dataesr/scientific-paragraphs-categorization huggingface dataset:
Marine DMS emissions The flux of DMS to the atmosphere has been assessed by several authors, but the resulting datasets are not readily available. However, a recent study from  Granier et al. (2019) , as part of the European Copernicus Atmosphere Service (CAMS) project, provides a climatology of DMS flux (here- after referred to as CAMS19). We used the latest version (3. 1) of this dataset. This climatology is computed using the DMS sea surface concentration from L11, the gas exchange coefficient of  Nightingale et al. (2000)  (with the quadratic formulation of the Schmidt number as a function of the temperature from Wanninkhof (2014); M. Gauss, personal communication), and wind fields from ERA5 reanalysis over the period 2000-2019 (at 0. 5 • and 3 h resolutions). The calculated flux also accounts for the sea-ice cover, which is usually assumed to linearly reduce the DMS emission.
Annual mean emission DMS flux into the atmosphere is presented in Fig. 6  as 2D annual mean fields, in Fig. 7  as yearly emissions per 10 • latitude bands, and in Fig. 8    period. The reference dataset added in the analysis here is the CAMS19 climatology described in Sect. 2. 2. 2. The flux of DMS features spatial patterns and seasonal cycles that stem from both the surface ocean concentration and the wind speed. To help understand how these main drivers impact the resulting flux, the maps of annual wind speed and the zonal monthly wind speed are shown in the Supplement (Fig. S5 ). Overall, the maps of annual mean flux show a large spatial variation, which mirror in part the patterns of annual mean concentration (see Fig. 1 ), with clear imprints from annual wind patterns (see Fig. S5 ). For instance, higher westerly winds and weaker trade winds have a visible impact on the annual flux, both in models and climatology.
Comparison with other studies To conclude this section, Table  6  summarises global mean emissions of the four CMIP6 models along with several estimates from other studies for the modern period. Figure  9  also provides a convenient way to compare models at a glance regarding their annual global mean concentration and emission. This table does not include previous estimates of ) for the same models and datasets as in Fig. 6. the flux calculated with the parameterisation of  Wanninkhof (1992)  since it has been revisited by the author, and the updated parameterisation of Wanninkhof (  2014 ) leads to significantly lower exchange coefficients (Sect. 3. 2. 1). Because of the weakest dependence on wind speed in the parameterisation of  Liss and Merlivat (1986) , UKESM1-0-LL has the lowest mean emission of 16.
Conclusions In this study, we analyse surface ocean DMS concentration and flux into the atmosphere from four CMIP6 ESMs (CNRM-ESM2-1, MIROC-ES2L, NorESM2-LM, and UKESM1-0-LL) over the historical and ssp585 simulations. The parameterisations of DMS in these ESMs have various degrees of complexity, and while they may have already been evaluated, either in a previous (e. g. Le  Clainche et al. , 2010)  or in their current version, it is the first time that this is done in a common coupled atmosphere-ocean simulation framework. Our study also provides an evaluation of the performance of the current generation of ESMs against the most up-to-date observational products, both in terms of mean state and of current and future trends. Our analysis of contemporary  climatologies of simulated surface DMS concentration shows that, overall, agreement is poor between models and also between models and reference datasets, such as the L11 dataset.
This could in part explain the unanimous low bias of the CMIP6 models when compared to L11. Models show a better agreement with observation-based estimates when compared to W20. The range of model global annual median DMS concentrations (1. 39-1. 90 nM) encompasses the W20 median (1. 65 nM), whereas that of L11 is 2. 25 nM. Our work also shows that models have better spatial correlation with W20 as a reference dataset (coefficients from 0. 13 to 0. 46 for annual fields) than with L11 as the reference (coefficients from 0. 08 to 0. 26). Analysis of the annual cycles in each of the 54 biogeographical provinces defined by  Longhurst (2007)  reveals that models better reproduce the annual cycles in mid to high latitudes (polar and westerlies biomes) than in low latitudes (trades biomes), in agreement with past studies (e.
A1. 2 Arctic analysis In the study of  Galí et al. (2019) , the mean DMS concentration and flux is computed on ice-free pixels only, since both are derived from satellite observations. In order to provide comparable results, we also computed the mean over icefree pixels only (with the same criterion as  Galí et al. (2019)  of > 90 % free water) along with the regular area-weighted mean. We used monthly sea-ice concentration datasets from each model to compute the means over ice-free pixels. We paid special attention to the calculation of the mean, which is thus done on 3D arrays (2D in space and 4 months per year) with missing data in pixels where the sea-ice cover exceeds the chosen threshold. The mean is calculated in a single step using a weighting that combines pixel area and available months duration (if any).
Acknowledgements. We gratefully acknowledge  Martí Galí ,  Nadja Steiner , and an anonymous reviewer for their comments that helped to improve and clarify this paper. Josué Bock  thanks  Martí Galí  for his help in using his climatology of  DMS  and for providing the map of Arctic regions. Josué Bock  thanks  Wei-Lei Wang  for his help in using his climatology of DMS. Josué Bock  thanks  Yanchun He  and  Mats Bentsen  for their advise in using NorESM2-LM datasets. The MIROC-team acknowledge  JAMSTEC  for use of the Earth Simulator supercomputer. Supercomputing time was provided by the  Météo-France/DSI  supercomputing center. Financial support. This work was supported by the  European Union 's  Horizon 2020 research and innovation program  with the  CRESCENDO  project under the grant agreement no.
641816 , the  TRIATLAS  project under the grant agreement no. 817578. Jerry Tjiputra  and  Jörg Schwinger  acknowledge  Research Council of Norway  funded projects KeyClim (295046) and  Columbia  ( 275268 ). Simulations of MIROC-ES2L are supported by the  TOUGOU  project " Integrated Research Program for Advancing Climate Models " (grant number:  JPMXD0717935715 ) of the  Ministry of Education, Culture, Sports, Science, and Technology of Japan (MEXT). JPM was supported by the  Met Office Hadley Centre Climate Programme  funded by  BEIS and Defra  (grant no. GA01101 ). RS acknowledges the European Union's  Horizon 2020 research and innovation programme  under grant agreement no. 101003536  ( ESM2025 -Earth System Models  for the Future). Review statement. This paper was edited by  Alexey V.
The wide use of cold-formed sections (CFS) in the field of steel constructions, favored by the multiple advantages they offer (lightness, ease of installation, etc. ), has led us to reflect on a new process for manufacture of metal beams allowing the design of very large span hangars and a reduction in instability problems. This paper presents a study of the theoretical and numerical behavior of a large span CFS beam with different webs, a solid web, a triangular corrugated web, and a trapezoidal corrugated web. These beams are stressed by a concentrated bending load at mid-span. Numerical modeling was done using the finite element software ABAQUS. The numerical results have been validated by the analytical results those obtained based on Eurocode 3. The load capacity and failure modes of the beams were discussed.
Early measurements of the HI rotation curves of gas-rich dwarf galaxies highlighted, for the first time, a large discrepancy between the observed rotation velocities and those predicted by ΛCDM simulations, especially in the inner parts  [18] [19] [20]. The DM density profile of dIrrs can be inferred by measuring the rotation of either the gas with HI or using the stellar Hα emission line. The rotation curve is derived from the observed line-of-sight velocity at any position in the galaxy velocity field. After the data analysis, the central DM distributions in these DM-dominated galaxies were found to be inconsistent with the 1/r behavior of cuspy profiles and indicate the presence of a constant-density core. These latter implies ρ(r) ∝ r -α with α = 0 in the inner regions. This discrepancy between observations and DM-only simulations led to the original small-scale problem, which has now become known as the cusp-core problem  [18, 19].
FIG. 5. Evolution of the core mass, defined as the dark matter mass within dB/4 from the center, where dB is the de Broglie wavelength corresponding to vsol. The lines show the Gaussian filtered data points with z = 0. 2. The shaded regions represent the corresponding standard deviations. compare the virial velocity of the simulated cores with the local dark matter velocity dispersion in their environment in Fig. 4  (see also Appendix C). Our simulations indeed verify that the baryonic gravitational potential gives rise to a radially stratified velocity distribution and confirm that the velocity dispersion of the soliton (and thus its virial temperature) closely follows the temperature of its immediate surrounding. In all runs with baryons, the central velocity dispersion di↵ers by up to a factor of two from the velocity dispersion at x vir /2, whereas in the dark matter only runs, the velocity dispersion in the center and at the outer radius are similar.
ACKNOWLEDGMENTS We thank the anonymous referee for helpful comments and suggestions that improved our work. We would like to thank  Dante Von Einzbern ,  Apolline Guillot  and  Georges Boole  for their constructive suggestions to improve the manuscript. YM is supported Acknowledgements I thank the three reviewers for their constructive feedback which helped to improve the quality of the manuscript. I thank  Joseph Silk  for useful comments and suggestions. I also thank  Eduardo Vitral  for illuminating discussions about Gaia data.
We continue earlier efforts in computing the dimensions of tangent space cohomologies of Calabi-Yau manifolds using deep learning. In this paper, we consider the dataset of all Calabi-Yau four-folds constructed as complete intersections in products of projective spaces. Employing neural networks inspired by state-of-the-art computer vision architectures, we improve earlier benchmarks and demonstrate that all four non-trivial Hodge numbers can be learned at the same time using a multi-task architecture. With 30 % (80 %) training ratio, we reach an accuracy of 100 % for h (1,1) and 97 % for h (2,1) (100 % for both), 81 % (96 %) for h (3,1) , and 49 % (83 %) for h (2,2). Assuming that the Euler number is known, as it is easy to compute, and taking into account the linear constraint arising from index computations, we get 100 % total accuracy.
An important key component in realistic string theory compactifications are Calabi-Yau manifolds. These manifolds have been studied extensively in the past, and thus they comprise some of the best datasets within the string theory community  [7] : 1. The first widely used dataset are the 7890 complete intersection Calabi-Yau, in short CICY, manifolds in three complex dimensions by Candelas et al. [8] [9] [10]. 2. The largest dataset, the Kreuzer-Skarke list, contains 473 million reflexive polytopes in four dimensions. These encode a toric ambient space, from which one obtains Calabi-Yau three-folds by considering the hypersurface defined by the canonical bundle  [11]. 3. CICY four-folds have also been classified and amount to 921 497 distinct configuration matrices  [12, 13]. The incredible progress in data science, in particular image recognition, over the past decade can in part be attributed to large and clean datasets  [14].
They for example determine the number of massless fermion generations in string theory compactifications. Thus, the goal is to identify performant algorithms in these wellstudied datasets of tangent bundle cohomologies, which can then generalize to more complicated vector bundles. In the rest of this paper, we will present two different approaches for learning Hodge numbers of CICY four-folds. First, we will treat the problem as a standard image classification task where the Hodge numbers are the image labels. For this purpose, we employ an Inception module based architecture  [16-18, 21, 22]  and show that a single set of hyperparameters generalizes well to all four Hodge numbers, yielding a mean accuracy over all Hodge numbers of 85 %. This suggests that we could scale the approach to a multi-task learning problem.
Subsequently, we show that all Hodge numbers can be learned simultaneously by utilizing a branched network with hard parameter sharing  [23, 24]  between the task specific substructures, which ultimately are responsible for learning the distributions of the Hodge numbers. The multi-task approach has several advantages, with respect to single-task architectures. From a technical side, multi-task learning has been shown to improve the overall performance of the models  [23]. From a physics and algebraic geometry perspective, a single model hints towards the definition of a unified framework from which it may be possible to extract meaningful theoretical information, such as closed form formulas. The model we developed is capable of learning at the same time, and without rescaling, the four dimensions of the tangent space cohomologies of CICYs, accounting for the heavy class imbalance present in the dataset.
This multi-task Ansatz leads to perfect performance on two of the four Hodge numbers and accuracy of 96 % and 83 % for h (3,1) and h (2,2) respectively, with a training ratio of 80 %. The outline of this paper is as follows. In Section 2, we discuss related works of learning cohomologies and earlier results on Calabi-Yau threefolds. Section 3 explores the dataset of CICY four-folds and presents the results of our classification experiments. This is followed by our main results in Section 4 in which we introduce our deep learning model CICYMiner, a multitask regression model based on chained Inception modules that predicts all four Hodge numbers at once. We conclude in Section 5 with some outlooks. Python codes for this paper can be found at: • https://github. com/robin-schneider/ cicy-fourfolds • https://github.
Related works The first paper utilizing machine learning algorithm to predict various different cohomology dimensions was written by He  [20]. The author tackled the problem of predicting Hodge numbers of CICY three-and four-folds, but also line bundles over these manifolds  [20]. These studies have later been extended to systematically investigate CICY three-folds with linear regression, support vector machines, and dense neural networks achieving accuracies ranging from 37 % to 85 %  [31, 32]  when using 70 % training data. The benchmarks have subsequently been improved by using an Inception-based architecture to accurately predict 97 % of the test data using only 30 % training data, essentially solving the problem of predicting h (1,1)   [21, 22]. This work was supplemented by more methodological studies in which the dataset was augmented with various other (topological) quantities.
Other works on CICY three-folds include  [33, 34]. An initial exploration of CICY four-folds has been started by He and Lukas  [20, 35]. The authors used a simple dense neural network and were able to predict h (1,1) with an accuracy of 96 %. This promising early result showed that the increased size of the dataset improves the performance significantly. However, in line with previous studies of h (2,1) on CICY three-folds, the authors were unable to accurately predict the value of the other Hodge numbers, reaching an accuracy of only 27 % for h (3,1). They were successful in improving this accuracy for a subset of the dataset by considering all configuration matrices of shape (4, 4) and using feature enhancement. This feat was achieved by supplementing the training samples with all up to degree four monomials of the defining polynomials and pushed the accuracy to 95 %.
(3. 5) Notice that the distributions of the Hodge numbers are, in general, imbalanced: for instance, h (2,1) vanishes for 70 % of the configuration matrices in the dataset. We find that 54. 5 % are favourable (i. e. h (1,1) is equal to the number of projective spaces), less than the 61. 9 % for CICY three-folds. 1  Hence, for slightly more than half of the cases we have h (1,1) = r, the number of projective ambient space factors. This number is important as it should be the baseline to compare any algorithm against.
Classifying Hodge numbers Problems in image recognition are usually formulated as classification tasks. Take the ImageNet dataset which consists of 14 × 10 6 data points with over 21 000 classes. That is about one order of magnitude larger, both in samples and classes, than predicting h (2,2). In this section, we will train one neural network to classify each of the four non-trivial Hodge numbers independently. We will use an architecture based on Inception modules  [16] [17] [18]  as was done for the best performing predictors of the CICY three-fold Hodge numbers  [21, 22]. This specific architecture has been shown to lead to the best performance on the input feature H W F kernel W x 1 x F kernel 1 x H x F W W H H F' F' C H W 2 F' H W 2 F' BN output feature.
These ambient space representations arise after splitting up the Koszul resolution 0 → ∧ K N * →. → N * → O A → O A | M → 0. (3. 6) which contains the antisymmetric products ∧ s N * of the defining hypersurfaces (N denotes the normal bundle, which contains the information about the polynomial degrees p i j ). Moreover, using an Inception based architecture lead to a performance increase of misclassification rate on the Im-ageNet dataset from 15. 3 % for AlexNet  [15]  using a standard convolutional architecture to 6. 7 % for the first version of GoogLeNet  [16]. We proceed as in earlier studies  [21, 22]  by considering different train:val:test splits with respectively 10 %, 30 %, 50 % and 80 % training and 10 % validation data. The architecture hyperparameters have been optimized using Bayesian Optimization Hyperband  [44, 45]  on the problem of predicting h (3,1).
Preprocessing and Evaluation Strategy We use the same dataset presented for the classification objective in the previous section. Given the strong class imbalance, we select the training set by using a stratified approach on h (2,1) in order to preserve the distribution of the samples. The validation set is then chosen totally at random, using 10 % of the samples. The remaining samples form the test set. We preprocess the input data by simply rescaling the entries of the configuration matrices in the training set to the interval [0, 1]. Matrices in the validation and test sets are rescaled accordingly, using the statistics obtained from the training set. The outputs of CICYMiner are, in fact, floating point numbers h(i, j) ∈ R + , as it is typical in regression tasks. They ultimately need to be rounded to integers to be directly compared with the true values and to compute the accuracy.
Ablation study CICYMiner introduces new elements, with respect to previous attempts at predicting Hodge numbers of CICYs  [21, 35] , namely: 1. Huber loss for robustness;   2. auxiliary branches. In this section, we separately analyse each new aspect, together with other variations of the architecture. Specifically, we analyse the impact of the batch normalization used in the Inception modules. We also address the use of attention mechanisms  [53] , used in the DeepMiner model, which in our case did not lead to an improvement in accuracy, but rather to a faster training. We proceed by modifying the backbone structure of CICYMiner. We first introduce the attention mechanism used in  [48]  for comparison. The Spatial Attention Module (SAM) and CHannel Attention Module (CHAM) are presented in Figure  6 : the full attention mechanism is the composition CHAM • SAM used between each Inception module in the main branch of the task-specific architecture in Figure  4.
As their role is to mine a richer variety of features to stabilise the shared representation, and learn better approximations of the output, the accuracy drops significantly in the case of highly imbalanced distributions. The largest drop impacts h (2,1) which suffers from predictions shifting towards zero. This shows that we indeed need a mechanism to get as much training information as possible through the addition of transformations and auxiliary branches, as in the CICYMiner. Finally, we analyse the impact of the attention modules: we insert such additional layers to improve the predictions of h (3,1) and h (2,2) only, as other Hodge numbers do not need additional transformations. The results do not strongly differ from the case without the attention modules, though h (2,2) drops by 2 % in accuracy.
Conclusion In this paper, we were able to show that Inception-based neural networks achieve good accuracy in predicting h (3,1) and h (2,2) and can reach perfect accuracy for the Hodge numbers h (1,1) , h (2,1). Earlier studies using dense architectures were only able to work accurately with h (1,1)   [35]. Moreover, we showed that only a fraction of the training data is needed to already obtain promising results. This stands in contrast to earlier studies on CICY three-folds for which it was not possible to accurately predict h (2,1) (the only remaining non-trivial Hodge number in that case). The significant increase in dataset size is responsible for a good part of the increase in performance: the risk of overfitting is strongly reduced and generalization over all configuration matrices is more robust.
In fact, recent research suggests that neural networks often admit power-scaling laws with dataset size and model parameters  [57]. It can also be noted that increasing the capacity of the model may be beneficial to the overall performance  [58]. However, the geometric and physical interpretability might then become quite complicated and involved, hence the suggestion to constrain the complexity of the CICYMiner architecture. It would be interesting to observe how far one can improve the accuracy of h (3,1) and h (2,2) by using larger networks or adding more data samples to the dataset, or even by just prolonging the training time on multiple GPUs. Additional data samples can in principle be easily generated via (in-)effective splits of the already existing configuration matrices. These redundant matrices had been discarded when compiling the initial dataset  [12].
Acknowledgements RS is funded in part by the  Swedish Research Council (VR)  under grant numbers  2016-03873 ,  2016-03503 , and  2020-03230. RS is grateful for 12 financial support from the  Liljewalch scholarship. HE is funded by the  European Union 's  Horizon 2020 research and innovation program  under the  Marie Skłodowska-Curie  grant agreement No  891169. HE is also supported by the  National Science Foundation  under Cooperative Agreement PHY-2019786 (The  NSF AI Institute for Artificial Intelligence and Fundamental Interactions , http://iaifi. org/). The work of RF is supported by a joint programme (PTC) between the Direction des énergies and the  Direction de la recherche tecnologique of the CEA Paris-Saclay. Computations were in part enabled by resources provided by the  Swedish National Infrastructure for Computing (SNIC)  at the HPC cluster Tetralith, partially funded by the  Swedish Research Council  through grant agreement no.