dataesr/scientific-paragraphs-categorization huggingface dataset:
Computerized clinical decision support systems A mobile phone application (TRiP(cast) score Ó 2018) has been developed (screenshot in Appendix Fig. A2 ) for IOS (https://apps. apple. com/us/app/trip-cast-score/id1438610930) and Android mobile phone platforms which can be downloaded in the App store of Apple or Android, without costs and is available in three languages; English, Dutch and French. It calculates an individual's absolute predicted risk for VTE (using validation data from this paper) once all patient data have been entered in the application. Decisions on thromboprophylaxis can then be made accordingly.
Nevertheless, some limitations have to be mentioned. Although the inclusion criteria of the POT-CAST trial were wide, some patient selection may still have been present. For instance, all patients had plaster cast, i. e. no brace. Patients with a history of VTE were not allowed to participate. However, as their VTE risk is certainly high, it may be reasoned that these patients do not need risk prediction at all, and should receive thromboprophylaxis in most circumstances. Furthermore, despite being the largest trial till date on this topic, few patients (23/1435) developed VTE which limits the accuracy of our validation statistics. The MEGA case-control study was also limited in terms of power. Yet, the predictive performance of the TRiP(cast) score (and previous TIP AND Leiden-TRiP scores) showed consistent results in both the MEGA and POT-CAST datasets indicating no overfitted prediction model.
Another limitation might be the use of data imputation which can introduce misclassification (in this case of patient characteristics). However, model performance was good and hardly differed between the imputed and the complete dataset. Lastly, to optimize the TRiP(cast) score performance, 14 variables were maintained which might be considered as relatively many items have to be scored. To anticipate this, we developed a computerized clinical decision support systems (CCDSSs) using a mobile phone application. We believe this can be a helpful tool in clinical practice as entering and summation of the items is greatly facilitated. Furthermore, studies have highlighted that the use of CCDSSs increases the proportion of patients who receive adequate prophylaxis  [22, 23]  and can be efficiently implemented in everyday clinical practice in emergency departments  [24].
Introduction The evolution of circumstellar discs from the initial reservoir of the interstellar medium (ISM)-dust and gas mixture towards planetary systems is governed by the growth and coagulation of dust grains, viscous spreading and accretion onto the central star (or on proto-planets), and dissipation of the primordial gas  (Williams & Cieza 2011). Although a large amount of high-resolution images and spectroscopic data have been collected during recent decades, the various stages of disc evolution remain poorly constrained by observations  (Wyatt et al. 2015). The main accretion phase corresponds to the Class II phases for T Tauri (TTS) and Herbig Ae (HAe) stars. The final phase is represented by debris discs, when the primordial reservoir has been fully dissipated and/or incorporated into planetesimals of gas depletion factors have been reported within these cavities (e.
2004 ). These early observations have motivated the present study, but their quality and sensitivity is outmatched by the current dataset and will therefore not be presented here. Observations of this system by the Submilliter Array (SMA), Combined Array for Research in Millimeter-wave Astronomy (CARMA), and the Atacama Large Millimeter/submillimeter Array (ALMA) have been reported, revealing an extended gas disc (from the 12 CO J = 3→2 transition) out to the 250 au main dust ring highlighted in early HST images, and a dust disc extending out to 56 AU from the 870 µm continuum observations  (White et al. 2016; Flaherty et al. 2016). The total mass of gas was revised to values much larger than initially derived thanks to the optically thin line 13 CO J = 2→1  (Miley et al. 2018). From the mm continuum emission, a double component with spectral indices consistent with the range of values observed in both debris and primordial discs was reported by  White & Boley (2018) , and an unresolved dust ring peaking at 220 au was detected from 1.
3 mm ALMA observations by  Miley et al. (2018). In this article, we present complementary, multifrequency observations with ALMA and the NOrthern Extended Millimeter Array (NOEMA) 1 (Sect. 2). We characterise the dust mm continuum and the gas emission, taking advantage of the spectral information to derive constraints on the grain growth and emission lines opacities (Sect. 3). We finally model the 12 CO and 13 CO lines with the radiative transfer code Diskfit  (Piétu et al. 2007)  to characterise the temperature and density laws in this disc (Sect. 4). In Sect. 5, we finally compare the derived morphology at mm wavelengths with the dust disc seen in optical/IR domain and use the new constraints on the gas and dust mass to discuss the origin of the gas and the evolution status of this peculiar system.
ALMA observations We obtained ALMA observations of HD 141569 in Band 3. The data were recorded in August 2015 for the 13 CO J = 1→0 (110. 201 GHz) and C 18 O J = 1→0 (115. 271 GH ) transitions during two runs with 39 and 44 antennas, respectively  (project 2013. 1. 00883, PI. Péricaud). The spatial resolution was 0. 76 × 0. 56 (baselines up to 1. 55 km), and the spectral resolution 0. 2 km s -1. The data were collected with relatively poor weather conditions (PWV∼ 4 mm). We used Ceres and 1550+054 for the flux and amplitude calibration, 1550+0527 and 1517-2422 for bandpass calibration and 1550+0527 for the phase calibration. In addition, we collected archival raw data from the project 2012. 1. 00698. S (PI. Boley) to complement our analysis in Band 7 (275-373 GHz), which includes the 12 CO J = 3→2 line at 345.
796 GHz. A preliminary analysis of this data set was reported in  White et al. (2016). Only a subset of the observations could be properly calibrated. The observations carried out with 32 antennas provide a resolution of 0. 43 × 0. 35 (baselines up to 650 m), and a spectral resolution of 0. 8 km s -1. The flux and amplitude calibrator is Titan, the phase and bandpass calibrator is 1550+0527. We used the CASA package to calibrate the ALMA data, and we carried out the imaging and analysis of all NOEMA and ALMA observations with the GILDAS software. The imaging was performed with natural weighting for both ALMA and NOEMA.
g. White et al. 2016; Miley et al. 2018). Thirdly, the u, v coverage and the field of view can vary significantly between instruments, and the signal-to-noise ratio as a function of (u, v) radius can be very different from one dataset to another (e. g. at 1. 3 mm). We estimate the dust spectral index β from the slope of the spectral flux density, and we first add quadratically a typical calibration uncertainty of 10% to the flux density values. The spectral index is defined as β = α -2, with α = log(F ν 1 /F ν 2 )/ log(ν 1 /ν 2 ), F ν. A fit to the three frequencies yields the slope α. We derive the spectral index β in two cases: (i) for the global disc using the maximum flux values measured at the shortest baselines (u, v) ∼ 0, (ii) for the double component model, which provides a more realistic description of the continuum emission than the single-component model.
The 13 CO J = 2→1 emission appears to be more compact than A94, page 5 of 16 A&A 635, A94 (2020) Notes. ( a) Archival data from project ALMA. 1. 00698. S. For non detections, we provide 3σ upper limits. References. ( b) From  Flaherty et al. (2016). Fig. 2. Maps of integrated CO emission for the four detected transitions (the continuum was not subtracted due to its very low level of emission). Top: NOEMA observations, from left to right: 12 CO J = 2→1 (first contour at 5σ, second contour at 15σ, then 15σ spacing with σ = 31 mJy beam -1 km s -1 ), and 13 CO J = 2→1 with 3σ spacing contours, σ = 23 mJy beam -1 km s -1. Dotted lines show negative contours in steps of 3σ. Bottom: ALMA observations, from left to right: 12 CO J = 3→2 with uniform weighting to highlight the central gas cavity (3σ spacing, σ = 40 mJy beam -1 km s -1 ), and 13 CO J = 1→0 1σ spacing contours starting at 2σ (for positive and negative contours), σ = 6.
Modelling We independently model the 12 CO J = 2→1, 13 CO J = 2→1, and 12 CO J = 3→2 lines with the Diskfit code  (Piétu et al. 2007 ). We assume power laws for the CO surface density (Σ CO (r) = Σ 0 (r/100 au) -p ), the temperature T ex (r) = T 0 (r/100 au) -q , and the gas velocity V(r) = V 0 (r/100 au) -a v. In this study, we fixed the velocity exponent so that a v = 0. 5 (Keplerian rotation). The disc is assumed to have a sharp outer edge at R out. The vertical density is assumed to have a Gaussian profile (see Eq. (  1 ),  Piétu et al. 2007) , with the scale height being a (free) power law of radius H(r) = H 0 (r/100 au) -h. The line emission is computed assuming a (total) local line width dV independent of the radius and local thermodynamic equilibrium (LTE; i. e. T 0 represents the rotation temperature of the level population distribution).
(2016). The spatial resolution and sensitivity of the NOEMA observations are not sufficient to provide a robust constraint, but point towards consistent values of the inner disc edge. The 13 CO J = 2→1 data suggest a larger value R in = 35 ± 5 au. This discrepancy should be taken with care because the beam size of these NOEMA data is more than four to five times larger than the ALMA beam for 12 CO J = 3→2. If confirmed, this result could be explained by the difference in opacity between the two isotopologues: since the 12 CO transition is 70 times more optically thick than the 13 CO transition, a larger inner radius for 13 CO could be indicative of a shallow increase of the density at the inner disc edge, while a sharp edge is expected to produce similar inner radii for both lines. A similar effect has been reported in the 15-70 au gas cavity of transitional disc J160421.
Acknowledgements. This work was supported by  "Programme National de Physique Stellaire " (PNPS from  INSU/CNRS. )This research made use of the SIMBAD database, operated at the  CDS, Strasbourg, France. This paper makes use of the following ALMA data:  ADS/JAO. ALMA2012. 1. 00698. S and  ADS/JAO. ALMA. 2013. 1. 00883. S. ALMA is a partnership of  ESO  (representing its member states),  NSF (USA) , and  NINS (Japan) , together with  NRC (Canada) ,  NSC  and  ASIAA (Taiwan) , and  KASI (Republic of Korea)  in cooperation with the  Republic of Chile. The Joint ALMA Observatory is operated by  ESO ,  AUI/NRAO , and  NAOJ. This paper is also based on observations carried out with the IRAM NOEMA interferometer and the IRAM 30-m telescope. IRAM is supported by  INSU/CNRS (France) ,  MPG (Germany) , and  IGN (Spain).
There is a growing interest in leveraging differential geometry in the machine learning community. Yet, the adoption of the associated geometric computations has been inhibited by the lack of a reference implementation. Such an implementation should typically allow its users: (i) to get intuition on concepts from differential geometry through a hands-on approach, often not provided by traditional textbooks; and (ii) to run geometric machine learning algorithms seamlessly, without delving into the mathematical details. To address this gap, we present the open-source Python package geomstats and introduce hands-on tutorials for differential geometry and geometric machine learning algorithms -Geometric Learning -that rely on it.
Despite this need, the adoption of differential geometric computations has been inhibited by the lack of a reference implementation. Projects implementing code for geometric tools are often custom-built for specific problems and are not easily reused. Some Python packages do exist, but they mainly focus on optimization (Pymanopt  [TKW16] , Geoopt  [BG18] ,  [Koc19] , McTorch [MJK + 18]), are dedicated to a single manifold (PyRiemann  [Bar15] , PyQuaternion  [Wyn14] , PyGeometry  [Cen12] ), or lack unit-tests and continuous integration (TheanoGeometry  [KS17] ). An open-source, low-level implementation of differential geometry and associated learning algorithms for manifold-valued data is thus thoroughly welcome. Geomstats is an open-source Python package built for machine learning with data on non-linear manifolds [MGLB + ]: a field called Geometric Learning.
Presentation of Geomstats The package geomstats is organized into two main modules: geometry and learning. The module geometry implements lowlevel differential geometry with an object-oriented paradigm and two main parent classes: Manifold and RiemannianMetric. Standard manifolds like the Hypersphere or the Hyperbolic space are classes that inherit from Manifold. At the time of writing, there are over 15 manifolds implemented in geomstats. The class RiemannianMetric provides computations related to Riemannian geometry on such manifolds such as the inner product of two tangent vectors at a base point, the geodesic distance between two points, the Exponential and Logarithm maps at a base point, and many others. The module learning implements statistics and machine learning algorithms for data on manifolds.
The code is objectoriented and classes inherit from scikit-learn base classes and mixins such as BaseEstimator, ClassifierMixin, or RegressorMixin. This module provides implementations of Fréchet mean estimators, K-means, and principal component analysis (PCA) designed for manifold data. The algorithms can be applied seamlessly to the different manifolds implemented in the library. The code follows international standards for readability and ease of collaboration, is vectorized for batch computations, undergoes unit-testing with continuous integration, and incorporates both TensorFlow and PyTorch backends to allow for GPU acceleration. The package comes with a visualization module that enables users to visualize and further develop an intuition for differential geometry. In addition, the datasets module provides instructive toy datasets on manifolds.
First Steps To begin, we need to install geomstats. We follow the installation procedure described in the first steps of the online documentation. Next, in the command line, we choose the backend of interest: NumPy, PyTorch or TensorFlow. Then, we open the iPython notebook and import the backend together with the visualization module. In the command line: Modules related to matplotlib and logging should be imported during setup too. More details on setup can be found on the documentation website: geomstats. ai. All standard NumPy functions should be called using the gs. prefix -e. g. gs. exp, gs. log -in order to automatically use the backend of interest.
The result is shown in Figure  1  (left). What happened? The mean of two points on a manifold (the sphere) is not on the manifold. In our example, the mean of these cities is not on the earth's surface. This leads to errors in statistical computations. The line sphere. belongs(linear_mean) returns False. For this reason, researchers aim to build a theory of statistics that is -by construction -compatible with any structure with which we equip the manifold. This theory is called Geometric Statistics, and the associated learning algorithms: Geometric Learning. In this specific example of mean computation, Geometric Statistics provides a generalization of the definition of "mean" to manifolds: the Fréchet mean. Notice in this code snippet that geomstats provides classes and methods whose API will be instantly familiar to users of the widely-adopted scikit-learn.
Tutorial: Elementary Operations for Data on Manifolds The previous tutorial showed why we need to generalize traditional statistics for data on manifolds. This tutorial shows how to perform the elementary operations that allow us to "translate" learning algorithms from linear spaces to manifolds. We import data that lie on a manifold: the world cities dataset, that contains coordinates of cities on the earth's surface. We visualize it in Figure  2. How can we compute with data that lie on such a manifold? The elementary operations on a vector space are addition and subtraction. In a vector space (in fact seen as an affine space), we can add a vector to a point and subtract two points to get a vector. Can we generalize these operations in order to compute on manifolds? For points on a manifold, such as the sphere, the same operations are not permitted.
A geodesic, roughly, is the analog of a straight line for general manifolds -the path whose, length, or energy, is minimal between two points, where the notions of length and energy are defined by the Riemannian metric. This code snippet shows how to compute the exponential map and the geodesic with geomstats. Similarly, on manifolds, the logarithm map is the operation that generalizes the subtraction of two points on vector spaces. The logarithm map takes two points on the manifold as inputs and returns the tangent vector required to "shoot" from one point to.
Initial point End point Geodesic Fig. 3 : Elementary operations on manifolds illustrated on the sphere. The exponential map at the initial point (blue point) shoots the black tangent vector along the geodesic, and gives the end point (orange point). Conversely, the logarithm map at the initial point (blue point) takes the end point (orange point) as input, and outputs the black tangent vector. The geodesic between the blue point and the orange point represents the path of shortest length between the two points. the other. At any point, it is the inverse of the exponential map. In Figure  3 , the logarithm of the orange point at the blue point returns the tangent vector in black. This code snippet shows how to compute the logarithm map with geomstats. log = sphere. metric. log( point=end_point, base_point=initial_point) We emphasize that the exponential and logarithm maps depend on the "Riemannian metric" chosen for a given manifold: observe in the code snippets that they are not methods of the sphere object, but rather of its metric attribute.
The Riemannian metric defines the notion of exponential, logarithm, geodesic and distance between points on the manifold. We could have chosen a different metric on the sphere that would have changed the distance between the points: with a different metric, the "sphere" could, for example, look like an ellipsoid. Using the exponential and logarithm maps instead of linear addition and subtraction, many learning algorithms can be generalized to manifolds. We illustrated the use of the exponential and logarithm maps on the sphere only; yet, geomstats provides their implementation for over 15 different manifolds in its geometry module with support for a variety of Riemannian metrics. Consequently, geomstats also implements learning algorithms on manifolds, taking into account their specific geometric structure by relying on the operations we just introduced.
Similarly, in fMRI, it is possible to extract connectivity graphs from time series of patients' resting-state images [WZD + 13]. The regularized graph Laplacians of these graphs form a dataset of SPD matrices. This provides a compact summary of brain connectivity patterns which is useful for assessing neurological responses to a variety of stimuli, such as drugs or patient's activities. More generally speaking, covariance matrices are also SPD matrices which appear in many settings. Covariance clustering can be used for various applications such as sound compression in acoustic models of automatic speech recognition (ASR) systems  [SMA10]  or for material classification  [FHP15] , among others. Covariance descriptors are also popular image or video descriptors  [HHLS16]. Lastly, SPD matrices have found applications in deep learning.
Manifold of SPD matrices Let us recall the mathematical definition of the manifold of SPD matrices. The manifold of SPD matrices in n dimensions is embedded in the General Linear group of invertible matrices and defined as: SPD = S ∈ R n×n : S T = S, ∀z ∈ R n , z = 0, z T Sz > 0. The class SPDMatricesSpace inherits from the class EmbeddedManifold and has an embedding_manifold attribute which stores an object of the class GeneralLinear. SPD matrices in 2 dimensions can be visualized as ellipses with principal axes given by the eigenvectors of the SPD matrix, and the length of each axis proportional to the squareroot of the corresponding eigenvalue. This is implemented in the Figure  4  shows a dataset of SPD matrices in 2 dimensions organized into 3 classes. This visualization helps in developing an intuition on the connectomes dataset that is used in the upcoming tutorial, where we will classify SPD matrices in 28 dimensions into 2 classes.
Classifying brain connectomes in Geomstats We now delve into the tutorial in order to illustrate the use of traditional learning algorithms on the tangent spaces of manifolds implemented in geomstats. We use brain connectome data from the MSLP 2014 Schizophrenia Challenge. The connectomes are correlation matrices extracted from the time-series of resting-state fMRIs of 86 patients at 28 brain regions of interest: they are points on the manifold of SPD matrices in n = 28 dimensions. Our goal is to use the connectomes to classify patients into two classes: schizophrenic and control. First we load the connectomes and display two of them as heatmaps in Figure  5. Multiple metrics can be used to compute on the manifold of SPD matrices  [DKZ09]. As mentionned in the previous tutorial, different metrics define different geodesics, exponential and logarithm maps and therefore different algorithms on a given manifold.
Here, we import two of the most commonly used metrics on the SPD matrices, the log-Euclidean metric and the affine-invariant metric  [PFA06] , but we highlight that geomstats contains many more. We also check that our connectome data indeed belongs to the manifold of SPD matrices: Great! Now, although the sum of two SPD matrices is an SPD matrix, their difference or their linear combination with nonpositive weights are not necessarily. Therefore we need to work in a tangent space of the SPD manifold to perform simple machine learning that relies on linear operations. The preprocessing module with its ToTangentSpace class allows to do exactly this.
Another class of machine learning algorithms can be used very easily on manifolds with geomstats: those relying on dissimilarity matrices. We can compute the matrix of pairwise Riemannian distances, using the dist method of the Riemannian metric object. In the following code-snippet, we use ai_metric. dist and pass the corresponding matrix pairwise_dist of pairwise distances to scikit-learn's K-Nearest-Neighbors (KNN) classification algorithm: This tutorial showed how to leverage geomstats to use standard learning algorithms for data on a manifold. In the next tutorial, we see a more complicated situation: the data points are not provided by default as elements of a manifold. We will need to use the lowlevel geomstats operations to design a method that embeds the dataset in the manifold of interest.
Tutorial context and description This tutorial demonstrates how to make use of the low-level geometric operations in geomstats to implement a method that embeds graph data into the hyperbolic space. Thanks to the discovery of hyperbolic embeddings, learning on Graph-Structured Data (GSD) has seen major achievements in recent years. It had been speculated for years that hyperbolic spaces may better represent GSD than Euclidean spaces  [Gro87]   This tutorial illustrates how to learn hyperbolic embeddings in geomstats. Specifically, we will embed the Karate Club graph dataset, representing the social interactions of the members of a university Karate club, into the Poincaré ball. Note that we will omit implementation details but an unabridged example and detailed notebook can be found on GitHub in the examples and notebooks directories of geomstats.