dataesr/scientific-paragraphs-categorization huggingface dataset:
The ANSYS Fluent 15. 0 code is used to solve the flow equations with the SIMPLE velocity-pressure coupling algorithm. UDF scripts have been developed to solve the additional λ 2 equation (Eq. 9) and to define the F volume force field that is applied in the central area of the domain (between x = 10 mm and x = 20 mm) in order to avoid side effects and to keep simple inlet and outlet boundary conditions. For steady-state simulations, the SIMPLE  [55]  or SIMPLEC pressure-velocity coupling methods are recommended  [56]. PISO (Pressure-Implicit with Splitting of Operators algorithm) would be recommended for transient calculations or steadystate computations on highly skewed meshes, which is 265 not the case in the present study. As the problem to be solved is complicated by the presence of a momentum source term (the body-force F that furthermore depends on the solution of an additional partial differential equation for the second Lagrange multiplier λ 2 in 270 Eq.
AcknowledgmentThis work was supported by French "Investments for the future" ("Investissements d'Avenir") programme managed by the National Agency for Research (ANR) under contract ANR-10-LABX-22-01 (labex SOL-735 STICE). This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 654663, SOL-PART project6. Appendix 740In this appendix, the range of values chosen for the weighting parameter W Φ is discussed and the check of key physical quantity balances is presented. A concluding remark identifies results in accordance with other published research works.
730 5. 5 AcknowledgmentThis work was supported by French "Investments for the future" ("Investissements d'Avenir") programme managed by the National Agency for Research (ANR) under contract ANR-10-LABX-22-01 (labex SOL-735 STICE). This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 654663, SOL-PART project6. Appendix 740In this appendix, the range of values chosen for the weighting parameter W Φ is discussed and the check of key physical quantity balances is presented. A concluding remark identifies results in accordance with other published research works.
In particular, ML models effectively tackle issues such as non-linearity of the data, the presence of zero values, and a reduced sample size. Thus, they have demonstrated a high potential for obtaining accurate predictive models using complex and noisy data  [37]. The monitoring of disease occurrence and epidemiological characteristics, in addition to environment preservation, is one of the most important actions to protect biodiversity. For this purpose, we assessed the basic epidemiological characteristics (prevalence, abundance, and intensity) of C. hamulosa in the French rock partridge, based on long-term sampling. Additionally, we used ML models to identify the environmental variables influencing parasite occurrence, and to map their presence probability in the French Alps.
Epidemiological Descriptors Epidemiological indexes of prevalence (number of infected animals/total animals) and intensity (number of parasites/positive animals) were computed for the whole population, by sex and age. Afterwards, prevalence data were compared using Fisher's exact test, and frequency distribution of parasite intensity and abundance using the Kruskal-Wallis test  [41]. To evaluate and represent the temporal trend of infection, a five-year aggregate prevalence was calculated and plotted. Data were aggregated at five-year intervals to minimize the unbalanced distribution of samples among years, and to derive a more robust trend.
Environmental Variables The variables used to build the models are reported in Table  1. Spatial dataset layers include bio-climatic  [42]  and topographical factors, represented as raster data. All the rasters were clipped using the French Alps shapefile as a mask layer  [43] , considered as a proxy for the host species' potential distribution. The rasters were rescaled at a resolution of 1 km 2 , aligned, and re-projected using the same coordinate reference system (CRS-WGS 84/UTM zone 32N). All spatial data manipulation and representation were done using QGIS 3. 6  [44].
Modelling Approach The modeling approach was set in two steps with the following objectives: (i) identify and interpret the relationships between parasite occurrence (parasite presence) and environmental covariates, and (ii) build a spatial model to predict the parasite habitat suitability across the French Alps (39,372 km 2 ). In the first step, a tree classification model was built with the CARET package  [45]  in the R statistical framework  [46]. Data was split into training (70% of points) and testing (30% of points) datasets. Resampling consisted in 10-fold cross-validated repeated three times and information gain was used as a splitting criterion. Although basic decision tree models are straightforward to interpret, they poorly predict the dependent variable for new values of the covariate.
This limitation is due to the fact that they provide only a single description on the relationships between response and predictors  [30]. Thus, in the second step, we built a random forest model (as implemented in the R package "randomForest"  [47]  to make more robust predictions. The following parameters were used to define the random model: (i) type of random forest = regression, (ii) number of trees = 500, (iii) number of variables tried at each split = 4. Variable importance was assessed based on mean decrease in accuracy, and the area under the curve value (AUC) was computed to evaluate model performances. AUC compares the model sensitivity (true positives) against "1-specificity" (false positives) over the entire range of the threshold. An excellent model has an AUC close to 1, whereas a poor model has an AUC close to 0  [48].
Motivation: Prediction of patient survival from tumor molecular 'omics' data is a key step toward personalized medicine. With this aim, the databases available are growing, with the collection of various 'omics' characterizations of patient tumors, together with their associated clinical outcomes for weeks to years of follow-up. Cox models with variable selection used with RNA profiling datasets are popular for identification of prognostic biomarkers and for clinical predictions. However, these models are confronted with the 'curse of dimensionality', as the number p of covariates (genes) can greatly exceed the number n of patients. To tackle this problem, variance-based pre-filtering and penalization methods are popular for dimension reduction. In the present paper, we study the impact of a pre-filtering step based on gene variability, and we evaluate the performance of the lasso penalization of the Cox model and four variants (i.
Introduction The roots of the 'P4' model of cancer medication lie in prediction combined with personalization, prevention, and participation  [15]. Prediction of the best treatment for a given 1 patient and prediction of various clinical outcomes, including overall survival, are both of growing interest. 'Omics' technologies now come with decreasing costs, which has made possible the molecular characterization of tumor samples of various types, including quantification of mutations and gene expression  [29, 32]. As a result, there are growing numbers of knowledge databases that include molecular profiling of patient tumors, together with clinical information from patient follow-up. Survival analysis from transcriptome profiling of cancer patients in terms of messenger RNA (mRNA) expression is now emerging for clinical use  [9].
The Cox proportional hazard model  [6]  is one of the most popular approaches in medicine to link covariates to survival data. [38]  and  [18]  showed that Cox model are at least as good as, or even better than, neural networks and other machine learning models. Cox regression models with lasso penalty for variable selection  [35]  are often used to identify a few prognostic biomarkers from among the thousands of genes profiled, and to obtain a parsimonious model for simpler and cheaper clinical applications. When considering the numbers of covariates, p (which can typically be 20,000 gene products), in relation to the number of patients in the databases, n (which can typically be only a few hundred), various issues occur due to the high dimensionality, which include the lack of stability of the selected genes  [16]  and over-fitting  [25].
[24]  showed that the lasso, ridge and elastic net penalties perform equally for low dimensional settings with few events. [3]  compared the lasso, elastic net, ridge and adaptive lasso penalties on simulated and real acute myeloid leukemia data, and on real breast cancer data. They used the integrated Brier score as the metric to judge the performance of the models, and the datasets they used comprised fewer than 300 patients. Pre-filtering procedures are popular methods that considerably reduce dataset dimensionality to avoid the curse of dimensionality issues. For instance, the less variable genes are subject to measurement noise and provide poor contributions to distinguish between patients  [23]. Moreover, pre-filtering the less variable genes has been shown to increase the identification power of differentially expressed genes  [13, 4].
To the best of our knowledge, no independent benchmark of univariate and multivariate (e. g. , lasso, elastic net, ridge, adaptive elastic net) Cox regression has been defined using The Cancer Genome Atlas (TCGA) datasets, with pre-filtering of the genes based on their variability, and according to well-established metrics. In the context of survival analysis using high-dimension mRNA-seq datasets, the goals of this paper are to: (i) compare four multivariate Cox penalty methods (i. e. , lasso, elastic net, adaptive elastic net, ridge) with univariate Cox regression and to each other; (ii) study the impact of pre-filtering the genes based on their interquartile range (IQR), and propose a rationale toward the fixing of a threshold; and (iii) study the impact of cohort size on the prediction performances.
The methodologies are assessed in terms of the quality of the prediction of overall survival and prognostic biomarker selection, along with the stability. To evaluate the Cox regression methods for prediction of overall survival and selection of genes correlated to survival, we use a panel of four cancers from TCGA (http://cancergenome. nih. gov/) that share different characteristics. Real datasets are used to study the prediction performances, and we provide realistic simulated datasets that maintain the complex structure of the molecular profiles of the patients to assess selection accuracy.
Penalization methods and univariate Cox selection for a sparse model The main goal of survival analysis is to predict survival times with a set of covariates X. All of the 20,000 genes included do not necessarily contribute to the prediction of survival, and selection procedures are useful to reduce the dimension while retaining the most informative covariates. For variable selection, we considered three alternative penalties in the likelihood of the Cox model: the lasso  [35] , the elastic net  [40] , and the adaptive elastic net  [41]  (implementation is provided in R script functions/learn models func. R). The adaptive elastic net uses a two-step procedure that includes the ridge regression  [36]. Briefly, these methods consist of the addition of a penalty term to the log-pseudo-likelihood l before the maximization: • The lasso β(lasso) = βargmaxl(β) -λ||β||1 • The elastic net β(EN ) = βargmaxl(β) -λ(α||β||1 + 1 -α 2 ||β|| 2 2 ) • The ridge β(ridge) = βargmaxl(β) -λ||β|| 2 2 • The adaptive elastic net (a two-step procedure) 1.
The weight of the penalty, λ, is computed by K-fold cross-validation (K=5) using the package glmnet  [12]  in R version 3. 6. 0 [27]. The weight λ that minimizes deviation in the cross-validation is given by λmin. For more details on the mathematical concepts used in this article, we refer the reader to the book 'The Statistical Analysis of Failure Time Data'  [17]. Univariate Cox selection consists of the learning of a Cox model individually for each gene. A p-value that corresponds to the statistical test with null hypothesis "βj = 0" is then assigned to each gene j with 1 ≤ j ≤ p.
These PIs are linear combinations of gene signatures for each patient that are computed in a testing dataset (as a random selection of 20% of the patients), with β coefficients estimated with the Cox model in a training dataset (as 80% of the remaining patients). This procedure is repeated 100 times, and boxplots of the C-indices can be drawn for all of the methodologies and for different IQR thresholds. As the β estimated are different for each penalization method, the PIs and the C-index are different for each method. For univariate Cox selection, the gene with the lowest p-value is selected from the training dataset, and we use the expression level of this gene as the risk prediction score to compute the C-index for the testing dataset (R script prediction quality. R). We took the estimator of the C-index given by  [14]  and theorized by  [26] , which is implemented in the package survcomp  [31] : C -index = (i,j)∈U 1i,j #U , where U is the union of all of the comparable pairs (the death of the patient with the lowest follow-up time has to be observed), #U is the size of U, and 1i,j is equal 1 if risk scores and survival data of patients i and j are in good agreement, and 0 otherwise.
The Cancer Genome Atlas dataset First, in a preliminary study, we included all of the 11 cancers for which more than 500 patients with mRNA-seq data were available in TCGA (http://cancergenome. nih. gov/) (R script cancer characteristics. R). We studied the 'time-to-death', also called 'overall survival', which was defined as the time between diagnosis and death. We computed multiple characteristics for these 11 cancers, including the C-index estimates computed with the ridge regression method applied over all of the genes (Fig. 1 ). Then, we selected four cancers with different characteristics (Table  1 ) as a representative panel to evaluate the five methods (i. e. , lasso, elastic net, adaptive elastic net, ridge, univariate Cox). We chose brain lower grade glioma (LGG) for its high C-index (0.
81), breast invasive carcinoma (BRCA) because many samples were available (1040), and kidney renal clear cell carcinoma (KIRC) and lung squamous cell carcinoma (LUSC) as they had similar numbers of patients (524, 474, respectively) and censoring rates (0. 69, 0. 67, respectively), but very different C-indices (0. 71, 0. 55, respectively). The clinical and mRNA-seq datasets were obtained using the Broad GDAC FIREHOSE utility (https://gdac. broadinstitute. org/). We used the RNA-seq data normalized according to expectation maximization (RSEM)  [20] , and for all of the estimations of β with the Cox regression models, the gene expression data were standardized. The Figures are shown for KIRC here in the main text, and the Figures  for BRCA,  LGG and LUSC are available as Supplementary Information.
Simulation pipeline and selection accuracy for different IQR thresholds We set up a simulation pipeline to assess the selection accuracy compared to the so-called ground truth, which is graphically explained in Supplementary Figure  S1  (R script functions/simulations func. R). First, we defined the ground truth as all of the genes selected in common by the lasso, elastic net, and adaptive elastic net, plus the genes selected by at least one of the three methods for the real TCGA dataset. We set the number N of genes of the ground truth as the median number of genes selected by the three methods, which corresponds to the number of genes selected by the elastic net. As an example, for KIRC and without pre-filtering, N = 55. Characteristics of the four cancers used. C-indices were computed with the ridge regression and all of the genes in the Cox model, and p 3 is the number of genes with an IQR ≥ 3.
To obtain realistic simulations, we calibrated a Weibull proportional hazard model on real TCGA data using the genes of the ground truth. Then we simulated survival times Ti, for i = 1,. , n, from TCGA mRNA-seq data using the  [2]  method. Censoring times Ci, for i = 1,. , n, are assumed to be uniform, and the censoring rate of the real survival data is achieved using the method proposed by  [37]. We define the follow-up times ti as ti = min(Ti, Ci), with Ti the survival time and Ci the censoring time, and the status δi = 1 T i ≤C i , for i = 1,. , n. In the following, we will indicate whether the results are obtained from real or simulated datasets. We estimate the selection accuracy of the four selection methods (i. e. , lasso, elastic net, adaptive elastic net, univariate Cox) by comparing the set of selected genes for the simulated data with the set of genes of the ground truth, using the sensitivity and the false discovery proportion (FDP) (R script selection accuracy.
Stability of the prognostic index and reliability of the selected set of genes We define a procedure as unstable if small changes in the input (patients) can cause large changes in the output (PIs, or set of genes with nonzero coefficients, also referred to as the 'selected genes'). To assess the robustness of the PIs, we compute 100 PIs for real TCGA datasets for each patient, using the bootstrapping method (i. e. , random sampling with replacement). This makes it possible to compute an IQR and a median for each PI from their empirical bootstrap distribution. Then we fitted the loess curves to estimate the relation between IQR and the median PI. We repeat this procedure for each penalization method (i. e. , lasso, elastic net, adaptive elastic net, ridge) (R script stability PI. R). For the stability of the selection, we randomly select genes from two separated subdatasets of the real TCGA dataset that share x% common patients, with x ∈ {100, 90, 80, 70, 60, 50} while the sample size of patients remains constant.
Then we compare the proportions of common genes selected from these two subdatasets. This procedure is graphically explained in Supplementary Figure  S2. To further assess the reproducibility of the set of selected genes, the dataset is then divided into two subdatasets with no common patients (x = 0). Each procedure is repeated for 100 times (i. e, 100 Monte-Carlo runs), and the proportions of common genes are drawn as a function of the proportion of common patients for each selection method (i. e. , lasso, elastic net, adaptive elastic net, univariate Cox) (R script stability genes. R).
Impact of the number of patients To assess the impact of the number of patients in a cohort to infer β, we use real TCGA datasets and we consider only a subset of nT patients for the training set (nT ∈ {25, 50, 100, 200, 400}), Figure  1 : Boxplots of the C-indices for the 11 cancers from the TCGA with more than 500 patients with mRNA-seq data available, computed with the ridge penalty and all of the genes in real datasets. PRAD, prostate adenocarcinoma; STES, stomach and esophageal carcinoma; LUSC, lung squamous cell carcinoma; LUAD, lung adenocarcinoma; THCA, thyroid carcinoma; COADREAD, colorectal adenocarcinoma; HNSC, head and neck squamous cell carcinoma; BRCA, breast invasive carcinoma; UCEC, uterine corpus endometrial carcinoma; KIRC, kidney renal clear cell carcinoma; LGG, brain lower grade glioma.
Prediction quality is cancer dependent Figure  1  shows the distribution of the C-index estimates for the 11 cancers using the estimation procedure described in section 2. 4 for the real TCGA datasets. Prostate adenocarcinoma (PRAD) has the lowest prediction quality, with a median C-index of 0. 50, which corresponds to pure random estimation. Different characteristics are observed among the four cancers we selected further. LGG shows the highest median concordance (C = 0. 81), KIRC ranks second (C = 0. 70), BRCA has intermediate predictive accuracy (C = 0. 66), and LUSC has low median concordance (C = 0. 55). This indicates that the overall survival prediction quality using a Cox model is cancer dependent.
Pre-filtering to keep only the most variable genes preserves prediction performance while reducing the dimension For all of the four cancers investigated, with the removal of the genes with IQR ≥ 4, the C-indices computed for the real TCGA datasets vary very slightly (Fig. 2 ; Supplementary Fig. S3 ). However, filtering of more variable genes (IQR ≥ 5) leads to accuracy reductions in three of the four cancers investigated. For KIRC, this pre-filtering step allows a reduction from 20,245 to 178 for the number of genes, while hardly affecting the prediction accuracy. The median C-index even increases for BRCA: for the ridge regression, this goes from 0. 66 without pre-filtering (20,248 genes) to 0. 70 when restricted to the most variable genes across the patients (IQR ≥ 4, 271 genes). We suggest that the C-index is used to determine the IQR thresholds for the pre-filtering step as follows: • Determine the different thresholds to test according to the distribution of IQR for each gene (in this study, typically 0,1,.
Gene selection leads to high rate of false positives and negatives and low stability performance We assess the selection performance using simulations of overall survival and follow-up time. Best results are obtained with the genes with an IQR ≥ 4. The ground truth, as the pool of genes used for this simulation, is comprised of 37 genes for KIRC that are chosen from Boxplots of sensitivity (A), false discovery proportion (FDP) (B), computed on simulated datasets as a function of the IQR threshold. Blue, the lasso; orange, the elastic net; green, the adaptive elastic net; dark red, univariate Cox. among the 178 genes with IQR ≥ 4, as detailed in the Materials and Methods section. The elastic net reaches the highest median sensitivity (0. 70), but with a median FDP of 0. 55 (Fig. 3 ). The lasso and adaptive elastic net penalties perform similarly, with sensitivities of 0.
3. 4 The ridge regression reduces the PIs more and is more robust than the lasso, elastic net and adaptive elastic net penalties Figure  4  shows that the PIs computed with the ridge penalty for the real TCGA subdatasets are more robust and reduced than for the three other methods (i. e. , lasso, elastic net, adaptive elastic net). Among the three selection methods, the PIs computed with the elastic net have the best robustness, while the adaptive elastic net performs the worst. Similar results are obtained for BRCA, LGG and LUSC (Supplementary Fig. 8 ). The squared 2-norm in the elastic net penalty brings stability to the estimation of β, whereas the two steps of the adaptive elastic net makes the estimation more unstable.
The univariate Cox model reaches a higher stability performance, but does not exceed 50% of common genes selected. Note that for identical datasets (100% of common patients), the pools of genes selected are not exactly the same, as the inferred λmin can differ due to the random partitions used in the cross-validation step. Boxplots of proportions of common genes selected in the two datasets as a function of the proportion of common patients in the two datasets. Blue, the lasso; orange, the elastic net; green, the adaptive elastic net; dark red, the univariate Cox.
Prediction accuracy reaches a plateau from different numbers of patients, which depends on the cancer As expected, concordance increases with the number of patients used to estimate β for the real TCGA datasets (Supplementary Fig. S10 ). This reaches a plateau in different ways, depending on the cancer considered. For KIRC, the plateau is not even clearly reached with 400 patients, whereas for LGG the plateau is reached for 100-200 patients. Except for LGG, for which the ridge regression performs similarly with the other penalized Cox methods, the ridge method slightly outperforms the other penalization methods when the numbers of patients are low. As the cover is different for each nT (i. e. , between each bootstrap runs, there are more common patients in the training sets for nT = 400 than for nT = 25), the variances are biased.