dataesr/scientific-paragraphs-categorization huggingface dataset:
E, keV Di plate Simulation 6,- I, a. u. The 2D lens was much thinner than the MUL lens; therefore, the drops of intensity, as described above, were also much smaller (Figure  8 ). As can be seen from Figure  8b  some glitches overlap, but this is not a problem for our algorithm. The reader can use the program from  [29]  to get the exact energy for each glitch. The 2D lens was much thinner than the MUL lens; therefore, the drops of intensity, as described above, were also much smaller (Figure  8 ). As can be seen from Figure  8 ,b some glitches overlap, but this is not a problem for our algorithm. The reader can use the program from  [29]  to get the exact energy for each glitch. At the magnified spectra of the diamond plate (Figure  9b ), one can see a not-predicted glitch at E = 16. 95 keV.
Conclusions The glitches of the intensity of X-ray beam passing through an optical element made of a single-crystal are a big problem for different experiments with X-rays. Mostly affected are the spectroscopic measurements where a big range of energies has to be scanned. However, any other experiment might be affected as well-especially at high energies, where the probability to "spot a glitch" is higher. Therefore, the possibility of precise modeling of glitches in any crystalline optical elements in arbitrary configuration is crucial. We have developed an algorithm for the precise determination of the crystallographic orientation of any X-ray optical element made of a single-crystal material, with respect to the beam. This algorithm was applied to experimental data measured at the BM31 beamline of ESRF, France.
Acknowledgments: We gratefully thank the experimental team:  Maxim Polikarpov  from the  Molecular Biology Laboratory (Hamburg, Germany ),  Qiuyuan Zhang  and  Helge B. Larsen  from the  Department of Mathematics and Physics, University of Stavanger (Stavanger, Norway) ,  Ragnvald Mathiesen  from the  Department of Physics, Norwegian University of Science and Technology, (Trondheim, Norway) ,  Hermann Emerich  from the  European Synchrotron Radiation Facility  ( ESRF ) for their contribution.
Simulation results The computational strategy presented above has been implemented in the FE Z-set software. The relevance of this approach has been evaluated in references  [3, 2, 8]  with 2D and 3D simulations of droplet spreading and capillary rise. Among other results, the contact angle provided by the simulations is equal to that of the Young -Laplace equation, as expected, at least as long as no dissipation is considered at the triple junction (see  [2] ). This work presents simulations of capillary rise into two different microstructures, and sketches first calculations of capillary pressure. The two structures are: a hexagonal arrangement of circular (half-)fibers disposed in staggered rows (structure 1) with a fiber volume ratio V f of 52%; a random microstructure (structure 2) made up of identical circular fibers with V f = 48%  [9].
We expect that training our model on the physics-only SOSE would produce similar results, although we did not attempt that here. In principle, our methods can be readily applied to any gridded temperature and salinity profile dataset. It may be possible to apply these methods to in situ data as well, if the user addresses the problem of non-uniform spatial and temporal sampling. In this paper, we focus only on applications to gridded datasets. To construct a state estimate, researchers bring a numerical simulation into better consistency with an observational dataset using the 4D-Var method. This method uses adjoint sensitivities to calculate the required changes in the "controls" (e. g. initial conditions, mixing parameters, boundary conditions) needed to improve the agreement between the simulation and the observational dataset  (Stammer et al.
, 2002; Wunsch and Heimbach, 2007). The B-SOSE domain extends from the Equator to 78 • S, but we only use data south of 30 • S to focus on the Southern Ocean and to avoid the model boundary. It uses bathymetry and coastline based on  Amante and Eakins (2009). B-SOSE solves the heat, salt, and momentum equations using a third- order direct space and time advection scheme with a 1 h time step. The time-evolving atmospheric boundary conditions use bulk formulae to solve for fluxes of heat, freshwater, and momentum, with 6-hourly atmospheric state variables as inputs  (Large and Yeager, 2009; Dee et al. , 2011). The state estimation process iteratively adjusts the atmospheric state variables and oceanic initial conditions to improve modeldata agreement. B-SOSE uses dynamic sea ice  (Losch et al.
Principal component analysis Each vertical profile in the full B-SOSE dataset is comprised of temperature and salinity values at multiple depth levels, at every grid cell and every output month. Values close to each other in the water column are correlated to some degree. Therefore, we do not necessarily need values of potential temperature (θ ) and salinity (S) at every depth level to capture most of the variability, and reducing the dimensionality of the data can improve the convergence of the training process. One specific dimension reduction technique is prin-cipal component analysis (PCA), which identifies the functions that capture most of the variability with depth in the dataset. The result is a representation of the dataset as a linear combination of eigenfunctions (i. e. principal components), sometimes called a principal component expansion or principal component decomposition.
Using this procedure, we can describe each profile using a small set of eigenvalues (i. e. coefficients of the principal component expansion) instead of a full set of temperature and salinity values. In addition to improving the speed and efficiency of the GMM algorithm, PCA reveals potential physical structures that may be useful for understanding the stratification of the SO  (Pauthenet et al. , 2017). We choose the number of principal components such that the percentage of variability explained (in a statistical sense) by the PCA expansion is sufficiently high for our purposes. Following Rosso et al. (  2020 ), we only keep values between 300 and 2000 m to exclude most of the surface seasonal variability from the dataset. Because the data are spaced on an irregular grid in the vertical direction, we first interpolate the temperature and salinity profiles onto a regular grid with 10 m cells in the vertical.
Following  Pauthenet et al. (2017) , at each grid cell and time we concatenate the temperature and salinity profiles into a single vector. We normalise each depth level for both temperature and salinity separately: subtracting the mean and dividing by the standard deviation calculated for all time periods on that particular depth level and variable. That is, we standardise the temperature values at each level using the distribution of temperatures at that same depth level, and we standardise the salinity values using the distribution of salinities at that same depth level. This is a slightly different approach from  Pauthenet et al. (2017) , in which the authors standardise across the entire dataset. We found that, for the work shown in this paper, the choice of normalisation approach does not make a large difference in the results (not shown).
After normalisation, we carry out PCA expansion. We keep the first three principal components (PCs), which together statistically explain 98 % of the variability across the thermohaline dataset. For completeness, we show the structure of the principal components in Appendix B. The coefficients associated with PC1 indicate a broad division between polar, high-latitude Southern Ocean waters and the subtropics (Fig. 1a ). The most negative PC1 coefficients are found in the Weddell Gyre, and we also see the imprints of the South Pacific Gyre and the ACC  (Vernet et al. , 2019). The coefficients of PC2 bear the imprint of the ACC and of its northward flow along the eastern Pacific Basin (Fig. 1b ). This northward flow is associated with the formation and export of Subantarctic Mode Water and Antarctic Intermediate Water  (Iudicone et al.
Gaussian mixture modelling Unsupervised classification attempts to identify subpopulations within a data distribution, without the assistance of any predefined labels. In our application, we attempt to identify data subpopulations in the abstract three-dimensional space defined by the PC coefficients (i. e. the "feature space"). Here, we use GMM, an algorithm that attempts to fit a set of multidimensional Gaussian functions to the data by iteratively adjusting the means and covariances of the Gaussians  (McLachlan and Basford, 1988 ; see Appendix C for more detail). This method has recently been used to classify Argo temperature profiles in the top 2 km of the North Atlantic Ocean and the Southern Ocean  (Maze et al. , 2017; Jones et al. , 2019). GMM is well-suited to ocean applications because it offers a probabilistic measure of classification in the form of posterior probabilities, which is useful when working with a highly correlated dataset.
We model the dataset, in the statistical sense of representing the dataset using a probability distribution, as a weighted sum of Gaussians: P(x) ≈ K k=1 λ k N x ; µ k , k , (2) where λ k is the weight associated with the kth Gaussian. The process of fitting the GMM uses expectation maximisation (EM), which consists of iteratively adjusting λ k , µ k , and k to decrease the model-data misfit. For additional details, see Appendix C. Once the weights, means, and covariances are fitted, each data vector x is associated with a posterior probability distribution across all of the K classes. Although we kept the random seed used in the initial guess fixed for this paper, our results are robust to the choice of random seed (not shown). This distribution is the set of likelihoods that the data vector belongs to any particular class, and the probabilities sum to one.
An edge detection approach towards identifying fronts For comparison with the GMM method, which uses properties of an entire training dataset to detect changes in thermohaline structure, we use a more local front detection method implemented by  Hjelmervik and Hjelmervik (2019)  in the North Atlantic. This method, called the Sobel method, directly examines spatial gradients in the principal component fields using a Sobel operator  (Duda and Hart, 1973). To do this, the PCs of each grid point are placed onto a rectangular grid with the same spacing as the data sampling, where points without data are masked. The strength of an edge at a point is found by the two dimensional convolution (represented by G x =   1 0 -1 2 0 -2 1 0 -1   , (4) and in the y direction the Sobel operator is G y =   1 2 1 0 0 0 -1 -2 -1  .
Discussion In this section, we discuss the sensitivity of our results to our choice of dataset (Sect. 4. 1), touch on the temporal variability in our results (Sect. 4. 2), discuss a possible connection with the Antarctic Slope Current (Sect. 4. 3), examine the sensitivity of the results to the choice of the number of classes K (Sect. 4. 4), and discuss the interpretation of posterior probabilities (Sect. 4. 5).
Sensitivity to choice of dataset We chose to use B-SOSE data for this study in order to (1) work with a dataset that features relatively uniform latitude-longitude coverage and (2) to allow us to examine temporal variability as well as spatial variability. B-SOSE is an observationally constrained estimate of the hydrographic structure of the Southern Ocean, so it accurately captures many features of large-scale and mesoscale structure  (Verdy and Mazloff, 2017). However, because B-SOSE is a numerical model run, it will no doubt have some biases with respect to observations, particularly on smaller scales. We expect that our results would not change dramatically on basin-wide scales across different state estimate and reanalysis products. To examine the differences of this bias on the class structure and the structure of the inter-class comparison metric, this study could be repeated with a purely observational dataset such as Argo.
One trade-off for such a study would be the fact that observational datasets are relatively sparse in terms of both spatial and temporal coverage relative to a state estimate or other numerical model run. One could attempt to use the same GMM trained on B-SOSE with Argo data, but possible biases between B-SOSE and the Argo dataset could make this challenging. It might be possible to adjust for those biases in the data cleaning and preparation step of the analysis; the standardisation process, which is already a part of the analysis presented here, is a step towards this bias removal and correction that may facilitate comparisons between models and observations. Alternatively, one could attempt to retrain the GMM using Argo data alone. This has been done in other studies, so it should be possible in principle (e.
Sensitivity to the maximum number of classes In this study, we chose K = 5 as the number of classes based on sensitivity tests and also based on a priori knowledge. Specifically, previous studies used a front structure with five broad regions, delineated by four fronts, so we might expect a value of around K = 5 based on this (e. g. Orsi et al. , 1995; Pollard et al. , 2002; Kim and Orsi, 2014). Generally, the choice of the maximum number of classes K can be thought of as a way to select models of varying degrees of complexity. Statistical models with lower K values are potentially easier to interpret, only capturing the most dominant structures in the dataset. For example, the probabilistic boundary between the two classes in a K = 2 statistical model roughly separates colder, fresher Antarctic waters from the warmer, saltier subtropical waters (Fig.
A more complex statistical model with higher K would capture more of the subtropical structure (not shown). This is consistent with sensitivity studies using temperature-only Argo data, where increasing K added details to the subtropical class structure while leaving the circumpolar class structure largely unchanged  (Jones et al. , 2019). Statistical models with much higher K values may capture more structure in the data, but increasing K also risks overfitting. That is, if we tune the GMM statistical model to match an increasing number of structures in PC space, we risk losing generality; the goal is to represent the dominant structures of the dataset without overfitting every small variation, some of which could represent noise in the data. This has a direct analogue with overfitting in terms of simple statistical models; it is unwise to use a 10th-order polynomial when a quadratic captures the dominant features of the dataset, because the higher-order polynomial is less likely to generalise to other similar datasets.
Conclusions In this study, we proposed a new metric for defining and identifying boundaries between coherent regimes of temperature and salinity structure. Our method uses Gaussian mixture modelling, a type of unsupervised machine learning, to establish a statistical model of thermohaline structure that is intended to capture the large-scale features of the dataset in both PC space and in geographic space. We developed our method in the Southern Ocean due to the presence of circumpolar structures and relatively clear fronts, but our approach could be applied to other regions or even to the global ocean as a whole. The I -metric provides a flexible, probabilistic method to define and identify boundaries in an oceanographic dataset without using ad hoc property contours; the boundaries are derived in a generalised method that reflects the structure of the dataset.
The I -metric has potential as a method for comparing different observational and numerical modelling datasets in a robust, algorithmic way that is not heavily affected by biases in the mean state between datasets. It features a parameter K that allows users to increase and decrease the level of complexity of the statistical model; the optimal value of K will vary between applications. The Sobel edge detection method may be useful for defining and tracking smaller-scale fronts and jets in model or reanalysis data. As discussed in  Chapman et al. (2020) , the field of oceanography needs to consider fronts and boundaries in a more general, application-specific way, due in part to the richness of ocean structure on different spatial scales. The I -metric was designed with this problem in mind; it is intended to be a complementary addition to the oceanographic toolbox as opposed to a replacement for any particular method.
and A4 , where there is an especially high correlation between the two in the last couple of years of the reanalysis product. That Figs. A2  and A4  show opposite signs in the correlation is equivalent to the reversal in sign that we would expect  (Cushman-Roisin and Beckers, 2011, chap. 15 and 18). Those figures also show that the magnitude of the correlation between the respective variables increases during the first 2 years of the dataset before flattening off. This is suggestive of the model spinning up towards geostrophic balance. As the first principal component statistically explains the first-order structure in the ocean, it primarily represents the density contrast produced by the thermohaline structure from the tropics to the poles.
Figures A1 and A3 illustrate the spatial resemblance between G y * PC1 and U and between G x * PC1 and V respectively, compared over June 2011 or as an average over the full B-SOSE period. The domain-averaged correlation is shown quantitatively in Figs. A2 and A4, where there is an especially high correlation between the two in the last couple of years of the reanalysis product. That Figs. A2 and A4show opposite signs in the correlation is equivalent to the reversal in sign that we would expect (Cushman-Roisin and Beckers, 2011, chap. 15 and 18). Those figures also show that the magnitude of the correlation between the respective variables increases during the first 2 years of the dataset before flattening off. This is suggestive of the model spinning up towards geostrophic balance. As the first principal component statistically explains the first-order structure in the ocean, it primarily represents the density contrast produced by the thermohaline structure from the tropics to the poles.
Acknowledgements. This work originated as a  Natural Environment Research Council (NERC) Research Experience Placement (REP)  project funded by the  SPITFIRE Doctoral Training Partnership  (grant no. NE/S007210/1 ). Simon Thomas is supported by studentship  2413578  from the  UKRI Centre for Doctoral Training in Application of Artificial Intelligence to the study of Environmental Risks  (grant no. EP/S022961/1 ). Daniel Jones is supported by a  UKRI   Future Leaders Fellowship  (grant no. MR/T020822/1 ). Daniel Jones  and  Simon Thomas  also received funding from the  NERC   ACSIS  project (grant no. NE/N018028/1 ). Etienne Pauthenet received funding from the  European Research Council (ERC)  under the European Union's  Horizon 2020 Research and Innovation programme  (grant no. 637770 ). The authors would like to thank  Emma Boland ,  Peter Haynes ,  Guillaume Maze , and  John Taylor  for comments that improved the quality of this work.
Financial support. This research has been supported by the  Natural Environment Research Council  (grant nos. NE/S007210/1  and  NE/N018028/1 ),  UK Research and Innovation  (grant nos. MR/T020822/1  and  EP/S022961/1 ), and the  European Research Council   H2020  programme (grant no. 637770 ; WAPITI). Review statement. This paper was edited by  Katsuro Katsumata  and reviewed by three anonymous referees.
Code and data availability. B-SOSE iteration 106 state estimate data are available from the Scripps Institution of Oceanography (http://sose. ucsd. edu/BSOSE6_iter106_solution. html, Verdy and Mazloff, 2021). The MITgcm source code that was used to create B-SOSE is available on GitHub (https://github. com/ MITgcm/MITgcm/tree/checkpoint67z, last access: 16 June 2021, https://doi. org/10. 5281/zenodo. 4968496, Campin et al. , 2021). Original climatological front positions from  Kim and Orsi (2014)  are available on ResearchGate (https://www. researchgate. net/publication/338420242_ACC_fronts,  Kim, 2021). The code used to carry out the analysis and figure creation for this paper is available via Zenodo  (Thomas, 2021)  (up-to-date repository: https://github. com/so-wise/so-fronts, last access: 4 May 2021, https://doi.
org/10. 5281/zenodo. 5500666, Thomas, 2021). This software uses scikit-learn  (Pedregosa et al. , 2011)  and pyxpcm  (Maze, 2020)  as foundations. We used Cartopy for mapping (Met Office,  2010-2021). Author contributions. DCJ designed the initial project, and SDAT and DCJ developed it further. SDAT wrote the software  (Thomas, 2021) , performed the analysis, and created the figures. AF proposed a significant improvement to the inter-class metric. EM and EP provided expert guidance on fronts, Southern Ocean structure, and dynamics. SDAT and DCJ wrote the initial manuscript, and all authors assisted with edits.
Figures Figures A1 and A3 illustrate the spatial resemblance between G y * PC1 and U and between G x * PC1 and V respectively, compared over June 2011 or as an average over the full B-SOSE period. The domain-averaged correlation is shown quantitatively in Figs. A2 and A4, where there is an especially high correlation between the two in the last couple of years of the reanalysis product. That Figs. A2 and A4show opposite signs in the correlation is equivalent to the reversal in sign that we would expect (Cushman-Roisin and Beckers, 2011, chap. 15 and 18). Those figures also show that the magnitude of the correlation between the respective variables increases during the first 2 years of the dataset before flattening off. This is suggestive of the model spinning up towards geostrophic balance.
For times prior to 9 months, we have in fact not used the exact adjoint values. Instead, we extended the databases of adjoint outputs for the surface fluxes beyond the 9-month windows with two parts: (i) monthly adjoint outputs between months 9 and 24 taken from computations for the year 2017 and (ii) beyond 24 months, a globally homogeneous value (i. e. , 1 GtC emitted at the surface is translated to an average concentration of 0. 38 µmol mol -1 , or parts per million, ppm). We have verified that the CO 2 and COS concentrations obtained by the resulting Jacobian matrix (Mx) match the one produced by the full LMDz transport model over the period well (see Fig. S3 ). In total, we have computed 15 stations × 12 years × 2 weeks × 12 months adjoint computations of 8 process time hours each on a local parallel cluster.
2010 ), respectively). So, using another existing LRU dataset will likely lead to a comparable GPP sink in the high latitudes. Another simplification of our study is that the current LRU approach does not take into account the feedback between COS vegetation sink and atmospheric concentrations. The atmospheric concentrations vary on seasonal and interannual timescales but have indeed been considered constant per latitudinal band. Such a feedback might have a significant impact on the total vegetation sink (see Fig. S18 ), in particular over the Amazon. Thus, refining our inverse system would require including the feedback between the atmospheric concentrations and the COS vegetation sink (first-order approach). This will involve representing the sharp drop of COS between the canopy and the boundary layer, which can reach 70 ppt in redwood forests  (Campbell et al.