dataesr/scientific-paragraphs-categorization huggingface dataset:
Asthma hospitalizations and GT data from July 2012 to June 2015 were used as a training set, with hospitalizations between the weeks of June 21, 2015, and June 19, 2016 being forecasted based on observed GT for that period. The predictive ability of the models was assessed by calculating  (1)  the correlation coefficients between the predicted variation in hospitalizations and the observed trend in hospitalizations for that period, (2) the correlation coefficients between the predicted variation in hospitalizations and the actual number of asthma hospitalizations (ie, without time series decomposition) for that period, (3) the average weekly difference between the numbers of predicted and observed hospitalizations, and (4) the number of weeks whose number of observed asthma hospitalizations fell outside the 95% CI for predicted admissions.
This difference was 23% in Portugal, 16%-17% in Finland, 32%-33% in Norway, and 21%-23% in Brazil. In 1 year, the number of weeks in which the absolute frequency of observed asthma hospitalizations did not fall within the predicted 95% CI ranged between 0 (Rio Grande do Sul) and 8 (Brazil as a whole). a Correlation coefficients between predicted weekly asthma hospitalization trends and actual observed hospitalizations after applying time series analysis methods (ie, after removing the trend component). b Correlation coefficients between predicted weekly hospitalization trends and actual observed raw numbers of weekly asthma hospitalizations. Table  3. Results of 1-year (June 2015-June 2016) forecasts for the number of asthma hospitalizations based on autoregressive integrated moving average models including common cold-related Google Trends data and asthma hospitalizations of the previous 3 years.
To control these secular trends, we applied time series analysis methods, removing the estimated trend components for both GT and hospitalization data. Finally, in this study, we solely considered asthma hospitalizations, even though only a minority of exacerbations resulted in hospitalization. Although trends in hospitalizations probably mirror those in exacerbations, an assessment of both hospitalizations and emergency department visits (whose data were not currently available for analysis) would probably more accurately reflect trends in exacerbations. Furthermore, the generalizability of our forecast models is limited, as such models require previous hospitalization data, which may not be easily available in all countries. This study had several strengths. In particular, we assessed 5 different countries (4 in Europe and 1 in South America) using nationwide data for a period of 5 years.
Acknowledgments The authors wish to thank the  Portuguese Ministry of Health  for providing access to the hospitalization data managed by the  Portuguese Central Health System Administration (Administração Central do Sistema de Saúde). Data from the  Norwegian Patient Registry  were used in this study. The interpretation and reporting of these data are the sole responsibility of the authors, and no endorsement by the  Norwegian Patient Registry  is intended nor should it be inferred. Article Processing Charges were funded by  National Funds through FCT-Fundação para a Ciência e a Tecnologia , IP, within  CINTESIS, R&D Unit  (reference  UIDB/4255/2020 ).
This paper presents a novel version of hypergraph neural network method. This method is utilized to solve the noisy label learning problem. First, we apply the PCA dimensional reduction technique to the feature matrices of the image datasets in order to reduce the "noise" and the redundant features in the feature matrices of the image datasets and to reduce the runtime constructing the hypergraph of the hypergraph neural network method. Then, the classic graph based semisupervised learning method, the classic hypergraph based semi-supervised learning method, the graph neural network, the hypergraph neural network, and our proposed hypergraph neural network are employed to solve the noisy label learning problem. The accuracies of these five methods are evaluated and compared. Experimental results show that the hypergraph neural network methods achieve the best performance when the noise level increases.
We find out that this proposed combination of the propagation scheme and the hypergraph neural network method significantly improves the accuracy of the hypergraph neural network method alone even when the noise presents in the labels. In this paper, our contributions are three-folds: a) In order to reduce the runtime constructing the graphs and the hypergraphs from the image datasets, we apply the dimensional reduction technique PCA to the image datasets. b) Propose the novel version of hypergraph neural network method combining the classic hypergraph based semi-supervised learning method with the hypergraph neural network method. c) Compare the accuracy performance measures of the classic graph based semi-supervised learning problem, the classic hypergraph based semi-supervised learning problem, the graph neural network method, the hypergraph neural network method, and our proposed hypergraph neural network method when we apply these five methods to solve the noisy label learning problem.
In the other words, the influence of the label noise is not important. This observation was employed in  [12]  to preserve an approximation of the labels using the running average of deep neural network's forecasts with a high learning rate. These approximations then can be utilized as the control (or supervision) signals to train the deep neural network. Inspired by the work of  [10] [11] [12]  and  [4] [5] [6] 13] , in this paper, we will develop the graph and hypergraph convolution neural network methods and apply these methods to solve the "noisy label learning" problem (using the image datasets such as MNIST, USPS, and FASHION MNIST). To the best of our knowledge, this work has not been investigated and developed.
HYPERGRAPH NEURAL NETWORK 3. 1. Problem formulation In this paper, we would like to solve the "noisy label learning" problem  [10, 21]. This problem can also be called the "label distribution learning" problem  [22] , to name a few. In this problem, let Xtrain={x1, x2,. , xl} be the training set, where xi ∈ m. xi can also be called the feature vector i or instance i or sample i of the training set with 1≤i≤l. Let YL={y1,y2,. ,yC} be the complete set of labels where C is the number of classes in the dataset. For each sample   , there is a label distribution  = {     The objective of the noisy label learning problem is to learn a mapping function :  →  between the sample x and its corresponding label distribution function d. In the other words, the goal of noisy label learning is to learn the conditional probability mass function (|), where  ∈   ,  ∈.
Hypergraph based semi-supvervised learning problem Given a set of images { 1 , … ,   ,  +1 , … ,  + } where  = || =  +  is the total number of images (i. e. vertices) in the hypergraph G=(V,E). The method constructing the incidence matrix H from the image dataset will be specified clearly in the Experiments and Results section. Let C be the number of classes. Please note that { 1 , … ,   } is the set of all labeled points and { +1 , … ,  + } is the set of all un-labeled points. Let  ∈  || *  the initial label matrix for n images in the hypergraph G be defined as follows: 𝑌 𝑖𝑗 = { 1 𝑖𝑓 𝑥 𝑖 ∈ 𝑐𝑙𝑎𝑠𝑠 𝑗 𝑎𝑛𝑑 1 ≤ 𝑖 ≤ 𝑙 -1 𝑖𝑓 𝑥 𝑖 ∉ 𝑐𝑙𝑎𝑠𝑠 𝑗 𝑎𝑛𝑑 1 ≤ 𝑖 ≤ 𝑙 0 𝑖𝑓 𝑙 + 1 ≤ 𝑖 ≤ 𝑛 (6) Let the matrix  ∈  || *  be the estimated label matrix for the set of images { 1 , … ,   ,  +1 , … ,  + }, where the point   is labeled as sign (  ) for each class j (1 ≤  ≤ ).
Hypergraph neural network From  [5] [6] , let: 𝑅 1 = 𝑅𝑒𝐿𝑈 (𝐷 𝑣 -1 2 𝐻𝑊𝐷 𝑒 -1 𝐻 𝑇 𝐷 𝑣 -1 2 𝑋𝜃 1 ) (8) (8) 𝑅 2 = 𝑅𝑒𝐿𝑈(𝐷 𝑣 -1 𝐻𝑊𝐷 𝑒 -1 𝐻 𝑇 𝑋𝜃 1 ) (9) (9) The output of the hypergraph neural network can be defined and computed as follows: 𝑍 = 𝑠𝑜𝑓𝑡𝑚𝑎𝑥 (𝐷 𝑣 - 1 2 𝐻𝑊𝐷 𝑒 -1 𝐻 𝑇 𝐷 𝑣 - 1 2 𝑅 1 𝜃 2 ) (10) or 𝑍 = 𝑍 = 𝑠𝑜𝑓𝑡𝑚𝑎𝑥(𝐷 𝑣 -1 𝑊𝐷 𝑒 -1 𝐻 𝑇 𝑅 2 𝜃 2 ) (11) Note that  ∈   *  1 is the feature matrix (i. e. the image dataset). 1 ∈   1 *  2 and  2 ∈   2 *  are two parameter matrices that are needed to be learned during the training process.
Dataset MNIST: This image dataset is the dataset containing the handwritten images from '0' to '9'. There are 70,000 images in the dataset. There are 60,000 images in the training set and 10,000 images in the testing set. Obviously, the number of classes in this MNIST image dataset is 10. Each image in the dataset is the 28by-28 matrix (gray scale image). Our first task in the preprocessing step is to convert this gray scale image to 1-by-784 vector. We achieve this task by concatenating every rows of the gray scale image to a "long" row vector. In the other words, we have the R 70,000×784 feature matrix. USPS: This image dataset is also the handwritten image dataset from '0' to '9'. However, in this dataset, there are just 9,298 images in the dataset. There are 7,291 images in the training set and 2,007 images in the testing set.
The number of classes in this USPS dataset is 10. Each image in the dataset is the 16-by-16 matrix (gray scale image). We concatenate every rows of the gray scale image (in this USPS dataset) to the 1by-256 "long" row vector. Thus, finally, we have the R 9,298×256 feature matrix. FASHION MNIST: This image dataset is the dataset containing images of shoes, clothes, caps, etc. There are 70,000 images in the dataset. There 60,000 images in the training set and 10,000 images in the testing set. The number of classes in this FASHION MNIST image dataset is 10. Each image in the dataset is the 28-by-28 matrix (gray scale image). We concatenate every rows of the gray scale image to the 1-by-784 "long" row vector. In the other words, we have the R 70,000×784 feature matrix. This FASHION MNIST image dataset is considered the hardest image dataset to test in our experiments.
Experiments and result In order to reduce the noise and redundant features in the input feature matrices and in order to reduce the time constructing the graphs and hypergraphs from the three image datasets, we apply the dimensional reduction PCA technique to the three input feature matrices. Finally, the MNIST dataset is transformed to the R 70,000×50 matrix. The USPS dataset is transformed to R 9,298×50 matrix. The FASHION MNIST dataset is transformed to R 70,000×300 matrix. The way constructing the graphs from the three image datasets can be found in  [25, 26]. Next, we will discuss how to construct the incidence matrix H of the hypergraphs from the three image datasets. Please note that the number of hyperedges in the hypergraph is equal to the number of images in the dataset  [27]. The image i belongs to hyperedge j if image i is among the k-nearest neighbor of image j or image j is among the k-nearest neighbor of image i.
In this paper, k is chosen to be 5. Finally, from the computed H, we can compute the two terms (  -1 2 𝐻𝑊𝐷 𝑒 -1 𝐻 𝑇 𝐷 𝑣 - 1 2 ) and (  -1   -1   ) in the symmetric normalized hypergraph Laplacian and the random walk hypergraph Laplacian used in the classic hypergraph based semi-supervised learning method, the hypergraph neural network method, and our proposed hypergraph neural network method. The two main differences of our methods with other semi-supervised learning methods  [28, 29]  solv-ing the image classification problem with noisy labels are: a) Other semi-supervised learning methods just used the subsets of the MNIST and the USPS datasets. For example, in  [28] , the authors just used 10,000 images from MNIST to evaluate their methods. In the other hand, our methods use the complete MNIST, USPS, and FASHION MNIST image datasets.
b) Our methods apply directly the PCA technique to the feature matrices of the three image datasets in order to reduce the time constructing the graphs and the hypergraphs of the three image datasets. To the best of our knowledge, this work has not been done before. The experimental results show that if we do not apply the PCA technique to the feature matrices of the three image dataset, the hypergraph neural network significantly outperforms the graph neural network. If we apply the PCA technique to the feature matrices of the three image datasets, the hypergraph neural network method does not significantly outperform the graph neural network method; however, both the hypergraph neural network and the graph neural network with PCA are better than the graph and hypergraph neural network without using PCA technique.
These claims will be clarified in Tables  1, 2 , 3, 4. In general, in this paper, what we want to achieve is clear: we would like to prove that the hypergraph neural networks (the current state of the art semi-supervised learning method and our proposed method) are at least as good as the graph neural network but sometimes lead to better accuracy performance measures. We run our five methods (Python code) on Google Colab with NVIDIA Tesla K80 GPU and 12 GB RAM. The following Tables 1, 2, 3, and 4 show the experimental results of our five methods. From the above three tables, we easily recognize initially and directly that when the noise level increases, our proposed hypergraph neural network outperforms the other methods (i. e. especially when the noise level reaches 45%). Second, from the experimental results, we see that the hypergraph neural network methods (both the current state of the art semi-supervised learning method and our proposed method) are at least as good as the graph neural network proposed by Thomas Kipf but sometimes lead to better accuracy performance measures.
CONCLUSION In this paper, we have proposed the novel hypergraph neural network method. Our contributions are: (1) Reduce the time constructing the graph and the hypergraph by initially applying the PCA technique to the image dataset, (2) Our novel hypergraph neural network method is in fact the combination of the classic hypergraph based semi-supervised learning method and the hypergraph neural network proposed by  [4]  (i. e. , the current state of the art semi-supervised learning method). The experimental results show that our proposed hypergraph neural network outperforms other semi-supervised learning methods as the noise level in the training set increases (~45%). In the other words, our proposed approach is quite robust to noise labels to some extent. Moreover, the hypergraph neural networks (the current state of the art method of semisupervised learning approach and our proposed method) are at least as good as the graph neural network proposed by Thomas Kipf, but sometimes lead to better accuracies.
The ATLAS Collaboration measured the inclusive  t cross section using a subset of the LHC Run 2 data, collected in 2015 and 2016  [14]  and a first differential measurement of the  t process was carried out by the CMS Collaboration using the 2016 and 2017 data sets  [15]. Theoretical predictions of the  t cross section exist at next-to-leading order (NLO) with the resummation of soft gluon corrections computed at next-to-next-to-leading-logarithm (NNLL) precision  [16, 17]  in perturbative quantum chromodynamics (QCD) with added EW corrections. Recently they have been matched to the complete set of NLO corrections of both QCD and EW origin  [18, 19]  using the M G 5_aMC@NLO (MG5_ MC@NLO) framework  [20]. This paper presents measurements of the inclusive and differential  t production cross section in final states with three or four isolated leptons (electrons or muons) with the ATLAS detector  [21]  at the LHC.
In addition, a set of normalised and absolute differential measurements are presented as a function of different variables which probe the SM predictions for the kinematics of the  t system. Some of these variables are found to be sensitive to potential EFT signals  [7] , while others are more interesting in the context of MC tuning  [22, 23]. The differential measurements were performed at both particle and parton level in different fiducial volumes in order to correct for various acceptance effects. For the first time, the  t cross section is measured with the full Run 2 data and includes differential measurements performed as functions of variables related to the  t system. This paper is structured as follows. Section 2 provides a brief description of the ATLAS detector. In Section 3, the simulation of signal and background processes is discussed, followed by the definitions of the final-state objects at reconstruction, particle and parton levels in Section 4.
Data and simulated event samples The analysis is performed on data from   collisions at √  = 13 TeV delivered by the LHC and recorded by the ATLAS detector between 2015 and 2018. The bunch spacing for this data-taking period was 25 ns with an average number of   interactions per bunch crossing ('pile-up') which varies by year and LHC beam conditions and was in the range from 10 to 70 for almost all events. After requirements on the stability of the beams, the operational status of all ATLAS detector components, and the quality of the recorded data, the total integrated luminosity of the data set corresponds to 139 fb -1. This value is derived from the calibration of the luminosity scale using - beam-separation scans, following a methodology similar to that detailed in Ref. [27] , and using the LUCID-2 detector  [28]  for the baseline luminosity measurements.
The simulated events were reweighted to match the pile-up conditions observed in the measured data. For processes featuring  boson,  boson or top-quark production, the ,  and top-quark masses were set to 80. 4 GeV, 91. 2 GeV  [35]  and 172. 5 GeV, respectively. The decays of bottom and charm hadrons were simulated using the E G program  [36]. The MC samples were either processed through a full simulation of the ATLAS detector based on G 4  [37, 38]  or a fast simulation (A F 2) relying on parameterised showers in the calorimeter  [39, 40]. The  t signal process was modelled using the MG5_ MC@NLO 2. 3. 3  [41]  generator together with E G 1. 2. 0, which provided a matrix element (ME) calculation at NLO in the strong coupling constant ( s ) with the NNPDF3. 0 [42]  PDF set. The functional form of the renormalisation and factorisation scales ( r and  f ) was set to  r,f = 0.
84 +0. 09 -0. 10 pb, which was reported in Ref. [48]  (based on Ref. [49] ). The uncertainties are due to the QCD scales, the proton PDFs, and  s. The measured differential cross sections are compared with theoretical expectations obtained with different generators. Alternative  t samples were simulated with S 2. 2. 1  [50]  generator at NLO QCD accuracy, using both inclusive and multi-leg set-ups. In both cases, dynamic  r and  f scales were used as in the nominal samples. The default S 2. 2. 1 parton shower was used together with the NNPDF3. 0 PDF set  [42]. The multi-leg sample was simulated using the MEPS@NLO prescription  [51] [52] [53] [54]  with up to one additional parton at NLO and with a merging scale of 30 GeV. Another sample was generated with the same MG5_ MC@NLO and E G versions as the nominal sample but using a different MC program for the modelling of the parton-shower and hadronisation: H 7  [55, 56]  instead of P 8.
5% on the measurements. Uncertainties associated with the jet selection arise from the jet energy scale (JES), the JVT requirement and the jet energy resolution (JER). The JES and its uncertainties are derived by combining information from test-beam data, collision data and simulation  [78]. The uncertainties in the JER and JVT increase at lower jet  T. The overall effect of uncertainties related to jet selection and calibration is approximately 2%. The efficiency of the flavour-tagging algorithm is measured for each jet flavour using control samples in data and in simulation. From these measurements, correction factors are derived to correct the tagging rates in the simulation. In the case of -tagged jets, the correction factors and their uncertainties are estimated from data using dileptonic  t events  [71].
Unfolding procedure To measure the differential cross-section distributions at particle and parton levels in the specific fiducial phase-spaces defined in Section 4. 2, an iterative Bayesian unfolding procedure is used  [88]. It relies on the Bayesian probability formula starting from a given prior of the particle-or parton-level distribution and iteratively updating it with the posterior distribution. The unfolding is performed using the R U package  [89]. The differential  t cross sections are calculated using the following equation: d𝜎 𝑡 t 𝑍 d𝑋 𝑖 = 1 L • B • Δ𝑋 𝑖 • 𝜖 𝑖 eff • ∑︁ 𝑗 [M -1 ] 𝑖 𝑗 • 𝑓 𝑗 acc • 𝑁 𝑗 obs -𝑁 𝑗 bkg , where  denotes the variable used for the differential measurement (with the bin-width Δ), the index  indicates the bin at particle (or parton) level and  the detector-level bin.
So-called 'pull tests' are performed as part of the binning optimisation to verify that the unfolding is stable for the selected number and range of bins. In addition, linear re-weightings are applied to the pseudo-data to test the ability of the unfolding procedure to correct the pseudo-data back to their underlying true spectra, obtained from the MC event record. The number of iterations used in the iterative Bayesian unfolding is also optimised with pseudo-experiments: for each iteration, a  2 per degree-of-freedom (ndf) is calculated by comparing the bin contents of the unfolded pseudo-data with those from the previous iteration. In the case of the first iteration, the unfolded pseudo-data are instead compared with the corresponding generator-level distribution. Iterations are performed until the  2 /ndf value of a given distribution stabilises at a constant value while the statistical uncertainty returned from the unfolding procedure is kept as low as possible.
The differential cross-section measurements were performed at particle and parton levels in specific fiducial volumes. The unfolded spectra from the measured data are compared with the predictions of different NLO QCD  t MC generators and theoretical predictions at NLO, NLO+NNLL and nNLO precision, based on a  2 /ndf and -value compatibility test. For most of the considered observables, good agreement between data and the predictions is observed. The differences between the various predictions are determined to be smaller than the uncertainties of the unfolded data. The ATLAS Collaboration.
Acknowledgements We thank  CERN  for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently. We acknowledge the support of  ANPCyT , Argentina; YerPhI, Armenia;  ARC, Australia ;  BMWFW  and  FWF , Austria; ANAS, Azerbaĳan; SSTC, Belarus;  CNPq  and  FAPESP, Brazil ;  NSERC ,  NRC  and  CFI ,  Canada ; CERN;  ANID, Chile ;  CAS ,  MOST  and  NSFC, China ;  Minciencias ,  Colombia; MSMT CR ,  MPO CR  and  VSC CR, Czech Republic ;  DNRF  and  DNSRC, Denmark ;  IN2P3-CNRS  and  CEA-DRF/IRFU , France; SRNSFG, Georgia; BMBF,  HGF  and  MPG , Germany; GSRI, Greece; RGC and  Hong Kong SAR, China ;  ISF and Benoziyo Center, Israel ;  INFN, Italy ;  MEXT  and  JSPS, Japan ; CNRST, Morocco; NWO, Netherlands; RCN, Norway;  MNiSW  and  NCN , Poland; FCT, Portugal; MNE/IFA, Romania; JINR;  MES of Russia  and  NRC KI , Russian Federation; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DSI/NRF, South Africa; MICINN, Spain;  SRC and Wallenberg Foundation, Sweden ;  SERI ,  SNSF  and  Cantons of Bern and Geneva, Switzerland; MOST, Taiwan ;  TAEK, Turkey; STFC, United Kingdom ;  DOE  and  NSF ,  United States of America.