dataesr/scientific-paragraphs-categorization huggingface dataset:
This was achieved through software development and formulation improvements of the MHE. First, we developed an open-source Python package (biosiglive  [43] ) designed for efficient (C++ based) real-time data streaming. Second, a real-time iteration scheme was used inside Acados, and algorithm adjustments were chosen to allow robust and fast solving. We have highlighted that receding horizon parameters influence the estimation results, leading to, for example, highfrequency kinematics trajectories or activation saturation. Fig. 5  shows that using frame 100% led to inconsistent saturated muscle activations (> 4%). This non-physiological result suggests that, when keeping frame 100% in the estimated trajectory (subproblem(t-4) in Fig. 2 ), the corresponding movement was not sufficiently filtered, as it went only once through the MHE.
The size of the MHE windows being small and the motion slow, interpolation effects should be low. However, the data should be acquired at a higher frequency in future work to avoid interpolation. The muscle parameters were not calibrated based on the participants, due to the yet unresolved challenge of calibrating muscles actuating more than one joint  [14]. So, the amplitude of the estimated activation and force might lack accuracy. Nevertheless, we evaluated the muscle force and activation time histories to show the relevance of the estimated muscle contributions. Only the subscapularis shows an activation almost three times higher than measured activity  [41] , which could be explained by the lack of scapulothoracic kinematics constraints or the noncalibrated muscle parameters (e. g. , isometric force or optimal length).
V. CONCLUSIONS We showed that trajectory optimization coupled with a MHE formulation can estimate muscle forces in real-time from experimental EMG-marker data. Real-time capabilities are good enough to be used in a clinical context. Biofeedback of estimated value was provided at 30 Hz with a 110 ms delay, on a complex model in experimental conditions. The estimated joint kinematics and muscle forces were consistent with the experimental motion and the literature. We are enthusiast that our algorithm provide consistent estimation for two different participants despite fine-tuning the parameters exclusively based on the first participant. Such a method could be used in clinical or industrial applications to give relevant real-time input data to assistive devices, leading to biomechanically informed interactions.
g. Callingham et al. 2019 ; Van Eck et al. 2019 ; Erceg et al. 2022 ). A 20 arcsec QU image cube for each LoTSS field co v ers an area of ∼58 deg 2 (7. 6 • × 7. 6 • ). The Q and U images are not deconvolved (due to computational and software limitations) and the cubes are compressed using the FPACK software 3 by a factor of 6. 4 (the default). The distance between LoTSS field centres is ∼2. 58 • and the full width at half-maximum (FWHM) of the HBA station beam at 144 MHz is 3. 96 •  (Shimwell et al. 2017 ). For our current work, we considered it unnecessary to run RM synthesis on the full field, so we extracted a smaller 4 • × 4 • area region around the centre of the QU cube (after unpacking the QU cube to its original state using FUNPACK ). This choice gave us full co v erage of the LoTSS sky area with no gaps between fields, while also providing significant o v erlap such that several polarized sources were detected in multiple Figure  1.
4 GHz. The visual inspection led to the removal of a small number of sources, in addition to identifying candidate pulsars (see Section 3. 5 ). For each entry in the final LoTSS RM Grid catalogue of 2461 polarized components, we extracted the single-pixel Q and U versus frequency spectra at the component location. While PYRMSYNTH was the most efficient RM synthesis software for running on the large cubes (with the 1 mJy beam -1 Stokes I threshold), we switched to using the RM-TOOLS package  (Purcell et al. 2020 )   6  to analyse the final selected polarized sources more comprehensively. Thus, we re-ran RM synthesis on the extracted spectra with RM-TOOLS , using the same Faraday depth range of ±120 rad m -2 , but with a higher sampling in Faraday depth of 0. 05 rad m -2 and weighting each channel by the inverse variance of the channel noise.
Because some sources have multiple RM entries (e. g. physical pairs), in total there are 1762 unique source redshifts,   where spectroscopic redshifts supersede photometric ones, leaving 824 phot-z in addition 938 spec-z. Therefore, 79 per cent of the RM Grid catalogue entries have associated redshifts. The distributions of spectroscopic and photometric redshifts are show in Fig. 19. The median for all redshifts is z med = 0. 6, while z med, spec = 0. 5 and z med, phot = 0. 7. Man y studies hav e inv estigated the dependence of the extragalactic RM on redshift (e. g. Oren & Wolfe 1995 ; Hammond et al. 2012 ; Xu & Han 2022 ). The high precision in the RM values from LoTSS, in addition to the high fraction of sources with redshifts, provides an excellent opportunity for new discoveries. The data presented here show a flat behaviour of the RRM versus redshift and a general decrease in the degree of polarization with redshift by a factor of ∼10 between z ∼ 0 and z ∼ 3.
2019 ). The radio morphology class can also be obtained using LOMORPH , and a preliminary analysis indicates that the largest class of polarized source are FR II ( ∼40 per cent). The rest of the sources are classified as FR I ( ∼20 per cent), hybrid ( ∼15 per cent) and a combination of compact and unresolved ( ∼25 per cent). It is striking to note the difference in the number of FR II relative to FR I ( ∼2x) for polarized sources compared to estimates for the general population 9 https:// github. com/bmingo/ LoMorph (i. e. bright, large radio AGN), where the opposite is the case, with two to three times more FR Is than FR IIs  (Mingo et al. 2019 ).
S U M M A RY We have produced an RM Grid catalogue from the LoTSS-DR2 data containing 2461 RM values o v er an area of 5720 deg 2 (Table  1  ). This is the largest low-frequency RM Grid to date. (i) The catalogue is derived from two non-contiguous sky areas: the 13 h field which has an area of 4240 deg 2 with a polarized source areal number density of 0. 48 deg -2 , and the 0 h field with an area of 1480 deg 2 and source density of 0. 29 deg -2. (ii) The RM values were derived the LoTSS Q and U images at an angular resolution of 20 arcsec across a frequency range of 120 to 168 MHz. The Faraday depth range was limited to ±120 rad m -2 and only polarized sources abo v e 8 σ QU were included in the catalogue. The median value of σ QU in the Faraday spectra of the detected sources across 844 individual LoTSS-DR2 pointings was 0.
g. RM pair studies  (Pomakov et al. 2022 ). In addition to this, RM synthesis will be run without any masking (the data were masked at 1 mJy beam -1 in Stokes I in this work), providing better sensitivity to highly polarized sources, which further enhances the disco v ery potential of the surv e y, and will enable a better quantification of the noise properties in polarization for each field. Extending the Faraday depth range to search for polarized sources with high | RM | values (i. e. > 120 rad m -2 ) will also be included, which becomes more important for fields which are closer to the Galactic plane. Ideally, a finer channelization would be used for the Galactic plane region (i. e. 48 kHz for a max/min RM of ±900 rad m -2 ), to decrease the effects of bandwidth depolarization. In the longer term, a deconvolution strategy for Q and U needs to be implemented.
In terms of the polarization calibration of the data, enhancements to reduce the widefield instrumental polarization without compromising the polarization data reliability are needed. An absolute polarization angle calibration strategy for each field, similar to that presented in Herrera  Ruiz et al. ( 2021 ) , would allow mosaicking of the data and thus enable us to obtain the maximum sensitivity of the LoTSS surv e y for polarization. Impro v ements in the ionosphere RM correction are also desirable since the RM errors are dominated by the residual errors in the ionosphere RM correction (i. e. ∼5 to 10 times larger than the measurement errors). The continuing advances in using the full LOFAR array to achieve an angular resolution of 0. 3 arcsec (e. g. Morabito et al. 2022 ; Sweijen et al.
AC K N OW L E D G E M E N T SSPO and MB acknowledge financial support from the Deutsche Forschungsgemeinschaft (DFG) under grant BR2026/23. MB acknowledges support from the Deutsche Forschungsgemeinschaft Downloaded from https://academic. oup. com/mnras/article/519/4/5723/6967143 by Chalmers University of Technology user on 16 March 2023.
under Germany's  Excellence Strategy -EXC 2121 'Quantum Universe ' -390833306. AMS gratefully acknowledges support from an  Alan Turing Institute   AI Fellowship   EP/V030302/1. KJD acknowledges funding from the  European Union 's  Horizon 2020 research and innovation programme  under the  Marie Skłodowska-Curie  grant agreement No. 892117  (HIZRAD). MJH acknowledges support from the  UK STFC  [ ST/V000624/1 ]. JHC and BM acknowledge support from the  UK Science and Technology Facilities Council (STFC)  under grants  ST/R000794/1 , and  ST/T000295/1  MB is supported by the  Polish National Science Center  through grants no. 2020/38/E/ST9/00395 ,  2018/30/E/ST9/00698 ,  2018/31/G/ST9/03388 , and  2020/39/B/ST9/03494 , and by the  Polish Ministry of Science and Higher Education  through grant  DIR/WK/2018/12.
This research made use of ASTROPY , a community-developed core PYTHON package for astronomy (Astropy Collaboration 2013 ) hosted at http://www. astrop y. org/, of  MATPLOTLIB (Hunter 2007  ), of  APLPY (Robitaille & Bressert 2012  ), an open-source astronomical plotting package for python hosted at http:// aplpy. github. com/, and of TOPCAT, an interactive graphical viewer and editor for tabular data (Taylor 2005 ). This research has made use of 'Aladin sky atlas' developed at  CDS, Strasbourg Observatory, France  (Bonnarel et al. 2000 ). LOFAR (van Haarlem et al. 2013 ) is the  Low Frequency Array designed  and constructed by  ASTRON. It has observing, data processing, and data storage facilities in several countries, which are owned by various parties (each with their own funding sources), and that are collectively operated by the ILT foundation under a joint scientific polic y.
Results We analysed a collection of 360 ancient oral, modern oral, sediment/soil and skin metagenomes, using stratified five-fold cross-validation. decOM estimates the contributions of these source environments in ancient oral metagenomic samples with high accuracy, outperforming two state-of-the-art methods for source tracking, FEAST and mSourceTracker. Conclusions decOM is a high-accuracy microbial source tracking method, suitable for ancient oral metagenomic data sets. The decOM method is generic and could also be adapted for MST of other ancient and modern types of metagenomes. We anticipate that decOM will be a valuable tool for MST of ancient metagenomic studies.
Under these circumstances, contamination assessment of aDNA samples is crucial not only to avoid misleading results after downstream analysis, but also to decide which samples are worth to be further sequenced  [7]. The task of Microbial Source Tracking (MST) is to quantify the proportion of different microbial environments (sources) in a target microbial community (sink)  [8]. MST enables quantification of contamination  [9]  in metagenomic sequencing data and to predict the metadata class of a given microbial sample. That is to say, if a researcher has sequenced their ancient metagenomic sample (sink) and collected a set of sources from environments where the sample might originate, an MST software estimates the contribution of each source to the sink and optionally reports a proportion for unknown sources.
FEAST, released 8 years after SourceTracker, uses an expectation-maximisation approach that reduced the running time of SourceTracker by a factor of 30 or more. It has been reported to require parameter tuning to achieve optimal performance  [13] , which is a resource-intensive procedure when handling large data sets. FEAST and mSourceTracker require a reference database which is necessary to build the taxonomy-based clustering tables that both methods use as input. Indeed, in both cases, metagenomic data must be grouped into bins or clusters of sequences sharing the same taxonomic classification, an information that is not only highly dependent on the database used, but also highly biased by the limited proportion of the microbial diversity that has been already sequenced and taxonomically annotated  [14].
Finally, these taxonomy-based clustering tables can also lead to misleading results depending on the sequence similarity metric and the threshold used to define them  [15]. To our knowledge, there are no reported referencefree methods for contamination assessment that use MST for large-scale metagenomic analyses  [13]. In this work, we seek to move away from database-dependent methods and use unsupervised approaches exploiting read-level sequence composition and the wealth of information contained in metagenomes that were previously sequenced. Over the past years and with the decrease of sequencing costs, large databases of metagenomic collections from all sorts of environments have become available  [16] [17] [18]. These metagenomic raw reads collectively require petabases of storage, which prohibits their reanalysis by most labs.
decOM was evaluated in a collection of ancient oral metagenomes with variable contamination levels. Our results show that decOM outperforms two of the most commonly used MST methods in the multi-class classification task of finding the most abundant source environment in a sink. We tested our methodology on a collection of 360 metagenomic data sets of ancient oral samples and its possible contaminants, in an external validation set of 254 ancient oral samples and on a simulated ancient calculus metagenome.
The microbial composition of a given aOral sample isolated from dental calculus has been modelled in previous studies as a mixture of DNA originating from dental plaque, skin bacteria, soil and other sources  [23, 24]. For this reason, we gathered 360 metagenomic data sets of diverse environment types: ancient oral (aOral), sediment/soil, skin, or modern oral (mOral) (Fig. 1 ). We used this collection of real metagenomic data to model the contribution of possible contaminants coming from sediment/soil and skin sources in a group of aOral samples. In addition, we included a set of mOral samples to assess whether our method can tell apart modern and ancient oral environments. The run accession codes for every aOral sample were retrieved from AncientMetagenomeDir  [1]  (v20. 12: Ancient City of Nessebar), a community-curated collection of annotated ancient metagenomic sample lists and standardised metadata.
Samples other than aOral were selected either because they had been used by competing MST methods or because they were labelled as aforementioned classes in well-known metagenomic databases such as curatedMetagenomicData  [25] , the HumanMetagenomeDB  [26]  or MGnify  [27]. We rely on the metadata of each metagenomic sample to assign a true label (i. e. environment type); however, there is no ground truth as to what is the true proportion of aOral, mOral, sediment/soil or skin content in any of them. Several variables accessible through the metadata of each run accession are plotted in the Supplementary File (Figs. 1, 2, 3 and 4).
Input data Both mSourceTracker and FEAST require taxonomybased clustering tables as input. We built these tables using Kaiju  [28]  and the reference database NCBI BLAST nr+euk (2021-02-24 release), a non-redundant protein database of bacteria, archaea, viruses, fungi, and microbial eukaryotes (information to download it in Supplementary File, Section 1). To exclude the possibility that the lower performance of competing methods was due to the poor quality of the input taxonomic profiles, we repeated the analyses using KrakenUniq (see Supplementary File Section 2). Also in this case, decOM improves over FEAST and mSourceTracker. Moreover, the latter two provide worse results compared to using Kaiju (see ROC and AUC plots in Supplementary Fig. 10  and 11 , respectively). On the other hand, decOM takes as input a binary k-mer matrix of distinct k-mers across a collection of metagenomic samples.
Mathematical formulation We consider a binary k-mer matrix M (as output by kmtricks) that indicates the presence/absence of each k-mer found across several metagenomic data sets, with N number of unique samples (columns) and K number of unique k-mers (rows). Each sample j is represented by a column vector m (j) = (m 1j , m 2j , m 3j ,. , m Kj ) where m i,j corresponds to the presence/absence of k-mer i in sample j. We will use the terminology of sink and sources to respectively denote the sample we want to evaluate the composition of, and the set of samples used as a database. Consider that the matrix M contains jointly all sources and potential sinks. Let a sample s (where s ∈ {1, 2,. , N } ) be a sink and m (s) be its col- umn vector. A source is a collection of L > 0 col- umn vectors used to build a matrix of sources M s of dimensions K × (L -1).
, w |C| � when multiplied by a sca- lar, as seen in the following operation: To analyse a new metagenomic sample, one needs only to compute a presence/absence vector of k-mers for this sample using kmtricks, then this new sink is compared against the pre-computed collection of sources. decOM incorporates a kmtricks module so that the user can give as input a simple FASTQ/FASTA file of their sink of interest, rather than a presence/ absence vector. Figure  2  provides a graphical representation of our pipeline. Finally, we are working to include the contribution of an unknown source by characterising it as the number of k-mers that are present in the sink and absent in all of the sources. decOM was implemented in Python 3. 6 as a conda package and the installation instructions are available in a GitHub repository  [31].
Microbial Source Tracking evaluated in four different experimental settings We perform a metagenomic Microbial Source Tracking to benchmark decOM, mSourceTracker, and FEAST, which all rely on an input matrix. For mSourceTracker and FEAST the input matrix corresponds to a taxonomy-based clustering table, whereas decOM takes as input a binary k-mer matrix across metagenomic data sets. Consider the set X = {m (1) , m (2) , m (3) ,. m (N ) } , where X contains all the column vectors of the aforementioned k-mer matrix. Let A = {m (s) } be a set of sink vectors, and B = {X \ m (s) } a set of sources. In order to esti- mate the proportion of source environments in each data set in our collection, we run our method in a leaveone-out fashion, i. e. every run of our method uses one different sample as sink and leaves the rest of the samples as sources.
One run of this experimental setup is described by Algorithm 1. Algorithm 1 Pseudocode of our method used to estimate proportions of sources in sink s Additionally, we Fig. 2  Graphical representation of decOM. Our method preprocesses an input k-mer matrix of aOral metagenomic samples and its possible contaminants, divides it into sinks and sources and then estimates and outputs the proportions of each source environment in the sink. The core idea in the classification step is that if a k-mer is present in the sink s represented by the vector m (s) , and in the source vector m (j) with environment label l j , then a ball is added to the bin with label l j (Ex: K-mer AAACG is present in the input sink S and in source S1 labelled as skin, S5 labelled as aOral and S7 labelled as mOral; hence, one ball is added to the bin of skin, aOral and mOral respectively).
Definitions for each performance metric used are specified in Section 5 of the Supplementary File. We also tested decOM on a validation set of 254 aOral samples, none of which belonged to the collection of 360 samples we used to construct the k-mer matrix. For this experiment, the aforementioned matrix is used as sources, whereas the 254 external aOral samples are used as sinks. Because all samples belong to the same class, precision and F1-score are not well-defined, whereas recall and accuracy are equivalent (see Section 5 in Supplementary File), which is why performance is measured using recall only. Finally, we tested decOM and its competitors on an uncontaminated simulated ancient oral data set and presented the estimated proportions.
Results We created decOM as reference-free and open-source Microbial Source Tracking method that is adapted to ancient metagenomic experiments. Our method takes as input a set of source vectors in the form of a presence/absence k-mer matrix (built from a collection of metagenomic data sets ready for the user to download), and one or more FASTA/FASTQ files to be used as sinks. It outputs a set of proportions (percentages) and a predicted metadata class per sink.
Simulated data set As a final experiment, we tested each of the methods on a simulated ancient dental calculus metagenome generated by other authors  [34]. A mock oral microbial community is created using representative genomes of microbes found in the human oral microbiome, further processed to appear similar to an ancient metagenomic sample. As in the validation set, we estimated the source environment contribution of the aOral, mOral, skin and sediment/soil microbial communities by using the samples from the 360 collection as sources. Results for all methods are in Fig. 4. Given that the synthetic metagenome comes from an uncontaminated mock oral microbial community that has been adapted to appear similar to an ancient calculus sample the expected content is to be 100% oral, decOM provides the highest estimation of oral contribution (ancient or modern), followed by mSource-Tracker and lastly by FEAST.
The consolidated running times can be seen in Table  3. decOM is considerably faster than the two other methods for creating a source matrix as we selected one partition of the large k-mer matrix produced by kmtricks and offered the pre-computed matrix in a Zenodo file for users to implement in their analyses. When producing a new vector, since decOM relies on kmtricks, it is also considerably faster than FEAST and mSourceTracker. However, our evaluation of the time here was based on Kaiju's running times. Optimising the creation of taxonomy-based clustering tables using faster alignment-free methods could improve time performance, potentially at the expense of results quality. Finally, all methods show comparable running times when performing the MST step.
Ancient oral metagenomic samples come from various environments (multi-source) After predicting the metadata class of each of the 360 samples in the collection, we also plotted the source proportions according to the estimation done by decOM, mSourceTracker and FEAST (Fig. 5 ). The proportion bar plots for mSource-Tracker and decOM are visibly more similar to each other than to FEAST, which seems to output more variable results. According to the estimation done by decOM, there are 4 main predicted groups in the collection with distinct source composition as seen in Fig. 5a : there is a group of samples that have a higher sediment/soil content, another class of samples with a higher skin content Fig. 4  MST on a simulated ancient dental calculus metagenome. Bar plots for the source environment proportion estimation obtained after evaluating each method using as sources all the samples from the 360 metagenomic collection, and using as sink a synthetic ancient oral data set.