dataesr/scientific-paragraphs-categorization huggingface dataset:
Additionally, we implemented the SA in the R package BiRewire (publicly available on Bioconductor  [20] ) and we showed a massive reduction in computational time requirements of our package and bound with respect to other existing R implementations  [22]  and bounds  [21]. Here (i) we introduce the problem of rewiring a DSN modeling a biological network in a way that the FCL of all the modeled entities is preserved: F-Rewiring; (ii) we formally show how this problem reduces to rewiring 2 bipartite networks; (iii) we provide a generalized bound to the SA for bipartite networks of any size; and (iv) we show the validity of the Markov chain convergence criteria (used in our previous work) for F-rewiring DSNs. Finally, we provide an overview of the functions included in a new version of BiRewire for F-Rewiring, and we show results from two case studies where solutions obtained with two network optimization methods (BioNet  [9] , and CellNOpt  [23] ) are assessed for statistical significance and intial reference network biases against constrained null models generated with BiRewire.
For uniformly distributed degrees 1 , i. e. p r = (1d) 2 , this bound reads as: N = |E| ln 1-d δ 2(1 -d). ( 4 ) A value of δ = 0. 00005 (corresponding to = 1 edge when |E| ∼ 20000), is used by default by our new implementation of the SA in the new version of the package BiRewire but this parameter can also be set to a user defined value, making our tool and bound suitable for the rewiring of bipartite networks of any size. Additionally, the choice of a suitable value for this parameter can be determined by visually inspecting the SA Markov chain convergence with a new dedicated function (described in "Overview of the new functions included in BiRewire v3. 0. 0" Section).
Results Overview of the new functions included in BiRewire v3. 0. 0 The R-package BiRewire (http://bioconductor. org/ packages/BiRewire/) was originally designed to efficiently rewire large bipartite networks (  [20] ). We have performed a major update, by including functions to: • read/write directed signed networks (DSN) from/to simple interaction format (SIF) files (functions birewire. load. dsg and birewire. save. dsg); • perform the transformation f (and its inverse f -1 ) to derive bipartite networks induced by positive and negative edges of a DSN, and vice-versa (functions birewire. induced. bipartite and birewire. build. dsg); • F-rewire a DSN by applying the switching-algorithm (SA) to the two corresponding induced bipartite networks with numbers of switching-steps automatically determined for both networks individually, using Eq.
2. Also in this case the inputted graph can be a bipartite network, an undirected network or a DSN (birewire. visual. monitoring. * functions); • perform an analysis of the trends of Jaccard similarity across SS. This function performs a user-defined number of independent runs of the SA, computing the mean value and a confidence intervals of the observed pairwise Jaccard similarities between the obtained rewired networks. The result is a dataset containing the Jaccard similarity scores computed and sampled at user-defined intervals of SS, and a plot similar to that showed in Figs. 3a  and 4a. This function takes in input a bipartite network or an undirected network or a DSN (birewire. analysis. * functions). Worthy of note is that, supporting the analysis of DSNs, our package can handle also generic directed graphs, therefore with BiRewire3 it is now possible to rewire any kind of unweighted networks.
Case study 1: BioNet The R package BioNet  [29]  provides a set of methods to map gene expression data onto a large reference biological network, and to identify (with a heuristic method) a maximal scoring sub-network (MSS), which a is a set of connected nodes (or module) with unexpectedly high levels of differential expression  [30]. Several other methods moving along the same lines exist (as, among others, EnrichNet  [6] ). Here we focus on BioNet because it can be considered a typical example among these methods, and we show how BiRewire3 can be used to estimate the impact of the reference network topology and the functional characterization level (FCL), i. e. sign-directed degree, of its nodes on the optimal module outputted by this tool. The initial reference network used by BioNet (the Interactome) is a large undirected protein-protein-interaction network assembled from HPRD  [31]  and encompassing 9,392 nodes and 36,504 edges.
In  [29] , the authors show an application of BioNet to gene expression data from a diffuse large B-cell lymphoma (DLBCL) patient dataset, with corresponding survival data. After determining gene-wise P-values for differential expression and risk-association, the authors aggregate them and fit a beta-uniform mixture model to the distribution of aggregated P-values that yields a final score (accounting for both considered factors) for each gene: the higher this score the more a gene is differentially expressed across the contrasted groups of patients. Then the methods proceeds with mapping these scores onto the Interactome nodes and, applying a heuristic method  [9] , it identifies a sub-network (referred to as a module) that is a sub-optimal estimate of the MSS. This module is shown in Fig.
3c  and the BioNet package vignette contains detailed instructions on how to reproduce this result. To evaluate the impact of the FCLs of the Interactome nodes on the module outputted by BioNet when used on the DLBCL dataset, we generated 1,000 F-rewired versions of the Interactome with BiRewire3 and used each of them as initial reference network in 1,000 individual BioNet runs, using the DLBCL dataset as input. To this aim we first conducted a BiRewire3 analysis (using the dedicated function of our package) to determine the number of switching-steps (SS) to be performed by the switching-algorithm (SA) in order to F-rewire the Interactome. This function makes use of the convergence criteria we designed in  [20] , which is based on the estimated time, in terms of SS, in which the Jaccard similarity (JS) between the original network and its rewired version at the k-th SS reaches a plateau (Fig.
3a ). In  [20]  we showed that this criteria is equivalent to other established methods to monitor Markov chain convergence when the states are networks. In addition its relatively simple formulation consents the analytical derivation of an estimated plateau time, i. e. our bound N. Neverthless, our package allows also a visual inspection of the optimality of the estimated bound N showing how independent are F-rewired versions of an initial network sampled at a number of user-defined SS intervals as well as every N SS (Fig. 2 ). These preliminary analyses resulted in a required number of SS equal to N = 170, 491 (Fig. 3a ) and showed that this number of SS is actually sufficient to generate unrelated F-rewired versions of the Interactome, thus to Fig. 4  CellNOpt study case. a Analysis of the Jaccard index trend across switching-steps (SS) while rewiring the two bipartite network induced by the positive (respectively negative) edges of the reference DSN (liver prior knowledge network (liver-PKN)) and estimation of the lower bounds for the number of switching-steps; b visual inspection of the switching-algorithm Markov chain convergence to verify the suitability of the estimated bounds (see Fig.
2  legend for further details); c Comparison of the CellNOpt scores and the rewired scores; d Empirical p-values of the CellNOpt scores across the entire family of models. e The liver-PKN used by CellNOpt as initial reference network; f The model outputted by CellNOpt when using the liver-PKN as initial reference network with superimposed the frequency of inclusion of each node in a set of 1,000 models outputted by CellNopt using F-rewired versions of the liver-PKN as reference networks simulate samplings from the uniform distribution of all the possible networks with the same number of nodes and FCLs of the Interactome (Fig. 3b ). Generating 1,000 Frewired versions of the Interactome sampled each N SS required ∼ 2 hours on a 4 core 2. 4 Ghz computer with 8GB memory. Running 1,000 independent instances of BioNet using each of these F-rewired Interactome as reference network and the DLBCL dataset in input resulted into 1,000 different module solutions (rewired solutions).
For each of the nodes included in the original BioNet module solution (Fig. 3c ), we quantified the ratio of rewired solutions including them and we investigated how this quantity related to the corresponding BioNet scores (Fig. 3d ). As expected, we observed a significant correlation (R = 0. 51, p = 0. 001). In fact, as per the definition of the MSS, it is reasonable that nodes with high scores (such as, for example NR3C1 and BCL2) tend to be included in the module outputted by BioNet regardless their edges and degree in the reference Interactome. Similarly, nodes with large negative scores (such as CDC2 and JUN) are included in the module only because they link high scored nodes and it is obvious that they do not tend to be included in the rewired solutions, as in this case the way they are interlinked to other nodes is crucial.
Nevertheless, a number of nodes (such as, SMAD4, SMAD2 and PIK3R1) have modest score but tend to be included very frequently in the rewired solutions. This hints that what leads the inclusion of such nodes in the BioNet module is their high FCL. As a confirmation of this, SMAD4, SMAD2 and PIK3R1 fall over the 99th percentile when sorting all the nodes in the Interactome (and included in the DLBCL) based on their FCL (which in this case corresponds to their degree). This is a proof that the reference network provides the BioNet outputted module with a positive impact, and that at least some nodes are included in the solution because of their high FCL. When extending this analysis to the nodes of the Interactome (included in the DLBCL dataset) that are not present in the module outputted by BioNet we observed again an expected significant correlation (R = 0.
51, p < 10 -16 ), and some nodes (such as JUP, MMP2 and ITGA6) with high scores frequently included in the rewired solutions (the fact that these nodes do not appear in the BioNet outputted module is due to the sub-optimality of the used heuristic). However we also observed a large number of nodes (such as RPL13A, STK17A and IDH3A) scored high but relatively infrequently included in the rewired solutions. This hints that these nodes are penalized by their low FCL in the reference Interactome, thus proving the existence of a negative impact provided by the reference Interactome to the BioNet outputted module, and that at least some nodes are not included in the solution because of their low FCL. An indication of both these types of impacts, together with diagnostic plots and statistics would complement and complete the output of many valuable and widely used tools, such as BioNet.
Case study 2: CellNOpt CellNOpt (www. cellnopt. org) is a tool used to train logic models of signal transduction starting from a reference directed signed network (DSN) called a prior knowledge network (PKN), describing causal interactions among signaling species (obtained typically from literature), and a set of experimental data (typically phosphorylation), obtained upon various perturbatory conditions (  [23] ). CellNOpt converts the PKN into a logic model and identifies the set of interactions (logic gates) that best explain the experimental data. This is performed through a set of Bioconductor packages supporting a number of mathematical formalisms from Boolean models to ordinary differential equations. Through a built-in genetic algorithm CellNOpt identifies a family of subnetworks from the reference DSN (from now, models) together with the value of the objective function (the model score δ) quantifying at what extent each model is able to explain the experimental data (the lower this value the better is the fit of the model to the data).
As described before, a large score calculated by CellNOpt indicates a large disagreement between data and network logic behavior at the measured nodes. Therefore the distribution of the δs outputted by CellNOpt when using these F-rewired networks gives an idea of the attainable base-line performaces, which are not derived from biologically meaningful models but depend only on the FCL (signed and directed node degrees) of the original liver-PKN. Based on these considerations, here we show how BiRewire3 can be used to identify such a threshold as the maximal δ value whose deviance from expectation is statistically significant. Similarly to the previous case study, this expectation can be empirically estimated by running a large number of independent CellNOpt runs using Frewired versions of the initial reference signaling network and the same experimental data.
16 available on Bioconductor at www. bioconductor. org/packages/CellNOptR/). On each of these F-rewired liver-PKN networks and the same phosphoproteomic dataset (obtaining one rewired model per each analysis), as well as a final run using the original liver-PKN network (obtaining a family of 1000 different models). When comparing the two populations of CellNOpt scores obtained from these two analyses we observed, as expected, a notably statistically significant difference (t-test p-value < 10 -16 , Fig. 4c ), indicating that in the Frewired networks the topology of the pathways originally interlinked in the liver-PKN is actually disrupted. Subsequently, using the distribution of scores of the rewired models we computed empirical p-values for the CellNOpt scores for the entire model family outputted by the final run (making use of the original liver-PKN).
Discussion BiRewire3 is a one-stop tool to rewire in a meaningful way any type of unweighted networks (undirected, directed, and signed) currently used to model different datasets and relations in computational biology (including presence-absence matrices, genomics datasets, pathways and signaling networks) in an computationally efficient way. It represents a significant and formally demonstrated advance with respect to its previous version  [20] , whose applicability was restricted to presence/absence matrices and undirected bipartite networks. We have previously shown that, thanks to an analytically derived lower bound to the number of steps of its underlying algorithm, the computational time requirements of BiRewire3 are vastly lower than those of other similar tools, reducing from months to minutes (on a typical desktop computer) when rewiring networks with tens of thousands of nodes and edge density ranging up to 20%.
Additionally, the core algorithm underlying BiRewire3 is based on a Markov chain procedure that could be easily parallelized in future implementations, to exploit the power of modern multicore computer architectures, thus reducing these time requirements even further. Our package is available as free open source software on Bioconductor and, as we showed in our case studies, it can be easily combined into computational pipelines together with a wide range of existing bioinformatics tools aiming at integrating signaling networks with experimental data.
Conclusion We have presented a computational framework implemented in a R package that could complement existing network based tools. This will be useful for computing a wide range of constrained null models testing the significance of the solutions of these tools, and to investigate how the topology of the used reference networks can potentially bias these results. Moreover, the range of applicability of BiRewire3 goes beyond computational biology, and includes all those fields making use of tools from network theory, from operative research, to microeconomy, and ecological research (an example of the application of BiRewire application in a micro-economy and technology patent study can be found at http://arxiv. org/abs/1509. 07285).
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The aim of this study is to compare the surface soil moisture (SSM) retrieved from ESA's Soil Moisture and Ocean Salinity mission (SMOS) with the output of the ORCHIDEE (ORganising Carbon and Hydrology In Dynamic Eco-systEm) land surface model forced with two distinct atmospheric data sets for the period 2010 to 2012. The comparison methodology is first established over the REMEDHUS (Red de Estaciones de MEDición de la Humedad def Suelo) soil moisture measurement network, a 30 by 40 km catchment located in the central part of the Duero basin, then extended to the whole Iberian Peninsula (IP). The temporal correlation between the in-situ, remotely sensed and modelled SSM are satisfactory (r N 0. 8). The correlation between remotely sensed and modelled SSM also holds when computed over the IP.
This is the case of the ESA's Soil Moisture and Ocean Salinity (SMOS) mission, in orbit since November 2009, which provides estimates of salinity over oceans and of surface soil moisture over continental surfaces  (Kerr et al. , 2001). Since SMOS is mainly sensitive to near surface soil moisture (top 5 cm), it is advantageous to assimilate the satellite data in land surface models and thus derive more important estimates for deeper surface state variables such as root zone soil moisture, a direct indicator of the water available to plants  (Draper, Reichle, De Lannoy, & Liu, 2012; Muñoz-Sabater, Jarlan, Calvet, Bouyssel, & De Rosnay, 2007). This information is very relevant to improve the characterization of surface/atmosphere interactions. The large scale nature of SMOS soil moisture estimates should ensure that they are more representative of the scales simulated by land surface models and thus perform better than in-situ observations in the assimilation process.
Due to the high temporal variability of the upper 5 cm soil moisture measured by SMOS, the sampling of observations is a critical issue  (De Rosnay, 2003). Thus this study starts with a presentation of the data sets and a quantification of possible biases introduced by the sampling. After these preliminaries, we compare SMOS and ORCHIDEE SSM over the REMEDHUS (Red de Estaciones de MEDición de la Humedad def Suelo) basin, where in-situ observations are available  (Martínez-Fernández & Ceballos, 2005). The analysis of the temporal variability is then extended to the entire IP for the SMOS and ORCHIDEE data sets, where the spatial correlation of the surface soil moisture structures is also studied. Afterwards, we discuss the relations between the temporal and spatial variability of rainfall and SSM as retrieved by SMOS and simulated by ORCHIDEE: first the relation between the spectral characteristics of precipitation and SSM is analysed; then the coupled rainfall-SSM co-varying patterns are identified and studied by means of the singular value decomposition (SVD) method.
The SMOS surface soil moisture product The ESA SMOS mission was launched on November 2, 2009. Over land, the SMOS mission aims at providing surface soil moisture (originally advertised to be the top 5 cm) data at a spatial resolution better than 50 km, with a target accuracy of 0. 04 m 3 /m 3 and a repeat cycle of less than 3 days. The payload is a novel 2-D synthetic aperture radiometer equipped with 69 L-band receivers regularly distributed over a Y-shaped antenna array. This new design allows observing all pixels within a 1000 km wide field of view at a range of incidence angles (from 0 to 65°) and polarizations  (horizontal, vertical, and mixed). The SMOS soil moisture retrieval algorithm consists in matching measured and modelled (surface emission) brightness temperatures. The modelled values are functions of polarization, incidence angle, soil moisture (through the soil dielectric constant) and other physical parameters influencing land emissivity at L-band, namely land surface temperature, soil roughness, vegetation optical depth and volume scattering albedo.
Information on land-cover and soil properties (e. g. clay fraction, bulk density, field capacity and wilting point) is also used in the forward modelling. The inversion (retrieval of geophysical variables) is performed by minimizing a cost function that accounts for the weighted squared differences between modelled and measured data  (Kerr et al. , 2012). The SMOS BEC L3 v. 001 soil moisture data from January 2010 to December 2012 over the IP has been selected for this research. It is obtained by quality-filtering and re-gridding of the newest version of L2 data (v. 551); grid points affected by radio frequency interferences (RFI) and/or with soil moisture Data Quality Index (DQX) greater than 0. 07 are discarded; and a DQX-inverse weighted average is applied to bin the data from ISEA to the 25 km EASE equal-area grid.
ORCHIDEE is forced with two different atmospheric datasets in order to frame the uncertainty introduced by this boundary condition and test the possibility of using remote sensing observations to evaluate the quality of these simulations. The first forcing is the one extracted from the ERA-Interim (ERA-I) re-analysis  (Balsamo et al. , 2012; Dee et al. , 2011). The corresponding simulation will be labelled OR-ERA. This type of atmospheric forcing is known to have biases that negatively affect land-surface simulations and can be corrected  (Ngo-Duc, Polcher, & Laval, 2005; Weedon et al. , 2011). Consequently the bias corrected product WATCH Forcing Data ERA-Interim (WFDEI) is also used  (Weedon et al. , 2014). The simulation which uses this forcing will be designated OR-WFD. The two forcing datasets share the same synoptic variability for all variables.
The bias correction process affects precipitation intensity, as monthly mean precipitation and the number of wet days have been changed in order to correspond to the values given in the Climate Research Unit (CRU) compilation of observations  (Harris, Jones, Osborn, & Lister, 2014). The ERA-I data are available at the horizontal resolution of the atmospheric model used in the re-analysis, i. e. 0. 75°by 0. 75°. On the other hand, for WFDEI the re-analysis has been extrapolated to the 0. 5°by 0. 5°resolution of the CRU data sets used in the bias-correction process. Thus soil moisture was simulated by ORCHIDEE at these two spatial resolutions. The overlap period between these two forcing data sets and SMOS available data is January 2010 to December 2012 and will thus be the focus for this study.
Since both ERA-I and WFDEI forced simulations were started in January 1979, the analysis period does not suffer from any spin-up artefacts. To facilitate the comparison of soil moisture daily means, the two ORCHIDEE simulations were remapped to their nearest neighbour on the 25 km EASA equal-area grid on which the SMOS BEC L3 product is provided. This preserves the spatial structures provided by the model, which is run at the coarser resolution of the atmospheric forcing. Having all surface soil moisture estimates on the same 25 km resolution grid allows to create a thinned version of the ORCHIDEE data in which all values which do not have corresponding SMOS observations are deleted. These two versions of modelled SSM are used for analysing the impact of sampling.