dataesr/scientific-paragraphs-categorization huggingface dataset:
Then the empirical mean of the inverses, 1 n n i=1 1 Xi , converges in distribution towards a Cauchy random variable, with a given position parameter, and dispersion σ = πf (0). This simple analogue of the central limit theorem for inverse effects, as well as a deeper study of its general domain of attraction, could help us to gain some future insights on the biological phenomena that could be effectively modeled as Cauchy processes. The Pure Jump Cauchy Process. As a pure jump process, we showed that the CP could capture pulsed evolution phenomena. Simulation studies demonstrated that there was a strong segregation signal between Gaussian and Cauchy processes, that were never mistaken from one another, and that the CP could other kinds of jumping patterns, such as the NIG. The empirical Lizards dataset study illustrated that, using a model that has as many parameters as the standard BM, and that is very efficient to fit, we could recover the main conclusions of  Duchen et al.
(2017) , who used a more complex and time consuming Lévy model. The Relaxed Random Walk Cauchy Process. The CP can be re-framed as a scaled relaxed random walk, where each branch has its own variance parameter, drawn from a gamma distribution with parameters scaled by the branch length. We emphasize here that this process is different from the classical RRW of  Lemey et al. (2010) , and implemented in BEAST  (Suchard et al. , 2018) , where the branch variance variables are identically distributed. This latter model cannot be associated to any trait evolution process on the tree, as opposed to the CP, which has a nice jump process interpretation. We showed that is could be described as a CP, but on a time transformed tree, where the square root of each branch length is taken. For trees with branches smaller than one, this leads to longer branches in the transformed tree, and hence possibly more jumping events than expected under a simple CP, as we observed for the WNV dataset.
This make our method practical to use in many situations. Theoretical Limitations. Unfortunately, this algorithm has several limitations, both theoretical and practical. Looking at Equation (4), we can see that the second term of the sum might imply a division by zero for tips a and b such that t k:a = t ℓ:b and y a = y b , i. e. for two tips that are simultaneously (i) at the same temporal distance from their least common ancestor, and (ii) with a same trait value. Although condition (i) is common, and in particular verified for ultrametric trees, condition (ii) is theoretically impossible, as the probability of observing two tips with the exact same continuous trait value is zero. However, on empirical datasets, where measures are subject to rounding approximations, it is not uncommon to encounter tips with equal trait values.
For instance, the well known Chelonia dataset  (Jaffe et al. , 2011)  has about 46% of its entries repeated, as body size are often reported up to the centimeter only. In such cases, our method cannot be applied directly. A simple solution could then be to add a reasonable amount of random noise to the tip measurements, to make sure that they are all distinct. Such a jitter is for instance often applied to continuous phylogeographic data in virology to account for sampling location uncertainty  (Dellicour et al. , 2022). A good knowledge of the biological system under study can help the practitioner choose this noise, that can also empirically compensate for intra-species variations or bias in the measurement process. In such cases, as our algorithm is relatively fast, several independent replicates of the noisy dataset can easily be generated in order to check the robustness of the analysis with respect to the added noise.
Numerical Robustness. Besides this theoretical limitation, we observed some numerical robustness issues of our algorithms for large trees with more than 200 tips, which impacted parameter inference (see Fig. 4 ). This issue is caused by the many sums that need to be computed in our algorithms. These sums involve terms of arbitrary size, positive or negative, that may almost cancel out, and lead to precision errors. Despite our best efforts to use robust computational tools, because of the very structure of the summations, we could not further improve our implementation, even when using arbitrary precision summation techniques. We stress here that it is important to check, on biological datasets, that the numerical likelihood computations and optimizations behaved properly. As a first step, we propose in our package cauphy to plot the profile likelihood around the estimated parameters, that should be smooth and with a clear maximum (which is the case for both empirical examples presented here, see supplementary Figures  S2  and S4 ).
E. 3 West Nile Virus Table  S1 : Fits of Gaussian (BM, OU and EB) and CP models on the WNV dataset from  Pybus et al. (2012) , on the MMC tree for the latitude and longitude traits. The first two lines are the log likelihood and AIC scores for the ML fit. The parameters are µ for the ancestral root value, σ for the Gaussian standard error or Cauchy dispersion, and θ represents the selection strength α for the OU, and the rate r for the EB. The computation time for each fit on a standard laptop is given in seconds. 2012 ), for the latitude and longitudes considered as two independent traits, using the Cauchy REML model fit. Measured traits are shown as a bar plot at the tips of the tree, with a color gradient encoding the trait value, from light yellow (small) to dark purple (large). Modes of the posterior trait reconstructions are showed at internal nodes, with a width proportional to the relative weight of the modes (nodes with only one color have a single mode), and the same color scale as tip values.
Introduction The structure of networks has long been one of the most studied research questions in network science. In this article, we introduce a method to generate networks of a chosen size, organized according to a structure that can be expressed as an arbitrary ranking function for node pairs. This process thus allows the generation of classic structures such as communities, blocks, and spatial organizations, but also more exotic ones. We subsequently show an application of this framework to study network properties, by extending the classic small-world experiment by  (Watts and Strogatz, 1998). A python library  (Cazabet, 2023)  allowing reproduction of the results and generating networks with custom structures is also introduced. edges between each pair of nodes is independent of the probability of observing edges between other pairs.
Structure Zoo To illustrate the expression power of the Structify-Net rank generation approach, we propose a collection of structures, available in the Python library under the name of Structure Zoo. This collection contains both classic structures widely found in the literature, together with original ones. Fig. 3  introduces matrix representations of the node-pair ranks of all structures in the zoo. The structures in the Zoo are only to be taken as examples, chosen arbitrarily among a few wellknown structure types, and a few original ones. The main interest of Structify-Net is for the users to be able to specify their own structure with their own rank functions. The Zoo only represents a set of toy examples.
Working With Node Attributes In the previous section, we have seen an experiment in random networks without metadata/attributes, i. e. , with interchangeable nodes. However, as mentioned in the model definition, it is possible to use any node information in the rank function. In this section, we provide two simple motivational examples. Let's imagine working with a dataset such as a global air transport network. Nodes correspond to airports and are identified by their name, location, and country. Edges might correspond to having at least one direct flight between two airports. To study a property of such a network, for instance, its clustering, average shortest path, or properties of a virus diffusion on that network, one would usually compare that property with its value in networks generated by a reference null model, such as ER or Configuration model.
Another possibility offered by Structifynet is to use the node attributes. For instance, we can consider only the airport positions, and rank node pairs according to the distance between them in the dataset, which corresponds to using the Spatial structure defined in the Zoo, using metadata instead of random positions. Alternatively, we could use the country information as metadata to the Assortative Block Structure of the Zoo. Of course, it could be possible to use already-existing methods such as block models or spatial models to do the same. Structify-Net simply offers a convenient way to do it, for any model, just by providing the appropriate function. But it is of course possible to go far beyond simple blocks or latent space, and to propose a custom ranking function based on the case study.
Python library An important aspect of such a generator is to allow other researchers to use it for their own needs, whether it be to generate networks according to a structure described in the structure zoo, or to define their own. We thus release with this paper a pip installable python library  (Cazabet, 2023) , together with its documentation (https://structify-net. readthedocs. io/ en/latest/). For convenience, the library is compatible with Networkx  (Hagberg et al. , 2008). Obtaining a rank model corresponding to one of those defined in the zoo, such as the nested structure, is as simple as calling it: 1 import s t r u c t i f y _ n e t. zoo as zoo 2 n=128 3 rank_model = zoo. s o r t _ n e s t e d n e s s ( n ) Generating a network as a Networkx object from it is straightforward: 1 import s t r u c t i f y _ n e t.
Software Several easy-to-use libraries propose to generate networks with blocks, following the Stochastic Block Model approach. Among the most popular, we can cite networkx  (Hagberg et al. , 2008)  and iGraph  (Csardi, Nepusz, et al. , 2006) , which include an SBM generation function allowing to define blocks of arbitrary sizes, arbitrary probabilities of observing edges between them, and then generate a graph accordingly. More advanced functions are proposed in the graph-tool (Tiago P. Peixoto, 2014) library, allowing to generate microcanonical, degree-preserving versions, and several other variants of block structures. The same libraries offer, under the name of geometric models, some possibilities for spatially constrained network structures. Most of these methods, however, do not allow setting the number of edges, since they instead require setting a threshold below which edges exist, or using an a priori function  (Waxman random graph).
Only the k-nearest neighbors method allows one to choose the number of edges among multiples of the number of nodes, but it is a deterministic generator. These libraries also contain other types of network generators with non-random structures, such as lattices, or networks defined by a process such as the forest-fire model. Another notable network generator is the LFR benchmark, which is implemented in networkx in a simplified version, or available as a standalone code to have access to all its settings. Software to work with graphons is much more scarce; we found an R library implementing graphon inference and graphon random graph generation (https://cran. r-project. org/web/ packages/graphon/index. html); a recent python code exists also, although not in the form of a documented library (https://github.
com/BenjaminSischka/GraphonPy). These libraries Remy  Cazabet et al. however have nothing to see, in terms of usage of capabilities, with Structify-Net. They are designed for completely different purposes. The reference library for working with ERGM is the R package ergm  (Hunter et al. , 2008) , focusing on model inference. (https://gvegayon. github. io/appliedsnar/the-ergm-package. html).
Fundings This work is supported by the  European Union   -Horizon 2020 Program  under the scheme " INFRAIA-01-2018-2019 - Integrating Activities for Advanced Communities ", Grant Agreement n. 871042 , " SoBigData++: European Integrated Infrastructure for Social Mining and Big Data Analytics " (http://www. sobigdata. eu). This project was partly founded by  BITUNAM  grant  ANR-18-CE23-0004.
Proteomics research encompasses a wide array of experimental designs, resulting in diverse datasets varying in structure and properties. This diversity has led to a considerable variety of software solutions for data analysis, each of them using multiple tools with different algorithms for operations like peptide-spectrum matching, protein inference, quantification, statistical analysis, and visualization. Computational workflows combine these algorithms to facilitate end-to-end analysis, spanning from raw data to detecting differentially regulated proteins. We introduce WOMBAT-P, a versatile platform designed for the automatic benchmarking and comparison of bottom-up label-free proteomics workflows. By standardizing software parameterization and workflow outputs, WOMBAT-P empowers an objective comparison of four commonly utilized data analysis workflows.
Furthermore, WOMBAT-P streamlines the processing of public data based on the provided metadata, with an optional specification of 30 parameters. Wombat-P can use Sample and Data Relationship Format for Proteomics (SDRF-Proteomics) as the file input to simply process annotated local or ProteomeXchange deposited datasets. This feature offers a shortcut for data analysis and facilitates comparisons among diverse outputs. Through an examination of experimental ground truth data and a realistic biological dataset, we unveil significant disparities and a low overlap between identified and quantified proteins. WOMBAT-P not only enables rapid execution and seamless comparison of four workflows (on the same dataset) using a wide range of benchmarking metrics but also provides insights into the capabilities of different software solutions.
Introduction Computational workflows play a crucial role in data-intensive sciences such as mass spectrometry(MS)-based proteomics by providing a way to automate and streamline complex analysis processes, and to make them easier to repeat and share with other researchers  1. The search for an optimal data analysis solution is mostly data-dependent and cumbersome in many ways. In an optimal scenario, one would require extensive tests using ensembles of differently designed and/or parametrized workflows, all of them providing results in a comparable and standardized manner. We are aware that multiple search engines provide different results for the same dataset, and how to integrate these results is an open question. In fact, on one hand, the combination of different workflows results in a boosted false identification rate of peptides and proteins, on the other hand their intersection decreases the identification power.
Standardization of this information has been initiated recently via the SDRF-Proteomics format linking data files to samples and attributes from the data acquisition  11, 12. However, this format still lacks both in details about the data analysis protocol and availability in ProteomeXchange public repositories such as the PRIDE database  13. Moreover, very few workflows are able to directly process this standardized information. Workflow outputs like reports on PSMs (peptide spectrum matches), peptides, proteins and differential expression/regulation can come in a myriad of different formats and depend on different levels of interpretation, making a direct and objective comparison a major challenge. Efforts to compare the output of different data analysis pipelines have been carried out quite extensively (e.
g. 14, 15, 16  ), but they are restricted to very few datasets. Nonetheless, these studies indicated large differences between performance of various workflows, which shows the importance to benchmark different workflows and different workflow modules. Furthermore, few platforms provide benchmarking results over both different workflows and different datasets without cumbersome adaptations to work with a particular dataset. While some efforts have been made to create central repositories for workflows, like Workflow Hub 17 and nf-core  18  , there are still relatively few workflows listed for proteomics there. This might be due to the relatively small size of the proteomics community, as well as due to the heterogeneity and multitude of vendor specific tools and workflows often used to characterize proteomic profiles.
To address these challenges, the WOMBAT-P platform has been developed to provide a comprehensive solution for defining, executing, and comparing ensembles of workflows. The platform captures both generic and user-defined specific benchmarks of performance, efficiency, and maintainability. These benchmarks are essential for evaluating workflow performance, its components, and hardware execution. They often use reference standard datasets and evaluate performance of quantitative pre-processing and statistical analysis such as a list of differential expressed proteins, against which performance of other workflows can be measured. This ensures operation at an acceptable level and allows exploring the applicability of new software tools and their parameters over different datasets. We demonstrate the WOMBAT-P platform with an ensemble of semantically equivalent and complete label-free quantification analysis workflows for the analysis of bottom-up proteomics data.
An overview of all processes is available in Suppl. Fig. 1. We used the release version 0. 9. 2. The first workflow (Compomics workflow) combines Compomics tools FlashLFQ  20  and MSqRob  21. The second workflow (MaxQuant workflow) is based on MaxQuant  22  and NormalyzerDE  23. In the third workflow (Proline workflow), we used SearchGUI 24 , Proline  25  , and PolySTest  26. Finally, we also included a workflow using tools from the TPP  27  , specifically PeptideProphet  29  , ProteinProphet and StPeter 30 with Comet 31 for database search and ROTS  28  for statistical analysis (TPP workflow). Multiple modules were written in Python and R scripts to facilitate conversion and parametrization within the workflows. Therein, we used MSnbase  32  for normalization in the Compomics workflow and conversion scripts from https://github.
Input options WOMBAT-P allows a variety of input files, either based on SDRF-Proteomics annotation or via parameters given by a YAML file with the specifications of https://github. com/bigbio/proteomics-sample-metadata/blob/master/sdrf-proteomics/Data-an alysis-metadata. adoc and the experimental design as tab-delimited file (see Fig. 1  for an overview of input options). Workflow inputs are harmonized using a general set of parameters. Initialization and parameterization of the workflows are based on tools from the SDRF-pipelines  11  and the ThermoRawFileParser 34 for file conversion. We extended the definition of the SDRF-Proteomics data format to include a generalized set of 30 data analysis parameters (see Supplementary Table  1  and the specification of the YAML file), thus enabling the reproducibility of the data analysis via annotations with controlled vocabularies.
Output options and benchmarks Intermediate and final files are stored in the results folder or a folder specified via the outdir parameter. In addition to the workflow-specific output, a standardized tabular format is provided at the peptide and protein level (stand_pep_quant_merged. csv and stand_prot_quant_merged. csv, respectively). For each of the workflows, WOMBAT-P calculates the same set of 32 benchmarking metrics for comparison between workflows and between different values of the data analysis parameters (see Supplementary Table  2 ). Scripts for post processing are available https://github. com/wombat-p/Utilities. We used the heatmap. 2 function from the gplots R package for the hierarchical clustering. For the Reactome pathway enrichment analysis of the differentially regulated proteins from each workflow  35  , we used the clusterProfiler R package  36.
Benchmarking Datasets Raw data files were downloaded automatically from PRIDE by WOMBAT-P when using SDRF-Proteomics files, as the links to the files in the online repository are provided in these annotations. Fasta files for the database search were retrieved from UniProt (UniProtKB/SwissProt version Feb 3, 2023) and Sigma-Aldrich (https://www. sigmaaldrich. com/deepweb/assets/sigmaaldrich/marketing/global/fasta-files/ups 1-ups2-sequences. fasta). The ground truth dataset (PRIDE accession number PXD009815)  25  contains a yeast background and 48 human proteins (Universal Proteomics Data Set, UPS) spiked at 10 different concentrations of UPS proteins (10 amol, 50 amol, 100 amol, 250 amol, 500 amol, 1 fmol, 5 fmol, 10 fmol, 25 fmol and 50 fmol). For experimental data from a standard LC-MS experiment, we used data from a study comparing COVID-19 negative and positive samples (PRIDE accession number PXD020394, from now on called COVID-19 dataset)  37.
Workflow registration WOMBAT-P data provenance that can be downloaded from the WorkflowHub as an RO-Crate (Research Object Crate  38  ), see https://workflowhub. eu/workflows/444. The WOMBAT-P metadata RO-Crate contains information about the workflow as well as its context. We used it to organize and share our workflow with other researchers in a standardized, interoperable, and reusable approach. The data provenance of WOMBAT-P was generated with WfExS-backend (https://github. com/inab/WfExS-backend), which is a high-level orchestrator to run scientific workflows reproducibly. It automates creating an RO-Crate by analyzing the structure and content of the computational workflow files. Creating an RO-Crate of the WOMBAT-P workflow starts with the WOMBAT-P GitHub repository link. WfExS-backend analyzes the workflow repository, finds the workflow files and extracts the metadata, including file names, formats, file sizes, script dependencies and execution environments needed to run the workflow.
Ground truth dataset Comparison of different data analysis software and pipelines was performed on data from a ground-truth spike-in experiment  25. Regarding the overall number of identified peptides and proteins, we observed that TPP reported a much lower peptide count than MaxQuant and Compomics (Fig. 2A ). We suspect that this is due to the prior filtering of peptides for protein FDRs (False Discovery Rate) in the TPP workflow. This also shows that the comparison at the same stage in the analysis is often hampered by even slightly different data treatment in the workflows. Despite the differences in peptide quantifications, all workflows showed similar numbers of proteins (Fig. 2A ). Proline and FlashLFQ from the Compomics workflow reported higher coverage of peptides and proteins across samples compared to TPP, which lacked a match-between-runs option (Fig 2B ).
In terms of quantified peptides, we observed that their similarity with respect to their relative abundances was generally higher within each workflow (Suppl. Fig. 3 ), likely due to variations in the methods used to quantify peptide and protein intensities. This trend was particularly noticeable in the TPP workflow, where quantification was based on StPeter, an algorithm that incorporates spectral counting. Furthermore, the workflows successfully grouped samples with the same UPS protein concentrations in most instances. The samples of the experiment consist of 48 human proteins spiked at levels of in yeast proteome. Thus, only all proteins annotated as this species (human in this dataset) are expected to vary between samples, while proteins of the other species (yeast in this dataset) are expected to be always detected at a constant level.