dataesr/scientific-paragraphs-categorization huggingface dataset:
This means that the pedological variability of the study area is more represented in the predicted clay content maps obtained using the VNIR-SWIR spectral bands images (TM_S, OLI_S, AST_S, and S2A_S) than in the spectral index images (TM_SI, OLI_SI, AST_SI, and S2A_SI). Thus, the maps predicted using the fusion images exhibited a wider distribution of clay content values than the other images (Figure  8 ). Finally, the variograms of the measured clay content values (dots in Figure  9 ) had higher variance than the predicted values, regardless of the sample datasets used for each satellite image. Thus, the spatial structures of the estimated clay contents obtained by the VNIR-SWIR spectral bands images exhibited very high sills compared to the spectral index images (Figure  9 ). By contrast, the variance obtained by the spectral index image fusion exhibited a very high sill and strong variations compared to those obtained by a single sensor spectral index image.
Clay Predictions Depending on the Multispectral Sensor The models based on multispectral images (i. e. , TM_S, OLI_S, AST_S, and S2A_S) provided acceptable accuracies with R 2 val values between 0. 60 and 0. 71, RMSEP values between 96. 45 and 115. 64 g/kg, MAEP values between 73. 29 and 91. 86 g/kg, RPD values between 1. 60 and 1. 90, and RPIQ values between 2. 59 and 3. 01 (Table  6 ). This performance variance could be explained by differences in satellite remote sensing datasets' acquisition dates (i. e. , date ranges), as previously shown by  [53]. Moreover, though the bands of each sensor cover similar spectral domains, they were not exactly the same (Table  1 ). Additionally, different acquisition conditions and view angles between the sensors can result in differences between the recorded datasets  [54].
94 and 132. 31 g/kg, MAEP values between 82. 89 and 109. 93 g/kg, RPD values between 1. 40 and 1. 86, and RPIQ values between 2. 16 and 2. 86 (results not shown). These performances, however, always remained lower than those obtained using the Fusion_S (Table  6 ). The models based on the four spectral index datasets (i. e. , TM_SI, OLI_SI, AST_SI, and S2A_SI) and the same soil samples (i. e. , 149 samples) performed poorly in estimating the clay content with R 2 val values between 0. 21 and 0. 53, RMSEP values between 125. 03 and 162. 89 g/kg, MAEP values between 99. 36 and 130. 59 g/kg, RPD values between 1. 14 and 1. 49, and RPIQ values between 1. 75 and 2. 28 (results not shown), and these performances always remained lower than those obtained using Fusion_SI (Table  6 ). The results of this paper suggest that the models based on satellite multi-sensor data fusion were the most precise for prediction and mapping of soil clay content.
Moreover, the improved accuracy of the results obtained using fusion images might be attributed to complementary spectral, spatial, and temporal information derived from the fusion of various satellite sensor datasets. For example,  [4]  demonstrated the potential of using fusion indices derived from multitemporal Landsat 8 imagery to predict static soil properties such as OC, sand, and CCE. Meanwhile  [26]  investigated multisource data fusion for topsoil clay mappings, such as proximally measured gamma (γ) ray spectrometry, apparent electrical conductivity (ECa), four terrain attributes, and the digital numbers (DNs) of an aerial photo. The results improved when the gamma-ray spectrometry data was integrated with the digital numbers (DNs) of the aerial photos  [26]. Ref. [27]  established an empirical surface soil moisture (SSM) model via the fusion of soil moisture networks, remote sensing data, and high-resolution land surface parameters.
Acknowledgments: The authors are grateful to  Yves Blanca  ( IRD-UMR LISAH Montpellier ), and  Zakia Jenhaoui  ( IRD UMR LISAH Tunis ) for conducting and supporting field soil sampling in 2009 and 2010 over the Lebna catchment, and to  Hedi Hamrouni  ( DG/ACTA Sol, Tunis ) and to everybody that directly or indirectly assisted in publishing this study. We want to thank the remote sensing editorial office, and three anonymous reviewers for their valuable and constructive comments.
We used the initial values provided in ref. [36]  and integrated the canonical DEs with the Mathematica package DiffExp  [38]  at 15-digit accuracy. We evaluated the permuted master integrals by permuting the canonical DEs as discussed in section 3. 3, rather than permuting the initial point as done for the GPLs. This way we verified also the consistency of the two approaches. We found full agreement. We construct the generating set κ (w) at weight w recursively starting from weight 0 where κ (0) ≡ {1}. We consider the Q-linear span C (w) 0 of the initial values at weight w, g (w) τ,σ (X 0 ), and weight-graded products of the lower-weight constants κ (w ) with w < w. We employ an adapted version of the program PSLQM3 from the MPFUN2020 package  [76] , which implements the three-level multipair PSLQ algorithm  [77, 78]  to search for integer relations using the initial values evaluated to 2000 digits.
Usage The library PentagonFunctions++ can be used either as a C++ library or through its Mathematica interface implemented by the package PentagonFunctions`. We give here only a brief demonstration and refer to the documentation supplied together with the library distribution  [87]. The library accepts as input the kinematical point given by the six Mandelstam invariants in eq. (  2. 3). The latter are assumed to be in ratios to the regularization scale, see eq. (3. 1). The pentagon functions are evaluated in their analyticity region P + 45 defined in eq. (2. 19) , which means that Im tr 5 > 0 by construction. Function values for parity-conjugated points with Im tr 5 < 0 can be obtained by manually changing the sign of the parity-odd functions, which we list explicitly in the supplementary file pfuncs charges.
Acknowledgments We are grateful to  Simon Badger  and  Heribertus Bayu Hartanto  for insightful discussions, and to  Robin Brüser ,  Johannes M. Henn ,  Leila Maestri  and  Tiziano Peraro  for useful suggestions at the initial stages of this work. We thank  Samuel Abreu ,  Simon Badger  and  Johannes M. Henn  for comments on the manuscript. The diagrams in figures 1 and 2 have been drawn with JaxoDraw [97]. This project has received funding from the  European Union 's  Horizon 2020 research and innovation programmes Novel structures in scattering amplitudes  (grant agreement No  725110 ), and  High precision multi-jet dynamics at the LHC  (grant agreement No  772009 ). DC is supported by the  French National Research Agency  in the framework of the  Investissements d'avenir program  ( ANR-15-IDEX-02 ).
Introduction Numerical simulations with a kinetic code such as EIRENE  [1]  are indispensable for both understanding and predicting the fuel and impurity transport in the edge and divertor areas of fusion devices. The transport determines impurity penetration towards the core, plasma exhaust and plasma-surface interaction (PSI) issues having impact on the duty cycle of ITER and DEMO. The insight into the interplay of transport and atomic-molecular (A & M) processes  [2, 3]  provided by modelling is key for understanding of the detachment phenomenon  [4, 5] , which is critical for many exhaust regimes envisaged for ITER and DEMO. EIRENE is a multi-purpose Boltzmann-equation Monte Carlo (MC) solver typically employed in an iterative scheme with a fluid plasma code, succinctly referred to as computational fluid dynamics (CFD) code in this paper, see figure  1.
A number of 2D CFD-EIRENE code packages such as SOLPS-ITER  [6, 7] , EDGE2D-EIRENE  [8] , and SOLEdge2D-EIRENE  [9]  are extensively employed by the fusion community. Also 3D codes are applied, such as EMC3-EIRENE  [10]  or SolEdge3X-EIRENE  [11] , and are more demanding in terms of CPU and memory requirements. All the mentioned kinetic-fluid packages are under active development. They provide self-consistently generated plasma distributions of macroscopic properties (2D or 3D), heat and particle fluxes to the wall, synthetic spectroscopy and radiative losses. An essential part of the neutral MC tracing procedure are the collisional-radiative models (CRMs) for A & M processes involving main-plasma species and intrinsic/extrinsic impurities. This includes ionization-dissociation-recombination of A & M species, break-up chains of molecules in plasma, and elastic processes.
The plasma fluid side of the packages is typically much less CPU time demanding than the EIRENE side. However, due to the strong non-linear coupling between neutrals and plasma, a large number of iterations of the coupled code systems is needed to reach a statistically stationary steady state. Despite hundreds or even thousands of CFD-EIRENE iterations are typically necessary to converge to a steady state solution, all the established packages mentioned above mostly provide sufficient performance allowing transport calculations for current devices. The situation becomes more difficult for ITER  [12] , DEMO and other large devices, for which the equilibration of the balance equations becomes much slower. In particular the particle balance poses a bottleneck, because the time scale for the particle balance τ * p scales as 1/(1 -R)  [13] , with the effective particle recycling coefficient R approaching unity for ITER and DEMO configurations.
Note that in addition, some ion species may also have to be treated kinetically (see section 2), in particular the often short lived molecular ones. This additional hybridisation of the plasma description is also handled by the kinetic NGM, since molecular ions are important players in the plasma edge chemistry, along atoms and molecules. Lowly charged impurity ions usually do not fully thermalize before being ionized, thus also can be preferred to be treated kinetically. The latter are often simulated by different codes e. g. ERO2. 0  [24]  in a test-particle approximation using the CFD-EIRENE plasma background as an input. It should be noted that kinetic ions are impacted by the electromagnetic fields and thermal force, thus more data exchange between the NGM trace ion kinetic solver and the fluid side of the CFD-EIRENE package is typically necessary.
The paper gives an overview of the fluid and hybrid fluid-kinetic methods mentioned and suggests the most perspective combinations to be developed. It focuses on the joint effort of EIRENE code developers within the EUROfusion framework aimed at transforming it into a neutral gas module (NGM) suitable for the integrated tokamak modelling. This effort also includes the optimization of the code parallelization by providing an OpenMP-MPI hybrid scheme to the already available MPI approach and some general code refactoring.
For the perpendicular direction and in the absence of plasma drifts, pressure diffusion approximations suffice  [26] , obtained by neglecting perpendicular inertia terms in the neutral momentum equation. These simplifications are based on a scale-analysis of the terms assuming perpendicular velocities are small compared to the parallel and thermal velocities  [26]. Extensions to the context of drifts that become of the order of these velocities are subject of ongoing research. In this project, we have significantly improved the existing fluid models for neutral atoms by deriving the transport coefficients and boundary conditions from the underlying kinetic description (AMJUEL/HYDHEL databases for the collisional processes and the TRIM database for the reflection physics, assuming an ideal flat surface)  [3, 16, 27].
Parallelisation of EIRENE The MC method implemented in EIRENE follows independent particles (in between iterations with a CFD code), even in non-linear cases involving collisions between tracked species, where the code relies on an iterative BGK approach  [19]. Massive parallelisation is thus in principle straightforward, as it involves communications only before and after the MC calculation itself. For a given accuracy (statistical noise level) parallelisation will reduce the wall clock time, or for a given wall clock time the accuracy can be improved. Reducing the statistical noise by one order of magnitude requires 100 times more test particles because of the square-root scaling characteristic of MC approaches. Because of the stratified sampling used in EIRENE (where one stratum often corresponds to a physical source, see section 1), different strategies are possible: the strata can be treated sequentially with particles distributed on all cores for each strata; or the strata can be treated in parallel, each one being allocated a number of cores on the basis of predefined criteria (involving the number of particles and the relative flux associated to a strata).
Acknowledgments The paper presents a joint effort within the  EUROfusion Theory and Advanced Simulation Coordination (E-TASC) , task 'NGM'  2019-2020  and the related O-EIRENE  HLST  project. This work has been carried out within the framework of the  EUROfusion Consortium  and has received funding from the  Euratom  research and training programme 2014-2018 and  2019-2020  under Grant Agreement No. 633053. The views and opinions expressed herein do not necessarily reflect those of the  European Commission. W. Van Uytven  is funded by a  PhD fellowship of the Research Foundation Flanders (FWO). Parts of the work were supported by the  Research Foundation Flanders (FWO)  under project Grant  G078316N. ORCID iDs D. V. Borodin https://orcid. org/ 0000-0001-8354-1387F. Schluck https://orcid. org/ 0000-0003-4634-0679  S.
Training process overview For a given template, we create a quasi-photorealistic synthetic dataset using rendering software. This process is described in detail in §5. 1. 1 and it is used to train DeepSfT with supervised learning. We also record a much smaller dataset with a real RGB-D camera capturing some representative deformations and poses of the object. We emphasize that the RGB-D camera provides only depth labels and not registration labels, so it cannot be used for supervised learning of the registration. Using both simulated and real data, we train DeepSfT in three steps. In the first step we use the synthetic data to train the Main, Depth Refinement and Registration Refinement Blocks end-to-end. In the second step we refine the Depth Refinement Block weights using real training data.
Templates We have tested DeepSfT with 5 objects represented by 3 thin-shell and 2 2D manifold templates shown in Table  5. We refer to these as DS1 to DS5. DS1 models an A4 paper sheet with very poor texture. DS2 models an A4 paper sheet with a richer texture and DS5 models an A4 paper sheet from a well-known public dataset  [71]. DS3 is a 2D manifold model of a soft toy and DS4 is a 2D manifold model of an adult sneaker. DS1, DS2 and DS5 can be modelled with a rectangular template, however DS3 and DS4 cannot. They were built with triangular meshes using dense SfM (Agisoft Photoscan  [72] ). We emphasize that no previous DNN-based work has been able to solve SfT for 2D manifold templates like DS3 and DS4 in the wide-baseline setting.
Synthetic datasets For each template a synthetic dataset was constructed by deforming the template with random quasi-isometric deformations and rendering the deformed template with fixed camera intrinsics and random viewpoints. We used Blender  [55] , which includes a physics-based simulation engine to simulate deformations with different degrees of stiffness using position-based dynamics. For DS1, DS2 and DS5 (rectangular templates) we simulated continuous videos with a high stiffness term and randomly located 3D anchor points. We applied tensile and compressive forces in randomised 3D directions. The simulation parameters are given in the Supplementary material. For DS3 and DS4 (2D manifold templates) we used rig-based deformations with hand-crafted rigs. We generated independent deformations for each image using random joint angles.
Real datasets Real datasets of each object were recorded with Microsoft Kinect v2 with deformations caused by hand manipulation, as shown in Table  5. Videos for DS1, DS2, DS3 and DS4 were recorded by us and the video for DS5 was provided in the public dataset (192 frames). The recorded depth maps were aligned with the RGB images using the extrinsic parameters and downsized to 270 Â 480 px. Note that these RGB-D videos do not provide labelled registration data.
Training/testing data splits We evaluate DeepSfT in terms of reconstruction and registration errors with synthetic and real test data. Synthetic test data were generated using the same process as the synthetic training data ( §5. 1. 2), using random configurations not present in the training data. Real test data were generated using the same process as the real training data, using new videos, consisting of new viewpoints and object manipulations not present in the training data. We also generated test data using two new real cameras: an Intel Realsense D435  [74]  (an RGB-D camera for quantitative reconstruction evaluation) and a Gopro Hero V3  [75]  (an RGB camera for qualitative evaluation). Table  6  shows their respective camera intrinsics. Table  4  shows the train and test split for all real datasets.
Evaluation with rectangular templates We show in Tables 7, 11 and 12 quantitative and qualitative results obtained with rectangular templates and synthetic test datasets, denoted by DS1S and DS2S, and real test datasets, denoted by DS1R, DS2R and DS5R. In terms of reconstruction error, DeepSfT is considerably better than the other methods, both in synthetic test data, where the RMSE remains below 2 mm, and for real test data, where the RMSE is below 10 mm. Kinect V2 has an uncertainty of about 10 mm at a distance of one meter, which partially explains the higher error for real data. The second and third best methods are IsMo-GAN and R50F respectively, also DNN-based. However, their errors are far worse compared to DeepSfT. CH17 obtains reasonable results when it is provided with ground-truth registration (CH17-GTR and CH17R-GTR).
Evaluation with 2D manifold templates The quantitative and qualitative results of the experiments for the 2D manifold templates DS3 and DS4 are provided in Tables  9, 11  and Table 8  Representative results and comparison of DeepSfT with other monocular depth reconstruction methods. The estimated depth maps and corresponding RMSE error in mm are shown for each method with one example input image from 4 templates (arranged in 4 columns). The results show a similar trend as with the rectangular template datasets: DeepSfT outperforms the other methods in terms of reconstruction error, with an RMSE of the order of millimeters, and in registration with an RMSE close to 2 px. The second best method is R50F, although its results are significantly worse than DeepSfT is. The results of CH17 and its variants are very poor.
Monocular depth estimation comparison We have compared object-generic monocular reconstruction method with DeepSfT. We use DenseDepth  [33]  and BTS  [34] , two state-of-the-art DNN monocular reconstruction methods. The former is based on DenseNet  [78]. We evaluated their ability to recover the object's depth with two experiments. 1) We test DenseDepth and BTS depth accuracy on the real datasets when they are pre-trained with the NYUDepth dataset  [73] , which contains RGB-D images from indoor scenes with different types of common objects. To make a fair comparison we have adapted our images to match the intrinsics of the NYUDepth dataset. We compute depth error only in the visible region of each image. We see that DenseDepth and BTS depth RMSE are several orders of magnitude higher compared to DeepSfT.
2) We fine tune DenseDepth and BTS with all training examples from DS1R, DS3R, DS4R and DS5R datasets at the same time and separately with each one of the templates. This restricts DenseDepth and BTS to detect four different objects in the first case, and to each one of the objects in the second case. The results are shown in Tables  19  and 8  where DenseDepth and BTS fine tuned versions are named as DenseDepth + FT4 and BTS + FT4 and DenseDepth + FT1 and BTS + FT1 respectively. In this case the errors have considerably reduced specially in the one object fine tune case, but they are still larger than the error achieved by DeepSfT. With this experiment we show that instance-level monocular reconstruction solutions such as DeepSfT are able to achieve much more accurate reconstruction results compared to object-generic methods such as  [33, 34].
Visual comparison of results computed from DeepSfT and other classical and DNN SfT methods with two test objects. The reconstructions are colored according to RMSE with heatmaps (middle column). The registration results are visualised with an overlay of the predicted template shape projected onto the input image. Registration errors are visualised with heatmaps (right column). n. u. stands for normalised texture map units. D. Fuentes-Jimenez, D. Pizarro, D. Casillas-Pérez et al. Image and Vision Computing 127 (2022) 10453112, with both synthetic test data, denoted by DS3S and DS4S, and real test data, denoted by DS4R and DS4R. Recall that the test datasets consist of unorganised images, unlike DS1, DS2 and DS5, and it is thus impossible to estimate registration reliably with DOF. Therefore we only compute registration error with synthetic data (DS3S and DS4S).
Deep neural networks (DNNs) are powerful learning models yet their results are not always reliable. This drawback results from the fact that modern DNNs are usually overconfident, and consequently their epistemic uncertainty cannot be straightforwardly characterized. In this work, we propose a new technique to quantify the epistemic uncertainty of data easily. This method consists in mixing the predictions of an ensemble of DNNs trained to classify One class vs. All the other classes (OVA) with predictions from a standard DNN trained to perform All vs. All (AVA) classification. First of all, the adjustment provided by the AVA DNN to the score of the base classifiers allows for a more fine-grained inter-class separation. Moreover, the two types of classifiers enforce mutually their detection of out-of-distribution (OOD) samples, circumventing entirely the requirement of using such samples during training.
In contrast to SVM-based learning, nowadays the OVA approach has been mostly discarded when training deep classifiers, in favor of All vs All (AVA) learning. The predictive uncertainty of DNNs is commonly categorized into aleatoric uncertainty and epistemic uncertainty  [23]. The former is related to randomness, typically due to the noise in the data. The latter concerns finite size training datasets. The epistemic uncertainty captures the uncertainty in the DNN parameters and their lack of knowledge on the model that generated the training data. In this paper, we propose to use OVA learning in order to improve the quantification of the epistemic uncertainty of the DNN. The underlying idea of our approach is that the score of a base classifier should be adjusted by a factor which approximates its local reliability in the input space from which the test sample originated.
II. RELATED WORK OOD detection is not a novel problem and has been studied before the deep learning revival in various branches of machine learning under slightly different taks: anomaly  [40] , outlier  [7]  or novelty detection  [58]. In the last few years, this task has seen increased attention from different communities and has been addressed with: predictive uncertainty estimation, ensemble methods, image reconstruction, etc. In the following we review briefly some of the methods related to our approach. Anomaly detection. Anomalies are linked to abnormal data detection. As building datasets for anomaly detection is a difficult task, we can make different assumptions. Assumption 1: we consider that we can collect data of anomalies; in this case, we assume that normal and anomaly data are available.