dataesr/scientific-paragraphs-categorization huggingface dataset:
In condensed media, such as liquid water, it is known that the stopping power values are smaller than in the gas phase as a result of the polarization of the medium by the charged projectile. We have observed that if the ionization potentials for liquid water (as provided by Dingfelder et al. 21 ) were used instead to calculate the stopping power, while keeping the same cross sections, the results would be smaller than the ones shown in Fig. 8  (solid blue line) by about 8% at 10 keV, 4% at 100 keV, and 2-3% for energies up to 100 MeV. The latter, although a very simple test, shows that for liquid water smaller stopping power values would be obtained, as expected from the polarization effect. For comparison, the difference between the mass stopping power values in vapor and liquid water according to the PSTAR database 60 are of 13.
Acknowledgements Computer time for this study was provided by the computing facilities  MCIA (Mésocentre de Calcul Intensif Aquitain) of the Université de Bordeaux  and of the  Université de Pau et des Pays de l'Adour. M. E. A. A. acknowledges the financial support of the  Consejo Nacional de Ciencia y Tecnología  ( CONACyT, Mexico ).
The scenarios were assessed via agroecosystem modelling using the MONICA model (MOdel for NItrogen and Carbon in Agroecosystems;  Nendel et al. , 2011; Section 2. 3. 1). MONICA provided spatiotemporally explicit scenario-specific outputs over NRW in the period 1971-2060 on: extracted residues, residues remaining on the field, SOC in topsoil (30 cm), mineral N use and nitrate leach ing. We combined MONICA outputs with energy and GHG emission data to estimate the effect of management on techni cal residue potentials and GHG emissions associated with the displacement of fossil fuels by bioethanol, changes in SOC, nitrous oxide emissions (N 2 O) and emissions from the pro duction of the utilized fertilizers (Section 2. 4). We analysed our results on technical residue potentials, SOC changes, nitrate leaching and GHG emissions (a) aggregated for the whole of NRW to identify regional impacts and (b) spatially explicit across NRW's landscape to explore their spatial vari ability.
| Pedoclimatic and land use data For the MONICA simulations, we used simulated histori cal     2015). Data on soil physical and chemical characteristics in NRW were retrieved  from Hoffmann, Enders, Siebert, Gaiser, and Ewert (2016). The SOC values initially pro posed in this database were modified such that they ap proximate the SOC levels proposed by  Grosz et al. (2017) , which have been shown to be closer to observed SOC contents on cropland. In order to ensure a consistent sim ulation of the SOC dynamics, data from long-term field experiments carried out in Müncheberg, where alternative residue managements and organic fertilization levels are tested  (Rogasik, Schroetter, Funder, Schnug, & Kurtinecz, 2004) , were used for calibrating model parameters  (Stella et al. , 2019). The most influential parameters on the rela tive change of SOC in NRW during the projection period were identified via sensitivity analysis  (Herman & Usher, 2017; Morris, 1991)  and then calibrated using an automa tized algorithm for optimization  (DE-MCz, Houska, Kraft, Chamorro-Chavez, & Breuer, 2015).
The simulation period was split into a spin-up  and a projection (2005-2060) pe riod. The spin-up allowed to determine the initial distri bution of C among soil organic matter pools  (Basso et al. , 2011). For each grid cell and crop rotation, the calibration of initial (1971) SOC allowed obtaining SOC concentra tions by the end of the spin-up in line with those reported in the soil database used in this study. Each rotation was simulated continuously without re-initialization of soil variables over the whole simulation period. Management during the spin-up period was set according to our ref erence scenario assumptions (see Ref, Section 2. 3. 5), in order to reach a common starting point for the scenario assessment in 2005. During the projection period, manage ment assumptions were varied according to the scenarios defined in Section 2.
Emissions from the production of the utilized fertilizer are calculated in function of mineral N applied, as estimated by MONICA (see Section 2. 3. 7). where FEm NRW is GHG emissions from production of utilized mineral N fertilizer (kt CO 2-eq ); FertEF is N fertilizer emission factor (g CO 2-eq /g N). The utilized data are shown in Table  2. (7) InN 2 OEm NRW = ∑ i Fert i × VoEF + Leach i × LeEF × NEF × N 2 OEF, (.
ACKNOWLEDGEMENTS This research was conducted in the context of the  SUSTAg  project, funded in the frame of the  ERA-NET FACCE SURPLUS  which has received funding from the  European Union 's  Horizon 2020 research and innovation programme  under grant agreement  652615. Utrecht University  has been funded by the  Netherlands Organisation for Scientific Research (NWO)  under the project number  ALW. FACCE. 4  and the  University of Bonn  by the  German Federal Ministry of Education and Research (BMBF)  under reference num ber FKZ 031B0170B. We express our gratitude to the interviewed stakeholders for their insightful inputs and thank  Regine Berges  (agrathaer) and  Richard Kayser  for their valuable assistance in designing and conducting the interviews. We thank  Ton Markus  from the  Cartography Department of the Faculty of Geosciences of Utrecht University  for support in producing the figures.
Introduction Following genetics and other biological domains, imaging neuroscience recently started to become a "big data" science  (Efron 2012; Thompson et al. 2017; Smith & Nichols 2018). The brain sciences have been proposed to be one of the most data-rich medical specialties (Nature Editorial 2016) due to amassing high-resolution imaging data. Several data collection initiatives stand out in the brain-imaging landscape  (Smith & Nichols 2018) , including the Human Connectome Project (HCP), the UK Biobank (UKBB) imaging Study, and the Enhancing NeuroImaging Genetics through Meta-Analysis (ENIGMA) Consortium. The UKBB is perhaps the most compelling, as this resource includes genetic profiling and an extensive variety of phenotyping descriptors. The data aggregation set out in 2006 to gather genetic and environmental data of 500,000 volunteers and is currently the world's largest biomedical dataset  (Sudlow et al.
, 2015). The participants will be followed for >25 years, including repeated measurements and full access to electronic health records. In 2014 UKBB launched its brain-imaging extension, aiming to gather several magnetic resonance imaging (MRI) modalities of 100,000 participants by 2022  (Miller et al. 2016). UKBB is specifically designed for prospective population epidemiology. Instead, the ambition of HCP lies in functional and anatomical connectivity in healthy subjects, whereas ENIGMA places an important emphasis on genetic profiling in combination with brain scanning in psychiatric and neurological disease. The creation, curation, and collaboration of large-scale brain-imaging datasets with thousands of subjects promises to enable more ambitious statistical analyses than are currently the norm  (Bzdok & Yeo, 2017).
Here, we address this need by first principles and investigated the precondition most likely to limit the success of deep learning on brain-imaging data: The extent to which nonlinear relationships in brain images are exploitable at currently available sample sizes. In short, kernel-based models have outperformed linear methods in many applications. Deep-learning models have again refined pattern extraction and thus further boosted prediction accuracy in structured data such as natural images. This study investigated the scaling behaviors of these three modeling regimes on brain-imaging data and compared it to the performance profiles on standard machine learning datasets. We thus provide some first answers to the question: "Do emerging large-scale brain-imaging datasets contain nonlinear information that can be exploited by currently available kernel and deep models?".
Results Our goal was to assess how much the analysis of brain-imaging data can benefit from using nonlinear methods or even deep learning. For results to be generalizable, we wished to shed light on the general types of information in brain-imaging data, and whether those properties demand more complicated models making the most out of increasing sample size. Gaining such important intuitions would allow us to not only observe that a certain approach works well on brainimaging data, but draw conclusions why that might be the case. To this end, we evaluated how the prediction performance scales with increasing sample sizes for model classes with increasing prediction capacity and datasets of increasing prediction difficulty. We considered the achieved prediction performance as a function of the available sample size to obtain a principled empirical assessment of sample complexity (J.
Friedman et al. 2001; Goodfellow et al. 2016; Abraham et al. 2017). Analyzing the empirical sample complexity allows for insight into the information content of data as perceived through the assumptions of a given model class. For example, linear models are blind to nonlinear patterns in data by construction. Nonlinear kernel methods assume that a certain type of nonlinear interaction (defined by the "kernel") is best suited to identify decision boundaries for accurate classification. Going one step further, deep neural networks also expect nonlinear interactions in the data, but, intuitively, they learn the kernel, rather than assuming it. We used three classes of learning algorithms to evaluate cross-validated prediction performance on reference datasets (Fig. 1 ): a) Classical linear models are used for a number of decades since the middle of the 20th century in various empirical domains  (Tikhonov 1963; Tikhonov et al.
Model performance on machine learning reference datasets To verify that we can obtain empirical estimates of the sample complexity of linear, kernel, and deep models, we initially examined two reference datasets that have been pervasively used in the machine learning community. This would not only validate our approach to chart the scaling behavior of predictive performance with increasing sample size, but also establish a point of comparison for performance differences between the three model classes and the brain-imaging data. The MNIST dataset (Modified National Institute of Standards and Technology dataset; LeCun & Cortes 2010) is an important classical benchmark datasets in the machine learning community. This resource consists of greyscale images of handwritten digits with the digit value ('0'-'9') to be classified from the raw pixel information.
To quantitatively characterize the effects of a more challenging prediction goal, we also analyzed Zalando's Fashion dataset ("Fashion-MNIST",  Xiao et al. 2017). The sometimes called "Fashion-MNIST" dataset consists of greyscale images of fashion products, for classification of ten categories of clothing. This resource was created to provide a more difficult prediction problem than MNIST while retaining the same number of targets (i. e. , 10 categories), dimensionality (i. e. , 28x28 = 768 variables), and sample size (i. e. , 70,000 images). To verify that our model implementations work as would be expected from the technical literature, we replicated several current-best prediction performances on the MNIST dataset. On the full dataset comprising 60,000 training observations, our logistic regression model achieved 91.
32±0. 90 % classification performance (out-of-sample prediction accuracy mean±standard deviation across resampling iterations), which is comparable to earlier work (91. 7% reported in  Xiao et al. 2017). The more modern support vector machine with a radial-basis-function kernel (RBF-SVM) achieved 96. 79±0. 65 % accuracy (98. 6% in LeCun & Cortes 2010). Finally, standard convolutional deep neural network model achieved 99. 03±0. 39 % prediction accuracy -in line with the 98. 9% reported by  LeCun et al. (1998)  based on a similar deep learning architecture. Our model performances replicated state-of-the-art classification accuracies that were reported in previous research in the technical communities. To carefully quantify the degree to which nonlinear structure can be exploited in MNIST and Fashion datasets, we compared the performance of linear models and nonlinear kernel support vector machines with gradually increasing number of training images.
Systematic improvements in prediction accuracy when moving from linear models to nonlinear models consistently indicated the existence of exploitable nonlinear information predictive of the digit category in the dataset. On the MNIST dataset (Fig. 2-A. 1), linear and kernel models performed indistinguishably for low sample sizes. Yet, we observed that linear models and kernel models have diverged in prediction accuracy starting at around 1,000 example images. Exceeding this sample size, the worst among the three kernel models (RBF-SVM) outperformed the best among the three linear models (logistic regression). In the Fashion dataset (Fig. 2-A. 2), the worst kernel model (sigmoid-SVM) began to outperform the best linear model (logistic regression) starting from 4,000 observations. This difference in performance scaling grew to 4.
03 percentage points (p. p. ) and 1. 76 p. p. at 8,000 observations for MNIST and Fashion, respectively. That is, we show a less prominent gap between linear and shallow nonlinear methods in one of two comparable datasets with a more complicated prediction goal (i. e. , detect clothing rather than handwritten digits). For sufficiently large sample sizes available for model training, kernel methods outperformed linear models in both the MNIST and Fashion datasets. Thus, kernel support vector machines could readily exploit nonlinear structure in the examined datasets that is inaccessible to simpler linear models by principle. Next, we examined more closely how the difference in 10-class prediction problem scales with increasing sample sizes in the MNIST and Fashion datasets. The sample size necessary to saturate the prediction performance of a classifier relates to the complexity of patterns that can be reliably derived from amount and dimensionality of observations available for model training.
The out-of-sample prediction performance of both linear and kernel models saturated with increasing sample size in MNIST. Performance of linear models (logistic regression) grew by 14. 67 p. p. from 71. 64±2. 62% to 86. 31±1. 06 % when the data availability grew from 100 to 1,000 observation, while the performance for shallow nonlinear models (i. e. , RBF-SVM) grew by 15. 60 p. p. from 72. 58±2. 34 % to 88. 23±1. 11 %. Improvements reduced to 3. 50 p. p. (5. 62 p. p. for RBF-SVM) from 1,000 to 8,000 image observations. This saturation of prediction accuracy was less pronounced when applying the same learning algorithms to images of the Fashion dataset: Linear models (logistic regression) grew by 10. 22 p. p. from 69. 34±2. 95 % to 79. 55±1. 67 % from 100 to 1,000 observations, but only 4. 31 p.
Model performance on brain-imaging data scales similar to linear models To assess how the performance of common linear models and nonlinear kernel models behaves on brain-imaging data, we created a range of classification scenarios using a currently largest brain-imaging dataset -the UK Biobank Imaging. We tried to specifically design the classification problems to be similar to key properties of MNIST and Fashion to facilitate comparison of the results between brain-imaging and machine learning reference datasets. As a classification target, we constructed a 10-class target variable based on subjects' age and sex in analogy to the data shape in MNIST and Fashion. Our UK Biobank data provided structural and functional MRI scanned in 9,300 subjects. We evaluated different views of the underlying brain data, corresponding to distinct and often used forms of brain-imaging data analysis: UK Biobank provides high level 'imaging-derived-phenotypes' (IDPs) of resting state functional brain MRI (ICA-based functional connectivity), and structural brain MRI (regional gray and white matter volumes), which brought the >100,000 grey-matter voxels per brain scan to a dimensionality that is akin to the dimensionality of MNIST and Fashion: fMRI p=1,485 variables, and sMRI p=164 variables.
We therefore ran additional control analyses on binary (sex) classification and continous (age) regression (Fig. 4 ). In our analyses of brain-imaging data (Fig. 2-B ), we observed different scaling behavior compared to benchmark machine learning datasets for common linear models and nonlinear kernel methods. Across the different views of the brain scans, model performance converged on the same pattern: For each sample size, accuracies for all examined models were mostly statistically indistinguishable. In this example of the currently largest brain-imaging dataset, we did not observe signs of accuracy saturation. That is, doubling the sample size yielded stable, mostly indistinguishable gains in accuracy. For example for sMRI IDPs (Fig. 2-B. 1) at a full training set of 8,000 observations, the best kernel model (polynomial-SVM: 37.
58±2. 08 %) performed indistinguishably from the worst linear model (LDA: 38. 26±1. 46 %). Performance of linear models (logistic regression) grew by 5. 78 p. p. from 26. 02±1. 98 % to 31. 80±1. 92 % (7. 23 p. p. from 24. 92±1. 81 % to 32. 14±2. 44 % for RBF-SVM) from 100 to 1,000 observations, indistinguishable from the 4. 97 p. p. (5. 29 p. p. for RBF-SVM) for 1,000 to 8,000 observations. Qualitatively equivalent results were observed for different dimensionality reduction techniques (Fig. 3-A ) in regression and binary classification settings (Fig. 4 ), and, importantly, for different prediction targets -sex, age, and the combined 10-class variable (Fig. 2+4 ). In contrast to the examined machine learning reference datasets, brain-imaging data revealed neither saturation of prediction accuracy with increasing sample size nor performance gains from kernel models with higher expressive capacity.
Performance of deep neural network models Finally, we compared the performance of deep neural network models on our brainimaging data. Both fully connected neural network architectures and common variants of convolutional neural networks systematically differed in the performance on the machine learning benchmark datasets compared to accuracy profiles in brain-imaging data. Fully connected neural networks outperformed all linear models and all but the best performing kernel model on the MNIST and Fashion datasets (Fig. 2-A ), but not for any examined representation of brain imaging data. Regarding sMRI and fMRI IDPs (Fig. 2-B ), sMRI voxels (Fig. 3-A ) and whole sMRI slices (Fig. 3-B ), fully connected neural networks performed indistinguishably from both kernel and linear models. The same held true for our control analyses of the regression and the binary classification (Fig.
4 ). Convolutional neural networks showed analogous scaling behavior. On both MNIST and Fashion datasets, convolutional neural networks outperformed the best performing kernel model by 2. 93 p. p. from 95. 63±0. 79 % to 98. 56±0. 36 % and by 3. 44 p. p. from 85. 63±1. 32 % to 89. 07±1. 20 % respectively at 8,000 observations (Fig. 2-A ). In contrast, on sMRI slices convolutional neural networks outperformed neither linear nor kernel models (Fig. 3-B ). Central axial, coronal, and sagittal slices yielded comparable prediction accuracy for logistic regression (36. 09±1. 38 %, 37. 58±1. 81, 37. 35±1. 21 % respectively) and convolutional neural networks (34. 74±1. 65 %, 36. 52±1. 83 %, 36. 15±1. 82 % respectively). Thus, machine learning reference datasets and brain-imaging data differed in that convolutional neural networks excel on the former, but fail to improve over simpler methods on the latter.
Taken together, we described three important ways in which predictive models performed systematically differently between the machine learning reference datasets MNIST and Fashion on the one hand and brain-imaging data on the other hand. First, performance of linear models saturated with increasing sample size on MNIST and Fashion (less so kernel and deep models), but not on brain-imaging data. Second, kernel models consistently outperformed linear models in MNIST and Fashion, which was not the case in our analyses of brain-imaging data. Third, deep models clearly outperformed linear and kernel models on MNIST and Fashion, but not on our brain-imaging data. Our quantitative investigation can therefore be taken to argue that the largest brain-imaging dataset currently at our disposal still do not reliably enable exploitation of complex configurations in data by modern pattern-learning algorithms.
Discussion Do today's kernel methods or deep neural network algorithms provide advantages for analyzing common brain images by drawing on shallow-nonlinear or deep-nonlinear information? Can the triumphs of kernel and deep methods in machine learning datasets be obtained in currently available brain-imaging datasets? Our study initiates quantitative answers to these increasingly important questions. We have profiled the degree to which complex nonlinear relationships can be extracted and exploited to improve prediction performance over linear models in structural and functional brain data from the UK Biobank. Our careful analyses delineate the scaling behavior of prediction performance with increasing number of training observations for three classes of learning algorithms: linear, kernel, and deep models.
Present sample sizes are too small to even fully exploit linear modeling A key finding that emerged from our analyses pertains to the performance trajectory of linear models with gradually growing sample size (i. e. , empirical sample complexity). Our prediction outcomes from brain-imaging data and reference datasets from machine learning differed in the way that the prediction accuracy increased with the availability of data from additional observations. In the machine learning datasets, we expected, and indeed observed, saturation of prediction performance of linear models. This effect was most prominent when carrying out digit classification on MNIST by means of logistic regression and linear discriminant analysis: The prediction performance increased rapidly as we grew the sample size from 100 to 1000 available images.
Limited success of exploiting nonlinear information in currently available brain-imaging data If nonlinear structure exists in a given dataset and is exploitable for a specific prediction goal and sample size, we expect an increase in prediction performance as we switch from classical linear models to always more expressive models (Jerome  Friedman et al. 2001; Ghahramani 2015; Bzdok & Yeo 2017). In a second set of analyses, we confirmed the expected increase in prediction performance with growing capacity to represent complicated patterns in one of the most popular machine learning benchmark datasets (digit image classification in MNIST), as well as a more difficult companion dataset (clothing image classification in Fashion). In particular, kernel methods consistently outperformed commonly used linear models, with accuracy gains of 4.
03 and 1. 76 p. p. on MNIST and Fashion, respectively, on average. Our ability to quantify the detection of nonlinear data configurations in MNIST and Fashion to distinguish 10 categories of images (10 digits or types of clothing) corroborates our application of kernel SVMs as a viable and effective tool to test for the existence of predictive nonlinear patterns in data from the brain-imaging domain. When information carried in these brain measurements are related to the prediction goal in complicated ways, an SVM with a nonlinear kernel extension is expected to largely outperform linear models if provided with brain scans from enough participants. However, we did not observe systematic performance gains in prediction accuracy when examining brain images from UK Biobank, although we empirically replicated them in our analyses on the MNIST and Fashion datasets.