dataesr/scientific-paragraphs-categorization huggingface dataset:
VII. Conclusion and future work This work provided the IRS mobility contribution by equipping specific buses designated by the IRS to provide a communication relay with the BS for surrounding moving vehicles. In addition, this work provides the optimization framework for selecting the best IRS-bus. The performance of the proposed models and strategies has been validated based on the bus and taxi dataset in the city of Rome (Italy). There are two proposed approaches to solve this optimization problem. Using MILP gives optimal results but with a very long processing time costs. That is why, an important contribution of this paper is the use of a LSTM-based encoder and decoder to approximate the behaviour of the MILP. The use of a LSTM-based encoder and decoder enhanced the taxi location detection behavior on a regular LSTM.
Although its does not give the optimum, our approximation is very good while extremely efficient in terms of execution speed. LSTM processing time takes hours for the training but a few seconds for the execution once trained, while MILP takes several days to go through the same input dataset to optimize an area like downtown of Rome. The only drawback to the LSTM is that it gets suboptimal results from MILP but it is acceptable when we hit the MSE of 0. 019. So, with our approach, we radically change the order of magnitude of the time needed to solve the IRS selection problem. Another novelty in this work is an MDP approach for IRS selection, which gives high result accuracy and low processing time for IRS bus prediction while allowing easily targeting session-level performance criteria. This method complement the first one by allowing to easily consider e.
Numerical results In this section, we show the performance and limitation of the proposed method by • presenting numerical convergence and CPU timing of our Monge-Ampère solver in 2D and 3D, • showing examples of two-dimensional adaptive mesh generation, • showing the limitation of using the monitor function with a variation near the boundary. Our numerical code is written in Python, where intensive computations parts were accelerated using Pyccel  [56] , a static compiler for Python, based on Fortran and C. A laptop with a quad 2. 6 GHz Intel Core i7, on ubuntu OS is used throughout the numerical tests. Wherever used, the notation #𝑐𝑒𝑙𝑙𝑠 refers to the number of cells in each direction.
Acknowledgments We warmly thank  G. Latu ,  G. Dif-Pradalier ,  V. Grandgirard  ( CEA-Cadarache ),  B. Nkonga  ( University of Nice ),  G. Huysmans  ( Iter Organization ),  B. Mourain  ( INRIA Sophi-Antipolis ) and  A. Buffa  ( EPFL ), for useful discussions and advices. This project started during the ANEMOS-ANR and EFDA-fellowship and  IPAM long program   Computational Methods in High Energy Density Plasmas  in 2012.
Satellite altimetry data are useful for monitoring water surface dynamics, evaluating and calibrating hydrodynamic models, and enhancing river-related variables through optimization or assimilation approaches. However, comparing simulated water surface elevations (WSEs) using satellite altimetry data is challenging due to the difficulty of correctly matching the 10 representative locations of satellite altimetry virtual stations (VSs) to the discrete river grids used in hydrodynamic models. In this study, we introduce an automated altimetry mapping procedure (AltiMaP) that allocates VS locations listed in the HydroWeb database to the Multi-Error Removed Improved Terrain Hydrography (MERIT Hydro) river network. Each VS was flagged according to the land cover of the initial pixel allocation, with 10, 20, 30, and 40 representing river channel, land with the nearest single-channel river, land with the nearest multi-channel river, and ocean pixels, respectively.
Thus, allocating VSs to a river network using the proposed AltiMaP framework improved our comparison of WSEs simulated by the global hydrodynamic model to those obtained by satellite altimetry. The AltiMaP source code (https://doi. org/10. 5281/zenodo. 7597310) (Revel et al. , 2023a)    and data (https://doi. org/10. 4211/hs. 632e550deaea46b080bdae986fd19156)  (Revel et al. , 2022)  are freely accessible online 25 and we anticipate that they will be beneficial to the international hydrological community.
This 105 study introduces the concepts and an overview of the satellite altimetry allocation algorithm; the source code (https://doi. org/10. 5281/zenodo. 7597310,  Revel et al. , 2023a)  and dataset prepared for HydroWeb using AltiMaP for use with MERIT Hydro (https://doi. org/10. 4211/hs. 632e550deaea46b080bdae986fd19156,  Revel et al. , 2022)  are provided.
Satellite altimetry data Although satellite altimetry missions were developed for ocean surface observations, they have increasingly been applied to 110 observe lakes and rivers  (Abdalla et al. , 2021; Calmant et al. , 2008; Calmant and Seyler, 2006; Yang et al. , 2022). Several agencies have already processed their original satellite altimetry data and produced data archives for studying WSEs, including the HydroWeb  (Crétaux et al. , 2011; Santos da Silva et al. , 2010) , Hydrosat  (Tourian et al. , 2016 (Tourian et al. , , 2022)) , Database for Hydrological Time Series of Inland Waters (DAHITTI;  Schwatke et al. , 2015) , Global Reservoirs and Lakes Monitor (G-REALM;  Birkett and Beckley, 2010) , Copernicus Global Land Service (CGLS;  Calmant et al. , 2013; Crétaux et al. , 2011), 115  River & Lake  (Birkett et al.
Hydrography data 120 An accurate flow direction map is essential for simulating realistic surface water dynamics at the global scale. The river network used in this study is a 3² flow direction map derived from the MERIT DEM  (Yamazaki et al. , 2017)  and water body datasets including the Global 1² Water Body Map (G1WBM;  Yamazaki et al. , 2015) , Global Surface Water Occurrence (GSWO;  Pekel et al. , 2016) , and OpenStreetMap, which are referred to as MERIT Hydro  (Yamazaki et al. , 2019). The 3² MERIT Hydro flow direction map was used to determine whether VSs were located on land, river, or ocean pixels. The 125 allocation procedure for the higher-resolution flow direction map is described in Section 2. 3.
AltiMaP variable identification The AltiMaP variables provided for each VS are listed in Table  2 ; the full dataset is provided in https://doi. org/10. 4211/hs. 632e550deaea46b080bdae986fd19156  (Revel et al. , 2022). The data primarily includes variables 180 related to VS metadata, VS allocation to the MERIT Hydro, and VS mapping to a coarse-resolution river network (e. g. , global 6¢). The VS metadata consists of the VS ID, name, longitude, latitude, and satellite name. Important parameters for VS allocation that are related to the MERIT Hydro river network can also be calculated for other river network datasets, by flagging and allocating VSs as described in Section 2. 3, and then adding 100 to the flag of any VS that is biased (Section 2. 4). The distance from a VS mapped to a river centerline to the unit catchment river mouth is an important parameter for understanding 185 differences in water surface dynamics between simulated and satellite altimetry observations.
The best and second-best candidate locations for VSs on the MERIT Hydro river centerline (10° × 10° grid) are also reported, along with their geometric distances from the VS location; for single-channel rivers, these data are not available. The river width at each VS location  The AltiMaP dataset produced allocation locations for 12,523 VSs worldwide that are listed in the HydroWeb database. In this section, we discuss the characteristics of VS flags and conditions that can lead to considerable bias in satellite altimetry compared to the MERIT DEM. 200.
Code availability The AltiMaP algorithm was published in https://doi. org/10. 5281/zenodo. 7597310  (Revel et al. , 2023a)  and is available for noncommercial use. The CaMa-Flood source codes are also available (https://github. com/global-hydrodynamics/CaMa-305 Flood_v4) under the Apache 2. 0 license.
Relapse-free survival was calculated from the diagnosis date to relapse date or the last follow-up date for patients who did not relapse. The Kaplan-Meier estimator was used to generate relapse-free survival probability curves and they were compared using log-rank tests. The Cox model was used to estimate relative risks of relapse based on potential prognostic variables. Variables associated with relapse with a statistical threshold of less than 20% were included in the models, except for variables for which more than 50% of the data was missing. Stata software version 14. 2 (StataCorp) was used for analyses. A total of 274 patients with AAV were included in this study, of which 147 (53. 6%) were male and 133 (48. 5%) had GPA. PR3-ANCA positivity was observed in 81% GPA patients, while 76.
DSFU-Net was trained on 198 421 samples of simulated diffuse scattering data and performed extremely well on the unseen simulated validation dataset in this work. On a real experimental example, DSFU-Net successfully reproduced the two components with a quality sufficient to distinguish between similar structural models based on the form factor and to refine short-range-order parameters, achieving values comparable to other established methods. This new approach could streamline the analysis of diffuse scattering as it requires minimal prior knowledge of the system, allows access to both components in seconds and is able to compensate for small regions with missing data. DSFU-Net is freely available for use and represents a first step towards an automated workflow for the analysis of singlecrystal diffuse scattering.
The latter two are most commonly used because they are the most generalisable; however, the modelling process is very challenging, being highly sensitive to the inputs, either of the disorder model or the parameterization of the algorithm. The development of the 3D-ÁPDF method  (Weber & Simonov, 2012)  and the Yell program  (Simonov et al. , 2014b)  allows for the direct refinement of local correlations in real space, but the consequent necessity of using a Fourier transform requires careful measurement and pre-treatment of the scattering data. While analytical approaches are limited in their applicability, they can provide a complete description of disorder for certain systems. Analytical models allow the diffuse scattering to be split into its constituent components  (Krivoglaz, 1996) , meaning that each one can be analysed separately, greatly simplifying the problem.
, 2018; Hao et al. , 2023; Liu et al. , 2022) , fill in gaps in data collected on area detectors  (Chavez et al. , 2022) , and solve simple protein structures from single-crystal diffraction  (Pan et al. , 2023). Variational autoencoders have been applied to elucidate the phase composition of thin films from scattering data  (Banko et al. , 2021) ; find structure-property relationships, e. g. band gaps, from powder diffraction data  (Lee et al. , 2022) ; and even predict new structures with specific band gaps  (Ren et al. , 2022). These are all examples of how neural networks can learn to extract a wide range of crucial underlying features of a dataset given appropriate training. In this context, deep-learning methods are well suited to solving the issue of decomposing diffuse scattering data into I SRO and I FF.
Since our ultimate goal is to translate input images (reconstructed planes of diffuse scattering) into topologically related images, we opted to apply a Pix2Pix generative adversarial network (Pix2PixGAN)  (Isola et al. , 2018) , which has demonstrated its strength in a variety of image-processing tasks, such as in converting satellite imagery to digital road maps. This article presents the curation of a large simulated training dataset; the design, training and validation of a tailored Pix2PixGAN; and its subsequent successful application to a real experimental example.
Creating a dataset Our Pix2PixGAN required both input scattering data and the corresponding ground truth (GT) I SRO or I FF output for training. A typical problem such as this requires tens of thousands of samples for adequate training and to ensure that the network will be generalisable to unseen problems. However, the amount of available data on real systems where similar analysis has been performed is extremely small  (Schmidt & Neder, 2017; Chodkiewicz et al. , 2016). It was, therefore, necessary to use a simulated dataset to train the networks. A mathematical description of the two components is given below. For a crystal with one disordered site per unit cell, occupied by either molecule A or B (a molecule could also be an atom or molecular fragment), the I FF (Q) component of the diffuse scattering comes from the difference in molecular form factors between A and B: I FF ðQÞ ¼ Nm A m B jF A ðQÞ À F B ðQÞj 2 ; ð1Þ where N is the number of unit cells, and m A and m B are the average concentrations of A and B.
F A (Q) is the molecular form factor of molecule A, equal to F A ðQÞ ¼ P N mol i f i ðQÞ expðiQx i Þ; ð2Þ where N mol is the number of atoms in the molecule; x i and f i (Q) are the atomic position, in Cartesian coordinates, and atomic form factor of atom i, respectively; and Q is the scattering vector in units of A ˚À1. The chemical SRO component of the diffuse scattering is given by I SRO ðQÞ ¼ P v v cosðQvÞ; ð3Þ where v is the intermolecular vector between two sites in the crystal and the sum is over all possible vectors. The term v is the Warren-Cowley SRO parameter  (Warren et al. , 1951)  for v, defined as v ¼ 1 À P AB v m A m B ; ð4Þ with P AB v equal to the pair probability of finding a molecule of type B at a vector v from the molecule A. The overall diffuse scattering is given by the product: I D ðQÞ ¼ I FF ðQÞI SRO ðQÞ: ð5Þ To obtain a sufficiently general dataset that encompasses all the factors that affect both components of the diffuse scattering, we simulated the scattering of many different pairs of molecules [F A (Q), F B (Q)] distributed on a range of lattices (v) with varying concentrations (m A , m B ) and pair probabilities (P AB v ).
To collate a list of A and B species, we extracted all examples from an online molecular-fragment library  (Guzei, 2014) , excluding those that were too similar, amounting to a diverse set of 58 molecules. A further four single atoms were added to the list as well as eight variations on the perovskite unit cell to include at least some extended structure types in the dataset. Forty-three of the molecules were randomly rotated about the Cartesian axes to expand the dataset further. Molecules were grouped according to their size and shape; details for this whole procedure are provided in Section 1. 1 of the supporting information. A small selection of molecules in each group was set aside to be included in a validation dataset of roughly 5-10% the size of the training dataset to test the network's generalizability.
Within each group, a list of molecule pairs was made using all possible combinations, resulting in a training dataset of 1049 pairs of molecules and a validation set of 98 pairs. For the SRO component, lists of the Warren-Cowley SRO parameters for each intermolecular vector (up to a certain cutoff, see Section 1. 3 of the supporting information), consistent with the concentrations of A and B, were generated. Since the SRO parameters, v in equation (3), are highly interdependent, it is not possible to just use random values to give a realistic configuration. Instead, we specified three target parameters,  [001]  ,  [010]  and  [100]  , along each crystallographic axis, and generated an atomic configuration consistent with these values using an MC simulation (further information can be found in Section 1.
We therefore supplemented the dataset with samples exhibiting such behaviour via an alternative approach. The values of the SRO parameters were defined using the damped oscillator function: x ¼ A expðÀdxÞ cosð!xÞ; ð7Þ where x represents the set of symmetry-equivalent interatomic vectors, taking integer values from 1 denoting the nearestneighbour shell to which the set of vectors belongs. A is the amplitude, d is a decay constant and ! is the frequency, with values varying randomly in the ranges 0. 6-1. 5, 0. 1-1. 2 and 0-1, respectively. These ranges were chosen to keep the maximum values of between À1 and 1, and to ensure that they decayed to zero before the last shell of neighbours. The concentration of each molecule was held constant at 0. 5. This produced a further 3864 sets of correlation parameters to use with molecules on hexagonal systems and 10 024 for tetragonal/cubic systems (equivalent to 14 additional disorder models per molecule pair).
We also considered the kind of experimental artefacts that could be present in real data. For example, reconstructed planes of diffuse scattering are not perfectly square and might contain dead zones from detector module gaps or masks. Such instrumental artefacts were extracted from five real singlecrystal test datasets collected on BM01 at SNBL, ESRF. Each one was reconstructed in Meerkat  (Simonov, 2019)  on a 256 Â 256 Â 256 grid, and the areas where the scattering was equal to zero were extracted. Having prepared lists of molecule pairs, SRO coefficients and artefacts, the complete training and validation datasets were generated using the following steps. For each molecule pair: (1) A set of SRO parameters and A/B concentrations was randomly selected from the pre-computed list, and the lattice parameters of the model were recalculated based on the sizes of A and B, their respective concentrations and assuming Vegard's law.
This examines the topological uniqueness of each sample and removes redundant planes, as too many such samples would result in our network overfitting and developing bias. (6) The square roots of the remaining scattering planes were taken to emphasize low-intensity features, and they were each normalized between À1 and 1 (as opposed to normalizing by the most extreme samples). This normalization was performed to avoid any bias arising from scaling and had the benefit of not minimizing the importance of any individual sample owing to a smaller scaling factor. (7) Each sample was multiplied by a randomly selected artefact plane. Regions where artefacts were present became the lower bound of À1, while everywhere else retained its previous intensity value. The final training dataset thus comprised 1049 molecule pairs, each with 28 sets of SRO parameters.
Two-hundred scattering planes were generated for each molecule pair (144 from MCgenerated SRO models and 56 from symmetry-restricted models), totalling 209 800 data samples. Subsequently, 5. 4% of samples were deemed not unique as a result of the Wasserstein distance check, reducing the total number of samples to 198 421. For the validation set, there were 98 molecule pairs, each with 12 MC-generated SRO models. Twelve scattering planes were calculated per model, giving 14 112 samples. This was reduced by the Wasserstein distance check, leaving 12 607 final validation samples.
Network construction A Pix2PixGAN  (Isola et al. , 2018)  is based on a GAN, a class of deep-learning frameworks developed by  Goodfellow et al. (2014). GANs comprise two neural networks: a discriminator, D, and a generator, G. The goal of D is to estimate the probability that any input sample belongs to the training data distribution, y $ p d (y). In other words, it is trained to correctly guess whether a given I FF (Q) sample is associated with the pool of I FF (Q) images. In contrast, G takes a latent variable z $ p z (z) and attempts to learn p d , i. e. the underlying features that describe I FF (Q), such that it can faithfully produce a new but realistic image. The two are trained in an adversarial manner, where D aims to label the training samples as real and those from G as fake, while G tries to trick the discriminator into believing its samples are real.
The term E represents the expectation value. G in a Pix2PixGAN differs from a conventional GAN by also employing a pixelwise L1 loss (equivalent to the pixel-wise mean error) between the GT and generated output: L L1 ðGÞ ¼ E x;y GT ;z y GT À Gðx; zÞ Â Ã : ð9Þ Thus, the loss for each of the parallel Pix2PixGANs can be written as LðGÞ ¼ arg min G max D L GAN ðG; DÞ þ L L1 ðGÞ; ð10Þ where we took as 100, following  Isola et al. (2018). G and D had their weights and biases frozen when training their respective opponent. For the additional training stage that used the output from the I FF (Q) generator as auxiliary information to the optimization of the I SRO (Q) generator, and vice versa, we multiplied the output of G SRO and G FF and calculated the smooth L1 loss between this and the GT: L L1Smooth ðG FF ; G SRO Þ ¼ E x; y GT ;z ½0:5jy GT À Gðx; zÞj 2 ; if jy GT À Gðx; zÞj< 1 E x;y GT ;z ½jy GT À Gðx; zÞj À 0:5; otherwise ( ð11Þ where y GT À Gðx; zÞ y SRO;GT y FF;GT À G SRO ðx; zÞG FF ðx; zÞ: ð12Þ Due to the Cauchy-Schwarz inequality, the two outputs multiplied did not correspond exactly to the normalized input scattering data we fed into D and G.
We tested some alternative architectures, including transformers  (Vaswani et al. , 2017) , different training strategies and loss functions over the course of the network development (more detail is given in Sections 2. 2 and 2. 3 of the supporting information), but found they were a detriment to overall network performance. Therefore, the following results were obtained through the network as described above. We implemented the parallel Pix2PixGANs in Python using the PyTorch module  (Paszke et al. , 2019)  and trained both simultaneously on the 198 421 scattering planes for 200 epochs beyond loss convergence on a NVIDIA RTX 3090. The final models are available on GitHub (https://github. com/dclw29/ DSFU-Net), including the trained generators, collectively referred to as DSFU-Net (diffuse scattering factorization U-Net) from hereon in, for users to extract their own I FF (Q) and I SRO (Q) data.
Validation dataset The 12 607 unseen scattering planes reserved as the validation dataset were input into DSFU-Net, and the I FF (Q) and I SRO (Q) outputs were analysed to assess DSFU-Net's performance. Fig. 3  shows two examples of input scattering planes, the generated outputs and the corresponding GTs. According to the mean squared differences between the outputs and the GTs, these two correspond to some of the best and worst examples. In the first example, the visual match between the generated output and the GT is excellent; the network essentially completely reproduces the form factor and SRO components. A schematic diagram of the network architecture (see Section 2 of the supporting information for more details). The discriminators were fed GT and generator output samples. They were trained to label the former as real and the latter as fake.
Both inputs to the discriminators were paired with their respective clean scattering data (i. e. without the artefacts). The generators were trained adversarially, receiving the scattering data with artefacts as input into both I FF (Q) and I SRO (Q) U-Net generators, which encoded and decoded this into our desired output. After one full iteration of training for the discriminators and generators, an additional training stage occurred where the I FF (Q) and I SRO (Q) generated outputs were multiplied, and the error between this and the clean scattering data was used to train the generators. The second example has areas where the decomposition is very good, but DSFU-Net struggles to recover the correct intensities in areas with low scattering. In this example, this is most noticeable at the top of the plane, which corresponds to a dead zone in the input scattering.