dataesr/scientific-paragraphs-categorization huggingface dataset:
Results and discussion The effect of our rotational pumping is analyzed through the determination of the rotational distribution. This tasks consists in fitting the REMPI spectra with a numerical function which, in short, is a sum of the lines corresponding to transitions X 2 Σ(v = 0, J , N ) → A 2 Π 1/2 (v = 0, J ). This approach considers, as in other studies  [27, 28] ,that the ion yield is essentially modulated by the resonant step of the REMPI process. The line parameters, such as their frequency positions and the Hönl-London factors, are directly calculated by the software PGOPHER  [26]  feeded by the accurate experimental constants found in  [29]. Essentially, the fitting procedure is an adjustment of the rotational populations lying in the states X 2 Σ(v = 0, J , N ) and an adjustment of the line widths (power broadening effects are taken into account).
ACKNOWLEDGMENTS This work has been carried out within the framework of the EUROfusion Enabling Research Project No. AWP17-ENR-IFE-CEA-01  " Preparation and Realization of European Shock Ignition Experiments " and has received funding from the  Euratom   Research and Training Program   2014-2018  under Grant Agreement No. 633053. The views and opinions expressed herein do not necessarily reflect those of the  European Commission. The authors thank  Professors Vladimir Tikhonchuk  and  Stefano Atzeni  for many useful discussions. We also thank the anonymous reviewers for their constructive comments.
Observations We simultaneously observed a sector of the Galactic Plane in 1. 15 and 2. 00 mm continuum wavebands using NIKA2  [13] [14] [15] [16] , which have angular resolutions of 11. 1 and 17. 6 arcsec, respectively. The region is centred on = 23. 9 • , b = 0. 05 • , and approximately covers an area of 2 deg 2 with fairly uniform sensitivity. The observations consist of pairs of scans centred on three different positions ( = 23. 3 • , 23. 9 • , 24. 5 • , with b = 0. 05 • ) with position angles alternating between ±30 • from the normal to the Galactic plane. Flux calibration is performed via observations of primary calibrators, mainly Uranus and Neptune, and pointing uncertainties are < 3 arcsec. The data were reduced using the NIKA2 collaboration's IDL pipeline. The results presented here were obtained from the 1.
Source extraction and determination of physical properties We extracted sources within the 1. 15 mm map using the Python astrodendro implementation of dendrograms  [17] , after smoothing the image to 13 arcsec resolution to slightly increase the signal-to-noise ratio. The global rms of the 1. 15 mm map, determined from the null maps produced by the IDL pipeline, is 4. 18 mJy per 13-arcsec beam in 2. 5-arcsec pixels. We catalogued 488 independent emission structures (dendrogram trunks), containing a total 1467 compact sources (leaves) that contain no further discernible substructures, that will be the focus of our analysis. We determined systemic velocities for all sources by first creating an average spectrum within each source footprint in overlapping 21 arcsec-resolution 13 CO (1-0) data from the FUGIN survey  [18] , and assigned the velocity corresponding to the brightest emission.
Acknowledgements AJR and NP would like to thank the  STFC  for financial support under the consolidated grant numbers  ST/N000706/1  and  ST/S00033X/1 , and the  Royal Society  for computing resources under Research Grant number  RG150741. We would like to thank the  IRAM  staff for their support during the campaigns. The NIKA2 dilution cryostat has been designed and built at the  Institut Néel. In particular, we acknowledge the crucial contribution of the Cryogenics Group, and in particular  Gregory Garde ,  Henri Rodenas ,  Jean Paul Leggeri ,  Philippe Camus. This work has been partially funded by the  Foundation Nanoscience Grenoble  and the  LabEx FO-CUS   ANR-11-LABX-0013. This work is supported by the  French National Research Agency  under the contracts "MKIDS", " NIKA " and  ANR-15-CE31-0017  and in the framework of the " Investissements d'avenir" program  ( ANR-15-IDEX-02 ).
Acknowledgements: This research is partially supported by the  Institut Universitaire de France , by the  French ANR  project  SingFlows , by  ERCEA Advanced Grant   2014 669689 -HADE , by  MEIC (Spain) projects Severo Ochoa   SEV-2017-0718 , and  PGC2018-1228 094522-B-I00 , and by  Eusko Jaurlaritza  project  IT1247-19  and  BERC program.
First hyperpolarizability in the liquid phase To compute the first hyperpolarizability of water molecules within the liquid phase, an explicit environment composed of point charges is used : the Polarizable Embedding model at the zerothorder (PE0)  41, 42  , implemented in the DALTON software  43  , release 2018. 2 package. As in our previous recent work  32  , the QM calculations were carried out on individual water molecules. Point charges represent the surrounding water molecules, and the same electrostatic description is used as for the MD (TIP4P/2005 model). The MD trajectories are used directly in the QM calculations without further optimization. We define the parameter R c as the maximal distance upon which neighbors are included in the PE formalism. The electrostatic field generated by this environment is spatially-heterogeneous in the vicinity of the target molecule and creates a new potential for the target molecule electronic Hamiltonian.
The electrostatic description could be refined by adding dipole, quadrupole or polarizability of the environment  42, [44] [45] [46] [47]  , but we shall see in the results that Eq. 2 becomes relevant only for longrange effects, where the point-charges electrostatic field is dominant. We have therefore chosen to keep the environment description as simple and robust as possible. To optimize parts of the QM/MM routines, the home-made software FROG is used *. The whole procedure is composed of the following steps: (1) Perform MD simulation using LAMMPS. (2) Read the MD trajectories using FROG to build the electrostatic environment for each water molecule defined into a sphere of radius R c centered on the mass center of the target molecule. If a neighbor possesses at least one atom in the sphere, the whole molecule is considered in the environment.
The output files for DALTON are created for 300 molecules for 8 selected MD configurations. (3) For each of the 2400 target molecules, calculate the electrostatic field, and its gradients, generated by the environment using FROG. (4) For each of the 2400 target molecules, calculate the value of β at the fundamental wavelength of 800 nm using DFT with the functional CAM-B3LYP  48  and the basis d-aug-cc-pVTZ  49  , using the quadratic response formalism as implemented in DALTON 50. (  5 ) Read all DALTON output files and analyze the data using FROG. The largest inaccuracy of our approach is due to the QM method and the corresponding functional. For the first hyperpolarizability of water molecules, the values in vacuum obtained with our method (DFT/CAM-B3LYP) are typically overestimated by about 10 % 32 in comparison to the golden standard for QM/MM calculation of small molecules (CCSD  [51] [52] [53]  ) The basis set d-aug-cc-pVTZ  49  used is widespread across the community  26, [51] [52] [53]  and present a good balance between accuracy and cost.
Acknowledgments: J. B. and P. Z. dedicate this article  Wojciech Pietraszkiewicz , great teacher and master, on the occasion of his 80th birthday. Financial support of these studies from Gda ńsk University of Technology by the  DEC-50/2020/IDUB/I. 3. 3  grant under the  ARGENTUM TRIGGERING RESEARCH GRANTS-EIRU program  is gratefully acknowledged. The subject of this paper has been presented and discussed during the  Colloque Francophone en Energie, Environnement, Economie et Thermodynamique  ( COFRET2021 ), held in Bucharest,  Romania ,  15-16 October 2021. The authors gratefully acknowledge the organizers:  Adrian CLENCI ,  Dumitru CHIRLES  , AN and  Monica COSTEA  for the possibility to have presented, which created the opportunity for several important discussions on the forgotten trends in the non-equilibrium and extended thermodynamics.
One aspect that is not very well-documented in the literature is the interaction between surface charge and streamer inception and propagation. Indeed, when an overvoltage event arises, streamers may appear in the insulation. Most simulation works focus on the study of streamers without considering the state of insulation beforehand where surface charge accumulates due to the application of a DC voltage. Therefore, in this work, which is a follow-up to our previous one  [32] , the discharge initiation and propagation in a liquid-solid insulation system under DC superimposed lightening impulse (LI) voltage condition is investigated numerically using finite element method (FEM) commercial software COMSOL Multiphysics ®. These simulations allow us to assess important quantities without implementing sophisticated experimental setups, and help define design rules for more reliable HVDC components.
the rising portion of the impulse voltage contributes to a milder upward slope of the conduction current, to a reduced peak and to a steeper tail at the end. Figure  13  shows the streamer average velocity during its propagation in oil (Figure  13a ) and along the oil-OIP interface (Figure  13b ) in the first case. The average velocity in a particular instant was calculated by dividing the travel distance by a defined time interval. This time interval differs depending on the streamer location. Before the streamer reaches the interface at around  = 147 ns (Figure  13a ), the time interval chosen was 3 ns since it was noticed that the streamer average velocity was changing rapidly. However, while propagating along the interface (Figure  13b ), the time interval was set at 100 ns. The last data point in the graph of Figure  13a  represents the average streamer velocity at 1.
Acknowledgements. This work is supported by the  ERC Synergy  Grant  WHOLE SUN  # 810218  and by the  DFG Collaborative Research Center   SFB 1456  (project  C04 ). LG acknowledges  NYUAD Institute  Grant  G1502. LH acknowledges an internship agreement between  SUPAERO  and the MPS as part of her Bachelor thesis. The source code is available at https://doi. org/10. 17617/3. OM51HE.
In 2020 the ATLAS Collaboration provided the most comprehensive dataset of the observation of light-by-light (LbL) scattering in the ultra-peripheral Pb-Pb collisions from the LHC Run-2  [1]. The statistics has been increased compared to the first analyses  [2, 3] , and the unfolded data were provided. The new results show a mild excess over the Standard Model prediction centered on the diphoton invariant mass region of 5 to 10 GeV. In terms of the total LbL cross section, the discrepancy between the experimental measurement and the theoretical estimation reaches the value of around 2σ. On the other hand, the LHCb Collaboration discovered a new state, X(6900), seen in the di-J/ψ spectrum at around 6. 9 GeV. This state has been confirmed very recently at ATLAS  [4]  and CMS  [5]. Apart from X(6900), these collaborations observed two other resonances in the vicinity, namely X(6600) and X(7300).
e. , Γ tot Γ X→J/ψ J/ψ ). The fit has been performed to the unfolded diphoton invariant mass spectrum of the ATLAS data. The CMS data is not used in the present analysis since the corresponding spectrum is not unfolded. We have explored both the scalar and pseudoscalar nature of X(6900), but the corresponding results of the fit turn out to be indistinguishable at the current level of statistical accuracy. The results for the two-photon width Γ X→γγ and the corresponding branching ratio are given in Table  1 , for the two scenarios (interference, no-interference) considered in Ref. [32]. The Table  1. The two-photon width and the corresponding branching ratio of X(6900) obtained in  [25]  by fitting the light-by-light scattering data of Ref. [1].
Acknowledgments This work was supported by the  Deutsche Forschungsgemeinschaft (DFG)  through the Research Unit FOR5327 [Photon-photon  interactions in the Standard Model  and beyond,  Projektnummer 458854507 ]. L. H. L. thanks the  Science and Technology Facilities Council (STFC)  for support via grant awards  ST/L000377/1  and  ST/T000864/1.
In addition, a new validation technique that does not require a different dataset is developed to avoid overfitting. The parametric network performance is compared to classical digital signal processing (DSP), and Deep Learning (DL) approaches using simulated data. Simulation results show that the proposed network outperforms the competing approaches in terms of Bit Error Rate (BER) while maintaining a relatively reduced computational complexity. In the scenarios considered, compared to the parametric network, the DSP approach introduces an OSNR penalty between 0. 2 dB and 1. 7 dB at a BER of 4 × 10 -3. Furthermore, simulation results demonstrate that the proposed network is way more flexible than other approaches since it can easily be adapted to a different scenario and coupled with other techniques.
These techniques are able to improve the performance of the system. However, these techniques require a large signal dataset and have difficulties tracking time-variant imperfections. Moreover, it is difficult for these approaches to benefit from the model knowledge of the system, and their computational complexity may be prohibitive at the moment  [35]. To benefit from the advantages of both model-based and ML/DL techniques, different approaches that aim to insert the system knowledge into an ML/DL network have been proposed  [36] -  [39]. For the coherent optical communications, most of the model-based ML/DL techniques focus on the compensation of nonlinear impairments related to the fiber propagation  [40] -  [45]. Compared to the classical digital backpropagation (DBP)  [46] -  [48] , it was demonstrated that the compensation of the nonlinear imperfections is improved or the computational complexity is reduced by using a modelbased ML/DL approach.
Model-based ML/DL approaches are usually combined with local DSP algorithms to mitigate the nonlinear and linear impairments. Unfortunately, integrating DL approaches into the classical DSP chain is a complicated task, and advanced training strategies are generally developed because of the different time-variant linear imperfections that impact the batches differently  [41] ,  [42] ,  [44] ,  [49]. Even if the integration of DL networks into the classical DSP chain has been of much interest recently, integrating the parametric model of linear impairments into a compensation network was not investigated. This paper proposes a model-based network that globally compensates for multiple linear imperfections of the dualpolarization (DP) optical chain. This parametric network aims to benefit from the model knowledge of the system to reduce the size of the training dataset and allow the tracking of timevarying impairments.
The main contributions of this paper are twofold. • First, we introduce a multi-layer parametric network based on the impairments model of the coherent optical chain. This technique can be used with different modulation formats. The network is easily adaptable since new impairments can be easily compensated for, and their positions can be freely arranged in the network architecture. Concerning the statistical performance, the proposed network outperforms some classical DSP algorithms and DL techniques; • Secondly, we propose a hybrid technique based on the knowledge of the symbol constellation for network training and validation. Compared to the conventional approach based on a large dataset, the proposed technique allows training of the network with a small number of pilot or preamble data.
Furthermore, this technique avoids the need for a separate validation database. Compared to our previous global compensation study  [31] , the main difference between the two approaches is in the use of a multi-layer parametric network. While our previous study focuses on a parametric model designed for single-polarization (SP) systems, the proposed study inherits the flexibility of multi-layer networks and can be deployed in a broader range of scenarios, such as DP systems. Furthermore, while our previous approach is difficult to combine with other ML/DL techniques (for example, for nonlinearity mitigation), using a multi-layer network allows us to easily integrate the proposed approach with other networks. The remainder of the paper is organized as follows. In section II, the model of the system is developed.
III. PROPOSED NETWORK ARCHITECTURE On the receiver side, the objective is to recover the transmitted signals x from the received signals y. This can be done using a Zero-Forcing (ZF) equalizer that inverts the global transfer matrix impact  [67]. Using this approach, the augmented transmitted signal can be estimated by x = Bỹ, (14) where B = F -1 (α) is a 4N × 4N real-valued matrix. Instead of inverting the matrix F(α) explicitly, a simple alternative is to estimate the matrix B directly using a training database. This approach can be implemented using a Least Squares (LS) estimator  [68]. However, this approach has some major drawbacks: • the time variability of some impairments will make the training ineffective, as the transfer matrix will have variations from the training to testing operations; • as B is a 4N × 4N matrix, the number of estimated parameters is 16N 2 parameters, which imposes to use of a large training database.
D. Validation During the pilot-based training, the number of pilot symbols is reduced and is relatively close to the number of unknown parameters. In this case, the proposed network architecture may suffer from overfitting. Generally, a validation dataset is used to avoid this problem. In this study, we propose an alternative approach for the validation stage that does not require any additional dataset. This approach exploits the symbol constellation. The unknown received data, which represents the testing data, will be detected at a specific interval. Then, the cost function from  (23)   The training and validation operations are detailed by using the Algorithm 1.
A. Performance in a DP Coherent System 1) Implementation details The signal generation and the imperfections impact are simulated by using Python's scientific libraries like NumPy  [72]  and SciPy  [73]. On the receiver side, the compensation network is implemented using the PyTorch framework  [74]  and the training is performed by using the ADAM optimization algorithm  [75]  with learning rates (LRs) of 10 -4 and 10 -2 for preamble training, and tracking training, respectively. The system parameters can be seen in Table  II. A number of 600600 symbols were considered for each independent simulation. Of these, 600 were used as a preamble, and 20000 as pilots (inserted periodically, each 30 th symbol is a pilot), resulting overhead of 3. 4%. The rest of the 580000 symbols were used as the payload.
The computation is performed on an unseen testing dataset. In this case, the overall accuracy is 66%. The points positioned in the center square of the constellation (5,7,13,15) have a better accuracy (69%), while the points on the corners of the constellation (0,2,8,10) have the lowest accuracy (62%). The errors generally appear between the neighbor constellation points. Complementary simulations were performed for values For the first case, the overall accuracy is 94%, while for the second is 99%. Also, the errors have a similar distribution in the confusion matrix.
Number of correct detections Total number of detections. (26) We consider a separate dataset containing 120000 symbols to compute the accuracy. From these symbols, 60000 were used for preamble-based training, 2000 for pilot-based training, and 59800 for validation. The same symbols used for pilotbased training and validation are also used for self-labeling training, totaling 60000 symbols. Figure 9 shows the accuracy and confusion matrix for a 16-QAM communication. Figure 9a displays preamble-based training, pilot-based training, and validation accuracy. We denote by "1 st validation" the accuracy corresponding to the unknown detected data after the pilot-based training, and "2 nd validation" the accuracy corresponding to the unknown detected data after the selflabeling training. For the preamble-based training, the accuracy increases from approximately 20% at 0 dB OSNR to 99% at 18 dB OSNR.
Accuracy = 100 × 100 Number of correct detections Total number of detections. (26) We consider a separate dataset containing 120000 symbols to compute the accuracy. From these symbols, 60000 were used for preamble-based training, 2000 for pilot-based training, and 59800 for validation. The same symbols used for pilotbased training and validation are also used for self-labeling training, totaling 60000 symbols. Figure 9 shows the accuracy and confusion matrix for a 16-QAM communication. Figure 9a displays preamble-based training, pilot-based training, and validation accuracy. We denote by "1 st validation" the accuracy corresponding to the unknown detected data after the pilot-based training, and "2 nd validation" the accuracy corresponding to the unknown detected data after the selflabeling training.
Both are defined as ( ) ( ) ( ) = å å < f a a , 1 5 m m l m l m dip 1, 2 12, , 2 ( ) ( ) ( ) = å å < f a a 16 m m l m l m quad 2, 2 12, , 2 where a l,m are the spherical harmonics coefficient of the radial magnetic field at the upper boundary (surface) of our models. In Figure  18  we show f dip (left panel) and f quad (right panel) from 32 dynamo cases: the 15 cases analyzed in details in this paper, to which we add the 17 published in  Strugarek et al. (2018) , using the EULAG-MHD code  (Smolarkiewicz & Charbonneau 2013). This allows us to extend our database and to compare nonlinear dynamo solutions obtained with two different MHD codes using very different numerical techniques, hence giving us confidence that the trend found in our simulations is not due to a given code. We observe a relatively good agreement between the ASH and EULAG databases for f dip and surprisingly find that the EULAG set of simulations produces systematically a weaker f quad compare to the ASH database.
(2017). We also find another potential interesting property for the DR of solar-like stars: a scaling law may not be the best fit to our simulations database. As in  Saar (2011) , we find that there is a clear change of trend for small Rossby numbers (see Figure  8 ). This is interestingly the change of rotation state from solar to almost uniform rotation. Determining for these various rotation states the exact transition in Rossby number will require more numerical study at higher levels of turbulence and continued dedicated observations. We intend to contribute to this effort with dedicated new simulations but also in preparing the scientific exploitation of PLATO  (Rauer et al. 2014). These various transitions of rotation profiles must impact the resulting dynamo and field properties. We have shown in the paper (Sections 5 and 6) that this is indeed the case.
We intend to do so in the near future as well as study in more detail the influence of a realistic atmosphere and of a wind  (Perri et al. 2021)  on the dynamo properties. We acknowledge partial financial support by DIM-ACAV+ ANAIS2 project, ERC Whole Sun Synergy grant #810218 and STARS2 starting grant #207430, ANR Toupies, INSU/PNST, Solar Orbiter, and PLATO CNES funds. We thank GENCI via project 1623 for having provided the massive computing resources needed to perform this extensive study. J. V. acknowledge Project 2019-T1/AMB-13648 and multiannual agreement with UC3M ("Excelencia para el Profesorado Universitario"-EPUC3M14)-Fifth regional research plan 2016-2020 founded by the Comunidad de Madrid. This work benefited from discussions within the international team "The Solar and Stellar Wind Connection: Heating processes and angular momentum loss," supported by the International Space Science Institute (ISSI).