dataesr/scientific-paragraphs-categorization huggingface dataset:
8 µmoles glucoraphanin per broccoli soup broccoli soup 280 ± 8. 8 µmoles glucoraphanin per Plasma GR: 0. 01 ± 0. 01 µmol L -1 GR: 0. 03 ± 0. 01 µmol L -1 Broccoli soup 1 day broccoli soup 452 ± 10. 6 µmoles glucoraphanin per 10 participants (3 Men and 7 women) aged 18-65 years NCT02300324 GR: 0. 04 ± 0. 02 µmol L -1 UPLC-MS/MS [29] Standard broccoli soup 1 day BENEFORTE broccoli soup 1 day GR: 84 ± 2. 8 µmoles glucoraphanin per broccoli soup 280 ± 8. 8 µmoles glucoraphanin per broccoli soup Urine GR and glucoerucin: 0. 54 ± 0. 29 µmol/24 h GR and glucoerucin: 1. 44 ± 0. 66 µmol/24 h Broccoli soup GR and glucoerucin: 1 day 2. 12 ± 0. 98 µmol/24 h.
Acknowledgements This work has been funded by the  European Research Council  for the Starting Grant 'DustOrigin', held by I. D. L. ,  University of Ghent , grant agreement ID no. 851622. It was supported by the  Agence Nationale de la Recherche (ANR)   SIRC  project (grant no. ANR-SPV202448 2020-2024 ). This work was supported by the  Programme National 'Physique et Chimie du Milieu Interstellaire ' by the  Programme National Cosmology et Galaxies of CNRS/INSU  with  INC/INP  and  IN2P3 , cofunded by  CEA  and  CNES , and by the  DIM-ACAV+ , a funding programme of the  Region Ile de France. F. G. and F. D. thank colleagues from  LERMA-CYU  for their support.
Acknowledgements The authors thank  Clarisse Gosset-Erard  ( LSMIS, Université de Lorraine ) for her advises on the creation of the figures,  Thomas Weissenberger  ( Université de Strasbourg ) for the access to the LCQ Fleet instrument,  Cyrille Lamboley  and  Patricia Lecomte  ( Restek, France ) for supporting our LC tests with the gracious loan of the biphenyl column, and  Kudzu Science  for providing the settled dust sampling kits. This work was supported by a Ph. D. grant from the  French Ministry of Higher Education, Research and Innovation  and the  University of Strasbourg.
Once crystallized, the compounds are essentially insoluble in coordinating and non-coordinating deuterated solvents, and thus solution-state spectroscopic data could not be obtained. The solid-state infrared spec-trum of 1 a was obtained, though the absorption bands due to metal-hydride stretching modes associated with the AlÀ HÀ Mg moieties could not be assigned, as these likely lie in the fingerprint region of the spectrum, as has been reported to be the case for other compounds containing hydride bridged units, AlÀ HÀ Mg. [14, 15]  Accordingly, the deuterated analogue of 1 a, viz. [Al 6 D 8 (NMe 3 ) 2 {Mg-( Mes Nacnac)} 4 ] 1 a-D, was prepared and its infrared spectrum acquired. Due to likely overlap with strong ligand absorptions, it was not possible to distinguish between AlÀ HÀ Mg and AlÀ DÀ Mg stretching bands in the spectra of the compounds.
This could not be adequately modelled for the structures of 1 a and 1 b. In contrast, disorder within the Al 6 core of less symmetric 1 c could be modelled, showing the Al 6 core disordered over two slightly offset sites, each with an atomic occupancy of 50 %. That said, related disorder over the hydride and Nacnac ligand sites could not be resolved. Thus, the metal hydride distances within the structure should not be considered as definitive. Attempts were made to acquire a neutron single crystal structure for 1 a, and thus accurately locate the hydride nuclear positions. To this end, and although the diffraction data were too weak for a full refinement, neutron diffraction images from two single-crystal specimens of the compound were obtained, and proved suitable for careful difference mapping analyses of the limited low-resolution data sets thus acquired.
Acknowledgements C. J. and L. M. thank the  Australian Research Council  for funding. Moreover, this material is based upon work supported by the  Air Force Office of Scientific Research  under award number  FA2386-21-1-4048. L. M. is a senior member of the  Institut Universitaire de France  and thanks the  Humboldt Foundation. The award of discretionary neutron beam time to proposal 13415 at the  Australian Centre for Neutron Scattering, ANSTO , is gratefully acknowledged. Open Access publishing facilitated by  Monash University , as part of the  Wiley -Monash University agreement via the Council of Australian University Librarians.
If pyrene forms intramolecular aromatic stacking interactions with imidazole, the stability and emission response of such exciplex should be strongly affected by protonation/ deprotonation of imidazole (pK a 7). Emission spectra of 2 and 3 collected at pH = 6-8. 5 (ESI, Fig. S11 † ) reveal only a minor difference in intensity but the shape of the emission spectrum remains unchanged, suggesting that imidazole is not in interaction with pyrene(s). In order to obtain a deeper insight into the photophysical processes in solutions of 2 and 3, we have collected timeresolved uorescence decay data (s in Table  1 , ESI, Fig. S12  and S13 †) and compared them with two referent compounds, A (free, non-stacked pyrene) and B (pyrene exciplex with another aromatic unit). 36  The data were collected at two emission wavelengths: 475 nm (characteristic for excimer/exciplex) and 400 nm (characteristic for non-stacked pyrene), and in two solvents, DMSO and water (only the latter stimulates aromatic stacking and hydrophobic interactions).
Analysis of time-resolved uorescence decay data (s in Table  1 ) shows (at 400 nm) the presence of long-lived emitting species in all cases, attributed to the free pyrene uorophore (in comparison to reference A), thus not in the interaction with another aromatic moiety (e. g. calixarene or another pyrene). Data collected at 475 nm reveal the presence of several shorterliving emissive species, which are by comparison to reference B and literature data 37 attributed to the pyrene excimer or exciplex. In an aqueous medium, analogues 2 and 3 show a similar distribution of three species, whereby two values of similar magnitude dominate (12. 66 and 47. 23 ns for 2; 26. 69 and 64. 65 ns for 3). In DMSO, at 475 nm both 2 and 3 show very similar dominant values, 47. 60 or 49. 57 ns, respectively, pointing out that upon exclusion of water, one dominant type of pyrene stacked with another aromatic moiety remains.
Limitations in filament desorption The collection and heat-pulse desorption from a catcher filament ensures on the one hand an efficient neutralization and in addition a well-confined atom-light interaction region, which is important for the required efficiencies for laser spectroscopy of the heaviest elements. The low-energy tailing for the gas-cell measurements arises from the direct collection on the silicon surface. The nuclear data are taken from Ref. [23]. On the other hand, the desorption from the filament poses an additional experimental challenge, as the required temperature, dictated by the adsorption enthalpy of the atoms of interest on the surface material, might not be reached. To test the limitation of the heat-pulse desorption, on-line produced actinium isotopes and their respective decay products were investigated with RADRIS.
Acknowledgements This experiment has been carried out as part of FAIR-Phase-0 at the beam line Y7/SHIP at the  GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany. This work has been supported by the  Bundesministerium für Bildung und Forschung (BMBF, Germany)  under Project No. 05P18UMCIA. This project has received funding from the  European Union 's  Horizon 2020 research and innovation programme  under grant agreement No  861198-LISA-H2020-MSCA-ITN-2019. RADRIS has received funding from  IN2P3-DSM/CEA  and  GSI  under the  French-German  collaboration agreement number  PN1064. E. K. , E. R. -R. and M. L. acknowledge funding from the  European Research Council (ERC)  under the European Union's  Horizon 2020 Research and Innovation Programme  (Grant Agreement No. 819957 ). A.
C. , P. C, A. d. R. , R. F. , F. I. , S. K. , J. R. and P. V. D. acknowledge funding from the  Research Foundation -Flanders (FWO)  and from the  EOS  (nr. 30468642 ) project of the  FWO and F. R. S. -FNRS  under the  Excellence of Science (EOS)  programm. T. W. acknowledges funding from the  Bundesministerium für Bildung und Forschung (BMBF, Germany)  under grant number  05P21RDFN1. Part of the results presented in this work are also part of the PhD thesis of J. W.
Such codes include RADEX  (van der Tak et al. 2007 ), RADMC-3D  (Dullemond et al. 2012) , LIME  (Brinch & Hogerheijde 2010) , MCFOST  (Pinte et al. 2022) , and MOLPOP-CEP  (Asensio Ramos & Elitzur 2018). Some other codes adopt a more holistic approach and take multiple physical phenomena into account as well as their coupling, for instance, large chemical networks, thermal balance, and radiative transfer. Furthermore, Hii region models such as Cloudy  (Ferland et al. 2017 ) reconstruct the chemical structure of ionized regions. They evaluate line intensities from input parameters including illuminating star properties, the medium density, metallicity, and elementary abundances. Shock models such as the Paris-Durham code  (Godard et al. 2019 ) and the MAPPINGS code  (Sutherland et al. 2018 ) compute the chemical structure of interstellar shocks and observables such as line intensities.
Here, the main input parameters are the shock velocity, pre-shock densities, and the intensity of the magnetic field. Finally, photodissociation region (PDR) models such as the Meudon PDR code (Le  Petit et al. 2006 ) describe the ultraviolet (UV) irradiated medium at the edge of molecular clouds in star-forming regions or diffuse interstellar clouds. They compute the thermal and chemical structure of these objects as well as observables such as the atomic and molecular line intensities. The input parameters mainly include the intensity of the incident stellar UV radiation field, the gas density or thermal pressure, the visual extinction, the metallicity and the cosmic ray ionization rate. In the following, we use the term "physical parameters" to refer to a subset of interest of the input parameters that a code uses to compute observables.
For each of these models, small changes in the physical parameters can lead to very different predicted observables. The adjustment of the physical parameters to allow the predicted observables to match the actual observations can therefore be used to estimate these physical parameters. Codes that model the observed environment more realistically lead to more meaningful estimations. However, the complexity of the physics considered in a code directly impacts its evaluation time and, hence, its applicability. On the one hand, a simple 0D code such as RADEX can run in just a few seconds. Such fast codes can be used directly for inference in minimization-based or Bayesian Markov chain Monte Carlo (MCMC) sampling approaches  (Robert & Casella 2004, chapter 7) , which require numerous iterative evaluations.
2012) , used for instance in  Jóhannesson et al. (2016) , relies on the SkyNet neural network  (Graff et al. 2014)  to emulate the full likelihood function. Emulating the full likelihood requires the assumption of a noise model and it is therefore either observation-specific or generic. For instance, SkyNet assumes a Gaussian likelihood with a fixed variance for continuous variable inference. In this work, we focus on full numerical code emulation to be able to apply the obtained emulator to any observation from any telescope, with any noise model and any set of lines. In practice, the emulation of a numerical model is based on a grid of precomputed models that spans the relevant parameter space, generated prior to any comparison with observations. A search for the point in the grid that best reproduces the observations is sometimes performed  (Sheffer et al.
2011; Sheffer & Wolfire 2013; Joblin et al. 2018). A better and more common way of exploiting the grid is to approximate the numerical model using interpolation methods, which permits the observables for new points to be predicted with a lower evaluation time  (Wu et al. 2018; Ramambason et al. 2022 ). In the following, a numerical code emulator defined from a grid of precomputed models using, for example, an interpolation method, is called a "surrogate model. " A grid of precomputed models is called a "dataset. " Interpolation methods have become the main approach to build surrogates of comprehensive ISM models over the last years thanks to their conceptual and implementation simplicity (e. g. ,  Wu et al. 2018; Ramambason et al. 2022). Nearestneighbor interpolation, linear interpolation, spline interpolation, and radial basis function (RBF) interpolation are the four most commonly used families of methods.
By definition, a surrogate model defined with an interpolation method passes exactly through the points of the dataset. This constraint does not guarantee a good level of accuracy with respect to new points. Besides, a surrogate model defined with an interpolation method requires the whole dataset to be stored, which can be very heavy if it contains many precomputed models or many quantities associated to each model. Finally, although they are generally faster than the original numerical codes, interpolation methods handle outputs (i. e. , observables) independently. Thus, they are quite slow when the number of outputs is large. In this work, we aim to derive accurate, fast, and light surrogate models. To do so, we relaxed the constraint of having the model pass through the points of the dataset.
In this case, deriving a surrogate model thus becomes a regression problem, which benefits from many recent advances in numerical optimization developed for machine learning. Such approaches have already been applied in ISM studies. For instance, in  Smirnov-Pinchukov et al. (2022) , a k-nearest-neighbor regression algorithm was used to emulate a protoplanetary disks model, while in  Bron et al. (2021) , a random forest was trained to emulate a chemistry model. However, most often, the versatile class of artificial neural networks (ANNs) is preferred to address the complexity of comprehensive ISM models. For instance, ANN emulators of astrochemical models were derived in  (de Mijolla et al. 2019; Holdship et al. 2021; Grassi et al. 2022 ). In addition, in  Grassi et al. (2011) , the authors derived a new simulation code and an associated ANN emulator.
Here, we emulate a state-ofthe-art ISM code, namely, the Meudon PDR code (Le  Petit et al. 2006). Such a code sometimes produces outliers due to potential numerical instabilities or physical bistabilities or multistabilities. It also predicts several thousands of observables from a handful of parameters, which is unusual in the machine learning community -except for networks that generate structured data such as images, text, or times series. In observations, only a fraction of these observables are measured. However, different observations can detect very different subsets of observables. To avoid having to derive one surrogate model per subset of observables, we chose to emulate the full code at once. We present five main strategies to derive high performance surrogate models in these conditions.
(in prep). We note that ANNs come with the ability to automatically and efficiently compute derivatives such as the gradient and the Hessian matrix, which Pierre Palud et al. : Neural network-based emulation of interstellar medium models enables using faster and more accurate inference methods. All proposed ANNs were implemented using the PyTorch Python library  1. The most accurate ANN obtained in this work has been made publicly available 2. The paper is structured as follows. Section 2 describes the emulation methods to be compared. Section 3 describes the Meudon PDR code and the dataset of precomputed models. It also introduces the framework used to compare surrogate models. In Section 4, we describe our design of ANNs that address the ISM numerical codes specificities. In Section 5, we compare these ANNs with classic interpolation methods with respect to speed, memory requirements, and accuracy.
Interpolation methods in ISM studies Interpolation methods yield functions that pass exactly through the points of a dataset of precomputed models. In this paper, four common families of interpolation methods are studied: nearest-neighbor interpolation, linear interpolation, spline interpolation  (Bojanov et al. 1993) , and RBF interpolation  (Fasshauer 2007, chapter 6). The nearest-neighbor interpolation assigns the value of the closest point in the dataset to a new point. It is fast but generally performs poorly in terms of accuracy. It is somewhat equivalent to a search for the closest point in a grid, which is common in ISM studies (e. g. ,  Sheffer et al. 2011; Sheffer & Wolfire 2013; Joblin et al. 2018). The piece-wise linear interpolation generally performs better, while remaining quite fast.
It first triangulates the dataset, so that a new point is associated to a cell of the triangulation. It then returns a weighted average of the cell point values. It was used in some ISM studies, such as in  Ramambason et al. (2022). Spline interpolation methods are based on piece-wise polynomials, yielding an even more accurate and still fast surrogate model. Finally, the RBF interpolation, used, for example, in  Wu et al. (2018)  to study a PDR, exploits the full dataset for each evaluation. For a new point, it returns a weighted sum of the values of all the dataset points, where the weights depend on the distance to this new point. Surrogate models defined with RBF interpolation are generally very accurate but slower than other interpolation methods. In ISM studies, datasets of precomputed models are often structured as uniform grids (i.
e. , as lattices,  Joblin et al. 2018; Wu et al. 2018 ). This structure is not necessary for RBF interpolation methods or in regression approaches, and other structures that can be obtained with, for example, Latin hypercube sampling  (McKay et al. 1979 ), Stratified Monte Carlo (Haber 1966) , or the low-discrepancy sequences used in Quasi-Monte Carlo methods  (Asmussen & Glynn 2007, chapter 9) , might yield more accurate surrogate models. However, a uniform grid structure has many advantages. First, it is often more convenient to manually inspect a dataset with such a structure. Second, it allows for the use of certain efficient interpolation methods such as splines, for which a uniform grid structure is mandatory. Also, the regularity of the grid can be exploited to accelerate nearest-neighbor and linear interpolations.
In this work, we aim to perform a fair comparison between interpolation and ANN regression methods and, thus, we restrict the structure of the dataset used for fitting to uniform grids. Figure  1  shows a comparison of the aforementioned interpolation methods on the log Rosenbrock function: log R : x ∈ R 2 → log 1 + (1 -x 1 ) 2 + 100 x 2 -x 2 1 2 , ( 1 ) which is positive and admits a minimum at  (1, 1)  such that log R(1, 1) = 0. The interpolation methods are fitted on a 7 × 7 coarse regular grid on the square [-1, 1] × [-0. 5, 1. 5]. They are then evaluated on a 101×101 much finer grid on the same square. The accuracy of each method is evaluated using the absolute error (AE) that quantifies how distant the prediction f ℓ (x) is to the corresponding true value y ℓ AE (f ; (x, y ℓ )) = | f ℓ (x) -y ℓ |.
Performing regression with neural networks By relaxing the constraint of passing exactly through the points of the dataset of precomputed models, the derivation of a surrogate model becomes a regression problem. In machine learning, a regression problem consists in estimating the function f : R D → R L that best maps input vectors x to output vectors y. This function f is learned from a dataset of precomputed models D = {(x n , y n ) ∈ R D × R L , n = 1,. , N}. In this work, the input vector x corresponds to a vector of physical parameters (e. g. , temperature, thermal pressure, volume density) and the output vector y to observables computed by a numerical code (e. g. , intensities of specific lines). To perform this estimation, functions f are parametrized with vectors θ. This parametrization restricts the search to a class of functions.
An ANN predicts all outputs at once using a sequence of intermediate computations, which is considerably faster. In addition, ANNs are known to yield very accurate surrogate models both in theory and in practice. Finally, an ANN comes with the ability to automatically and efficiently compute the derivative of its outputs with respect to its inputs, using automatic differentiation  (Paszke et al. 2017). Overall, to address the complexity of ISM numerical models, exploit prior knowledge on the regularity of the function to approximate, and efficiently predict all outputs simultaneously, we adopted the rich and versatile class of ANNs. Below, we introduce this class of functions and then describe the approach used to fit an ANN to a dataset.
Fitting a neural network to a dataset In regression, once the class of function is set (here with an ANN architecture), the parameter θ is adjusted so that f θ fits the dataset D of precomputed models. A loss function L(f ; D) quantifies the distance between predictions f ℓ (x n ) and the corresponding true values y nℓ. It is based on an error function, such as the absolute error (AE, Eq. 2) or the squared error (SE), as follows: SE (f ; (x, y ℓ )) = ( f ℓ (x) -y ℓ ) 2. (4) The loss function summarizes the set of N × L errors obtained on the dataset D. The mean is often used for computational efficiency of evaluation and differentiation, yielding, for example, the mean squared error (MSE) or the mean absolute error (MAE). Obtaining the best function f boils down to minimizing the loss function with respect to the parameter θ f ∈ arg min θ L (f θ ; D).
g. , Shalev-Shwartz & Ben-David 2014, chapter 14) accelerates the search by using "batches" instead of the full dataset in gradient evaluations. Preconditioned variants such as RMSProp  (Tieleman & Hinton 2012)  or Adam  (Kingma & Ba 2017)  exploit the local geometry of the loss function to escape from saddle points and further accelerate convergence to a good local minimum. This optimization procedure is often called "training phase" or "learning phase" with ANNs, because the network progressively learns from data as the loss function decreases.
The Meudon PDR code: A representative ISM model The Meudon PDR code 4  (Le  Petit et al. 2006 ) is a 1D stationary code that simulates interstellar gas illuminated with a stellar radiation field. It can simulate the physics and chemistry of a wide variety of environments, such as diffuse clouds, PDRs, nearby galaxies, damped Lyman alpha systems, circumstellar disks, and so on. It permits the investigation of effects such as the radiative feedback of a newborn star on its parent molecular cloud. The user specifies physical conditions such as the thermal pressure in the cloud P th , the intensity of the incoming UV radiation field G UV (scaling factor applied to the  Mathis et al. 1983  standard field), and the depth of the slab of gas expressed in visual extinctions, A tot V. The code then iteratively solves large systems of multiphysics equations.
First, the code solves the radiative transfer equation at each position on an adaptive spatial grid, considering absorption in the continuum by dust and in the lines of key atoms and molecules such as H and H 2  (Goicoechea & Le Bourlot 2007). Then, from the specific intensity of the radiation field, it computes the gas and grain temperatures by solving the thermal balance. The heating rate takes into account the photoelectric effect on grains as well as cosmic ray heating. The cooling rate is estimated from the nonlocal thermodynamic equilibrium (non LTE) excitation in the energy levels of the main species by considering radiative and collisional processes as well as chemical formation and destruction. Additional processes can either heat or cool the gas, such as H 2 heating or gas-grain collisions.