dataesr/scientific-paragraphs-categorization huggingface dataset:
However, in many cases such a strategy of directly performing a GWAS would not be possible and/or tractable as individual-level data for the largest imputation panels are not publically available. However, SURFBAT could easily be performed at the same time as imputation opening up the possibility for online imputation servers such as the one in Michigan  [56]  to also facilitate GWAS without having to share their data. This is demonstrated in the analysis of the Brugada dataset where SURFBAT is able to achieve similar results to a direct GWAS against the control group of 1000G+FGR but without the requirement of jointly manipulating the case and control data together in order to calculate PCs and to perform the association testing. Even if individual-level data are available, for a huge control panel, merging the data with the case group, calculating PCs, and performing the GWAS can all be highly time consuming.
Finally, we saw in the real data example that SURFBAT could return inflated test statistics; this was dealt with using genomic control. This inflation was however not apparent on the simulated dataset; certainly because in this instance the case individuals were simulated as mosaics of the control individuals and hence the surrogate parent model was very effective. As imputation reference panels increase in size, surrogate parents should be more readily found and hence SURFBAT should not suffer from inflation.
), 𝑟(𝑘) is a simple function that gives the index of the partner haplotype to haplotype 𝑘. Explicitly, 𝑟(𝑘) = 𝑘 + 1 if 𝑘 is odd and 𝑟(𝑘) = 𝑘 -1 if 𝑘 is even. We implemented the calculation of both 𝜌 𝑖 𝑗′ and 𝜋 𝑖 𝑗′ within the existing imputation algorithm IMPUTE5, for both positions that are not genotyped (e. g. 𝑗′) and that are genotypes (e. g. 𝑗), alike. Note that there is an implicit assumption that the two haplotypes within an individual on the control panel share a relatively similar ancestry -in the context of our study, this is reasonable for the 1000G individuals and is also respected by the FranceGenRef panel by design  [47] [48] [49]. This is because the individuals of FranceGenRef were recruited based on grand-parent birthplace data taking individuals with all four grand-parents born within a small locality hence approximately insuring that such individuals have both maternal and paternal haplotypes from a similar region.
A comparison of the two tests are given in Supplementary Figure  1  for the Brugada dataset example; the unpaired test attributed smaller p-values to the SNPs that are likely not following the null hypothesis near SCN10A on chromosome 3 and HEY2 on chromosome 6. In order to perform SURFBAT, only genotyping array data for the case individuals are required and WGS data for the controls individuals who must be formed into to a phased imputation reference panel. The cases are imputed against the controls using IMPUTE5 and the '--surfbat' flag activated, which also calculates the per-SNP test-statistics and corresponding p-value. There is the possibility to place thresholds on the minor allele frequency (MAF) and the imputation quality (INFO score), with default settings placed at 0. 01 and 0. 4 respectively.
Creating a control panel We took the haplotypes from the 1000G (Phase 3) from all populations, as were made available by imputation software IMPUTE2  [66]. This dataset was merged with the whole genome sequencing positions of FGR. In order to prepare the FGR data, we used the sequencing data quality control pipeline RAVAQ  [67] , and phased the data using SHAPEIT4  [68]. Merging and manipulation of the data file was achieved using the R-package gaston  [69] , plink v1. 9  [70] , and pbwt  [71] ; variants with a difference in minor allele frequency greater than 0. 1 between FGR and the non-Finnish European 1000G individuals were removed from the control panel as these were deemed to likely represent a batch effect between the sequencing data of FGR and the public 1000G data. This panel can then be used either directly as a control group, or as an imputation reference panel for the purpose of SURFBAT.
Simulation study Our simulated study involved simulating a group of 450 individuals who were constructed as mosaics of the control group using the R-package Mozza (https://github. com/genostats/Mozza) which leveraged the Li-Stephens Markov process of forming new mosaic haplotypes. To keep calculation time short, we only simulated chromosomes 10-22 and each chromosome was simulated separately. At each instance when a mosaic tile was drawn for a new case individual, we assigned a 50% chance to copy from a haplotype from the African continent super population from 1000G (AFR) and 50% from FGR. A tile length of 10cM was used for the simulation. We simulated a pool of 20,000 haplotypes; our 450 simulated case individuals' 900 haplotypes were sampled from this pool in order to create two association signals on chromosomes 11 and 20.
On chromosome 11, we sampled an excess of haplotypes with tiles copied from FGR haplotypes overlapping base-pair position 66602100 (near the middle of the chromosome). On chromosome 20, we sampled an excess of FGR haplotypes that carry an alternative allele for the common variant rs197819. This variant was chosen at random among a set of candidate variants with at least a MAF of 0. 2 in both AFR and FGR. Genotyping data for the case group was simulated by extracting positions from the UK biobank SNP-array (details here: https://biobank. ndph. ox. ac. uk/showcase/refer. cgi?id=149601).
Brugada study We took 346 individuals with whole-sequencing data affected with Brugada syndrome as a real-data example. These individuals were recruited in the West of France and so we can assume that they can be accurately imputed using a reference panel built of FGR and 1000G  [48]. To perform GWAS, we analysed all common bi-allelic variants (minor allele frequency above 0. 01) that were present in our control panel (1000G+FGR). GWAS was carried out in the R-package gaston, using logistic regression adjusted for six principal components (PCs); PCs were calculated from pruned data and this was also achieved using gaston. To apply SURFBAT to the Brugada case individuals, we require only genotyping data for these individuals. We simulated this scenario by extracting positions from the UK BioBank SNP-array from the WGS data for the 346 individuals; this array was designed to facilitate genotype imputation and hence would be a logical choice for future applications of SURFBAT.
The data from the extracted array positions were phased with SHAPEIT4 and then supplied to IMPUTE5 with the required option (--surfbat) in order to calculate genome-wide SURFBAT p-values. Finally, to demonstrate the interest of the concept of using an imputation reference panel as a control panel, we simulated a scenario where we have both case and control individuals with genotyping array data. In this circumstance, both cases and controls were imputed and a GWAS was performed on the imputed dosages. For this we took control individuals from 569 individuals of the FrEx database who have genotyping data (Illumina OmniExpressExome array). Positions corresponding to this array were extracted from the 346 case individuals and we then phased (SHAPEIT4) and imputed (IMPUTE5) the 346 case and 569 control individuals together using 1000G+FGR as a reference panel.
Funding This work was supported by  LABEX GENMED  funded as part of " Investissement d'avenir" program  managed by  Agence Nationale pour la Recherche  (grant number  ANR-10-LABX-0013 ), and by the  French regional council of Pays-de-le-Loire  ( VaCaRMe  project). This work was also supported by the  POPGEN  project as part of the  Plan Médecine Génomique 2025  ( FMG2025/POPGEN ) and by  Inserm  cross-cutting project GOLD. This work was also partially funded by a  Swiss National Science Foundation  project grant no. PP00P3_176977.
Data Availability Data from the FranceGenRef panel will be submitted to the French Centralized Data Center of the France Medicine Genomic Plan that is under construction. Enquiries for the use of this data can be addressed to GENMED LABEX (http://www. genmed. fr/index. php/en/contact). Those wishing to access the Brugada data on a collaborative basis should contact Richard Redon and Christian Dina (richard. redon@inserm. fr andchristian. dina@univ-nantes. fr). Summary information for the FrEx dataset is available at http://lysine. univ-brest. fr/FrExAC/, wishing to access the data on a collaborative basis should contact Emmanuelle Génin (emmanuelle. genin@inserm. fr).
Fractures are modelled as ellipses or disks whose properties (orientation, size, position, transmissivity) are governed by statistical laws derived from field observations  [12, 8, 24]. This model has been enriched in  [18, 17]  to include the evolution of fracture network formation (nucleation, growth and arrest). The networks generated with an arrest rule contain large numbers of T-shape intersections (where a fracture stops on another one) compared to X-shape intersections (the two fractures cross each other). With no arrest rule, the networks rather contain X-shape intersections. In this paper, the DFNs we consider are generated with the software DFN. lab with no arrest rule. Examples of such networks are displayed in Figure  1. The largest test case contains 1,176,566 fractures embedded in a cubic domain of size  = 200m (labelled "L200": right panel).
Algorithm The mesh of the DFN is generated according to the algorithm described in  [10, 35]. It is implemented in the C software MODFRAC. Parallelism is achieved using posix-threads. The mesh step can be the same in the entire network, in which case the mesh is said to be matching at the intersections between fractures. One can also vary the mesh step from one fracture to another, in which case the mesh is generally nonmatching at the intersections between fractures. Figure  4  shows an example of a matching and an example of a nonmatching mesh.
Computational resources and mesh quality We perform the mesh generation using the software MODFRAC for the three test cases of Figure  1  on a Laptop Intel Core i7 4 cores CPU 32GiB RAM with 4 posix-threads. The quality () of a triangle  with edge lengths   ,  = 1, 2, 3 and area | |, is defined as in  [9] : 𝛿(𝑇) := 4 √ 3 |𝑇 | 𝑙 2 1 + 𝑙 2 2 + 𝑙 2 3. (9) The quality () is equal to 1 for an equilateral triangle. The lower (), the worse the quality of. Table  2  gives examples of a mesh and its properties for the three test cases L100, L150, L200 and also the mesh generation time.
Parametric studies have been carried out using the Python tool Prune (Inria). In all the test cases, the linear system is solved with the Intel Pardiso LU solver from Intel MKL library  [33]. Except where indicated otherwise, all the simulations are carried out using the Inria cluster CLEPS on a partition with 4 Intel Xeon E7-4860 v2 with 12 cores, 2. 6-3. 2GHz and 3TB RAM. In all the tables reported in this section, the number of dofs is the one after static condensation. 𝐾 𝑥 = 𝑄 in, 𝑥 𝐿 Δ𝑝 𝐷.
Step (PT5): Vertex insertion algorithm to build the polygonal-triangular mesh The vertex insertion procedure used in Algorithm 3 has been implemented in a Matlab code, named NEF-flow-polygons (Inria). It takes 00:17:11 to load the nonmatching mesh and to insert the vertices for the L150 test case and 01:11:47 for the L200 test case. In both cases, about half of the time is dedicated to loading the mesh data. Figure  13  shows the polygonal mesh with the red dots representing the inserted vertices. For L200, the red dots are rather inside the cube (since the selected fractures are the ones of the test L150 and therefore rather located inside the embedding cube). Hence, a smaller number of red dots are seen on the cube surface, and these dots belong to the largest fractures, common to the test cases L150 and L200.
For L150, 3. 5% cells of the polygonal-triangular mesh are polygons, whereas this number is 1% for L200. Hence, the computational time to run Algorithm 3 can be improved, especially as there are several loops. A  version included in the mesh generator would be much more efficient (also as there would be no need to read the mesh data files). Step (PT6): Flow computation on the new polygonal-triangular mesh The last stage is to run the flow simulations on the polygonal-triangular mesh built at step (PT5) using the NEF++ software. Table  13  and Table  14  report the number of dofs, the number of nonzeros (nnz) in the linear system matrix, and the relative error on the equivalent permeability RelErr(  ) and the relative error (in %) on the global mass conservation | in,  - out,  |/ in,  for the test cases L150 and L200, respectively.
Acknowledgments. This research has been partially supported by the  LABEX AMIES ANR-10-LBX-0002-01  project. The authors warmly thank  Patrick Laug  for his fruitful collaborative work regarding mesh generation. The authors are also grateful to the  Lab-Com fractory (CNRS, Université de Rennes 1 and Itasca Consultants)  for providing the geometry and transmissivity data for all the DFN considered in this paper. The present simulations presented in this paper were carried out using the Inria CLEPS experimental testbed (https://paris-cluster-2019. gitlabpages. inria. fr/). The authors warmly thank  Simon Legrand  ( Inria, Paris ) for his technical help with CLEPS.
Although off-line software tools are available for reducing artifacts  (Mutanen et al. , 2022) , controlling for quality of EEG signals in real-time is the most effective strategy for recording reliable TMS evoked potentials (TEP). Utilizing a software that enables setting of stimulation parameters based on real time visualization EEG signals, may be critical for recording good quality TEPs, and has been successfully implemented in the study of brain-injury patients  (Casali et al. , 2013 , Casarotto et al. , 2016 , Rosanova et al. , 2018 , Sinitsyn et al. , 2020). A free-release MATLAB-based tool, called rt-TEPs (real-time TEP), is available to assist in the implementation of this approach  (Casarotto et al. , 2022). Together with tools that enable on-line assessment of TEP quality, other tools have been developed to control for confounding factors such as the auditory evoked potentials (AEP) produced by TMS ''clicks".
Acknowledgements European Union's  Horizon 2020 Framework Program for Research and Innovation  under the  Specific Grant  Agreement No. 945539  ( Human Brain  Project  SGA3 ) (to MM, MR);  Fondazione Regionale per la Ricerca Biomedica  ( Regione Lombardia ), Project  ERAPERMED2019-101 ,  GA 779282  (MR);  Tiny Blue Dot Foundation  (to MM);  Canadian Institute for Advanced Research: Azrieli Program on Brain, Mind , and  Consciousness (MM).
The paper concerns the numerical resolution of the inverse source problem for electroencephalography (EEG). We propose an approach which is able to take into account some heterogeneity properties (namely a varying electrical conductivity) of the head tissues, in particular of the skull layer. It combines two consecutive steps: (i) a data completion procedure from the scalp to the cortex using the quasi-reversibility (QR) method, (ii) a source estimation method from these cortical transmitted data within the brain (modeled as sphere), developed in the software tool FindSources3D (FS3D). Numerical simulations in the case of the multi-layered spherical head model illustrate both the promising and limiting features of the approach.
g. [21]. Depending on the source model, two big classes of methods implemented in software libraries devoted to the resolution of inverse EEG/MEG problems can be distinguished: -Minimum Norm Estimation (MNE) methods, where the source term is assumed to be distributed on the cortex surface (within the brain, which should be known from MRI), its amplitude (moments) being unknown  [14, 25, 29, 63]. This leads to a number of degrees of freedom much bigger than the number of data. Solutions to this underdetermined linear inverse problem are obtained by norm minimization of the output error combined with a statistical modelization of the source distibution, see ‡  [26, 42]. -Dipolar source estimation methods (of dipole fitting family) use a source model reduced to a few pointwise dipoles, make no assumption on their positions, leading to an overdetermined non-linear problem.
Furthermore, the number of sources is assumed to be known a priori. To overcome these drawbacks, we develop a new method which consists of two steps. The approach firstly transmits the recorded data from the scalp to the cortex, ‡ And the dedicated software MNE https://mne. tools/stable. § The software EEGLAB (signal processing features), https://sccn. ucsd. edu/eeglab; see also Brainstorm (source estimation using weighted minimum-norm estimates, beamforming), https://neuroimage. usc. edu/brainstorm, FieldTrip, https://www. fieldtriptoolbox. org. and then applies a source reconstruction method in the brain. The data transmission issue from the scalp to the cortex amounts to Cauchy problems for Laplace-Poisson PDE whose solutions carry harmonicity properties. They remain ill-posed (additional assumptions are required to ensure existence, uniqueness, and stability of solutions) and have been studied in  [5, 12, 23, 31].
We propose to generalize it to a varying conductivity and to study its performance as a data transmission procedure from scalp to brain surface (cortical mapping). This step is central to take into account the heterogeneity of the overall head tissue. We provide theoretical results as well as a numerical study for spherical domains. Different configurations are tested: one single QR method for transmission through several -3 or 4 -homogeneous layers, with or without modeling of fontanels in the skull. We then combine it with a source reconstruction method within the brain. Among the different approaches, we focus on the one developed in the software tool FindSources3D (FS3D) which belongs to the (static) dipolefit class in a spherical representation of the head with piecewise homogeneous conductivity.
In particular, the brain is assumed to be a sphere and the conductivity in the brain to be constant. FS3D makes use of an efficient analytic method that allows to retrieve both the number and the characteristics of dipolar sources (locations, moments, even in time correlated situations), see  [12]. It involves the computation of the spherical harmonic coefficients from the approximated Cauchy data on the cortex. Then, FS3D considers best rational approximation on families of 2-D planar cross-sections in order to locate singularities and to determine the expected quantity of brain electric sources. From those planar singularities, the sources are finally estimated, together with their moment, in a last clustering step. Through this process, FS3D is also able to recover time correlated sources, which is an important advantage with respect to other software tools addressing the same problem.
The inverse source problem We denote by Γ * ⊂ Γ an open subset of Γ with meas(Γ * ) = 0. The inverse problem for EEG consists in reconstructing the source F of the form (4) from a single Dirichlet measurement f = u | Γ * of a solution u to (5) on Γ *. More precisely, the aim is to determine the quantity Q, the locations (c q ) and moments (p q ), q = 1,. , Q, in the source F generating the data f. In experiments, a finite number of surface electrodes, on which voltages are recorded, are attached to the boundary. Consider L well-separated pointwise electrodes {e } L =1 on Γ *. Measurements are given by u(e ) = f (e ) = U , = 1,. , L, (13) with U = (U ) L =1 ∈ R L. The function f has to belong to (the trace space) H 1/2 (Γ * ) and is chosen from the measurements U as an appropriate interpolant of u at points e.
Assume that Ω 0 is a ball, hence S 0 = S 0 , the sphere centered at 0, of radius r 0 > 0. In this spherical setting, we solve the inverse source problem using the following four-steps process, a method which is implemented in the FS3D software ¶  [12]. These main bricks are summarized below. Step 1: Anti-harmonic projection. From u and ∂ n u on S 0 , we get their expansions on the spherical harmonics and that of ũ, see  [  , useful information about the locations of sources is obtained from the study of the singularities s d,p,q of f d,p in D d,p , illustrated by Figure  2  (we typically take D = 13, P = 20). • For fixed p, d, each function f d,p has Q poles s d,p,q in D d,p of multiplicity 3, that are also branched singularities (of order 3/2) if Q ≥ 2; if Q = 1, f d,p is rational with a single triple pole in D d,p (recall that Q is the quantity of dipolar sources c q ).
Gathering all the D × Q estimations ĉd,q for a family of directions d = 1,. , D , form in Ω 0 a collection of points clouds around the Q sources locations c q. Whenever the sources are far enough one from the others in the chosen slicing directions, and the data not too noisy, we indeed obtained D × Q estimations ĉd,q of the source locations, given by the Q line extrema in D directions (Figure  2, (c) ). These clouds are separated by a clustering algorithm which returns Q clusters. The + Matlab optimization toolboxes: fmincon, lsqlin. respective mean values (barycenter) of these clusters are furnished as initial values for the estimated positions. Once the source locations are fixed, the data depend linearly on the moment values. A first estimation of these moments is obtained by minimizing the L 2norm of the residual error at the electrodes.
Generation of synthetic data Synthetic data are generated by solving the forward problem (5) (see Section 2. 1) for the neonatal head models (a) and (b). The subtraction method is implemented with FreeFem++ (see  [32] ). Discretization is performed with 3D Finite Elements of type P2. Error estimates are proved in  [3]. We use a tetrahedral mesh of the three-layer spherical domain Ω, composed of 617 167 elements. The measurement region Γ * on scalp corresponds to the union of small patches around electrode positions. Three sets of electrode positions with 33, 61 and 257 electrodes are examined (see Figure  3 ). In practice, the mesh is refined around the electrode positions using the Mmg remeshing software  [15]. The surface mesh of the scalp also explicitly includes the boundary of small circular patches representing the electrodes around each electrode position, thanks to the level-set meshing capabilities of Mmg on triangular surface meshes (see Figure  4 , left).
Sea ice concentration, volume and drift We take sea ice concentration from the climate data record of the EUMETSAT Ocean and Sea Ice Satellite Application Facility (OSI-SAF,  Lavergne et al. , 2019). To cover the period 2000-2018, we use two different versions of the product: the  OSI-450 (1980 OSI-450 ( -2015) )  and the  OSI-430-b (2016present). Sea ice volume and thickness are evaluated using two independent datasets: outputs from the Pan-Arctic Ice-Ocean Modeling and Assimilation System (PIOMAS,  Zhang and Rothrock, 2003)  and data produced by combining the observations retrieved from the CryoSAT-2 and SMOS satellites, referred to as CS2SMOS (version 2. 2,  Ricker et al. , 2017). PIOMAS data are the results of coupled ocean-sea ice model simulations with the daily assimilation of satellite sea ice concentration and sea surface temperature.
The main interest of the PIOMAS dataset is that it is available for the whole simulated period and has been thoroughly evaluated against ice thickness observations (e. g. Schweiger et al. , 2011; Laxon et al. , 2013; Stroeve et al. , 2014) , meaning that some of its biases are known. For this reason, it is regularly used as a reference for large-scale sea ice thickness evolution in the Arctic (e. g. Spreen et al. , 2020; Davy and Outten, 2020). For evaluating the sea ice drift, we use the low-resolution OSI-SAF sea ice drift product that provides 2 d integrated sea ice displacement  (Lavergne et al. , 2010). This product includes information about summer ice drift and the uncertainties associated with the drift retrieval from June 2017 onwards. For each dataset, we process OPA-nex output in order to compare them with observations in a consistent way.