dataesr/scientific-paragraphs-categorization huggingface dataset:
We tuned l using generalized cross-validation  (Golub et al. , 1979)  and considered 100 candidate values on an evenly spaced logarithmic scale between 10 -3 and 10 5. This can be regarded equivalent to assuming a flat but discrete hyper-prior (a prior distribution of the hyper-parameters assumed for the model parameters) on the distribution of candidate regularization-strengths. Note that this procedure is computationally efficient and, on our problem, returned entire regularization paths within seconds. While this approach is standard-practice in applied machine learning and particularly useful with massive and high-dimensional data, many other methods exist for data-driven choice of the prior which may be more appropriate in situations on smaller datasets and where parameter inference, not prediction, is the priority.
Regression trees are non-parametric methods and recursively subdivide the input data by finding combinations of thresholds that relate value ranges of the input variables to the target. The principle is illustrated at the right bottom of Figure  1. For a fully grown tree, each sample falls into one leaf of the tree which is defined by its unique path through combinations of input-variable thresholds through the tree. However, regression trees tend to easily overfit. This is counteracted by randomly generating alternative trees from bootstrap replica of the dataset and randomly selecting subset of variables for each tree. Importantly, thresholds are by default optimized with regard to a so-called impurity criterion, for which we used mean squared error. Predictions are then averaged, which mitigates overfitting and also explains how continuous predictions can be obtained from thresholds.
Stacked cross-validation We used a 10-fold cross-validation scheme. To mitigate bias due to the actual order of the data, we repeated the procedure 10 times while reshuffling the data at each repeat. We then generated agepredictions from each layer-1 model on the left-out folds, such that we had for each case one ageprediction per repeat. We then stored the indices for each fold to make sure the random forest was trained on left-out predictions for the ridge models. This ensured that the input-layer train-test splits where carried forward to layer-2 and that the stacking model was always evaluated on left-out folds in which the input ages are actual predictions and the targets have not been seen by the model. Here, we customized the stacking procedure to be able to unbox and analyze the input-age predictions and implement opportunistic handling of missing values.
To implement opportunistic stacking, we considered the full dataset with missing values and then kept track of missing data while training layer-1. This yielded the stacking-data consisting of the age-predictions and missing values. Stacking was then performed after applying the feature-coding of missing values. This procedure made sure that all training and test splits were defined with regard to the full cases and, hence, the stacking model could be applied to all cases after feature-coding of missing values.
Statistical inference Rejecting a null-hypothesis regarding differences between two cross-validated models is problematic in the absence of sufficiently large unseen data or independent datasets: cross-validated scores are not statistically independent. Fortunately, cross-validation yields useful empirical estimates of the performance (and its dispersion) that can be expected on unseen data  (Hastie et al. , 2005, Ch. 7. 10). Here, we relied on uncertainty estimates of paired differences based on the stacked cross-validation with 10 folds and 10 repeats. To provide a quantitative summary of the distributions of paired split-wise differences in performance, we extracted the mean, the standard deviation, the 2. 5 and 97. 5 percentiles (inner 95% of the distribution) as well as the number of splits in which a model was better than a given reference (Pr <Ref Þ.
Analysis of brain-behavior correlation To explore the cognitive implications of the brain age D, we computed correlations with the neurobehavioral score from the Cam-CAN dataset. Table  5  lists the scores we considered. The measures fall into three broad classes: neuropsychology, physiology and questionnaires ('Type' columns in Table  5 ). Extraction of neuropsychological scores sometimes required additional computation, which followed the description in  Shafto et al. , 2014, (see also 'Variables' column in scores). For some neuropsychological tasks, the Cam-CAN dataset provided multiple scores and sometimes the final score of interest as described in  Shafto et al. , 2014 , had yet to be computed. At times, this amounted to computing ratios, averages or differences between different scores.
In other scores, it was not obvious how to aggregate multiple interrelated sub-scores, hence, we extracted the first principal component explaining between about 50% and 85% of variance, hence offering reasonable summaries. In total, we included 38 variables. All neuropsychology and physiology scores (up to #17 in Table  5 ) were the scores available in the 'cc770-scored' folder from release 001 of the Cam-CAN dataset. We selected the additional questionnaire scores (#18-23 in Table  5 ) on theoretical grounds to provide an assessment of clinically relevant individual differences in cognitive functioning. The brain age D was defined as the difference between predicted and actual age of the person BrainAge D ¼ age pred À age; (5) score age ¼ ageb 1 þ age 2 b 2 þ age 3 b 3 þ ; (7) The estimated linear association between the residualized score and the brain age D was given by b 1 in score resid ¼ BrainAge D b 1 þ ; (8) To obtain comparable coefficients across scores, we standardized both the age and the scores.
Data acquisition MEG recorded at a single site using a 306 VectorView system (Elekta Neuromag, Helsinki). This system is equipped with 102 magnetometers and 204 orthogonal planar gradiometers is placed in a light magnetically shielded room. During acquisition, an online filter was applied between around 0. 03 Hz and 1000 Hz. This resulted in a sampling-frequency of 1000 Hz. To support offline artifact correction, vertical and horizontal electrooculogram (VEOG, HEOG) as well as electrocardiogram (ECG) signal was concomitantly recorded. Four Head-Position Indicator (HPI) coils were used to measure the position of the head. All types of recordings, that is resting-state, passive stimulation and the active task lasted about 8 min. For additional details on MEG acquisition, please consider the reference publications of the Cam-CAN dataset  (Taylor et al.
Channel selection It is important to highlight that after SSS, the magnetometer and gradiometer data are reprojected from a common lower dimensional SSS coordinate system that typically spans between 64 and 80 dimensions. After SSS, magnetometers and gradiometers are reconstructed from the same basis vectors, which makes them linear combinations of another  (Taulu and Kajola, 2005). As a result, both sensor types contain highly similar information and yield equivalent results in many situations  (Garces et al. , 2017). Consequently, after applying SSS, the MNE software manipulates a single sensor type for source localization and uses as degrees of freedom the number of underlying SSS dimensions instead of the number of channels. Note, however, that after SSS, magnetometers and gradiometers can still yield systematically different results in sensor-space analyses despite being linear combinations of another.
The whitening operator was based on the empty room noise covariance and applied to the MEG signal and the forward model. We applied no noise normalization and used the default depth weighting  (Lin et al. , 2006)  as implemented in the MNE software  (Gramfort et al. , 2014)  with weighting factor of 0. 8  (Lin et al. , 2006)  and a loose-constraint of 0. 2. The squared regularization parameter l 2 was expressed with regard to the signal-tonoise ratio and fixed at the default value of 1 SNR 2 with SNR ¼ 3 for all subjects. This conservative choice was also motivated by the computational burden for optimizing the regularization parameter. Optimizing this hyper-parameter would have required pre-computing hundreds of MNE solutions to then perform grid search over the derived source-level outputs.
Structural MRI For preprocessing of structural MRI data we used the FreeSurfer (version 6. 0) software (http://surfer. nmr. mgh. harvard. edu/)) (Fischl, 2012). Reconstruction included the following steps (adapted from the methods citation recommended by the authors of FreeSurfer http://freesurfer. net/fswiki/FreeSur-ferMethodsCitation): motion correction and average of multiple volumetric T1-weighted images  (Reuter et al. , 2010) , removal of non-brain tissue  (Segonne et al. , 2004) , automated Talairach transformation, segmentation of the subcortical white matter and deep gray matter volumetric structures  (Fischl et al. , 2002; Fischl et al. , 2004)  intensity normalization  (Sled et al. , 1998) , tessellation of the gray-matter/white matter boundary, automated topology correction  (Fischl et al.
fMRI The available fMRI data were visually inspected. The volumes were excluded from the study provided they had severe imaging artifacts or head movements with amplitude larger than 2 mm. After the rejection of corrupted data, we obtained a subset of 626 subjects for further investigation. The fMRI volumes underwent slice timing correction and motion correction to the mean volume. Following that, co-registration between anatomical and function volumes was done for every subject. Finally, brain tissue segmentation was done for every volume and the output data were morphed to the MNI space.
Computing environment For preprocessing and feature-extraction of MEG, MRI and fMRI we used a high-performance Linux server (72 cores, 376 GB RAM) running Ubuntu Linux 18. 04. 1 LTS. For subsequent statistical modeling, we used a golden Apple MacBook 12' (early 2016) running MacOS Mojave (8 GB RAM). General purpose computation was carried out using the Python (3. 7. 3) language and the scientific Python stack including NumPy, SciPy, Pandas, and Matplotlib. For embarrassingly parallel processing, we used the joblib library.
MRI and fMRI processing For anatomical reconstruction we used the shell-scripts provided by FreeSurfer (version 6. 0) software  (Fischl et al. , 2002). We used the pypreprocess package, which reimplements parts of the SPM12 software for the analysis of brain images (The Wellcome Centre for Human Neuroimaging, 2018), complemented by the Python-Matlab interface from Nipype  (Gorgolewski et al. , 2011). For feature extraction and processing related to predictive modeling with MRI and fMRI, we used the NiLearn package  (Abraham et al. , 2014).
Acknowledgements This work was partly supported by a 2018 'medecine numerique' (for digital medicine) thesis grant issued by  Inserm  ( French national institute of health and medical research) and Inria (French national research institute for the digital sciences ). It was also partly supported by the  European Research Council Starting  Grant  SLAB ERC-StG-676943. We thank  Sheraz Khan  for help with the Freesurfer segmentation and data management of the Cam-CAN dataset. We thank  Mehdi Rahim  for advice with the model stacking framework and data management of the Cam-CAN dataset. We thank  Donald Krieger  and  Timothy Bardouille  for help with the MEG co-registration. We thank  Danilo Bzdok  for feedback on the first version of the preprint.
Code availability We share all code used for this publication on GitHub: https://github. com/dengemann/meg-mri-surrogate-biomarkers-aging-2020. (Engemann, 2020 ; https://github. com/elifesciences-publications/ meg-mri-surrogate-biomarkers-aging-2020) Our stacked model architecture can be compactly expressed using the StackingRegressor class in scikit-learn  (Pedregosa et al. , 2011)  as of version 0. 22.
Data availability We used the publicly available Cam-CAN dataset (https://camcan-archive. mrc-cbu. cam. ac. uk/dataaccess/). All software and code necessary to obtain the derivative data is shared on GitHub: https:// github. com/dengemann/meg-mri-surrogate-biomarkers-aging-2020 (copy archived at https://github. com/elifesciences-publications/meg-mri-surrogate-biomarkers-aging-2020). The following previously published dataset was used:.
First, the multidiffusion implementation strategy is presented, and then an application to the Gray-Scott reaction-diffusion model is presented to illustrate the new capabilities  [21, 22]. We would like to underline that the proposed strategy allows an increase of the multiphysics simulations in Abaqus (including strong couplings), while keeping the native features of the software in term of modeling library (including mechanical behaviors). The application is here limited to a classical problem in order to illustrate such possibilities, but extensions and applications are widely open to a lot of coupled problems that include mechanics (metal/hydrogen, water/polymer, metal/lithium ions as previously underlined, but also electro-magneto-mechanics, etc. ).
Introduction of a multidiffusion process in Abaqus In order to solve a complex problem with mechanics and multidiffusive fields in a finite element (FE) software, it is mandatory (i) to have a finite element formulation that includes as many degrees of freedom (DOFs) per node as the number of unknown fields, and (ii) to introduce the correct weak formulation for all of these DOFs for solving the problem. Introducing extra DOFs is complex; one may exploit the unused mechanical DOFs (rotations, numbered from 3 to 6, or the third displacement component in 2D problems), adding extra features to the elements (see  [23, 24]  for phase field implementation in Abaqus) through an User ELement (UEL) routine  [25]. One approach of particular interest has been proposed by Chester  [26]  to solve coupled thermo-chemo-mechanical problems in polymers (this work has been applied in  [27]  for a simple adsorption process).
) can be required in the output database file. It is worth noting that all the studies mentioned above, in which an UEL was used to redefine the problem, have also superimposed an additional layer of element taken from the Abaqus library in order to visualize the results. As demonstrated in  [29] , it is possible to go further and extend the Abaqus finite element formulation by superimposing an UEL to an Abaqus element: the terms that are not included by default in the formulation can be introduced through the UEL. The approach chosen in the present study combines the advantages of keeping the features of the Abaqus libraries (materials, elements, etc. ) and of adding extra terms and DOFs in the finite element formulation by using a superimposed UEL. Thus, the implementation work is optimized because the mechanical behavior does not need to be redefined.
We have implemented the GS reaction in Abaqus by introducing DOFs 12 and 13; the details of the RHS vector and of the AMATRX matrix have been adapted from  [48]  by considering constant diffusion coefficients, in particular. Computations have been performed with the 'coupled temp-displacement' procedure, even if no mechanical nor temperature field is computed. It is especially worth noting that, in addition to the GS reaction simulation presented here, a full "coupled-temp displacement" Abaqus simulation can be run in the same computation. In order to evaluate the ability of our implementation to simulate a GS process accurately, all the results are compared with those given by the Python script written by D. Bennewies  [44].
Results The Abaqus results for u (NT12) and v (NT13) are presented in Figures  4a-8a , with the corresponding Python reference results for u shown in Figure  4b. All Abaqus computations have been performed with a constant time increment of 10 s, while the python's one is equal to 1 s. It can be observed that our implementation in the Abaqus code is able to reproduce quite well the results obtained with another software, for various configurations. It may be noted that the U-skate geometries exhibited by Munafo  [41, 46] ) could not be generated, as in  [44].
Discussion An important feature observed in our simulations is a non constant velocity of the pattern front, with a strong influence of the (F,k) parameters. This behavior is consistent with results obtained by other methods, especially in  [44]. From the Figures 4 to 8, it might be observed that the front velocity computed by Abaqus has the same order of magnitude than the one obtained using Python. We have also investigated the effects of the element size and of the time increment (see  [46]  for a more complete investigation of the time increment influence). The influence of the element size is illustrated in Figure  9  for (F,k) = (0. 006, 0. 037). When the element size increases, the generated pattern is strongly influenced by the mesh structure and tends to a square rather than a circle.
Transmission electron microscopy (TEM) imaging For TEM measurements, we used formvar coated copper grids in conjunction with the method of negative staining with a 1% (w/v) solution of uranyl acetate. Jeol JEM-2100 and Jeol JEM-1400 (Japan) transmission electron microscopes were used. Fibrils lengths on TEM images were measured with ImageJ/Fiji software  [11, 12]. To analyse the effect of SDS treatment on the estimated fibril lengths, we added SDS to the fibril solutions to a final concentration of 2% (w/v) prior to sample preparation. Carbon coated grids were used for this experiment, as well as for all experiments with the Rnq1 fibrils.
The TAE solution  [35]  was used as a running buffer (pH was adjusted with acetic acid). For DNA staining, the corresponding part of the gel was cut off and placed into ethidium bromide solution for at least 1 h. A digital camera (Canon PowerShot G12) was used to obtain images. The rabbit polyclonal anti-Sup35 antibody SE4290  [36]  and mouse monoclonal anti-His antibody (GE Healthcare, #27-4710-01) were used to detect Sup35 or His 6 tag, respectively. The HRP conjugated secondary antibody (anti-mouse and anti-rabbit, GE Healthcare) was used for detection. Signals were recorded with the GeneGnome device (SynGene). The images of the stained DNA ladder and Western blotting signals were combined, scaled and aligned with the GIMP (gimp. org) software for further analysis in ImageJ/Fiji.
crbm. cnrs. fr/index. php?route=tool s&tool=26 and https://drozdovapb. shinyapps. io/ AGECalibratoR_2/) and as a standalone application (the source code is deposited on https://github. com/drozdo vapb/AGECalibratoR). For the estimation of aggregates molecular weights profiles corresponding to DNA ladder, background for Western blotting signal and the Western blotting signal are required. These data can be loaded into the graphical user interface of AGECalibratoR, which returns the arbitrary molecular weight of aggregates calculated according to the mobility of the DNA ladder on the same gel. The detailed user manual with a ready to use example is provided in the supplementary material. Two different strategies of molecular weight estimation were implemented in the AGECalibratoR. The first is the median of the molecular weight distribution, and the second is the value corresponding to the main peak in the OD profile.
Acknowledgments This work was supported by  PRC CNRS  and  RFBR  grants  PRC1524  and  17-54-150002 , respectively (development of web interface for application and its testing), by  SPSU  grants  39468250  and  32693900  (development of the algorithm), by the  Ministry of Science and Higher Education of the Russian Federation  project  2019-0219  (development of the Shiny app and application manual), by the  State research program   0112-2016-0015  (estimation of spheroplasting efficiency), the RSF grants  18-14-00050  (optimization of spheroplast lysis) and  19-76-00026  ( Sup35NM  protein purification, in vitro fibril generation and TEM analysis), and the RFBR grants  18-34-00537  (plasmid construction for the Rnq1 protein purification, in vitro fibril generation, comparative analyses of SDD-AGE and TEM results),  18-34-00536  (optimization of  SDD-AGE and protocol of Western blotting ),  19-04-00173  (testing of application).
Patients This is a retrospective cohort study based on data and samples from 52 patients already available in the Centre Antoine Lacassagne tumor bank and collected during routine practice between 2013 and 2016. Patient tumor characteristics were: clinical stages I to III B biopsy-proven BC, with an indication for post-surgery adjuvant therapy. Tumor phenotypes were classified into three subtypes: triple-negative (estrogen receptor, progesterone receptor and Her-2 non-over-expressed); luminal (estrogen receptor and/ or progesterone receptor positive and Her-2 non-overexpressed); Her-2 over-expressed (Her-2 over-expressed, estrogen receptor and progesterone receptor either positive or negative)  [31]. After surgery, all patients were treated according to current guidelines, with sequential chemotherapy including anthracyclines (epirubicin and cyclophosphamide) and taxanes followed by radiotherapy.
Patients with Her-2 over-expressed tumors were treated with trastuzumab concurrently with taxanes and continued for one year. Patients with luminal BC were then treated by endocrine therapy with tamoxifen or an aromatase inhibitor, based on menopausal status. Clinical, histological, radiological and therapeutic data were retrospectively extracted from our facility's digital records or collected by a clinical data monitor. Follow-up data were either extracted from our facility's digital records or retrieved by telephone if patients had changed facilities during surveillance. Written informed consent was obtained from all study participants. All procedures performed in this study involving tissue collection and analyses were following the ethical standards of the institutional and/or national research committee (French National Commission for Informatics and Liberties N°17003 and National Institute Health data N°1515251018).
Data-preprocessing, metabolite identification, statistical and pathway analysis Sample collection, preparation and data-processing using MZmine  [32, 33]  are shown in Supplementary Material S1 and Supplementary Fig. 1  Metabolites obtained from positive and negative ionization modes were combined. Only metabolites with no null values after pre-processing were selected for analysis. When a metabolite was detected in both positive and negative modes, only the mode offering the highest average intensity was considered. After these steps, 1271 metabolites were identified. To eliminate noisy data, a filtering function was applied before statistical analysis. Finally, statistical analysis was performed on 449 metabolites. The identification of metabolic pathways was performed using MetaboAnalyst database sources  [34].
PCA k-means clustering, combines PCA to reduce the number of dimensions of a dataset and the k-means method to minimize the intracluster variance for a chosen number of k clusters  [43] [44] [45]. Spectral clustering  [46, 47]  is based on graph theory. It consists of identifying dense regions in a multidimensional dataset, i. e. observations that can form a non-convex set but are close to each other. Sparse k-means clustering was developed in 2010 by Witten and Tibshirani  [8]. This method is based on a Least Absolute Shrinkage and Selection Operator (LASSO) approach  [48]  and combines the LASSO approach and the k-means method which simultaneously find the clusters and select features. SIMLR clustering  [42]  was developed to analyze scRNA-seq data. This method searches for appropriate cell-to-cell similarity metrics to perform dimension reduction and clustering.