dataesr/scientific-paragraphs-categorization huggingface dataset:
For the sake of simplicity, we use this analytical description of the disc temperature for our model -instead of self-consistently computing the temperature using a Monte Carlo approach (see e. g. Liu et al. 2022 ). In Section 5. 4 , we discuss the reasons for such choice and the caveats that come with it. The expected surface brightness of the disc can then be determined assuming dust thermal emission. In order to create mock images of our disc models, we use the code RADMC-3D. 1  We set the extrinsic parameters (such as the distance, sky coordinates, inclination, and position angle) in accordance with observations (see Section 3 ), and we produce synthetic images of the discs according to the radiative transfer computation. Then, we use the CASA package  (CASA Team et al. 2022 )  to produce mock observations with the same beam and antennae configuration of the original ALMA data.
In order to do this we have retrieved from the DSHARP Data Release webpage. 2  the visibility files of the DSHARP observations. In our analysis we use the same version of CASA used by the DSHARP team (v 5. 1. 1-5) to ensure that the data and the models have been processed in the same way  3  We created synthetic visibilities from the radiative transfer image at the UV coordinates of the observations using the CASA task ft. We then apply the CLEAN algorithm to generate a synthetic ALMA image to compare with the observed image. We use the scripts provided by the DSHARP team in order to make sure that we use the same CLEAN parameters as the observations. To reduce the computational time, it is common in the field to employ the simpler approach of a convolution with a Gaussian beam. While this is often satisfactory, we noticed in early tests that the detailed shape of the emission profile in the gap is different from images produced by the CLEAN algorithm.
D S H A R P DATA S A M P L E In this section, we describe the systems we use for our analysis. DSHARP is a very high resolution ( ∼0. 035", or 5 au) observational campaign that targeted 20 protoplanetary discs with the goal of finding and characterizing substructures in the dust continuum emission at 240 GHz. We examined the entire DSHARP catalogue and excluded the systems that are not suitable for our study of the gap-filling effect. These include 3 single systems that show signs of spirals (i. e. IM Lup, Elias 27, and WaOph 6) and two binary systems  (HT Lup and AS 205) , where the individual discs either show signs of spirals or lack clear substructure. Spirals are not compatible with the assumption of perfect azimuthal symmetry in our disc model and we therefore discard the discs showing this signature.
, as this w ork w as originally conceived as part of the LEAPS program at Leiden Observatory. GR also acknowledges support from an STFC Ernest Rutherford Fellowship (grant number ST/T003855/1). BT acknowledges support from the Programme National 'Physique et Chimie du Milieu Interstellaire' (PCMI) of CNRS/INSU with INC/INP and cofunded by CNES. This w ork w as funded by the European Union under the European Union's Horizon Europe Research & Innovation Programme grant number 101039651 (DiscEvol). Views and opinions expressed are ho we ver those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.
The first search for ultra-rare K + decays into the π + e + e -e + e -final state is reported, using a dataset collected by the NA62 experiment at CERN in 2017-2018. An upper limit of 1. 4 × 10 -8 at 90% CL is obtained for the branching ratio of the K + → π + e + e -e + e -decay, predicted in the Standard Model to be (7. 2 ± 0. 7) × 10 -11. Upper limits at 90% CL are obtained at the level of 10 -9 for the branching ratios of two prompt decay chains involving pair-production of hidden-sector mediators: K + → π + aa, a → e + e -and K + → π + S, S → A A , A → e + e -.
Assuming an axion mass of 17 MeV/c 2 , lower bounds of B(K L → π 0 aa) > 10 -7 and B(K + → π + aa) > 2 × 10 -8 (differing by the K L /K + lifetime ratio) are predicted  [3] , allowing a test of the QCD axion explanation for the 17 MeV anomaly. • A scenario involving a dark scalar (S), and a dark photon (A ) with masses satisfying the condition m S ≥ 2m A leads to a prompt cascade process K + → π + S, S → A A  [3]. The case of prompt A → e + e -decay leads to the same final state as the K π4e decay. The NA62 experiment at CERN collected a dataset of K + decays into final states containing lepton pairs in 2017-2018. The first search, performed using this dataset, is reported here for the K π4e decay, and for pair-production of hidden-sector mediators in the prompt decay chains K + → π + aa, a → e + e -(denoted K πaa ) and K + → π + S, S → A A , A → e + e -(denoted K πS ).
Beam, detector and data sample The layout of the NA62 beamline and detector  [13]  is shown schematically in Fig. 1. An unseparated secondary beam of π + (70%), protons (23%) and K + (6%) is created by directing 400 GeV/c protons extracted from the CERN SPS onto a beryllium target in spills of 3 s effective duration. The central beam momentum is 75 GeV/c, with a momentum spread of 1% (rms). Beam kaons are tagged with a 70 ps time resolution by a differential Cherenkov counter (KTAG) that uses nitrogen gas at 1. 75 bar pressure contained in a 5 m long vessel as the radiator. Beam particle positions, momenta and times are measured by a silicon pixel spectrometer consisting of three stations (GTK1,2,3) and four dipole magnets forming an achromat; a toroidal muon sweeper (scraper, SCR) is installed between GTK1 and GTK2.
Background estimation Background from five-track and seven-track K + decays is evaluated with simulation; all K + decays with branching ratios exceeding 10 -8 are considered. Background from coincidences of pairs of three-track K + decays in time (with one track not reconstructed) is evaluated with dedicated simulation of pairs of decays occurring within 25 ns; coincidences of all types of three-track K + decays with products of branching ratios exceeding 2 × 10 -6 are considered. The probability of two decays occurring within this 25 ns time window is dependent upon the instantaneous beam intensity, and is accounted for by normalising the total estimated background to the data in the momentum excess region ∆p > 20 GeV/c. Contributions from all possible triple coincidences of one or more K + → π + π + π -decays with K + → µ + ν decays and beam halo particles, and contributions from coincidences of threetrack decays with inelastic interactions of beam particles in GTK3, are found to be much smaller than those from coincidences of pairs of three-track decays, and are neglected.
Acknowledgements We are grateful to  Matheus Hostert  and  Maxim Pospelov  for suggesting this study, and for the discussions of the phenomenology of pair-production of dark states. It is a pleasure to express our appreciation to the staff of the  CERN laboratory  and the technical staff of the participating laboratories and universities for their efforts in the operation of the experiment and data processing. The cost of the experiment and its auxiliary systems was supported by the funding agencies of the  Collaboration Institutes. We are particularly indebted to: F. R. S. -FNRS  ( Fonds de la Recherche Scientifique -FNRS) , under Grants No. 4. 4512. 10, 1. B. 258. 20 ,  Belgium ;  CECI (Consortium des Equipements de Calcul Intensif) , funded by the  Fonds de la Recherche Scientifique de Belgique (F.
R. S. -FNRS)  under Grant No. 2. 5020. 11  and by the  Walloon Region, Belgium ;  NSERC (Natural Sciences and Engineering Research Council) , funding  SAPPJ-2018-0017 ,  Canada ;  MEYS (Ministry of Education, Youth and Sports)  funding  LM 2018104 ,  Czech Republic ;  BMBF (Bundesministerium für Bildung und Forschung)  contracts  05H12UM5 ,  05H15UMCNA  and  05H18UMCNA ,  Germany ;  INFN (Istituto Nazionale di Fisica Nucleare) ,  Italy ;  MIUR (Ministero dell'Istruzione, dell'Università e della Ricerca), Italy ;  CONACyT (Consejo Nacional de Ciencia y Tecnología), Mexico ;  IFA (Institute of Atomic Physics) Romanian CERN -RO No. 1/16. 03. 2016  and  Nucleus Programme   PN 19 06 01 04 ,  Romania ;  MESRS (Ministry of Education, Science, Research and Sport), Slovakia ;  CERN (European Organization for Nuclear Research), Switzerland ;  STFC (Science and Technology Facilities Council) ,  United Kingdom ;  NSF (National Science Foundation ) Award Numbers  1506088  and  1806430 , U.
High-temperature X-ray diffraction was performed on a PANalytical X'pert MDP diffractometer equipped with a backward monochromator, an Anton-Paar HKT16 chamber, a scintillation detector, and a Cu-Kα (l = 0. 15418 nm) radiation generator. Measurements were performed from room temperature to 300 °C, with 25 °C increments, and at a heating rate of 3 °C/min. The last diffractogram at 25 °C was recorded after cooling down at room temperature. Data acquisition was performed in the 2θ range 10°-80°, with a step size of 0. 017°. The patterns were analyzed using the Eva Bruker ® software and compared to the PDF database using the FindIt ICSD software. In the diffractograms, the two peaks at 39. 5 and 46° belong to the aluminum sample holder; their slightly low theta shift is related to its thermal dilation.
Observations and data set reduction The observations were obtained at the IRAM 30-meter telescope (hereafter 30m) using the heterodyne Eight MIxer Receiver (EMIR) in one atmospheric windows E090 band at 3 mm  (Carter et al. 2012 ) from 84. 5 to 115. 5 GHz. The Fast Fourier Transform Spectrometer (FTS) was connected to the EMIR receiver. The FTS200 backend provided total bandwidth of ∼32 GHz with a spectral resolution of 195 kHz (0. 5 km s - 1  ). The full field of view of 5 square degrees was covered using rectangular tiles with a position angle of 14 • in the Equatorial J2000 frame to follow the global morphology of the Orion B cloud. Details of the observation strategy can be found in  Pety et al. (2017). Data reduction was carried out using CLASS, which is part of the GILDAS 1 software, following the standard steps: removal of atmospheric emission, gain calibration, baseline subtraction, and gridding of individual spectra to produce regularly sampled maps with pixels of 9 size.
Details of each step can be found in  Pety et al. (2017). Each datacube covers a velocity range of 120 km s -1 (240 channels spaced by 0. 5 km s -1 ) centered at the rest line frequency (see Table  1 ). The spatial coordinates of the data cubes are centered onto the photon-dominated region (PDR) of the Horsehead Nebula at the coordinates (05h40m54. 270s, -02 • 28 00. 00 ) and rotated by an angle of 14 • counterclockwise with respect to the Equatorial J2000 frame. The properties of the resulting maps, including the spatial resolution of the molecular line emission maps and the root mean square (rms) noise levels from the mean spectra are reported in Table  1.
Column density maps From the C 18 O and 13 CO (1-0) zero-order moment maps (see Fig. 4 ), we derived the column density N H maps of each cloud layer by using the following equations  (Orkisz et al. 2019; Roueff et al. 2021) : N C 18 O /N H = 5. 6 × 10 -7 2 , N13 CO /N H = 2. 5 × 10 -6 2. (1) In these equations, N H represents the total column of hydrogen, including the contributions of atomic and molecular hydrogen, N H = N(HI) + 2N(H 2 ). We assumed local thermodynamic equilibrium and an optically thin emission. We used the standard equations described in  Mangum & Shirley (2015) , the param-eters values from the Cologne Database for Molecular Spectroscopy (CDMS;  Endres et al. 2016) , and the dust temperature T dust map from  Lombardi et al. (2014). We assumed that the dust temperature is a good estimate for the excitation temperature of 13 CO (1-0) and C 18 O (1-0).
The Orion B cloud layers we identified are not distinguished by  Lombardi et al. (2014) : the T dust map is therefore the same for all cloud layers. More details on the assumptions made to compute the column density can be found in Sect. 2. 4 of  Orkisz et al. (2019). Figure  5  shows the column density maps of each layer of the cloud deduced from the 13 CO (1-0) and C 18 O (1-0) data sets. In the following, we distinguish the column density deduced from the 13 CO (1-0) and from the C 18 O (1-0) data sets with the notation N 13 H and N 18 H , respectively. For the C 18 O (1-0) emission, we only kept the pixels with a column density N 18 H higher than 10 21 cm -2 because at lower values, the signal to noise ratio becomes marginal. For the 13 CO (1-0) emission, we only kept the pixels with a column density N 13 H higher than 10 20 cm -2.
e. , ∼ 0. 2 pc,  Arzoumanian et al. 2011; Orkisz et al. 2019). Second, we took the widths of the filaments into account. We removed the filaments with an unresolved width, namely lower than the resolution of the data sets (i. e. , ∼ 0. 02 pc). Excessively large filaments (i. e. , 0. 28 pc) are also removed because they are unstable. Third, we analyzed the shape of the filaments by computing their mean curvature radius and comparing it to the width of the filament in order to remove the very curvy filaments (i. e. , ratio between curvature radius and width < 1. 5) but keeping the largescale loops. Finally, we measured the relative contrast to determine how many times denser the filament is compared to its surrounding medium. We put a lower limit on the relative contrast at ∼ 0. 5. Filaments are removed if they are rejected by more than one criterion.
To identify any preferential orientation of the velocity field with respect to the density structures, we built this histogram for different column density thresholds. We kept only the histograms with enough pixels to build them, namely with small error bars (<0. 0005). We chose five values of the threshold based on the visual extinction values estimated by  Pety et al. (2017) , representing diffuse gas (10 20 cm -2 and 10 21 cm -2 ), translucent gas (3. 5 × 10 21 cm -2 ), the environment of filaments (10 22 cm -2 ), and the dense cores (2. 5 × 10 22 cm -2 ). In the different subregions, the histograms peak around 0 • and/or 180 • for the 13 CO and C 18 O data set. The peaks are wider and noisier for the maps using the C 18 O (1-0) data set because the histograms are built on a smaller number of pixels than those using the 13 CO (1-0) data set.
In the histograms of NGC 2024, the Cloak, and the lowvelocity layer associated with Orion B9, a change of pattern is visible between the histogram angles built from the 13 CO(1-0) data set, and those using the C 18 O(1-0) one. In NGC 2024, the histogram peaks at 180 • in 13 CO whereas in C 18 O, the histogram peaks at 0 •. The 13 CO and C 18 O emissions do not trace the gas from the same spatial area in NGC 2024: a more extended region is detected in 13 CO (1-0) compared with the restricted area showing C 18 O (1-0) emission. Thus, this result suggests a change in the mechanisms responsible for the kinematics depending on the traced volume of gas. For Orion B9 from the low-velocity layer and the Cloak, the difference between the two lines can be explained by the low number of pixels available in the C 18 O data set, resulting in large error bars on the histograms.
Acknowledgements. We thank the referee for thoughtful comments that helped to improve the paper significantly. This work was supported in part by the  French Agence Nationale de la Recherche  through the  DAOISM grant   ANR-21-CE31-0010  and by the  Programme National "Physique et Chimie du Milieu Interstellaire" (PCMI)  of  CNRS/INSU  with  INC/INP , co-funded by  CEA  and  CNES. We thank " le centre Jules Jensen " from  Observatoire de Paris  for its hospitality during the workshops devoted to this project. This research has made use of data from the  Herschel Gould Belt Survey (HGBS)  project (http://gouldbelt-herschel. cea. fr). The HGBS is a Herschel Key Programme jointly carried out by SPIRE Specialist Astronomy Group 3 (SAG 3), scientists of several institutes in the  PACS Consortium (CEA Saclay, INAF-IFSI Rome and INAF-Arcetri ,  KU Leuven, MPIA Heidelberg ), and scientists of the  Herschel Science Center (HSC).
The model was tested using high and low resolution input temperature profiles, such as those expected from simulations and observations, respectively. We find that the proposed deconvolution and deprojection algorithm is robust with respect to the quality of the data, the morphology of the cluster, and the deprojection scheme used. The algorithm can recover unbiased 3D radial temperature profiles with a precision of around 5% over most of the fitting range. We apply the method to the first sample of temperature profiles obtained with XMM-Newton for the CHEX-MATE project and compared it to parametric deprojection and deconvolution techniques. Our work sets the stage for future studies that focus on the deconvolution of the thermal profiles (temperature, density, pressure) of the ICM and the dark matter profiles in galaxy clusters, using deep learning techniques in conjunction with X-ray, Sunyaev Zel'Dovich (SZ) and optical datasets.
Using deep learning techniques, Convolutional Neural Network (CNN) models have also been used to infer the dynamical mass of galaxy clusters  (Ho et al. 2019; Ramanah et al. 2020; Ho et al. 2021; de Andres et al. 2022). In particular,  Yan et al. (2020)  used mock datasets of stellar mass, soft X-ray flux, bolometric X-ray flux, and Compton y-parameter images as input to train a CNN model to infer the mass of galaxy clusters, and  Gupta & Reichardt (2020 , 2021)  trained CNN models to estimate cluster masses used mock SZ, cosmic microwave background (CMB) lensing maps. Ferragamo et al. (2023) , using a combination of an auto-encoder and a random forest regression technique on a sample of 73 138 mock Comptony parameter maps from the hydrodynamical simulations of the Three Hundred Project  (Cui et al.
Simulations In this work, training of the neural network is undertaken using the gas mass-weighted 3D temperature profiles, T 3D , of galaxy clusters from the Three Hundred Project  (Cui et al. 2018; Ansarifard et al. 2020). These simulations are based on the 324 Lagrangian regions centred on the z = 0 most massive galaxy clusters selected from the MultiDark darkmatter-only MDPL2 simulation  (Klypin et al. 2016) , carried out with the cosmological parameters from the Planck mission (Planck Collaboration XIII 2016). MDPL2 is a periodic cube of comoving size equal to 1. 48 Gpc containing 3840 3 dark matter particles. The selected regions were resimulated with the inclusion of baryons and were carried out with the code GADGET-X  (Beck et al. 2016). To treat the baryonic physics several processes were included such as: metallicity-dependent radiative cooling, the effect of a uniform time-dependent UV background, a sub-resolution model for star formation from a multi-phase interstellar medium, kinetic feedback driven by supernovae, metal production from SN-II, SN-Ia and asymptotic-giantbranch stars, and AGN feedback  (Rasia et al.
Model fitting The IAE model is tested/fitted on the validation sample consisting of the remaining 115 galaxy clusters in the sample which were not used in the training stage. We have verified that the validation sample is representative of the full sample: about onethird of the validation clusters have cool cores, and the fractions of relaxed/disturbed clusters and smooth/irregular profiles are similarly distributed in the training and validation samples. 3 https://github. com/jbobin/IAE We employ Markov chain Monte Carlo (MCMC) analysis to estimate the parameters of the IAE models and use the publicly available emcee python package  (Foreman-Mackey et al. 2013 ) for this purpose. The parameter estimation is undertaken on all the IAE parameters: the five anchor point weights Λ = [λ 1 , λ 2 , λ 3 , λ 4 , λ 5 ], and the amplitude (normalisation) parameter α.
suitable for application to such observations, we first extrapolated the simulated temperature profiles to 0. 005 R 500 by fitting a  Vikhlinin et al. (2006)  parametric model in the inner regions (up to 0. 5 R 500 ). We then re-trained the IAE model in the full radial range of [0. 005-2] R 500 with the simulated dataset, augmented by the parametric model extrapolation in the very central regions.
Observed sample We then use this updated IAE model on the latest CHEX-MATE Data Release 1, DR1 sample  (Rossetti et al. , in prep. )  to deconvolve the temperature profiles. The DR1 sample is a 'technical but representative' sub-sample, which was built to test our pipeline for the extraction and reconstruction of the radial temperature and density profiles. It is composed of 30 clusters, whose distribution in mass, redshift, and Planck signal-to-noiseratio (S/N) reflect the properties of the CHEX-MATE parent sample. Table  A. 1 provides the details of all the clusters in the DR1 sample. For data reduction and analysis, we used the XMM-Newton Science Analysis System (SAS), version 16. 1. We refer to  Bartalucci et al. (2023)  for details on the data reduction procedures (calibration, standard pattern cleaning, removal of noisy MOS CCDs, and light-curve filtering) and on the detection of contaminating sources.
From the EPIC images in the 0. 7-1. 2 keV band, we extracted both mean and median surface brightness radial profiles, centered on the peak and on the centroid within R 500. For the temperature profile, we extract spectra in concentric annuli centered on the surface brightness peak, using the MOS-spectra and PN-spectra ESAS tools  (Snowden et al. 2008 ) embedded in SAS. For each region, we perform a joint fit of the MOS1, MOS2, and PN spectra with an adsorbed thermal model, to which we add a model for all the background components (Galactic foregrounds, CXB, Cosmic-ray particle background, residual soft protons). We estimate priors for the parameters of this background model that are allowed to vary within their uncertainty during the joint fit with the cluster parameters, running the Markov chain Monte Carlo method within XSPEC (see  Rossetti et al.
This can be also seen in the bottom panel where the ratio between reconstructed 3D temperature profiles with and without applying smoothing is seen to be less than 1% over most of the radial range. Figure  22  shows the logarithmic derivatives of the 3D temperature profiles of the clusters in the DR1 sample obtained with the IAE model. Also, in the bottom panel, we show the difference in logarithmic derivatives derived from IAE and parametric models (∆). We find that, although dispersion in the difference increases with the radius, the difference is consis-7 https://pypi. org/project/loess/ tent with zero throughout the radial range. While it is difficult to quantify this difference in the inner region, since logarithmic derivatives are close to zero, in the range [0. 5-2] R 500 the difference in logarithmic derivatives between the IAE and the parametric model can be more than as 20%.
Discussion and conclusions Classical statistical modelling techniques can be sensitive to inaccuracies and may lead to poor performance if the data are complex (non-linear) and/or have a dynamic structure. Data-driven (model-agnostic) deep-learning techniques are now becoming increasingly popular. They make use of the topology to learn the underlying structure of the data, and often have been found to give superior performance in terms of accuracy and precision when the underlying structure of data are non-linear. However, one typically requires a massive dataset and vast computational resources to train the neural network, limiting their applicability for some scenarios. In this paper, we demonstrate the first use of deep learning techniques to build a model of galaxy cluster temperature profiles and apply this model to the problem of temperature profile deprojection.