dataesr/scientific-paragraphs-categorization huggingface dataset:
Unbalanced labeled data Experimental setup and goals. In our last experiment, we show that L γ -PageRank, adapted to the multi-class setting described in Section 2. 3, can improve the performance of G-SSL in the presence of unbalanced labeled data. The experimental setup is as follows: graphs with two balanced classes (in size) are built using the datasets from the preceding experiments. The parameters of the graphs' construction follow the guidelines provided in Section 4. 2. For the Planted Partition, the configuration is n = 200, C avg = 3, C out = 0. 1. Then, unbalanced labeled points are drawn at random: 2% from one class and 6% from the other. Lastly, L γ -PageRank, in the multi-class setting, is applied for a grid of µ values and the best performance, assessed by MCC, is recorded. For the planted partition, the procedure is repeated over 15 realizations of the labeled points and for 100 graph realizations.
For the other datasets, 100 realizations of labeled points are employed. Results and discussion. Table  3  displays the performance L γ -PageRank in the presence of unbalanced labeled data. It is important to stress that, in this framework, a unique value of γ * is used to retrieve all the clusters at the same time, precluding the notion of an optimal γ as defined in Section 3. 3. However, one value of γ seems to perform better, we denote it as γ = Best. The results confirm that the introduction of γ helps to improve the classification in the presence of the unbalanced labeled data.
Conclusion This work proposed L γ -PageRank, an extension of PageRank based on (non necessary integer) powers of the (combinatorial) Laplacian matrix. Our analysis shows that the added degree of freedom offers more versatility than standard PageRank, providing the potential to address some of the limitations of G-SSL. Precisely, we showed that when clusters are obtained via the sweep-cut procedure, L γ -PageRank can significantly outperform standard PageRank. Further, we showed that the multiclass approach also benefits from our proposition, as performance was enhanced in the presence of unbalanced labeled data. These improvements were possible due to the L γ (γ > 0) operator coding for graphs whose topology can reinforce the separability of clusters. The richness of such graphs comes from the sign of edges, allowing to code for similarities but also to emphasize dissemblance between individuals.
Thus, while 2 nodes can only be disconnected on the initial graph, they can 'repulse' themselves in these topologies. Notably, we have shown that there is an optimal graph (related to an optimal γ) on which the classification will lead to a maximal performance. We proposed a simple yet efficient algorithm to estimate the optimal γ and hence determine the best topology for analyzing a given dataset. The procedures proposed in this work open the door for more in-depth study of the L γ -graphs and what determines their optimal topology. They also pave the way towards the extension of other standard clustering tools, such as Unsupervised Learning via Spectral Clustering, to exploit these richer topologies. = r (r + 1), which is monotonocally increasing with r. Thus, the task is the partition that minimizes r and consequently h (γ) S.
The Orf20 protein was reported to involve the Tn916 integrase for DNA sequence specificity  [31]. However, this result needs to be confirmed because the Orf20 version used lacked the N-terminal helix-turn-helix (HTH) DNA-binding domain due to misidentification of the start codon  [32]. The NicK relaxase has been shown to be essential for conjugation and the nic site within ICEBs1 oriT was identified  [33]. Up to now, no MOB T relaxase has been characterized biochemically or structurally. MOB T relaxases are non-canonical relaxases that harbor a PF02486 domain. This domain is also found within Rolling Circle Replication (RCR) initiator proteins of the Rep_trans family which are involved in the maintenance of many small Firmicutes plasmids  [34]. A structural and biochemical characterization of the active site of the Rep_trans RCR initiator protein encoded by the pSTK1 plasmid (Geobacillus stearothermophilus) has been performed recently  [34].
Rep_trans sequences include RepSTK1 whose 3-D structure was recently solved  [34] , and several members of the Rep proteins belonging to the pT181 family  [46]. As expected, RelSt3 groups with the MOB T proteins (Fig. 1a ). The topology of the tree clearly indicated that MOB T and Rep_trans from the pT181 family are distantly related (Fig. 1a ). Interestingly, the RepSTK1 sequence grouped with MOB T sequences rather than with other   [90] , whose structure have been solved recently (PDB ID 4CIJ)  [34]. Besides the well-characterized RepC (pT181) and RepD (pC221) proteins, Rep_trans proteins from 5 other members of the pT181 family of staphylococcal plasmids were included: RepE (pS194), RepI (pUB112), RepJ (pC223), RepN (pCW7) and the Rep from pKH6 plasmid  [46]. b MOB T relaxases (red boxes) and Rep_trans proteins (blue boxes) are linked according to their global sequence identity (see the bottom panel).
Taken together, these data argue in favor of RelSt3 being a bona fide MOB T relaxase. To identify conserved motifs among MOB T proteins, we recovered 2016 sequences of proteins harboring the same architecture as RelSt3, i. e. with a N-terminal HTH domain and a PF02486 domain (see Materials and Methods for details). To our knowledge, this architecture is only found in proteins encoded by ICEs (and not by plasmids), suggesting that they correspond to relaxases involved in conjugation and not to RCR Rep_trans proteins. Multiple sequence alignment followed by WebLogo analysis allowed the identification of 6 conserved motifs (Fig. 1c ), distinct from all other motifs found in the other MOB families  [22, 23]. Among these motifs, 5 have already been identified in Rep_trans proteins, whereas an additional motif, called N″, was found between motifs N′ and I (Fig.
RelSt3 structure model To obtain further structural data of a MOB T relaxase, we built a 3D model of the tertiary structure of the RelSt3 relaxase domain (PF02486) by homology. As phylogenetic analysis indicated that RepSTK1 was the closest protein to RelSt3 for which an experimental structure has been solved (Fig. 1 ), the X-ray structure of RepSTK1 (PDB 4CIJ) was used as a template. Like the RepSTK1 structure, the RelSt3 model is crescent-shaped, with two lobes of similar secondary structure patterns, each involving 5 beta-strands:  4 )  [34]. The underlined elements are absent from the template structure RepSTK1. The two 5-strand beta-sheets are adjacent and form a continuous 10-strand sheet, whose structure and position in the sequence are highly conserved with Rep_trans proteins (despite RelSt3 and Rep_trans proteins being poorly conserved in sequence, Fig.
Phenotype analyses of RelSt3 point mutations confirmed the relationship between MOB T and Rep_trans proteins. We showed that the catalytic tyrosine of RelSt3 is located in the conserved motif III as in Rep_trans proteins. This is the first characterization of catalytic motif for a MOB T relaxase. We also demonstrated the involvement of the 3 conserved acidic residues D72, D177 and E280 (located in motifs N′, I and IV, respectively) in relaxation activity, as demonstrated for RepD variants  [34]. These results suggest that both MOB T and Rep_trans families (i. e. the PF02486 domain) use 3 distant acidic residues in primary sequence to coordinate their cationic cofactor. In addition, we analyzed the involvement of two other conserved residues of motif III in RelSt3 activity, K254 and E257. Both residues are important for RelSt3 nicking activity, indicating that they could assume a structural role within the active site.
Indeed, our 3D structural model of the PF02486 RelSt3 domain suggests that E257 could interact with the catalytic Tyr, and that K254 could interact with the acidic residues D72 and E280 that are assumed to coordinate the maintaining them in the correct position. A B Fig. 7  RelSt3 active site characterization. a Relaxation activity of RelSt3 point mutants. Dose-response relaxation activity was measured for the point mutants on the catalytic Tyr (Y252) in motif III, and on the adjacent K254 and E257 residues in motif III, and for the point mutants on the 3 conserved acidic residues involved in cation coordination (D72A, D177A and E280A). Relaxation experiments were performed on the pBR322-oriT substrate following the standard conditions described in Materials and Methods (Fig. 5c ). The standard deviation of 3 replicates is shown.
Another striking difference with HxH endonucleases is that RelSt3 and Rep_trans structures harbour their conserved catalytic Tyr residue on one of the central beta-strands (strand beta9 in RelSt3 model), whereas the HxH proteins have their catalytic Tyr residue(s) on an alpha-helix close to the cationic cofactor. These observations suggest that the catalytic assembly orchestrating a Tyr residue and a divalent cation to cleave a DNA substrate arose at least twice in evolution, giving rise to the HxH endonucleases on one hand, and to the Rep_trans/MOB T families (harbouring the PF02486 domain) on the other hand, as a remarkable example of evolutionary convergence.
Phylogenetic analysis and identification of conserved motifs BLAST searches were performed using the NCBI non redundant (nr) database. The multiple alignment for the phylogenetic analysis was built with the MultAlin interface  [65]. Only homologous positions (54 in total) were selected manually for phylogenetic analysis. A tree was constructed with PhyML 3. 1 (downloaded from http:// www. atgc-montpellier. fr/phyml/versions. php) [66]. The JTT model of amino acid substitution was chosen  [67] , and a gamma correction with four classes of sites was used. The alpha parameter and the proportion of invariable sites were estimated. The robustness of the tree was tested with PhyML by non-parametric bootstrap analysis (100 replicates). To identify the conserved motifs in MOB T relaxases, we first constructed a set of MOB T sequences using NCBI's CDART (Conserved Domain Architecture Retrieval Tool) application, with the RelSt3 sequence as a query  [68].
All sequences harboring the RelSt3 architecture (N-terminal HTH domain and PF02486 domain) were aggregated together with the sequences harboring the NicK domain (PF02486 domain only, lacking the HTH domain). A total of 2016 sequences were then clustered using the CD-HIT suite  [69] , giving rise to 711, 383 and 261 clusters according to sequence identity cut-off of 98, 95 and 90%, respectively. One member of each cluster was selected for sequence alignment with Muscle  [70]  or ClustalW  [71] , and the resulting alignments were submitted to the WebLogo 3 interface  [72]. The resulting files were very similar for all sequence identity cut-offs (used for CD-HIT clustering) and multiple alignment programs used.
Analytical ultracentrifugation analysis Sedimentation velocity assays with RelSt3 were performed at 1 and 5 μM in buffer 20 mM Tris-HCl pH 7. 5, 500 mM NaCl. Samples were centrifuged for 16 h at a rotor speed of 42,000 rpm in a Proteomelab XL-I analytical ultracentrifuge (Beckman Coulter) at 25 °C in a four hole rotor AN60-Ti equipped with 12 mm double-sector cells with epon centrepieces. Detection of the protein concentration as a function of radial position and time was performed by absorbance measurements at a wavelength of 280 nm. The following parameters were calculated using Sednterp 1. 09 (http://www. jphilo. mailway. com/download. htm) and used for the analysis of the experiment: partial specific volume υ = 0. 734 mL/g, viscosity η = 0. 01054 P, and density ρ = 1. 0192 g/mL. Sedimentation velocity data analysis was performed by continuous size distribution analysis c(s) using the program Sedfit 15.
Secondary structure prediction, circular dichroism (CD) and differential scanning calorimetry (DSC) assays Secondary structure content was predicted using the PSI-pred  [77] , SABLE  [78] , JPred4  [79] , PredictProtein  [80] , APSSP  [81]  and Phyre2  [47]  programs. Far-UV CD spectra were obtained from 180 to 260 nm with a Chirascan Plus spectropolarimeter (Applied Photophysics, Ltd. , UK) equipped with a Peltier temperature control unit (20 °C). RelSt3 protein was loaded at 20 μM in CD buffer (50 mM sodium phosphate pH 7. 0, 500 mM NaF) on a flat quartz cell of 0. 1 mm path length. Spectra were recorded with a scan speed of 60 nm. min -1 and 1 nm spectral bandwidth. After an average of 3 scans and subtraction of buffer contribution, raw data were converted to mean residue ellipticity (deg.
cm 2. dmol -  per residue) using Pro-Data Viewer software (Applied Photophysics, Ltd. , UK), and was deconvolved using SELCON3, CONTINLL and CDSSTR algorithms available at the DichroWeb site  [82, 83] , with the reference data set #3. Data were also deconvolved with the CDNN program  [84]. Thermal denaturation curves were followed at 195 and 222 nm from 20 to 80 °C (1 °C/min), and finally a 180-260 nm spectrum was recorded after cooling the sample back to 20 °C. Differential scanning calorimetry (DSC) experiments were performed with a VP-DSC microcalorimeter (Microcal, Malvern Panalytical, Vénissieux, France). 500 μL of 6. 6 μM RelSt3 was incubated with a heating rate of 60 °C/h in buffer A (20 mM Tris-HCl pH 7. 5, 500 mM NaCl, 2 mM β-mercapto-ethanol). The experiments were done twice.
Homology modeling Ten 3D models of the tertiary structure of the RelSt3 PF02486 domain (residues C61-D285) were built by homology with MODELLER  [85] , using as a template the X-ray structure of the RepSTK1 protein (PDB 4CIJ, 30% sequence identity with the RelSt3 PF02486 domain). The model with the best Discrete Optimized Protein Energy (DOPE) score  [86]  was then refined by a molecular dynamics simulation of 100 ns in explicit solvent, and the most representative structure was selected by clustering the conformations selected from each ps of the simulation. Molecular dynamics simulation were performed with the NAMD software  [87] , using the charmm36 force field  [88] , and a box of explicit TIP3P water molecules. Counter-ions were added to neutralize the system.
Supercoiled plasmidic DNA relaxation assays Relaxation assays were adapted from Lorenzo-Diaz et al, 2011  [54]. Plasmidic DNA (200 ng) of pBR322-oriT (Additional file 4, Table  S2 ) was incubated 20 min at 30 °C with increasing amounts of RelSt3 protein (WT or variants, see figure legends), in R buffer  [20 mM  Tris-HCl pH 7. 5, 200 mM NaCl, 5 mM MnCl 2 , 0. 05 mM EDTA, 1% glycerol (w/v) and 1 mM β-mercapto-ethanol] with a final volume of 20 μL. Reactions were stopped by addition of final concentrations of 0. 5% SDS and 100 μg/ mL of proteinase K, followed by a second incubation at 30 °C for 20 min. Samples were electrophoresed on 1% agarose gel in Tris-Borate-EDTA-1X for 20 h at 2. 5 V/ cm and the gel was stained with ethidium bromide. Gel pictures were captured using a Bio-Rad XR+ system, and bands were quantified with Image Lab software (Bio-Rad Laboratories).
Acknowledgements We thank  Alexandre Kriznik  from the  Biophysics and Structural Biology Platform , part of  UMS2008 IBSLor  ( Université de Lorraine, CNRS, INSERM ), for his advices and technical support during CD and DSC experiments. We are particularly grateful to  Bertrand Raynal  from the molecular biophysics platform of the  Institut Pasteur in Paris  for analytical ultracentrifugation experiments. We also thank  Rémi Leblay  and  Mégane Winterstein  for technical assistance.
Funding This work was supported by the  Université de Lorraine  and the  Région Grand-Est. This work was co-funded by the french  PIA  project " Lorraine Université d'Excellence"  , reference  ANR-15-IDEX-04-LUE , and by the  European Union  through the  Regional Operational Program  of the  European Regional Development Fund (ERDF). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
For strains QUCCCM 26 and 56, the 16SrDNA gene was amplified via PCR using primers BS1F 5' GATCCTKGCTCAGGATKAACGCTGGC3' and CPL10R 5' GCCGGCTCTTCAAC3'. The internal primers 5' TTTGCGGCCGCTCTGTGTGCCTAGGTATCC3', 63F 5' CAGGCCTAACACATGCAAGTC-3′, and 1389R 5'-ACGGGCGGTGTGTACAAG-3′ were applied for sequencing of the cyanobacterial strains. The assembled sequences corresponding to the four strains under investigation were submitted in GenBank (BankIT), and the accession numbers are cited in Table  1. The phylogenetic analysis was performed using Clustal X 2. 0  (Larkin et al. 2007 ).
Acknowledgements The authors would like to thank  Mahroof Eroth ,  Dr. Ahmed Easa , and  Dr. Abdulrahman Al Muftah  from  Qatar University, Andy Selwood from Cawthron Institute , and the  QDVC team  for their support. This work was supported by  QDVC and Qatar University  [Project  QUEX-CAS-QDVC-14/15-7 ].
Participants Nineteen right-handed volunteers (11 females, mean age: 24 years old) with no self-reported hearing/vision loss or neurological pathology were recruited for the experiment and received monetary compensation for their participation. Prior to the experiment, each participant provided a written informed consent in accordance with the Declaration of Helsinki (  2008 ) and the Ethics Committee on Human Research at Neurospin (Gif-sur-Yvette). The data of seven participants were excluded from the analysis due to the absence of anatomical MRI, technical issues with the head positioning system during MEG acquisition, abnormal artifacts during MEG recordings, and two participants not finishing the experiment. These datasets were excluded a priori, and were neither visualized nor inspected.
M/EEG data preprocessing Signal Space Separation (SSS) correction  (Taulu & Simola, 2006) , head movement compensation, and bad channel rejection was done using MaxFilter Software (Elekta Neuromag). Trials containing excessive ocular artifacts, movement artifacts, amplifier saturation, or SQUID artifacts were automatically rejected using rejection criterion applied on magnetometers (55e -12 T/m) and on EEG channels (250e -6 V). Trial rejection was performed using epochs ranging from -0. 8 s to 2. 5 s following the first press initiating the time production trial. Eye blinks, heart beats, and muscle artifacts were corrected using Independent Component Analysis  (Bell & Sejnowski, 1995)  with mnepython. Baseline correction was applied using the mean value ranging from -0. 3 s to -0. 1 s before the first key press.
Preprocessed M/EEG data were analyzed using MNE Python 0. 13  (Gramfort et al. , 2014)  and custom written Python code. For the analysis of evoked responses in the time domain, a low-pass zero phase lag FIR filter (40 Hz) was applied to raw M/EEG data. For time-frequency analyses, raw data were filtered using a double-pass bandpass FIR filter (0. 8 -160 Hz). The high-pass cutoff was added to remove slow trends, which could lead to instabilities in time-frequency analyses. To reduce the dimensionality, all evoked and time-frequency analyses were performed on virtual sensor data combining magnetometers and gradiometers into single MEG sensor types using 'as_type' method from MNE-Python 0. 13 for gradiometers. This procedure largely simplified visualization and statistical analysis without losing information provided by all types of MEG sensors (gradiometers and magnetometers).
M/EEG-aMRI coregistration Anatomical Magnetic Resonance Imaging (aMRI) was used to provide high-resolution structural images of each individual's brain. The anatomical MRI was recorded using a 3-T Siemens Trio MRI scanner. Parameters of the sequence were: voxel size: 1. 0 x 1. 0 x 1. 1 mm; acquisition time: 466s; repetition time TR = 2300 ms; and echo time TE= 2. 98 ms. Volumetric segmentation of participants' anatomical MRI and cortical surface reconstruction was performed with the FreeSurfer software (http://surfer. nmr. mgh. harvard. edu/). A multi-echo FLASH pulse sequence with two flip angles (5 and 30 degrees) was also acquired  (Jovicich et al. , 2006; Fischl et al. , 2004)  to improve coregistration between EEG and aMRI. These procedures were used for group analysis with the MNE suite software  (Gramfort et al.
, 2014). The co-registration of the M/EEG data with the individual's structural MRI was carried out by realigning the digitized fiducial points with MRI slices. Using mne_analyze within the MNE suite, digitized fiducial points were aligned manually with the multimodal markers on the automatically extracted scalp of the participant. To insure reliable coregistration, an iterative refinement procedure was used to realign all digitized points with the individual's scalp.
Time-frequency analysis To analyze the oscillatory power in different frequency bands using cluster based permutation, we used DPSS tapers with an adaptive time window of frequency/2 cycles per frequency in 4 ms steps for frequencies ranging from 3 to 100 Hz, using 'tfr_multitaper' function from MNE-Python. Time bandwidth for frequency smoothing was set to 2. To receive the desired frequency smoothing the time bandwidth was divided by the time window defined by the number of cycles. For example, for 10 Hz frequency time bandwidth was 2/0. 5, resulting in 4 Hz smoothing. We used -0. 3 s to -0. 1 s before the first press as the baseline. The statistical analyses performed on theta (3-7 Hz), alpha (8-14 Hz), β (15-40 Hz), and γ bands (41-100 Hz) used spatiotemporal cluster permutation tests in the same way as for evoked response analyses.
Cluster based statistical analysis of MEG and EEG data Cluster-based analyses identified significant clusters of neighboring electrodes or sensors in the millisecond time dimension. To assess the differences between the experimental conditions as defined by behavioral outcomes, we ran cluster-based permutation analysis  (Maris & Oostenveld, 2007) , as implemented by MNE-Python by drawing 1000 samples for the Monte Carlo approximation and using FieldTrip's default neighbor templates. The randomization method identified the MEG virtual sensors and the EEG electrodes whose statistics exceeded a critical value. Neighboring sensors exceeding the critical value were considered as belonging to a significant cluster. The cluster level statistic was defined as the sum of values of a given statistical test in a given cluster, and was compared to a null distribution created by randomizing the data between conditions across multiple participants.
Binning procedure of behavioral and neuroimaging data All cluster-based analyses were performed on three conditions defined on the basis of the objective performance in time production (FOJ: short, correct, long) or the subjective self-estimation (SOJ: short, correct, long) separately for each experimental block. Before the binning, the behavioral data were Z-scored on a per block basis to keep the trial count even in each category. Computing these three conditions within a block focused the analysis on local variations of brain activity as a function of objective or subjective performance. To overcome limitations of arbitrary binning, and to capitalize on the continuous performance naturally provided by the time production and the time selfevaluation tasks, we also used a single trial approach, which investigated the interactions between the first and second order terms.
The appropriate degrees of freedom and overfitting concerns are addressed through cross-validation procedures. Importantly, interactions between two nonlinear predictors can be modeled as well. In that case, the fitted function takes a form of a plane consisting of two predictors. Mathematically, this is accomplished by modeling tensor product smooths. Here, we used thin plate regression splines as it seemed most appropriate for large data sets and flexible fitting  (Wood, 2003). In all presented analyses, we used a maximum likelihood method for smooth parameter optimization  (Wood, 2011). GAMM analyses were performed using the mgcv R package  (Wood, 2009, version 1. 8. 12). GAMM results were plotted using the itsadug R package  (Van Rij et al. , 2016, version 1. 0. 1). Although not widely used, GAMMs are useful for modeling EEG data  (Tremblay & Newman, 2015).