dataesr/scientific-paragraphs-categorization huggingface dataset:
Predictive Boolean logic models We aim at learning Boolean logic models from a PKN and an experimental dataset. In fact, any learned model has to be supported by some evidence in the prior knowledge. For example, looking at Fig. 1 , it is clear that the logic model in (b) is not just some arbitrary model, but it is strongly related to the PKN in (a). To be more precise, given a PKN (V, E, σ) we consider only Boolean logic models (V, φ) without feedback-loops and such that, for each variable v ∈ V , if w occurs positively (resp. negatively) in φ(v) then, there exists an edge (w, v) ∈ E and ((w, v), 1) ∈ σ (resp. ((w, v), -1) ∈ σ). Notice that feedback-loops may occur in the PKN, i. e. a cycle in the graph (V, E, σ), but not in the Boolean logic models. In order to characterize the trajectories and steady states of Boolean logic models, we follow the investigations of  [33]  and reformulate the immediate consequence operator T P introduced in  [3]  for a logic program P.
Learning as optimization For a given PKN (V, E, σ), there are exponentially many candidate Boolean logic models (V, φ) having an evidence on it. Therefore, authors in  [52]  put forward the idea of training Boolean logic models by comparing their corresponding predictions to experimental observations at a pseudo-steady state. In this context, two natural optimization criteria arise in order to conduct the learning: (1) model accuracy (biologically meaningful), and (2) model complexity (Occam's razor principle). In fact, this is a typical scenario on automatized learning of predictive models  [18]. We now provide the precise formulation for each optimization criteria as defined in  [52]. Let (V, E, σ) be a PKN. Let ξ = ((ε 1 , ω 1 ),. , (ε n , ω n )) be an experimental dataset over (V, E, σ).
Introduction to Answer Set Programming Answer Set Programming (ASP;  [5, 21] ) provides a declarative framework for modeling various Knowledge Representation and Reasoning problems. The unique pairing of declarativeness and performance in state-of-the-art ASP solvers allows for concentrating on an actual problem, rather than a smart way of implementing it. The basic idea of ASP is to express a problem in a logical format so that the models of its representation provide the solutions to the original problem. Problems are expressed as logic programs and the resulting models are referred to as answer sets. Although determining whether a program has a answer set is the fundamental decision problem in ASP, more reasoning modes are needed for covering the variety of reasoning problems encountered in applications.
Hence, a modern ASP solver, like clasp  [25]  supports several reasoning modes for assessing the multitude of answer sets, among them, regular and projective enumeration, intersection and union, and multi-criteria optimization. As well, these reasoning modes can be combined, for instance, for computing the intersection of all optimal models. This is accomplished in several steps. At first, a logic program with first-order variables is turned by efficient database techniques into a propositional logic program. This is in turn passed to a solver computing the answer sets of the resulting program by using advanced Boolean constraint technology. For optimization, a solver like clasp uses usually branch-and-bound algorithms (other choices, like computing unsatisfiable cores, exist). The enumeration of all optimal models, as in our paper, is done in two steps.
Then, a rule is of the form H:-B 1 ,. , B n. where H (head) is an atom and any B j (body) is a literal of the form A or not A for an atom A where the connective not corresponds to default negation. Further, a rule without body is a fact, whereas a rule without head is an integrity constraint. A logic program consists of a set of rules, each of which is terminated by a period. The connectives :-and , can be read as if and and, respectively. A statement starting with not is satisfied unless its enclosed proposition is found to be true. The semantics of a logic program is given by the stable models semantics  [27]. Intuitively, the head of a rule has to be true whenever all its body literals are true. In ASP every atom needs some derivation, i. e. , an atom cannot be true if there is no rule deriving it.
Proposition 4. 1. Let (V, E, σ) be a PKN. Let ξ be an experimental dataset over (V, E, σ) with size N ξ. Let k ∈ N define the discretization scheme. Let us denote with µ and µ k , the corresponding minima for Θ f and Θ f k over the space of models M (V,E,σ) and with respect to ξ: µ = min (V,φ)∈M (V,E,σ) Θ f ((V, φ), ξ) µ k = min (V,φ)∈M (V,E,σ) Θ f k ((V, φ), ξ). Then 10 -2k µ k converges to µ when k increases, with an exponential speed: µ k = 10 2k µ + O(10 k ). Moreover, any Boolean logic model minimizing Θ f , also minimizes Θ f k within the following tolerance t k : t k = 2 N ξ µ k + N ξ µ k. Notice that µ k increases exponentially with k. Furthermore, as we shall see it in Section 5, in practice, µ k is significantly greater than N ξ provided that k ≥ 1. Hence, in practice, the tolerance t k is relatively small.
Input instance Let (V, E, σ) be a PKN. We represent the nodes in V as facts over the predicate vertex/1, namely vertex(v) for all v ∈ V. 2  Further, facts over the predicate edge/3 represent edges in E with their signature, that is, edge(v,w,s) for all (v, w) ∈ E and ((v, w), s) ∈ σ. Facts over predicates stimulus/1, inhibitor/1, and readout/1 denote nodes in V S , V K , and V R respectively. Let ξ = ((ε 1 , ω 1 ),. , (ε n , ω n )) be an experimental dataset over (V, E, σ). Recall that each ε i is a truth assignment over variables in V S ∪V K. Then, we represent experimental conditions as facts over the predicate exp/3, namely exp(i,v,ε i (v)) for all v ∈ V S ∪ V K and 1 ≤ i ≤ n. Finally, let k define the discretization scheme as in Section 4. 2. We represent discretized experimental observations as facts over the predicate obs/3, namely, obs(i,v,10 k δ k (ω i (v))) for all v ∈ dom(ω i ) and 1 ≤ i ≤ n.
Logic program We now describe our encoding for learning Boolean logic models as described in Section 3. Our ASP encoding is shown in Listing 2. : -edge (U ,V , S ). sub ( set (U , SU , set (W , SW , T ) ) ,N +1 , V ) : -edge (U ,V , SU ) , sub ( set (W , SW , T ) ,N , V ) , U < W. in (U ,S , set (U ,S , T ) ) : -sub ( set (U ,S , T ) ,N , V ). in (W , SW , set (U , SU , T ) ) : -in (W , SW , T ) , sub ( set (U , SU , T ) ,N , V ). { conjunction (C ,N , V ) } : -sub (C ,N , V ). path (U , V ) : -conjunction (C ,_ , V ) , in (U ,_ , C ). path (U , V ) : -conjunction (C ,_ , V ) , in (W ,_ , C ) , path (U , W ). : -path (V , V ). : -conjunction ( C1 ,N , V ) , conjunction ( C2 ,M , V ) , N <M , in (U ,S , C2 ) : in (U ,S , C1 ). exp ( E ) : -exp (E ,_ , _ ). mapped ( V ) : -conjunction (_ ,_ , V ).
In line 27 we declare with lower priority (@1) the minimization over the size of logic models (Eq. (  3 )). Meanwhile, in lines 28 and 29 we declare, with higher priority (@2), the minimization of the residual sum of squares between the Boolean predictions and experimental observations (Eq. (  5 )). The next result shows that our ASP encoding is sound and complete with respect to the multi-objective optimization problem described in Section 3 and according to some k defining the discretization scheme. We refer the reader to the appendix for a detailed proof. Proposition 4. 2. Let (V, E, σ) be a PKN and let ξ be an experimental dataset over it. Let k define the discretization scheme. Let L be the logic program given in Listing 2 and let τ ((V, E, σ), ξ, k) be the instance encoding as described above (e.
Benchmark generation In order to study the performance of our ASP-based approach over realistic biological data, we generated in silico numerical datasets based on a real and large-scale prior knowledge network (PKN). We use a generic PKN related to signaling events upon stimulation of cellular receptors in hepatocytes. After compressing the network as described in  [52] , the corresponding graph has 30 nodes and 56 edges. Meanwhile, there are 180 possible hyperedges and thus, 2 180 hypergraphs describing Boolean logic models can be derived from this PKN. The method used to generate our benchmarks is illustrated in Fig. 2. We start deriving a (random) Boolean logic model (V, φ gold ) from the PKN. Then, using this model as our gold standard, a Boolean dataset ξ 0 is generated by computing the model predictions (outputs) for several experimental conditions (inputs).
Then, several numerical datasets ξ i , i. e. values in [0, 1], are generated by adding a Gaussian noise with zero mean and standard deviation from to 0. 1 to 0. 6. This way, we generated several numerical datasets based on the predictions made by (V, φ gold ). Finally, experiments were run considering each in silico numerical dataset together with the PKN, and using either binary, or multi-valued discretization. 4.
Experiments Overall performance. We show the overall performance of the experiments run in Table  1. Datasets ξ 0 to ξ 3 lead to the same optimal fitness to data (Θ f N -1 ξi ), optimal model size (Θ s ) and number of optimal models (# opt ), using similar CPU times. However, for datasets ξ 3 to ξ 6 , CPU times grow clearly faster when using binary discretization than multi-valued. Moreover, learning on datasets ξ 4 and ξ 5 leads to more fitted Boolean logic models when using multi-valued discretization. Therefore, we conclude that multi-valued discretization provides a better overall performance than binary discretization for both, finding an optimal model and enumerating all of them. Completeness. Interestingly, for dataset ξ 6 despite of the difference in CPU times, the fitness to data (Θ f N -1 ξi ) and model size (Θ s ) are the same regardless of the discretization scheme.
Thus, in order to overcome this issue, we rely on our theoretical result in Proposition 4. 1. Therein, we prove that the minimization of Θ f can be successfully addressed by enumerating suboptimal models of Θ f k. Towards this end, we allow the enumeration of suboptimal logic models by considering a tolerance over model fitness or model size. To be more precise, let T f , T s ∈ N be the tolerances under consideration over model fitness and size, respectively. Then, for each ξ i and some optimal model (V, φ opti ) with respect to ξ i , we enumerate suboptimal Boolean logic models (V, φ) such that, Θ f k ((V, φ), ξ i ) ≤ Θ f k ((V, φ opti ), ξ i ) + T f Θ s ((V, φ)) ≤ Θ s ((V, φ opti )) + T s. For example, for dataset ξ 6 , according to Proposition 4. 1 and using k = 3 (i. e. 1000-valued) one should consider up to 0.
5% of tolerance over the optimum. By doing this, in a few seconds we are able to enumerate 22181 Boolean models which can be easily inspected towards the identification of the optimal ones with respect to Θ f. This study confirmed that the 4 optimal models for binary discretization (without tolerance) are the only one minimizing Θ f. Notably, for k ≤ 2, the tolerance to consider is at least 5% of the optimum. Unfortunately, over ξ 6 , such tolerance yields millions of suboptimal models which is useless in practice. For further discussion, we refer the reader to Section 7. In what follows we report experiments corresponding to enumerate suboptimal models according to the discretization scheme given by k = 2. Table  1 : Computing all optimal Boolean logic models. Datasets ξ 0 to ξ 6 correspond to the in silico datasets generated as illustrated in Fig 2.
Discretization ξi Binary 10-valued 100-valued topt t all #opt Θ f N ξ i Θ f k 10 2k N ξ i Θs topt t all #opt Θ f N ξ i Θ f k 10 2k N ξ i Θs topt t all #opt Tolerance over model fitness. First, we evaluate the impact of several tolerances only over model fitness. Towards this end, we have fixed T s = 0 and considered tolerances T f corresponding to 2%, 4%, 6% and 8% of the optimum fitness with respect to ξ 3. For the sake of illustration, we take tolerances always relative to ξ 3 since it provides an intermediate fitness to data. Results are shown in Fig. 3. Firstly, for datasets ξ 0 and ξ 1 we found the same behavior with small impact of the tolerances under consideration. Secondly, datasets ξ 2 and ξ 3 have shown not the same, but very similar behavior with respect to the number of models found for each tolerance.
Thirdly, datasets ξ 4 to ξ 6 have also shown similar results for each tolerance. Notably, for datasets ξ 1 , ξ 2 and ξ 3 the number of suboptimal models grows clearly slower than for datasets ξ 4 , ξ 5 and ξ 6. It is worth noting that for the latter cases, even if the considered tolerance correspond to a relatively small ratio of the optimum (i. e. 1% to 4%), the number of suboptimal models reaches quantities which are useless in practice. Therefore, this promotes the use of a more refined discretization scheme for such datasets. 1 ). Considered tolerances T f correspond to 0. 02, 0. 04, 0. 06 and 0. 08 times the optimum with respect to ξ 3. The corresponding percentage with respect to each dataset ξ i is reported in the table at the top left corner of the figure. Datasets ξ 0 and ξ 1 have shown the same behavior (blue bar).
For datasets with low levels of noise the number of suboptimal models grows clearly slower than for datasets with high level of noise. Tolerance over model size. Next, we evaluate the impact of several tolerances only over model size. We have fixed T f = 0 and considered tolerances T s = 2, 4, 6, 8. Results are shown in Fig. 4. Datasets ξ 0 to ξ 3 have shown exactly the same behavior for each tolerance value. Further, for all datasets the number of Boolean logic models grows exponentially as we increase the tolerance over model size. Notably, minimization over model size is based on Occam's razor principle (parsimony). Hence, there is no experimental evidence in order to select among this large number of models. On one hand, one can consider that larger logic models overfit the available dataset by introducing excessive complexity  [52, 46].
Meanwhile, modern ASP tools allow handling complex preferences and multi-objective optimization, guaranteeing the global optimum by reasoning over the complete solution space. In this context, ASP offers a unique pairing of declarativeness and performance to address combinatorial multi-objective optimization problems like the one at hand. Herein, we have extended our previous work in order to consider: (1) numerical datasets, (2) a multiobjective optimization formulation and (3) feedback-loops in the PKN. Notably, in order to cope with such extensions, we have proposed several discretization schemes and elaborated upon our previous ASP encoding. In order to study the performance of our ASP-based approach towards real-world biological data, we have generated in silico numerical datasets based on a real and large-scale PKN.
Nonetheless, either real or more elaborated in silico (e. g. based on ordinary differential equations) datasets would be required for a further and biologically significant analysis. Moreover, when using real-world datasets, mechanistic descriptions available in popular databases  [53, 35, 10]  might be used (if they exists) to validate the inferred logical interactions. Although, the method shown herein is highly dependent on the specificity of experiments and thus, a proper biological validation would imply reproducing the experiments on the same or very similar settings. Altogether, our experiments have shown that current ASP tools are mature enough to cope with realworld problem instances. Nevertheless, given the ability to enumerate such a large number of Boolean models, the way to select among them arises in order to provide new insights to biologists.
Moreover, it was found that for 30% of the space of possible inputs, all behaviors agree on the given outputs. Hence, in practice this approach may provide a way to extract robust insights despite the high variability. Several interesting issues could be investigated in the future. Firstly, it would be interesting to consider other discretization schemes based on the nearest integer or ceiling functions. Also, rather than truncation using discrete levels as a power of 10, one could consider discrete levels as a power of 2 or any other base. Notably, each discretization scheme may have an impact on both, performance and fitness to data. Moreover, considering real-world datasets and their inherent noise, opens very interesting questions. In particular, one could try to identify what is the most significant information in a given dataset, based on what it is actually used by each scheme and the models they recovered.
Traditional techniques based on field measurements, particularly using destructive sampling, are considered most accurate in estimating biomass  [5, 8]. However, field measurements are restricted in terms of spatial distribution, repetitivity and cost, and are generally upscaled to larger areas using remote sensing data  [9]. On the other hand, direct measurement of forest carbon stocks using space-borne sensors is also currently not feasible and researchers combine remote sensing based vegetation maps with carbon density values obtained either from the available global databases or local field-based measurements  [10, 11]. However, tropical forests present a challenging environment for biomass estimation as biomass levels are high, forest canopy is heterogeneous, often tall and largely closed with multiple layering in these forests.
05) as well as all predictor variables significant at a level 0. 01. For each scenario, the overall best model was selected using the corrected Akaike Information Criteria (AICc)  [48] , which is more adapted to small sample size than AIC  [49]. For FOTO, azimuth directions were modelled separately, and only predictor variables computed from the best direction were retained for the two last scenarios. The accuracy of the predictive models was assessed estimating leave-one-out cross-validation (LOOCV)  [50] , and reporting root mean squared error (RMSEcv) and adjusted determination coefficient (adj. R 2 ). The statistical analyses were performed within R Software, using leaps, car and DAAG packages (cran. r-project. org/).
Limitations and Future Work This study demonstrates for the first time how vertical and horizontal descriptors of the canopy complement each other to improve the performance of Lidar-based models of AGB in multi-layered tropical forests. With RMSE errors below 10%, these results open up new research avenues to map AGB over large areas with a good accuracy. Despite this promising result, uncertainties remain with respect to field-based AGB estimation, plot positioning accuracy and robustness of Lidar descriptors. Here, field biomass was computed using DBH alone due to data limitations. Nevertheless, upon availability, models integrating DBH along with wood specific gravity, total height, and forest type, would provide more accurate estimations  [58]. Plot positioning had been a known difficulty with Lidar-based models of forest parameters  [59].
Conclusions Lidar is a state of the art technology for characterizing forests structures. Currently, most of the Lidar-based models of forest parameters relied on variables describing the vertical properties of the point data at either plot or stand level, thus neglecting information about the horizontal arrangement of forest canopies, which was largely used in 2D optical remote sensing. In dense and multilayered canopies, like those found in the humid tropical forest, the limited capabilities of Lidar signal to penetrate to the ground could limit the potential of such approaches. In this study, using a coarse density aerial Lidar over a mountainous wet evergreen tropical forest, we assessed the capability, complementarity and enhancement of three recently proposed methods for assessing aboveground biomass at the plot level.
Acknowledgments The research has been supported by  IFPCAR (Indo-French Promotion Center for Advanced Research)  through the joint project number  4509-1  " Controlling for Uncertainty in Assessment of Forest Aboveground Biomass in the Western Ghats of India " between UMR AMAP, Montpellier and the  National Remote Sensing Centre, Hyderabad. The authors also greatly acknowledge the  French Institute of Pondicherry (IFP)  for its financial support to  Udayalakshmi Vepakomma  for visiting IFP and for providing field control data from its long term monitoring plot in Uppangala.
01 g m -2 is applied as a first guess in the NOFlux model to avoid null values of NO emission. Indeed, very little is known about mineral N dynamics and subsequent NO emission at low soil moisture, but experimental studies show low emission even during the dry season  (Scholes et al. , 1997). The principal advantage of this NO parametrization is to depend on different factors at two levels. The first level concerns climatic impacts and environmental parameters, such as precipitations, soil texture and pH, temperatures, wind speed, and the second level concerns intrinsic processes of N turnover in the soil, through the organic matter degradation from vegetation and livestock, and the microbial dynamics. The majority of the first-level variables are easily available on site or/and from atmospheric model reanalysis and global databases; the second level is a sophistication of the model, making it possible to add biotic processes in this parametrization of NO emission.
Soil moisture Soil moisture has a strong influence on NO emission from soils, particularly in hot and dry regions, at the global, regional or local scale  (Williams et al. , 1992; Yienger and Levy, 1995; Meixner et al. , 1997; Hartley and Schlesinger, 2000; Yan et al. , 2005; Feig et al. , 2008; Hudman et al. , 2012). This variable needs to be well reproduced by the model in order to calculate reliable NO release. Volumetric soil moisture is calculated by STEP at different soil layers, using a tipping bucket approach. Figure  2  shows the volumetric soil moisture calculated by STEP between 0 and 2 cm from 2004 to 2008, compared to the volumetric soil moisture measured at Agoufou at 5 cm depth in  2005 , 2006 , 2007 and 2008. From 2006 to 2008 , these measurements are actually an average of three data sets from soil moisture probes oper-ating at the top, middle and bottom locations of dune slopes.
After purification using the ExoSAP-IT w Kit (USB Corporation), sequencing was done using a capillary sequencer (Applied Biosystems 3730 DNA Analyzer) in combination with an ABI Prism BigDye Terminator Cycle Sequencing Kit. Any Rv0678 mutant was considered as potentially causing clofazimine resistance. For pyrazinamide, known resistance-conferring pncA mutations plus all novel mutations in the pncA gene not previously described were considered as resistant. 34, 35 LC Sequence Viewer (version 7. 0. 1) was used for analysis. Mutations were identified using NCBI BLAST and comparing with the M. tuberculosis H37Rv sequence (GenBank accession number NC_000962). An isolate was defined as heteroresistant if both WT and mutant nucleotides conferring resistance at a specific locus were detected.
Data analysis The primary data were read into an EpiData file for analysis (EpiData Analysis, version 2. 2. 2. 183, freely available at http://www. epidata. dk). To determine differences between observed values, x 2 values, ORs and 95% CIs for categorical data were calculated. Additional analyses were done with R software (R Core Team 2015; http://www. R-project. org). For contingency tables with nominal values (levels of drug concentrations) we calculated Cramer's V (a Pearson's x 2 -derived statistic) as the measure of association. To calculate the MIC ratios between ofloxacin and gatifloxacin and between ofloxacin and moxifloxacin, we applied a censored Tobit regression, with gatifloxacin or moxifloxacin, respectively, being the dependent right-censored variable above an MIC of 4 mg/L.