dataesr/scientific-paragraphs-categorization huggingface dataset:
In case of a purely additive model, i. e. a model without S i ¼ ∑ i ST i ¼ 1. Otherwise, ∑ i S i < 1 and ∑ i ST i >1. For practical purposes, a model is considered "mostly additive" when ∑ i S i >0:6  (Saltelli et al. , 2004). The variance-based measures of sensitivity are attractive because they quantify sensitivity across the whole input space, they can deal with nonlinear responses, and they can measure the effect of interactions in non-additive systems  (Saltelli and Annoni, 2010). Global Sensitivity Analysis is used in model evaluation, where the model guarantees a value of the target output of interest for each combination of inputs obtained by multivariate sampling from the inputs pdfs. In order to apply GSA to the data set without an existing model, it is first necessary to develop an effective metamodel or response curve of the dataset.
The metamodel then serves as an interpolator within the data space to obtain the expected outputs (d50) for each combination of inputs sampled by GSA. To construct an efficient metamodel of d50 from the data set, machine learning techniques were employed. The Sobol' GSA was performed on the machine learning predicted d50 in order to: i) identify first-order (direct) and higher-order (interaction) effects for each of the 16 input factors, i. e. each available explanatory variable; ii) rank the explanatory variables according to their importance; and iii) select the subset (reduced dimension) for the development of a parsimonious model in Step 3. Two machine learning techniques Random Forest (RF) and eXtreme Gradient Boosting (XGBoost) were applied and compared on their ability to predict accurately the observed d50 values based on the rest of the dataset features (candidate explanatory variables).
The n = 93 dataset was split by stratified sampling into a training subset (80 %) and a test subset (20 % of the data) using the R package 'caret'. The former was used to train the machine learning predictor and the latter was used for independent testing. Highly correlated variables can impair the performance of RF and XGBoost for feature selection. Hence, before the machine learning application, a VIF (Variance Inflation Factor) multicollinearity test was performed in R, to ensure that only independent variables (VIF < 4) are used in the analysis. RF is a machine learning method for classification and regression that operates by constructing a multitude of decision trees (e. g. Breiman, 2001). Decision tree methods have the advantage that they can deal with categorical variables better than multiple regression analysis (MRA).
RF can be viewed as an enhancement of Classification and Regression Trees (CART;  Breiman et al. , 1984). Each tree is constructed on a bootstrap sample of the dataset (bootstrap aggregating = bagging). At each split of the data, only a random subset of the independent variables is available for making the split (feature bagging). The Random Forest analysis was performed in R using the packages randomForest, caret, and missForest. XGBoost belongs to the family of boosting methods based on ensembles of weak learners in which the trees are grown subsequentially to predict the residuals of the previously fitted tree, optimizing a loss function. In eXtreme Gradient Boosting (XGBoost)  (Chen et al. , 2015; Chen and Guestrin, 2016) , predictions of the trees are weighted based on a learning rate to allow for a progressive compensation of the previous tree weaknesses and, among other features, it adds regularization to control for overfitting and can deal with missing data.
XGBoost has been shown to often outperform other tree ensembles such as Random Forest. The "gain" indicator is used to measure the relative importance of the predictors. However, the variable "gain" does not inform on the existence of important interactions that could be inferred from the data. If the model is non-additive (i. e. there are nonnegligible interactions between input factors), variable importance is better described using Sobol' sensitivity indices. Parametrization of XGBoost was achieved through 5-fold cross-validation and a random tuning grid using the R packages 'xgboost' and 'caret'. Goodness of fit/prediction for the machine learning predictors was evaluated with the FITEVAL software  (Ritter and Muñoz-Carpena, 2013). For a given array of observed and predicted values, FITEVAL calculates the goodness of fit/prediction measures Nash-Sutcliffe Efficiency (NSE;  Nash and Sutcliffe, 1970) , Kling-Gupta Efficiency (KGE;  Gupta et al.
Step 3: parsimonious model -multiple regression analysis The knowledge gained from the machine learning and Global Sensitivity Analysis (most important variables and interactions) was used to inform the Multiple Regression Analysis (MRA). The aim of the MRA was to derive a statistical equation with combinations of the most important variables and their interactions. The MRA was performed with the R package 'autoLm'  (Pohlert et al. , 2021) , which does automatic linear fitting of model variants consisting of all possible combinations of independent variables and a user-specified set of transformations (e. g. x 2 , x 0. 5 , x -1 , ln(x)). Regressions were performed for untransformed (non-logarithmic) and logarithmic d50 values. Additionally, an Analysis of Covariance (ANCOVA) was carried out in R because it can take into account categorical variables.
The predictive capability of a regression model is usually assessed by testing it against independent data, i. e. data points which were not used for calibration. However, if experimental data are scarce or originate only from a small number of experiments, it is often advantageous to use all available data points for calibration, in order to capture as much variability in experimental conditions as possible (cf. Reichenberger et al. , 2019). However, this implies that there are no independent data points left for model evaluation, and in this case the predictive capability of the regression model can be assessed with a cross-validation analysis. Thus, we used the n = 93 dataset to develop the MRA model and performed a k-fold crossvalidation analysis, analogously to e. g. Chen et al. (2016)  and  Reichenberger et al.
(2019). Like in  Reichenberger et al. (2019) , the kfold cross (k = 2-12) validation analysis was conducted with the Python package 'scikit-learn'  (Pedregosa et al. , 2011). Three predictive accuracy measures were computed: i) predictive r 2 (Pearson r 2 between the measured and the predicted ΔP values of the validation data set), ii) predictive squared correlation coefficient Q 2  (Consonni et al. , 2010) , and iii) RMSEP (root mean square error of prediction). In addition to the full regression equation with all important variables identified in Step 2, reduced equations with decreasing number of independent variables were tested in the cross-validation exercise in order to identify if a more parsimonious model could be found.
Step 4: comparison with existing methods The d50 predicted with the various methods were compared to assess their differences and their performance against the observed d50 values from the dataset. In addition to the RF, XGBoost and MRA d50 predictions, two other existing methods were compared. First, the d50 predicted as the geometric mean of min and max values given in the KINEROS manual  (Woolhiser et al. , 1990)  based on USDA soil texture class. Finally, d50 was predicted with  Foster et al. (1985)  equations (Tables  S1, S2 ) and the weighted geometric mean  (Foster et al. , 1995)  (Eq. S1). Boxplots were constructed to assess the difference among the distributions of d50 values provided by each approach, and a test performed to indicate groups of significantly different medians (α = 0.
Consolidated dataset characteristics The consolidated d50 dataset (n = 93) was tested to ensure good data representation cross the full d50 range. The cumulative distribution function (CDF) of d50 (Fig. 2 ) shows biphasic behaviour: an almost linear increase until a cumulative probability of 87 % and a d50 value of about 9 μm, and then a much flatter increase, indicating that the data points are much sparser in the high range than in the low range. Descriptive statistics of d50 are given in Table  S1. In general, there is a good coverage and overlap of the ranges for d50 values obtained from measurements (4. 3-47. 2 μm) and those estimated with VFSMOD-W (3. 0-29. 0 μm) and DREAM_ZS (1. 1-22. 4 μm), and other d50 statistics are also similar among the three sources (Table  S1 ). The six d50 values from  Deizman et al.
989, PBIAS = -0. 703 %, NSE = 0. 983; for DREAM_ZS: R 2 = 0. 753, PBIAS = -6. 61 %, NSE = 0. 474). This is expected, however, because data availability was much better in the studies where d50 was calibrated with VFSMOD_W than in the studies where it was calibrated with DREAM_ZS. For the Raleigh dataset (Muñoz-Carpena, 1993) and the Bartow dataset  (Kuo, 2007)  calibrated with VFSMOD-W, full rainfall, run-on and VFS outflow hydrographs were available for each event. In contrast, for DREAM_ZS no detailed hyetographs and run-on hydrographs were available, and consequently estimated hydrographs had to be used from the storm rainfall and runoff totals (with the exception of the Kinston dataset, where rainfall and run-on hydrographs were inversely estimated using the experimental VFS outflow hydrographs).
Machine learning d50 metamodels The prediction accuracy of the Random Forest analysis are presented in Fig. S6. Preliminary tests revealed that removing the variable d50_method decreased the performance of RF only slightly, indicating that the variable is not important and predictions can be done without d50_method. Consequently, this variable was excluded in the final RF analysis. According to RF standard variable importance measure (%IncMSE, percent increase in mean squared error when the variable is permuted), the five most important explanatory variables were mean rainfall intensity, eroded sediment yield normalized to source area, tillage, slope length of the source area, and peak runoff rate. Performance measures for the training, test and full datasets are compiled in Table  3 , where prediction accuracy for the external validation was good (NSE = 0.
827). The main results of the Gradient boosting with XGBoost are presented in Fig. S7. The measure of variable importance calculated by XGBoost ("gain", relative contribution of the corresponding variable to the model calculated by taking each variable's contribution for each tree in the model) attributed importance to 3 of the same variables as RF, but 2 of the top 5 importants variables were different (clay and silt contents of eroded soil) (Table  4 ). The goodness of fit for the external validation was also good but slightly worse than for RF (NSE = 0. 814, Table  3 ). This was caused by an outlier from the DREAM_ZS calibration (d50 value of 20. 24 μm, likely too high), which was correctly identified by XGBoost. The prediction for the training dataset was nearly perfect (NSE = 0. 999), and for the full dataset was also the highest (0.
This is illustrated by the d50 dataset showing a predominance of particles in the USDA silt textural range (2-50 μm, Fig. 2 ). Although the ranking according to the "gain" measure from XGBoost metamodel is somewhat different from the S i and S Ti rankings (Table  4  and Fig. S7 ), the sets of the four most important input variables are the same. GSA, as a variance decomposition technique, offers a more robust variable importance ranking and is used here as the basis for the selection of variables (Table  4 ). We added slope_length_field (m) as a variable to account for the contributing source area. While longer lengths increase the contributing area, this influence can be attenuated by the increase deposition of coarser sediment along the soil catena before exiting the field edge.
All approaches have been calibrated using the training data set and then extrapolated to the test dataset. Eq. (  1 ) yielded three negative d50 values against the full n = 93 dataset. Therefore a modification of the MRA equation was introduced for predictive use whereby if the equation predicts d50 smaller than the minimum value in the test dataset (1. 1 μm; Table  S1 ), the prediction is set to 1. 1 μm. This filter moderately improved the fit for the full MRA equation and two of the reduced ones with a small bias (Table  3 ). The predictive equation uses regular d50 (not log-transformed) and for each of the six independent variables, an increase of the value of the variables leads to an increase of the d50 value, which is in agreement with the current process understanding for these variables.
However, I 30 was not available for most of the studies in the compiled test dataset. Peak runoff rate, together with slope and hydraulic roughness, determines the sediment transport capacity (USDA-ARS, 2016). Hence, it influences deposition after detachment and consequently the particle size distribution of the eroded sediment at the field outlet. However, a caveat needs to be added here: Since the peak runoff rate enters the equation linearly, the equation may provide unreliable d50 estimates for very high peak runoff rates (higher than the largest observed value in the test dataset, 131 mm h -1 normalized to the source area). Measured hydrographs with very fine temporal resolution (e. g. 5 min) and very high and narrow peaks should therefore better be aggregated to a larger time step (e.
The reduced equation variant that performed second best after the full equation was the equation without mean rainfall intensity (r 2 = 0. 703, Table  5 , eq. (  2 )): d50 μm ð Þ ¼ 5:92212 þ 37:07292 tillage þ 0:40592 Ei_g_m2 ð Þ 0:5 þ 0:12848 peak_runoff _rate À 27:52124 slope_length_field ð Þ À 1 À 1:44531 silt ð Þ À 0:5 (2) It is interesting that among the five reduced MRA variants the equation without rainfall intensity performed best, given that mean rainfall intensity was identified by Random Forest and XGBoost as the most important variable, and by the Sobol' GSA as the second most important. This may be explained by the smaller structural flexibility of the MRA approach compared with machine learning. For a visual assessment of the quality of the fit of the MRA equation compared to the machine learning metamodels, we plotted observed against predicted d50 values and also the residuals for the full n = 93 dataset (Fig.
For the MRA approach (NSE = 0. 717) there are 7 data points outside the 20 % deviation threshold. The three largest underpredictions of d50 (14-21 μm) belong to the  Deizman et al. (1987)  dataset (conventional tillage): The observed values are 24-31 μm, but the predicted ones only 9-12 μm. The largest overprediction (15 μm) occurred for a data point of  Spatz (1999)  with observed d50 = 2. 85 μm (DREAM_ZS calibration). For the reduced MRA equation without rainfall intensity there are 5 data points outside the threshold (not shown). The three largest underpredictions of d50 (16-22 μm) belong again to the  Deizman et al. (1987)  dataset (conventional tillage), while the largest overprediction (18 μm) occurred for the same data point of  Spatz (1999)  as above. In summary, although the MRA equations were outperformed by the two machine learning approaches, their fit is still quite good given their parsimonious nature.
(Moriasi et al. , 2007) ; negative values of PBIAS indicate overestimation. Table  3  gives an overview of prediction measures of the three prediction methods (XGBoost, RF and MRA) and their 95 % confidence intervals for: i) the n = 76 training subset; ii) the n = 17 test subset and iii) the n = 93 full dataset. For the calibration, according to all three computed accuracy measures (NSE, KGE and RMSE) XGBoost performed best and the MRA equations worst (NSE < 0. 7). However, for the validation the order was reversed with respect to NSE and RMSE. Here, the reduced MRA equation yielded the best results (NSE = 0. 868), substantially better than for the calibration. With respect to the Kling-Gupta Efficiency KGE XGBoost still performed best in the validation. The fact that MRA performed better for the validation (test subset) than for calibration (training subset) was most probably by chance, i.
e. due to the quasi-random splitting of the data. For instance, in spite of the stratified splitting of the data all three data points of  Deizman et al. (1987) , which showed the strongest underestimation for the fit to the full dataset, ended up in the training subset and probably affected the goodness-of-fit here. The filtered MRA approach shows a slight improvement for the training and the full dataset compared with the original MRA approach. The test subset did not contain MRA predictions <1. 1 μm, so it was not affected by the filtering; the slightly different confidence intervals for the test subset are only due to different random seeds for the block bootstrapping. For all methods and goodness-of-prediction measures, the wide confidence intervals for the test subset can be explained by the small size of the test subset (n = 17).
The Foster predictions are the highest of all the methods. As suspected, the  Foster et al. (1985)  equations overestimate d50 for edge-of-field situations, because they are meant to represent eroded sediment directly after detachment. However, they also failed to reproduce the observed variation of d50 values This is due to the fact that the  Foster et al. (1985)  predictions only depend on the static particle size distribution of the topsoil, while other source area characteristics, and dynamic event characteristics and responses of the source area to the rainfall event (Table  2 ) are not considered. In a pesticide mitigation regulatory context, using a constant default value of d50 = 20 μm proposed by  Brown et al. (2012)  with the full dataset yields NSE = -1. 54, and using a constant value of 5.
4 μm (the median of the d50 dataset, Table  S1 ) yields NSE = -0. 09. Hence, the fit with the MRA equation constitutes a major improvement compared with the use of constant d50 values. The effect of using a more predictive, dynamic MRA d50 approach in long-term pesticide exposure assessments needs to be demonstrated in terms of changes in predicted environmental concentrations in surface water (PECsw). Repeating the machine learning with a reduced set of explanatory variables (the same six variables used in the MRA equation) yielded that the training and testing performances of Random Forest and XGboost were not significantly affected compared with the full set of variables (Table  S10 ). This supports the novel variable reduction step used here  (Carmona-Cabrero et al. , 2022) , where the six variables in the final MRA equation contain sufficient information for predicting d50.
Conclusions and outlook In this study a new estimation equation for the median sediment particle diameter in runoff d50 was derived based on a comprehensive dataset of runoff events compiled from 13 surface runoff studies from Europe and the US. Applying machine learning methods and Global Sensitivity Analysis to the dataset we were able to identify the six most important independent   (Woolhiser et al. , 1990)  for the respective USDA texture class; Foster: d50 predicted with  Foster et al. (1985)  equations and weighted geometric mean according to WEPP manual  (Foster et al. , 1995). Crosses indicate the arithmetic mean; center lines show the medians; notches represent the 95 % confidence interval of the median; box limits indicate the 25th and 75th percentiles as determined by R software; whiskers extend 1.
The MRA equation performed satisfactorily in a kfold cross-validation analysis and in a predictive performance comparison with machine learning and other existing approaches to predict d50. Unlike previous approaches, the new equation incorporates dynamic event characteristics (peak runoff rate, rainfall intensity, sediment load) in addition to static soil (silt fraction) and land (tillage and slope length) characteristics. This approach demonstrated to be much more accurate than the existing static methods. While the approach is empirical (data driven), the equation components are physically consistent with current understanding of processes controlling d50. Future work should increase the dataset by incorporating more studies to test the validity of the equation under a wider set of conditions, notably for observed d50 values larger than the maximum value in our test dataset.
Acknowledgements This research was funded by  Bayer AG, Monheim, Germany. RMC also acknowledges support from the  USDA National Institute of Food and Agriculture (USDA-NIFA ;  2016-67019-26855 ) and  USDA-NIFA Hatch  projects  1024705  and  1024706 , the  University of Florida (USA) , and  Universidad Pública de Navarra (Spain)  for the support received during his sabbatical year when part of this work was developed. Thanks are due to four anonymous reviewers for their constructive criticism.
Conclusion(s): The uterine volume was diminished after HSCT, regardless of the conditioning regimen. The physiopathology needs to be further investigated: specific impact of a high dose of an alkylating agent; impact of hormone deprivation around puberty; poor compliance to HRT; or different myometrial impact of HRT compared with endogenous ovarian estrogens? Clinical Trial Registration Number: ClinicalTrials. gov/NCT 03583294 (enrollment of the first subject, November 11, 2017; enrollment of the last subject, June 25, 2021). (Fertil Steril Ò 2023;119:663-72. Ó2023 by American Society for Reproductive Medicine. ) El resumen está disponible en Español al final del artículo. Key Words: Uterus, hematopoietic stem cell transplantation, MRI, chemotherapy, total body irradiation W ith the improvement of survival rates, the reproductive outcome of childhood cancer survivors (CCSs) emerged as a main issue for their long-term quality of life  (1).
A medical consultation with a physician specialized in oncofertility was proposed after MRI to evaluate the ovarian function and estimate the observance of hormone replacement therapy (HRT) in premature ovarian insufficiency (POI) cases. The present study FERTILEA included prospectively women from the LEA cohort with the main objective to assess the uterine volume using the MRI techniques. Data obtained from pelvic MRI and gynecologic assessment were prospective; however, we also had retrospective data from the same women collected for 16 years in the context of the LEA program.
The following parameters were recorded: uterine volume measured on T2-weighted imaging (anteroposterior Â transverse Â craniocaudal dimensions) Â 0. 52) and uterine body-to-cervix ratio. The ADC values of the myometrium were measured on an ADC map by placing 2 regions of interest (ROIs). We measured 2 ROIs and used the mean value, rather than just 1 ROI, to reduce random variability in the measurements. All case data have been analyzed with a double-blinded reading by 2 independent radiologists, without knowing any information concerning the type of MAC regimen.
Study Endpoints The main study endpoint was the uterine volume. The secondary endpoints were uterine body-to-cervix ratio and ADC (Â 10 À3 mm 2 /second). In the HSCT group, we also collected data about the type of AL, type of MAC, age at HSCT, pubertal status at the time of HSCT, hormonal status at the time of the study (POI or spontaneous menstruations), HRT or not in case of POI, spontaneous pregnancy or pregnancy obtained after assisted reproductive technology, and follow-up (early miscarriage before 12 weeks of gestation, late miscarriage between 12 and 22 weeks of gestation, and live birth). Premature ovarian insufficiency was defined as a hypergonadotropic hypogonadism in women aged <40 years. In the HSCT group, we further defined 2 subgroups of women by evaluating the independent effects of the type of MAC on the uterine volume: a group of women with hypoestrogenism composed of women with POI not treated with HRT vs.