dataesr/scientific-paragraphs-categorization huggingface dataset:
Such a uncertainty term is denoted by BR. The BLS spectrometer was not calibrated by other metrology standard, as the method is intrinsic. So the data provided by calibration are not applicable and we can assume the uncertainty term BR=0. The frequency resolution of the measurement system depends on the number of samples, i. e. the difference between two measurement frequency points along the horizontal axis. We used 2048 samples in a 0 -30 GHz span in the BLS spectrum measurement. Thus, we have a frequency interval of 14. 66 MHz. The characteristic peak of Brillouin scattering has a Lorentzian distribution  [91] , also known as a Cauchy distribution (a probability density function). The Lorentzian function versus the frequency shift of optical signal, is given in the following expression : 𝐿(𝑓) = ( γ π ) * [ 1 γ 2 +(f-f0) 2 ] = ( 1 πγ ) * 1 1+(f-f0)²/γ 2 (3) where γ is half of the frequency width at half maximum (FWHM): γ = FWHM/2, f0 is the assumed true value for the Brillouin frequency shift.
More details can be found in Ref. [12]. To simulate the effects of nonzero values of d and c H W in the HVV vertex, a reweighting method is implemented for the HISZ basis and Warsaw basis, respectively, and applied to the aforementioned SM VBF signal sample. For the d coefficient in the HISZ basis, as detailed in Ref. [9] , two weights are calculated by the HAWK program  [39, 40, 60]  for each event using generator-level information: w 1 ¼ 2 • ReðM Ã SM M CP-odd Þ=jM SM j 2 and w 2 ¼ jM CP-odd j 2 = jM SM j 2 with a specific amount of CP mixing (given in terms of d), to model the contribution from the interference term and the quadratic term, respectively, as shown in Eq. (1). For the interpretation in the Warsaw basis, a reweighting of the reconstructed OO distribution at different values of c H W is obtained by dσ dOO ¼ dσ dOO NLO × dσ dOO MG5 c H W = dσ dOO MG5 c H W ¼0 ; PHYSICAL REVIEW LETTERS 131, 061802 (2023) where "MG5" labels the prediction from MADGRAPH  [61, 62]  using SMEFTSIM  [27, 28] , and "NLO" labels the aforementioned SM VBF signal sample.
In the TT and TL categories, the dominant Higgs boson backgrounds are from the ggF process, and the contributions from non-ggF Higgs processes, e. g. , VH, ttH, and tH, are found to be negligible. In the LT category, Higgs boson backgrounds are still mostly from the ggF process, while those from non-ggF Higgs processes increase to about 1%-3% of the VBF event yield. This novel BDT-based strategy improves the significance of VBF signal by 10% with respect to the latest H → γγ analyses [77] with the same dataset. The signal yield is extracted via a combined unbinned maximum-likelihood estimation applied to the m γγ distribution of observed data in each OO bin, as shown in Fig. 2  The modeling of the continuum background relies on both simulation and data-driven methods. The m γγ shape of the γγ component is estimated using the SHERPA sample, while the m γγ shapes of the γj and jj components are obtained using data control regions formed by inverting the tight photon identification and isolation requirements.
All other Higgs boson production modes are considered as backgrounds and are normalized to their SM predicted yields. The expected ΔNLL curve is obtained using a pseudodataset where the event yields and distributions in the signal regions are set to the SM expectations for both the signal and background processes. Both the theoretical and experimental systematic uncertainties are incorporated into the likelihood model of the measurement as nuisance parameters. Theoretical uncertainties arise from the modeling of VBF and ggF processes because of the missing higher-order terms in the perturbative QCD calculations, the modeling of the underlying event and parton shower, the parton distribution functions, and the value of α s. These uncertainties are estimated by following the procedure described in Ref.
; ANAS, Azerbaijan; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; ANID, Chile; CAS, MOST and NSFC, China; Minciencias, Colombia; MEYS CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS and CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF and MPG, Germany; GSRI, Greece; RGC and Hong Kong SAR, China; ISF and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway; MEiN, Poland; FCT, Portugal; MNE/IFA, Romania; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DSI/NRF, South Africa; MICINN, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TENMAK, Türkiye; STFC, United Kingdom; DOE and NSF, United States of America. In addition, individual groups and members have received support from BCKDF, CANARIE, Compute Canada and CRC, Canada; PRIMUS 21/SCI/017 and UNCE SCI/013, Czech Republic; COST, ERC, ERDF, Horizon 2020 and Marie Skłodowska-Curie Actions, European Union; Investissements d'Avenir Labex, Investissements d'Avenir Idex and ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes cofinanced by EU-ESF and the Greek NSRF, Greece; BSF-NSF and MINERVA, Israel; Norwegian Financial Mechanism 2014-2021, Norway; NCN and NAWA, Poland; La Caixa Banking Foundation, CERCA Programme Generalitat de Catalunya and PROMETEO and GenT Programmes Generalitat Valenciana, Spain; Göran Gustafssons Stiftelse, Sweden; The Royal Society and Leverhulme Trust, United Kingdom.
Acknowledgements TJW acknowledges the support from  NSAF  (Grant no. U2130123 ),  Strategic Priority Research Program  of the  Chinese Academy of Sciences  (Grant no. XDB16 ),  International Partnership Program of Chinese Academy of Sciences  (Grant nos. 181231KYSB20200033  and  181231KYSB20200040 ),  Shanghai Science and Technology Program  (Grant no. 21511105000 ), and  Oversea Training Program   of Ministry of Science and Technology. MC acknowledges the support from  UK Research and Innovation (UKRI)  and the  UK Engineering and Physical Sciences Research Council (EPSRC)  (Fellowship " In-Tempo" EP/S001573/1 ), and the  Royal Society  ( RGS\R1\201365 ). JCD acknowledges the support of  NASA  ( SBIR  grant  80NSSC22PB067 ). The authors wish to acknowledge  Drs. Jean-Pierre Wolf ,  Jerome Kasparaian ,  Clara Saraceno , and  Olga Kosareva  for enlightening discussions.
The RAMSES code We use the adaptive-mesh-refinement (AMR) code RAMSES  (Teyssier 2002)  which integrates the Euler equations in their conservative form using a second-order finite volume Godunov scheme. In this work, we do not take into account magnetic fields or gravity. In addition, we use a uniform grid, which is well suited to the study of turbulent boxes. Our setup follows the classical one designed for investigating compressible turbulence in molecular clouds using turbulent boxes. The boundary conditions are periodic for all hydrodynamical quantities. The gas thermal evolution is isothermal. We use the HLL Riemann solver combined with a minmod slope limiter for the hyperbolic part and upwind for the dust solver (see e. g. Toro 1999 , for more details). In our experience, this combination of solver and slope limiter is the best compromise between accuracy and robustness.
( 16 ) This analytic formulation naturally yields the limits St ≪ 1 and St ≫ 1. The particle velocity is updated using a CIC interpolation of the gas density and velocity from the grid. The particles are then moved using the second-order midpoint scheme of RAMSES  (Teyssier 2002). This scheme is very similar to the one used by  Mattsson et al. (2019a)  using the PENCIL code (Pencil Code Collaboration 2021). As mentioned earlier, with this implementation, the numerical resolution of the dust depends on the number of particles used, but the accuracy of the drag estimate is limited to the grid resolution used for the gas. Finally, this two-fluid implementation does not take into account the back-reaction of the dust onto the gas.
Postprocessing of the grid versus particle data In this study, we analyse sets of data that encompass both Eulerian and Lagrangian variables. Our analysis is based mostly on volume-weighted probability density functions (PDFs) and density cuts through the computational domain. We use well-tested suites of postprocessing tools, as follows. For the grid quantities (monofluid), we simply bin the grid cells according to the value of the density for the PDF and the slices are straightforward. We use the OSYRIS 2 visualisation package for RAMSES. For the particle quantities (Lagrangian dust and tracers), we follow the procedure described in  Price & Federrath (2010)  and  Price et al. (2011). First, all particles have the same mass, m p , which is equal to the total mass of the dust species divided by the number of particles).
To produce density maps, we project the particle distribution onto a regular grid, which has the same dimensions as the grid used for the monofluid. We then use the Smoothed-particle hydrodynamics (SPH) density calculation routine from the PHANTOM code  (Price et al. 2018) , where the density and smoothing length are iterated self-consistently using classical SPH procedures. We produce cross-section slices of the density field using the SPLASH visualisation software  (Price 2007). To obtain the volume-weighted PDF from the particles, we follow  Price et al. (2011)  and again interpolate the density on an adaptive grid. barycentre). The clumping factor C X of a quantity X is defined as C X = ⟨X 2 ⟩/⟨X⟩ 2. A clumping factor C X > 1 indicates that the field X shows significant variation. The RMS velocity and the density clumping factor of the barycentre and of the ten different dust species are shown.
Acknowledgements. This work was granted access to the HPC resources of CINES (Occigen) under the allocation  2018-047247  made by  GENCI. We gratefully acknowledge support from the  PSMN (Pôle Scientifique de Modélisation Numérique)  of the  ENS de Lyon. B. C. and F. L. have received fundings from the  French national agency   ANR   DISKBUILD   ANR-20-CE49-0006. This work was supported with funding from the  European Union 's  Horizon 2020 research and innovation programme  under the  Marie Sklodowska Curie  grant agreement No  823823  ( RISE DUSTBUSTERS  project). B. C. acknowledges financial support from " Programme National de Physique Stellaire" (PNPS) of CNRS/INSU ,  CEA  and  CNES, France. U. L. acknowledges financial support from the  European Research Council (ERC)  via the  ERC Synergy Grant ECOGAL  (grant  855130 ).
39, 40  ) and with current ab initio data obtained with the AIMPRO (hollow diamonds) and SIESTA (hollow squares) codes. Corresponding linear x -dependencies are shown (dashed lines), for reference purpose. Be-Te Raman percolation doublet of Zn 0. 89 Be 0. 11 Te  28  , matched in Be content with Cd 0. 89 Be 0. 11 Te, helps to fix ideas. Two impurity modes are involved in this case, a lower/minor TO Be Be-Te and an upper/dominant TO Zn Be-Te. The subscript and superscript refer to the vibrating bond and to its local environment, respectively. The two modes are separated by Be-Te ∼ 20 cm -1 and exhibit Raman intensities differing by roughly an order of magnitude. Figure  2a  displays an overview of the four-mode {2 × (Cd -Te), 2 × (Be -Te)} TO Cd 1-x Be x Te Raman frequencies (curves) and intensities (color code) in absence of mechanical coupling (see below) by analogy with Zn 1-x Be x Te  28.
(High-pressure) X-ray diffraction measurements. High-pressure powder X-ray diffractograms are recorded on the PSICHÉ (Cd 0. 89 Be 0. 11 Te) and CRISTAL (Zn 1-x Be x Te, x = 0. 045 , 0. 14 and 0. 21) beamlines of SOLEIL synchrotron using radiation wavelengths of 0. 3738 and 0. 485 Å, respectively. The high-pressure data are recorded with a similar Chervin type diamond anvil cell  59  as used for the Raman measurements, with 300 μm in diameter diamond culet. In both PSICHÉ and CRISTAL measurements, Ne and Au are used as the pressure transmitting medium and for pressure calibration, respectively. The high-pressure X-ray data are treated by using the DIOPTAS  60  software at PSICHÉ and the DATLAB software at CRISTAL. The latter was kindly made available on site by K. Syassen (Max-Planck Institut für Festkörperphysik, Stuttgart, Germany).
Reference B 0 versus x curves for Cd 1-x Be x Te at mod- erate Be content ( x ≤ 0. 3 ) are independently obtained by applying the SIESTA  32, 33  and AIMPRO (Ab Initio Modeling PROgram  29, 30  ) codes to 64-and 216-atom fully-relaxed and partially-relaxed disordered zincblendetype supercells, respectively. The full relaxation is concerned with the lattice constant, the atom positions and the supercell shape. The partial relaxation is done so as to prevent any supercell distortion and hence maintain the cubic structure needed for a strict application of the Birch-Murnaghan 41 equation of state. Each supercell represents a random Cd ↔ Be substitution, obtained by adjusting the fractions of individual Te-centred tetrahe- dra to the binomial Bernoulli distribution  36. At each x value, B 0 is estimated by fitting the pressure dependence of the volume unit cell with the Birch-Murnaghan equation of state  41.
Further AIMPRO Raman calculations, using the formula given by de Gironcoli  61  , are done on parent-like supercells containing Be-(x~0) or Cd-paired ( x~1) impurity motifs. The motivation is to imitate the limiting-cases Raman signals due to the non-polar, i. e. , purely-mechanical, TO's of the host and impurity species. In their current versions the AIMPRO and SIESTA codes do not take into account the long-range electric field accompanying the Raman active polar LO's. Further simulations thus resorted to QE code  33  , giving access to the frequency ω T of the non-polar TO, to the frequency ω L of the Raman-active polar LO and to the high-frequency relative dielectric constant ε ∞ , defined at ω ≫ ω T , of each parent compound. The QE calculations are performed on 2 × 2 × 2 cubic zincblende-type 64-atom super- cells depending on pressure.
Acknowledgements We acknowledge assistance from the  PSICHÉ  (Cd 1-x Be x Te, Proposal n°. 20220436 , co-resps. O. P. & A. P. ) and  CRISTAL  (Zn 1-x Be x Te Proposal n°. 20110018 , resp. A. P. ) beamlines of synchrotron  SOLEIL  for the high-pressure X-ray diffraction measurements, from the  Plate-forme de Spectroscopie-Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie-Sorbonne Université  (http:// impmc. sorbo nne-unive rsite. fr/ fr/ plate formeset-equipements/plate forme de spectroscopie. html), from the  Nuclear Magnetic Resonance  platform of  Institut Jean Barriol  (CNRS FR 3843,  Université de Lorraine -https:// www. ijb. univ-lorra ine. fr), from the Ellipsometry core facility of LCP-A2MC ( Université de Lorraine -https:// lcp-a2mc. univ-lorra ine. fr) and from the IJL core facility ( Université de  Lorraine-http:// ijl.
Currently, there are three publicly available, well-documented, and user-friendly FEM implementations for screening mechanisms in Python. The computational backbones of these are derived from the open-source FEM frameworks FEniCS  [57, 58]  (implemented both in C++ and Python) and SfePy  [59]  (implemented in Python). The ϕ-enics code  [60] , which is built on top of the FEniCS library, offers a 1-dimensional implementation of Vainshtein models. A more recent FEniCS-based code, SELCIE, has been presented in Ref. [56]  and offers an implementation of chameleon theories in 2 and 3 spatial dimensions. The package has been employed for computing the chameleon field profiles in cosmic voids  [61]  and around halos  [62]. The outer boundary conditions are set by the asymptotic behavior of the scalar field infinitely far away from matter sources.
Since numerical implementations are limited to finite simulation boxes, the boundary conditions are typically imposed at distances sufficiently large compared to the Compton wavelength of the field. This approach is practical for many laboratory setups and isolated astrophysical configurations but can be computationally prohibitive if simulation domain is required to be very large. Adaptive mesh refinement techniques are often employed to reduce the computational cost in such situations. Alternatively, Ref. [63]  presents a SfePy-based FEM package femtoscope, which offers a rigorous support for accurately implementing boundary conditions at infinity. The approach exploits a coordinate mapping from the infinite computational domain to a finite one, hence making the problem with an unbounded domain computationally tractable  [64].
Earlier examples of using FEM solvers in the context of screening mechanisms can be found in Ref. [65]  for chameleon theories and in Ref. [24]  for symmetrons. Particularly, using FEniCS-based FEM solvers, Burrage et al. [65]  simulated non-trivial density configurations in order to optimize for fifth force effects in laboratory experiments. Elder, Vardanyan, et al. [24]  employed the commercially available FEM implementations in MATLAB alongside the custom-developed relaxation-based solvers in order to model symmetron fifth forces in Casimir experiments.
As part of the LOCal Universe Screening Test Suite (LOCUSTS) project, Shao et al. [145]  solved for the scalar field for n = 1 Hu-Sawicki f (R) gravity applying the ECOSMOG  [52, 146, 147]  code to a constrained N-body simulation from the ELUCID project  [148, 149]  (inferred using the SDSS DR7 galaxy catalog), using 20 f R0 values in the range 10 -7 -10 -6. Both the BORG and ELUCID density fields used to produce screening maps are constrained assuming no modification to gravity. Hence, these maps implicitly assume that the low redshift Universe has matter fields which are similar for all reasonable modified gravity and ΛCDM models on the scales of the reconstruction. The first constrained density fields which include the effects of modified gravity have now been produced  [150]  from CosmicFlows peculiar velocity data  [151] , through an extension of the ICECORE package  [152].
ACKNOWLEDGMENTS This work is part of the project initiated in the Perimeter Quantum Gravity workshop that happened in the winter of 2018. The authors thank the organizers of the workshop. Research at Perimeter Institute  is supported by the  Government of Canada  through the  Department of Innovation, Science and Economic Development Canada , and by the  Province of Ontario  through the  Ministry of Research, Innovation and Science. Q. P. was supported by an  NSERC   Discovery grant  awarded by  Maïté Dupuis  during this work.
The image is then re-converted to multi-channel k-space signal (green box) and the overall process is repeated over I iterations. During the training stage, all UNets are trained one-by-one fully (purple boxes) to reconstruct the reference volume xtarget based on the dataset processed up to the right image domain (i. e. , after the green box and prior to blue box to train). with 390 066 parameters with buffers and 388 338 without. They are trained for 300 epochs, resulting in 100 h long trainings for each pipeline overall, with RAdam optimizer and learning rate of 5 × 10 -4. The minimized cost function is the sum of an L1 loss applied to complex-valued images and multiscale SSIM over the magnitude images. All training experiments were run on the Jean-Zay supercomputer over a single NVIDIA Tesla V100 GPU with 32GB of VRAM.
Dataset A total of 123 SWI volumes were acquired on patients with non-Cartesian 3D GRE sequences at 3T (Magnetom Prisma, Siemens Healthcare, Erlangen, Germany) with a 64-channel head/neck coil array. The protocol was approved by local and national ethical committees (IRB: CRM-2111-207). Patient demographics, a study flow diagram and an illustration of SPARKLING trajectories are provided in the supplementary materials (Section S1). The dataset covers a wide range of pathologies (aneurysm, sickle cell anemia, multiple sclerosis) and off-resonance related artifact levels. Four different variations of the recently proposed full 3D SPARKLING  11  sampling pattern were used, but the vast majority (n = 102) were acquired using the following parameters: A 0. 6 mm isotropic resolution, a field-of-view of 24 cm in-plane (N = 384) over 12.
The dataset was then split into training (n = 99), validation (n = 11) and testing (n = 11) sets according to balanced age, gender, weight, off-resonance pre and post-correction visibility, and pathology type and visibility distributions. Two acquisitions were excluded due to strong motion (n = 1) and insufficient off-resonance correction (n = 1) caused by braces. In both cases, the self-estimated off-resonance correction still considerably improved the images. Minor quality concerns were raised regarding skin fat artifacts (n = 6) and partially deactivated readout coils (n = 2) without causing exclusion. Although the trainings were carried out from complex-valued to complex-valued volumes, the SWI specific processing was applied afterwards for visualization and scoring as described in. 12 The low frequencies were extracted by applying a Hanning window over the central third of k-space, before being removed from the phase image to obtain a high frequency map, subsequently normalized to produce a continuous mask.
Baselines Diverse baseline models are proposed to assess the contributions of the different features involved in our pipeline. A first baseline detailed in the supplementary materials (Section S3) is given by replacing the neural networks by conventional CS reconstruction using sparsity promoting regularization in the wavelet domain (Symlet eight basis decomposed over three scales). The L 1 -norm was used for R function with  = 10 -7 for thresholding the wavelet coefficients. To compensate the absence of buffers to learn acceleration schemes over iterations, the FISTA  47  algorithm available in the pysap-mri package was used. The data consistency is implemented with F , with SVI coefficients reduced to L = 5. This baseline noted BASE R is used to determine to what extent the contribution of neural networks is critical for improved image quality.
All of them show significantly higher scores than both baselines. Their ΔB 0 -weighted SSIM score follow the same ranking as those previously observed in Figure  1B  prior to image reconstruction when solving Eq. (  10 ): the SVI coefficients reach a better score as compared to MFI (second) and MTI (third) coefficients. This suggests that none of the diverse correction approaches carried by the different coefficients are better suited than another to help UNets compensate for the missing correction. Finally, the SVI 1∕2 pipeline improves the SVI approach with regard to ΔB 0 -weighted SSIM, while not significantly F I G U R E 4 Detailed structural similarity index measure (SSIM) scores distributions for different correction coefficients and pipelines over testing dataset. The SSIM and ΔB 0 -weighted SSIM distributions averaged over testing dataset in Table  1  are detailed for all pipelines over reversed logarithmic scales.
F I G U R E 5 Reconstructed SWI images over all pipelines. The reconstructed SWI images with three 4 mm in-plane (axial, sagittal, coronal) minimum intensity projections are provided for all color-coded pipelines (following the convention adopted in Figure  4  with regard to the color coding) for acquisition 68 from testing dataset. Various details are pointed out with blue arrows: both baselines provide blurred and incorrect details over axial slices, up to no detail at all over sagittal slices, while both details and textures are recovered by the four proposed pipelines. pipeline competes with reconstruction two to three times slower depending on the evaluation criteria.