dataesr/scientific-paragraphs-categorization huggingface dataset:
Real HIV dataset The HIV reverse transcriptase dataset we analyzed is based on the nucleotide alignment provided in  (Lemoine et al. 2018 ) which we downloaded from https://github. com/evolbioinfo-/booster-workflows/tree/master/data/vih. This is an alignment of 9,147 HIV-1 group M polymerase sequences. The authors indicate that this alignment contains recombinant sequences, which we have removed based on the JPHMM output file provided in their supplementary data (https://github. com/ evolbioinfo/booster-workflows). We then extracted the B subtype sequences from this alignment using their annotation file "pol_nonrecombinant. txt". Finally, we added the reference sequence HXB2 (GenBank TM accession number K03455) from which the position numbering and the ancestral amino acids in the DRMs notation are derived.
The resulting alignment contains 3,557 B subtype sequences and 1,043 nucleotide positions. As outgroup, we downloaded the group M subtype reference alignment (user-defined range 2258-3300) from the Los Alamos HIV database (https://www. hiv. lanl. gov/content/index). We removed subtype B sequences from the outgroup and added the sequences to Lemoine et al MSA, resulting in an MSA of 3,592 nucleotide sequences which we translated into amino acids. After tree reconstruction and rooting (as explained in subsection "Tree reconstruction by maximum likelihood") we visually checked the rooting of the tree with Itol  (Letunic and Bork 2019). We removed from the MSA 11 sequences classified as B (but likely recombinant), which were placed among the outgroup and obtained a monophyletic group of 3,546 B subtype sequences and the corresponding rooted tree.
Synthetic HIV-like alignment We used the sierrapy (https://github. com/hivdb/sierra-client/tree/master/python) fasta command to locate (positions and sequences) the DRMs present in the HIV-1 subtype B MSA of 3,557 sequences. The list of mutations used by sierrapy can be found at "https://hivdb. stanford. edu/hivdb/by-mutations". Then, we replaced positions with DRMs with unknowns in the corresponding sequences. The phylogeny, thus unaffected by DRMs, was reconstructed as explained in subsection "Tree reconstruction by maximum likelihood". This phylogeny was therefore different from the one representing the real data because the aim here was not the same. In the first case, with the real data, we did not remove the DRMs because we wanted to be agnostic of any convergence before applying ConDor.
Rhodopsin dataset Protein data of rhodopsin and fish habitat were retrieved from https://github. com/ Clupeaharengus/rhodopsin/tree/master/phylogeny_habitat. We extracted the 2,056 sequences from "spp_to_keep. txt" from the file "final_alignment. translated. fullrhodopsin. fasta" and removed 7 badly aligned sequences. We used the same sequences used for rooting than in  (Hill et al. 2019 ) (Huso huso and Polyodon spathula). The habitat was provided in the file "rabo_allele_hab. tsv" from the repository provided in  (Hill et al. 2019).
MEME We used MEME  (Murrell et al. 2012)  to search for positions under episodic positive selection on the nucleotidic HIV-1 MSA. The threshold for significant positions was set at a p-value of 0. 05, without correction for multiple testing, as their test tends to be conservative and "traditional setting of multiple testing (multiple tests on the same data) does not directly apply here" (https://github. com/veg/hyphy/issues/851 and https://github. com/veg/hyphy/issues/188). Thus, the proportion of false positives we expect is approximately equal to 0. 05 multiplied by the number of positions that are under positive selection (here 0. 05x32≈2).
PCOC We used PCOC  (Rey et al. 2018)  to detect convergent positions based on the knowledge of the habitat (marine vs fresh/brackish water). We used the profile C10 (-CATX_est 10) with 4 gamma categories (--gamma) and fixed the posterior probability threshold of a position to be above 0. 8 (f 0. 8). For the convergent scenario (-m) corresponding to the different clades of nodes which exhibit the convergent transition, we considered that the convergent tips were those with the fresh/ brackish water environment. Then, we retrieved all internal nodes the tips of which were in the convergent environment and completed the scenario, as described in the user guide (https://github. com/ CarineRey/pcoc).
BayesTraits In the rhodopsin dataset, correlations between fish habitat and mutations detected as convergent by ConDor were measured with BayesTraits 'discrete dependent' model  (Pagel 1994; Pagel & Meade 2006). Prior to running the software, we transformed our data into discrete binary traits. This way, marine habitat was annotated as 1 and fresh/brackish water as 0. Similarly, for a given position, the convergent change had the value 1 and the other amino acids at that position the value 0. We followed the procedure detailed in http://www. evolution. rdg. ac. uk/BayesTraitsV3/Files/-BayesTraitsV3. Manual. pdf to assess whether the dependence between both traits was more likely than their independence. The dependence hypothesis was retained if the Bayes factor was greater than 10. Priors for the transition rates were estimated using the output provided by the maximum likelihood models as described in the user guide.
List of the 37 DRMs and their detection status on the real HIV-1 subtype B MSA. This table presents the 37 DRMs that we used as true convergent events for the real HIV-1 subtype B MSA. The chosen DRMs correspond to the "Essential DRM Data" data from the Stanford University Drug resistance database (https://hivdb. stanford. edu/pages/poc. html) from which we selected only mutations found in at least 12 sequences and more than 2 EEMs, i. e. , found in two distinct clades in the real HIV-1 tree. Number of sequences: number of sequences in which the corresponding DRM was 6 found in the real data. Number of EEMs: number of independent emergence-events of mutation that was inferred for the DRM by ancestral reconstruction and counting. Detected: If they were detected or not as convergent by ConDor and thus found as true positives.
2017)  available at https://github. com/arzwa/MultilocusIsland. In the following sections, we build up a theoretical approximation to this fairly general multilocus model, and validate the approximations by comparing numerical results against individual-based simulations. We first derive the dynamics at a single locus, considering both deterministic and stochastic models. Next, we derive an approximation to the effective migration rate for the multilocus model using a rather general argument based on the reproductive value of migrant individuals. Lastly, we approximate the allele frequency dynamics of the multilocus model by plugging in the effective migration rate, which captures the effect of LD among selected alleles on the dynamics at a neutral locus, in the single locus theory.
e. (E[p 1 q 1 ],. E[p j-1 q j-1 ], E[p j+1 q j+1 ],. , E[p L q L ])). To solve this system of 2L nonlinear equations, we use the fixed point iteration outlined in sec. S2. 3. The numerical methods used in this paper are also implemented in the Julia package available at https://github. com/arzwa/MultilocusIsland.
Latent class analysis (LCA) based on 3-month FACE study data categorized patients into six clusters based on 21 parameters from HF condition to SDB characteristics, resulting in meaningful clinical phenotypes  [19]. This categorization effectively differentiated between clusters with respect to prognosis at the 3-month follow-up (see graphical abstract)  [19]. The current analysis used 2-year follow-up data from the FACE study to determine whether the effects of ASV differed between patient clusters.
Study design The multicenter, prospective, observational cohort FACE study (NCT01831128) was conducted at 28 centers in Europe between November 2009 and September 2018  [20]. Ethical approval, the study protocol was approved by 'Le Comité consultatif sur le traitement de l'information en matière de recherche en santé' (C. C. T. I. R. S no 09. 418). The study was conducted in accordance with local laws/regulations, International Conference on Harmonization-Good Clinical Practice (ICH-GCP), ISO 14155 Standard Operating Procedures, and the Declaration of Helsinki and its current revision. An Executive Steering Committee provided independent oversight of the study.
Statistical analysis Statistical analyses were performed using SAS v9. 4 (SAS Institute), and a p-value of ≤0. 05 was defined as statistically significant. Baseline comparisons between groups were performed using the Mann-Whitney test for quantitative variables and the Chi-squared test or Fisher test for qualitative variables. All available data were included in the analyses unless consent for data usage was revoked  [20]. Variables with <20% missing values were imputed using multiple imputations: ten imputed datasets were constituted using a Monte-Carlo Markov Chain for quantitative variables and fully conditional specification for qualitative variables. Imputed datasets were combined using Rubin's rules. Two-year event-free survival (primary and secondary endpoints) was estimated using the Kaplan-Meier method and compared between the ASV and control groups using a two-sided log-rank test.
Sources of funding The FACE study was supported by unrestricted grants from ResMed. R. T. , S. B. and J-L. P. are supported by the French National Research Agency in the framework of the "Investissements d'avenir" program (ANR-15-IDEX-02) and the "e-health and integrated care and trajectories medicine and MIAI artificial intelligence" Chairs of excellence from the Grenoble Alpes University Foundation. This work was partially supported by MIAI @ Grenoble Alpes, (ANR-19-P3IA-0003).
Tomography analysis X-ray tomography was employed to image the specimen at several stages of the bending test. For each scan, numerous projections were taken at equally spaced angular positions at a constant load. These projections were then processed using a filtered-back projection algorithm to create a three-dimensional volume. The specimens were imaged using the Vtomex tomograph by phoenix|x-ray systems (Niels-Bohr-Strasse 7, Wunstorf 31515, Germany) at Laboratoire MATEIS (INSA Lyon, France)  [24] [25] [26] [27]. The scanning parameters for each experiment are provided in Table  1. Volume reconstruction was performed using the Phoenix system's proprietary software, "datos|x", version 2. 0. Prior to reconstruction, the offset from the ideal rotational axis was corrected, and a multi-material filter, a beam hardening correction and a low noise filter were applied.
Finally, the volume and center of mass were calculated for each labeled ball. Subsequent data analysis was performed using Mathematica 13. 1 from Wolfram Research, Inc. (100 Trade Center Drive, Champaign IL 61820-7237, USA). For each tomograph, the vertical distance between the support balls and the loading ball was determined and their positions examined for any deviations from the ideal setup. In the results presented in this study, no significant misalignments were detected. If the testing fixture was tilted, the measured distances were corrected accordingly.
Numerical methods The primary FEA-model used in this study is shown in Fig. 6a ). Due to the problem's symmetry, modeling only half of the setup is sufficient. The model was implemented in ANSYS Mechanical Release 2022R1 by ANSYS Inc. (Southpointe 2600 Ansys Drive, PA 15317, Canonsburg, USA) using an APDL (Ansys Parametric Design Language) script. This approach provides detailed control of the model and complete documentation of all input parameters and model changes. The model consisted of approximately 50,000 SOLID186 20-node brick elements and 200,000 nodes (the exact numbers depend on the specimen's thickness). The contact between the balls and the specimen was modeled through symmetrical contact using CONTA174 and TARGE170 elements, with a friction coefficient of 0. 5. A mesh convergence analysis was conducted for specimen deflection to ensure consistent results.
Radiography Fig. 9a ) and Fig. 9c ) present results from radiograph analysis in comparison to linear and non-linear FEA. Note that for better visualization, only every twentieth measurement from the experimental data is shown. The maximum load has doubled compared to tomography experiments. While tendencies align closely with non-linear FEA, there is an offset of approximately 190 μm in the ball distance at 1 N for both specimens. The origin of such an offset is discussed in the following section. Correcting each measured distance by this difference, Fig. 9b ) and d) are obtained. This correction eases a comparison of the tendencies between the experimental measurements and non-linear FEA results. With increasing load, higher deflections are measured compared to FEA. A maximum deflection of about 620 μm and 580 μm was measured for specimen C and D, respectively, exceeding 4 times the specimen's thickness.
Summary This work serves as a follow-up to a previous publication on the Ballon-Three-Balls-test  [14]. That publication discussed and quantified the influence of non-linear effects on the measured strength through Finite-Element-Analysis (FEA). To validate these theoretical findings experimentally, deflection measurements via X-ray tomography were employed in the present work. The specimen's deflection is determined from a three-dimensional reconstruction (tomograph) of the specimen and load/support balls. Two-dimensional radiographs provide a continuous alternative to discontinuous tomography measurements. Through this approach, the amount of deflection data is substantially increased. In general, excellent agreement between the deflection obtained through tomography and through FEA was observed.
Acknowledgements  M. Staudacher  gratefully acknowledges financial support by the  Austrian BMVIT  and  BMWFW  in the project " CharAM " ( FFG 877684 ) of the  COIN/IraSME program. The authors are grateful to the  JECS Trust  for funding the visit of  M. Staudacher  to  INSA Lyon  (Contract No. 2022305 ). The authors further thank  SKF Austria AG  for providing the Si 3 N 4 bearing balls.
46  c. Data for the METTL3-14-BA complex structures deposited to the Protein Data Bank (PDB). All the crystallized BAs bind in the METTL3 active site (Figure  3A ). BA1 and BA6, that are missing the methionine part of the SAM analogue or have a polar urea group in the linker, respectively, are the least potent of the crystallized compounds (see Table  1 ). Furthermore, in their crystal structures with METTL3, they reveal divergent interactions of their SAM-like moiety compared to SAM (Supplementary Figure  1 ). For BA2 and BA4, however, the interaction of their SAM-like moiety is the same as for SAM (Figure  3B-F ). Both ligands bind with their SAM moiety in the active site lined with METTL3 hydrophobic residues and form polar contacts to conserved residues, namely D395, R536, H538, and N539 via the methionine part and D377, I378, F534, N549, and Q550 via the adenosine moiety of 5'-N-SAM.
Acknowledgments This work was supported by a grant of the  Swiss National Science Foundation  to A. C. (grant number  310030-212195 ). The MD simulations were carried out at  Eiger@Alps  at the  Swiss National Supercomputing Center (in Lugano, Switzerland). This work was further supported by a grant of the  French Agence Nationale de la Recherche (ANR) , Project  ARNTools , to M. E. Q. (grant  ARNtools-19-CE07-0028-01 ). The QM/MM study was supported by the  NIH  Grant  R35-GM141930  to Q. C. Computational resources from the project  BIO230101  allocated through ACCESS are greatly appreciated; part of the computational work was performed on the Shared Computing Cluster which is administered by  Boston University 's Research Computing Services (URL: www. bu. edu/tech/support/research/).
Data availability All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. The coordinates of the METTL3-14-bisubstrate analogue complexes have been deposited in the Protein Data Bank under accession numbers 8PW9 (BA1 complex), 8PW8 (BA2 complex), 8PWA (BA4 complex), 8PWB (BA6 complex).
The calibration problem in machine learning classification tasks arises when a model's output score does not align with the ground truth observed probability. There exist several parametric and non-parametric post-processing methods that can help to calibrate an existing classifier. In this work, we focus on binary classification cases where the dataset is imbalanced, meaning that the negative class significantly outnumbers the positive one. We propose new parametric calibration methods specific to this case and a new calibration measure focusing on the primary objective in imbalanced problems: detecting infrequent positive cases. Experiments on several datasets show that, for unbalanced problems, our approaches outperform state-of-the-art methods in many cases.
A common and complex situation arises when dealing with highly unbalanced datasets in binary classification problems  [6]. This imbalance is characterized by a disproportionate number of instances of the negative class compared to those of the positive class. As a result, it can have a negative impact on the performance of the fitted model. Many real-world problems are inherently imbalanced such as medical diagnostic  [1]  or fraud detection  [7] , and resampling methods are commonly used to achieve better performance. However, these resampling methods introduce a bias in the dataset, making the calibration process even more important  [8] [9] [10]. Because resampling methods are often used to enhance performance in imbalanced problems, it is crucial to have good calibration methods in this context  [6].
Traditional re-calibration frameworks need to extract a calibration set from training to fit the shape of miscalibration with unseen data  [5]. Yet, in general, the larger the training dataset, the better the performance. Moreover, in imbalanced data, we might have difficulties retrieving samples belonging to the minority class, which makes the size of the training dataset even more crucial to achieve good performance. Thus, achieving good calibration on a small calibration set is essential to keep more data for training. To do so, we propose new parametric calibration techniques to deal with imbalanced data, where the data is rebalanced, that perform well with respect to small calibration sets. Conventional calibration error measurements are generally computed on the entire validation or testing dataset  [4].
But when we are faced with problems of detecting rare events (such as disease or fraud detection), we are generally interested in the small number of observations detected as positive by the model. In this paper, we introduce a new measure of calibration error specific to the unbalanced case that considers only the observations with the highest positive class scores. The data and code ensuring the reproducibility of the experiments presented in this work are available at https://github. com/theoguilbert/imbalanced calib. Contribution. In this paper, we focus on imbalanced binary classification with undersampling and a low amount of data available for the calibration set: • The existing calibration metric ECE is discussed and tuned to reflect the intuition one might want to have in the context of detecting rare events.
Related work To cope with imbalanced datasets, the skew in class distributions can be mitigated thanks to traditional methods such as oversampling or undersampling  [6, [11] [12] [13]. While the first requires the creation of synthetic data, this work focuses only on undersampling techniques. Such techniques impact calibration, and it is needed to re-adjust the posterior probability obtained from the model trained on the balanced data. In  [8] , the authors showed that we could derive a straightforward relation between the posterior probability and the readjusted one under the assumption that training and testing distributions are similar (i. e. no prior shift). Thus this method corrects miscalibration due to resampling but does not correct miscalibration due to inherent properties of the model as shown in  [2].
In the general case of calibration (dealing with a dataset more or less balanced), few works have been done on new parametric methods. In  [15] , the authors introduced parametric methods restricted to a polynomial non-decreasing shape. While this method has been developed in the context of balanced calibration, based on this work, we will introduce polynomial methods as well (with some differences and variants) in the context of imbalanced classification with undersampling techniques, where the legitimacy of these methods is even stronger. Usually, we calibrate a model on a hold-out calibration set following the same distribution as the training one. However, with undersampling techniques, the training distribution is shifted to a balanced one. Thus a distribution shift occurs between training and calibration sets resulting in poor calibration.
There exist several kinds of distribution shifts such as covariate shift, prior probability shift, and concept shift  [16, 17]. In  [18] , the authors proposed a method to calibrate posterior probability in an imbalanced dataset under prior probability shift and likelihood shift. Prior probability shift corresponds to the case where the class distribution is different between train and test (P train (class) ̸ = P test (class)). Likelihood shift corresponds to the case where the feature distribution giving one class is different between train and test without introducing new semantic labels (P train (f eature|class) ̸ = P test (f eature|class)). In  [18] , the authors approach the likelihood shift as a calibration problem and propose a unified way to deal with calibration and re-adjusting the score of a test sample regarding the prior probability shift between training and testing.
Formalization Let D = {(x i , y i )} N i=1 be a supervised dataset with N independent observations obtained from the joint distribution (X, Y ) ∼ F XY (x, y) where X ∈ X ⊂ R d and Y ∈ Y = {c + , c -}. As |Y| = 2, we are in a binary classification problem and, by convention, c + (resp. c -) is the positive (resp. negative) class. We define D + (resp. D -) as the subset of D containing all the positive (resp. negative) samples from D. Assuming that we are in a highly unbalanced problem, the number of elements in D + is much smaller than the number of elements in D -; i. e. |D + | ≪ |D -|. Similarly, let us define D tr , D cl , and D ts as the training, calibration, and test datasets, respectively. Following the standard supervised classification setup, we use D tr to fit a probabilistic classifier model h : X → [0, 1].
When the binning scheme is adaptive (same number of samples per bin), the weighted average of gaps corresponds to the ACE (see Figure  1b ). inherently calibrated and overestimates the true probability in low-confidence intervals and underestimates it in high-confidence intervals. These estimators have several biases, coming from binning schemes, hyperparameters such as the number of bins, and the finite sample size used to estimate the per-bin statistics  [4, 14, 21, 22]. Furthermore, imbalanced datasets have a non-symmetric data distribution across the confidence interval. Since the ECE computes a weighted average of the errors across each bin, the bins with few data points will have insignificant weights compared to others. Consequently, degenerate measurement can arise since ECE will mainly be determined by the first bins, resulting in low ECE but a mediocre reliability diagram  [9].