dataesr/scientific-paragraphs-categorization huggingface dataset:
The considered one is a first-order Butterworth filter  [1]  with cutoff frequency of 1. 25 Hz. Step 3. Removing the residual unphysical acceleration values, keeping the consistency requirements They remove residual peaks that exceed defined thresholds (varying with speed levels). For that, they move the position of the vehicle when the peak in acceleration appears in order to fulfill the thresholds. In order to prevent inconsistency, a 5th-degree polynomial interpolation with constraint on the space traveled plus minor conditions was applied on a 1s window around the peak points. Step 4. Cutting off the high-and medium-frequency reponses generated from step 3 This step is the same as the step 2 but using the results of the step 3. The methodology of  [3]  seems very specific to the NGSIM dataset, or at least some trajectory dataset, and by extension can not be easily applied to others.
For using the algorithm on other trajectory datasets, their method requires some fine-tuning of the parameters. As explained in the main text, the 1714 observation units from the I-80 dataset, available in the NGSIM study, have been recorded at moments of the day when traffic is evolving, it goes from fluid to dense traffic. Therefore, we consider that there are three groups in the data: a first group corresponding to a fluid (high-speed) traffic, a second one for in-between fluid and dense traffic, and a third groups corresponding to the dense (low-speed) traffic. Our local regularity approach, and the kernel smoothing induced, are applied for each group separately. The three group clustering was performed using a Gaussian mixture model estimated by an EM algorithm initialized by hierarchical model-based agglomerative clustering as proposed by Fraley and Raftery  [2]  and implemented in the R package mclust  [7].
E. 2 Household Active Power Consumption The Household Active Power Consumption dataset is part of the Monash University, UEA, UCR time series regression archive  [9]  and was sourced from the UCI repository 1. The data measures diverse energy related features of a house located in Sceaux, near Paris every minute between December 2006 and November 2010. In total, its represents around 2 million data points. These data are used to predict the daily power consumption of a house. Here, we are only interested in the daily voltage. The dataset contains N 0 = 746 time series of µ = 1440 measurements. Figure  10a  presents a sample of five curves from this dataset. The estimation of the local regularity H t 0 , plotted in Figure  10b , is around 0. 5 with K 0 = 73.
E. 3 PPG-Dalia The PPG-Dalia dataset is also part of the Monash University, UEA, UCR time series regression archive  [9]  and was also sourced from the UCI repository 2. PPG sensors are widely used in smart wearable devices to measure heart rate  [6]. They contain a single channel PPG and 3D accelerometer motion data recorded from 15 subjects performing various real-life activities. Measurements from each subject are segmented into 8 second windows with 6 second overlaps, resulting in N 0 = 65000 time series of µ = 512 features. Here, we are interested in the PPG channel. A sample of five curves is plotted in Figure  11a. The estimation of the local regularity H t 0 is also around 0. 5 (see Figure  11b ) with K 0 = 25.
Localization of the NLS in the Tat BD The most common type of NLS, classical NLS (cNLS), is imported into the nucleus via interaction with importin-α. The most characterized monopartite cNLS has a consensus sequence of K(K/R)X(K/R), ensuring the optimal interaction with importin-α  (Lange et al. 2007 ). The Tat BD contains nine amino acids ( 49 RKKRRQRRR 57 ) and thus is substantially longer than necessary for binding to importin-α. We used several software progrаms to predict the potential NLS(s) in the BD. NLStradamus  (Nguyen Ba et al. 2009) , seqNLS  (Lin and Hu 2013) , NucPred  (Brameier et al. 2007 ) and cNLS Mapper  (Kosugi et al. 2009 ) predicted an NLS that roughly corresponded to the BD (fig. 2A ), while PSORT II  (Horton et al. 2007 ) predicted three NLSs ( 49 RKKR 52 , 50 KKRR 53 and 55 RRRP 58 ) overlapping the Tat BD.
2000)  and thermodynamic  (Hodel et al. 2001 ) studies demonstrated that a monopartite cNLS requires a lysine in the P1 position, followed by basic residues in positions P2 and P4. However, in three importin-α/NLS PDB structures obtained for viral proteins (beak and feather disease virus capsid protein (PDB ID 4HTV), HIV-1 viral protein R (Vpr) (PDB ID 5B56), and influenza A virus nucleoprotein (NP) (PDB ID 5V5O)), an arginine residue was substituted for a lysine in the P1 position (fig. 3A ; supplementary fig. 6 ). We obtained a consensus logo structure for the region that directly interacted with importin-α. The P1 position was always occupied by lysine in eukaryotic proteins (fig 4B), while the presence of arginine residues in the P1 position of some viral NLSs produced a slightly different consensus sequence of the viral NLS ((K/R)(K/R)X(K/R)) (fig.
Overlapping of NLSs and NoLSs Several reports previously described overlapping NLS(s) and NoLS(s) (for discussion, see  (Scott et al. 2010 )); however, a comprehensive mapping of both NLSs and NoLSs has never been performed. We used the datasets of experimentally established NLSs (supplementary tables S3 and S4) and predicted NoLSs  (Scott et al. 2011 ). In addition, we used a dataset of experimentally established NoLSs for which we predicted NLSs using the NLStradamus program (supplementary table  S5 ). Both prediction strategies demonstrated that NLSs and NoLSs more frequently overlapped in viral proteins than in human proteins (fig. 8A ). Estimates of the minimal content required for NoLS function vary. According to one report, a protein region can function as an NoLS if it contains more than either three arginine residues or five lysine residues  (Musinova et al.
Molecular docking Docking was performed through two different approaches. Full-length coarse-grained docking of the SGRKKRQRRR peptides was performed with standalone CABS docking  (Kurcinski et al. 2015). The importin-α structure with PDB ID 5SVZ was cleared of the NLS peptide and water molecules. The default parameters for sampling efficacy (simulation cycles 50) were used, and no additional restraints were applied. Full-atom docking of tetrapeptides was performed using the importin-α structure with PDB ID 5SVZ (a 30 Å x 45 Å x 45 Å docking box with the center at 80. 559, 21. 365, 100. 184 was used to cover both NLS sites). Docking was performed with the Qvina-W package  (Hassan et al. 2017) , which implements the AutoDock Vina  (Trott and Olson 2010)  scoring function optimized for blind docking.
NLS/NoLS bioinformatic analysis We used 106 experimentally annotated NLSs of 88 viral proteins and 269 experimentally annotated NLSs of 228 human proteins (supplementary tables S4 and S5). The dataset of the NLSs of human proteins was published elsewhere  (Lisitsyna et al. 2020)  The presence of potential NoLSs in the human and viral protein datasets with experimentally determined NLSs was predicted by the NOD server  (Scott et al. 2010) , and the putative NLSs of the proteins in the NoLS dataset were predicted by NLStradamus  (Nguyen Ba et al. 2009 ). The diversity and number of clusters of positive amino acids in an NLS were evaluated by custom R-script. The cluster was defined as a region in the NLS in which arginine residues and/or lysine residues/histidine residues were interspersed with another amino acid (there may be several such gaps, but each gap was not to be greater than one amino acid).
, and NLSs described in recent papers were included (supplementary tableS6). All NLSs of viral proteins were found via a search of UniprotKB database or published papers (supplementary tableS2). The NoLS dataset consisted of 24 experimentally determined NoLSs in 23 viral proteins and 71 NoLSs in 65 animal proteins (supplementary tableS5). (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is.
Acknowledgements We would like to thank  S. Dokudovskaya ,  P. V. Lidsky ,  A. A. Zharikova  and  A. A. Mironov  for stimulating discussions and valuable suggestions, and  D. M. Potashnikova  and  M. A. Tikhomirova  for technical support. A. O. Z. is grateful to  Dr. G. Armeev  for the comments on the quality assessment of crystal structures. We are grateful to  Dr J. Borowiec  for EGFP-nucleolin plasmid. The following reagents were obtained through the  NIH AIDS Reagent Program, Division of AIDS, NIAID, NIH :  HIV-1 HXB2   GST-Tat Expression Vector  ( GST-Tat 1 (86R )) from  Dr. Andrew Rice  (cat#  2367 ) and HIV-1 LTR lacZ Reporter Vector (pHIVlacZ) from  Dr. Joseph Maio  (cat # 151 ). Docking experiments were carried out using the equipment of the shared research facilities of  HPC computing resources at Lomonosov Moscow State University.
, and NLSs described in recent papers were included (supplementary tableS6). All NLSs of viral proteins were found via a search of UniprotKB database or published papers (supplementary tableS2). The NoLS dataset consisted of 24 experimentally determined NoLSs in 23 viral proteins and 71 NoLSs in 65 animal proteins (supplementary tableS5). (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is bioRxiv preprint doi: ; https://doi. org/10. 1101/2021. 04. 20. 440437 this version posted April 20, 2021. The copyright holder for this preprint. CC-BY-NC 4. 0 International license made available under a 18.
, 2016). Thus, integrated hydrological-hydraulic approaches are required (e. g. ,  Nguyen et al. , 2016; Hocini et al. , 2020). Such approaches are now enabled by the increasing informative richness of multi-source datasets provided by high-resolution hydrometeorology and satellite remote sensing in complement to in situ measurements. Nevertheless, reaching high-resolution accuracy and computational efficiency for large-scale applications remains a difficult challenge because of multi-scale non-linear hydrodynamic processes over large computational domains and multiple uncertainty sources. These uncertainties could be reduced by the optimal combination of models and multi-source datasets, including highresolution maps and spatially sparse in situ flow measurements but also the growing amount of earth observation data provided by new generations of satellites, drones and sensors (e.
, 2010). Still, the underlying issue of the adequate combination of numerical models and multi-source data that is heterogeneous in nature and of varied spatio-temporal resolutions remains. In order to exploit this wealth of hydrological and hydraulic information, the complexity of integrated models has to be adapted to observation types and patterns, while retaining a good representation of spatial and temporal river network variabilities and relatively low computational costs over entire catchments, i. e. , large computational domains. The challenging search for consistency between such datasets and models, generally involves the calibration of high-dimensional multi-variate parameter vectors, and corresponding inverse problems are often ill-posed or even ill-conditioned -see discussions about "equifinality"  (Bertalanffy, 1968; Beven, 2000)  in hydraulic inverse problems in  Garambois and Monnier (2015) ,  Larnier et al.
"Max order" refers to the maximum demonstrated scheme order. "Sources available" means that the source code is freely accessible, either through direct download or upon request. (Brisset et al. , 2018)  tional numerical model, and a sequential data assimilation technique is performed for correcting water level forecasting. A summary of some established 1D and 2D numerical hydraulic models, external coupling methods and optimizationassimilation methods is presented in Table  1. Note that largescale modeling of river routing-flooding is still generally performed with simplified models and/or external couplings, while enhancing the computational efficiency and realism of multi-dimensional models is important in the field of hydrological-hydraulic modeling. Furthermore, it is essential to investigate state-parameter estimation, from multisource datasets, for improving the accuracy of hydrodynamic variables estimated with such models.
Variational data assimilation (VDA) is an adequate method to tackle such highdimensional and multi-variate hydrodynamic inverse problems from heterogeneous datasets  (Lai and Monnier, 2009; Monnier et al. , 2016; Brisset et al. , 2018; Larnier et al. , 2020; Garambois et al. , 2020; Pujol et al. , 2020; Malou et al. , 2021). One can identify DassFlow2D  (Monnier et al. , 2016)  as the only 2D full hydraulic model with a second-order solver with accurate wet-dry front treatment, parallel computation and adjoint-based variational data assimilation capabilities. This work focuses on the following scientific problems: (i) the effective representation of river network flows through multi-D basin-scale hydraulic-hydrological numerical modeling, (ii) the inference from multi-source data of spatiotemporally distributed river channel parameters and inflows through a VDA approach, and (iii) the upstream informational feedback of river network observations to integrated hydrological models.
The present study details upgrades to the DassFlow variational data assimilation framework (DassFlow2D-V2, see  Monnier et al. , 2016)  in the form of (i) a new multi-D hydraulic computational code relying on an internal mesh coupling and a single finite-volume solver and (ii) the integration and differentiation of a GR4 hydrological module, (iii) with the implementation of a regularization strategy based on  Larnier et al. (2020) , leading to DassFlow2D-V3. One strength of the DassFlow platform is its variational data assimilation (VDA) algorithm. It can solve highdimensional optimization problems with descent algorithms using gradients computed with the adjoint model. The adjoint model is obtained via the automatic differentiation tool Tapenade  (Hascoet and Pascual, 2013). This allows the sihttps://doi.
org/10. 5194/gmd-15-6085-2022 Geosci. Model Dev. , 15, 6085-6113, 2022 multaneous inference of numerous model parameters, which may be needed over large domains. Let us remark that this is not the case for stochastic methods, where computational cost can increase dramatically with the number of sought parameters. The variational method also enables tackling multivariate data assimilation problems, i. e. , with composite control vectors (bathymetry, friction, boundary conditions, hydrological parameters), given multi-source datasets, heterogeneous in nature, and spatio-temporal resolutions (see, e. g. ,  Brisset et al. , 2018 , Larnier et al. , 2020 , Pujol et al. , 2020 , and Malou et al. , 2021). To apply these unique capabilities at the scale of a river network, there is a need to develop a model with both sufficient complexity and a reasonably low computational cost.
, 2018)  in a semi-distributed setup. The resulting integrated tool chain has been differentiated and via the VDA algorithm enables information feedback within the whole computational domain (basin) and especially from downstream to upstream. The source code and synthetic cases presented in this study are available online (https://doi. org/10. 5281/zenodo. 6342723, Pujol et al. , 2022) , and the current updated version of the code is available upon simple request (http://www. math. univ-toulouse. fr/DassFlow, last access: 27 June 2022). The remainder of this article is organized as follows. In Sect. 2, the modeling hypothesis, the computational resolution and inverse methods are detailed. In Sect. 3, the multi-D coupling scheme is validated on a series of academic cases and several academic and real-like inference setups are investigated.
It consists in the Riemann fluxes being calculated for each cell K i using the state from the same corresponding Ke cell over an interface of length m e i. In the end, the flux crossing the interface e = ∪e i is equal to the sum of the fluxes crossing the e i interfaces: F e = i=1. n m e i F e i U n K i , U n Ke , n e i ,K. This type of internal interface has been implemented in the numerical solvers from  Monnier et al. (2016)  in the Dass-Flow platform, which includes a solver with second-order accuracy in space. This solver, developed in  Couderc et al. (2013)  and  Monnier et al. (2016) , is accurate and robust for wet-dry front propagations and fully applies in the present context. Note that the lateral distribution of variables across the 1D-2D interface is not constrained. The source code and synthetic cases are available upon simple request.
The widely used, parsimonious and robust conceptual hydrological model GR4  (Perrin et al. , 2003) , in its state-space version from  Santos et al. (2018) , was chosen in this study for parsimony and differentiability reasons. The original lumped hydrological numerical model has been deployed in a semidistributed manner in the DassFlow framework. F e = i=1. n m e i F e i U n K,i , U n Ke , n e i ,K. The model is composed of two non-linear stores for production (soil moisture accounting) and routing and a Nash cascade composed of a series of linear stores replacing the unit hydrograph from  Perrin et al. (2003). Being a set of ODEs with explicit dependency to parameters, this hydrological model (Eq. 4, see detailed GR4 equations in Appendix C) is differentiable. Moreover, the Fortran code is differentiable with the automatic differentiation tool Tapenade  (Hascoet and Pascual, 2013).
Inverse algorithm: variational data assimilation Given spatio-temporal flow observables, provided by in situ and airborne sensors for instance, the inverse algorithm consisting in variational data assimilation (VDA) aims at estimating the unknown or uncertain "input parameters" of the hydrological-hydraulic chain composed of a hydraulic model, presented in Sect. 2. 2, and a hydrological model, presented in Sect. 2. 3. Detailed know-how on VDA may be found in online courses (see, e. g. ,  Bouttier and Courtier, 2002, and Monnier, 2014). This group of VDA algorithms relies on cost gradients, i. e. , variations, here computed by the adjoint model, to minimize a misfit to the observed reality (see Fig. 5 ). The adjoint model of the whole toolchain composed of DassFlow multi-D with GR4 modules is obtained by automatic differentiation with the Tapenade engine (Hascoet and Pascual, 2013).
15 ) and two are located in the Bayonne area (Pont-Blanc and Lesseps; blue points in Fig. 15 ). At the four upstream points of the modeled river network, four sub-catchments are modeled with four lumped hydrological models (Sect. 2. 3). Their drainage areas are about 7811, 842, 2480 and 2464 km 2. The hourly discharge has been extracted from the HYDRO 2 database, while the rainfall data from the radar observation reanalysis ANTILOPE J+1, which merges radar and in situ gauge observations, is provided by Météo France. The interannual temperature data are provided by the SAFRAN reanalysis by Météo France and then used to calculate the potential evapotranspiration using the Oudin formula  (Oudin et al. , 2005). The rainfall and potential evapotranspiration are at a spatial resolution of a 1 km 2 square grid and are processed at an hourly time step.
Then, a multi-D model is built based on the 1D-like-only model, with the addition of a 2D mesh of a floodplain (Fig. 16a ). On the 1D-like-only model, the goal is to analyze 1Dlike signal propagation representation at a low computational cost. The Adour 1D-like model is built similarly to the Garonne 1D-like model, using DEM data to determine minor bed bank line placement and build the quadrangular cells. Bathymetry comes from 25 × 25 m DEM data, aggregated from fine lidar data from public databases, extracted at each cell. This rough approximation is sufficient to show the potential of the DassFlow assimilation tool chain for a large-scale river network. This 1D-like-only model contains 1409 cells. A 24 h simulation runs in around 13 s, using uncalibrated parameter estimates. Then, a multi-D model is obtained: the existing 2D mesh from a Telemac model is coupled to a 1D-like mesh, similarly to the reference Telemac-Mascaret model from the regional flood forecast center SPC-GAD.
The depth-dependent friction law helps to reduce misfits across flow regimes. 6. High-resolution simulations of real flows can be obtained on complex river networks including floodplains and confluences with reduced simulation costs. To our knowledge, the present numerical tool is the first one proposing large-scale multi-D river network modeling with VDA capabilities. This new toolchain opens the way for the resolution of large-scale high-dimensional hydrologicalhydraulic inverse problems that can be considered given constraints from multi-source datasets. The methods for direct and inverse modeling can be applied at multiple spatial scales including with a fine resolution (imposing finer calculation time steps to respect the Courant-Friedrichs-Lewy (CFL) condition in the forward hydraulic model).
Building and constraining the models is, however, dependent on data availabil-ity and the informative content of observations, which may be linked to the spatial scale. Short-term perspectives will aim to tailor the data assimilation algorithm to perform complex data assimilation experiments at basin scale using various multi-source datasets. To be actually operational, improvements pertaining to the construction of 1D-like models from global public databases are needed to deploy the multi-D approach to a large number of river networks. Coupling is ongoing with the SMASH spatially distributed hydrological platform  (Jay-Allemand et al. , 2020; Colleoni et al. , 2021) , on which the French flash flood warning system VigiCrues Flash  (Garandeau et al. , 2018)  is based. Note that the addition of lateral flows (surface and subsurface runoff) would simply consist in imposing additional inflows on the boundary of the river/floodplain domain, which is numerically identical to the upstream flows imposed and inferred here (see such lateral coupling in 1D with inferences from sparse satellite altimetry data in  Pujol et al.
Acknowledgements. This study was rendered possible by the adaptation of covariance matrices in the inverse algorithm from the DassFlow1D algorithm (Larnier et al. , 2020) by  Lilian Villenave  ( INRAE Aix-en-Provence ) and the implementation of final tricks in Perl scripts for adjoint post-processing in DassFlow by  Kévin Larnier  ( CS Group Toulouse ). The authors greatly acknowledge  Pascal Finaud-Guyot  ( HydroSciences, University of Montpellier ) for fruitful discussions related to hydraulic solvers. They warmly thank  Laurent Dieval  from  SPC-GAD France , the operational flood forecasting service for the Gaves-Adour-Dordogne river networks, for providing data for the Adour case and also for interesting discussions. They also thank  Robert Mosé  ( ICUBE, University of Strasbourg ), the PhD director of  Léo Pujol.
L. Pujol et al. : Multi-dimensional hydrological-hydraulic model    Code and data availability. The current DassFlow code is available on demand at https://www. math. univ-toulouse. fr/DassFlow/ download. html (last access: 27 July 2022). The exact version of the model used in this article is archived on Zenodo (https://doi. org/10. 5281/zenodo. 6342723, Pujol et al. , 2022) , as are input data needed to run the main direct/inverse simulations.