dataesr/scientific-paragraphs-categorization huggingface dataset:
Below we explain each of different data files present in the MAELIA input dataset, and the nature of data, that is available at Portail Data INRA repository (https://doi. org/10. 15454/3ZTCF5): • Administrative divisions: Spatial data containing information concerning the second-(ADM2, department. shp ) and forth (ADM4, communes. shp ) -order French administrative divisions, referent to provinces and communes respectively. These data serve as a basis for delineating the territory. • Water catchment area: General information regarding the characteristics of the water catchment area ( ZH. shp ). • Soil mapping units (SMUs) and detailed quantitative soil data ( soils. shp ). Each SMUs of the 1:1 0 0 0 0 0 0 French soil map  [3]  were tagged to the dominant Soil Typological Unit (STU). Then pedotransfer rules  [4]  were used to transform qualitative data of STU into quantitative values describing characteristics and properties of the corresponding soil.
Finally, this soil data were improved using soil analyses provided by the farmers. • Agricultural fields: The French Land Parcel Identification System (LPIS) (v2017), a geographical database  [5, 6]  , was used to provide the boundaries of fields and field blocks (islets) of each farm investigated. For each of the three land-use scenarios, field data is composed by two different geographical units to represent farm's agricultural area: islets ( islets_base. shp, islets_coexistence. shp, islets_complementarity. shp and islets_synergetic. shp ) and parcels ( parcels_base. shp, parcels_coexistence. shp, parcels_complementarity. shp and parcels_synergetic. shp ). Islets are formed by one or a set of contiguous georeferenced parcels belonging to the same farm and delimited by natural (e. g. hedges, ditches) or artificial elements of the landscape (e.
• Economic information. The economic_info. csv file contains information regarding the crop prices and premiums, milk prices, feeding costs, water costs, and average variable costs for each crop. These data were provided by agricultural advisors from the CRAPL for 2015, 2016 and 2017. For the remaining simulated period (2005 to 2014) they were extrapolated using the agricultural producer price index for each year for each input and output  [10].
2021 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license ( http://creativecommons. org/licenses/by/4. 0/ ) Specifications Table Subject Agricultural Sciences Specific subject area Territorial crop-livestock systems Type of data Shape (  *. shp) and csv files How data were acquired -Primary data were collected for the period from July 2014 to September 2018. Farmer surveys (general information about the farms and farmers' decision management rules) were realised in March and April 2019. -Field boundaries correspond to the French Land Parcel Identification System (LPIS) of the year 2017. -Soil data was collected from the Geographical Database of French Soils (BDGSF) at a scale of 1:1. 0 0 0. 0 0 0, and improved with soil analysis from the farmers. -Meteorological data was collected from SAFRAN dataset (8 km × 8 km) of Météo France.
-Simulation data (second dataset) corresponds to the outputs of MAELIA. Data format Raw and simulated. Parameters for data collection Farmer surveys were realised face-to-face based on a uniform template. Description of data collection Data were collected for seven farms, 195 fields, 70 crop rotations and 15 crops. Farmers' decision management rules and general information about the farms (e. g. crops, equipment, average crop yields) was collected via surveys. Each farmer was interviewed individually. Data source location Institution: INRAE Region: district of Pays de Pouzauges, Vendée Country: France from 46. 7 °N to 46. 9 °N latitude and, 0. 7 °W to 0. 9 °W Data accessibility Repository name: Data INRAE Title: Replication Data for TCLS study in Vendee, France Data identification number: https://doi.
f y x}. In contrast, an encoding approach based on combinators, similar to the one implemented in Sledgehammer  [52] , would blindly enumerate all possible SK terms for z until the right one, S (K (S f)) K, is found. Given the definitions S z y x ≈ z x (y x) and K x y ≈ x, the E prover  [59]  in auto mode needs to perform 3757 inferences to derive the empty clause. For the third challenge, the idea is that, when applying t ≈ t to perform rewriting inside a higher-order term s, we can encode an arbitrary context as a fresh higher-order variable z, unifying s with z t; the result is (z t )σ, for some unifier σ. This is performed by a dedicated fluid subterm superposition rule (FLUIDSUP). Functional extensionality is also considered a quintessential higher-order challenge  [14] , although similar difficulties arise with first-order sets and arrays  [34].
Definition 3 (Green contexts) We write t = s u p to express that u is a green subterm of t at the green position p and call s p a green context. We omit the subscript p if there are no ambiguities. In a βη-normal representative of a green context, the hole never occurs applied. Therefore, inserting a βη-normal term into the context produces another βη-normal term. Another key notion is that of a fluid term. Fluid terms are certain variable-headed terms and λ-expressions into which the calculus must rewrite to be refutationally complete. Fluid terms trigger the FLUIDSUP rule, which complements the familiar superposition rule SUP. Definition 4 (Fluid terms) A term t is called fluid if (1) t ↓ βη is of the form y ūn where n ≥ 1, or (2) t ↓ βη is a λ-expression and there exists a substitution σ such that tσ↓ βη is not a λ-expression (due to η-reduction).
Implementation Zipperposition  [27, 28]  is an open source superposition prover written in OCaml. 1  Its raw performance might not be comparable to highly optimized provers such as E and Vampire, but its code is easier to maintain and modify. Our rough estimate is that it is about three times slower than E. Originally designed for polymorphic first-order logic (TF1  [21] ), Zipperposition was later extended by Cruanes with an incomplete higher-order mode based on pattern unification  [53]. Bentkamp et al. [12]  extended it further with a complete λ-free clausal higher-order mode. We have now implemented a clausal higher-order mode based on our calculus. We use the order λ (Sect. 3. 6) derived from the Knuth-Bendix order  [45]  and the lexicographic path order  [43]. We currently use the corresponding nonstrict order λ as.
Our most competitive configuration, Zip-coop, emerges as the winner on both problem sets containing λ-expressions. The raw evaluation data show that, on higher-order TPTP benchmarks, Zip-coop does not solve any problems that no other cooperative prover solves. This probably says more about the benchmark set than about the prover. By contrast, on SH-ll benchmarks Zip-coop uniquely solves 21 problems, and on SH-λ benchmarks, it uniquely solves 27 problems, w. r. t. other cooperative provers.
Acknowledgment Simon Cruanes patiently explained Zipperposition's internals and allowed us to continue the development of his prover. Christoph Benzmüller  and  Alexander Steen  shared insights and examples with us, guiding us through the literature and clarifying how the Leos work. Maria Paola Bonacina  and  Nicolas Peltier  gave us some ideas on how to treat the extensionality axiom as a theory axiom, ideas we have yet to explore. Mathias Fleury helped us set up regression tests for Zipperposition. Ahmed Bhayat,  Tomer Libal , and  Enrico Tassi  shared their insights on higher-order unification. Andrei Popescu  and  Dmitriy Traytel  explained the terminology surrounding the λ-calculus. Haniel Barbosa ,  Daniel El Ouraoui ,  Pascal Fontaine ,  Visa Nummelin , and  Hans-Jörg Schurr  were involved in many stimulating discussions.
The quantitative integration of geophysical measurements with data and information from other disciplines is becoming increasingly important in answering the challenges of undercover imaging and of the modelling of complex areas. We propose a review of the different techniques for the utilisation of structural, petrophysical and geological information in single physics and joint inversion as implemented in the Tomofast-x 25 open-source inversion platform. We detail the range of constraints that can be applied to the inversion of potential field data. The inversion examples we show illustrate a selection of scenarios using a realistic synthetic dataset inspired by real-world geological measurements and petrophysical data from the Hamersley region (Western Australia). Using Tomofast-x's flexibility, we investigate inversions combining the utilisation of petrophysical, structural and/or geological constraints while illustrating the utilisation of the L-curve principle to determine 30 regularisation weights.
, 2016) , thus we introduce and detail the different constraints implemented in Tomofast-x before providing a realistic synthetic application 75 example using selected functionalities. We illustrate the use of Tomofast-x by performing a realistic synthetic study investigating several modelling scenarios typically encountered by practitioners, and provide information to get free access to the source-code and to run it using the synthetic data shown in this paper. We perform single physics inversion of gravity data and study the influence of prior information using several amounts and types of constraints, and run joint inversion of gravity and magnetic data. The flexibility of Tomofast-x is exploited to test 80 the effect of structural constraints combined with petrophysical and geological prior information that are yet to be demonstrated in the published literature.
The current version of Tomofast-x is now more versatile as development is now directed toward use for exploration targeting and the monitoring of natural resources (kilometric scale). Lastly, in addition to inversion, Tomofast-x offers the possibility to assess uncertainty in the recovered models. The uncertainty assessments include: statistical measures gathered from the petrophysical constraints; posterior 120 least-squares variance matrix of the recovered model (in the Least Squares with QR-factorization algorithm -LSQR -sense of Paige and Saunders 1982, see 2. 5), and the degree of structural similarity between the models (for joint inversion or structurally constrained inversion). From a practical point of view, associated with the inversion algorithm is a user manual covering most functionalities and a reduced 2D Python notebook illustrating concepts (see Sect.
General design The implementation we present extends the original inversion platform "Tomofast"  (Martin et al. , 2013 (Martin et al. , , 2017)). Tomofast-x is an extended implementation proposed and modified by  Martin et al. , 2018 , Giraud et al. (2019d , 2019c) ,  Martin et al. (2020) ,  Ogarko et al. (2020). Tomofast-x follows the object-oriented Fortran 2008 standard 130 and utilizes classes designed to account for the mathematics of the problem. This introduces enhanced modularity based on the implementation of specific modules than can be called depending on the type of inversion required. The utilisation of classes in Tomofast-x also eases the addition of new functionalities and permits to reduce software complexity while maintaining flexibility. Our implementation uses an indexed hexahedral solid body mesh, giving the possibility to adapt the problem geometry, allowing to regularize the problem in the same fashion 135 as  Wiik et al.
(2015)  or to perform overburden stripping. By default, the sensitivity matrix to geophysical measurements is stored in a sparse format (using the Compressed Sparse Row format) to reduce memory consumption and for fast matrix-vector multiplications. Attention has also been given to computational aspects. The only dependency of Tomofast-x is the Message Passing Interface (MPI) libraries, which eases installation and usage. This allows optimal usage of multi-CPU 140 systems regardless of the number of CPUs. Parallelization is made on the model cells using a domain decomposition approach in space. That is, the model is divided into nearly equal, non-overlapping contiguous parts distributed among the CPUs, hence enforcing minimum load imbalance. Consequently, the code is fully scalable as the maximum number of CPUs is not limited by the number of receivers or measured data points.
Geological framework The original geological model is based on a region in the Hamersley province (Western Australia). It was built 345 using the map2loop algorithm  (Jessell. et al. , n. d. )  to parse the raw data and the Geomodeller® implicit modelling engine for geological interpolation  (Calcagno et al. , 2008 , Guillen et al. , 2008)  to model the contacts, stratigraphy and orientation data measurement in the area (see geographical location in Figure  2 ). Data used to generate the model comprise the 2016 1:500 000 Interpreted Bedrock Geology map of Western Australia (https://catalogue. data. wa. gov. au/dataset/1-500-000-state-interpreted-bedrock-geology-dmirs-016, last 350 accessed on 02/12/2020) and the WAROX outcrop database (https://catalogue. nla. gov. au/Record/7429427, last accessed on 02/12/2020).
Geophysical simulations and model discretization The core 3D model is discretised into  ×  ×  = 103 × 113 × 33 cells of dimensions equal to 999 × 996 × 745 m 3. For both gravity and magnetics, we generate one geophysical measurement per cell along the 380 horizontal axis, leading to  ×  = 11,639 data points for each method, and add 10 padding cells in each horizontal direction to limit numerical border effects in the forward calculation, leading to a total of 123 × 133 × 33 = 539,847 model-cells. We simulate a ground gravity survey by locating the measurements 1 m above ground The noise component was generated as follows. For each gravity measurement, we first add a perturbation value randomly sampled from the standard normal distribution of the whole dataset multiplied by 9% of the measurement's amplitude.
2D model simulation in a 3D world As mentioned above, we perform the inversion of geophysical data along a 2D profile for simplicity and to simulate the challenging case of 2D data acquired in a 3D geological setting, in a part of the model where subhorizontal or gently dipping features can be observed. The philosophy of the numerical study presented here 425 is summarized in Figure  5. The 2D geological Sect. considered is shown in Figure  6  (the black line marked in Figure  3  and Figure  4 ). Geological certainty is estimated using a measure of the dispersion away from the perfectly uninformed case 430 where the all rock units are equiprobable. In each model-cell, this measure, which we write  , is calculated as a function of the standard deviation  of the probability  of observing the different rock units, as follows: 𝝈 𝜓 ′ = 𝟏 𝒄𝒂𝒓𝒅 -𝝈 𝜓 , ( 18 ) where  is the geological cardinality of the model and is equal to the number of possible rock units observed in one location across the entire ensemble.
440 The probabilities of observation of the different lithologies are shown in Figure  7. Note that for the purpose of the tests we perform on gravity data inversion, we reduce the set of probabilities by grouping rock units into fictitious units with the same density contrasts as single rock units. This reduces the number of rock units to six units that can be distinguished by gravity inversion as several units may be assigned the same density contrast. To inverse model the data shown in Figure  8 , we generate a mesh centred on the profile (oriented along the y- While we focus on a 2D section extracted from a 3D model presented here (see location in Figure  3  and Figure  4 ), the 3D model and the associated gravity and magnetic datasets shown here are made publicly available (see 460 Sect.
Sensitivity analysis summary: comparison of constrained inversions Tomofast-x was developed with the intent of providing practioners with an inversion platform accounting for various forms of prior information and geophysical datasets. We have tested a series of constraints involving joint inversion, geological and petrophysical information. The inverted density contrast models for inversion using 695 global smallness and smoothness constraints, joint inversion using the cross-gradient technique, geologicallyderived smallness and smoothness constraints, and ADMM bound constraints (both global and using geological information) are shown in Figure  17. e ), (f) and (g), and (h) and (i) indicates that while it has a less significant influence on the results, incorporating geological information in the definition of the smoothness term also influences inversion results significantly.
Lastly, comparison of cases (a) and (b), and (d) and (e) suggests that the utilisation of geological information to adjust the smallness strength spatially has an effect on inversion that is, with the cross-gradient 710 constraints (where structural information is passed on from another geophysical dataset), the lowest. From the results shown in Sect. 4. 2 through 4. 5 and compared in Figure  17 , it is possible to make a qualitative, speculative ranking of the constraints accordingly with their influence on the resulting model (from the most important influence to the least important influence): ADMM bound constraints > smoothness constraints > smallness constraints > cross-gradient constraints. This 715 observation is also corroborated by the values of the root-mean-square misfit between the true and inverted model.
Future research includes the utilisation of implicit geological modelling (in the sense of  Calcagno et al. , 2008)  with Tomofast-x to define geological structures and rules that inversion will be encouraged to follow. It also 740 comprises the incorporation of topological laws previously used a posteriori  (Giraud et al. , 2019b ) directly into inversion. The electrical capacitance tomography component of Tomofast-x  (Martin et al. , 2018) , which we have not detailed here, can be extended to acoustic/seismic or electromagnetic data inversions that rely on the resolution of similar non-linear inversion problems. It opens the door to more versatility in the code and can be applied to joint inversion in similar ways but on more than two physical domains. 745 In addition, future developments comprise the collaborative and joint inversion of seismic and potential field data.
Conclusion We have introduced the open source joint inversion platform Tomofast-x and demonstrated its capabilities with a realistic dataset taken from the Hamersley region in central Western Australia. The geophysical theoretical background of Tomofast-x was explained in depth to guide users in understanding and using the modelling 790 approach implemented in the source code. We leveraged the modularity of Tomofast-x to study the sensitivity of inversion to prior structural, geological and petrophysical information, joint inversion, and the code's scalability. We tested a new combination of constraints incorporating geological structural information in the smoothness term and dynamic prior model definition using petrophysical knowledge (ADMM bound constraints), a feature usually not available to most inversion software.
795 Our sensitivity analyses on prior information and different constraints reveal that constraints using petrophysics (ADMM clustering bound constraints) dominate over gradient-based constraints (smoothness and cross-gradient constraints), which in turn exert more influence onto inversion than smallness constraints. This shows the importance of prior information in inversion and illustrates the need to study the space of geophysically equivalent models. 800 The examples described here were designed to replicate a typical, rigorous approach to the development of a geoscientific model and be relevant to real-world application. The aim to ensure rigour and reproducibility of the result presented is facilitated by the release of the source code, datasets, and a reduced, modified python version of the algorithm that accompany this paper.
Source code, documentation and data availability 805 The source code for Tomofast-x as used in this manuscript can be found in  Ogarko et al. (2021)  (https://zenodo. org/record/4454220#. YFwpEK8zZaQ). The latest versions will be available from the Github https://doi. org/10. 5194/gmd-2021-14 Preprint. Discussion started: 30 March 2021 c Author(s) 2021. CC BY 4. 0 License.
Scaling tests Although Tomofast-x can run on personal computers in a few seconds or minutes for 2D inversions and small 3D volumes (typically a few minutes on a laptop for models smaller than approx. 100,000 model cells), it necessitates 950 a supercomputer for realistic size 3D case studies (e. g. , models exceeding 500,000 model cells and 10,000 geophysical data points). We assess Tomofast-x's parallel efficiency using the strong scaling as an indicator. The strong scaling curve is given by plotting the number of CPUs as a function of user time. It is complemented by the relative speedup curve t t ⁄ , where t and t are respectively the user times to complete inversion using the number of CPUs 955 n = 1 and a given number of CPU n , respectively. We performed the scaling tests on the EOS machine from the CALMIP supercomputing centre (https://www.
direction) and add padding to either side and the northern and southern extremities. The resulting model comprises 455  ×  ×  = 13 × 133 × 33 cells of dimensions equal to 2998 × 996 × 745 m. Note that we increased model-cells' size in the direction perpendicular to the profile. The gravity and magnetic datasets along the profile each comprise 113 data points evenly distributed along the line.
Acknowledgements Appreciation is expressed to the CALMIP supercomputing centre (Toulouse, France), for their support through 820 Roland Martin's supercomputing projects no. P1138_2018, no p1138_2019 and for the computing time provided At the first and last iteration of the inversion, the diagonal elements of the posterior covariance matrix of the 860 recovered model is calculated in Tomofast-x. This calculation is performed following  (Kostina et al. , 2009)  who introduce an extension of the LSQR algorithm where such matrix is calculated at each iteration. The variances are part of the outputs of Tomofast-x for further analysis by the user, such as the estimation of uncertainty in the recovered property model.
2014) ], the variance explained by a grouping factor, and the residual variance, respectively. We conducted multiple simulations for a quantitative trait drawn from a multivariate normal distribution with the variance components specified in Tables  1  and 2. In the power analysis testing the marginal genetic effect, we simulated a single causal variant and specified its effect size b explaining 0. 1% of the trait variance. In the power analysis testing the gene-environment interaction effect, we specified d so that the (standardized) geneenvironment interaction term explaining 0. 1% of the trait variance (standardized main genetic and environmental effects each explains an additional 0. 1% of trait variance). See Supplementary material for more details. When simulating related individuals, we generated data for nuclear families with 2 parents and 3 offspring, if not specified otherwise.
Efficient computation The calculation of the parameters in Equations 24 and 25 requires inverting the trait covariance matrix R y. This step is prohibitive in large datasets, so we have developed several solutions to mitigate the computational burden. When R y is dense, we follow the low-rank LMM approach implemented in the custom R package biglmmz. Our package is built on the top of two R packages bigstatsr and bigsnpr with statistical methods for large genotype matrices stored on disk  (Priveet al. 2018). When R y is sparse, we apply special linear algebra methods for sparse matrices implemented in the R package Matrix; a similar approach was recently proposed for biobank-scale association studies  (Jiang et al. 2019). In both analytical derivations and analysis of family-based data, we make use of the block structure of relationship matrices whenever possible.