dataesr/scientific-paragraphs-categorization huggingface dataset:
Bioinformatics Analyses All analyses were performed using the R programming language (version 4. 2). The heatmaps and correlation plots were generated using "pheatmap" (version 1. 0. 12). The figures and plots were generated using ggplot (version 3. 3. 0). For statistical comparisons, we implemented the Wilcoxon test using the "stat_compare_means" function from the ggpubr package. We categorised the patients using reference cut-off values for the NC and RBD, IgG, IgM and IgA titres. The patients were stratified using only the IgM and IgG values given that there was a statistically significant correlation between the IgA and IgG values. The intensity of antibody responses was defined as follows; (-) negative, (+) 1-2 fold above the threshold value and (++) more than 2 fold above the threshold value.
We consider the kernel completion problem with the presence of multiple views in the data. In this context the data samples can be fully missing in some views, creating missing columns and rows to the kernel matrices that are calculated individually for each view. We propose to solve the problem of completing the kernel matrices with Cross-View Kernel Transfer (CVKT) procedure, in which the features of the other views are transformed to represent the view under consideration. The transformations are learned with kernel alignment to the known part of the kernel matrix, allowing for finding generalizable structures in the kernel matrix under completion. Its missing values can then be predicted with the data available in other views. We illustrate the benefits of our approach with simulated data, multivariate digits dataset and multi-view dataset on gesture classification, as well as with real biological datasets from studies of pattern formation in early Drosophila melanogaster embryogenesis.
Introduction Multi-view learning is a machine learning paradigm referring to a learning situation where data contains various, often heterogenous, modalities that might be obtained from different sources or by different measurement techniques  [1]. For example a dataset might contain images with captions, both of them describing the same data samples but from different points of view. Learning by taking into account all the views and their interactions is expected to give better results than learning from each single view independently, as the views are likely to carry complementary information and regularities. Gathering multi-view data can be very expensive and in some situations (such as some biological applications, or medical diagnosis from several physical examination devices) it might be outright impossible to simultaneously measure all the views under investigation.
Multi-view kernel matrix completion Dealing with missing samples or features is a much studied problem in data sciences. Missing data often refers to missing feature values in the dataset, for example in a recommendation system a feature of a data sample is missing if an user has not given a rating to one item in the catalogue. Usually the data samples are stacked in a matrix, and the matrix structure is used in filling in the missing values here and there in the matrix. Matrix completion approaches often consider a low-rank approximation with which the missing values are inputed  [27, 28]. In addition to matrices built directly from the features, matrix completion can be used in filling in individual missing values in a kernel matrix. However matrix completion is not always applicable to kernel completion, since kernel matrices have properties (symmetry, positiveness of eigenvalues) that matrix completion algorithms might not guarantee to preserve.
In this case (v ) = K (v )  : v ) ]. This is the approach we follow in our experimental section, however any proper kernel approximation is equally valid to be used in our algorithm. ,P [ K (v ) P,P ] -1 / 2 and K (v ) ≈ (v ) [ ( Obviously, the kernel matrix K (v ) contains missing rows and columns if some of the data is missing for this view. We denote the set of indices where data is available for view v as I (v ) , and the size of the set as i (v ) ≤ n. Whenever clear from the context which view is in question we might leave the superscript out, denoting I (v ) = I. We denote the section of the kernel matrix of view v containing the known values as K (v )   I ; this is a matrix of size i (v ) × i (v ). We have summarized this notation (among the notation introduced in next section describing the CVKT algorithm) in Table  1.
For example let us consider a dataset with three views, 0, 1 and 2, from which we want to fill in missing values in view 0. If view 1 only has samples available where 0 does, and view 2 only where 0 does not, CVKT naturally will not be able to learn a predictive mapping from view 2 to 0 as there are no training samples for this configuration. The same logic applies similarly also to other settings, for example if view 1 is as described above and view 2 is full, CVKT should be trained only with view 2. Otherwise in training it would learn a mapping { 1 , 2 } → { 0 } , while it should predict { 2 } → { 0 }. Multi-view learning paradigm focuses on data where different representations (or views) are drawn from one source. The various views describe different aspects of the same data, and may contain complementary information to each other.
Experiments In this section we empirically validate our approach (CVKT) in order to illustrate and validate its properties and performance. 2  In our experiments we aim to show that CVKT performs the kernel matrix completion accurately, and we do this with simple 2 The CVKT code and the datasets used in the experiments are available at riikkahuusari. com. simulated data alongside with a real dataset from study of pattern formation in Drosophila melanogaster embryogenesis. We further show its utility for classification problems with multi-view datasets containing also class labels (handwritten digits and timeseries data on gestures). Our results show that using CVKT-inputed kernel matrices in learning problems will yield superior performance w. r. t classification accuracy, compared to other ways to fill in the data in the kernel matrices.
We wish to highlight that NMF applied on the individual views is not applicable in missing views setting by itself, since in this case the whole row of data is missing. Moreover, the NMF approaches assume that the features for the data are available, which is something we do not require (we require only the incomplete kernel matrices). Also, the NMF methods require vectorial data from all the data views, while as a kernel method our CVKT can 3 https://github. com/aalto-ics-kepaco/MKC_software handle views of widely different data types, as long as a kernel can be defined on them.
Drosophila melanogaster pattern formation data set We now turn to a kernel completion task with a complex realworld multi-view dataset in order to validate our CVKT approach. Image multiplexing is a relevant application of the cross-view kernel transfer method in biology. To study how cell fates are established by gene regulatory networks in the field of developmental biology, it has recently been proposed that a first necessary step is to integrate multiple views from heterogeneous image datasets  [2]. Gene regulatory networks describe the sequence of interaction between various chemical species inside a cell or within a tissue, which ultimately lead to cell differentiation into a variety of functional types. The number of variables in these networks can go up to hundreds and each of them have to be measured separately with specific reporters.
In this model system a graded profile of nuclear localization of a transcription factor named Dorsal (Dl) establishes the dorsoventral (DV) stripes of gene expression. Four datasets of fixed images were acquired to visualize nuclei (referred to as M, for morphology), protein expression of doubly phosophorylated ERK (dpERK, V1), Twist (V2), and Dorsal (V4), and mRNA expression of ind (V3) and rho (V5). The first dataset contains 108 images stained for dpERK and Twist. The second dataset contains 59 images stained for dpERK, ind , and Dorsal. The third dataset contains 58 images stained for dpERK, ind , and rho. The fourth dataset contains 30 images stained for Twist, ind , and rho. Examples of the images the data contains can be seen in Fig. 3. The distribution of the variables are shown on Fig.
4. 4 n order to quantify the success of the proposed CVKT method, we select randomly samples to be missing for each of the views. The samples are selected in addition to the already missing samples, meaning that the selection is done in the teal coloured areas in Fig. 4. We then complete these samples with the information available in the other views. Note that we do not try to complete the truly missing samples, as our goal is to evaluate our algorithm and we want to be able to compare the completion results to known values. Thus for example when we consider view 2, we will only deal with datasets 1 and 4 (see Fig. 4  ), and we have five problems of different sizes. In addition to validating our method, this experiment mimics a real cross-validation situation when some samples in the data are truly missing.
Example images from the embryo dataset. In these images the colours identifying the views are modified so that they correspond over the datasets, e. g. dpERK is shown in red in all the images. In the dataset the views are highly correlated, a fact that can be exploited in the kernel completion task. Figure is adapted from Villoutreix et al. [2]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article). Our CVKT performs better in most of the views than other state-of-the-art methods with respect to CA error measure, shown in Table  3. Moreover, from Fig. 5  we can see that the structure of the kernel matrix is learned very well; however the exact values in our learned kernel matrices are slightly different ("lighter" images), which is no doubt then seen in the error measures.
Thus, with this method we cannot compare the view-specific performance, but show comparisons to this common representation. With MIC we also use SVM classifier, with RBF kernel. In order to perform classification we divide the data in half for training and testing, and this selection is the same for all the kernel matrices. Both training and testing sets contain samples for which the views were assumed missing in completion task. We report the accuracies on test data averaged over five different selections for missing data in Fig. 6  for the digits dataset. Our CVKT performs the classification superiorly to other kernel completion methods, and comparably to using the original fully known kernel matrix up to the case with 30% of missing data. The MIC method does not perform as well as CVKT in most of the views, except in two where it is the same with the lowest amount of data missing.
However even in these views its performance drops much more rapidly with level of missing data than for example CVKT, and for 50% of missing data it performs always worse than even mean or zero inputed kernels. In previous experiments the mean imputation has sometimes performed similarly to CVKT with respect to matrix completion error measures. It is the case also with the digits dataset (see Table  4  ), but the classification accuracy CVKT obtains is consistently higher than that of mean imputation (see Fig. 6  ). This is as expected; the inputed mean values do not carry meaningful information about the data samples they are supposed to represent, and thus will not allow for successful classification. It is interesting to notice that for view 'fou', the classification accuracy after completing 10% missing data is higher with CVKT kernel than with the original full kernel matrix.
We follow the same experimental protocol also for the uWaveGesture dataset, where we consider the 896 training samples in three views, with 8 classes. We report the completion error measures in Table  5. Again, according to some error measures, the mean imputation seems to be performing better than the dedicated matrix completion methods. However, again, from Fig. 7  , we can see that CVKT performs better in the subsequent classification task in most of the cases. It is clear that CVKT retains more relevant information about the data than the simple imputation methods, yet this is not always reflected in the completion error mea-sures. The MIC method performs here better than other baselines, but were we to consider MKL-style combinations of the individual kernels used in experiments of Fig.
7  , the performance of CVKT and MIC would be almost identical. Furthermore, we performed statistical testing to assess the significance of our classification results, excluding the MIC method since it cannot be used for individual views, nor can it be used in the task of kernel matrix completion. First of all, we consider the McNemar test. We compared the CVKT-based classification to the four other methods: classification with full kernels, MKC-filled kernels, and mean and zero-inputed kernels. We show in Tables  6  and 7  the obtained p-values, and also how often the null hypothesis was rejected (p-value threshold 0. 05), i. e. how often the two classification results were significantly different. We observe that the differences mostly grow with the level of missing values. For the digits dataset, the CVKT results with 10% and 20% of missing data are almost indistinguishable from the full classification according  After observing that the null hypothesis is in all the cases rejected, we proceed with the pairwise comparisons (CVKT to MKC, mean imputation and zero imputation) and perform the Nemenyi test by comparing the differences of the average rankings to the critical difference value CD = q α k (k + 1).
Our method completes the kernel matrices in a way that allows using them successfully in machine learning applications, as demonstrated with experiments on datasets of handwritten digits and images of flowers. The competing method, MKC, performed worse than expected. It might be that the assumptions of the chosen algorithm, MKC embd(ht ) , are not optimal for this specific problem, and one of the slower ones would have performed better. In  [22]  it is assumed that each view has a small basis set of samples with which the view can be characterized, and it might not be the case in our experiments. Additionally, the experimental setting is challenging with a lot of missing data samples. As the data is randomly missing from views for some data samples, even in lower levels of missing data, only one or two views might be available.
Acknowledgements This work is mainly granted by the french national project  ANR  Lives  ANR-15-CE23-0026 , and by the  Turing Center for Living Systems (CENTURI)  for PV. For the most part work by  RH has been done in Aix-Marseille University  -the part in  Aalto University  has been funded by  Academy of Finland  grants  334790  (MAGITICS) and 310107 (MACOME).
In this paper, a comprehensive validation exercise of 3D physics-based numerical simulations (PBS) of seismic wave propagation is presented for a low-to-moderate seismicity area in the south east of France, within the Rhône River Valley, that hosts several operating nuclear installations. This area was hit on Nov 11, 2019, by an unusually damaging Mw 4. 9 earthquake (Le Teil event). The numerical code SPEED ( http://speed. mox. polimi. it/ ), developed at Politecnico di Milano, Italy, was used to validate the simulations against the available recordings. When comparing simulations with records, a good to excellent agreement was found up to 8-10 Hz, showing that, even without a very detailed 3D numerical model of the medium, the PBS may provide realistic broadband predictions of earthquake ground motion.
, 2015; Evangelista et al. , 2017; Infantino et al. , 2020; Sangaraju et al. , 2021)  and to construct a prototype of a near-source simulated accelerograms dataset with the aim of complementing recordings datasets, still relatively sparse in such near-source conditions  (Paolucci et al. , 2021). After a brief overview of the case study in Section 2, the 3D numerical model is introduced in Section 3, while the verification and numerical convergence tests are discussed in Section 4. In Section 5, simulated ground motion is successfully compared with the recorded one on a broad frequency range, up to about 8 Hz, where the convergence tests have shown that the accuracy of numerical wave propagation is reasonably preserved. Furthermore, Goodness of Fit tests show good to excellent scores. Since the main role of 3D PBS is to highlight regionand site-specific features of earthquake ground motion that cannot be resolved by the ergodic empirical GMMs, and that may lead to biased estimates for seismic hazard assessment, in Section 6 the main findings related to the 3D site amplification features in the Rhône Valley are summarized and compared with 1D approaches for site amplification estimation.
e. , the Cevennes Fault System -CFS) striking NE-SW and dipping to the southeast  (Delouis et al. , 2019; Ritz et al. 2020). The earthquake was generated by the seismic rupture of a segment of the La Rouvière fault (LRF, see red line in Figure  1 ), which is located at the North-Eastern part of the CFS. The LRF was not identified as a potentially active fault in the Database of Potentially Active Faults for Metropolitan France -BDFA (https://bdfa. irsn. fr/,  Jomard et al. , 2017) , but it was already listed on the geological map of the Aubenas area  (Elmi et al. 1996). The 8 km-long La Rouvière fault is oriented NE-SW (azimuth from N030 to N050), it dips steeply to South-East and is located between, and parallel to, the Saint Remèze fault (part of the Cévennes fault) to the North-West and the Marsanne fault to the South-East.
Verification analyses with Hisada code As a preliminary step of the modelling procedure, simulations were performed using the Hisada code, based on the analytical integration of Green's functions  (Hisada and Bielak, 2003). This code allows to compute the ground motions in a horizontally layered half-space originating from a finite-fault kinematic source model, providing solutions with a maximum frequency resolution of about 1-2 Hz at most. Hisada's solution has been used in a preliminary phase to calibrate and validate the crustal model profile, the assumptions on the quality factor, the slip model on the extended fault and the source time function adopted. Concerning the source, two different parametrizations have been tested: a point source (shown herein) and an extended fault (not shown in this paper).
0s), where simulated ground motions exceed significantly the empirical predictions. Such a trend is consistent with the findings from residual analysis of Montélimar recordings with respect to recorded datasets in Europe and in Italy; -the systematic underestimation of the empirical GMMs for the long-period spectral ordinates is even more pronounced for the vertical components of ground motion, for which both simulations and recordings tend to be systematically above the 84 th percentile of the empirical predictions; -at intermediate periods (see SA(0. 5s)-H and SA(0. 2s)-V) a better agreement is found between numerical simulations and empirical predictions.
Conclusions In this paper, a comprehensive validation exercise of physics-based numerical simulations (PBS) of seismic wave propagation is presented. The target area is an industrial region in South-Eastern France within the Rhône Valley, which hosts several operating nuclear power plants  (Cruas and Tricastin). This low-to-moderate seismicity area was hit by an unusually shallow (1 km depth) Mw 4. 9 earthquake rupturing the La Rouvière fault, near Le Teil, at about 15 km distance from the Cruas NPP. The recordings available for the Le Teil earthquake, although limited in number, were used for validation of the PBS. The numerical code SPEED was used for this purpose. In the recent past, this numerical code underwent several successful validations with earthquakes in a wide range of magnitudes, spanning from 3 to 6.
) occurred south of Le Teil in 1773, 1873 the 1923, with maximum macroseismic intensities up to Imax=VII MSK (SISFRANCE database, www. sisfrance. net). The August 8, 1873 earthquake, at around 8 km southward from Le Teil, was the largest shock ever felt in this region, with an estimated Mw of around 4. 1 and a focal depth of about 3 km (FCAT catalogue, Manchuel et al. , 2018). An earthquake was located near Le Teil in November 1923, with an inferred Mw of around 3 and Imax=IV MSK.
Comparison and validation with experimental data Seakeeping tests were performed at the MARIN (Maritime Research Institute Netherlands, Abeil (2017)) on the Windkeeper SWATH ship. Fig. 3  shows a sample of the 3D panel distribution of the geometry used for the BEM simulations. The ship was tested in regular waves (Amplitude Amp = 1 m) and irregular waves (JONSWAP spectrum whereby   = 1. 5 m and   = 9. 5 s). Within the scope of this study, only the amplitude of vertical motion in two points located along the longitudinal axis are studied. In Figs. 4a  and 4b , the first peak of amplitude is attributable to heaving motion (resonant frequency of 0. 6 rad s -1 ), which is perhaps not sufficiently damped since the amplitude of motion is a bit higher than expected in regular waves at  = 19 m (see Fig.
, 2010) , using for instance, Maximin distance  (Svenson and Santner, 2010) , Euclidean distance  (Keane, 2006) , or the well-known Hypervolume infilling criterion  (Emmerich et al. , 2006 (Emmerich et al. , , 2011;; Luo et al. , 2014). Recently, merit functions aimed at computing and reducing uncertainty of the predicted Pareto front have been developed  (Picheny, 2015; Binois et al. , 2015; Passos and Luersen, 2018b). In particular,  Passos and Luersen (2018b)  have proposed and validated, on a real-world composite panel application, the efficiency of a new merit function: Minimization of the Variance of the Predicted Front (MVPF). In the present work, the MVPF approach is applied to solve the SWATH hull form optimization problem, using the "moko" open-source R package  (Passos and Luersen, 2018a).
Consequently, simulations are performed with free sinkage and fixed trim without fins. Finally, in a third level of fidelity, fins are added to the geometry to balance the Munk moment. Fins drag is then considered. Gaussian processes and the "Minimization of the Variance of the Predicted Front" algorithm are used to populate the metamodel database. The final design is elected according to a new proposed criterion, the "Median Compromise of the Pareto Front". The first case, considering the wetted surface, shows that seakeeping performance and wetted surface are indeed opposite functions. Geometries which minimize vertical amplitude of motion have a large horizontal semi-axis and large strut inclination angle, but those parameters increase the wetted surface. The use of a multi-objective algorithm to find the best compromise is then justified.
The advantage lies in the convolutional layers that treat the inputs or the physical signals with different filters in order to diversify the features, which are then used to train the dense layers. This approach helps the model to achieve good generalisation while preventing over-fitting  [9]. CNN and PCA approaches have shown great results in former articles, but in this study, we are going to use the same dataset to explore their performance and compare them in terms of reliability, execution time, precision and embedding difficulty. This comparison can be used to choose the right approach for industrial applications. Engineers will be able to identify the needed performance for their ongoing application and pick the suitable method.