dataesr/scientific-paragraphs-categorization huggingface dataset:
+ y Treatment Time Block Time Error Block effects are assumed to be random and autoregressive in time; thus, the corresponding covariance structure is defined by two parameters (variance and autoregression coefficient). The error is assumed to be time-dependent and is described through a diagonal covariance structure depending on four parameters (the error variances for consecutive time points). The model parameters, i. e. , 12 fixed effects for treatments in time (interpreted as marginal means) and six variance parameters, are estimated and tested as in Example 1, and they constitute a summary of the dataset analysis. Example 3. Let us consider a more complicated example of a one-dimensional LMM based on an experiment that involves plant phenotyping (see http://cropnet. pl/plantphenodb/index.
php?id=250). In this study, a number of plant genotypes were grown over two years in plots arranged in blocks. Among many traits, the heading date and grain yield were observed. The corresponding model to explain the grain yield can be summarised in informal notation as:  where a general mean m and a simple covariance structure of the Error are assumed. The effects of the genotype, year, their interaction, and the covariate heading date are assumed fixed, while block effects are random, independent, and with a simple covariance structure; likewise, the error. Estimates of all the fixed effects and variance parameters, tests for the fixed effects, and the marginal means for all factor level combinations are needed draw scientific conclusions from the experiment. A summary including the statistics and their provenance can be used for dataset documentation and search purposes.
Exemplary queries. Below, we demonstrate the benefits of the structured LMM results for the exploration of datasets from scientific studies. The collection of semantic models, aggregating the results of statistical analyses of the experimental datasets, accommodates data summaries and documents the applied analytic approaches in a FAIR way. Ontological annotations of their individual elements enable the use of semantic reasoning in data processing. Asking adequate queries allows us to discover the studies that report specific statistical conclusions and to analyse the investigative methodology. The use cases discussed below concern semantic models of statistical analyses of the results of agricultural scientific experiments, such as the Example 3 described above. In a general scenario for these experiments, a number of plants (representing different species and varieties) are cultivated under different environmental conditions (e.
g. , soil or weather attributes) and treated with different experimental factors (e. g. , drought or chemicals), and a number of phenotypic traits are observed (e. g. , plant height or yield). The corresponding datasets frequently undergo statistical analysis by the LMM (e. g. 35 ) to explain the traits by means of other characteristics. The use cases, formally specified as queries in the SPARQL language, are provided in Additional Examples 34 and can be run in a triple store at http://lmm. cropnet. pl/sparql.
Q1: Find statistical models for a particular dataset The same dataset can be analysed differently. Depending on the research type, an analyst can decide to use only one specific model or to try multiple modelling assumptions; one or more LMMs can be documented and stored. The query allows one to retrieve all statistical models used to analyse a particular dataset. The obtainment of the specification of each LMM (e. g. , by formulas, terms, covariance structures, associated estimation and testing methods) enables researchers to study and repeat the same analysis (e. g. , to validate the results for the original data, reanalyse an updated dataset or apply the same model to another observed variable). In the case of multiple LMMs per dataset, verification of the model fit criteria can be performed in subsequent steps of the analysis for statistical model selection (e.
Q2: List the dependent and/or independent variables The coexistence of variables in experimental datasets can be indicative of the research directions undertaken in the collected studies. This knowledge of the available results is useful to identify reference studies or to conduct research accordingly, e. g. , to replicate, enrich or bypass the existing approaches. A set of useful queries about the analysed variables allows one to carry out the following: • check what variables were analysed together and in which studies (e. g. , "Is there any experiment where both chemical X and chemical Y were used?", "Were rainfall and plant height co-analysed somewhere?") lmm. cropnet. pl/sparql?savedQueryName=variables. • identify the studies that attempted to explain particular observed variables and to check what variables were considered explanatory for them, successfully or not (e.
Discussion In this work, we focused on providing explicit semantics for the elements of LMM analysis. The described methodology can be used in applications of the LMM to any dataset. The domain of scientific experimentation is a specifically justified use case to start with, as LMMs are frequently used in scientific studies where designed experiments are performed. However, specific cases of LMM analyses also include fixed effect models, linear regression models (e. g. , linear regression fitted by least squares, or linear regression using shrinkage, such as LASSO regression for variable selection or ridge regression for multicollinearity) and random effect models. Thus, there is a vast area of applications of LMM analysis, and hence, our approach to documenting it can also be broadly applicable.
In chemometrics and materials science, a multiple linear regression model is sought that describes the (quantitative) structure-activity relationship (QSAR) and provides good prediction of a compound's activity on the basis of its physical or chemical properties  38. In these applications, as well as frequently in the domain of observational studies, the number of available and potentially independent variables exceeds the number of observations, which prohibits the application of the classical estimation method. The attention is shifted from the individual model parameters and their statistical significance, which are not of primary interest, to the predictive value of the whole model and its application to subsequent datasets. For now, we do not apply the proposed approach in this context, but we claim that this extension is possible and can be pursued by interested teams in the appropriate domains of applications linear model fitting.
The application of public ontologies rooted in the general knowledge schema allows the annotated statistical concepts to be placed in a general context. Hence, LMMs and other statistical approaches to data analysis, when documented with an STATO-based semantic model, can be semantically related to each other and processed analogically in the sense of semantic reasoning and technological aspects (RDF and SPARQL). Thus, for the sake of different statistical analyses and data integration, further specific modules extending the STATO can be developed. In the description of the proposed annotation system, we did not elaborate on the methodological aspects of fitting linear mixed models related to methods of parameter estimation and hypothesis testing. This is a vast area of consideration in mathematical statistics, and we were able to mention only the most frequently used methods for estimation and basic statistical tests.
The issue of the statistical methodology is also relevant when considering the various software programs used to fit linear mixed models. Statistical packages such as R (lme4  39  in Example 1; nlme 40 in Example 3) or Genstat  41  (Example 2) usually address the non-estimability of fixed effects in a similar way by providing estimates of a set of selected (linearly independent) parametric functions. In each case, it is important for the user to understand the exact meaning of the estimated effects, which depends on the design of the experiment. Both systems, R and Genstat, can provide the marginal means that are interpreted as absolute effects, which, to some extent, solves the problem of the interpretation of the partial results of the basic estimation. However, a comparison of the whole methodology used in LMM fitting with these and other packages is beyond the scope of this paper.
In our derivation, we restrict attention to an LMM with binary design matrices. With this assumption, the model parameters yield a standard interpretation of the effects and pairwise contrasts the interpretation of the relative effects. With other forms of the design matrices, the interpretation can become more complicated. Additionally, other types of linear parametric functions, with coefficients different than just -1, 0 and 1, can be useful. The semantic annotation of these models and functions is, of course, possible but requires more concepts, that is, extension of the model presented here. The same concerns a larger class of possibly nonlinear functions that can be defined only by proper formulae. Domain-specific semantics of the datasets, which allow one to understand the underlying research questions, are beyond the scope of this paper; nonetheless, they are crucial for real-life use cases where the LMM is frequently applied.
We assume that all inputs to the modelling, i. e. , the dependent and independent variables, come from a properly annotated dataset constructed according to domain-specific standards (such as the Minimum Information recommendations, e. g. , MIAPPE  42, 43  ), and this annotation provides domain-specific semantics. This information is necessary to properly construct the statistical model and interpret the obtained estimates in terms of the variable names, units, etc. , and to exploit the ontological knowledge for experimental metadata-based semantic search (e. g. 44 ) to further improve the data discoverability.
The proposed semantic model is primarily supposed to explain the core assumption of the statistical modelling process and to provide a context for the statistical conclusions obtained from the analysis. Comprehensive dataset summaries contribute to a better understanding of the structure of the research data, while semantic annotation is essential for the interpretation of shared datasets. We hope that this work can contribute to the promotion of semantic approaches to research data description, especially the richer description of processed data to enhance their interoperability. Although the present study describes a methodology related to formalising the description of linear mixed models for summarising experimental datasets, with the goal of efficient automated processing, the general approach of using a formal representation of the data analysis for scientific data discovery is also applicable to other data processing methods, in particular those that produce uniform, interpretable results.
acknowledgements Grants from  Narodowe Centrum Nauki  ( National Science Centre ), project no. 2016/21/N/ST6/02358 ; the  UK BBSRC and Research Councils  ( BB/L024101/1 ,  BB/L005069/1 ); the  European Union  ( H2020-EU. 3. 1, 634107 ,  H2020-EU. 1. 4. 1. 3 , 654241 ,  H2020-EU. 1. 4. 1. 1 , 676559 ,  H2020 731013 (EPPN 2020  ); the  IMI  ( 116060 ) and the  NIH  ( U54 AI117925 ,  1U24AI117966-01 ,  1OT3OD025459-01 ,  1OT3OD025467-01 ,  1OT3OD025462-01 ) are acknowledged.
Data availability The data generated during the current study are available in the GitHub repository https://github. com/hcwi/ SemanticLMM and Zenodo  33. The datasets that served as use cases (i. e. , raw experimental data from plant phenotyping experiments) were derived from the following public domain resources: PlantPhenoDB (http:// cropnet. pl/plantphenodb) and URGI Plant and Fungi Dataverse (https://data. inra. fr), in particular the DROPS project data  35.
Co-inertia analysis and supervised analysis which integrated multiple datasets indicated a strong congruency between chemical and genetic patterns. Two distinct genetic units were located at the edge of the distribution area in the south of Italy and in the northeast of Spain, and were associated with two distinct chemotypes. Our results confirmed the existence of three genetically distinct entities, suggesting speciation. All French populations and the Italian Piedmontese population were genetically homogeneous but separated in two distinct chemotypes. The dominant chemotype was present in the center of the native range in southeastern France and was at the origin of the current most cultivated French varieties. Its main compounds were linalyl acetate, linalool, and caryophyllene oxide. The second French chemotype was found in south of Massif Central and presented high abundance of valuable linalyl and lavandulyl acetates.
We inferred independently the structure of the chemical and genetic diversity using an unsupervised discriminant approach based on principal components, called DAPC (discriminant analysis on principal component  [20] ). This method was chosen because it integrates the two steps of analysis: identify the optimal number of groups (unsupervised analysis) and pinpoint discriminant variables between these identified groups (supervised analysis). The congruency between the patterns of variation of chemical and genetic data was analyzed with a multidimensional co-inertia analysis and a novel supervised analysis which integrated multiple datasets. Finally, major and discriminant compounds were correlated with latitude and altitude of the sampled populations.
The optimal number of genetically distinct groups is unambiguously evaluated to 3. Indeed, the cross validation process finds a success of assignment of 100%, whatever the number of PCs selected. One group corresponds to the isolated Calabrese plants (Ica), another contains the Pyrenean plants (all individuals of Sar1 and Sar2) and the last group clusters all French individuals and the Italian Piedmontese plants (Figure  1 ). The procrustean co-inertia analysis (PCIA) measures the congruency between the structure of wild individuals from chemical and genetic data. The m 2 is high (0. 60) and significant (p = 0. 001, 999 permutations), indicating a good concordance between the two datasets. The DIABLO analysis is a complementary approach to co-inertia analysis (DIABLO: Data Integration Analysis for Biomarker discovery using Latent variable approaches for Omics studies,  [21] ).
It combines the two datasets to better understand the interplay between all variables. The Figure  2  materializes the three genetic populations on the right and confirms graphically the congruence of the structures of the individuals at the chemical and genetic level. Interestingly, the two French chemotypes belong to the same genetic population. The two individuals of Sar2 presenting the chemical composition of the cluster 3 (two triangles among the squares in Figure  2b ) are genetically similar to other Spanish plants. The genetic groups are more homogeneous than the chemical clusters. The analysis of molecular variance AMOVA indicates that most of the molecular variance is among genetic clusters (53%), 15% is among sampled sites within genetic clusters, and 32% within sampled sites (Table  3 ).
Discussion This study is the first to analyze the structure of the chemical and genetic diversity of natural populations of true lavender, over its native range. The composition in secondary metabolites of the inflorescences was determined for 65 samples originating from 14 natural sampled sites of the true lavender. The same plants were genotyped with 206 repeatable AFLP markers. Twenty-five samples from 4 cultivars within 5 cultivated fields were included in the study to establish the link between wild populations and cultivated varieties. Genetic and chemical data were used to infer population structure by determining homogeneous groups without prior knowledge. The discriminant analysis of principal components (DAPC,  [22] ) was successfully performed on both genetic and chemical data to infer the optimal number of clusters among the individuals without labeling the data (no information about geographical localization and population membership).
Finally, DAPC identified unambiguously three distinct genetic units and four distinct chemotypes among the natural populations of true lavender (Figure  1 ). Methodological advances in statistical approaches facilitate multi-dataset analysis. When data of different natures are collected on the same sample, two different approaches are available and complementary: co-analysis and combined integrative analysis. Co-analysis uses classically procrustean co-inertia analysis and aims at prospecting for the common structure of the data. Each dataset is ordinated separately and co-inertia superimpose the two ordinations in a second time to identify common pattern. On the other way, integrative analysis combines the different datasets in one file before the analysis. It aims at identifying variables that are highly correlated between the datasets and discriminative between a priori known groups of samples (see  [23]  for details about use of these methods, scripts, and interpretation of the results).
AFLP fragments shorter than 50 bp and monomorphic fragments were discarded. The profiles were normalized and each marker was scored in presence or absence based on the R script described in Herrmann et al. [40]. We used a very restrictive coding method based on 13 duplicated samples to achieve a repeatability of 100%. Eighty-two individual plants were successfully genotyped with 206 highly repeatable polymorphic markers. Results were reported in a binary matrix of presence/absence of each marker for each individual.
The oven temperature would finally remain at 240 • C for 5 min. Finally, we could obtain reliable profiles for 90 samples (65 from wild sites and 25 from cultivated fields; see Table  2 ). The preprocessing of GC-MS analyses was performed with the R package MSeasy  [41]  that detects putative compounds in a complex metabolic mixture. In brief, all mass spectra of all 90 samples were computed in one matrix. Unsupervised hierarchical clustering was then performed to group similar spectra into one cluster. We visually checked the correspondence of each cluster to a putative molecule and merged or split the cluster when needed. Similarly to AFLP markers, we checked for repeatability of chemical profiles by analyzing five samples thrice. We selected compounds that allow 100% repeatability for the number of peaks and 99.
Statistical Analyses The data analysis pipeline consisted of four main steps: identifying homogeneous groups of samples using chemical and genetic data separately, pinpointing the compounds that discriminate the chemically homogeneous groups, analyzing the structure of genetic variability, and finally evaluating the concordance between the genetic and chemical structure of the individuals. The first two steps were implemented by using the integrative approach of discriminant analysis of principal components (DAPC,  [21] ) implemented in the package adegenet  [43]. DAPC implemented both unsupervised and supervised classification, and proposed several tools to optimize and evaluate the classification. In the first step, DAPC performed a principal component analysis (PCA). PCA provided new synthetic axes that optimized the representation of the square of the Euclidean distances between individual profiles.
Based on the binary matrix of fingerprinting genotypes, analysis of molecular variance (AMOVA) was performed using GenAlex 6. 5  [45]  to estimate the hierarchical structure of the genetic diversity among genetic clusters identified by DAPC, among sampled sites and within sampled sites. The genetic differentiation between the genetic groups identified with DAPC was determined using PHI PT , an analogue of F st adapted to binary data. Significance of pairwise estimates of PHI PT was obtained by using 9999 permutations and confidence interval at 95%, by 10,000 re-samplings. The fourth step is to evaluate the concordance between the structure of the individuals based on genetic and chemical dataset. A procrustean co-inertia analysis (PCIA) was performed. Contrary to the bidimensional Mantel test, PCIA provides the capacity to deal with higher dimensional spaces.
Indeed, PCIA fitted a set of points to another based on the ordination of distance matrices. Euclidean distance was calculated for chemical data and the Jaccard index on AFLP band sharing was used on the genetic dataset. These distance matrices were thus ordinated by principal coordinate analysis (PCoA) and the concordance of the two PCoAs was evaluated by a statistic called m 2 which varies between 0 (no concordance) and 1 (perfect concordance). The significance of this statistic was tested using the function protest (package vegan  [46] ). We applied the DIABLO framework of the R package mixOmics  [47]  because it integrated simultaneously the two data sets in a supervised analysis and provided a visual representation of the congruency of the two datasets (DIABLO stands for Data Integration Analysis for Biomarker discovery using Latent variable approaches for Omics studies).
Acknowledgments: We are grateful to  Romain Laneyrie ,  Nicolas Boyer ,  Philippe Moja ,  Cyrille Conord ,  Méluzine Godin ,  Sarah Martineau  for their help in plant sampling, technical and stewardship assistance. We also thank  Cédric Yvin  (ITEIPMAI) and  Eric Chaisse (CRIEPPAM)  for their technical contributions and expertise in lavender. We thank  Thibaut Jombart  and  Stéphane Dray  for their help in transposing their method/package to our data. We thank  Mark H Van Niekerk  and  Frédéric Hache  for their help in English correction of the manuscript. Finally, we thank one reviewer and the editors for their help in improving the manuscript.
Funding: This research was funded by the Special Accounts Allocated to Agricultural and Rural Development run by the  French Ministry for Agriculture (Compte d'Affectation Spécial pour le Développement Agricole et Rural CasDAR -project  7040   « Amélioration des stratégies de lutte contre le dépérissement de la lavande et du lavandin »)  and a collaborative program-cluster 9 of the Rhône-Alpes region.
Patient Samples All samples from patients with MM were collected from the IFM/DFCI 2009  19  clinical trial (ClinicalTrials. gov identifier: NCT01191060) after written informed consent, and clinical and genomic data were de-identified in accordance with the Declaration of Helsinki. Myeloma cells were purified from bone marrow by CD1381 cell selection, and control DNA originated from peripheral blood mononuclear cells. Multiple cytogenetic loci were also evaluated with fluorescence in situ hybridization including for t(4;14), t (14;  16), and del17p; International Staging System (ISS), progression-free survival (PFS) and overall survival (OS) data were collected for all patients. The MM Research Foundation (MMRF) CoMMpass (ClinicalTrials. gov identifier: NCT01454297) data set was used to validate findings (Appendix, online only).
Recursive Partitioning We used recursive partitioning analysis to identify patient groups at different risk levels. First, we used multivariate Cox model in R using "survival" package for variable selection. GSS, IgH translocations, deletion 13, 1p, 17p, gain1q, and gains in hyperdiploid chromosomes as well as mutations in 10 driver mutations detected by "dndscv" were used for variable selection. Variables reached to significance level of 0. 1 were then used for recursive partitioning with "rpart" package in R. We evaluated the stability of the tree construction using "ipred" package. Brier score using out-of-bag estimator with 1,000 bootstrapping.