dataesr/scientific-paragraphs-categorization huggingface dataset:
Root windows were scanned at monthly intervals during 3 years starting in January 2007. This scanning was started 6 months after setting up the access well to avoid recording overproduction of roots at the onset, as often occurs in mini-rhizotron experiments  (Yuan and Chen, 2012 ). Long-term observations are also highly recommended to avoid the risk of overestimating fine root turnover  (Strand et al. , 2008). Root growth monitoring was conducted following a procedure described in  Maeght et al. (2007). Images of the soil and roots in direct contact with each window were used to estimate root length, radius, and time of root appearance/disappearance (from which root turnover was inferred). We used the Gimp freeware package 1  to digitize roots and classify them as live or senescent. Senescent roots are often difficult to identify with certainty  (Majdi et al.
Analysis of Root Sample Images Root length measurements were obtained using IJ_Rhizo's implementation of the method developed by  Kimura et al. (1999). IJ_Rhizo  (Pierret et al. , 2013)  is a software designed to measure roots washed from soil samples and developed in the ImageJ 2 macro language. The approach developed by  Kimura et al. (1999)  is based on discriminating each pixel of the medial axis (or skeleton) of each digitized root according to its number of orthogonal and diagonal (vertical or horizontal) neighbors. We also used IJ_Rhizo to compute frequency distributions of root radius classes (i. e. , the cumulated root length par root radius class).
Statistical Analyses All numerical data processing and statistical analyses were performed within the R environment (version 3. 0. 2; R Development Core Team, 2013). We first explored our dataset using a principal component analysis (PCA; "ade4" package, version 1. 6-2). RLD and root radius values are reported as mean ± 95% confidence interval. We applied analysis of variance with Tukey's HSD post hoc tests to determine differences in root radius at different soil depths. We assessed fine root survival at the depth of each root using a Kaplan-Meier survival analysis  (Kaplan and Meier, 1958 ) implemented in the "survival" package (version 2. 37-4) of the R environment. For each individual root, we recorded the time of emergence and the time to either an event (death) or the end of the study (i.
ACKNOWLEDGMENTS This research was funded by the  French Institute of Research for Development (IRD), France , the  French Institute for Natural Rubber (IFC) ,  France , and  Michelin/Socfinco/SIPH Rubber Tree Plantations Companies. We would also like to thank all our  Thai counterparts from Khon Kaen University (KKU) ,  Land Development Department (LDD) , and the owner of the plantation ( Mr. Chaipat Sirichaiboonwat ) who kindly welcomed us. The authors also wish to thanks  Drs. D. Nandris  and  F. Do  ( IRD ) for their interest in and support of this research.
Reactive transport For the reactive transport problem, we have first implemented in DuMu X a one-phase multicomponent transport model. As starting point we used the single-phase, two-component model already implemented in DuMu X. This model implements a one-phase flow of a compressible fluid, that consists of two components. The primary variables are the pressure p and the mole or mass fraction of dissolved components x. In our model, we want to impose the velocity and consequently the pressure. So, we have first removed the pressure from the set of primary variables. Then, we have increased the number of dissolved components from two to N. We have named this new model 1pN c for one-phase N-component. The last component is a locally developed code for chemical equilibrium called ChemEqLib  [1, 5].
This code solves the chemical equilibrium problem that consists of mass actions laws and mass conservation laws. The proposed formulation can involve both homogeneous (aqueous complexation) and heterogeneous reactions (mineral dissolution/precipitation and ion exchange). For minerals, one does not know a priori which species are in the solid form, and which are dissolved, leading to a system of equations that is of complementarity type. In the ChemEqLib code, this is handled by an outer loop over the possibly dissolved mineral species, and a check as to whether the included species are not over-or under-saturated (see  [6] ). At each of these outer iteration, a non-linear system is solved using a globally convergent Powell's hybrid method. To solve the reactive transport subsystem, we have coupled the 1pN c and ChemEqLib codes.
Logic models of signaling pathways are a promising way of building effective in silico functional models of a cell, in particular of signaling pathways. The automated learning of Boolean logic models describing signaling pathways can be achieved by training to phosphoproteomics data, which is particularly useful if it is measured upon different combinations of perturbations in a high-throughput fashion. However, in practice, the number and type of allowed perturbations are not exhaustive. Moreover, experimental data are unavoidably subjected to noise. As a result, the learning process results in a family of feasible logical networks rather than in a single model. This family is composed of logic models implementing different internal wirings for the system and therefore the predictions of experiments from this family may present a significant level of variability, and hence uncertainty.
, 2000; Yeang et al. , 2005; Barrett and Palsson, 2006; Szczurek et al. , 2008; Sparkes et al. , 2010; Atias et al. , 2014). An optimal experimental design can be applied to either: (i) experimental setup selection, that is the optimal choice of species to perturb and measure, or (ii) perturbations selection, where one perturbation indicates which species will be perturbed in one experiment. In this work, we focus on experimental design for selecting an optimal signaling perturbation set by considering the experimental setup fixed and a set of initial measurements from low combinatorial (i. e. , single stimulus or inhibitor species) perturbations. We use training algorithms to identify a family of Boolean models explaining the data according to a prior knowledge network. This family needs to be discriminated by measuring the effect of additional perturbations.
In contrast, but similarly to  Szczurek et al. (2008) , we find the smallest number of perturbations to optimally discriminate all pairs of models at once. This approach is tailored to high-throughput technologies that are designed to measure the effects of tens of perturbations in a single run. We provide a precise characterization of the combinatorial problem related to the optimal selection of signaling perturbations, together with an Answer Set Programming  (Gebser et al. , 2012)  based solution to this problem included within the open source python package caspo, which is freely available for download 1. We applied our method to two case studies using in silico and real phosphoproteomics datasets to measure the impact of our approach in a real setting. We show that optimal logic models with few input-output behaviors can be learned by combining a set of low combinatorial perturbations with a minimal set of greater combinatorial perturbations.
In the artificially generated data, we obtained that phosphoproteomics measurements from 64 low combinatorial perturbations can be enriched with 10 combinatorial perturbations (from the 1630 possible) to identify a family of logic models with a fitness quality (mean square error) equal to one of the golden standard logic model used to generate the data. In the real dataset, we obtained that phosphoproteomics measurements from 12 low combinatorial perturbations can be enriched with 31 combinatorial perturbations (from the 120 available) to identify a family of logic models with a fitness quality at a 15% distance from the fitness of logical models explaining optimally all 120 responses to the perturbations considered.
Background In this paper, we are interested in the discrimination of models based on synchronous Boolean networks  (Kauffman, 1969). Importantly, we restrict ourselves to BNs describing models of immediate-early response as introduced in Saez-Rodriguez et al. (2009). Since we focus on fast (early) events, it is assumed that oscillation or multi-stability caused by feedback-loops  (Remy et al. , 2008)  cannot happen until a second phase of signal propagation occurring at a slower time scale. Therefore, BNs with feedback-loops are not considered  (Macnamara et al. , 2012). Several related methods within this framework were published in the last few years in order to learn BNs from a prior knowledge network (PKN) and a phosphoproteomics dataset  (Mitsos et al. , 2009; Saez-Rodriguez et al. , 2009; Guziolowski et al.
, 2013; Sharan and Karp, 2013; Videla et al. , 2014). A PKN is a signed and directed graph describing causal relations among a set V of nodes representing biological species. An experimental setup is defined by three subsets of V, namely, possible stimuli (V S ), possible inhibitors (V I ), and measured species (V M ). A signaling perturbation is a combination of present/absent stimuli and inhibitors. Then, a phosphoproteomics dataset provides phosphorylation activities (in this context, immediate-early responses) of a set of measured species or readouts under several signaling perturbations. Note that any signaling perturbation is described by an n-dimensional Boolean vector, i. e. , p ∈ B n , where n = |V S | + |V I | and B = {0,1}. More precisely, if the j th position in p is assigned to 1 (resp.
0), the corresponding stimulus or inhibitor is said to be present (resp. absent) in the experimental perturbation p. In general, aforecited methods for learning BNs explore the space of models compatible with the topology given by the PKN aiming at the minimization of two criteria, namely, the difference between data and model predictions, and the model size. On the one hand, the difference between data and model predictions is measured by means of the Mean Squared Error (MSE). On the other hand, the size of a BN is defined as the sum of its formulas' length. Further, due to the inherent noise in experimental data, we are interested not only on optimal but also nearly optimal BNs. That is, BNs having MSE and size within given tolerances with respect to the corresponding minimal values. In this context, it has been shown that the exhaustive enumeration of nearly optimal BNs explaining phosphoproteomics dataset with respect to a PKN leads to a large number of them  (Guziolowski et al.
Discriminating Input-Output Behaviors In this section, we introduce our method to discriminate input-output behaviors in a pairwise fashion. We assume that we are given a set B of input-output behaviors. For instance, this set may result from the learning of BNs from given PKN and phosphoproteomics dataset. In what follows, we denote by D a selection of signaling perturbations. In theory, all combinatorial perturbations of stimuli and inhibitors could be considered. Nonetheless, in order to consider the limitation of current technology, in general, we restrict ourselves to perturbations having at most s stimuli and i inhibitors, with 0 ≤ s ≤ |V S | and 0 ≤ i ≤ |V I |. Then, we denote with P the set of such possible signaling perturbations. Notably, the total number of perturbations is given by: s ∑ j=0 ( |V S | j ) × i ∑ j=0 ( |V I | j ) where ( n m ) denotes the binomial coefficient, i.
Experimental Design Powered by Answer Set Programming The method described in Section 2 is implemented in the publicly available python package caspo. Our software strongly relies on a form of logic programming known as Answer Set Programming (ASP)  (Gebser et al. , 2012). ASP provides a declarative framework for modeling knowledge-intense combinatorial (optimization) problems. Moreover, state-of-the-art ASP solvers offer powerful implementations. In our context, the ASP logic program is satisfiable for positive integers k, s, i if there exists a selection of k signaling perturbations in P satisfying (1). Then, the solving consists of considering, starting from k = 1, increasing values for k until the ASP logic program is satisfiable. Once the solver finds the smallest k or reaches kmax, it proceeds to solve the multiobjective optimization problem in lexicographic order: first, by maximizing the pairwise differences over the Boolean models' outputs as defined in (3), and then by minimizing the complexity of experimental perturbations, as defined in (5).
The Loop for Learning and Discriminating Input-Output Behaviors In what follows we assume the existence of a method for learning nearly optimal BNs and their corresponding set of input-output behaviors. Further, such a method must be parametrized specifying allowed tolerances with respect to optimal fitness and size. Also, we assume an implementation of the method described in Section 2. In our case, we rely on the python package caspo, which implements both methods providing an unified framework. In order to evaluate our method in a systematic way, we have implemented the workflow shown in Figure  1   2. For a more detailed description, we refer the reader to pseudo-code algorithms (Algorithm S1 and S2) provided in Supplementary Material. We start by learning strictly optimal input-output behaviors from a given PKN and initial dataset.
Then, the workflow follows a "cautious" strategy in the sense that it will try to discriminate among input-output behaviors as soon as we find more than one. Every time we discriminate among a set of input-output behaviors, an optimal set of signaling perturbations is proposed. Then, both the set of perturbations and the corresponding measurements obtained after performing the experiments are added to the dataset used for learning and the workflow starts over. Notably, in our simulations, measurements are extracted automatically from either artificial or real datasets available beforehand. Meanwhile, in real case studies, measurements would be provided by concrete wet experiments. Importantly, there are cases when the learning method returns a single optimal input-output behavior. In such cases, the workflow explores nearly optimal behaviors by considering a range of tolerances, first over the optimal model size and then over the optimal MSE.
Extending the discrimination procedure to nearly optimal behaviors allows ensuring that the complete workflow is robust to noise in data. Nonetheless, after considering certain ranges of tolerances on both size and fitness to data, there could be only one input-output behavior. In such a case, we interpret the behavior at hand to be robust enough and the workflow terminates. Otherwise, the workflow has two additional stop conditions: (1) when all proposed signaling perturbations for discrimination are already present in the dataset used for learning; (2) when the number of experiments in the dataset reaches a given maximum number of allowed experiments.
Experimental Design on Artificial and Real Case Studies We evaluate our approach using the workflow described in Section 4 for real-world signaling pathways in human liver cells, and both artificial and real phosphoproteomics datasets. At every loop iteration, we compute two metrics over the learned input-output behaviors: (1) the learning MSE, which is computed with respect to the dataset used for learning, and (2) the testing MSE, which is computed with respect to the complete space of signaling perturbations under consideration (either artificial or real datasets available beforehand).
Artificial Case Studies The PKN was introduced in Saez-Rodriguez et al. (  2009 ) and here we use a variation that we used also in  Guziolowski et al. (2013). Further, to motivate our study, we considered the experimental setup (choice of stimuli, inhibitors, and measured species) from a publicly available phosphoproteomics dataset  (Alexopoulos et al. , 2010). It contains 7 stimuli, 7 inhibitors, and 15 readouts. Using the PKN, we have generated 100 random BNs as our gold standards. We require that every gold standard has size between 28 and 32, and between 2 and 4 AND gates. Next, for each gold standard, an artificial Boolean dataset is generated by performing the simulation of every possible signaling perturbation over the network. That is, each artificial dataset consists of 2 14 signaling perturbations with their corresponding output measurements.
Moreover, toward more realistic phosphoproteomics datasets, we add random noise to Boolean outputs using the distribution Beta(α = 1, β = 5). In this context, the loop starts with a dataset of size 64 having all perturbations (and the corresponding artificial measurements) including all combinations of 0 or 1 stimulus with 0 or 1 inhibitor. For the following iterations, optimal sets of signaling perturbations are chosen among all combinations of 0-3 stimuli with 0-2 inhibitors. The maximum number of perturbations to discriminate a given set of behaviors was set to 5, and the maximum number of experiments allowed in the dataset used for learning was set to 80. Additionally, for each gold standard dataset, starting from the same 64 initial datasets, we performed 50 random selections of 10 and 16 experiments.
Real Case Study To validate this approach on a real phosphoproteomic dataset, we used a larger PKN than in the in silico dataset. The reason being that 2 phosphoproteomics datasets were available for this PKN: a low combinatorial one referred to as screening, where only 1 stimulus was perturbed per experiment, and the followup, which had greater combinatorial perturbations. The PKN and datasets were introduced in  Melas et al. (2012). The PKN was constructed from several sources of information; it was pruned using the screening dataset to keep only the signaling pathways that show a significant response on specific cells. The follow-up dataset had 120 combinatorial signaling perturbations and was used to learn optimal BNs fitting the data. The experimental setup for this dataset consisted of 12 stimuli, 3 inhibitors, and 16 readouts.
In this context, the loop starts with a dataset having the 12 responsive experiments from the screening dataset. Then, in the following iterations, optimal sets of perturbations are chosen among the available experiments in the follow-up dataset. It is worth noting that at each iteration, there may be several optimal sets of perturbations to discriminate behaviors at hand. Thus, we executed the loop 30 times and at each iteration, one among all optimal sets of signaling perturbations was randomly chosen. The maximum number of perturbations to discriminate a given set of behaviors was set to 5, and the maximum number of experiments allowed in the dataset used for learning was set to 50. Additionally, starting from the same 12 initial datasets, we performed 30 random selections of 20 and 38 experiments.
These experiments were added to the initial datasets and we learned BNs from randomly selected experiments. Finally, we computed the testing MSE of this family of BNs with respect to the total 120 experiments. In Figure  2 , we show the evolution of the learning MSE for 100 artificial datasets and the 30 real data executions. In Figure  3 , we show the evolution of the testing MSE for the same artificial and real datasets. For the artificial dataset, we observe that the learning MSE remains constant independent from the number of experiments used; while for the real dataset, it slightly increases with the number of experiments. For the real case, we observe a significative difference in the learning MSE of the logic models learned from a low combinatorial set of experiments (screening data) compared to the MSE of those learned from a more combinatorial follow-up dataset (Figure  2B ).
For both datasets, we observe that the testing MSE converges to the optimal MSE obtained when using the full available datasets. For the artificial case, the testing MSE converges exactly to the optimal MSE (0. 047) after 10 experiments; a random selection of experiments is far from reaching this MSE value. For the real case, it converges to an MSE (0. 149) at a 15% distance from optimal MSE after 31 experiments; a random selection of experiments shows comparable results. In contrast to a random selection, the proposed method guarantees selecting perturbations that can propose networks The Y -axis shows the learning MSE obtained at each iteration, it represents the quality of the learned models with respect to the experiments used in the learning step.
Proposing Experiments to Discriminate Input-Output Behaviors Using the real-case PKN and the complete follow-up dataset (120 experiments), we explored the space of nearly optimal BNs by setting 0. 2% of tolerance with respect to the minimum MSE. By doing this, we found 35208 BNs describing 32 logical input-output behaviors. Notably, in regards of the available experimental observations and their intrinsic uncertainty, such behaviors explained the data equally well. Next, we identified 6558 optimal sets of signaling perturbations, having 0-3 stimuli combined with 0-2 inhibitors, in order to discriminate among the 32 input-output behaviors. Each optimal set consists of 9 signaling perturbations yielding 3378 pairwise differences. In Figure 4A, we show one example of optimal signaling perturbations.
Discussion The main result of this paper is that the experimental design loop combining learning and discriminating steps shows a fast convergence of the testing MSE (computed with respect to the complete space of signaling perturbations under consideration) to an approximation of its optimal value: in the real case study, based on a very small initial screening dataset (12 perturbations), 30 well-chosen perturbations are enough to learn input-output behaviors whose fitness with respect to the total follow-up perturbations is 15% greater than the optimal MSE. This confirms that follow-up phosphoproteomics assays can be highly redundant and should be designed carefully.
Testing MSE Non-Monotonic Evolution In artificial case studies, the learning MSE (computed with respect to the dataset used for learning) remains somehow constant when new perturbations are added to the dataset. This suggests that the 64 perturbations from the initial dataset may be enough to constrain the training method in a part of the search space, which is close to an optimal Boolean network. Then, introducing suboptimality searches in the loop allows us to explore efficiently the search space of Boolean networks around such an optimum. On the contrary, the learning MSE for the real case study appears to be very heterogeneous at each iteration of the proposed workflow. The best models optimizing the fitness to the 12 screening data (single stimulus) are at a very small distance (0. 07), suggesting that the Boolean networks explaining properly the data should be easy to identify.
However, as soon as the observations from additional perturbations (each consisting of a combination of different stimulus and inhibitor species) is added to the dataset, the learning fitness increases to (0. 11-0. 15) showing a significant variability. This suggests that the best models optimizing each dataset are placed in different parts of the search space and that the training dataset is not robust to small variations. Altogether, values for testing MSE evidence that the discriminative method should be always applied iteratively: after some iterations, it may appear that, although a family of optimal BNs has been totally discriminated, applying a step of discrimination for a closer model to the optimal BNs finally allows to identify BNs with a better fitting. Concretely, our analysis strongly suggests that not only the 120 follow-up perturbations are redundant, but also that additional experiments to the 120 at hand are needed to improve the robustness of the BNs identification process.