dataesr/scientific-paragraphs-categorization huggingface dataset:
e. , Var( XF GS ) = O(S 2 /n)). In this way, we establish both theoretical and practical guarantees for our proposed model to reach stable over a large set of hyperparameters, small datasets, and noisy labels based on this parallel implementation. Pooling layer When implementing the form of pooling operation to aggregate information from the outputs of parallel FGS convolutional layer, instead of using some popular pooling functions such as max and average pooling, we apply the state-of-the-art pooling operation -gated max-average pooling  [27]  to capture the local and global information from all the nodes and graph structure. The rationale behind the gated max-average pooling, is that it considers "responsive" strategy (i. e. , improving translation invariance and scale f gated (X F GS ) = σ W X F GS f max (X F GS ) + 1-σ W X F GS f avg (X F GS ), where W is the trainable weight matrix, X F GS is the output matrix from the parallel FGS convolutional layer after concatenation operation.
IV. EXPERIMENTAL SETTINGS Directed and Undirected Datasets Joining the previous works practice, we use three undirected citation networks benchmark datasets for semi-supervised learning evaluation, including Cora-ML (this Cora dataset consists of Machine Learning papers), CiteSeer and PubMed. We also evaluate our method on four directed networks -Cora, IEEE 118-bus system (IEEE bus), Texas 2000-bus system (TX bus), and South Carolina 500-bus system (SC bus). The dataset statistics are summarized in Table V (in Appendix X). We provide the more details about datasets description on Github in the Appendix X. Baseline Methods On undirected networks, we compare LFGCN with the following state-of-the-art semi-supervised classification approaches which include (i) using the label matrix as input: label propagation (LP)  [34] ; (ii) using the feature matrix as input: DeepWalk (DW)  [35] , graph attention networks (GAT), GNN with ChebNet polynomials filter (Cheb-Net), GCN, GNNs with convolutional ARMA filters (ARMA), Graph Markov Neural Networks (GMNN)  [12] , Large-Scale Learnable Graph Convolutional Networks (LGCNs)  [36] , Shortest Path Graph Attention Network (SPAGAN)  [37] , APPNP, VPN, and MixHop.
E. and τ of 1% and 2%, respectively, in smaller network of less than 1,000 nodes. The best hyperparameter configurations of LFGCN for each dataset by using standard grid search mechanism are available at Github link in Appendix X. V. RESULTS 1. Performance analysis Tables I and II report the average accuracy delivered by LFGCN and competing methods for undirected and directed networks, respectively. The best performance for each dataset is marked in bold. We find that LFGCN outperforms all competing approaches in all datasets, except for PubMed (LFGCN delivers the second best accuracy result). The improvement gain of LFGCN over the next most accurate method ranges from 0. 29% (for CiteSeer over GMNN) to 4. 27% (for directed IEEE 118-Bus over GMNN). Remarkably, methods that are applicable both to undirected and directed networks (i.
e. ,  [5, 6, 8, 12, 22, 23, 24, 36, 37] ) tend to deliver noticeably lower accuracy results for a directed networks (especially on weighted-directed networks), while the new LFGCN method yields a more stable performance across both directed and undirected networks. In turn, PubMed (unweighted-undirected), GMNN outperforms LFGCN up to 2. 63%. Based on the obtain results, the new LFGCN approach tends to be the most competitive and, hence, preferred node classification method for sparser networks with higher label rates. Furthermore, the IEEE 118-Bus dataset is the smallest among the considered data, and we might expect to observe lower accuracy results for this dataset due to a limited training set. However, the accuracy yielded by LFGCN is among the highest ones across all datasets. For PubMed, it has the lightest tails for the degree distribution and a weak structural info (i.
e. , with very few links per node on average), thus LFGCN is not the best exploration choice. We provide the training time per epoch on all datasets in the Appendix X (see Tables VI VII and VIII). 2. Ablation study by removing individual components in LFGCN To discover the vital components in the success of our LFGCN, we investigate the contributions of individual components proposed in Section III-B to the performance of LFGCN. We conduct experiments by removing individual component separately (in the spirit of leave-one-out operation) from our LFGCN architecture, leading to a network without P-DropEdge, parallel structure, residual block, or gated max-average pooling. Table  III  provides the comparison results between LFGCN without P-DropEdge, parallel structure, residual block, or gated maxaverage pooling.
4. Evaluation of LFGCN-specific parameters During grid search over three parameters (i. e. , α, σ, and γ), we find that: (i) the regularization parameter α which used to specify the relative importance of a graph in clustering strongly relates to the probability of initial conditions for random walks when the self-refreshing process works, and it strongly influences the network's generalization ability and node classification performance for all datasets; (ii) the free unifying parameter σ provides enough flexibility to construct a canonical formulation of different graph-based semi-supervised methods -Table  I  and Table  II  indicate that the optimal value of σ depends on both the types of networks (undirected and directed) and label rate not on the size of network; (iii) the fractional power parameter γ substantially impacts the accuracy of node classification for the small datasets (see e.
Hyperparameter sensitivity In the sensitivity analysis setting, we have the ability to analyze the sensitivity of the node classification accuracy to variation from three LFGCNspecific parameters -α ∈ {0. 1,••• ,1}, σ ∈ {0,0. 1,••• ,1}, and γ ∈ {0. 001,0. 01,0. 1,1}. In this case, we only show the results from sensitively analysis for LFGCN model on IEEE 118-bus dataset. First, we perform the parameter learning experiments on four scenarios with a fixed parameter γ. Figure  2  shows that the accuracy substantially decreases when α is larger than 0. 8, especially in γ equals to 0. 001 and 0. 01 (see Figure  2 (a), 2(b)). Setting γ = {0. 1,1}, we observe that the classification accuracy nearly monotonic decreases while increasing α. Additionally, LFGCN generally gives consistent and higher accuracy for γ = {0.
001,0. 01} when the α parameter is within the range of {0. 1, 0. 2, 0. 3, 0. 4}. We then explore the variation of accuracy based on tuning parameter γ within the range of [0. 001,0. 002,•••,0. 01] (setting σ ∈ {0,0. 1,•••,1} at the same time), however, it is hard to obtain the optimal (σ, γ) combination through gathering finite experimental results (100 runs) since some of the results are very close. Therefore, we run the following experiments to demonstrate the impact evaluation of γ: Figure  3  shows that there exists a more profound difference between the shapes of approximate Gaussian distributions by fixing the parameter σ than fixing the parameter γ. These findings imply that σ tends to be a more important factor in the LFGCN approach for small datasets. Fig. 3 : Generalized Gaussian density of accuracy of LFGCN (two blue dashed lines represent lower and upper bounds, respectively): (a) the red filled curve is the PR-based method (σ = 0), blue filled curve is the NL-based method (σ = 0.
VI. CONCLUSION We have proposed a new Lévy Flights Graph Convolutional Network (LFGCN) method for semi-supervised learning on graphs that enables to better capture the intrinsic local graph topology. In addition, to further mitigate over-fitting and over-smoothing, we have proposed a new preferential P-DropEdge algorithm, based on censoring higher edge betweenness order statistics. We have investigated theoretical properties of LFGCN and have validated utility of individual components of the LFGCN architecture. Our numerical studies have indicated that the new LFGCN method tends to outperform all competing deep learning approaches on both unweighted-directed and unweightedundirected graphs in all considered datasets, except of PubMed. The gain in learning accuracy of LFGCN over the next best competitor ranges from 0.
29% to 4. 27%, and the highest gain has been achieved for the IEEE 118-Bus dataset which is the smallest among the considered datasets. Furthermore, in contrast to the competing approaches, LFGCN tends to deliver a more stable performance across directed and undirected networks regardless of the label rate. In the future we plan to advance the proposed LFGCN technique to learning on multilayer networks, explore utility of P-DropEdge combined with other order statistics on graphs, and enhance graph learning process with topological information on the underlying deep neural network.
1996; Vernazza et al. 2015). The most detailed information on the processes, conditions, timescales, and chronology of the early history of the solar system (e. g. ,  Neveu & Vernazza 2019; Kruijer & Kleine 2019 and references therein) , including the nature and evolution of the particles in the pre-planetary solar nebula, has so far come from the study of all these extraterrestrial materials. Recovering intact samples of such materials is therefore a critical goal of planetary studies. However, we are not very efficient at recovering the meteorites that hit the Earth. Estimates based on previous surveys  (Bland et al. 1996)  and on collected falls [Meteoritical Bulletin database 1 ] indicate that, for meteorites with masses greater than 100 g, probably less than 1 in 500 that fall on Earth are currently recovered.
(2017). As of today, there are 38 meteorites with reliable reconstructed orbits, 22 of which were detected by camera networks (see Table  1 ). Among the remaining 16 meteorites, 14 are the result of random visual observations such as the Chelyabinsk event (data from security cameras were used for orbit computation;  Borovička et al. 2013a ) and two meteorites were detected as asteroids before their fall (Almahata Sitta and 2018LA). During the same time interval , 397 meteorites were recovered after their falls were witnessed by eye (Meteoritical Bulletin Database). The main limitation of current networks is their size. Most of these networks consist of a fairly small number of cameras spread over a comparatively small territory. Altogether, they cover only 2% of the total surface of the Earth  (Devillepoix et al.
2019; [35]   data reduction pipeline (section 3. 3); and build centralized network and data storage architectures (section 3. 2. 3). The FRIPON project is designed as a real-time network with the aim of triggering a field search within the 24 h that follow the fall in order to recover fresh meteorites. As of today, FRIPON-France consists of 105 optical all-sky cameras and 25 receivers for radio detection. These assets are homogeneously distributed over the territory, although the radio network is slightly denser in the south of France (Fig. 2 ). Starting from 2016, scientists from neighboring countries were interested in joining the scientific project through the use of the FRIPON-France 3  hardware, software, and infrastructure. This was the case for Italy (PRISMA network;  Gardiol et al.
All the data from the FRIPON network are stored and processed in Marseille. The data processing consists of monthly astrometric and photometric reduction of the calibration images and daily processing of multi-detections. Two databases host the data. One stores the raw data and the other stores higher-level, processed data, such as orbits and trajectories. These data are available to all coinvestigators of the network 4. On request, national data can be sent to a different reduction pipeline for alternate processing and storage 5.
Data storage and access The FRIPON stations are composed of a Linux minicomputer, a wide-angle camera, and a manageable switch guaranteeing the isolation of the network of the host institute. The installation is done with an automated deployment system based on a USB key. When connecting to the host, the station establishes a secure VPN tunnel to the central server of The data collected on the server are then indexed in a database. During this operation, visuals are generated. When an optical event groups at least two stations, the FRIPON pipeline is executed to generate the dynamical and physical properties of the incoming meteoroid such as its orbit, its mass and its impact zone. All the data are made available through a web interface that is accessible to the worldwide community in real time 7.
Detection strategy The acquisition and detection software FreeTure was specifically developed by the FRIPON team and runs permanently on the minicomputers (see  Audureau et al. 2014  for a full description). The images corresponding to single detections by FreeTure are stored locally and a warning (time and location) is sent to the central server in Marseille. If at least one other station detects an event within +/-3 seconds, it is then treated as a "multiple detection". We note that we implemented a distance criterion of less than 190 km to avoid false detections. This value was determined empirically by manually checking one year of double detections. This strategy works well during the night, but leads to 30% of false detections mainly during twilight. Radio data corresponding to the last week of acquisition are only stored locally.
Optical data Scientific optical data are CCD observations recorded at a rate of 30 frames per second (fps). This acquisition rate is necessary to avoid excessive elongation of the meteor in the images in the case of high speed fireballs. For example, a typical bolide with an average speed of 40 km/s at 100 km altitude at the zenith leads to a 20 • /s apparent speed on the sky and to a four pixel elongated trail on the CCD. It is larger than the average width of the point spread function (PSF; typically 1. 8 pixels), but still easy to process for centroid determination. No dark and flatfield corrections are made. However, almost no reference star is measurable on a single frame with such an acquisition speed, as the limiting magnitude is about zero. It is thus necessary to record images with a longer exposure time for calibration.
-Meteors are mainly detected at small elevations (typically below 30 • ). These records are therefore affected by nonlinearities of the atmospheric extinction. -A uniform cloud layer can be the source of an under estimation of bolide magnitude. The first photometric measurements of the FRIPON network are reflected in the histogram of all detections in subsection 4. 1. 2. Routines to merge all light curves into one are now under development. As our data reduction is based on dynamics, the photometric curves are only used at present to detect major events. To summarize, the astrometric reduction allows us to obtain an accuracy of one-tenth pixel or 1 arcmin for meteor measurements. Photometry is at that time only usable for events with an absolute magnitude lower than -8 with an accuracy of 0.
Radio The aim of FRIPON radio receivers is an accurate measurement of meteor velocities through the Doppler effect, allowing a much better determination of the orbital data (especially semimajor axes). In Table  4 , we present the value of the initial velocity and effective surface-to-mass ra- tio derived for a meteor observed on 15 October 2018 at 1:15 UTC by five cameras. The accuracy achieved with the radio data leads to errors one order of magnitude lower compared to that achieved with only the visible images. However, it seems at present that only about 30 % of the optical detections lead to a detectable radio signal and that several bright radio events do not have any visible counterpart. For this reason, radio data have not been widely used yet, and further work is needed to improve our understanding of the complex phenomena associated with the generation of radio echoes by the plasma surrounding the meteors.
Combining infrasound with optical observations, such as those collected by the dense network of cameras operated by FRIPON, would contribute to fill gaps in existing observation systems and help constraining source parameters, such as trajectory and energy deposition. The results become even more interesting in Europe, where the integration of national networks allows for a better characterization of smaller-energy events  (Ott et al. 2019). The Atmospheric dynamics Research InfraStructure in Europe (ARISE) supports such multidisciplinary approaches by providing an extensive infrasound database for the estimation of NEOs potential risk and societal impact.
Other records An extensive database of images covering a large area may be used for additional purposes. The study of transient luminous events (TLEs), such as sprites or spatial debris re-entries, may be cited as examples  (Cecconi et al. 2018). Since the Summer of 2017, the software FreeTure contains an experimental real-time algorithm for the detection of TLEs. This algorithm runs along with the meteor detection part on selected stations with a view to help localize TLEs observed by the future CNES space mission TARANIS  (Blanc et al. 2017). The FRIPON network infrastructure can also be used to conduct large-scale light pollution monitoring campaigns using the all-sky calibration images collected over time  (Jechow et al. 2018).
The FRIPON observations show that the distribution of the orbits of incoming bolides appears bimodal, comprising a cometary population and a main belt population. Sporadic meteors amount to about 55% of all meteoroids. In addition, we found no evidence for the presence of interstellar meteoroids in our sample. Overall, it appears that the range of sensitivity of the FRIPON network encompasses particles originating both from comets and asteroids. A first estimate of the absolute flux of meteoroids bigger than 1 cm amounts to 1,250 /year/10 6 km 2 , which is a value compatible with previous reports. We also estimate the flux of meteorites heavier than 100g to 14/year/10 6 km 2 , which is a value compatible with data from other fireball networks but lower than those obtained from collecting meteorites.
Acknowledgements. FRIPON was initiated by funding from  ANR  (grant  N. 13-BS05-0009-03 ), carried by the  Paris Observatory, Muséum National d'Histoire Naturelle, Paris-Saclay University and Institut Pythéas (LAM-CEREGE ). Vigie-Ciel was part of the  65 Millions d'Observateurs project , carried by the  Muséum National d'Histoire Naturelle  and funded by the  French Investissements d'Avenir program. FRIPON data are hosted and processed at  Institut Pythéas SIP (Service Informatique Pythéas) , and a mirror is hosted at  IM-CCE (Institut de Mécanique Céleste et de Calcul des Éphémérides / Paris Observatory ) with the help of IDOC 9 (Integrated Data and Operation Center), supported by  CNRS  and  CNES. PRISMA is the  Italian Network for Systematic surveillance of Meteors and Atmosphere. It is a collaboration initiated and coordinated by the  Italian National Institute for Astrophysics (INAF)  that counts members among research institutes, associations and schools 10.
PRISMA was partially funded by 2016 and 2020 Research and Education grants from  Fondazione Cassa di Risparmio di Torino  and by a 2016 grant from  Fondazione Agostino De Mari (Savona). FRIPON-Bilbao  is supported by a grant from  Diputacion Foral Bizkaia (DFB/BFA ). FRIPON-MOROI was supported by a grant of the  Romanian Ministery of Research and Innovation, CCCDI -UEFISCDI , project number  PN-III-P1-1. 2-PCCDI-2017-0226/16PCCDI/2018 , within PNCDI III. Rio de Janeiro camera is hosted and partially maintained by  MAST (Museum of Astronomy and Related Sciences)/MCTIC. The  Meteorix  project acknowledges supports from labex  ESEP (Exploration Spatiale des Environnements Planétaires), DIM-ACAV+ Région Île-de-France ,  Janus CNES ,  IDEX Sorbonne Universités and Sorbonne Université. We thank  Maria Gritsevich  for comments which have been very helpful in improving the manuscript.
Methodological approach This descriptive research work relies on a three-step methodology: sample definition, data collection, and data analysis. The first step was building a sample of institutions from Costa Rica and France that are dedicated to developing training activities for the growth of SMEs. Nine Costa Rican and three French institutions were included in the sample. For reasons of confidentiality, we do not provide the names of the institutions; instead, we identified each institution with a number and classified it according to type: The second step concerns the data collection process. An in-depth interview was conducted within each of the institutions, which consisted of a meeting oriented towards understanding the perspectives of informants regarding their experiences or situations, and capturing them as expressed in their own words  (Taylor & Bogdan 1987).
The interviews were conducted in person or by video conference. The duration of each in-depth interview was approximately one hour. This made it possible to find out the support given to SMEs through various activities carried out with these types of companies (introduction, training, follow-up, etc. ), and, in turn, to determine whether any of these activities were focused on promoting digital marketing among international SMEs. Notably, the interviews carried out in Costa Rica were conducted in Spanish, while the interviews in France were done in English. However, for coherence and understanding, all results were translated into English. Finally, once the interview process was completed, data analysis, was carried out with ATLAS. ti software. This software was chosen because it is a tool that makes it possible to perform a qualitative analysis of predominantly large volumes of textual data  (Justice, 2005).
The UCLA method  [32]  uses a linear relationship to connect a soil wetness index with SM, index derived on a daily scale. In a similar manner,  [33]  use the VTCI (Vegetation Temperature Condition Index) instead of the soil water index in their downscaling methodology, which is derived on a daily basis by rescaling the LST of each pixel between two extreme LST values, per NDVI interval. The thermal inertia method is used by  [25]  to relate daily averaged SM estimates to diurnal changes in the soil temperature, calibrating their model on a monthly basis in order to reduce the impact of vegetation biomass on the estimates  [17]. In this context, this study aims to improve the robustness of the SEE(SM) model used within the DISPATCH methodology and hence the accuracy of the disaggregated dataset.
Three separate measurements per sampling point were performed, which means that a total of 120 measurements (for 2011) and 90 measurements (for 2015) were taken within the entire area each sampling day. As reported in  [18] , soil particle analysis at each sampling point, with a mean clay fraction of 0. 24 and a mean sand fraction of 0. 37, was used to classify soil texture. The approach described in  [55]  was then used to convert the gravimetric measurements to volumetric values. These in situ measurements serve here as a validation dataset for the downscaled SM products. Each of the 3 by 3 km sampling areas contain 9 pixels of 1 km resolution. Since the measurements performed are point measurements, they have been aggregated (simple average) to a 1 km resolution in order to be used in the validation process.