger. It is also interesting to understand how to stage computations, so that we avoid performing the same computation twice. For this problem, we have to be careful, because values that are precomputed don't have the same size as their original description, and this may not be supported by the native compute chain of evaluation. Indeed, the following experiment fails. This examples makes Coq fail, because the definition of mag with the pragma Eval native compute in makes that the value 10 10 6 is precomputed, thus creating a huge object of the Gallina language, which is then passed as a program for the OCaml compiler to compile when constructing z1.
This works, but the resulting program is one order magnitude slower than what runs in the interactive theorem prover. The reason is that the BigZ library exploits an ability to compute directly with machine integers (numbers modulo 2 31 )  [3] , while the extracted program still views these numbers as records with 31 fields, with no shortcuts to exploit bit-level algorithmics. This raises several questions of trusted base: firstly, the Coq system with the ability to exploit machine integers directly for number computations has a wider trusted base (because the code linking integer computation with machine integer computation needs to be trusted). This first question is handled in another published article by Armand, Grégoire, Spiwack and Théry  [3]. Secondly we also have to trust the implementation of the native compute facility, which generates an OCaml program, calls the OCaml compiler, and then runs and exploits the results of the compiled program.
Obviously, we would need to interface with a library for large number computations in such a setting. Such libraries already exist, but none of them have been formally verified. We believe that the community of formal verification will produce such a formally verified library for large number computations, probably exploiting the advances provided by the CompCert formally verified compiler  [33]  (which provides the precise language for the implementation), and the Why3 tool  [20]  to organize proofs of programs with imperative features, based on various forms of Hoare logic. In their current implementation, our algorithms run at speeds that are several orders of magnitude lower than the same algorithms implemented by clever programmers in heavy duty libraries like mpfr  [21]. For now, the algorithms for elementary operations are based on Karatsuba-like divide-andconquer approaches, with binary tree implementations of large numbers, but it could be interesting to implement fast-Fourier-transform based multiplication as suggested by Schönhage and Strassen  [38]  and observe whether this brings a significative improvement in the computation of billions of decimals.
, 2017). At the start and end of the transect used for leaf sampling, two 0. 25 m 2 squares were laid out and weeds and crop plants in each square were cut and the biomass was separated, dried for 24 h at 105°C and weighed to determine dry mass. The farmers managing the different fields were interviewed about the preceding crops, soil tillage, pesticides, fertilisation and other measures applied in the sampled fields (Table  S1 ). These data were also used to calculate the agricultural intensification index proposed by  Herzog et al. , (2006)  for each field. The original index includes three indicators: livestock density, amount of nitrogen applied (kg/ha) and number of pesticide applications. Only the two latter were applicable to our study. 2. 2 DNA extraction, PCR and 454 sequencing In total, 18 farmers out of 24 provided a sample of harvested wheat kernels from the fields sampled in July.
The sample pool was sent to Eurofins MWG Gmbh (Germany) for adaptor ligation and sequencing on 1/4 of a plate using a GS FLX++ 454 sequencer (Roche, Switzerland). Before sequencing the amplicon pool was purified by gel extraction. Raw sequence data were deposited in the Sequence Read Archive (http://www. ncbi. nlm. nih. gov/sra) under accession number SRP061762.
Bioinformatics and species identification Raw 454 sequence data were quality filtered and clustered using the SCATA pipeline (Brandström Durling et al. , [http://scata. mykopat. slu. se]) as described previously  (Karlsson et al. , 2016). Briefly, sequences were screened for matches to the primer sequences (allowing 1 mismatch) and the sample identifying tags. Sequences shorter than 500 bp and those with low quality scores were discarded. Sequences passing the quality control step were clustered into operational taxonomic units (OTUs) at 1. 5% dissimilarity cut-off in SCATA. Mock communities of 10 Fusarium species were included as positive controls as described in a previous publication  (Karlsson et al. , 2016). The mock communities were used to determine the cut-off which best reflected Fusarium species and to set a limit for low-abundance OTUs as these may be the result of sequencing and PCR errors  (Tedersoo et al.
, 2010). Consequently, OTUs with less than eight reads per OTU were removed as these occurred as contaminants in the mock communities. In addition, singletons were removed on a per-sample-basis. A first screening for Fusarium OTUs was done by subjecting the most abundant sequence in each OTU to a BLAST search against sequences in GenBank. OTUs that did not yield any hit with identity and coverage >70% were considered chimeric or artificial and removed. The remaining OTUs were screened for hits to Fusarium species or their teleomorph names, which were included in further analyses. Fusarium species identification was performed by including reference Fusarium TEF1 sequences in the clustering in SCATA. For OTUs related to F. avenaceum, BLAST analysis was performed with sequences in GenBank. The OTUs were identified to the species level with 99.
Statistics The OTU table generated from 454 sequencing data was multiplied with the amount of Fusarium present estimated with real-time PCR and was used as input for the statistical analyses. All statistical analyses were performed in R (R Core Team, 2014). Pairwise co-occurrence of Fusarium OTUs was tested using the probabilistic model implemented in the 'cooccur' package version 1. 2  (Griffith et al. , 2016). OTU pairs with only one co-occurrence were excluded from the analysis, which left 28 pairs tested. In order to visualise Fusarium community composition between fields, non-metric multidimensional scaling (NMDS) was applied using the function metaMDS in the 'Vegan' package  (Oksanen et al. , 2013). The NMDS was performed on Bray-Curtis dissimilarities calculated from log-transformed data to account for unequal variance between abundant and rare species.
Subsequently, continuous explanatory variables were fitted to the ordination using the envfit function. The effect of cropping system and agricultural intensity on Fusarium community composition was tested using multivariate generalised linear models (GLMs). A model including the number of 454 reads, field pair and cropping system was fitted to each OTU using the manyglm function in the 'mvabund' package with a negative binomial probability distribution package  (Wang et al. , 2012). Significance was assessed using the anova function in 'mvabund', which provides a multivariate test for the community composition and univariate tests for each OTU. The likelihood-ratio test was used and p-values were adjusted for multiple testing. Interview data from one of the fields (12C) was incomplete and was therefore excluded from the analysis of agricultural intensity.
Finally, the effect of agricultural variables on Fusarium communities was evaluated with redundancy analysis (RDA) using the rda function in the 'Vegan' package. Correlated variables were avoided, e. g. the amount of nitrogen applied which is correlated with crop biomass. Model selection started from a model including the number of 454 reads and field pair as conditional variables. Crop diversity, type of fertiliser, crop biomass, weed biomass, number of fungicide applications and type of soil tillage were included in the model selection. Crop diversity was calculated as the number of different crops grown on the fields in the last three years. Leys were counted as two crops regardless of the duration of the ley. Forward model selection was performed with the ordistep function and data were logtransformed prior to analysis.
Results Fusarium TEF1 sequences were obtained from harvested kernels from all fields by highthroughput 454 sequencing. The number of 454 reads per sample was 497-3681 with a median of 1982. In total, 12 Fusarium operational taxonomic units (OTUs) were identified from 18 samples of winter wheat kernels (Fig. 2a ). Reads were distributed between four different OTUs related to F. avenaceum. The number of Fusarium OTUs per field ranged from two to eight with a median of 4. 5. Fusarium avenaceum was the most frequent species recovered and was present in 94% of fields, followed by F. poae (83%), F. graminearum (78%) and F. tricinctum (72%) (Table  S2 ). The amount of Fusarium DNA in the samples was 20-1667 pg per 100 ng wheat DNA (Fig. 2b ). In terms of abundance, F. graminearum dominated the dataset with 84% of total DNA, followed by F.
The use of HTS of amplicon markers is clearly advantageous for detecting many Fusarium species simultaneously. Amplicon sequencing does not require beforehand selection of which species to survey, as opposed to real-time PCR with species-specific primers. Therefore, amplicon sequencing is especially useful for detecting Fusarium species colonizing new areas. Amplicon sequencing provides the relative abundance of each species in a community but not the total abundance. Therefore, we complemented the HTS data with real-time PCR quantification of Fusarium spp. using the same primers. Fusarium DNA was estimated to vary 100-fold between samples. The TEF1 is single-copy in Fusarium  (Geiser et al. , 2004) , which allows for quantitative comparisons of both total and relative abundances between species.
The agricultural intensity index included the amount of nitrogen applied (kg/ha) and the number of pesticide applications. Data were analysed with multivariate generalised linear models. One field was excluded from the analysis of agricultural intensity due to missing data. ** P < 0. Fields are paired and numbered on a south-western gradient starting from the north (Fig. 1 ). Two fields managed with reduced tillage are marked in bold in a). In b), the abundances of Fusarium OTUs are represented by the area of the circles and colorcoded as in Fig. 2a. 17 fields were included in the analysis.
Acknowledgements We would like to thank the farmers for their participation in the study. We also thank  Véronique Edel-Hermann  for help with identification of  Fusarium OTUs  and  Maria Jonsson ,  Maria Kedmark  and  Rickard Almers  for technical assistance. This work was supported by the  Swedish Research Council for Environment, Agricultural Sciences and Spatial Planning (Formas) , [grant number  2010-1945 ]. The funder had no role in study design, data collection and interpretation, writing of the report, or the decision to submit the work for publication.
Inference of fine-scale recombination maps We estimated and compared the local recombination rates in Z. tritici and Z. ardabiliae using two methods implemented in the Ldhat  [41]  and Ldhelmet  [13]  packages. As θ substantially varies along genomes and between species, we generated recombination maps using three scaled effective population size values as inputs (θ = 0. 05, 0. 005 and 0. 0005). For both Ldhat and Ldhelmet, we find that the three different input θ values only have a marginal influence on the recombination rate estimates obtained (Fig. 1A ). We therefore proceeded with the recombination map estimated using a θ of 0. 005, similar to the median of θ values estimated in 10-kb windows in Z. tritici (θ = 0. 0139) and in Z. ardabiliae (θ = 0. 0087) (Table  1 ). To assess the performance of the two methods and input parameters for the fungal datasets, we first compared the inferred recombination maps of Z.
SNP density and filtering based on confidence intervals Ldhat and Ldhelmet have been developed for recombination analyses in animals  [13, 21, 41]  and their performance on data from haploid eukaryotes with high recombination rates have not been tested. Therefore, we next assessed the robustness of the composite likelihood approach using simulations with distinct sample sizes and SNP densities. We report that the interval program infers recombination rate with the highest reliability for intermediate diversity levels (θ = 0. 0005 or 0. 005). Furthermore, while larger sample size decrease the variance in estimate, we show that Ldhat reliably infers recombination when as few as 10 haploid genomes are used (Fig. 2 ). We observe that ρ generally tends to be underestimated and its estimation variance is larger for small sample sizes.
Putative sequencing errors Sequencing errors can impact linkage disequilibrium estimates as they appear as unlinked singletons in population genomic datasets. Such potential effects are partially accounted for at two levels in our analyses. First, our data sets are based on de novo assembly of each individual genomes, which already corrects for putative sequencing errors in the sequencing read outs. Second, many of the SNPs discarded for having a large confidence interval in the estimation of recombination rates by LDhat are singletons. In order to further assess the potential impact of putative sequencing errors, we ran LDhat on the Z. tritici data set after discarding all singletons and filtering for confidence interval as described above. The resulting recombination map appeared to be highly correlated to the map including all singletons (Table  2  and Figure  S1 ), and the correlation of the filtered map with the crossingover map was significant, but less than when including them (Kendall's tau = 0.
Effect of population structure Previous studies reported that Z. tritici strains are sampled from a globally panmictic population  [42, 43]. However in a recent study based on whole genome data, we report evidence for slight population structure, notably between Iranian isolates vs. European isolates  [44]. In order to assess whether this structure could bias our recombination estimates, we generated a new recombination map using LDhat on a reduced sample of eight strains of Z. tritici. We excluded the two Iranian isolates in our dataset as well as three German isolates forming a separate cluster, yet non-significant. We report that the resulting map is highly correlated to our recombination map (Figure  S1 ) as well as to the crossing-over map (Kendall's tau = 0. 3237, p-value < 2. 2E-16) (Table  2 ) suggesting that population structure has little impact on our inference of recombination rate.