dataesr/scientific-paragraphs-categorization huggingface dataset:
VII. THE ROLE OF CUBIC ANISOTROPY To investigate and understand this behaviour further, we performed a set of temperature dependent SANS measurements on the substituted sample in the field perpendicular orientation. For the first measurement, the sample was HFC at 200 mT to 50 K and then the magnetic field was decreased to 0 mT, forming the pinned helical state, as seen previously in Fig. 7(e). From this point, SANS measurements were performed as the sample was cooled down to 5 K, and, after resetting the magnetic state upon a subsequent cooling procedure, as the sample was heated from 50 K to 58 K. The resulting SANS data is shown in Fig. 11(a). For increasing temperature data, the partially pinned helical state gradually rotates and orients along the 100 axes at higher temperatures, before disappearing at T C.
ACKNOWLEDGMENTS This work was supported by the  UK Skyrmion  Project  EPSRC Programme Grant  ( EP/N032128/1 ). Experiments at ILL neutron source were supported by experiment time awarded under proposal no. 5-42-488. Experiments at the  ISIS Pulsed Neutron  and  Muon Source  were supported by a beamtime allocation from the  Science and Technology Facilities Council , proposal number 1920655. M. N. Wilson  acknowledges the support of the  Natural Sciences and Engineering Research Council of Canada (NSERC).
2 ± 0. 4  [75]. In our parameter range, this amounts to T /T ∞ BKT ≈ 0. 05, i. e. an essentially low-temperature setting. To simulate the quench-induced dynamics, we simulated Eq. (  1 ) using the software package XMDS  [76] , starting from initial condition ψ(x, y) = 0, with a random realization of the initial noisy field η(x, y), which is devoid of any phase coherence. This is akin to an input condition with N atoms, all with the initial energy larger than the cut-off energy cut , which enter the cut-off region at a rate governed by γ until the gas reaches thermal equilibrium (actual values of N are given below). This can be seen as an instantaneous thermal quench (cooling) from T T ∞ BKT to T = 10 nK T ∞ BKT. To confirm the broad validity of our findings, we have also explicitly verified that temperature quenches from pre-formed equilibrated 2D thermal clouds at temperatures T > T ∞ BKT (rather than from an initial noisy condition) yield the same qualitative findings and practically identical long-term winding number combinations (histograms; see subsequent Fig.
In Ref. [90]  it was shown that the temperature-induced decay does not fit the Caldeira-Leggett superconductivity model, i. e. , the observed decay rate does not match simple models of quantum tunnelling and thermal activation of phase slips. Using a truncated Wigner approximation, Ref. [91]  attributed some of the disagreements between the theory and experiment to thermal fluctuations, however exact identification of the decay mechanism remains an open question. Data supporting this publication is openly available under an Open Data Commons Open Database License  [92]. excellent agreement. In this Appendix we carry out finite duration quenches from a high to a low temperature, in an explicitly 2D geometry, thus assessing the 2D nature through the radial width w. In Fig. B1 (a) it is seen that our analysis agrees with this prediction, indicating optimal experimental geometries for observing larger winding numbers.
Acknowledgements We would like to thank  Fabrizio Larcher  for his early involvement in this work. We thank  I-Kang Liu ,  George Stagg  and  Jean Dalibard  for discussions and  Jérôme Beugnon  for comments on the manuscript and providing us with the experimental data of Ref. [17]. TB thanks  EPSRC Doctoral Prize Fellowship Grant  No. EP/R51309X/1. We acknowledge financial support from the  Quantera ERA-NET  cofund project  NAQUAS  through the  Engineering and Physical Science Research Council , Grant No. EP/R043434/1. The work of BAM who also acknowledges a  Visiting Professorship.
Over the years, the model has been improved and adapted to different situations. Studies in the late 1990s and early 2000s were mainly dedicated to improving the quality of the radial functions adopted for  ,ℎ- () and especially for  ,ℎ ()  [105]. Connected with that was also the development of recipes for refining the contraction or expansion of the atomic densities  [106] , which are difficult to determine from diffraction intensities. Instead, in the past decade, the improvement mainly concerned the possibility of modelling core deformations or modelling simultaneously the electron charge and spin density distributions. Last but not least, a number of databank schemes have been proposed, each of them intended to store transferable atomic electron density parameters for modelling large or complicated molecules (especially biological macromolecules) that are more problematic to investigate accurately, as required for a proper charge density analysis.
All these improvements are possible thanks to the inherent flexibility of a model like the Hansen and Coppens's one. A special technical feature is the possible definition of a local coordinate system for each atom in the crystal, instead of referring to the crystal orientation matrix. This enables the transferability of a set of multipoles from one atom to another of the same element, provided that it is also embedded in a sufficiently similar chemical environment. In fact, this was the purpose of the original model, although implemented only much later  [107]  when sufficient amount of data allowed the construction of databases of experimentally determined atomic multipoles for special classes of molecules  [107, 108] , to be used to improve structural refinement of poorly diffracting species and to enable a sensible reconstruction and mapping of the electrostatic potential and electric moments.
This approach was later generalized by means of theoretically calculated atomic multipoles, with the advantage of allowing the study of (macro) molecules for which experimental models cannot be easily devised  [109] [110] [111]. While these approaches are now consolidated and their potential is wellknown, new applications emerge, such as those aiming at using these databases for modelling crystal structures measured with an emerging technique such as electron diffraction  [112]. GThe flexibility of the multipole model was especially adopted to detect special features, such as the tiny deformations occurring to core electrons in atoms bonded in molecules or covalent solids  [113]. For this reason, an extended Hansen and Coppens' model was proposed, where the aspherical atomic density refers not only to the valence, but also to the core electrons: () = �� ,ℎ- () +  ,ℎ- () +  ,ℎ- () +  ,ℎ- ()�  =1  (9)  Noteworthy, the contraction/expansion of the core-shell is also refined, which has a fundamental importance, not only for the chemical implications, but also for the correct determination of the atomic displacement parameters that otherwise would be biased.
Funding: A. G. gratefully acknowledges the  French Research Agency (ANR)  for financial support through the  Young Investigator Project QuMacroRef  (Grant No. ANR-17-CE29-0005-01 ). P. M. thanks The  National Centre of Competence in Research (NCCR)  " Materials' Revolution: Computational Design and Discovery of Novel Materials (MARVEL) " of the  Swiss National Science Foundation (SNSF).
Data and simulated event samples The analysis uses data collected by the ATLAS detector during pp collisions at a centre-of-mass energy of √ s = 13 TeV from 2015 to 2018. The average number µ of additional pp interactions per bunch crossing (pile-up) ranged from 14 in 2015 to about 38 in 2017-2018. After data-quality requirements, the data sample amounts to a total integrated luminosity of 139 fb -1. The uncertainty in the combined 2015-2018 integrated luminosity is 1. 7%  [37] , obtained using the LUCID-2 detector  [38]  for the primary luminosity measurements. Candidate events were selected by a trigger that required at least two leptons (electrons and/or muons). The trigger-level thresholds for the transverse momentum, p T , of the leptons involved in the trigger decision were different according to the data-taking periods.
Acknowledgements The authors thank the  French National Research Agency  in the framework of the  Investissements d' Avenir program  ( ANR-15-IDEX-02 ), through the funding of the " Origin of Life " project of the  Univ. Grenoble-Alpes , the  Labex ARCANE  and  CBH-EUR-GS  ( ANR-17-EURE-0003 ), for funding.
Acknowledgments We warmly thank  P. Charbonneau ,  M. Fuchs  and  T. Franosch  for many useful exchanges,  E. Agoritsas ,  G. Biroli ,  J. Kurchan ,  T. Maimbourg ,  G. Szamel  and  P. Urbani  for many discussions about the theoretical modeling, and  F. Roy  for many insights about the numerical solution of the DMFT equations. We thank the referees for providing many useful suggestions that improved considerably the paper after the first revision. This project has received funding from the  European Research Council (ERC)  under the European Union's  Horizon 2020 research and innovation programme  (grant agreement n. 723955 -GlassUniversality).
Context. The pursuit of more realistic spectroscopic modelling and consistent abundances has led us to begin a new series of papers designed to improve current solar and stellar abundances of various atomic species. To achieve this, we have began updating the three-dimensional (3D) non-local thermodynamic equilibrium (non-LTE) radiative transfer code, MULTI3D, and the equivalent onedimensional (1D) non-LTE radiative transfer code, MULTI 2. 3. Aims. We examine our improvements to these codes by redetermining the solar barium abundance. Barium was chosen for this test as it is an important diagnostic element of the s-process in the context of galactic chemical evolution. New Ba ii + H collisional data for excitation and charge exchange reactions computed from first principles had recently become available and were included in the model atom.
As a result, the solar abundances are extremely important to stellar astrophysics. Consequently, very accurate measurements of the solar abundance are needed, which employ sophisticated model atmospheres and spectrum synthesis techniques such as 3D hydrodynamics and non-local thermodynamic equilibrium (non-LTE) physics. In recent years, with the development of faster and larger computers, it has been possible to develop and implement these methods  (Asplund et al. 2003; Steffen et al. 2015; Klevas et al. 2016; Amarsi et al. 2016; Mott et al. 2017; Amarsi & Asplund 2017; Nordlander et al. 2017). One of the main aims of this paper series is to report on our development of the one dimensional (1D) and three-dimensional (3D) statistical equilibrium codes -MULTI 2. 3  (Carlsson 1986 ) and MULTI3D  (Leenaarts & Carlsson 2009 ) -as we include new or better physics into their program flows.
96 × 7. 96 × 3. 65 Mm in the x, y, and z dimensions, respectively. These are used as independent input for our statistical equilibrium code MULTI3D (Sect. 2. 5) and then the output are averaged together, therefore applying the ergodic approximation that averaging in time is equivalent to averaging over space. In this case it is assumed that averaging in time is equivalent to averaging across the disc of the Sun. The emergent fluxes from these snapshots have an equivalent width variance of only ∼ 0. 75 mÅ, suggesting that including further snapshots to the study will not greatly improve the results presented in this study, only increase the computational times. Line opacities were collected from the MARCS database and are sorted into 12 opacity bins. Continuous absorption and scattering coefficients are taken from  Hayek et al.
MULTI3D MULTI3D is an message passing interface (MPI)-parallelised, domain-decomposed 3D non-LTE radiative transfer code that solves the equations of radiative transfer using the Multi-level Accelerated Lambda Iteration (ALI) method  (Rybicki & Hummer 1991 , 1992)  for 3D model atmospheres. Every element that is modelled by MULTI3D is assumed to have no effect on the model atmosphere, as it is in MULTI 2. 3. This is a good assumption for barium as it is not an electron donor nor does it have a high impact on the overall opacity, unlike magnesium or iron, for example. At present, it will accept three types of 3D model atmospheres formats as direct input, including those computed using Bifrost  (Gudiksen et al. 2011) , and stagger. While Bifrost models are read using MPI IO, the stagger models are, at present, not read this way due to complications in converting byte ordering.
However, the added delay to the code's run time is minimal, and only becomes noticeable when MULTI3D is run on several hundred CPUs. In addition to these two types of model atmosphere, the code will also accept any 3D model formatted so that the temperature, T , density, ρ, electron number density, n e , and x, y, and z velocity fields are supplied on a Cartesian grid that is both horizontally periodic and equidistantly spaced. Therefore, it is relatively straightforward to convert almost any 3D model to this input format for MULTI3D. We have introduced new coding for computing fluxes inside MULTI3D along with the appropriate post-processing routines designed to extract the flux data. All of the output flux data computed for the work presented here was calculated using a Lobatto quadrature scheme and the appropriate corresponding weights  (Abramowitz & Stegun 1972).
Systematic differences in the equivalent widths of less than 2. 2 % were found between intensities computed with MULTI 2. 3 and intensities computed with MULTI3D. This translates to abundances differences much less than 0. 01 dex. The reason for these small differences is likely because of the way each code solves the radiative transfer equation; MULTI3D uses a direct 1D integration of the radiative transfer equation when computing spectra from 1D model atmospheres 3  , while MULTI 2. 3 utilises a faster Feautrier method. However, abundance uncertainties found here are far smaller than the errors we report in Sect. 5. Therefore, we were satisfied that comparing 1D output from MULTI 2. 3 with 3D output from MULTI3D was adequate. We ran MULTI3D in short characteristic 3D solver mode and used the solar stagger model as input.
Model of Barium atom The model atom of barium is constructed as follows. The energy levels for the Ba i and Ba ii levels are extracted from the NIST database. Of these, we include eight energy states of Ba i up to the energy of 2. 86 eV, and all available levels of Ba ii up to 9. 98 eV. Fine structure is retained for the three lowest terms of Ba ii: 6s 2 S (ground state), 5d 2 D (∼ 0. 65 eV), and 6p 2 P • (∼ 2. 6 eV) (Table  1 ). Transitions between these terms are typically used in the barium abundance analysis of cool stars. Other levels are merged into terms, and their energy levels are represented by the weighted sum of the individual components (weighted by the statistical weights of the levels). In total, the model is comprised of 110 states and is restricted by the ground state of Ba iii at 15.
The radiative bound-bound transitions for Ba ii were extracted from the Kurucz database, 26. 03. 2017. We also compared the data with the NIST database. For the combined terms, the lines were merged and the transition probabilities coadded as described in  Bergemann et al. (2012a). The oscillator strengths of the four diagnostic lines used for the present analy-A&A proofs: manuscript no. Ba_nlte Notes. The wavelengths are given in air. The equivalent widths correspond to the measurements in the solar KPNO flux atlas and are given in mÅ. The Van der Waals broadening parameters are taken from  Barklem et al. (2000). The log g f values reported here are derived from the very accurate transition probabilities taken from De Munshi et al. (  2015 ) and  Dutta et al. (2016). In total, the model contains 284 spectral lines in the wavelength range from 1330 to 202930 Å.
Computing abundance corrections A grid of abundances for all four barium lines were computed using MULTI 2. 3. These were fit to the solar spectrum using a χ 2 code that treats abundances, macroturbulent broadening and wavelength shifts as free parameters (see Sect. 2. 6 for details of line shifts). The macroturbulences found ranged from 1. 5 -1. 9 km s -1. The code also normalises the fit to a local continuum for each line using two patches of spectrum either side of the line. We fixed the rotational broadening to v sin i = 1. 6 km s -1  (Pavlenko et al. 2012). The 1D LTE we attain represent the best statistical fit from this χ 2 code. We computed the four barium lines in 1D non-LTE, 3D LTE and 3D non-LTE using three abundances; A(Ba) = 2. 17, 2. 27 and 2. 35 -covering typical abundances reported in the literature for the solar barium abundance.
Line blending corrections The four barium lines we model here suffer from the effects of blending with other atomic and molecular species. Naturally, this impacts the abundances we derive when we assume that the line is clean. This is what was done when synthesising the lines with MULTI3D and MULTI 2. 3, as these codes do not currently possess the capability to synthesise blends. To examine this, we used the VALD3 5 database together with the barium line information extracted from the model atom to create new line lists for the 5 http://vald. astro. uu. se/ 1D LTE spectrum synthesis code, MOOG 6. This code was chosen as the interactive plotting tool makes recomputing synthetic spectra and fitting it with observed data very simple. Lines were computed with and without and the abundance of the clean barium line was adjusted until its line strength matched the blended line.
(2015)  and  Dutta et al. (2016)  represent the most accurate transition parameters published. As such, the barium abundances we find from each diagnostic line used here are all in very good agreement (once the blending corrections are included). We have presented this work as part of a larger series of papers designed to report on the development of the MULTI3D spectrum synthesis code. Up until now we have added new coding that allows it to read standard stagger model atmospheres; include the effect of charge transfer between hydrogen and ions; compute flux data based on hard-coded quadrature schemes; and compute multi-component transitions caused by HFS or isotope splittings. Further physics and mathematical techniques will be added as the project progresses that will be presented in future papers in this paper series.
Acknowledgements. This work made heavy use of the  Max Planck Computing & Data Facility (MPCDF)  for the majority of the computations. This project was funded in part by Sonderforschungsbereich  SFB 881  " The Milky Way System " (subproject  A5 ) of the  German Research Foundation  (DFG) and by the  Research Council of Norway  through its  Centres of Excellence scheme , project number  262622. SAY and AKB gratefully acknowledge support from the  Ministry for Education and Science (Russian Federation) , project Nos. 3. 5042. 2017Nos. 3. 5042. /6. 7, 3. 1738Nos. 3. 5042. 2017/4. 6/4. 6. BP is partially supported by the  CNES ,  Centre National d'Etudes Spatiales.
Event selection and sample composition Split SUSY, as characterised by the simplified models discussed in this paper, would reveal itself in events containing jets, significant p miss T from undetected neutralinos, and an absence of photons and leptons. Candidate signal events are required to satisfy a set of selection requirements that define a signal region (SR). Conversely, event samples that are enriched in the same background processes that populate the SR, while being depleted in contributions from SUSY processes, are identified as control regions (CRs). In this analysis, CRs are used to assess the residual differences in tagger performance between data and simulation. The CRs are chosen to have an SM background composition similar to that of the SR. This permits a validation that the simulated event samples can accurately predict the SM background yields without significant systematic bias.
This resampling technique is done to ensure an adequate generalisation that is largely independent of kinematical features related to the physics process. The cτ 0 values assigned to the SM jets are generated randomly according to the cτ 0 distribution obtained per batch for the LLP jet class. The training of the domain branch uses batches of 10 000 jets, drawn from samples of µ+jets data and simulated W(→ ν)+jets and tt events. The DNN is trained using the class and domain batches simultaneously. Events in the domain batch are assigned the same cτ 0 values as used by the class batch. For the domain batch, only the six highest p T jets are used, and jets may be reused multiple times per epoch. The DNN is initially trained to predict only the jet class to determine the optimal scheduling of the learning rate α, which decays from an initial value of 0.
The unclustered component of p miss T is varied within its uncertainties. The uncertainty in the number of pileup interactions is determined by varying the inelastic pp cross section within its uncertainty of ±5%  [87]. The renormalisation and factorisation scales of the aforementioned four dominant SM backgrounds are varied independently per process by factors of 0. 5 and 2  [88]  to estimate the migration of events between categories. An uncertainty of ±2. 5% in the integrated luminosity is assumed  [89]. The LLP jet tagging efficiency determined from simulated events of split SUSY models, MC , may require the application of corrections to account for sources of potential mismodelling. The corrections are applied by reweighting simulated events as follows: w = 1 -data 1 -MC (N LLP -N tag LLP ) data MC N tag LLP = 1 -SF MC 1 -MC (N LLP -N tag LLP ) SF N tag LLP , (2) where N LLP denotes the number of LLP jets and N tag LLP the number of LLP jets that are also tagged per event.
Acknowledgments We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at  CERN  and at other  CMS institutes  for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies:  BMBWF  and  FWF (Austria) ;  FNRS  and  FWO (Belgium) ;  CNPq ,  CAPES ,  FAPERJ ,  FAPERGS , and  FAPESP (Brazil) ;  MES (Bulgaria) ;  CERN ;  CAS, MoST , and  NSFC (China) ;  COLCIENCIAS (Colombia) ;  MSES  and  CSF (Croatia) ;  RPF (Cyprus) ;  SENESCYT (Ecuador) ;  MoER ,  ERC IUT ,  PUT  and  ERDF (Estonia) ;  Academy of Finland ,  MEC , and  HIP (Finland) ;  CEA  and  CNRS/IN2P3  (France);  BMBF ,  DFG , and HGF.
4. The wall shear stress (  [12, 13, 14] ): this is related to the mechanical stress that the blood exerts on the endothelial cells, of paramount importance in aneurysms and plaque formation. The QoI listed have to be reliably estimated in vivo, with the additional constraint of being estimated fast, ideally in real time. For this, two main approaches are available. The first consists in a purely data-driven strategy where learning techniques are used to build an approximation of the observable-to-QoI map given a sufficiently large dataset. The second consists in using an a priori description of the physics involved by means of a mathematical model, often given in the form of a Partial Differential Equation (PDE), and then solve an inverse problem. On the one hand, since we are dealing with space fields estimation, the pure data-driven learning approach will in general need an exceedingly large data set to meet the accuracy constraints of the application.