dataesr/scientific-paragraphs-categorization huggingface dataset:
p-value tests for statistical enrichments of the different types of Boolean functions (BFs) in the reference biological dataset. A low p-value indicates that the corresponding type of BF is enriched in the reference biological dataset when compared to the ensemble of all BFs. For k > 2 when the p-value shown is 0, it was smaller than what we could measure, and when the p-value shown is 1, its deviation from 1 was smaller than we could measure. Here, EF corresponds to effective functions, UF to unate functions (all sign combinations), CF to canalyzing functions, NCF to Nested Canalyzing functions and RoF to Read-once functions.
The enrichment ratios ER for the RoFs and NCFs in the ensemble of odd bias BFs, EFs and UFs. These ratios indicate the extent of the over-representation of such functions in the reference biological dataset. ER > 1 suggests that there is indeed an enrichment of RoFs and NCFs within the EFs, UFs and CFs in the reference biological dataset when compared to that expected in the ensemble of all EFs, UFs and CFs.
The relative enrichment ratio ER of the NCFs in the CFs and RoFs. fs,0/f0 denotes the fractions of functions that are NCFs in the space of all CFs or RoFs and fs,1/f1, the equivalent fraction in the reference biological dataset. ER = (fs,1/f1)/(fs,0/f0) denotes the enrichment ratio and it indicates the extent of the over-representation of such functions in the reference dataset. Computations are reported for BFs with k ≤ 8 inputs. The low p-values indicate that there is an enrichment of NCFs within the CFs and RoFs in the reference dataset when compared to that expected in the ensemble of all CFs and RoFs.
ACKNOWLEDGMENTS A. Subbaroyan  would like to thank  Sathish Kumar  for discussions, and  Sneha Subbaroyan  for help with figures. A. Samal acknowledges support from the  Max Planck Society, Germany , through the award of a Max Planck Partner Group in Mathematical Biology. IPS2 benefits from the support of  Saclay Plant Sciences-SPS  ( ANR-17-EUR-0007 ).
The JACO-CL strain belongs to the Pseudomonas syringae Phylogroup 7 clade a and displays flexible genomic traits The genome of the JACO-CL strain was sequenced by coupling the Oxford Nanopore Technology (ONT) and the Illumina technology. The assembly is composed by two circularized sequences (one chromosome and one plasmid), resulting in 6,043,462 bp for the chromosome and 42,253 bp for the plasmid. The genome annotation resulted in 5,352 CDS, 16 rRNA, 70 tRNA and 2 tmRNA. Genome annotation and genomic analysis suggest genome plasticity and flexibility of the JACO-CL strain. First, we found two prophages (JACO-CL PP1 and JACO-CL PP3) displaying similarity with PHAGE_Vibrio_VP58. 5_NC_027981 and PHAGE_Salmon_118970_sal3_NC_031940 (Supplementary Data Set 2). Secondly, we identified the 42,253 bp plasmid, thereby stressing the JACO-CL genome plasticity.
, 2006). To investigate the type of JACO-CL PAI, we first inferred a phylogeny based on the avrE effector located in the JACO-CL hrp/hrc gene cluster and reference PG7 strains carrying the S-or T-PAI island (Figure  3a ). The avrE is a conserved effector of the hrp/hrc cluster present on both S-and T-PAI strains. However, avrE divergently evolved in the two distinct PAIs. A phylogenetic tree shows that JACO-CL carries a S-PAI configuration and this was confirmed by genome structural analysis (Figures  3a  and 3b , Supplementary Data Set 4). In addition, KEGG analysis also corroborates that T3SS is not complete in JACO-CL as expected for S-PAI strains that have a reduced T3SS (Supplementary Data Set 5). More specifically, JACO-CL harbors only a hrp/hrc cluster containing both avrE and avrF and their relative chaperons (Figure  3b ).
Interestingly, through genome functional annotation, we found three complete Hop effectors (HopAJ2, HopAN1 and HopJ1) located in the genome of JACO-CL but not physically related with the PAI (Supplementary Data Set 4). To investigate the possible Horizontal Gene Transfer (HGT) of the tree Hop effectors from other P. syringae PGs, we compared the JACO-CL alleles with those already described in P. syringae and available at the Pseudomonas-Plant Interaction (PPI) http://pseudomonas-syringae. org. We also added alleles retrieved from Genebank (BLASTP > 50% of protein coverage). Phylogenetic relationships between the Hop protein sequences indicate that both HopAJ2 and HopAN1 are highly divergent from alleles previously described in other P. syringae PGs (Figure  3c ). This result indicates that both Hop effectors were not recently acquired through HGT from existing alleles distributed in the P.
The adaptive potential for disease resistance is mediated by a polygenic architecture To investigate the genetic architecture underlying the adaptive potential of response to the P. viridiflava strain JACO-CL, we inoculated 192 whole-genome sequenced A. thaliana accessions of the TOU-A population. Quantitative variation in disease resistance to the JACO-CL strain was observed between the 192 TOU-A accessions (Supplementary Data Set 6). Similar quantitative variation among TOU-A accessions was observed in response to either the bacterial pathogens Xanthomonas campestris pv campestris (Xcc) and Ralstonia solanacearum  (Debieu et al. , 2016; Demirjian et al. , 2022; Desaint et al. , 2021; Huard-Chauveau et al. , 2013)  or natural infections in the native habitats of the TOU-A population  (Roux & Frachon 2022).
thaliana (Supplementary Data Set 8)  (Kawakatsu et al. , 2016). GWA mapping revealed that the natural variation in the expression of AT5G18310 is controlled at the worldwide scale by one QTL located in the 5' region of AT5G18310, with top SNPs that were common with the top SNPs identified in response to the JACO-CL strain (Figure  S1 ). This suggests that modification of cis-regulation of AT5G18310 mediates genetic variation of the response to the JACO-CL strain in the TOU-A population. Estimating the expression level of AT5G18310 in TOU-A accessions contrasted in their response to the JACO-CL strain could support this hypothesis. In addition, AT5G18130 is located nearby a dynamic QTL (QTL20, Figure  5c ) encompassing two genes (AT5G18350 and AT5g18360) encoding for Toll/Interleukin-1 receptor nucleotide-binding site leucine-rich repeat (TIR-NBS-LRR) proteins.
org database with an e-value of 1e-6. We enriched this existing effector database with T3SS effector proteins reported previously in the P. syringae PG7  (Bartoli et al. , 2014). Only complete effectors (alignment length ≥ 25%) were kept in the analysis. In addition, putative effector proteins and/or proteins found in the CEL were manually blasted in GenBank for further annotation. Phylogenetic relationships for the three complete Hop proteins (HopAJ2, HopAN1 and HopJ1) found in the JACO-CL genome were estimated by comparing these Hops with alleles retrieved at the PPI database and on GenBank through BLASTP of the JACO-CL Hop sequences. Amino acid sequences of each Hop were individually aligned with MAFFT v7. 271  (Katoh and Standley, 2013) and a Maximum Likelihood (ML) tree was inferred with MEGA7  (Kumar et al.
thaliana accessions; 'ε' is the residual term. Inference was performed using ReML estimation, using the PROC MIXED procedure in SAS v. 9. 4 (SAS Institute Inc. , Cary, North Carolina, USA). The 'accession' factor was treated as a fixed effect. Because A. thaliana is a highly selfing species  (Platt et al. , 2010) , Least-squares means (LS-means) obtained for each accession from model (1) correspond to the genotypic values of accessions. To explore genetic variation among the eight strains, we used the following model at each dai: LS-means of disease indexi = μtrait + strainj + ɛj (1) where 'μ' is the overall mean of LS-mean values; 'strain' accounts for differences among the six strains of the P. syringae complex for which symptoms were observed on plants; 'ε' is the residual term. Inference was performed using ReML estimation, using the PROC MIXED procedure in SAS v.
, 2017). In order to better characterize the genetic architecture associated with natural genetic variation in response to JACO-CL, a local score approach was applied on the set of p-values provided by EMMAX. This local score approach increases the power of detecting QTLs with small effect and narrows the size of QTL genomic regions  (Bonhomme et al. , 2019; Fariello et al. , 2017). In this study, we used a tuning parameter ξ of 2 expressed in -log10 scale. Significant phenotype-SNP associations were identified by estimating a chromosome-wide significance threshold for each chromosome  (Bonhomme et al. , 2019). Based on a custom script  (Libourel et al. , 2021) , we retrieved all candidate genes underlying QTLs by selecting all genes inside the QTL regions as well as the first gene upstream and the first gene downstream of these QTL regions (Dataset 7).
ACKNOWLEDGMENTS This work was funded by the  Région Midi-Pyrénées  ( CLIMARES  project) and the  LabEx TULIP  ( ANR-10-LABX-41 ). This work was performed in collaboration with the  GeT core facility, Toulouse, France  (http://get. genotoul. fr),and was supported by  France Génomique National  infrastructure, funded as part of " Investissement d'avenir" program  managed by  Agence Nationale pour la Recherche  (contract  ANR-10-INBS-09 ). Part of this work was carried out on the Toulouse Plant-Microbe Phenotyping facility (https://www6. toulouse. inrae. fr/tpmp/),which is part of the  Laboratoire des Interactions Plantes-Microbes-Environnement  ( LIPME) -UMR INRA441/CNRS2594. We are grateful to Jérôme Gouzy  for having conducted the assembly of the JACO-CL strain. We are also grateful to  Fabrice Devoilles  for his assistance during growth chamber experiments.
Beamforming is a popular method for functional source reconstruction using magnetoencephalography (MEG) and electroencephalography (EEG) data. Beamformers, which were first proposed for MEG more than two decades ago, have since been applied in hundreds of studies, demonstrating that they are a versatile and robust tool for neuroscience. However, certain characteristics of beamformers remain somewhat elusive and there currently does not exist a unified documentation of the mathematical underpinnings and computational subtleties of beamformers as implemented in the most widely used academic open source software packages for MEG analysis (Brainstorm, FieldTrip, MNE, and SPM). Here, we provide such documentation that aims at providing the mathematical background of beamforming and unifying the terminology.
Introduction Initially created for sonar and radar applications, the beamforming technique has been introduced into neuroscience as a method for interpreting the neural basis of  MEG and EEG data ( van Drongelen et al. , 1996; Van Veen and Buckley, 1988; Van Veen et al. , 1997 ). Since its first implementation in neuroscientific open source toolboxes (namely, Nutmeg  [ Dalal et al. , 2004; Dalal et al. , 2011 ]  and FieldTrip  [ Oostenveld et al. , 2011 ] ), beamforming has become a widely applied source reconstruction technique in the field and is now implemented in various M/EEG signal processing software packages. Features such as the ability to resolve deeper sources  ( Backus et al. , 2016; Quraan et al. , 2011; Wilson et al. , 2010 )  or to suppress external noise  ( Litvak et al. , 2010; Sekihara et al.
The forward field is determined by the location of the source, the sensor or electrode configuration, and the volume conductor model. The forward field is also commonly referred to as the gain matrix or lead field, although the latter in the strict sense only refers to the relationship among many sources and one electrode or sensor. It is evident from Eq. (  5 ) , that the spatial filter  depends solely on the forward field matrix and the inverse of the data covariance matrix. The above formula represents a vector beamformer; the scalar case is given by: 𝐰 ⊤ ( 𝑟 ) = [ 𝐥 ⊤ ( 𝑟 ) 𝐑 -1 𝐥 ( 𝑟 )] -1 𝐥 ⊤ ( 𝑟 ) 𝐑 -1. (6) Now, the  × 1 vector  (  ) =  (  ) (  ) describes the forward field for a specific orientation  at location. Consequently, the beamformer output per location is now a scalar, representing only the orientation specified by the forward field.
By using this scalar normalisation, the resulting beamformer is rotationally invariant, but at the same time ensures an array gain independent of source depth. This latter version of the vector array-gain beamformer is implemented in FieldTrip and MNE-Python. Unit-noise-gain beamformers Another spatial normalization strategy is implemented in the unit-noise-gain beamformer, which is also referred to as the weight-normalized beamformer or the Borgiotti-Kaplan beamformer, as it was originally proposed by  Borgiotti and Kaplan (1979). This variant uses two constraints for the spatial filter calculation,  ⊤ (  )  (  ) =  and  ⊤ (  )  (  ) = 1. It is the first constraint that is used to solve the minimization problem ( cf. Borgiotti and Kaplan, 1979 ) , with  being determined by the second constraint.
The SVD spectra all show a cliff at their effective rank. A Singular value spectrum of a full-rank data covariance matrix with 204 sensors. B Singular value spectrum of the covariance matrix in A after removing 3 ICA components. C Singular value spectrum of a full-rank covariance matrix with two sensor types (102 magnetometers and 204 gradiometers), note the additional, smaller cliff due to the two sensor types. D The same data as in C but after applying Signal Space Separation. The data used for all figures is the "sample data set " from MNE-Python, which is a dataset with auditory and visual stimulation  ( Gramfort, Luessi, Larson, Engemann, Strohmeier, Brodbeck, Parkkonen, Hämäläinen, 2014 ). The figures shown here all rely on the subset of the data with stimulation in the right visual field.
The code to reproduce the figures can be retrieved from https://github. com/britta-wstnr/beamformer _ examples. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article. ) ( Taulu et al. , 2003 ) , which can result in the loss of several tens of linear components (see below for more detailed discussion). It is advisable to check the quality of the data covariance matrix by inspecting the rank and condition number, and also the singular value spectrum of the matrix, which is obtained by a Singular Value Decomposition (SVD). Plotting the singular values on a logarithmic axis provides an indication of the effective numerical rank of the covariance matrix. Typically, the singular value spectrum of an ill-conditioned matrix shows a "cliff" at its effective rank, with the numerically irrelevant components having singular values several orders of magnitude smaller than the rest ( Fig.
Signal space separation leads to severely rank deficient covariance matrices The application of SSS to MEG data for cleaning ( e. g. , through the MEGIN software, using MNE-Python's mne. preprocessing. maxwell_filter function or the TSSS toolbox in SPM) often results in a severe rank-deficiency. In a 306channel data set, it is not unusual for several tens, sometimes above 200 spatial components to be removed from the data ( cf. Fig 1 ). In this case, regularization by means of diagonal loading is not sufficient for good beamformer performance. Using a truncated pseudo-inverse in combination with pre-whitening of the covariance matrix (and forward field) has worked well on all examples we tested and can be a good first choice. Details on if and how this can be implemented in the different toolboxes are given in Section 4.
Beamformer implementations in open source software In this section, we compare the support for beamformer implementations in four frequently used open source M/EEG data analysis toolboxes: Brainstorm, FieldTrip, MNE-Python, and SPM (DAiSS toolbox). We present how those toolboxes implement the different beamformer variants and examine how they handle issues with beamforming source reconstruction. The rather independent development of beamformer implementations across the toolboxes resulted in considerable differences in the user interfaces and nomenclature of different options. However, it is important to note that the actual implementations in the toolboxes all depend on the formulas discussed in this paper. Thus, the different implementations converge well in their output and all yield reliable source localization for typical signal-to-noise ratios, as has lately been shown by  Jaiswal et al.
(2020). Apart from differences regarding the beamformer implementations, the toolboxes differ also on a bigger scale: while FieldTrip and MNE-Python are script-based analysis toolboxes, Brainstorm and SPM are primarily used via a graphical user interface (GUI), although they can be used with scripted analyses as well. While FieldTrip, Brainstorm and SPM rely on MATLAB, MNE-Python is written in Python. Part of these differences can be attributed to the historic development of the toolboxes, influenced in part by the available hardware and software as well as the specific research questions of the authors and maintainers of these toolboxes.
Youssofzadeh, https://github. com/vyoussofzadeh/DICS-beamformer-for-Brainstorm ). In FieldTrip , a beamformer is calculated and applied to the sensor data covariance in a single step, using the function ft_sourceanalysis. This function takes a precomputed sensor data covariance matrix or CSD matrix and a configuration structure as input. The configuration structure cfg contains the settings, but also the forward model. Specifying cfg. method = 'lcmv' computes an LCMV beamformer, while cfg. method = 'dics' computes a DICS beamformer. All other options and beamformer specifications are also specified in this configuration structure ( cf. Tables  S1-S4 ). If data whitening is required, this can be done prior to the computation of the sensor covariance and the forward model using the function ft_denoise_prewhiten.
Regularization is applied by setting the parameter reg in make_lcmv() or make_dics(). The default for both functions is 0. 05, corresponding to a regularization with 5% of the average sensor power. If the data is rank-deficient, MNE-Python automatically computes a truncated pseudo-inverse with the possibility to manually set the rank for the truncation. DAiSS (SPM) has several options for regularization with the most commonly used being User-specified regularisation (specified as a percentage, the same as in FieldTrip) and Manual truncation which reduces the dimensionality of the data prior to beamforming. For rank-deficient data, it is recommended to use the latter option and set it to be below the first "cliff" in the eigenvalue spectrum (see Fig. 1  ).
Forward field rank reduction Brainstorm 's default for forward model rank reduction is automatically applied as part of the source modeling procedure, testing each forward field for its rank at "single " floating-point precision and removing any smaller components. FieldTrip 's default for rank reduction depends on the input data: while for EEG data the rank of the leadfield is not reduced, for MEG data the rank is reduced from 3 to 2. The default behaviour can be changed by setting cfg. reducerank to either 'yes' (rank will be reduced by 1) or 'no' when calling ft_sourceanalysis. A rank-reduced forward field will by default be back-projected into the original space while omitting one direction, meaning it will still have 3 columns. This can be changed by setting cfg. backproject to 'no'. MNE-Python does not reduce the rank of the forward field by default.
Combining sensor types and pre-whitening Brainstorm allows multiple sensor types, but cautions the user about mixing EEG and MEG. For all sensor types, the cross-covariances between sensor types are defaulted to be forced to zero; however, the user can override CROSS_COVARIANCE_CHANNELTYPES = false in the code to be true if they want to test using the full cross covariances. The noise covariance matrix is then used to pre-whiten the forward model and data to balance the disparity in units, similar to MNE-Python, for a combined model. FieldTrip has a dedicated function for whitening ( ft_denoise_ prewhiten ), which can be used when sensor types are to be combined. The whitening matrix is applied to both the numeric data, and added as a balancing scheme to the sensor array. Optionally, the cross-terms between different sensor types can be set to zero, prior to the computation of the whitening matrix with the option cfg.
split. When using whitened data for the covariance computation and subsequent analysis, the forward model needs to be computed from the balanced sensor array. MNE-Python combines different sensor or channel types through pre-whitening of the covariance matrix, leadfield, and data. Furthermore, the cross-terms between EEG and MEG channels in the covariance matrix are set to zero. In DAiSS (SPM) , there is an option to fuse sensor types in the Covariance features module. It is assumed that the sensor signals are already properly scaled prior to running DAiSS. One way this can be done is by using the Whitening option in the Reduce function ( spm_eeg_reduce ). As in FieldTrip, the whitening matrix in this case is applied to both the data and the sensors. There are options to set the cross-terms to zero both when whitening and when computing covariance matrices for beamforming.
Conclusion and outlook In this technical note we provided a concise overview of the beamformers that are most commonly used for source reconstruction of EEG and MEG data. In addition, we detailed some practical considerations and best practices that need to be taken into account when employing beamformers. Finally, we compared the settings that are needed to perform the described beamformer analyses for four commonly used open source software toolboxes. This work complements earlier work  ( Jaiswal et al. , 2020 ) , which compared and discussed the behavior of the beamformers as applied with the respective toolboxes' default options. Here, we show that all toolboxes have sufficient functional flexibility in order to accommodate the different beamformers we described. In addition, most toolboxes provide flexibility with respect to estimation and regularization of covariance matrices, and with respect to data whitening.
Acknowledgment We thank  Caroline Witton ,  Jukka Nenonen ,  Amit Jaiswal , and  Lauri Parkkonen  for useful discussions. This work was supported by the  Innovative Training Network ,  Child-Brain , funded by the  Marie Curie Actions of the European Commission  ( H2020-MSCA-ITN-2014 ). The  Wellcome Centre for Human Neuroimaging  is supported by core funding from  Wellcome  [ 203147/Z/16/Z ]. The UK MEG community is supported by the  MRC UKMEG Partnership  grant  MR/K005464/1. This work was supported by the  European Union 's  Horizon 2020 Marie Sk ł odowska Curie Individual Fellowship  (grant agreement  893912 ) to BUW. This work was supported by an  ERC   Starting Grant  ( ERC-StG-640448 ) to SSD. This work was supported by the  ERC Starting  Grant  SLAB ERC-StG-676943  and the  French   ANR-19-DATA-0023  to AG.
At FIR wavelengths, the dust model assumed by MAGPHYS includes a warm (30-80 K) and a cold (20-40 K) component, and the prior distribution of luminosity-weighted dust temperature (T dust ) peaks around 37 K with a 1σ dispersion of ∼20%. Such a dust temperature is comparable to those of widely adopted spectral templates at around median L IR ∼10 12 L e , including  Chary & Elbaz (2001)  and  Magdis et al. (2012,  which is based on the model of  Draine & Li 2007). For a full description of the models and parameters assumed by MAG- PHYS, see da  Cunha et al. (2008 Cunha et al. ( , 2015) )  and  Battisti et al. (2019). Here we only include five or three bands of Herschel data and ALMA 1. 15 mm flux densities for our SED modeling. Further optical/NIR counterpart matching, uniform HST and Spitzer photometry, and panchromatic SED fitting will be presented by another paper of the ALCS collaboration, and certain conclusions on T dust and redshift distribution depending on the FIR z phot values may be further revised.