dataesr/scientific-paragraphs-categorization huggingface dataset:
calculation of the wavelet parameters, however, relies on a quadratic approximation of the frequency-domain wavelet to determine the half-power point frequencies. Practically, this wavelet transform and filtering method is implemented with the function wavetrans of the Matlab toolbox jLab (J. M. Lilly, 2021 ). An online course describes this specific method of using the wavelet transform as a narrow band-pass filter (J. M. Lilly, 2022). For the low-frequency band, in contrast to the approach used for the models, we explicitly lowpass the drifter velocities before calculating the variance in spatial bins. This low-pass variance is added to the mean velocity field squared to obtain the low-frequency KE. The low-pass filter is also achieved here by using a wavelet transform but by setting the Morse wavelet parameters γ to 3 and β to 0 and by setting the half-power point frequency to 0.
5 cpd (J. M. Lilly & Olhede, 2009, Section IV. A. ). For the near-inertial band, we also apply a wavelet transform method but one that continuously changes the center frequency of the wavelet to follow the local inertial frequency as the drifter latitude changes. This specific method is now coded in the function inertialextract, also part of the Matlab toolbox jLab (J. M. Lilly, 2021). The function is used by specifying the wavelet duration parameter P = ν/Δν. With ν = -f and Δν = -0. 1f, we obtain P = 10. The function is implemented by passing as arguments the times, longitudes, and latitudes of a drifter trajectory. The function calculates the local inertial frequency based on the latitude and subsequently returns the instantaneous complex-valued inertial oscillation amplitudes in kilometers.
Data Availability Statement This paper uses software made available by the Pangeo project, by jLab (J. M. Lilly, 2021)  and by the "cmocean" package  (Thyng et al. , 2016). MITgcm LLC4320 output is available at https://data. nas. nasa. gov/ecco/data. php?dir=/eccodata/llc_4320. The surface drifter data are available at https://www. aoml. noaa. gov/phod/gdp/ hourly_data. php. HYCOM output can be accessed via the OSiRIS infrastructure. Co-authors B. K. A. and J. F. S. can be contacted for details on OSiRIS access. The Matlab code used to process the MITgcm LLC4320 and HYCOM outputs into the results used in this paper, the results from MITgcm 4320, HYCOM, and processed drifter data, and the code used to produce all of the plots in the paper are provided in  Arbic et al. (2022) ; https:// doi.
Through this simulation, we explore the behaviour of our estimators, demonstrate their properties, and show advantages over alternative methods. A demonstration of our method is given for a sample of 150 French individuals with downsampled sequencing data. Conclusions. We find that our method can provide accurate relatedness estimates whilst holding advantages over existing methods in terms of robustness, independence from external software, and required computation time. The method presented in this paper is referred to LowKi (Low-depth Kinship) and has been made available in an R package (https://github. com/genostats/LowKi).
~ 4 ~ In adaptation to this recent trend of low-depth sequencing studies, a number of methods have been proposed to estimate relatedness coefficients from such datasets. The specificity of these methods is that they work upon genotype likelihoods or posterior probabilities, thus incorporating the uncertainty of genotype calls. These include Hidden Markov Model (HMM) based methods, maximum likelihood expectation based methods, and method-of-moment estimates. The former two approaches can be computationally heavy while moment-basedestimators present a quick and simple alternative. However, the loss of information entailed by analysing genotype likelihoods as a proxy for true genotypes will lead to biased estimates of relatedness which methods using moment-based-estimators need to account for.
Moment-based methods have so far only been developed for estimation of the kinship coefficient and the one software that performs this estimation requires an intermediate step from an existing HMM method. We propose here LowKi, a method to directly estimate genetic relatedness matrices from genotype likelihoods in a single step, which has now been incorporated into the genetic data management and analysis R-package 'Gaston'  (11). LowKi calculates moment estimates of relatedness in the form of a genetic relatedness matrices (GRMs) with suitable adjustments for the genotype uncertainty that is present with low-depth WGS data. For a pair of individuals  and  ′ , LowKi provides estimates of   ′ , the kinship coefficient of individuals  and  ′. This is the probability that a pair of randomly drawn alleles from individual  and  ′ at the same locus will be in a state of Identity-by-Descent (IBD).
We found that it sufficed to fit regression models between point-wise moment estimators and a summary statistic of the genotype likelihood fuzziness to obtain accurate estimates (denominated in the text as 'adjusted estimates'). To assess our approach, we have analysed both simulated and real data. Firstly, we used a simulation dataset which constitutes 1,444 simulated whole-genome sequences derived from the complex pedigree structure of the genetic isolates of Cilento  (12) (13) (14). This simulation dataset was first produced to assess phasing and imputation methods  (15)  before being used as a tool to explore heritability estimation  (16). Here we overlay a second layer of data simulation to convert our simulated sequencing data into low-depth sequencing data. To complement our simulation analysis, we also apply our models to a real dataset of 150 individuals from the FranceGenRef WGS panel (Labex GENMED http://www.
genmed. fr/). These individuals have been sequenced to a depth of 30-40× so we down-sampled individual bam files to create a dataset representative of WGS data at a depth of 2. 5×. Our aim was to show that we can recover relatedness matrices similar to GRMs calculated on high quality genotypes from low-depth data in an expedient manner. We compared our approach to two existing methods: SEEKIN (v1. 01)  (17)  and NGSRelateV2 (v2)  (18, 19). We show that our estimates are accurate and are less time consuming to compute than those provided by alternative software.
Relatedness estimation from genotype likelihoods in CilentoSim Our primary simulation dataset (here denoted as 'CilentoSim' and described in the Methods) comprises 1,444 individuals and 490,995 genetic variants across the 22 autosomal chromosomes (see Methods). We established that this variant set was appropriate for the calculation of a GRM as this set captured the known pedigree structure of Cilento. This is seen by comparing the kinship and fraternity GRMs (calculated from the simulated genotypes) to the true IBD sharing matrices calculated based on records of all haplotype mosaics created in the simulation (see Methods) (Supplementary Figure  1 ). For Kinship, the GRM gives a very precise estimate of the exact simulated IBD-sharing fractions. For fraternity, the GRM estimates are highly correlated with the simulated IBD-sharing despite a lower precision compared to kinship.
We artificially reduced the depth of our simulated sequencing data by drawing random alleles from each simulated individual genotype to a specified depth and then replacing in our simulation the true genotype with three genotype likelihoods. The method used here is based on the simulation proposed by  Kim et al. (20) , uses a simplified version of the genotype likelihood model of GATK  (21) (22) (23) , and is described fully in the Methods. We used this additional layer of simulation to give new datasets with average read depths of 2. 5×, 5×, and 10×. We applied our method alongside SEEKIN and NGSRelateV2. In Figure  1a , the off-diagonal elements of our estimated GRM matrices are compared to the the 'Full GRM' estimates from ~ 7 ~ complete simulated genotypes. As a moment estimator, SEEKIN is also compared to the 'Full GRM' but NGSRelateV2 (a maximum likelihood estimator) is compared to the simulated IBD sharing probabilities (which are similar but not identical to the Full GRM estimates, see Supplementary Figure  1 ) to give a fairest assessment of the three methods.
Comparison to existing software on simulated data In Figure  1b  and 1c , relatedness estimates given by two alternative algorithms, SEEKIN and NGSRelateV2, respectively, along with running times for these programs. SEEKIN only produces an estimate for the kinship matrix and indeed uses in part a similar momentestimator to our method presented here. SEEKIN gave very accurate kinship estimates. The key specificities of SEEKIN involve an intermediate step of the imputation software BEAGLE (v4. 1)  (24) , the leveraging of an external reference panel (here the 1000 Genomes Project phase 3 haplotype reference panel  (25)  was used) and a re-weighting based on the imputation quality of variants in the summation that forms each GRM entry. As the initial step of BEAGLE cannot be avoided, we include the runtime of BEAGLE into the run time of SEEKIN.
For lowdepth data, running BEAGLE is very time consuming. We followed the recommendations for using BEAGLE as described by the authors of SEEKIN. The use of BEAGLE will change the data in two particular ways: firstly, the uncertainty present in the initial data will be largely removed as BEAGLE will effectively take the prior information given to it in the form of genotype likelihoods and add more precision based on similarities between pairs of individuals in the sample or between individuals in the sample and the external panel of reference haplotypes using the same haplotype clustering HMM machinery as is applied in BEAGLE's haplotype phasing and genotype imputation methods. Secondly, running BEAGLE is likely to require the removal of some variants. For example, on our simulated dataset with genotype likelihoods created using a mean depth of 2.
5×, for our initial dataset of 490,995, BEAGLE returns information for only 340,464 variants. In Supplementary Figure  2 , the difference in precision is displayed between the initial genotype likelihoods supplied to BEAGLE (for a random selection of 25,000 variants) and the posterior genotype probabilities. This demonstrates the importance of the use of BEAGLE to the SEEKIN method. A different approach is proposed by NGSRelateV2 which directly estimates relatedness parameters through maximum likelihood estimation. Indeed, for the fraternity matrix, the true IBD coefficients were estimated more precisely with NGSRelateV2 than with a GRM on simulated genotypes (a comparison can be made between Figure  1  and Supplementary Figure  1 ). This software also produces additional information as it gives estimates for all nine condensed identity-by-descent states.
Testing with real data We also applied our method, SEEKIN, and NGSRelateV2 to a set of real genotypes. 150 individuals with WGS data were made available to us from the FranceGenRef panel; of which all individuals are not closely-related except for two pairs of siblings. We down-sampled this dataset from 30-40× to 2. 5× in order to create realistic low-depth WGS data. The estimates of the Kinship and Fraternity matrix entries for these two sibling pairs are given in Table  1.
~ 11 ~ Moment-estimators on down-sampled data can were compared against moment-estimators on the original 30-40× data with one exception: the estimates from NGSRelateV2 on downsampled data were compared to the estimates of NGSRelateV2 applied the original 30-40× data. This was because with a sample size of 150, the fraternity coefficients in particular may be imprecisely estimated even on the original data and so it would not necessarily be fair to benchmark NGSRelateV2 against GRM estimates. All methods were able to distinguish the two pairs as being closely related compared to all other pairs (Supplementary Figure  3 ). All methods produced accurate estimates for the kinship coefficient but the fraternity coefficient proved difficult for all methods to estimate accurately. One intuitive solution is to use the same approach as SEEKIN and first performed ~ 12 ~ imputation with BEAGLE; this allowed us to significantly improve our estimates of the fraternity coefficients between the two sibling pairs (Supplementary Figure  3 , panel (c)).
This allowed us to have improved estimates for the fraternity matrix. In every case, LowKi underestimates both fraternity coefficients; however, NGSRelateV2 gave overestimations. Even without knowing the true fraternity coefficients, an overestimation is apparent as NGSRelateV2 returned fraternity coefficients outside of the expected range of likely coefficients between siblings in an outbred population (approximately between 0. 1 and 0. 4)  (26). LowKi's estimates remain within this range. When running NGSRelateV2 on data without down-sampling, we found significantly lower fraternity coefficients for the two sibling pairs (Table  1 , Supplementary Figure  3 ).
The NGSRelateV2 model expects genotype likelihoods to accurately reflect the probabilities of the unobserved value of the hidden genotype. This may explain why it gave very good estimates in the simulation based on Cilento (where data was created with a naïve version of the GATK models and was generated from simulated genotypes) but performed less well in the more complex real data scenario. To correct for bias in the estimates of LowKi, we introduced an innovative simulation extrapolation type approach that could account for unseen error models and the inherent reduction in variance typical to low-depth genetic data. These adjustment methods proposed should be robust to different sources of bias arising from genotype uncertainty coming from different types of bioinformatics pipeline. This could give more flexibility than likelihood based methods such as lcMLkin  (27) , NGSRelateV2, as well as similar methods proposed for estimating inbreeding coefficients  (28).
Note that we did not test lcMLkin here following its assessment in the publication presenting SEEKIN  (17). The adjustment technique developed for LowKi could be harnessed in other areas of research involving shallow sequencing data. We showed that the alternative to such bias-correction, using an external imputation algorithm, could also lead to lengthy run times and a reliance on the accuracy of the external ~ 14 ~ algorithm. Notwithstanding such observations, the methodology of SEEKIN that uses the intermediate step of BEAGLE is clearly often highly effective and can also be used in conjunction with LowKi. Indeed, BEAGLE probably worked exceptionally well in the case of our CilentoSim dataset due to the many pairs of very closely related individuals in the sample. However, in the circumstance where only a small sample size is present or when an appropriate reference panel cannot be ascertained (both might be the case in studies of ancient DNA or small isolated populations for examples), it is beneficial to have a method for proceeding directly to relatedness estimates from genotype likelihood data.
Conclusion LowKi was effective at computing very accurate GRMs in a large sample of individuals with a full spectrum of IBD-sharing between pairs of related individuals in a detailed simulation study. We complemented this analysis by assessing an example of real low-depth genetic data from FranceGenRef, where our re-adjusted relatedness coefficient estimates were able to quickly and accurately identify the pairs of siblings in the sample. By analysing real data, we have illustrated that our estimators perform well outside of the idealised setting of a simulations. Real data will harbour phenomena such as allele-balance bias  (29)  or regionspecific sequencing error rates (30) so it was important to verify our estimators on an example of true sequencing data. When comparing to existing methods, LowKi does not require the use of intermediate.
We also only retained 490,995 variants by first selecting those with a minor allele frequency above 5% and then by performing pruning on linkage disequilibrium with Gaston. In the Cilento cohort, there are 19 individuals with whole-genome sequencing data. These individuals were sequenced to an average depth of 50-60×. From this dataset, we took a list of per-variant mean read depths and scaled each entry so that the global mean read depth.
Testing existing software To run SEEKIN (v1. 01), we first applied BEAGLE (v4. 1). BEAGLE was given reference haplotypes from the 1000 Genomes project (Phase 3) and was run in windows of 750 variants with buffers of 250 variants. We found that BEAGLE required very long runtimes, hence we set the parameter 'modelscale' equal to 3 which the authors of BEAGLE suggested in the software's manual as an appropriate setting to increase both speed and accuracy when applying BEAGLE.
software such as BEAGLE and requires the least computation time. The innovative adjustment method applied in LowKi gives flexibility to the method to account for different possible sources of bias. The LowKi methods proposed here for estimating relatedness have been made available at https://github. com/genostats/LowKi and work in conjunction with the existing R-~ 15 ~ package Gaston. This represents a fast and accurate standalone option for computing kinship and fraternity coefficients from low-depth sequencing data.
Acknowledgments We would like to thank kindly all of the participants of the  Vallo di Diano  project and the Cilento cohort. We acknowledge the  Center of Biological Resources (CHU Nantes ,  Hotel Dieu ,  CRB ,  Nantes, F-44093, France) , the  Dijon CRB , the  CEPH  and the  Genomics and Bioinformatics Core Facility of Nantes (GenoBiRD, Biogenouest). We thank the  FranceGenRef Consortium  for giving us the opportunity to work with the FranceGenRef sequencing data for this project. We are also very grateful to  Emmanuelle Génin  for her valuable advice and insights regarding this project.
~ 25 ~ 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.
Moreover, the interactions between categories of scientific vocabularies, measured by metrics of the "cognitive extent of science", with a method based on the lexical diversity of titles of fixed quotas of research articles  [12] , denote greater interdisciplinarity with larger networks of collaborations, in most disciplines. On the other side, a recent comprehensive analysis of trends in SKG outcomes  [1]  observes that SKG efficiency is primarily significant in global encyclopedic databases of scientific results, with the ability to enrich "classic metadata" about publications. However, knowledge graph "incompleteness" causes serious obstacles to the expressive power of graphs as a whole  [13]  (we refer to the definition of graphs given in the article quoted above, where graphs «accumulate and convey knowledge of the real world, whose nodes represent entities of interest and whose edges represent relations between these entities».
Background and Other Works Methodologies for SKG design are now confronted by a simple scientific context: digital analytics of scholarly content progresses slowly and is reported as being in an early phase only (see, e. g. , the Open Research Knowledge Graph wiki: https://gitlab. com/TIBHannover/orkg/orkg-frontend/-/wikis/home 2 August 2022), while the disconnection between research on information behaviors and research on information systems development has been recently highlighted in a comprehensive review  [19]. In this context, however, research resources are available, in adjacent scientific spheres, and addressing the considerable structural diversity of digital community networks  [20]. A wide range of suitable technologies are available, to express the adversarial learnings of academic dispute, with entity alignment techniques  [21] , with dynamic community discovery  [6] , and with architectures of message-passing graph subnetworks  [22]  (see also http://snap.
In SKG GRAPHYP, we use triplets of nodes shaped into graph subnetworks, with three parameters, mass, intensity, and attention, which measure the documentary behaviors of the users on the items (see below, 3. 2 Subnetworks of cognitive communities). Community detection also assumes a data quality assessment approach among the alternatives, and it is proposed to use a classifier as a judge  [29]. New designs in that direction can be mentioned with generative adversarial networks (Vanilla GAN) and adversarial autoencoders  [29].
Adversarial classification of citations, (negative citation, disputing citation, etc. ) has also been studied by citation networks. Recently, without mention of cliques, the first large scale study of 4 million papers investigated the "expression of disagreement in scientific literature"  [2] , by analyzing disagreement between two papers as well as statements indicative of disagreements inside the communities; it explored a data framework of in-text citations. The impact of disagreement on self-citation, and on citation impact, was also analyzed in depth. In our approach of cliques, GRAPHYP's conceptual framework differs, by a systemic capture of the whole search history of users and items for meaningful keywords illustrating a research question. More fundamentally we propose a modeled information retrieval record.
In such an approach, graphs are supposed to have their own added value in representing the manifold of cognitive information, with the application of a specific expressive symmetry in the construction of information. [17]  refers to C. E. Shannon, with the concept of "Rate Distortion Manifolds", and raises the "necessary conditions gauging the reliability of a source entropy rate relative to a channel capacity", which are defining a research program for information representation, within which our own research question is housed with SKG GRAPHYP representation of manifolds of cliques. In their research program, the authors observe, "introducing simplicial methods to analyze the underlying combinatorial structure of the manifold, we may recover graph-theoretic models as suited to the navigation through various types of information highways, systems of coding, symbolic dynamics and complexity".
Graph matchings of subnetworks of cognitive communities Subnetworks of documentary practices are themselves structured in flows of data geometrically oriented by an entity alignment, which could make it possible to detect, in a controversy, a preferred community identified in a self-supervised mapping of adversarial representation of all observable communities. A novel functionality is required to build up the semantic adversarial representation of cognitive communities of knowledge. Proposed in the SKG GRAPHYP, this functionality is necessary to identify, within a manifold of communities, typical adversarial positions and controversies. This implies firstly representing each community in a specific modeling of all "possible" manifolds, within a dedicated subnetwork. Tailored subnetworks are now accessible in graph neural networks (GNN) with a topologically aware message-passing scheme based on substructure encoding  [40] , which successfully overcomes the former inability of GNN to detect and count graph substructures, via subgraph isomorphism counting.