dataesr/scientific-paragraphs-categorization huggingface dataset:
Radiological glioma growth was quantified by manual measurements of tumour diameters on successive MRI studies (T2/FLAIR sequences). For older imaging data available only as jpeg images we computed the volume using the ellipsoidal approximation  [39]. CT image analysis (patient subgroup 8, 10). Patients included were participants in the study SCALAMATH. CT images of lung cancer nodules were obtained in DICOM format. An experienced radiologist (EA) localized the lesion and then an image expert (OLT) performed the segmentations following the same methodology as with subgroups 1-7. Glioma cells. Primary glioma cells (L0627) were kindly provided by Rosella Galli (San Raffaele Scientific Institute, Milan, Italy) and were grown in complete medium: Neurobasal (Fisher) supplemented with B27 (1:50) (Fisher); Glutamax (1:100) (Fisher); Penicillin-streptomycin (1:100) (Lonza); 0.
Athymic nu/nu (Harlan) mice of 4-6 weeks of age were used. Brain colonization assays were performed by injecting 100  PBS into the left ventricle containing 100,000 cancer cells. Anesthetized mice (isofluorane) were injected retro-orbitally with d-luciferin (150 mg/kg) and imaged with an IVIS Xenogen machine (Caliper Life Sciences). Bioluminescence analysis was performed using Living Image software, version 3. Cell culture. H2030-BrM3 (abbreviated as H2030-BrM) was cultured in RPMI1640 media supplemented with 10% FBS, 2 mM l-glutamine, 100 IU ml -1 penicillin/ streptomycin and 1 mg ml -1 amphotericin B. Statistical analysis. Linear regressions of the log (MTV) versus log (TLA) to construct the scaling laws were performed using the Matlab Statistics and Machine Learning toolbox command fitlm.
Acknowledgements. This research has been supported by the  James S. Mc. Donnell Foundation 21st Century Science Initiative in Mathematical and Complex Systems Approaches for Brain Cancer  (Collaborative awards  220020560  and  220020450 ),  Ministerio de Economía y Competitividad/FEDER, Spain  (grant number  MTM2015-71200-R ),  Junta de Comunidades de Castilla-La Mancha  (grant number  SBPLY/17/180501/000154 ). Research in the Brain Metastasis Group is supported by  MINECO  grants  MINECO-Retos SAF2017-89643-R (M. V. ) ,  Bristol-Myers Squibb-Melanoma Research Alliance   Young Investigator Award 2017  ( 498103 ) (M. V. ),  Beug Foundation's Prize for Metastasis Research 2017  (M. V. ),  Fundación Ramón Areces  ( CIVP19S8163 ) (M. V. ),  Worldwide Cancer Research ( 19-0177 ) (M. V. ),  H2020-FETOPEN (828972 ) (M.
Data extraction The present work was made on French data which were collected from official databases  [4]. Data that were considered were hospitalizations in (i) non-ICU units and (ii) in ICU units, (iii) deaths in the hospital, and (iv) returns to home. These data were collected daily from March 1 st towards May 22 nd of 2020. They were assessed by regions (or sub-regions) selected to keep comparable number of patients within each unit. Indeed, regions were divided in smaller areas if effectives were high, as in Ile-de-France, Grand-Est, Hauts-de-France, Auvergne-Rhône-Alpes and Provence-Alpes-Côtes d'Azur. Therefore, the following 26 regions or sub-regions were assessed : Paris, Hauts-de-Seine, Val-de-Marne, Seine-saint-Denis, Essonne, Yvelines, Val d'Oise, Seine-et-Marne, Haut-Rhin, Bas-Rhin, Moselle, Grand-Est (other), Nord, Hauts-De-France (other), Rhône, Auvergne-Rhône-Alpes (other), Bouches-du-Rhône, Provence-Alpes-Côtes d'Azur (other), Bourgogne-Franche-Comté, Centre-Val-de-Loire, Occitanie, Nouvelle-Aquitaine, Pays-de-la-Loire, Normandie, Bretagne, Corse.
Software. Hospital data were analysed using MONOLIX-Suite 2019 software. (Lixoft®, Antony, France), which combines the stochastic expectation-maximization (SAEM) algorithm and a Markov Chain Monte-Carlo procedure for likelihood maximization. To ensure the best possible convergence, a large number of iterations (15000 for K1 and 2000 for K2) were used. K1 and K2 refer to the SAEM procedure of MONOLIX, called "iterative kernels". During K1, the sequence of step sizes is constant, which allows the exploration of the parameter space. During K2, the step sizes decrease to ensure convergence. Three Markov chains were used. Parameter values of regions, sub-regions and whole France were obtained by computing conditional distribution. Structural model design. Model with and without lockdown effect on k I were compared using Akaike's information criterion (AIC), defined as: AIC = OFV + 2.
Acknowledgements We are pleased to thank the anonymous referees for their helpfull comments and suggestions. Open Access This article is licensed under a Creative Commons Attribution 4. 0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
Statistical analysis. Statistical analyses were based on previous studies  25, 26, 33, 35, 36, 67  and were carried out using SPSS version 22. 0 (SPSS, IBM). Post-block sequence report task. This task was administered in the Cued group only. Performance on this task was used to test whether participants followed the instruction to learn the serial order of the cued sequence trials. Due to technical reasons, data from one participant in the Sleep subgroup was not recorded. First, the percentage of correct button presses (out of 12) was calculated after each block, then these were averaged across epochs (i. e. , blocks of five, see below). These averaged values were submitted to mixed design ANOVAs separately for the Learning Phase and the 12-h post-learning offline delay to reveal whether participants followed the instruction and ascertain that the cuing manipulation was effective.
ASRT task. Epochs of five blocks were analyzed instead of single blocks: The Learning Phase consisted of five epochs, while the Testing Phase consisted of one epoch. On average, the Cued group showed slower RTs compared with the Uncued group, possibly as a result of the cuing manipulation (for more details see the Supplementary Materials). Hence, to ensure that potential between-group differences in statistical learning are not due to this group difference, we standardized the original RT values. To this end, first we transformed the data by dividing each participants' raw RT values for the random trials with their own average performance of the first epoch of the Learning Phase [for a similar approach see  68  ]. In the next step, we multiplied all data by 100 for easier interpretability and presentation.
Data from one participant in the Uncued Sleep subgroup is missing due to technical problems. To contrast performance against chance level, we calculated the percentage of high-probability triplets participants generated and subtracted the value of chance level (25%, percentage of the 16 high-probability triplets out of the 64 possible triplets). These scores were then submitted to a mixed design ANOVA. Since we did not expect any difference across the groups and the sample size was reduced here, a Bayesian mixed design ANOVA was also conducted and reported similarly as described above.
Do the uncued and cued groups show different statistical learning performance in the learning phase? We tested potential group differences in statistical learning by conducting a mixed design ANOVA on standardized RT data of the statistical learning scores (i. e. , difference between random high-vs. random low-probability trial types) with EPOCH (1-5) as a within-subject factor and INSTRUCTION (Uncued vs. Cued) and SLEEP (Sleep vs. No-sleep) as between-subject factors. Note that, for the Learning phase, the Sleep vs. No-sleep subgroup comparison can reflect time of day effects rather than the effect of sleep per se as the Sleep subgroup was first tested in the evening and the No-sleep subgroup was first tested in the morning. The ANOVA revealed significant statistical learning (INTERCEPT: F(1, 92) = 214.
Acknowledgements This research was supported by the  National Brain Research Program  ( 2017-1. 2. 1-NKP-2017-00002  to D. N. );  Hungarian Scientific Research Fund  ( NKFIH OTKA PD 124148  to  K. J. ,  NKFIH OTKA K 128016 ),  Janos Bolyai Research Fellowship of the Hungarian Academy of Sciences  (to K. J. ), the ÚNKP-19-3  New National Excellence Program  of the  Ministry for Innovation and Technology  (to K. H. ), and the  IDEXLYON Fellowship of the University of Lyon  as part of the  Programme Investissements d' Avenir  ( ANR-16-IDEX-0005  to D. N. ). D. N. is thankful for the support of  IMÉRA. The authors thank the help of Balázs Török in data acquisition and data analysis.
We consider the large sum of DC (Difference of Convex) functions minimization problem which appear in several different areas, especially in stochastic optimization and machine learning. Two DCA (DC Algorithm) based algorithms are proposed: stochastic DCA and inexact stochastic DCA. We prove that the convergence of both algorithms to a critical point is guaranteed with probability one. Furthermore, we develop our stochastic DCA for solving an important problem in multi-task learning, namely group variables selection in multi class logistic regression. The corresponding stochastic DCA is very inexpensive, all computations are explicit. Numerical experiments on several benchmark datasets and synthetic datasets illustrate the efficiency of our algorithms and their superiority over existing methods, with respect to classification accuracy, sparsity of solution as well as running time.
Datasets To evaluate the performances of algorithms, we performed numerical experiments on two types of data: real datasets (covertype, madelon, miniboone, protein, sensit and sensorless) and simulated datasets (sim 1, sim 2 and sim 3). All real-world datasets are taken from the well-known UCI and LibSVM data repositories. We give below a brief description of real datasets: • covertype belongs to the Forest Cover Type Prediction from strictly cartographic variables challenge 1. It is a very large dataset containing 581, 012 points described by 54 variables. • madelon is one of five datasets used in the NIPS 2003 feature selection challenge 2. The dataset contains 2600 points, each point is represented by 500 variables. Among 500 variables, there are only 5 informative variables and 15 redundant variables (which are created by linear combinations of 5 informative variables).
The 480 others variables were added and have no predictive power. Notice that madelon is a highly non-linear dataset. • miniboone is taken form the MiniBooNE experiment to observe neutrino oscillations 3 , containing 130, 065 data points. • protein 4 is a dataset for classifying protein second structure state (α, β, and coil) of each residue in amino acid sequences, including 24, 387 data points. • sensit 4 dataset obtained from distributed sensor network for vehicle classification. It consists of 98, 528 data points categorized into 3 classes: Assault Amphibian Vehicle (AAV), Dragon Wagon (DW) and noise. • sensorless measures electric current drive signals from different operating conditions, which is classified into 11 different classes 5. It is a huge dataset, which contains 58, 509 data points, described by 48 variables.
We generate three synthetic datasets (sim 1, sim 2 and sim 3) by the same process proposed in  Witten & Tibshirani (2011). In the first dataset (sim 1), variables are independent and have different means in each class. In dataset (sim 2), variables also have different means in each class, but they are dependent. The last synthetic dataset (sim 3) 1 https://archive. ics. uci. edu/ml/datasets/Covertype 2 https://archive. ics. uci. edu/ml/datasets/Madelon 3 https://archive. ics. uci. edu/ml/datasets/MiniBooNE+particle+identification 4 https://www. csie. ntu. edu. tw/ ˜cjlin/libsvmtools/datasets/multiclass. html 5 https://archive. ics. uci. edu/ml/datasets/Dataset+for+Sensorless+Drive+Diagnosis has different one-dimensional means in each class with independent variables. Detail produces to generate three simulated datasets are described as follows: • For sim 1: we generate a four-classes classification problem.
Each class is assumed to have a multivariate normal distribution N (µ k , I), k = 1, 2, 3, 4 with dimension of d = 50. The first 10 components of µ 1 are 0. 5, µ 2j = 0. 5 if 11 ≤ j ≤ 20, µ 3j = 0. 5 if 21 ≤ j ≤ 30, µ 4j = 0. 5 if 31 ≤ j ≤ 40 and 0 otherwise. We generate 250, 000 instances with equal probabilities. • For sim 2: this synthetic dataset contains three classes of multivariate normal distributions N (µ k , Σ), k = 1, 2, 3, each of dimension d = 50. The components of µ 1 = 0, µ 2j = 0. 4 and µ 3j = 0. 8 if j ≤ 40 and 0 otherwise. The covariance matrix Σ is the block diagonal matrix with five blocks of dimension 10 × 10 whose element (j, j ′ ) is 0. 6 |j-j ′ |. We generate 150, 000 instances. • For sim 3: this synthetic dataset consists of four classes. For class k = 1, 2, 3, 4, i ∈ C k then X ij ∼ N (0, 1) for j > 100, and X ij ∼ N ( k-1 3 , 1) otherwise, where N (µ, σ 2 ) denotes the Gaussian distribution with mean µ and variance σ 2.
Experiment setting We randomly split each dataset into a training set and a test set. The training set contains 80% of the total number of points and the remaining 20% are used as test set. In order to evaluate the performance of algorithms, we consider the following three criteria: the classification accuracy (percentage of well classified point on test set), the sparsity of obtained solution and the running time (measured in seconds). The sparsity is computed as the percentage of selected variables. Note that a variable j ∈ {1,. , d} is considered to be removed if all components of the row j of W are smaller than a threshold, i. e. , |W j,i | ≤ 10 -8 , ∀i ∈ 1,. , Q. We perform each algorithm 10 times and report the mean and standard deviation of each criterion. We use the early-stopping condition for SDCA and SPGD-ℓ 2,1.
Experiment 1 In this experiments, we study the effectiveness of SDCA. For this purpose, we choose the ℓ 2,0 regularization, and perform a comparison between SDCA-ℓ 2,0 -exp and DCA-ℓ 2,0 -exp. Furthermore, we will compare SDCA-ℓ 2,0 -exp with msgl and SPGD-ℓ 2,1 , two algorithms for solving the multi-class logistic regression using ℓ 2,1 regularization (c. f Section 4. 2). The comparative results between are reported in Table  2  and Figure   datasets (covertype, sensit, sensorless and sim 3) while SDCA-ℓ 1,0 -exp gives better results on 2 datasets (madelon and protein). The two biggest gaps (3. 49% and 1. 17%).
Experiment 2 In this experiment, in order to study the effectiveness of different non-convex regularizations ℓ q,0 , we compare three algorithms SDCA-ℓ 1,0 -exp, SDCA-ℓ 2,0 -exp and SDCA-ℓ ∞,0 -exp. The results are reported in Table  2  and plotted in Figure  2. In term of classification accuracy, SDCA-ℓ 1,0 -exp and SDCA-ℓ 2,0 -exp are comparable and are slightly better than SDCA-ℓ ∞,0 -exp. SDCA-ℓ 1,0 -exp produces similar results with SDCA-ℓ 2,0 -exp on 6 out of 9 datasets, where the gap is lower than 0. 3% in classification accuracy. For protein, sensorless and sensit, SDCA-ℓ ∞,0 -exp provides slightly better classification accuracy than SDCA-ℓ 1,0 -exp and SDCA-ℓ 2,0 -exp. This is due to the fact that SDCA-ℓ ∞,0 -exp selects much more variables than the two others. As for the sparsity of solution, SDCA-ℓ 2,0 -exp is the best on 8 out of 9 datasets (except for protein).
SDCA-ℓ 1,0 -exp selects moderately more variables than SDCA-ℓ 2,0 -exp, from 5. 67% to 17. 19%. In contrast to SDCA-ℓ 2,0 -exp, SDCA-ℓ ∞,0 -exp suppresses less variables than SDCA-ℓ 1,0 -exp and SDCA-ℓ 2,0 -exp on all datasets, except covertype. Especially, on dataset sensorless, SDCA-ℓ ∞,0 -exp selects 60. 42% (resp. 43. 23%) more variables than SDCA-ℓ 2,0 -exp (resp. SDCA-ℓ 1,0 -exp). In term of running time, SDCA-ℓ 1,0 -exp is the fastest and SDCA-ℓ 2,0 -exp is the slowest among the three algorithms. SDCA-ℓ 1,0 -exp is up to 3. 4 time faster than SDCA-ℓ 2,0 -exp and 2. 06 times faster than SDCA-ℓ ∞,0 -exp. Overall, SDCA-ℓ 1,0 -exp and SDCA-ℓ 2,0 -exp provide comparable results and realize a better trade-off between classification and sparsity of solution than SDCA-ℓ ∞,0 -exp.
Experiment 3 In this experiment, to study the effect of the approximation functions (capped-ℓ 1 and exponential approximation), we compare two algorithms: SDCA-ℓ 2,0 -exp and SDCA-ℓ 2,0 -capℓ 1. It is worth to note that capped-ℓ 1 function is nonsmooth, hence the resulting approximate problem is a nonsmooth (and nonconvex) problem. The results are reported in Figure  3  and Table  2. For sensit, madelon, sim 1, sim 2 dataset, both algorithms have similar performance in all three criteria. The differences in terms of accuracy are negligible (< 0. 1%), while the gaps of sparsity and running time are mostly the same. For sim 3 and miniboone dataset, both algorithms choose the same number of features. However, SDCA-ℓ 2,0 -capℓ 1 is faster than SDCA-ℓ 2,0 -exp (by 41% and 67% respectively), while SDCA-ℓ 2,0 -exp gives better (or similar) result in terms of classification accuracy.
For covertype, sensorless and protein dataset, SDCA-ℓ 2,0 -exp provides better results than SDCA-ℓ 2,0 -capℓ 1. SDCA-ℓ 2,0 -exp furnishes results with higher classification accuracy in 2 out of 3 cases (covertype and sensorless) while having lower lower sparsity in 2 out of 3 cases (protein and sensorless). In terms of running time, SDCA-ℓ 2,0 -exp is faster than SDCA-ℓ 2,0 -capℓ 1 by at least 1. 5 times. Overall, SDCA-ℓ 2,0 -exp clearly shows better results SDCA-ℓ 2,0 -capℓ 1 in three criteria. This implies T l i (x) ≥ F i (x) + ǫ l i ≥ F i (x) for all l ≥ 0, i = 1,. , n. We also observe that x l+1 is an ǫ l -solution of the following convex problem min x T l (x) := 1 n n i=1 T l i (x) (A. 1) Therefore T l (x l+1 ) ≤ T l (x l ) + ǫ l = T l-1 (x l ) + 1 n i∈s l [T l i (x l ) -T l-1 i (x l )] + ǫ l = T l-1 (x l ) + 1 n i∈s l [F i (x l ) + 2ǫ l -T l-1 i (x l )] + ǫ l , (A.
Comparative results on both synthetic and real datasets. We have proposed two novel DCA based algorithms, stochastic DCA and inexact stochastic DCA for minimizing a large sum of DC functions, with the aim of reducing the computation cost of DCA in large-scale setting. The sum structure of the objective function F permits us to work separately on the component functions F SDCA-ℓ 2,0 -exp outperforms the two related algorithms msgl and SPGD-ℓ 2,1. We are convinced that SDCA is an efficient variant of DCA, especially for large-scale setting.
Acknowledgement The first two named authors were supported by the  China Scholarship Council. The second author's work was done during his visit at  Institut Camille Jordan, Université Claude Bernard Lyon  1 in 2018-2019. The first author was supported by the  Israel Science Foundation  (grant no. 1970/18 ) during the revision of this work. An extended abstract of this paper will appear in the Proceedings of the 32nd Conference on Formal Power Series and  Algebraic Combinatorics  (FPSAC '20).
For better reference, we have chosen to formulate our results in the introduction in terms of number fields. But as is well known, given a number field k and a linear algebraic k-group G, the restriction of scalars functor Res k 4 we explicitly compute the Euler characteristic of the arithmetic spin groups Γ m,n. Acknowledgements. H. K. , S. K. , and R. S. acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foun- dation) 281869850 (RTG 2229) and 338540207. J. R. acknowledges support by ANR grant ANR-16-CE40-0022-01 -AGIRA. 2. Profinite invariance of fundamental rank and dimension mod 4 Q as for instance introduced in [48, Section 2. 1. 2, p. 49] comes with a natural isomorphism Res k Q.
Consequently, all parameter combinations that match the synthetic 60 keV line with the observed line result in a large correlation which can be seen by the yellow line in Fig. 5. Nevertheless, the obtained parameter set for the best correlation fits the measurement well, see Fig. 6. Figure  7  shows for the same calibration measurement the result of ECC AMR after 5 iterations. The initial grid was chosen to ∆o = 500 ADU and ∆g = 10 ADU/keV, leading to 400 initial correlations and a final resolution of ∆o ≈ 2 ADU Figure  9  shows the correlation map for the same dataset but using ECC AMR with disabled adaptive mesh expansion. The global maximum cannot be found in this case because the initial grid shows near the global maximum a relatively low correlation value of cor ≈ 3. 2 which is only 44 % of the maximal initial correlation value.
Acknowledgements Most of the present work was carried out while the second author was a postdoc at IRMAR. He would like to thank the  IRMAR  and the  Université de Rennes  for hosting him during this period. We would like to thank  Thiago Fassarella  and  Néstor Fernandez Vargas  for many valuable discussions on this topic. We also thank  Nicolas Tholozan  who helped us to understand the action of Φ top on the symplectic 2-form on the monodromy side. We're also thankful to the anonymous referees for providing many suggestions to improve the content and clarity of the text. F. L. acknowledges the support of  CNRS  and the project Foliage  ANR-16-CE40-0008. V. R. was supported by the grants  PAPIIT IN-106217 ,  CONACYT 219722 , and the  PRESTIGE postdoc program  (coordinated by  Campus France  and co-financed under the  Marie Curie Actions -COFUND  of the  FP7 ).
Outline of our approach The approach to adjusting for biases based on empirical evidence involves fitting a hierarchical model to the data from trials included in each of a collection of meta-analyses  (17). For our investigations we used data from the Risk of Bias in Evidence Synthesis (ROBES) study  (6). Within each meta-analysis extracted from the ROBES database, we selected the two trials with the highest and lowest model-based bias estimates, and then elicited opinion on which trial was judged to be more biased. We examined agreement between model-based and opinion-based estimates of bias within selected pairs of trials.
ROBES study The ROBES database consists of meta-analyses extracted from the April 2011 issue of the Cochrane Database of Systematic Reviews, in which Cochrane review authors had implemented the 'risk of bias' tool to assess potential biases in included trials  (22). The ROBES study  (6)  included 228 metaanalyses in total, from Cochrane reviews that reported information on all five recommended risk of bias domains: sequence generation, allocation concealment, blinding, incomplete outcome data and selective outcome reporting. Review authors had recorded whether there was a low, high or unclear risk of bias in each bias domain, together with comments or quotes from the trial publication to justify each judgement. Meta-analyses were excluded if they included fewer than five trials or if a summary estimate was not reported in the review (for example, because pooling was considered inappropriate).
Selection of pairs of trials within meta-analyses For each meta-analysis, we selected a pair of trials with the highest and lowest model-based bias estimates, representing the least and the most biased trials among those included in the meta-analysis, for each of four bias domains: allocation concealment; sequence generation; blinding and incomplete outcome data. These pairs were selected in order to present them to expert assessors, asking them which trial of each pair they judged to be at the greatest risk of bias in each domain examined. The process of selecting pairs of trials is described in detail below. For each bias domain in turn, we first sampled 30 meta-analyses from the ROBES study. Metaanalyses included in the ROBES study were sampled from the Cochrane Database of Systematic Reviews in April 2011.