dataesr/scientific-paragraphs-categorization huggingface dataset:
First, the database used here is the generalist NCBInr database. The methodology can be used with other databases including individual reconstructed genomes and metagenome-assembled genomes (MAGs), as soon as COGs can be predicted for phylogenetic positioning (which is possible for any full genomes). The resolution of phylopeptidomics depends on several parameters: the nature of the biological sample, the depth of the experimental dataset, and the database coverage for the taxa present in the biological sample. Here, we have shown that a relative biomass quantitation using phylopeptidomics can be obtained at species level. Sub-species and even strain-resolved levels  [21]  are theoretically possible if enough MS/MS spectra are recorded. The limitations in terms of maximum number of quantifiable species in the sample are an open question.
If enough mass spectrometry time is allowed, mixtures of several hundred species could be analyzed by phylopeptidomics, rendering the approach consistent with fecal microbiota analysis through genome-resolved metagenomics  [22]. In order to assess the limitations of the approach for strainresolved level on the one hand, and maximum number of quantifiable organisms on the other, new experimental standards are needed. A control of the nature and exact quantities of microorganisms is required for synthetic standards representative of real microbiome samples  [23]. While assembling such experimental datasets is unfortunately time-and resource-consuming, we urge the scientific community to join efforts at producing such standards for improving bioinformatic pipelines for metaproteomics in general.
Database and MS/MS assignments For the interpretation of MS/MS spectra, the NCBInr fasta file was downloaded  (13 February 2015). The Mascot search engine (Matrix Science) was used for peptide inference. Molecular ion peak lists were extracted with Mascot Daemon software (version 2. 5. 1; Matrix Science) using the extract_msn. exe data import filter (ThermoFisher). Data import filter options were set to 400 (minimum mass), 5000 (maximum mass), 0 (grouping tolerance), 0 (intermediate scans), and 1000 (threshold), as described  [26]. Peptide assignation with Mascot was done with the following parameters: full trypsin specificity, maximum of one missed cleavage, mass tolerances of 5 ppm on the parent ion and 0. 5 Da on the MS/MS, static modification of carboxyamidomethylated cysteine (+ 57. 0215), and oxidized methionine (+ 15.
Taxa with more than 10 missing COGs were excluded from the pool of taxa with calculated distances. A total of 14,237 taxa out of 16, 548 were retained. For groups of taxa with the same set of associated COGs, only one representative was retained, with other taxa in the group inheriting distance results from this taxon. COG sequences were concatenated into a supervector, which was aligned using MUSCLE in profile mode to the predefined masked MSA. Upon complete taxa addition to the alignment, CLUSTAL W (v2. 1)  [33] , recompiled as Windows 64 b using MSYS/MinGW, was used to generate a PIM out of the MSA of all aligned taxa supervectors. PIM pair results were the distances used to evaluate the phylogenetic distance between organisms. We chose not to fix distance inconsistencies by methods such as maximum likelihood, maximum parsimony, UPGMA, or neighbor-joining after comparing signature quality using different phylogenetic tree generation and seeing degradation or marginal improvement compared with raw PIM distances, at the cost of very high time and computer power requirements (data not shown).
Post-processing of Mascot dat files Mascot dat files were parsed using the Python version of Matrix Science msparser v2. 5. 1 with function ms_peptidesummary  [34]. Peptide-spectrum matches (PSMs) were validated with a Mascot expectation value below 0. 1 using Mascot identity threshold (MIT) and allowing multiple PSMs per MS/MS spectrum. Peptides associated with spectra were assigned to taxa using NCBI databases. In the 2015 version of NCBI data files, each header of the nr. fasta file was the concatenation of the complete set of protein identifiers matching the sequence, with a gi identifier per entry. The first gi entry per non-redundant sequence was called firstgi in our data process. The taxonomy file gi_taxid_prot. dmp was used to perform gi to taxid matching. For newly introduced "WP_" RefSeq accessions aiming at identifying each non-redundant sequence with a single multispecies accession, file ftp://ftp.
ncbi. nlm. nih. gov/refseq/release/ release-catalog/release68. AutonomousProtein2Genomic [35] dated 06 January 2015 was used to complement gi to taxa mapping. Corresponding Python sqlite databases created were gi2firstgi. sql and firstgi2taxid. sql, allowing fast peptide to taxid mapping through gi identifiers. For post-march 2016 versions, this database structure has been modified to match Accession. version-based NCBI files following NCBI phasing out of sequence gis. Individual MS/MS spectra (Mascot queries) associated with peptide sequences (PSM) and protein sequences by Mascot were directly mapped to taxa using gi2firstgi and firstgi2taxid databases. In addition to the raw number of PSMs per taxon obtained, a collation of information was performed following the NCBI taxonomical tree from direct assignation to "canonical" taxonomical levels: species, genus, family, order, class, phylum, and superkingdom.
For each taxon at each level, the total peptide sequences and total PSMs were counted, as well as specific or unique peptide sequences and corresponding specific PSMs. For the 2018 version used to process the ZymoBIOMICS sample, accessions were used as sequence identifiers, and the mapping of accessions to taxa was performed using as-sembly_summary_refseq. txt and assembly_summary_genbank. txt files downloaded from ftp://ftp. ncbi. nlm. nih. gov/ genomes/ASSEMBLY_REPORTS [36], to map taxids to RefSeq assemblies (GCF) and GenBank assemblies (GCA), then the GCF/GCA *_assembly_report. txt files to map GCF/GCA to nucleotides, and the *_genomic. gff. gz files to map GCF/GCA to protein accessions.
Phylopeptidomics signature fit Taxa were filtered retaining those with MS/MS attribution, number of missing COGs lower than 10, and an assembly level quality "Complete genome" as extracted from file assembly_summary_refseq. txt  ([36] ). The matrix of taxa pair distances and the vector of the number of PSMs per taxon were used to calculate a phylopeptidomic signature fit. The two distance vectors for S. flexneri 2a str. 301 and S. Bongori NCTC 12419 were extracted from the full matrix, and the corresponding x values were used to compute the sum of the two theoretical signatures (function y = N×[A × exp(-x/a) + (1 -A) × exp(x/b)]) compared with actual MS/MS taxa data points. The "L-BFGS-B" method from the Python package scipy. optimize was used to best fit the sum of signature functions y = N×[A × exp(x/a) + (1 -A) × exp(x/b)] to the proteomic signal.
Default values for the variables were A = 0. 45, a = 0. 013, b = 0. 082, and N = #TSMs (taxon). Normalization was applied to the parameters during search space exploration, using the correction factors 1/A, 1/a, 1/b, and 1/100. Bounds used were: default value ± 0. 05 for A, ± 0. 001 for a and b, and 0 to #TSMs × 5 for N. The objective function was the sum of quadratic errors between taxa data points and the corresponding estimate based on the sum of signatures. The tolerance for termination was set to 0. 01. A similar setup was used to obtain the fit of the ZymoBIOMICS Microbial Community Standard D6300. Organisms to be quantified were set as Pseudomonas Escherichia coli, Salmonella Lactobacillus fermentum, Enterococcus faecalis, Staphylococcus aureus, Listeria monocytogenes, Bacillus subtilis, Saccharomyces cerevisiae, and Cryptococcus neoformans.
The S. flexneri 2a str. 301 and S. bongori NCTC 12419 signatures are displayed respectively in blue-and orange-filled areas. The relative percentage of S. flexneri calculated using phylopeptidomics signatures is thus 1492/3050 = 49% compared with 50% expected therefore be adjustable, using the A REF coefficient. For the three S. flexneri MS/MS datasets, calculated coefficients a REF and b REF were similar, 0. 013 and 0. 082, respectively, and the A REF coefficients were 0. 4, 0. 44, and 0. 45 (Supplementary Table.
However, if no MEPs could be obtained on the TA muscle, then they were recorded on the APB muscle, still with the B70 coil. For therapeutic stimulation, the motor cortical representation of the painful region was targeted with the coil held in posteroanterior orientation. In patients with orofacial pain, upper limb or hemibody pain, a flat B65 figure-of-eight coil was used and the site of cortical stimulation was determined using a TMS Navigator system, integrating individual brain magnetic resonance imaging (MRI) data (Localite, Sankt Augustin, Germany). Targeting was performed according to the previously described functional anatomy of the precentral gyrus  (Ayache et al. , 2016). For hemibody pain, the hand area was targeted. In patients with pudendal neuralgia or lower limb pain, an angled B70 figure-of-eight coil was used  (Hodaj et al.
Statistical analysis Data are presented as mean ± standard deviation (SD). The significance level of p value was set at 0. 05. Statistical analyses were performed using the Stata 13. 0 software (StataCorp, College Station, Texas, USA). Parametric or non-parametric tests were used depending on whether the data had a normal distribution or not, as shown by the Shapiro-Wilk test. First, analyses on baseline data were performed according to the origin of pain: orofacial pain, limb neuropathic pain, and pudendal neuralgia. Kruskal-Wallis or one-way ANOVA test was used for quantitative variables (age, pain syndrome duration, VNS scores of permanent and paroxysmal pain, daily number of pain paroxysms, and NPSI, HAD, and SF-36 PCS and MCS scores) and Fisher's exact test for categorical variables (gender, medications).
Location-scale Dirichlet process mixtures of Gaussians (DPM-G) have proved extremely useful in dealing with density estimation and clustering problems in a wide range of domains. Motivated by an astronomical application, in this work we address the robustness of DPM-G models to affine transformations of the data, a natural requirement for any sensible statistical method for density estimation and clustering. First, we devise a coherent prior specification of the model which makes posterior inference invariant with respect to affine transformations of the data. Second, we formalise the notion of asymptotic robustness under data transformation and show that mild assumptions on the true data generating process are sufficient to ensure that DPM-G models feature such a property. Our investigation is supported by an extensive simulation study and illustrated by the analysis of an astronomical dataset consisting of physical measurements of stars in the field of the globular cluster NGC 2419.
, 2009). This is specially important considering that often scarce to no a priori guidance about dimensional constants might be available, thus making the model calibration a daunting task. The motivating example of this work comes indeed from astronomy, the dataset we consider consisting of measurements on a set of 139 stars, possibly belonging to a globular cluster called NGC 2419  (Ibata et al. , 2011). Globular clusters are sets of stars orbiting some galactic center. The NGC 2419, showed in Figure  1 , is one of the furthest known globular clusters in the Milky Way. For each star we observe a four-dimensional vector (Y 1 , Y 2 , V, [Fe/H]), where (Y 1 , Y 2 ) is a two-dimensional projection on the plane of the sky of the position of the star, V is its line of sight velocity and [Fe/H] its metallicity, a measure of the abundance of iron relative to hydrogen.
Out of these four components, only Y 1 and Y 2 are measured in the same physical unit, while dimensional constants need to be specified in order to relate position, velocity and metallicity. A key question arising with these data consists in identifying the stars that, among the 139 observed, can be rightfully considered as belonging to NGC 2419: a correct classification would be pivotal in the study of the globular cluster dynamics. Astronomers expect the large majority of the observed stars to belong to the cluster: the remaining ones, called field stars or contaminants, are Milky Way stars, unrelated to the cluster, that happen to appear projected in the Figure  1 : An image of the remote Milky Way globular cluster NGC 2419 (about 300 000 light years away from the solar system). Picture by Bob Franke, with permission (www.
bfastro. com). same region of the plane of the sky. In general the contaminants have different kinematic and chemical properties with respect to the cluster members. Considering the nature of the problem, this research question can be formalised as an unsupervised classification problem, the goal being the identification of the stars which belong to the largest cluster, which can be interpreted as the NGC 2419 globular cluster. Admittedly, the terms of such a classification problem are not limited to the considered dataset but, on the contrary, are ubiquitous in astronomy and, more in general, might arise in any field where data components are incommensurable. Bayesian nonparametric methods for density estimation and clustering have been successfully applied in a wide range of fields, including genetics  (Huelsenbeck and Andolfatto, 2007) , bioinformatics  (Medvedovic and Sivaganesan, 2002) , clinical trials  (Xu et al.
In this paper we investigate the effect of affine transformations of the data on locationscale DPM of multivariate Gaussians (DPM-G)  (Müller et al. , 1996) , which will be introduced in Section 2. This is a very commonly used class of DPM models whose asymptotic properties have been studied by  Wu and Ghosal (2010)  and  Canale and De Blasi (2017) , among others. While rescaling the data, often for numerical convenience, is a common practice, the robustness of multivariate DPM-G models under such transformations remains essentially unaddressed to date. We fill this gap by formally studying robustness properties for a flexible specification of DPM-G models, under affine transformations of the data. Specifically, our contribution is two-fold: first, we formalise the intuitive idea that a location-scale DPM-G model on a given dataset induces a location-scale DPM-G model on rescaled data and we provide the parameters mapping for the transformed DPM-G model; second, we introduce the notion of asymptotic robustness under affine transformations of the data and show that, under mild assumptions on the true data generating process, DPM-G models feature such robustness property.
As a by-product, we show that the original assumptions of  Wu and Ghosal (2010)  and  Canale and De Blasi (2017)  for ensuring posterior consistency of Dirichlet process mixtures can be simplified by removing a redundant assumption regarding the finite entropy of the model. This result, proven in Lemma 1, can be of independent interest. Our theoretical results are supported by an extensive simulation study, focusing on both density and clustering estimation. These findings make the DPM-G model a suitable candidate to deal with problems where an informed choice of the relative scale of different dimensions seems prohibitive. We thus fit a DPM-G model to the NGC 2419 dataset and show that it provides interesting insight on the classification problem motivating this work. The rest of the paper is organised as follows.
In Section 2 we describe the modelling framework and introduce the notation used throughout the paper. Section 3 presents the main results of the work, with two-fold focus on finite sample properties on the one hand, and large sample asymptotics on the other. A thorough simulation study is presented in Section 4 while Section 5 is dedicated to the analysis of the NGC 2419 dataset. Conclusions are discussed in Section 6. Proofs of all results are postponed to Appendix A.
1. This result implies that, for any invertible affine transformation g, modelling the set of observations X (n) with a DPM-G model (1), with base measure (2) and hyperparameters π, is equivalent with assuming the same model with transformed hyperparameters π g , for the transformed observations g(X) (n) := (g(X 1 ),. , g(X n )). As a by-product, the same posterior inference can be drawn conditionally on both the original and the transformed set of observations, as the conditional distribution of the random density fπg , given g(X) (n) , coincides with the conditional distribu- n). Proposition 1 thus provides a formal justification for the procedure of transforming data, e. g. via standardisation or normalisation, often adopted to achieve numerical efficiency: as long as the prior specification of the hyperparameters of a DPM-G model respects the condition of Proposition 1, transforming the data does not affect posterior inference.
Large n asymptotic robustness We investigate the effect of affine transformations of the data on DPM-G models by studying the asymptotic behaviour of the resulting posterior distribution in the large sample size regime. To this end, we fit the same DPM-G model fπ , defined in (  1 ) and (  2 ), to two versions of the data, that is X (n) and g(X) (n) , by using the exact same specification for the hyperparameters π. Under this setting, the assumptions of Proposition 1 are not met and the posterior distributions obtained by conditioning on the two sets of observations are different random distributions which, thus, might lead to different statistical conclusions. The main result of this section shows that, under mild conditions on the true generating distribution of the observations, the posterior distributions obtained by conditioning fπ on the two sets of observations X (n) and g(X) (n) , become more and more similar, up to an affine reparametrisation, as the sample size n grows.
More specifically we show that the probability mass of the joint distribution of these two conditional random densities concentrates in a neighbourhood of {(f 1 , f 2 ) ∈ F ×F s. t. f 1 = | det(C)|f 2 •g} as n goes to infinity. Henceforth we will say that the DPM-G model (1) with base measure (2) is asymptotically robust to affine transformation of the data. The rest of the section formalises and discusses this result. We consider a metric ρ on F which can be equivalently defined as the Hellinger distance ρ(f 1 , f 2 ) = { ( f 1 (x) -f 2 (x)) 2 dx} 1/2 or the L 1 distance ρ(f 1 , f 2 ) = |f 1 (x) -f 2 (x))|dx between densities f 1 and f 2 in F , and we denote by • the Euclidean norm on R d. Moreover, we adopt here the usual frequentist validation approach in the large n regime, working 'as if' the observations X (n) were generated from a true and fixed data generating process F * (see for instance  Rousseau, 2016).
Simulation study We ran an extensive simulation study with a two-fold goal: 1) providing empirical support to our result on the large n asymptotic robustness of a DPM-G model, under affine transformations of the data; 2) investigating whether an analogous robustness property holds when DPM-G models are adopted to make inference on the clustering structure of the data. To this end, we considered two distinct data-generating distributions, which allowed us to highlight different facets of DPM-G models. In the first case, data are generated from a mixture of bivariate Gaussians, distribution which satisfies the conditions of Theorem 1. This study complements our asymptotic result with a numerical investigation of the finite n behaviour of DPM-G models, when data undergo an affine transformation.
Moreover, the same data are used to perform a numerical study on the effect of data transformation and sample size on the number of clusters on the estimated partition. While not directly related to theoretical results of Section 3, this part of the study is relevant in view of the astronomical application of Section 5 where a DPM-G model will be used for unsupervised clustering. The second scenario we considered does not satisfy the set of assumptions of Theorem 1, as data are generated from univariate Student's t-distribution with two degrees of freedom, thus breaking assumption A2. Our study, in this case, aims at assessing the robustness of DPM-G models when the sufficient conditions of Theorem 1 are not met.
Data from Student's t-distribution The second part of the simulation study deals with the same simulation scenarios (n ∈ {100, 300, 1 000} and c = {1/5, 1/2, 1, 2, 5}) considered in Section 4. 1, with the difference that data are generated from a Student's t-distribution with two degrees of freedom. It is important to stress that such a distribution does not have finite variance and therefore does not meet assumption A2 of Theorem 1. Also in this case we considered 100 replicates for each considered simulation scenario. We analysed each dataset with a univariate version of the DPM-G model specified in (  1 ) and (  2 ). That is, we considered a univariate Gaussian kernel and a base measure defined as the product of two independent distributions, a univariate normal distribution for the location parameter µ ∼ N (m 0 , s 2  0 ) and an inverse-gamma distribution for the scale parameter Pólya urn scheme 2.
Posterior inference was drawn based on 5 000 iterations, after a burn-in period of 2 500 iterations. We assessed the convergence of the chains by visually investigating traceplots, which did not provide indication against it. Also for these data, for any considered sample size n and for any pair of values c 1 and c 2 taken by the constant c, we approximately evaluated the L 1 distance between the suitably rescaled estimated posterior densities obtained conditionally on X (n) c 1 and on X (n) c 2. The results of such analysis are displayed in Figure  4  and indicate that, as the sample size grows, the L 1 distance decreases. This qualitative findings suggest that asymptotic robustness might hold also for data generated from a distribution not meeting the assumptions of Theorem 1.
Astronomical data The large n asymptotic robustness to affine transformation of the DPM-G model makes it a suitable candidate also for analysing data whose components are not commensurable and for which an informed choice of the relative scale of different dimensions seems prohibitive. We fitted the DPM-G model, specified as in (1) and with base measure (2), to the NGC 2419 dataset described in Section 1. The ultimate goal of our analysis consists in classifying stars as belonging to the NGC 2419 globular cluster or as being contaminants: an accurate classification is crucial for the astronomers to study the dynamics of the globular cluster. Since the large majority of the stars in the dataset is expected to belong to the globular cluster, with only a few of them being contaminants, we will identify the globular cluster as the largest group in the estimated partition of the dataset.
Prior to any analysis, data were standardised component by component, the legitimacy of such procedure following from the robustness results of Theorem 1. Hyperprior distributions were specified for the location parameter of the base measure (2) and on the DP precision parameter α. Specifically, B 0 ∼ IW (6, diag(  15 )) and m 0 | B 0 ∼ N (0, B 0 ), specification chosen to guarantee a prior guess on the location component µ flat enough to cover the support of the data and centered at 0. In addition, α was given a gamma prior distribution with unit shape parameter and rate parameter equal to 5. 26, so that, a priori, α 0 := E[α] 0. 19. This leads to an expected number of components K n in a sample of size n = 139 from a DP equal to n i=1 α 0 /(α 0 + i -1) 2, thus reflecting the prior opinion of astronomers who would expect two distinct groups of stars in the dataset.