dataesr/scientific-paragraphs-categorization huggingface dataset:
Characterization The possible functional groups on the surface of the materials was analyzed by Fourier transform infrared spectrophotometry (FTIR) using an attenuated total reflectance (ATR) iS50 apparatus equipped with a diamond crystal at the range of wavenumber between 4000 and 500 cm -1 , while the crystallinity was examined by X-ray Diffraction using a D2 phaser diffractometer (AXS, Bruker) with Kα radiation of Cu (k = 1. 5418 A°) and a current/voltage of 10 mA/30 kV. The diffraction patterns were recorded from 10 to 70 (2 theta values) at a rate of 1. 2 min -1. The former oxides were identified by comparison with the pattern of the international center of diffraction data (joint committee of powder diffraction Standard, JCPDS). X-ray Fluorescence (XRF, S8 TIGER, Bruker, Billerica, MA, USA) was used to identify the major minerals and chemical compound present in the clays.
Characterization The possible functional groups on the surface of the materials was analyzed by Fourier transform infrared spectrophotometry (FTIR) using an attenuated total reflectance (ATR) iS50 apparatus equipped with a diamond crystal at the range of wavenumber between 4000 and 500 cm -1 , while the crystallinity was examined by X-ray Diffraction using a D2 phaser diffractometer (AXS, Bruker) with Kα radiation of Cu (k = 1. 5418 A • ) and a current/voltage of 10 mA/30 kV. The diffraction patterns were recorded from 10 to 70 (2 theta values) at a rate of 1. 2 min -1. The former oxides were identified by comparison with the pattern of the international center of diffraction data (joint committee of powder diffraction Standard, JCPDS). X-ray Fluorescence (XRF, S8 TIGER, Bruker, Billerica, MA, USA) was used to identify the major minerals and chemical compound present in the clays.
Furthermore, the band observed at 540 cm -1 corresponds to ν2, the deformation mode of Al-O-Si group, and the bands at 470 cm -1 are attributed to Si-O-Si deformation. In addition, the peak observed at 690 cm -1 belongs to Si-O-H stretching vibrations  [13]. Quantitative phase identification of the clay samples was carried out using the MAUD (Materials Analysis Using Diffraction) software (Lutteroti). As shown in Figure  2 , predominantly two phases were identified in both clay samples. These correspond to the.
X-Ray Diffraction (XRD) Analysis Quantitative phase identification of the clay samples was carried out using the MAUD (Materials Analysis Using Diffraction) software (Lutteroti). As shown in Figure  2 , predominantly two phases were identified in both clay samples. These correspond to the kaolinite phase with d001, d002, d003 and d004 crystallographic planes at 2θ values of 12. 3°, 24. 8°, 37. 6° and 51. 1°, respectively, and the quartz phase with d100, d10-1, d200 and d2-12 planes corresponding to 2θ values of 20. 8°, 26. 6°, 42. 4° and 50. 1°, respectively. The composition of LAG was found to be 56. 49% kaolinite and 43. 51% quartz with YAG being 71. 98% kaolinite and 28. 02% quartz. The average crystallite sizes of the kaolinite and quartz phases in the LAG clay samples were found to be 92 Å and 1958 Å, respectively.
2. X-ray Diffraction (XRD) AnalysisQuantitative phase identification of the clay samples was carried out using the MAUD (Materials Analysis Using Diffraction) software (Lutteroti). As shown in Figure2, predominantly two phases were identified in both clay samples. These correspond to the kaolinite phase with d 001 , d 002 , d 003 and d 004 crystallographic planes at 2θ values of 12. 3 • , 24. 8 • , 37. 6 • and 51. 1 • , respectively, and the quartz phase with d 100 , d 10-1 , d 200 and d 2-12 planes corresponding to 2θ values of 20. 8 • , 26. 6 • , 42. 4 • and 50. 1 • , respectively.
Acknowledgements This project is funded by  Italian Education, University and Research Ministry (MIUR) ,  French National Research Agency (ANR)  and co-funded by  European Union 's  Horizon 2020 research and innovation program  under the framework of  ERA-NET Cofund MarTERA (Maritime  and  Marine Technologies  for a new Era). This work was supported by the  Agence Nationale de la Recherche  through the  LabEx ARCANE programe  ( ANR-11-LABX-0003-01 ) and the  Graduate School on Chemistry, Biology and Health of Univ Grenoble Alpes CBH-EUR - GS  ( ANR-17-EURE-0003 ). The authors acknowledge support from the  plateforme de Chimie NanoBio ICMG FR 2607  ( PCN-ICMG ).
The mathematical expressions of these two EoSs can be found elsewhere,  35, 40  but to fix the ideas, it seems important to recall that the average deviations between calculated and experimental data on a huge pure-component database containing more than 300 000 experimental data calculated with the tc-PR and I-PC-SAFT EoSs are, respectively, as small as 1. 9 and 3. 6%. In addition, the parameters required to use such EoSs are available in the open literature for thousands of pure components. 41, 42 se of the Entropy Scaling Concept to Correlate Self-Diffusion Coefficients. State of the Art. The Tv-residual entropy, denoted s Tv-res , is a departure function expressing the difference between the entropy of a real fluid and that of a perfect gas at the same temperature and molar volume as the real fluid; it can be estimated using an equation of state in a straightforward manner.
To develop our entropy scaling-based models for the estimation of self-diffusion coefficients, ∼2400 subcritical gas, subcritical liquid, and supercritical data associated with 72 pure substances were considered. All of these data were extracted from the database of self-diffusion coefficient measurements proposed by Suaŕez-Iglesias et al. 13  This database was selected because it serves as a reference for comparing models that correlate self-diffusion coefficients. ] [45] [46]  The many data are graphically represented in Figure  4   where Nb data is the total number of data taken into account, Y ES,i exp and Y ES,i calc are the logarithm of the experimental and calculated (according to eq 5) values of the reduced self-diffusion coefficient at the given temperature and pressure of data point i, and D self,i exp and D self,i calc are the equivalent experimental and calculated values of the self-diffusion coefficient, respectively.
Notably, some experimental data points were removed from the database after application of the following filters • Data associated with pressures outside of the range [10 -3 MPa; 10 2 MPa] were considered (i) potentially inaccurate and (ii) outside of the pressure range for most applications. Therefore, they were discarded. • To eliminate out-of-chart data, the absolute deviation ΔY i = |Y ES,i calc -Y ES,i exp | was calculated for each data point and compared to the average deviation ΔY estimated for the species under consideration. Data such that ΔY i > ΔY̅ + 3σ (where σ denotes the standard deviation, and ΔY̅ , the MAPE on Y ES ) were discarded. As a double check, it was verified graphically that each datum eliminated by the test deviated strongly from the general trend and could be considered an outlier.
(2) If at least five experimental data points were available in the dense state (X ES < 0) and fewer than three experimental data points were available in the dilute gas region (X ES ≥ 0), then the specific parameters a 1 , a 2 , and a 3 were fitted to these data, whereas b, c, and d are fixed to the universal values. (3) If less than five experimental data points were available at the dense state (X ES < 0), no parameters were fitted (the component was disregarded, and no deviations with experimental data were calculated), but universal b, c, and d parameters were used to predict self-diffusion coefficients in the dilute gas region. Two sets of component-specific parameters were determined for 72 chemical species, one to be used with the I-PC-SAFT EoS and the second with the tc-PR EoS. The EoSs were used for estimating thermodynamic properties: density and residual entropy.
However, in the absence of a more comprehensive database, and because three a i parameters were sufficient to represent most of the studied substances in the dense state, the a 4 parameter was not introduced. Parametrization Strategy 2: Use of Chemical-Family-Specific Parameters. To overcome the potential lack of experimental data for a given compound, a second parametrization strategy for the proposed model equation (eq 4), involving chemical-family-specific parameters instead of component-specific parameters, is proposed. These parameters can be estimated, provided a sufficient number of representative compounds and data are available. For this reason, only four chemical families were eventually defined: n-alkanes, branched alkanes, cycloalkanes, and permanent gases. Parameters related to a given chemical family were fitted against all of the experimental data available for all of the components of the chemical family.
Their associated relative energies have been found to be quite similar, 45. 75 and 45. 52 kcal mol À1 , respectively. To complete this study, the kinetics of the singlet and triplet channels are modeled with the MESMER (Master Equation Solver for Multi-Energy Well Reactions) code by applying the RRKM and Landau-Zener (with WKB tunnelling correction) theories, respectively. It is found that the canonical rate-coefficients of the singlet path are 2-orders of magnitude higher than the ratecoefficients of the forbidden reaction. In addition, the concerted mechanism has been investigated that would lead to the formation of the imine derivative and nitrogen extrusion in the first step of the decomposition. After a careful analysis of CASSCF calculations with different active spaces and their comparison with single electronic configuration methods (MP2 and B3LYP), the concerted mechanism is discarded.
] [43]  Single electronic configuration calculations have been carried out with the Møller-Plesset (MP2)  44  and DFT/B3LYP  45  methods in conjunction with the def2-TZVPPbasis sets. 46, 47 aphical analysis of the molecular geometries, vibrational normal modes and vectors defining the seam of crossing of minimum energy crossing points (MECP) has been performed with the program MacMolplt. 48 Analysis of molecular orbitals have been carried out with the programs Gabedit  49  and Molden. 50 he labelling convention for the electronic states is based on their energetic ordering (S 0 , S 1 ,. ; T 0 , T 1 ,. ), where 0 denotes the lowest energy state in each spin state (singlet, S, or triplet, T). The construction of the potential energy curves (PECs) has been done with a linear interpolation method  [51] [52] [53] [54] [55]  using the full space of nonredundant internal coordinates, which are built as follows.
Acknowledgements This work has been supported by projects  UMA18-FEDER-JA-049  and  P18-RT-4592  of  Junta de Andalucı ´a  and  FEDER  founds. The authors thank  R. Larrosa ,  D. Guerrero  and  F. Moreno  for the technical support in running the calculations and the  SCBI (Supercomputer and Bioinformatics) of the Univ. Malaga  for computer and software resources.
H S is contextual, whereas H C is not! At this point an interesting question arises: Can the two embeddings be ascribed some physical distinction? To answer this question (in affirmative), we ran several different experiments on W(5, 2), H ′ C s, H ′ S s and their complements. By the complement, G , of a configuration G ⊂ W(2N -1, 2) we mean the set of all line-contexts of W(2N -1, 2) that are not in G. We tested by computer the contextual nature of all H C , H S , H C , H S of W(5, 2) and the results of our analysis are summarized in Table  1. Our calculations were performed with the software Magma and the computation resources of the supercomputer of the Mésocentre de calcul de Franche-Comté. All our codes and results are available on the Quant-Cert GitHub page (https:// quant cert. github.
Acknowledgements This work was supported by the  Conseil Régional de Bourgogne Franche-Comté , mobility Grant GeoQuant, the  Thomas Jefferson Fundation  and by the  Slovak VEGA Grant Agency , Project #  2/0004/20. Part of this work was done during a visit of HdB and a one-year stay of FH at the  Mathematics and Statistics Department of Auburn University. Both authors wish to acknowledge the people of the department that made our work here possible, in particular  Dr. Luke Oeding  for his precious help and friendship as well as  Drs. Gaetan Bakalli  and  Mucyo Karemera  for their hospitality and enthusiastic discussions about mathematics and life. The authors would also like to thank the reviewers for their valuable comments on quantum contextuality that helped to improve the quality of our work.
Acknowledgements P. H. is grateful to the  French Ministry of Higher Education, Research and Innovation  for a PhD fellowship. The authors thank the  CNRS  and the  University of Strasbourg  for financial support. M. D. is grateful to the  French National Agency of Research (ANR)  for the grant allocated to this project ( C-Sil ,  ANR-CE07-19-0016 ). Dr. Trevor A. Hamlin  ( Free Uni. of Amsterdam ) is thanked for fruitful discussions. Dr. Emeric Wasielewski  ( Uni. Strasbourg ) is acknowledged for helpful discussions on NMR experiments. We thank  Dr. Lydia Karmazin  ( Uni. Strasbourg ) for X-ray analyses. V. G. thanks the  UPSaclay, CNRS and Ecole polytechnique  for financial support of this work. This work was granted access to the HPC resources of CINES under the allocation 2020-A0070810977 made by  GENCI.
Partial least square regression (PLSR) is a reference statistical model in chemometrics. In agronomy, it is used to predict components (response variables y) of chemical composition of vegetal materials from spectral near infrared (NIR) data X collected from spectrometers. PLSR reduces the dimension of the spectral data X by defining vectors that are then used as latent variables (LVs) in a multiple linear model. One difficulty is to determine the relevant dimensionality (number of LVs) for the given data. This step can be very time consuming when many datasets have to be processed and/or the datasets are frequently updated. The paper focuses on an alternative, bypassing the determination of the PLSR dimensionality and allowing for automatizing the predictions. The strategy uses ensemble learning methods, such as averaging or stacking the predictions of a set of PLSR models with different dimensionalities.
Introduction Near-infrared spectroscopy (NIRS) is a fast and a nondestructive analytical method based on the physical and the chemical properties of organic products. It is used in many agronomic contexts, particularly to evaluate the nutritive quality of forages. Basically, spectral data X (matrix of n observations × p wavelengths) are collected on samples of the material to study (e. g. , forages) using a spectrometer, and targeted response variables Y = {y 1 ,. , y k } (k vectors of n observations, e. g. , chemical compositions) are measured in a laboratory. For each response variable, a regression model is built between the training data X and y and then used to predict the response variable for new collected spectra. NIRS generate highly correlated variables, then ill-conditioned matrices X.
Therefore, for predictions, the usual multiple linear regression model (MLR) is generally not applicable. Partial least squares regression (PLSR)  [1] [2] [3]  is a regularization method very efficient for NIRS data in particular in agronomic contexts  [4] [5] [6]. The general principle is to reduce the dimension of X to a limited number a << p of orthogonal n × 1 vectors, referred to as scores, computed to maximize their squared covariance with y. The a scores are finally used as regressor latent variables (LVs) in an MLR. The determination of the dimensionality a (number of LVs) relevant for the available data is an important step in PLSR modeling. Many strategies have been addressed in the literature for guiding such a determination  [7] [8] [9]. All of these strategies often require decisions based on expertise.
In general, some prediction error rates measuring the model performance are estimated for the different dimensionalities a = 0, 1, 2, etc. , LVs (for instance by cross-validation; CV) and the dimensionality showing the minimum error rate are selected. For data collected on heterogeneous biological material such as forages, however, it is frequent that the error curve does not have a "U-shape" with a clear minimum, in particular when the sample size of the training dataset becomes large (n > 500 observations). In such a context, the determination of a can become very time consuming in practice, in particular when many datasets (different types of forages and chemical compositions) have to be processed and/or when the datasets are periodically updated with new reference observations (spectra plus laboratory chemical composition).
This last case implies many times re-running the overall process of determining relevant dimensionalities a. An alternative strategy is to automatize the PLSR predictions, bypassing the determination of a. An approach for such automatization, which is presented in this paper, uses ensemble learning methods that average or "stack" the predictions of a set of PLSR models with different dimensionalities a. Some methods of model averaging have already been implemented for PLSR in the past  [10, 11]. Nevertheless, their performances have not been explored on real datasets of forages. Forage datasets generally contain complex intrinsic material (mixing of stems, leaves, different stages of development, and geographical areas, etc. ) and therefore information. The objective of this paper is to present different averaging and stacking methods, and to compare their performances for a large panel of forage datasets to the usual PLSR (i.
e. , where an optimal number a of LVs is determined from the examination of an estimate of the prediction error rate). Six spectral datasets X, each collected on a different type of forage, and nine response variables y (each representing a component of the chemical composition) were considered. The methods of averaging and stacking evaluated in this paper were implemented with the same a priori (i. e. , without any preliminary model optimization) for all the datasets {X, y}. This corresponds to an "omnibus" strategy (i. e. , a same model and parameterization are applied everywhere), well suited and easy to apply when many datasets of spectra and response variables have to be processed.
The first method (AVG) assumes simply a uniform importance for each model, i. e. , w r = 1/(A + 1). The three next methods (referred to as AVG-CV, AVG-AIC, and AVG-BIC, respectively) are detailed in Section 2. 2. 3. All assume that weight w r decreases when the performance of prediction of the model decreases. Assume that d r is a prediction error rate estimated on the training data {X, y} for the PLSR model with r LVs. In the three methods, pattern w is computed from the rates {d 0 , d 1 ,. , d A } given as input data in a bi-square weighting function  [13]. Examples of bi-square function curves are given in Figure  1. The principle is as follows. Let us note d r the error rate normalized to an upper limit d up that represents the value above which the model with r LVs is removed from the average displayed in Equation (2): • d r = d r /d up if d r < d up • d r = 1 if d r ≥ d up (this case implies a null weight).
• AVG-CV: For the PLSR model with r LVs, the error rate dr is th error of predictions (RMSEP) estimated on the training data {X fold (K = 5) CV (RMSEPCV). The K-fold CV was repeated ten ti puted by the average of the ten RMSEPCV estimates; • AVG-AIC: dr is the Akaike information criterion  [15, 16] : AIC = l Finally, the fifth method of computing w (AVG-SHENK) was proposed by Shenk et al. [14]  for their local (i. e. , k-nearest-neighbors based method) PLSR algorithm referred to as "LOCAL". For each new observation x new to predict and the PLSR model with r LVs, the weight w r is defined by the product between the root mean squared x-residuals for x (i. e. , the residuals between x new and its projection to the model PLS space) and the norm of the b-coefficients vector. As before, the final weights are normalized to sum to 1, such as in Equation (3).
• AVG-CV: For the PLSR model with r LVs, the error rate d r is the root mean squared error of predictions (RMSEP) estimated on the training data {X, y} from a random K-fold (K = 5) CV (RMSEP CV ). The K-fold CV was repeated ten times and d r was computed by the average of the ten RMSEP CV estimates; • AVG-AIC: d r is the Akaike information criterion  [15, 16] : AIC = log(SSR) + 2 df, where SSR is the sum of the squared residuals computed on the training data {X, y} and df the complexity (or "effective" dimension or number of degrees of freedom) of the model. The AIC penalty "2 df " increases when the complexity of the model increases (in contrary to SSR) and counter-balances the optimism of SSR to measure the performance of the model for predicting new observations. When several models are compared (i.
Datasets and Software The study datasets are presented in Table  1. The data were collected from forages of tropical areas (TROP1 and TROP2), France (LUS1-2 and THEIX), and Belgium (WAL) and from various species (grasses, legumes, sorghum, mixtures) and various types of vegetal materials (stems, leaves, green, and preserved forages, etc. ). All the biological samples collected on the field were dried and grounded, and the absorbance spectra X were collected on Foss NIR Systems Instruments 4500, 5000 or 6500 models. The spectral range 1100 nm to 2498 nm (2 nm step) (Figure  2 ) was used, except for dataset WAL for which the range was 1300 nm to 2398 nm (2 nm step). Nine components of the chemical compositions y (Table  2 ) were pling sizes available for the models ranged from n = 797 observations t tions, depending on the datasets {X, y} (Table  3 ).
Only three dataset WAL) contained less than 1000 observations. Before fitting the models, the spectra were pre-processed by a sta ate (SNV) transformation, followed by a Savitzky-Golay 2nd derivat order 2 and window of 11 spectral points). This pre-processing was forage data  [21, 26] , even if not always optimal. Other pre-processing m been used but comparing preprocessing was beyond the objective of t illustrates the variability (clustering) between the six spectral datasets All the computations (spectra pre-processing and PLSR model c implemented with the package Jchemo  [27]  written in the free languag  Nine components of the chemical compositions y (Table  2 ) were studied. The sampling sizes available for the models ranged from n = 797 observations to n = 5694 observations, depending on the datasets {X, y} (Table  3 ).
Only three datasets (all coming from WAL) contained less than 1000 observations. Before fitting the models, the spectra were pre-processed by a standard normal variate (SNV) transformation, followed by a Savitzky-Golay 2nd derivation (polynomial of order 2 and window of 11 spectral points). This pre-processing was efficient to predict forage data  [21, 26] , even if not always optimal. Other pre-processing methods could have been used but comparing preprocessing was beyond the objective of this paper. Figure  3  illustrates the variability (clustering) between the six spectral datasets. Pepsine-cellulase organic matter digestibility  [31]  1 Dry matter; 2 Organic matter.
Overall Approach to Evaluate the Models The method of evaluation of the performance of the models was identical for all the datasets. Let us consider a given dataset {X, y} of sample size n. We randomly split the dataset into two parts: The split of {X, y} between {X train , y train } and {X test , y test } was randomly repeated 100 times to consider, in the results, the sampling variability. The final performance was measured by an average (over the 100 above repetitions) relative error rate. This average relative error rate was defined by the ratio of the mean RMSEP test (over the 100 replications) to the mean of the response y. This standardization by the mean (as for a coefficient of variation) allowed for summarizing the results of the nine variables together. Agronomic data, such as forages, have large intrinsic variability due to the heterogeneity of their biological material.