dataesr/scientific-paragraphs-categorization huggingface dataset:
The (vertical) distance between the two parts M. d and the overlap length M. l are the two parameters related to this criterion. Finally, our last criterion is the presence of holes inside the shape. They represent missing data due to occlusions during the acquisition process, or when the leaf has been partially eaten by an insect, for instance. To evaluate the influence of this criterion on the robustness of each geometric model, we have generated hexagonal leaves with square holes of varying edge length (H). Generated dataset. We generated a synthetic dataset by varying each criterion independently as summarized in Table  1. The amount of noise is defined with respect to the leaf length. For example, N = 0. 15 corresponds to an uncertainty of 1. 5 cm for a 10 cm-long leaf. The default density value D = 5, 000 points is chosen so that the leaf boundary is densely sampled and to avoid sampling inhomogeneity to be interpreted as holes.
Some examples of synthetic data are shown in Fig. 2. We have chosen to vary each criterion independently to better study their individual effects on leaf area estimation methods, although our code is able to generate synthetic leaves with as many different artefacts as desired. In order to take randomness of the sampling and/or the noise into account, we created 10 point clouds for each parameter value, leading us to generate 1240 synthetic point clouds in total. Note that each point cloud is a different approximation of an hexagon which area remains equal to 1.
Real data In order to evaluate the geometric models in real-life scenarios, we have scanned a set of selected plants, collected and measured their leaves to obtain ground truth area measurements. Species were chosen in order to test leaves with different (a) (b) (c) (d) (e) (f) (g) (h) (i) Fig. 2. Examples of synthetic data generated from a flat hexagon: (a) shape with an increased length/width ratio, (b) shape with an increased curviness, (c) shape with an increased concavity, (d) shape sparsely sampled, (e) shape regularly sampled, (f) shape with a nonuniform sampling, (g) shape with a high acquisition noise, (h) shape with misalignment, (i) shape with a hole. length/width ratios, curvatures and concavity levels. Some resulting point clouds are shown in Fig. 3. Table  2  provides an overview of the selected dataset.
(a) (b) (c) (d) (e) The last plant is a maize plant (Zea mays L. ) scanned with two different devices: a Faro 3D X130 laser scanner, and a multiview system made of 9 Sony-RX0 cameras. We used the Colmap software  [31]  to generate the 3D point clouds from the images. Leaves are elongated, curved and show some torsion. Both the LiDAR and photogrammetry point clouds contain occluded areas, hence holes. The registration of LiDAR point clouds led to small but noticeable misalignments. The photogrammetry datasets exhibit a variable point density. The leaf areas were measured with a Licor LI-3100 Leaf Area Meter.
Mesh reconstruction We selected four simple and readily available meshing methods, that have already been applied to leaf surface reconstruction. We discarded those requiring additional manual work, such as the ones presented in  [32, 10]. 2. 5D Triangulation. Considering a leaf is a 2-dimensional object, the simplest approach to reconstruct its surface is to triangulate the projections of its points onto a plane and to lift the resulting triangles back to the original points  [11, 9]. This process, sometimes called 2. 5D triangulation, uses the least-square fitting plane to project the 3D points followed by a 2D Delaunay triangulation. In our tests, we use the CloudCompare software  [33]  to perform such computations. It adds an optional postprocessing stage which removes triangles with edges longer than a given threshold.
Implicit modelling Implicit modelling has been applied with success to point clouds and constitutes a major approach of surface reconstruction from such data  [42, 43, 44, 45]. Methods from this ap-proach fit an implicit function to a set of points. A level-set of this function is then extracted and meshed to approximate the sampled surface. Screened Poisson Reconstruction. Surface reconstruction from a point cloud with normal vectors can be formulated as a Poisson problem. This formulation was proposed by Kazhdan et al. to reconstruct watertight surfaces  [43]  and was further extended to open surfaces  [44]. This method is known as screened Poisson reconstruction. The authors provide the source code as well as executable software on their web page together with usage examples. The main parameter of the screened Poisson surface reconstruction algorithm is the importance pw of point interpolation during the screened Poisson formulation (so-called point weight in the provided software).
Methodology We evaluated the accuracy of the selected methods by comparing their results to the ground truth values. For each method, we used the set of best parameters identified through the sensitivity analysis described in Section 3. 3. 1. Each method has been applied on each of the 1240 synthetic leaf models generated as described in Section 3. 1. 1. Additionnally, for each real dataset presented in Section 3. 1. 2, methods have been tested on raw and on filtered point clouds (see Section 3. 3. 2). Once the leaf areas were estimated, each method has been evaluated based on its signed mean relative error (SMRE): S MRE = 1 n n i=1 A e i -A t i A t i where n is the number of point clouds considered and A t i and A e i are the ground truth area and the estimated area for the i th point cloud, respectively.
We have also used the unsigned mean relative error (UMRE), defined as U MRE = 1 n n i=1 ∥A e i -A t i ∥ A t i to determine the norm of the relative error on each dataset, in order to check for compensation phenomenon in the SMRE computation. According to our study the UMRE is less informative than the SMRE and the reliability of the SMRE is enough to draw our conclusions.
Sensitivity analysis We performed a parameter sensitivity analysis to determine which parameters need to be carefully tuned in order to reach the most accurate leaf area estimate with each method, and how to tune these parameters. In addition to the leaf area, we also checked the geometry and topology of the generated surface to discard inaccurate surfaces: parameter values leading to nonmanifold surfaces, surfaces with holes or self-intersections are considered as non-optimal regardless of the accuracy. A subset of the synthetic data described in Section 3. 1. 1 has been randomly chosen and used to conduct this analysis. 130 of the 1240 generated point clouds have been clustered according to the 11 criterion parameters. This allowed us to test each method parameter with respect to each criterion independently.
We varied the value of each parameter individually according to the identified set of values to be tested. Table  4  summarizes the optimal values found. The SMRE was computed for each parameter value among all point clouds of a data set defining a criterion parameter. Among all tested values of a parameter, the one that reaches the SMRE closest to zero among all data sets while generating a geometrically and topologically correct surface was chosen as the optimal value of the parameter. Finally, we have checked that the combination of optimal values for all parameters of the method generates better results than the combination of one optimal value for a given parameter and default values for the other ones. For some methods, parameters may depend on the point cloud density or size. In such cases, a fixed value for such parameters is not suitable.
Point cloud pre-processing In this study, we assume that the point clouds have been segmented to only include leaf. However, input point clouds may still contain noise. As an additional contribution, we studied the effect of pre-processing filters on the leaf area estimated by the selected methods. To do so we selected two classical filters. The Statistical Outlier Removal filter (SOR)  [46]  is based on the distance from a point to its neighbours: it discards points with a distance higher than the standard deviation computed on the entire point cloud. Based on the definitions of Moving Least Square surfaces (MLS)  [47] , the MLS filter proposed in Cloud-Compare projects each data point on a smooth surface defined as the stationary point of a projection operator. While it can be used to up-or down-sample a point cloud, we only used it to reduce the amount of noise in the point clouds.
Many variants of the MLS approach have been proposed in the literature. In addition to the version proposed in CloudCompare, we have experimented the Algebraic Point Set Surface (APSS) definition proposed by  [48]. We ran the leaf area estimation methods on raw input point clouds as well as SOR filtered point clouds, MLS filtered point clouds and SOR + MLS filtered point clouds. Results show a negligible difference of leaf area estimation between raw data with SOR filtered data on the one hand, and between MLS filtered data and SOR+MLS filtered data on the other hand. This demonstrates that the SOR filter may be useful to remove major outliers but is not enough to improve leaf area estimation in noisy point clouds. On the contrary, the MLS filter both improves the accuracy of all methods and reduces the dispersion of the estimates.
Results on real data We evaluated the accuracy of each selected method on the point clouds derived from real acquisitions. In this evaluation, we considered as error measure the signed relative error between the estimated leaf area and the ground truth as recovered from manual measurements. Fig. 7  shows the box-and-whisker charts of errors for all leaves of each plant and each geometric model. Point clouds were filtered using either the MLS filter proposed in CloudCompare or the APSS framework of  [48] , with 30 nearest neighbours and 5 successive projections on the implicit surface. For the sweet chestnut, the red oak and the silver birch data, the most robust and accurate methods are the Bézier Leaf Model and the Trimmed Bézier method. It is to be noted that the B-Spline method has failed to produce a mesh for some leaves, leading to a zero estimate for their area.
The most accurate methods are the Trimmed Bézier method and the Incremental Reconstruction. These results are consistent with those on synthetic data since the behaviour of each model can be explained by the combination of multiple criteria. However, results on real data highlight the impact of additional criteria on the estimated areas, such as the intrinsic nature of the noise near leaf borders like in the birch dataset or the presence of holes separating a point cloud into multiple clusters like in the oak or the maize photogrammetry datasets. We show in Fig. 8  to 10 the meshes computed by each method for one leaf of each dataset.
The tuning of the Incremental Reconstruction method across our synthetic data was the most sensitive. A second conclusion drawn from the results obtained on synthetic data sets is that the leaf curviness, acquisition noise and misalignment are the criteria impacting the most the accuracy of the results. The parametric models we tested are robust to noise as well as to misalignment up to a threshold, but cannot properly fit a highly curved leaf. The Incremental Reconstruction method is robust to curviness and misalignment but is sensitive to noise. An additional conclusion derived from the experiments on real data sets is that the MLS filter improved the accuracy and robustness of all methods, but not the SOR filter. Hence we recommend systematically filtering the raw point clouds with this filter before further processing.
We have designed 1240 synthetic leaf point clouds based on these criteria and tested the methods on them, after a careful sensitivity analysis that led us to design an automatic way to set the parameter values for each of them. We have also evaluated the methods on six acquisitions of real plants that had been previously manually measured and we have tested the additional effect of denoising the point clouds as a pre-processing step. Our results show that the use of both a moving-least squares (MLS) filter and Bézier surface fitting is recommended. However, this may not work in some cases and precisely estimating leaf area from point clouds remains a challenging issue. Our analysis is a first work highlighting useful data pre-processing and assessing how various geometric models can estimate leaf areas.
The obtained mapping is then smoothed by a Gaussian filter to eliminate background noises from the machine as well as vibrations in the handling room. Figure  8  shows the obtained map after the application of a Gaussian filter. We perform an image analysis using image treatment software 'ImageJ'-version 1. 52. This image processing allows, by a threshold adjustment of the initial image, to highlight the impacts and defects recorded of the samples surface (Figure  9 ), and consequently to analyze information about the number and diameter of generated defects during the aging process. The obtained mapping is then smoothed by a Gaussian fi noises from the machine as well as vibrations in the handlin obtained map after the application of a Gaussian filter. We perform an image analysis using image trea This image processing allows, by a threshold adjust the impacts and defects recorded of the samples su analyze information about the number and diamete ing process.
Funding: This work was founded by the  SFERA-III  project from the  European Union 's  Horizon 2020 research and innovation program  under grant agreement No  823802. Institutional Review Board Statement: Not applicable. Funding: This work was founded by the  SFERA-III  project from the  European Union 's  Horizon 2020 research and innovation program  under grant agreement No  823802. Institutional Review Board Statement: Not applicable. Coatings 2022, 12, 1087.
Kim et al. (2018) , from observations and model simulations, support a key role for ocean dynamics, rather than external forcings, in Atlantic multidecadal variability during the last half century. O  'Reilly et al. (2019)  used proxy data over a period of more than 300 years to investigate the internally generated AMO and the externally forced AMO components. In addition, they analysed a long ensemble simulation over the same period to estimate the external forcing of the AMO in the proxy datasets. The proxy AMO is found to closely follow the accumulated forcing of the North Atlantic oscillation (NAO) over almost the entire analysis period, referred to as an 'internal' source of AMO. Finally, in a study about predictability,  Athanasiadis et al. (2020)  provided evidence that ocean dynamics may drive part of the observed decadal atmospheric variability.
In their vision, the NAO partly drives ocean circulation anomalies and AMO. Obviously, one can argue that the signal of AMO has been estimated for centuries and millennia well before the industrial era: see, for instance,  Knudsen et al. (2011). Thus, the studies cited above seem quite limited for establishing the unforced or forced nature of AMO. Recently, however,  Mann et al. (2021)  addressed this problem and showed this oscillation can be due to pulses in volcanic activity in the last millennium. The great majority of these studies has been performed by runs of Global Climate Models (GCMs). In this framework, following a first attempt briefly described in  Pasini et al. (2017) , here we address this problem via a neural network (NN) model specifically developed for modelling relationships amongst variables in small datasets  (Pasini 2015).
Data In this investigation, we base on annual data related to the AMO index and to the following radiative forcings: the warming part of the anthropogenic forcing RFWARM (GHGs + BC RFs), its cooling part given by sulphates (RFSOX), RF from solar activity (RFSOLAR) and RF from volcanoes (RFVOL). In particular, we consider the AMO index calculated with the method of  Enfield et al. (2001)  and download this record from www. esrl. noaa. gov/ psd/ data/ times eries/ AMO. Data about anthropogenic radiative forcings are downloaded from the freely available dataset collected at http:// www. stern davidi. com/ datas ite. html, referred to a paper by  Stern and Kaufmann (2014). Here the data on GHG concentrations are taken from the NASA/GISS website and the related RF calculations are performed through standard formulas  (Ramaswamy et al.
(2017) ,  Pasini and Amendola (2019) ,  Pasini et al. (2020). Here, we briefly sketch the main characteristic features of the tool, leaving further details to its presentation paper  (Pasini 2015). The NNs considered in this tool are feedforward with one hidden layer, endowed with hyperbolic-tangent transfer functions at the hidden level and a linear function at the output neuron. It is worthwhile to stress that in the present study the training technique of this tool is modified by considering a quasi-Newton backpropagation method-the so-called Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm  (LeCun et al. 1998 )-which is more suitable for handling small datasets with respect to the standard backpropagation adopted previously. This leads to differences in AMO attribution results when compared with those of our previous attempt  (Pasini et al.
2017). In order to obtain a nonlinear relationship between inputs and targets (to be approximated by outputs) which can be generally valid, a training-validation-test procedure must be applied. Usually, the free parameters of the NNs (i. e. the connection weights) are fixed on the training set by stopping the training phase when the error on the validation set begins to increase; then, the generalisation performance is measured on a third set, unknown to the NNs, the so-called test set. In our tool, developed for analysing small datasets, a generalised leave-one-out procedure is adopted for training, validation and test, which works as follows. In a dataset formed by annual inputs-target patterns, starting from the first year we extract a single inputs-target pattern from the total available dataset and consider it as test set.
2016; O'Neill et al. 2016; Gidden et al. 2019; Smith et al. 2020). For natural forcings, we consider a future with a constant low value of RFVOL (it is difficult to hypothesise frequency and strength of future eruptions) and two different scenarios for the solar activity, as shown in Fig. 8. In the first scenario, we consider that until the end of this century RFSOLAR shall remain in a high-power regime, and in the second one, we hypothesise its return to the values of the low-power regime which characterised the period before 1910: this is done by a first-order Fourier series with a superimposed decreasing trend up to 2050 and a return to values comparable at the low-power regime of the first 60 years (1850-1910) of the observed dataset for the last 50 years (2050-2100). We consider the structure of the networks fixed in the last step of our procedure, when the value of the AMO index for 2011 was reconstructed.
sinφ A + cosφ A. cosφ A. cos∆λ). r E with latitudes φ A , φ B i , longitudes λ A , λ B i , ∆λ = λ B i -λ A and r E the conventional Earth radius equal to 6, 378, 137 m. The boundaries of the region Ω are determined thanks to the Matlab function boundary. This function returns a vector of points indices P B that represents a compact boundary around this area. It is possible to obtain less detailed boundaries by tuning the parameter FaceAlpha of the function, with a value less than one. The following step aims at meshing the map. Remark 2. The covered area is usually very large and its meshing is required to build an adapted environment for robotic simulations. From the computational mechanics domain, the in-book chapter is of interest for the mesh generation methods and mesh adaptivity issues  (George et al.
, 2007). This paper is dedicated to numerical solutions for computation in mechanics, but it presents some rules, advices and methodology for the surface domains. A regular map meshing of the region Ω could be done by different shapes of different sizes (see Fig. 5 ), which particularities are discussed in Section 4. 5. Matlab software offers the library Generate Mesh for triangular mesh for a 2-D geometry. Another option is to perform map meshing thanks to the Multiparametric Toolbox 3. 0 3 library  (Herceg et al. , 2013) , that allows adjusting the size and choosing the shape of each finite element. From this library, the functions Polyhedron, meshGrid or isInside are available. Hence, according to the function Polyhedron and the previous determined vector P B , an entity Zone is created from the area of interest.
ACKNOWLEDGMENT Authors want to thanks the company  Bathy drone Solutions (BDS)  for its participation in the experiments, and the  Department of Economic Transformation, Industry, Knowledge  and  Universities of the Andalusian Government  ( PAIDI 2020 ) [Ampliación Aquacollect, ref. P18-HO-4713 ]. The  Region Hauts de France  and the  French government  are warmly acknowledged for the co-funding of the  CPER ECRIN  and the  VERDEAU  project.
Data Collection The measured data used in this study to calibrate and validate the model, as well as to determine the upstream limit conditions, include discharge (Q), salinity (Sal), suspended particulate matter (SPM), and water quality variables, i. e. , phosphate (PO4), ammonium (NH4), nitrate (NO3), dissolved silica (DSi), dissolved oxygen (DO), total (particulate and The data for the marine boundaries were extracted from outputs of simulations performed by a coastal marine model ECO-MARS3D  (Cugier et al. , 2005b; Lazure and Dumas, 2008; Ménesguen et al. , 2019) , providing water elevation, temperature, salinity, SPM, PO4, NH4, NO3, DSi, DO, TOC, and phytoplankton (Phy) at 4-km spatial and hourly temporal resolutions. The use of the above database is detailed in section 2. 3. 3.
Forcings and Boundary Conditions C-GEM is constrained by a set of riverine and marine boundary conditions. The riverine boundary conditions include river discharge (Q), SPM, and the state variables of water quality concentrations, which were linearly interpolated to obtain the daily values between the adjacent available measurements (Table  3 ). The marine boundary conditions include water elevation, water temperature, salinity, and the same water quality variables extracted from ECO-MARS3D at an hourly temporal resolution that allows capturing the tidal cycle. SPMs for the marine boundary conditions were collected from REPHY (REPHY, 2021) and linearly interpolated to obtain the data at the required time scale (Table  3 ). The annual means of boundary conditions are summarized in Table  4.
Model Calibration The data used to calibrate and validate the model were obtained from the multiple databases mentioned in section 2. 2. The locations of these stations along the estuaries are presented in Figure  1. Calibration was implemented based on 2015, an average year in terms of river discharge. The performance of the hydrodynamics modules was first evaluated by comparing the simulated salinity with observed salinity along the estuary. Then the mass transport was calibrated using longitudinal SPM profiles as an indicator. Good agreement with in situ data for salinity and SPM was reached by setting a maximum value of 100 m s -2 to the dispersion coefficient generated by the equations described in  Volta et al. (2014). This dispersion value is in agreement with the previous study in the Scheldt estuary  (Arndt et al.