dataesr/scientific-paragraphs-categorization huggingface dataset:
Experiments In this section, we study the performances of the second-order recursive algorithm (SR defined by (  8 )) for ridge linear regression, and the stochastic newton algorithm (SN defined by (  9 ) and (  13 )) for both ridge linear regression and ridge logistic regression. We use the statistical software R  [24]  to carry out our numerical experiments. In these experiments, we compare our methods to the averaged implicit stochastic gradient descent (AI-SGD) proposed by  [29]  and available in the R-package sgd. As SR and SN algorithms, AI-SGD algorithm is also a recursive algorithm, but it is a first order method. However, it usually achieves superior results to classical stochastic gradient descent. When the data are regularized, we also compare our methods with the cyclical coordinate descent (CDD) proposed by  [8]  and available in the R-package glmnet.
Results and comments For real data, the choice of regularization parameter λ is of course important and in practice it is often chosen using a cross-validation step. In  [28] , authors suggest to set λ to 1/n with n the number of observations, which is in the range of the smallest values that would generally be applied in practice. In the Python-package sklearn  [23] , the value of λ also defaults to 1/n. However, when data are sequentially obtained, crossvalidation approach is forbidden and n is unknown, but it is always possible to arbitrarily choose the value of λ so that strong correlations are taken into account. We therefore decided to perform experiments with λ = 1 and λ = 1/n. For BUZZ dataset, we employ ridge linear regression to predict the activity volume. Results obtained for BUZZ dataset, are stated in Table  3.
The proposed algorithms perform better than AI-SGD on BUZZ with higher explained variance and lower RMSE on both training sample and test sample, but they perform slightly worse than CCD. However, it is no less important to remember that CCD is a iterative method, while our algorithms are recursive. For COVTYPE dataset, we use ridge logistic regression to predict the variable "covertype". We can observe from Table  4  that the proposed method achieves the same accuracy as CCD on COVTYPE, which is remarkable as our method is recursive. Moreover, it provides higher accuracy than AI-SGD on both training sample and test sample.
aureus isolates retrieved from the PATRIC database yielded GTM models with reasonable accuracy for all drugs (balanced accuracy values ≥0. 75). The GTMs represent data in the form of illustrative 2D maps of the genomic space and allow for antibiotic-wise comparison of resistance phenotypes. In addition to that, the maps were found to be useful for the analysis of genetic determinants responsible for drug resistance based on the data from the PATRIC database. Overall, the GTM-based methodology is a useful tool for the illustrative exploration of the genomic sequence space and modelling AMR and can be used as a tool complementary to the existing ML methods for AMR prediction.
Data acquisition and pre-processing Pathosystems Resource Integration Center (PATRIC) database  [27]  was used to retrieve bacterial genomes of S. aureus with available AMR profiles, e. g. labelled as resistant or susceptible according to experimental minimal inhibitory concentration (MIC) breakpoints. A contigsbased representation thereof was downloaded from the PATRIC database. The detailed pre-processing protocol is provided in Supplementary Information Text S1. The final number of pre-processed S. aureus isolates was 5773. The overall number of antibiotics after pre-processing was 11. The antibiotics against S. aureus and the corresponding number of resistant and susceptible data points extracted from the PATRIC database after decreasing the majority class size, i. e. by randomly removing data points of the majority class until reaching the class ratio of 1:1 are reported in Table  S1.
Generation of k-mers Given the lengths of bacterial genomes, the number of generated k-mers can soar up to tens of millions, depending on k-mer length. Such datasets with an extremely small number of samples relative to the number of features, commonly denoted as 'fat data', are reputedly difficult ML challenges  [14]. Therefore, an additional preprocessing procedure was applied to reduce the number of features. Namely, PCA and kernel PCA (kPCA) were used for feature space reduction. In more detail, k-mers (10-, 15-, and 30-mers) were generated using two programs: dsk for 10-mers  [28]  and Kmer-db for 10-, 15-, and 30-mers  [29]. Herein, Kmer-db was used to calculate kmer counts and estimate distances between sequences using different metrics (i. e. Jaccard, cosine, max, min, ani, Mash). The Kmer-db approach was applied for the generation of kernel-PCA pre-processed descriptors, whereas for PCA pre-processed descriptors the dsk tool was used since it enabled direct extraction of k-mers' counts in the text format.
Analysis of resistance determinants using genome features landscapes Besides the comparative analysis of the resistance profiles, the GTM can be used to analyse the distribution of the genomic features and their relationship with the resistance. For this purpose, data on genomic features, which are defined segments of genome usually related to protein and RNA-coding genes, present in the PATRIC database were used  [27]. The genomes from PATRIC are annotated by these features using either the original information provided in GenBank or annotations assigned using a RAST pipeline  [27] ,  [44]. In this context, the maps can be used either to visualize the distribution of sequences containing the specific genetic feature and compare it with the resistance landscapes or select a specific part of the map and determine which genetic features are abundant in this particular zone on the map.
aureus was 48. 8 M, from which the overall number of generated unitigs was 2. 4 M. The descriptors were pre-processed in a way to remove rare and quasi-constant descriptors, hence leading to the reduction of the feature space to ~976 K (number of unitigs). Quasi-constant (variance threshold of 0. 05) and rare descriptors (k-mers present in •1 % of the dataset) were filtered out since their inability to differentiate across sequences. However, such significant feature space dimensionality reduction was still not sufficient, thus compelling us to apply Jaccard kernel PCA (kPCA) pre-processing and finally retrieve first 300 principal components (PCs) as descriptors. The 300 first PCs were chosen as they allowed us to preserve the variance of the original dataset.
• We captured and make available a novel eye-tracking dataset including the eye-gaze activity and head movements of 50 participants freely exploring three different virtual scenes in a variety of conditions. The dataset is also made available for the community, along with our framework implementation 1. Overall, we believe that our results will open the way for natural and intuitive manners of designing and generating realistic gaze animations for real-time applications. 1. https://github. com/igoude/saliency-driven-gaze.
4) The position and duration of the new fixation are randomly sampled, using the fixation map and the predetermined fixation duration distribution. 5) An animation of the character's eyes and head is computed to reach this new fixation point, simultaneously generating eye blinks in a consistent way. Our Gaze Simulation process is built on three main com-ponents (presented vertically in Figure  1 ) that are strongly data-driven: a saliency model, a saccadic model and an eye-head animation model: 1) The saliency model takes as input the image of the scene rendered from the point of view of the character and generates a saliency level (a scalar value) for each pixel of this image. This saliency map is predicted by a network called MSI-Net which is itself trained on a dataset combining images (of natural scenes) and eye-tracking data (filtered fixations of viewers).
While there might be some domainshift issue due to the current model being trained on 2D natural images and applied to 3D rendered scenes, this approach has already been used with success on rendered 3D objects  [22]. Additionally, the scenes that we use are quite sparse in objects and details. This means that visual attention will be mostly drawn by low-level features, such as color or luminance contrasts, which are very well extracted by deep saliency models. These elements are further discussed in Section 6. 2) The saccadic model captures the probabilities of saccade kinematic variables (saccade amplitude and orientation) as well as duration, which enables us to generate realistic transitions between different eye fixation points. This model relies on a saccadic map and a probability of fixation duration, which can be extracted from existing eye-tracking datasets.
Implementation details This workflow was implemented in Unreal Engine 5, using MetaHuman characters to apply our gaze simulation model. The saliency model is trained on natural images and implemented in C++ with the Libtorch library. The saccadic map and the fixation duration probability used by the saccadic model are extracted from the data gathered by David et. al. [23]. The results to be presented in this section were computed using a Dell Precision 7528 (CPU intel CORE i7 vPro 8th Gen, GPU NVidia Quadro M2200, 32GB RAM). Our model has a low impact on performance as the gaze simulation process occurs only once at the end of each fixation, i. e. , every 100 to 400 ms. The computation time regarding the scene rendering depends on both the complexity of the scene and the rendering quality expected.
Eye-Gaze Data Collection This section briefly presents the experimental details for the collection of the ground truth eye-gaze activity, and we refer the reader to the supplementary material for the full experimental description. Fifty participants, who volunteered for our experiment, were equipped with an HTC Vive Pro Eye Head Mounted Display, which includes a built-in eye-tracker used as an assessment tool of saccadic eye movement  [25]. Participants were immersed in the four virtual scenes presented in Section 3. 3 (see Figure  2 ). The lobby room was used for training purposes, as well as for checking eye-tracking accuracy between trials, while the waiting room, bar, and poker table scenes were used for collecting ground truth data. For each of these three scenes, we also included combinations of the two following situations: 1) Populated: the scene either included virtual characters or not.
In the Actor configuration, the character's eyes, head and eye blinks were animated using the recorded data of three participants randomly chosen from the user study presented in Section 4. 1. We chose 15 seconds of the collected data corresponding to the beginning of their immersion when they discovered the lobby. Participants were instructed to watch each video as many times as they wanted, before and while answering how much they agreed with the five following statements (answered on a 5-point Likert-scale ranging from 1: strongly disagree to 5: strongly agree), which were designed to judge the realism of eye-head animations: S1 The character's eye activity is realistic, it resembles that of a real human S2 The character seems aware of his environment, he is part of the scene S3 Apart from what he is looking at, the movement of his eyes and head resemble those of a human S4 The character seems to be looking at the opposite character or at the objects on the table  S5  Apart from what he is looking at, the movement of his eyes and head seem realistic to me S 1 is intended to provide a general idea of the realism of the animation of the eyes, while S 3 and S 5 are more focused on the joint realism of the eye and head movements.
This model provides a solid basis for the simulation of characters freely exploring their environment, as well as for generating more elaborate gaze behaviors. We demonstrated, through both objective and subjective evaluations, the achieved level of realism and the contributions of the various components of our solution. A key point in our approach is the coupling of a saliency and a saccadic model that can both be tuned by providing datasets corresponding to the desired context of usage. In the following, we will present the limitations of our approach. Visual saliency model: We rely in our approach on the deep saliency model MSINet, which was trained to predict the saliency of natural images. Because of discrepancies between virtual and real scenes, its performance can be impacted when the visual rendering quality differs significantly from real images.
In our implementation, we therefore use a physically-based rendering engine that realistically simulates light interactions to render High Dynamic Range images. Relying on a saliency model learned on natural images might however become more problematic in situations that involve low realism or non-photorealistic rendering, such as creating eye-gaze animations for cartoon characters, which might require to specifically train the saliency model using a different dataset (e. g. , comics  [33] ). Saccadic model: Similarly, our saccadic model uses a single saccadic map for all our visual examples. However, previous work has shown that eye movements are specific to an environment and a task  [34] , and can also be influenced by the individual  [35]. In an ideal situation, creating realistic eye-gaze animations would require to use a different saccadic map for each specific environment, task, character, etc.
While this would be necessary to simulate specific behaviors, such as the gaze behavior of a person reading which displays most saccades to the right in an Europeanlike culture and only occasionally to the left when starting a new line, creating these maps requires specific datasets which are extremely tedious to acquire. In specific cases, it would also be possible to rely on the existing literature on the subject, e. g. , to create saccadic maps typical of children behaviors  [35] , or representative of certain pathologies  [36]. Furthermore, the saccadic map used in our model was abstracted from the data of the VR study for 360 videos  [23]. This can potentially have an effect on the resulting realism, as VR is known to induce various biases, including eye-gaze differences compared to real situations  [24] ,  [37] , whether it is due to the restricted field of view or to the absence of other stimuli (e.
AlphaFold predictions A SBGrid consortium installation of AlphaFold version 2. 3  70, 71  was run on a local server equipped with a NVIDIA Tesla P100 GPU in order to predict the structure of the ACKR3 monomer and ACKR3/β-arrestin1 heterodimer. The full databases were used, with max_template_date = 2023-04-09. The model_preset option was set to "monomer" for ACKR3 and to "multimer" for the heterodimer. All other parameters were left to their default values.
Acknowledgments This research was funded by  European Union 's  Horizon2020   Marie Skłodowska-Curie Actions  (MSCA) to OO, RL, TD, SG and CB who are part of the  Marie Skłodowska-Curie Innovative Training Network ONCORNET2. 0 " ONCOgenic Receptor Network of Excellence and Training " ( MSCA-ITN-2020-ETN ). Technical assistance of  Drs. Simon Mobach  is highly valued. The work of MA-S, RL and CdG was supported by  European Union 's  Horizon2020 MSCA Program  under grant agreement  641833  [ONCORNET]. Mass spectrometry experiments were carried out using the facilities of the  Montpellier Proteomics Platform (PPM, BioCampus Montpellier). This work was supported by the regional funds  FEDER/Région Occitanie ,  MUSE ,  Labex EpiGenMed  and the  French Agence Nationale de la Recherche  (project  ANR-21-CE44-0007-01 ,  LEUKOCEPTOR ).
Finally, we include the coefficient A ε,np as an example of a multiscale problem for which we are not aware of any explicit homogenization results. We will see nevertheless that the non-intrusive MsFEMs that we introduced above provide good approximations compared to their intrusive G-MsFEM counterparts for all test cases. A reference solution u ε h is computed on a uniform 1024 × 1024 mesh T h by means of a standard P 1 finite element method using FreeFEM++  [61]. The mesh T h (as well as the coarse mesh introduced below) consists of squares cut in two along a diagonal that is in the same direction for all squares, i. e. , such as the meshes in Figure  1. The FreeFEM++ scripts to perform all different MsFEMs can be found at  [62]. We compare the reference solution u ε h to MsFEM solutions obtained on a coarse mesh T H for varying H.
Funding. The first author acknowledges the support of  DIM Math INNOV. The work of the second and third authors is partially supported by  ONR  under grant  N00014-20-1-2691  and by  EOARD  under grant  FA8655-20-1-7043. These two authors acknowledge the continuous support from these two agencies. The fourth author thanks  Inria  for the financial support enabling his two-year partial leave (2020-2022) that has significantly facilitated the collaboration on this project.
Feature Importance and Models tuning and selection The permutation feature importance benefits from being model agnostic and can be calculated many times with different permutations of the feature. Here we estimated the cross-validated permutation importance, with 10 repeats and with balanced accuracy as scoring metric. Balanced accuracy is the accuracy adapted to imbalanced data and is defined as the arithmetic mean of sensitivity (true positive rate) and specificity (true negative rate). While thresholding at 0. 05, we obtained 6 features for the training dataset 1 and 8 features for the training dataset 2. The 2 sets of features have 3 common features: N a LF , T SC and f 2. Therefore, we can consider these 3 features as "universal" epileptogenic markers, as they are important independently of the training dataset.
The difference in features highlights the fact that each training dataset has a different pattern selective of EZN. Some features, were totally useless, with a poor permutation feature importance score, such as the categorical features "lesional patient" and "lesional zone", make this information not meaningful to predict EZN with these models. The selected features are used in the models for hyper-parameters tuning stage. The model selection was based on a cross-validated validation-score higher than 0. 65 and a difference score lower than 0. 1, resulting in 12 models selected. Next, models were trained on their respective training dataset and provide a (optimized) prediction for each patient. The model with the highest mean testing balanced accuracy, for each training split, was selected for the next stage.
Model Testing and Probabilities Before converting prediction into x 0 and running simulations in the VEP framework, we evaluated performances of the two best logistic regressions, tuned using each training sub-dataset. Models -6- performances were evaluated against clinician' hypothesis about the EZN. Via graphical analysis (statistical analysis is borderline with few points), we found out that logistic regression predictions are quite robust when using splitted training dataset compared to the three surrogate models with shuffled targets and to models fitted on the whole training dataset without any splitting. This shows that our splitting approach using spectral embedding was quite efficient. The performances obtained on models trained with the whole dataset with the correct labels are comparable to those of the surrogate models (Figure  2 ).
Comparison of different priors At the group level, we analyzed 26 seizures from 9 patients as the test dataset using the VEP pipeline. We previous section logistic regression 1 and logistic regression 2, respectively. Parameters resulting from model inversion permit simulation proper to each prior. This was also done for the clinical hypothesis of the EZN, using the VEP-EI prior, and the resulting EZN estimation was used as reference in the performance evaluation approach. Evaluation of performance was made with 2 different metrics specifically used while dealing with imbalanced data: balanced accuracy and F 0. 5 -score (Figure  3 ). These scores were computed for each prior' EZN estimation against the EZN estimation of the VEP-EI prior. Bootstrapped paired t-test shows a significantly (p < 0.
Limitations and Perspectives In the present study, we based data selection on the clinical hypothesis which lies on SEEG recording analyzes and implantation spatial sampling, considering it as ground truth. As SEEG recordings analyzes may suffer from spatial sampling problems, using it as ground truth is debatable, especially when the ground truth is usually considered to be the brain region which once removed leads to no more seizures  (Lüders, Najm, Nair, Widdess-Walsh, & Bingman, 2006). Nevertheless, we had to make a choice for a ground truth using such a prospective database, where the majority of the patients do not have had a surgery, and the choice was to use the best estimation of the EZN common to all patients at the moment of this study. In future, applying a similar approach on seizure-free patients only will be needed to confirm these results.
Data Acquisition We obtained the dataset from 25 patients with drug resistant focal epilepsy who underwent a standard pre In addition, 23 Na-MRI was acquired using a dual-tuned 23 Na/ 1 H QED birdcage coil and a multi-echo density adapted 3D projection reconstruction pulse sequence on a whole-body 7-Tesla Magnetom Step 2 MR system (Siemens, Erlangen, Germany) (for acquisition information see MRI acquisition section of the article). To ensure a sufficient number and distribution of TEs, 3D 23 Na MRI volumes were obtained at 24 echo times (TEs) ranging from 0. 2 ms to 70. 78 ms. This approach also takes into account the 5 ms readout of the sequence, needed to acquire 23 Na signal with short T 2 * decay. Signal quantitative calibration into sodium concentration was performed using six tubes (80mm length, 15mm diameter) filled with a mixture of 2% agar gel and sodium at different concentrations: two tubes at 25mM, one at 50mM, two at 75mM and one at 100mM.
Data preprocessing To construct the individual brain network models, we performed a volumetric segmentation and cortical surface reconstruction from the patient-specific T 1 -MRI data using the recon-all pipeline of the FreeSurfer software package (http://surfer. nmr. mgh. harvard. edu). The cortical surface was parcellated according to the VEP atlas (H. E. Wang et al. , 2021)  (code available at https://github. com/HuifangWang/VEP atlas shared. git). We used the MRtrix software package to process the DW-MRI  (Tournier et al. , 2019) , using the iterative algorithm described in  (Tournier, Calamante, & Connelly, 2012)  to estimate the response functions and subsequently used constrained spherical deconvolution  (Tournier, Calamante, & Connelly, 2007)  to derive the fiber orientation distribution functions.
, 2018). The "not EZN" label corresponds to the concatenation of PZ and NIZ labels. These labels are mostly diagnosed based on SEEG recordings processing, using the Epileptogenic Index (EI)  (Bartolomei et al. , 2008). Hence, the classification was focused on the region with one of those labels. While setting the procedure, we observe a huge variability in Na features patterns, making the model performing poorly. We then decided to split the training dataset to deal with this issue. We tuned the models on both training datasets. The resulting tuned models were used to predict the EZN in of the test dataset patients, providing 2 priors for the VEP pipeline. The whole procedure is detailed below. All priors definitions are summarized and illustrated in Figure  5. -19-.