dataesr/scientific-paragraphs-categorization huggingface dataset:
This limits the detection power of the FDR approach. An alternative strategy to treat multiple responses is to apply multivariate testing procedures, such as Multivariate ANOVA (MANOVA)  (Warne, 2014). These methods replace multiple univariate tests by a single multivariate one to assess the statistical significance of the ANOVA model, including all the variables in the dataset. This avoids the need for multiple-testing corrections, but suffer from the effects of statistical noise, particularly when the number of variables is large, leading to a remarkable lack of discriminatory power. The multivariate test statistic often contains noisy contributions from a large number of (insignificant) variables, and factors affecting only a few of them can potentially be overlooked due to the overall statistical noise.
The enhanced statistical power brought by variable selection leads to improved ASCA modeling; for a given effect (factor/interaction), VASCA identifies significant associations with reduced subsets of variables, filtering out those not accounting for the effect itself, and narrowing down the subsequent ASCA analysis to a limited amount of meaningful responses. VASCA is here assessed with simulations and with a real dataset from a multi-omic clinical experiment, and compared to ASCA and the BH (FDR) method in terms of statistical power, and to partial least squares discriminant analysis (PLS-DA) and its sparse counterpart (sPLS-DA) in terms of exploratory power. We also include a comparison with an early approach for variable selection in ASCA, the ASCA-genes method by  Nueda et al. (2007).
ANOVA Simultaneous Component Analysis The most established ASCA pipeline, consistent with that of ANOVA, is based on several steps: (i) factorization of the data according to the factors/interactions of the experimental design under study; (ii) significance testing (based on permutation tests) for factors/interactions; (iii) visualization of significant factors'/interactions' effects using Principal Component Analysis (PCA) to understand separability among levels and, optionally, post hoc testing of levels using confidence intervals. The interested reader can find an example of all these data analysis steps in the Supplementary Material. The code for reproducing this example is included in the aforementioned online repository. A detailed description of the ASCA modeling framework is provided next.
Factorization of the data Let X be an N Â M data matrix with N the number of conducted trials and M the number of responses or variables recorded in a series of designed experiments. For the sake of simplicity and without loss of generality, we will consider the case of a design encompassing two fixed factors. The data in X can be decomposed as X ¼ 1m T þ A þ B þ AB þ E; (1) where 1 is a vector of ones of suitable length (N Â 1), m (M Â 1) denotes a vector containing the mean values of all the M measured variables, while A and B represent the factor matrices, AB the interaction matrix and E the residual matrix, all of size N Â M. The idea behind this decomposition is to partition the variation in the dataset X, according to the different factors/interactions of the design. In this article, we use the technique referred to as ASCAþ  (Thiel et al.
We will illustrate this difference with simulated examples. ) In this regard, variable selection in VASCA resembles the step-up BH procedure  (Benjamini and Hochberg, 1995)  and generalizes ASCA, since it includes the significance assessment for the entire dataset with M variables. For this reason, VASCA is at least as powerful as ASCA. Moreover, both ASCA and VASCA generalize ANOVA, since (V)ASCA applied to an individual response variable boils down to an ANOVA based on permutation testing, thus, robust to deviations from the normal distribution  (Anderson and Braak, 2003). Let us define: U m ¼ argmax fv1;. ;vmg2f1;. ;Mg X v¼v1;. ;vm S v (8) as the sub-set of m variables U m ¼ fv 1 ;. ; v m g that maximizes the sum statistic P v2Um S v. We refer to S Um as the corresponding multivariate statistic for this sub-set, i.
Evaluation in simulation examples We devised four simulated experiments in order to compare VASCA with ASCA and ASCA-genes, and the BH procedure to control the FDR, simply referred to as FDR from now on. For simplicity and for the sake of clarity, in the first three examples we simulate a single factor with two levels, where each level includes 20 subjects (thus, a total of 40) for which 400 variables are collected. This choice is motivated by the nature of typical omics experiments (Tenorio-Jimenez et al. , 2019). In the first and the last examples, we consider a two factor/multi-level problem, in which ASCA-genes can be applied thanks to the increased number of degrees of freedom. To simulate the background in the multivariate data X, we use the SimuleMV tool  (Camacho, 2017)  available together with ASCA and VASCA in the MEDA Toolbox at https://github.
com/josecama chop/MEDA-Toolbox. SimuleMV allows to simulate a dataset with a certain level of correlation. The inputs to SimuleMV are the size of the data matrix (number of rows and columns) and a level of correlation between 0 (absence) and 10 (maximum correlation). In our simulations, we chose Levels 7 and 8. Each simulated experiment is repeated 1000 times and average and standard deviation results are presented for the P-values, along with Type I and Type II error rates. For comparison purposes, FDR was implemented from the (empirical) probability distribution obtained through permutation testing, and corrected P-values were computed through the BH procedure. In all cases, the permutations used the same seed for the random generation engine in the four methods, ASCA, FDR, ASCAgenes and VASCA.
QQ-plots for ASCA and VASCA (Supplementary Fig. S6 ) show that the P-values are uniformly distributed under the null-hypothesis, as expected, while the empirical false positive rate (FPR) (Table  1 ) is very close to the significance level of 0. 01 for both ASCA and VASCA and is almost identical regardless of the chosen test statistic. The FDR, however, attains an FPR much lower than the significance level, as a result of the BH correction procedure-which aims to control the FDR at the significance level, and results in too conservative corrections in terms of the FPR in this case. Similar results are obtained for X drawn at random from a multinormal distribution, rather than using the SimuleMV tool (These results can be found in the software repository. ). A major strength of ANOVA, also inherited by ASCA, VASCA or the FDR, is the possibility to analyze complex experimental designs with several factors and interactions.
In a second experiment we simulate datasets with two factors, of four and three levels, respectively, according to a balanced full-factorial design with four replicates. This design provides a total number of 4 Â 3 Â 4 ¼ 48 experiments (rows). X is simulated as in the previous example, independently from the factors, so that no significant association is expected. With this example, we can compare VASCA to ASCAgenes in terms of Type-I error. The simulation follows (We implicitly assume that C is built from F using deviation coding. ): X SimuleMVð40; 400; 7Þ F FullFactorialð4; 3; 4Þ The empirical FPR is presented in Table  2. We see that ASCAgenes is slightly over optimistic in comparison to VASCA. From this simulation, we can conclude that when the responses in X and the factors in C are independent, we obtain a uniform distribution of the P-values in ASCA and VASCA which conveniently adjusts the Type-I error to the significance level.
If we apply bootstrapping along with VASCA, we reduce the FPR to a reasonable (but still slightly overoptimistic) level. Finally, we wanted to check what would happen if we repeat the same simulation scheme of the example, but with a much smaller bias in the three variables, so that the variance that reflects the  Comparison of P-values computed with FDR, ASCA and VASCA (without and with bootstrapping). For each method, average P-values from 1000 simulations are shown together with a shaded area corresponding to one standard deviation. For the FDR, we represent the P-values in increasing order from left to right (from the most to the least significant variable), corrected following the procedure of BH. Whenever a corrected P-value exceeds 1, a value of 1 is used instead. For ASCA, a single P-value is shown, corresponding to the P-value for the dataset with 400 variables averaged over the 1000 simulations.
For VASCA, the P-value at each number of variables m represents the significance of the dataset including the most significant m variables. The inset represents a detail for the first (most significant) 10 variables. Control limits of statistical significance (a ¼ 0:05 and a ¼ 0:01) are also represented Table  1. Example 1: Type-I error measured as false positive rate (FPR) for FDR, ASCA and VASCA using the sum-of-squares (SSQ) and the F-ratio as test statistics for a significance level of 0. 01 Method FPR (SSQ) FPR (F-ratio) FDR 9. 3Â10 -5 9. 3Â10 -5 ASCA 0. 01 0. 01 VASCA 0. 0108 0. 0108 connection between them and the factor is 10 times smaller than in the previous case. For this purpose, we recompute significant responses as: X i r i þ 0:5 Á C; with r i $ N ð0; 1Þ; i ¼ 1; 2; 3 and repeat the simulation.
2. Multivariate relationship between three variables in X and C. Comparison of P-values computed with FDR, ASCA and VASCA (without and with bootstrapping). For each method, average P-values from 1000 simulations are shown together with a shaded area corresponding to one standard deviation. For the FDR, we represent the P-values in increasing order from left to right (from the most to the least significant variable), corrected following the procedure of BH. Whenever a corrected P-value exceeds 1, a value of 1 is used instead. For ASCA, a single P-value is shown, corresponding to the P-value for the dataset with 400 variables averaged over the 1000 simulations. For VASCA, the P-value at each number of variables m represents the significance of the dataset including the most significant m variables.
Results on real data The BIOASMA dataset (Gomez-Llorente et al. , 2020) comprises clinical, biochemical, anthropometrical parameters, inflammatory biomarkers, metagenomic and metabolomic data for 46 children (12 girls and 34 boys, aged 4-13 years) with an allergic asthma diagnosed based on the Spanish Guidelines for Asthma Management (GEMA criteria 4. 4)-  (Moral et al. , 2016). The children were also classified into normal-weight (n ¼ 13), overweight (n ¼ 8) and obese (n ¼ 25) according to the age and sex-specific thresholds proposed by  Cole et al. (2000). Biochemical data were obtained by routine methods. Inflammatory biomarkers were determined by ELISA and by XMAP Luminex technology. Metabolomic data were obtained by one-dimensional proton nuclear magnetic resonance (1D 1 H-NMR) spectra of blood plasma samples.
Short chain fatty acids were determined by Gas Chromatography-Mass Spectrometry. Metagenomic data were obtained by 16sRNA barcoding sequencing and the Amplicon sequence variants (ASVs) were normalized by the rarefaction method  (Gotelli and Colwell, 2001). Deriving potential biomarkers from this dataset represents a real challenge  (Gomez-Llorente et al. , 2020) , given the low sample size and the complexity of the experimental design: two potential conflicting factors (asthma severity and weight classification/status) with three levels each are taken into account and the individuals distribution is significantly unbalanced. community, and that, beyond its inference and variable selection capabilities, VASCA can be a competitive exploratory tool for, e. g. biomarker identification.
Multi-factor models In this section, we consider simultaneously the two factors of the BIOASMA dataset in a single analysis round. Supplementary Figure  S17  shows the comparison of the P-values returned by ASCA, FDR and VASCA for two levels in each factor: persistent asthma versus the rest (occasional and frequent asthma) and normo-weight versus the rest (overweight and obese). No statistically significant results were obtained accounting simultaneously for the three levels in any of the factors. For two factors and two levels (one class versus the rest), only VASCA found statistically significant results, and with the single multi-factor model we obtain the same findings of the previous factor-wise analyses. sPLS-DA also failed in finding statistically significant results. An advantage of VASCA over (s)PLS-DA is its flexibility to handle uncorrelated factors in a single model, simplifying the analysis of complex experimental designs.
Case study The case study is a building connected to a combined solar and heat pump system as shown in Fig. 2. The model was developed in the European MacSheep project  [46]. The project aimed to develop and evaluate compact combined renewable energy systems based on solar thermal and heat pump technology for space heating and hot water. The energy and economic performance of several systems were assessed and compared by means of a different model designed in Trnsys17. Most of the components involved in these models have been validated against experimental data from prototypes or commercial products as indicated in Ref. [47]. The reference system presented in Fig. 2  was chosen to evaluate the TypSS algorithm due to its detailed holistic nature and as it was somewhat time consuming to evaluate in repetitive dynamic simulations (20 min for a single simulation) during system characterization.
For the periodic dataset given above, the CV(RMSE) was found to be 15. 8% for backup energy, 6. 2% for energy stored in the tank and 2. 2% for internal room temperature, suggesting that the model is reliable. CVðRMSEÞ ¼ 1 x YEAR Â ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi P n period i¼1 À x TYPSS i À x YEAR i Á 2 n period v u u t ¼ 1 x YEAR Â RMSE (9) Where: n period is the number of periods. x TYPSSi is the value of criterion x obtained by the short sequence for period i x YEARi is the value of criterion x obtained by the reference annual sequence for period i x YEAR is the mean value of criterion x in the reference annual sequence. RMSE is Root-Mean Square Error.
A range of n sim (1000-3000) is used to assess the stability of power estimates. The performance measure is the predicted power. All analyses were carried out in R version 4. 0. 5, using the following packages: bpmodels  [11]  for branching process modelling, lme4 for generalized linear mixed modelling, and the map_dfr() function of the purrr package to repetitively apply functions for the simulation coding. [12]  In the following sections, we describe each step in detail, which together with the code provided, can be used to replicate the simulation (https://github. com/ruwanepi/CATI-powersim-shared. git).
Model fit was assessed using the ratio of sum of squares of Pearson residuals to the residual degrees of freedom (to estimate overdispersion), inspection of the width of confidence intervals, and plotting of response by random effect levels (to estimate the benefit of including the random effect, as compared to using a generalized linear model (GLM)). As the health of individuals in the same ring may be correlated, regression modeling approaches that account for the clustered nature of the data should be used for the study analysis. This includes GLMM, generalized estimating equations (GEE) and generalized additive models (GAM). GLMM uses random effects to account for contextual factors from the rings that alter the relationship between the exposure and the population effect, while GEEs infer the population-averaged effect across all rings.
The reflected light intensity data were recorded using four photodiodes PDA36 (Thorlabs Inc. , Newton, NJ, USA) installed inside a full-scale production VAR furnac (Retech, Ukiah, CA, USA) on top of the vacuum chamber. The photodiodes we equipped with interferential filters to remove contributions due to thermal radiation the molten pool and with pinholes designed to limit the photodiode vision field an prevent any overlapping of the vision fields of the photodiodes throughout the enti melt. The recorded photodiode signals were calibrated with the hypothesis that the av erage arc luminosity under each photodiode is identical during the melt plateau. Th position of the arc luminosity centroid at every instant was then derived from the cal brated signals using the following formula:.
𝑥    and     ( The reflected light intensity data were recorded using four photodiodes PDA36A (Thorlabs Inc. , Newton, NJ, USA) installed inside a full-scale production VAR furnace (Retech, Ukiah, CA, USA) on top of the vacuum chamber. The photodiodes were equipped with interferential filters to remove contributions due to thermal radiation of the molten pool and with pinholes designed to limit the photodiode vision field and prevent any overlapping of the vision fields of the photodiodes throughout the entire melt. The recorded photodiode signals were calibrated with the hypothesis that the average arc luminosity under each photodiode is identical during the melt plateau. The position of the arc lu-minosity centroid at every instant was then derived from the calibrated signals using the following formula: x g = ∑ (x i V i )/ ∑ V i and y g = ∑ (y i V i )/ ∑ V i (1) where (x i , y i ) is the position of photodiode i, which delivers the voltage V i.
Modelling of the Arc Patterns The modelling of the observed arc patterns is based on the idea that it is possible to represent complex patterns as a combination of elementary distributions with simple dynamics. Three individual elementary distributions were introduced (Figure  4 ): namely, an immobile and uniform distribution covering the entire ingot top surface (hereafter referred as "arc component U"), a distribution of disc shape with a linear translational motion (hereafter referred as "arc component T") and a distribution of disc shape with a rotational motion (hereafter referred as "arc component R"). and used eventually as boundary conditions in the ingot model. Because of the asymmetric nature of the patterns described by the arc, a 3D model of the ingot was necessary. The dedicated simulation software RAVEL (version 2, CNRS, Nancy, France) describing the ingot growth and solidification, recently developed at Institut Jean Lamour, was adopted in the present work.
the U component is assumed to be constant for reasons of simplicity and that of the arc component R is zero during the stirring plateau, due to the stability of the arc observed during this time interval. On the other hand, the radius of the U, T and R components were kept constant throughout the whole stirring sequence and set respectively to 0. 415 m (ingot radius), 0. 15 and 0. 10 m. In addition, the current density and the power carried by each arc component were considered to be uniform. All of this data allowed us to define the power and current density distributions produced by each arc component at the top of the ingot that may be used as boundary conditions in the RAVEL software. Figure  8  compares the trajectory of the arc centroid during half of a stirring period obtained experimentally (in blue) to that simulated from the present model (in green) using the input data detailed above.
All of this data allowed us to define the power and current density distributions produced by each arc component at the top of the ingot that may be used as boundary conditions in the RAVEL software. Figure  8  compares the trajectory of the arc centroid during half of a stirring period obtained experimentally (in blue) to that simulated from the present model (in green) using the input data detailed above. Overall, there is satisfactory agreement between both trajectories, which validates our modelling approach. The best agreement between the experimental and modeled trajectories in the first half of the stirring period (left figure) compared to that in the second half of the stirring period (right figure) may be explained by the fact that the parameters of arc components T and R were adjusted using the data from the first half of the stirring period.
3D Model of the VAR Ingot It is not the purpose of this paper to detail the simulation software RAVEL (Remelting using plasma Arc, Vacuum arc or ELectron beam). Such a description will be the subject of a future publication. Essentially, RAVEL is a 3D extension of the axisymmetric simulation code SOLAR, which has been developed at IJL during the last 25 years and extensively validated and used by several industrial partners  [12, [18] [19] [20] [21]. Implemented using OpenFOAM ®  [22] , the 3D solver code accounts for all the main physical phenomena addressed in 2D VAR simulation CFD codes, such as SOLAR. A non-exhaustive list of these phenomena is given below:.
Simulation Results and Discussion As an example, we present the results of a simulation of the growth and solidification of a Ti64 ingot in the case where the arc describes during the entire remelting the pattern B. The full melt of a 750 mm diameter Ti64 electrode into an 830 mm diameter crucible was simulated using the RAVEL software. During the entire melt, we considered that the arc moved over the ingot top surface following the idealized B pattern as computed in the previous section. Note that, for the purpose of the present simulation, the pattern was kept constant throughout the full melt. The thermophysical properties of the Ti64 alloy required for the melt simulation were taken from Valencia and Quested  [23] , except for the emissivity, which was taken from Boivineau et al. [24].
Conclusions This paper describes our efforts to investigate the influence of transient and asym metrical distributions of the energy and current density at the ingot top caused by an ensemble arc motion on the solidification conditions of a VAR ingot. The VAR melt of Ti64 alloy electrode was simulated using the 3D dedicated software RAVEL, insid which a simplified representation of the pattern followed by the arc centroid at the ingo top surface, such as observed experimentally under the presence of a time-varying magnetic field, was implemented. The simulation results indicated that the dynamic and thermal conditions in th molten pool were seriously influenced by the time and position dependent arc distribu tion, resulting in significant asymmetries and three-dimensional features as well as tran sient effects.
Fluorescence signals of the hybridized Agilent Oligo Microarrays were detected using Agilent's DNA microarray scanner (Agilent Technologies) and analyzed using Agilent Feature Extraction Software and the Rosetta Resolver gene expression data analysis system (Rosetta Biosoftware). To highlight the most relevant pathways and genes, bioinformatics analyses were achieved. Gene ontology analysis and functional annotation of differentially expressed genes were performed using the DAVID web tool (https://david. ncifcrf. gov/summary. jsp). Gene annotations of Biological Process, Cellular Component and Molecular Function, together with annotations from the KEGG pathway database, were used, and only gene ontology terms that presented at least five genes in common with our gene expression matrix were considered in the analysis.
TIRFM Electroporated cells were plated on fibronectin-coated glass coverslips 24 h before TIRF microscopy (Ti-Eclipse, NIKON). Cells were fixed and vinculin was immunostained as described above with anti-vinculin (1/150, Sigma-Aldrich) and then secondary antibody Alexa-568. The TIRFM system and image acquisition are controlled by MetaMorph software (Version 7. 6, Molecular Device). The 25 × 25-mm glass coverslips were installed in a microscopy chamber and cells were covered with 50 µl of 1× PBS. The parameters of the TIRFM angle were previously determined on C2C12 cells. Cells of interest (carrying the desmin:GFP fusion) were identified by epifluorescence at 488-nm. Area and adhesion patches were analyzed using a macro developed by O. Cardoso (MSC Paris University, Supplementary Figure  S1 ).