dataesr/scientific-paragraphs-categorization huggingface dataset:
Results A few basic premises. Given the large number of simulations carried out and the wealth of information contained in them, it is not possible to exhaust all possible applications of this simulation database in this paper. We have therefore chosen to proceed as follows. In Sect. 3. 1, we present an overview of the distribution of all streams in Galactic coordinates. This coordinate space will be the one used in the remainder of the entire article. This first section allows us to show qualitatively how the global distribution of streams varies, depending on the Galactic potential used. We then move on (Sect. 3. 2) to present the global system of streams as a function of their distance from the Sun. In this section, we also show the kinematic properties of the streams, such as proper motions and line-of-sight velocities, that can be directly compared to Gaia data or other astrometric and spectroscopic surveys.
This section also allows us to show the variety of morphologies that the stars which escaped from globular A44, page 5 of 50 clusters can take. In Sect. 3. 3, we explore this issue in more detail, showing how these morphologies depend primarily on the orbital characteristics of the clusters and their distance from the Galactic center. For the most interesting cases, we compare the tidal structures predicted by our simulations with streams found in observational data. For this purpose, we make use of the galstreams library of stellar streams in the Milky Way  (Mateu 2023) , which constitutes a unique and public database summarizing angular positions, distances, proper motions, and line-of-sight velocity tracks for nearly a hundred Galactic stellar streams. Any stream that is not included in this library is not be compared to our simulations in the context of this paper.
This is expected given that this range samples a bite of the Sun-side of the Galactic disk and that this range has a relatively small volume. In this, as in the following distance ranges, the v os maps show that the tidal material at A44, page 7 of 50 negative Galactic longitudes has, on average, positive v os while material at positive Galactic longitudes has, on average, negative v os , which is due to the solar reflex velocity. This is the same trend observed for the whole set of radial (i. e. , line-of-sight) velocities in Gaia DR3; for instance, we refer to the bottom panel of Fig. 5  from  Katz et al. (2023) , although less extreme velocities are reported in their plot since their dataset is dominated by disk stars, whereas our maps have a high proportional A44, page 9 of 50 contribution of halo stars (additionally, they use median values in their bins, while we use an average).
More specifically, we compare the projected density distribution of the simulated stream to observations in the ( , b), ( , µ cos(b)), ( , µ b ), and ( , D) planes. As for the projected density distributions derived from the models, we calculated them by taking into account all the 51 simulations realized for each cluster, that is, both the reference simulation and those realized by a Monte-Carlo sampling of the uncertainties. Overall, the agreement between models and observational data is excellent for all Galactic models used. By looking at more extended regions in the sky than those covered by current observations, it should be possible to better constrain the streams, as well as favor or otherwise disfavor some of these models. NGC 3201. NGC 3201 is an outer cluster at a distance of about 4.
Acknowledgements. The authors are grateful to  Nicolas Leclerc  for his help in the construction of the e-TidalGCs project website. The authors wish to thank  H. Baumgardt  and  E. Vasiliev  for making the globular cluster data used in this paper publicly available, as well as  C. Mateu  for developing the galstreams library and making it available to the community. SF and PDM would also like to thank  P. Bianchini ,  P. Bonifacio ,  R. Ibata ,  D. Katz ,  N. Martin , for their interest in this work and their comments. Finally, the authors are grateful to the referee for their suggestions and remarks, which greatly improved the paper and the presentation of the results. This work has made use of the computational resources available at the  Paris Observatory , as well as those obtained through the DARI grant  A1020410154  (PI:  P.
The dataset used may be identified by either the robust parameter or the beam size. For each molecule, the selected robust or beam size is the same for all disks in the MAPS sample. For datasets selected based on the robust parameter the difference in beam value between major and minor axis is typically of order ≤0. 02 ′′. Between sources there is also a slight beam size difference of ≤0. 02 ′′. At a distance of ∼120 au this represents a difference of ∼2. 5 au; therefore, we consider beam size variations negligible in our calculations of the vertical profile. In addition to the information presented in  Notes. (a) For molecules that were selected based on the robust parameter, the beam value corresponds to the mean value of all sources. In all J = 2-1 transitions the typical deviation from the mean value between sources is 6.
1. 00168. S (P. I. G. Blake) and the ALMA Large Program DSHARP  (Andrews et al. 2018). After self-calibration we can detect emission from 12 CO, 13 CO, C 18 O, HCN, CN, and HCO + J = 3-2 in WaOph 6. Due to the moderate spatial resolution of the dataset (0. 3-0. 4 ′′ ), in this study we only analyse 12 CO, 13 CO, and HCO + data, where we can confidently study the vertical distribution of the disk. The integrated moment maps for all molecules observed in WaOph 6 and details on the self-calibration steps are found Appendix A. Overall, our sample consists on two Herbig and four T Tauri stars  (Öberg et al. 2021; Andrews et al. 2018). There are three disks with spirals, and four with rings and gaps  (Huang et al. 2018a,b). Additionally, various sources show distinct kinematical features such as signatures of late infall in GM Aur  (Huang et al.
CO 13 CO C 18 O far side near side where we assume the central star is located. This same centring has been performed on the Elias 2-27 and WaOph-6 datasets, and therefore we consider the centre of the image as the stellar location. If the inclination, flaring, and resolution of the disk allow the identification of upper and lower surfaces, it is possible to confidently trace both vertical profiles independently. In cases when the surfaces cannot be visually identified separately we assume that the peak of emission of the channel map comes from the upper surface, which is expected to be brighter than the lower surface. From the extracted location of the maxima, geometrical relations can be used to obtain the vertical profile of the emission (see  Pinte et al. 2018a , for more details). To trace the maxima we use our own implementation of the method (ALgorithm For Accurate Height Over Radius, ALFAHOR), which relies on masking each channel through visual inspection to identify separately the near and far sides of the emission from the upper layer (see Fig.
2021b ) used a publicly available implementation of the Pinte et al. (2018a) method, DISKSURF  (Teague et al. 2021b). In DISKSURF the search of the emission maxima can be blind or constrained with initial expected values of the minimum and maximum z/r, the minimum S/N and selected channels. While this allows for a systematic search and characterization of the channel emission, in some cases pixels from the bottom surface are incorrectly classified as located in the upper surface, and the other way around. This induces noisier vertical profiles, as there is a large data spread caused by the contamination of pixels from the lower surface of the disk. The S/N cutoff is also problematic when dealing with emission from less abundant molecules. By masking the channels after visual inspection, we reach locations of lower S/N and avoid contamination from 1 A repository with the mask and code developed for this study can be found at https://github.
Brightness temperature calculation The brightness temperature (T b ) profiles are obtained from the peak intensity (I) using the complete Planck law. The relationship between both parameters is the following, T b = hν k ln -1 1 + 2hν 3 Ic 2 , ( 2 ) where h is the Planck constant, k the Boltzmann constant, c the speed of light and ν the frequency of the emission. The temperature profiles are computed from the azimuthally averaged peak intensity maps. To accurately de-project the data, we used either the best-fit power-law model or the exponentially tapered powerlaw model of each molecule. The azimuthally averaged peak intensity profile is obtained using the GoFish package  (Teague 2019) , a ±30 • wedge across the semi major axis (as done in  Law et al. 2021a ) and radial bins half the size of the beam semi-major axis.
5 km s -1. Therefore, CN, HCO + , and 13 CO J = 1-0 would likely have higher brightness temperature profiles if we compared them at the same spectral resolution as the rest of the tracers. The brightness temperature of all molecules shows a steep turnover in the inner 50 au, which is likely due to effects of beam smearing. At the source distance, the beam major axis of each tracer takes a value between 13 and 30 au and 50 au in the case of CN. Additional perturbations in the temperature profiles may be due to line flux subtraction from the continuum emission, as we are using the continuum-subtracted datasets. The dust features are indicated in the top of the right panel of Fig. 2  for reference.
Other tracers For the MAPS programme targets we are able to trace the vertical profile of HCN, H 2 CO, HCO + and C 2 H in the same way as with the CO isotopologues. In the case of WaOph 6, the lack of spectral and spatial resolution in the data only allowed us to recover the surface of HCO + , even though HCN and H 2 CO emission data are available too (see Appendix A). The vertical profiles of these molecules are shown, compared to the CO vertical layers, in Fig. 9. Elias 2-27 has observations of CN N = 3-2 hyperfine transitions from which the emitting surface has been recovered (Paneque-Carreño et al. 2022). However, as we are able to recover the emitting surface of CN N = 1-0 only in HD 163296 (shown in Fig. 2 ), we do not display this molecule in Fig. 9.
Structure in HCN and H 2 CO The HCN and H 2 CO vertical profiles are well sampled (see all of the extracted data points in Appendix B) and show distinct morphologies, which in most cases do not follow an exponentially tapered power law or a single power-law model. These profiles are presented separately in Fig. 11  for all disks in the MAPS sample except MWC 480, which is not included due to the lack of data points for HCN emission. Overlaid on the profiles are the locations of rings and gaps found in the integrated emission of each corresponding molecule and the edge of the millimetre continuum  (Law et al. 2021a). HCN shows a step-like profile in HD 163296, with peaks that mostly coincide with gaps in the integrated HCN emission. IM Lup shows a peak in the HCN profile at ∼270 au, which is in between a gas gap and a ring and also coincides with the single peak seen in the H 2 CO vertical profile.
GM Aur and AS 209 may have tentative HCN peaks around ∼150 au; however, the data do not allow us to properly characterize the profiles and there is a large dispersion in the recovered data points from the channel maps. While HCN is expected to trace high layers in the disk atmosphere  (Visser et al. 2018; Bergner et al. 2021) , it is clear that this is only the case in HD 163296 (see also Fig. 10 ). The H 2 CO vertical profiles can be traced with less scatter in all disks and for HD 163296, IM Lup and GM Aur we see clear peaks. In all cases there seems to be a peak close to and just inwards with respect to the edge of the millimetre continuum. The peaks in the vertical profile of HD 163296 and IM Lup coincide with gas gaps, as was the case for HCN. GM Aur has gas rings and gaps detected only in the molecular emission at small (<100 au) radii; however, it has a strong, well constrained rise in the emitting layer close to the continuum edge.
In HD 163296 and IM Lup there seems to be a correlation between the presence of line emission gaps and the peaks in the vertical structure for both HCN and H 2 CO. It could be that the substructure of the molecular emission affects our profiles, as we are tracing the data directly from the channel maps, assuming that the emission maxima trace an isovelocity curve. However, we do not see this effect in GM Aur, where H 2 CO also has a strong vertical perturbation, and we note that most of the gaps in the molecular emission at outer radii in HCN and H 2 CO have a very low-contrast  (Law et al. 2021a). Therefore, we do not expect them to have such a noticeable impact on the retrieved profile. All vertical profiles show peaked features beyond the continuum emission border, and therefore it is also unlikely that this is an effect of continuum over-subtraction.
Acknowledgements. We thank the referee for the constructive comments. This paper makes use of the following ALMA data: #2015. 1. 00168. S, # 2016. 1. 00484. L, # 2016. 1. 00606. S, # 2017. 1. 00069. S and # 2018. 1. 01055. L. 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. Astrochemistry in Leiden is supported by the  Netherlands Research School for Astronomy (NOVA) , and by funding from the  European Research Council (ERC)  under the  European Union 's  Horizon 2020 research and innovation programme  (grant agreement No. 101019751 MOLDISK ).
III. EXPERIMENT For the purpose of providing experimental reference data for validating simulation software for radar-plasmasignatures, hypersonic shock tunnel experiments were conducted. Following the design in  [27]  a spherical wind tunnel model was placed in the Mach 8 hypersonic flow of the Shock Tunnel B (STB) at ISL. Plasma was generated in the high temperature region around the stagnation point of the sphere and the change of microwave reflectivity was observed with a radar system. Simultaneously, the emission of light coming from the high temperature regions was observed with a synchronized high-speed camera system as reference. Each of the different experimental aspects is covered in detail below.
ACKNOWLEDGMENT The authors thank ISL's shock tunnel team, namely  Berthold Sauerwein  ( ISL ),  Rémy Kempf  ( ISL ),  Myriam Bastide  ( ISL ) for the lively support during the experiments;  Friedrich Leopold  ( ISL ) for providing the experimental facilities;  Marcel Warnke  ( FHR ) for his dedicated support with the experimental radar system and the related discussions;  Carlos Salzburg  ( FHR ) for his support of the electromagnetic simulations and the team around  Jan Martinez Schramm  ( DLR ),  Alexander Wagner  ( DLR ) and their team from the spacecraft department of the  German Aerospace Center (DLR) in Göttingen  for the discussion that lead to the idea of this study.
Then, Newton's equations of motion have been integrated using the velocity Verlet algorithm, implemented in the lammps software. [55] This numerical method allows to access to the time evolution of the position and the velocity of each atom. The simulations have been run with an elementary time step t = 1 fs. The first 20 000 steps ( relax = 20 ps) correspond to a transient regime devoted to the relaxation/thermalization. The velocity data have been collected during the 1000 subsequent steps for the determination of the velocity auto-correlation function (), defined as 𝛾(𝜏) = ⟨ ∑ N i v i (t)v i (t + 𝜏) ⟩ ⟨ ∑ N i v i (t)v i (t) ⟩ ( 6 ) where v i (t) is the velocity at time t of the atom i and ∑ N i is the summation over the N considered atoms. The vDOS corresponds to the real part of the Fourier's transform of (): g(𝜔) = ∫ ∞ 0 𝛾(𝜏) cos(𝜔𝜏)d𝜏 (7) From the (vDOS), the thermodynamic quantities such as the vibrational entropy per molecule S vib can be extracted.
Acknowledgements This project has received funding from the  European Research Council (ERC)  under the European Union's  Horizon 2020 research and innovation programme  (Grant agreement No. 101019522 ). A. F. thanks the  "Ministère de l'Enseignement Supérieur et de la Recherche " for a Ph. D. grant. S. M. acknowledge the  China Scholarship Council (CSC)  for a Ph. D. grant.
Results and Discussion The validity and applicability of the chosen models are checked initially by comparing the charge particle distribution of the ALICE data  [23, 24]  with the model calculations with the same kinematic cuts employed in data. This comparison is shown in Fig. 1  where the left panel compares the results from EPOS LHC, SYBILL 2. 3d, QGSJET II-04 and PYTHIA colour reconnection (gluon splitting mode) models with √    = 7 TeV pp collisions at ALICE. It is observed that a reasonably good agreement is obtained by all the models, with the EPOS LHC model giving the best results. A similar exercise is done for the heavy-ion system (Pb-Pb √    = 2. 76 TeV) also Ronald Scaria by using the EPOS LHC and the ANGANTYR mode in PYTHIA. It is observed that the PYTHIA ANGANTYR model with colour reconnection gives the best description of the dataset.
With this "quality assurance" study hinting at the applicability of the models, we further go ahead by dividing the generated dataset into ten equal multiplicity (centrality) classes. Strangeness production in the various models is studied through the multiplicity dependence of the kaon to pion (/) ratio. It is observed in Fig. 2  that the general trend of increasing / ratio seen in data  [25]  is followed only by the EPOS LHC model. The QGSJET II-04 model shows that the / ratio remains constant over increasing multiplicities, while the SYBILL 2. 3d and PYTHIA GS models show a decreasing trend at low multiplicities. The PYTHIA ANGANTYR models remain well below all the other models with only minor variations with multiplicity. This indicates the importance of the core-corona picture used in EPOS LHC in explaining the strangeness enhancement observed in experiments.
Acknowledgement  R. Scaria  acknowledges financial support from  Council for Scientific and Industrial Research (CSIR), India. S. D. acknowledges the support from the  postdoctoral fellowship of CNRS, France. R. Sahoo  and C. R. S. acknowledge the financial support under the  ALICE  project (Project No. SR/MF/PS-02/2021-IITI (E-37123 )). The authors acknowledge the Tier-3 computing facility in the experimental high-energy physics laboratory of  IIT Indore , supported by the  ALICE  project.
Acknowledgments We thank  J. Bouttier ,  P. di Francesco ,  S. Komatsu ,  M. Mariño ,  S. Nechaev ,  D. Serban ,  A. Sportiello  and  N. Terziev  for discussions. We are especially grateful to  I. Kostov  for illuminating comments. F. L. -M. is grateful for hospitality to organisers of the Varna ICMS-2022 workshop (organised by the  International Center for Mathematical Sciences in Sofia  and supported by the  Simons Foundation ). The research of V. K. was supported in part by the  National Science Foundation  under Grant No. NSF   PHY-1748958. V. K. thanks the  Interdisciplinary Scientific Center Poncelet  ( CNRS UMI 2615 ), where a part of the work was performed, for kind hospitality. A. G. is thankful to the  Basis Foundation  grant No. 20-1-1-23-1. The work of V. M. was funded by the  "Basis" Foundation  grant No.
[20, 21]. While both methods aim to minimize the meansquared error on the training dataset (first term in Eq. (  17 )), they favour different solutions. The KRR finds predictions with small RKHS norm ∥f ∥ H k due to the regularization term (favouring smooth log Ψ). The relevance-vector regression instead favours solutions which have small weights w, due to a zero-mean gaussian prior on them  5. We make one final approximation for the simulations in this article to reduce the computational cost. We assume that the distribution of the previous state Ψ (n) is sufficiently close to the distribution of the propagated state (Λ -Ĥ)Ψ (n) , and sample from Π(x) = Ψ (n) (x) 2 , ( 22 ) instead of |(Λ -Ĥ)Ψ (n) (x)| 2 , reducing the number of evaluations of Ψ (n) required.
We wrote the code for the numerical simulations with the jax library  [60] , using the sampler from netket  [61, 62]  and we optionally parallelized it using mpi4jax  [63]. All of the simulations in this article were run serially on a NVIDIA V100 gpu. For completeness, in this appendix we provide the reference energies used for benchmarking purposes and and present several additional numerical experiments that we performed to further support the results in the main text.
C Additional Numerical Experiments In order to benchmark our method we computed reference energies with exact diagonalization (ED) using using the SpinED package  [48, 49] , and did Quantum Monte Carlo (QMC) simultations using the loop algorithm from the Alps package  [50, 51]. For the QMC simulations we fixed the inverse temperature at β = 1000 and ran 10 5 thermalization steps followed by 10 6 sweeps. In Table  1  we provide energies for the TFI model in two dimensions and in Table  2  for the AFH model in one and two dimensions.
III. DATASETS The adjustment of parameters, i. e. , the fitting procedure, presented in this work has been carried out using two different datasets, CODATA18 and DATA22. The CODATA18 dataset consists of data that was used in the latest CODATA adjustment in Ref. [1] , but restricted only to the subset most relevant for constraining NP. This subset contains observables related to the determination of the Rydberg constant R ∞ , the proton and deuteron radii, r p and r d respectively, the fine-structure constant α, and the relative atomic masses of the electron, proton, and deuteron: A r (e), A r (p) and A r (d), respectively. The inputs are listed in Tables  S1, S3 , and include theory uncertainties in Table  S2. The other observables and parameters included in the CODATA 2018 adjustment are very weakly correlated with the selected data, and can be neglected for our purpose.
The DATA22 dataset combines the updated CO-DATA18 inputs with the additional data that improve the overall sensitivity to NP (see Table  S6  and S9 ). In particular, we include the measurements of transition frequencies in simple molecular or molecule-like systems, the hydrogen deuteride molecular ion (HD + )  [33] [34] [35] , and the antiprotonic helium atom (p 3 He and p4 He)  [36, 37]. These have an enhanced sensitivity to the NP models with mediators that have large couplings to quarks (and thus nuclei). The three benchmark models of this type are the Higgs portal, hadrophilic and ULD scalars, cf. Sec II. The CODATA18 dataset is used as a reference point to verify the implementation of the inputs and the adjustment procedure, while DATA22 is used to obtain our nominal results. The full list of data in the two datasets, as well as further discussion of the importance of including certain observables when constraining NP, is given in Supplemental Material, Sections.
V. RESULTS First, we perform the control fit, i. e. , the least-squares adjustment assuming SM, based on the CODATA18 dataset with inflated experimental uncertainties when there are tensions in the data  [1] , see also Sec. S2. Resulting χ 2 per degree-of-freedom (dof) is χ 2 SM /ν dof 0. 95 (ν dof = 78 -44 = 34), indicating an overall good description by the SM, and the use of correct expansion factors. The output g SM values and relative uncertainties (see Table  S5 ) are in excellent agreement ( 0. 2 σ) with the latest CODATA recommended values  [1] , validating our procedure. Next, we perform adjustments based on the DATA22 dataset, assuming either the SM or one of the NP benchmark models in Sec. II. We do not inflate experimental errors, since mild tensions in the data could be a hint of NP.