dataesr/scientific-paragraphs-categorization huggingface dataset:
1. Table 2 also includes the average value of the coherence time (τ o ) for each dataset measured at the DIMM monitor at ∼500 nm. The data reduction was performed using a ZIMPOL customary pipeline developed at ETH Zürich. As a first step, the images were remapped to a square grid of 1024 × 1024 pixel 2 with a pixel scale of 3. ′′ 6 × 3. ′′ 6, bias-subtracted, and flat-fielded. Subsequently, the individual images were recentered using a simple Moffat function to estimate the centroid position, as no coronograph was used. This resulted in two individual cubes, one per filter. For the point-spread function (PSF) subtraction, the individual filter datasets (N_Ha and Cnt_Ha) were considered separately to apply a standard angular differential imaging (ADI) processing technique using classical-ADI (cADI), smart-ADI (sADI), and radial-ADI (rADI, see  Lafrenière et al.
To correct for the flux loss related to the ADI processing, fake planets were regularly injected into the original data cubes before PSF subtraction (every 20 pixels at three different position angles, with a flux corresponding to 100 ADU). The cubes were then reprocessed using the different ADI algorithms, allowing us to estimate the flux loss by computing the azimuthal average of the flux losses for fake planets at the same radii (e. g. ,  Jorquera et al. 2021). The contrast curves at 5σ were then obtained using the pixel-to-pixel noise map divided by the ADI flux loss and corrected for small number statistics following the prescription of  Mawet et al. (2014)  but adapted to our 5σ confidence level at small angles with ZIMPOL. The same method was applied for the ASDI dataset to illustrate the gain in speckle subtraction in the inner region below ∼100 mas.
Data analysis As a general result, we do not detect any obvious point-like companion in the analyzed datasets. In the cases of TW Hya and HD163296, we detect some faint point-like emission, the nature of which is discussed in the corresponding subsections below. Our analysis of the data reveals that, for the cases of TW Hya, T Cha, and RXJ1615, the best contrast in the ADI Cnt_Ha and N_Ha images is obtained for the sADI and sPCA reductions at small separations, while cADI is better at larger separations given the larger number of frames used, minimizing the readout and background noise. In the case of LkCa15, the faintest object of the sample, cADI provides the best contrast even at small separations, as we are probably entering a low-flux regime for which the temporal evolution of the PSF becomes less critical.
TW Hya For TW Hya, the atmospheric conditions were very good and stable, and so we only rejected 7 images (out of 82). The total rotation field is ∼108 degrees. The images in the two individual filters show an elongated PSF, and the elongation direction changes with the parallactic angle along the exposure. As a result, the final images show a "butterfly" pattern. This effect, known as a wind-driven halo (WDH), was studied in detail by  Cantalloube et al. (2020)  and is related to high wind-speeds in the upper layers of the atmosphere. Thanks to the simultaneity of the N_Ha and Cnt_Ha images, this elongated emission is partially suppressed in the ASDI image. The ASDI image in Fig. 2  shows a faint emission feature located at a separation of ∼160 mas SW (magenta circle). We note that this is the only faint emission that is detected in all of the ASDI image regardless of the data processing applied (e.
HD 163296 HD163296 was observed twice: in August and September 2018. In the first dataset, the observing window was not exactly within the specified local sidereal time interval, which is why the target was reobserved later. We note that this is a difficult target for service observations from Paranal Observatory, as it crosses the meridian close to the zenith: the target declination, -21 • 57 ′ 21 ′′ , is close to the observatory latitude, 24 • 37 ′ 39 ′′ S. Hence, we can only obtain data before and/or after the meridian crossing, when the rotation rate is smaller. As a consequence, both datasets show a small rotation field of ∼7 and 9 degrees, respectively. In the first dataset (Aug 2018), the first 130 images were obtained with an individual exposure time (DIT) of 30 s, and a large fraction of them were close to (or at) the saturation level, and so we rejected them.
The loop then opened, and once it was recovered, a second sequence of 220 unsaturated images with DIT = 20 sec was obtained, but covering only a rotation field of 1. 6 degrees. In the second dataset (September 2018), we obtained a total of 255 images, each of 20 s exposure. In this case, the loop was more stable, and we rejected 12 images out of 255 with the lowest fluxes. We performed our analysis on the second dataset, and the final images are displayed in Fig. 2. For completeness, we include an image with a larger field-of-view (FOV) in the Appendix (Fig. B. 1), displaying the position of the planet candidates reported for this source. Without considering the planet candidate proposed by  Pinte et al. (2018)  at 2. 4 arcsec (which is outside the ZIMPOL FOV), we do not detect any clear signal from the planet candidates reported in the literature.
On the other hand, we detect a faint emission in the N_Ha and ASDI images at a separation of ∼171 mas SW of the central source (magenta circle, Fig. 2 ). Interestingly, this emission is not observed in the continuum image. However, we note that a small field rotation can imply important self-subtraction. We therefore also analyzed the derotated images without subtracting the PSF (named "nADI" here). The nADI images are displayed in Fig. 4  (FOV of 0. 29 × 0. ′′ 29) and in Fig. 5  (FOV of 0. 58 × 0. ′′ 58). In the former, we can clearly see a bright point-source emission at a separation of ∼43 mas (4. 3 au) in the SE direction (top left panel, red circle). To further investigate the nature of this emission, we also analyzed the nADI unsaturated data obtained in 2018 August 18, and checked that the bright spot appears approximately at the same location.
5m Baade telescope in Las Campanas Observatory 10 days after the ZIMPOL observations. We obtained two spectra of 60 seconds each with the 5 arcsec slit on April 30 2018 -10 days after the ZIMPOL data was obtained-under photometric conditions. The target was observed at airmass 1. 02. A spectrophotometric standard star was observed immediately after RXJ1615 at airmass 1. 07, and with the same slit. The spectra were reduced with a dedicated pipeline. The processing includes bias subtraction and flat-field correction. We used thorium-argon (ThAr) exposures obtained after the science spectrum to wavelength-calibrate the data. We then fluxcalibrated the science spectrum using the standard star. We used the spectrum to perform synthetic photometry, deriving an R-band magnitude of 11 mag, close to the tabulated value of 11.
We note that we estimated a continuum flux density of ∼2×10 -13 erg/s/cm 2 /Å in the ZIMPOL data, which is comparable to the value derived by  Cahill et al. (2019)  for an extinction value of 1. 2 mag. Hence, we adopted this value for A v. Mendigutía et al. (2013)  studied data for HD163296 from five epochs obtained on timescales from days to months. We converted their provided maximum and minimum H α luminosities into fluxes using their assumed distance of 130 pc, obtaining line fluxes of 1. 5 -2. 0 × 10 -10 erg/s/cm -2. Using the ZIMPOL data, we report a H α line flux of 0. 82 ± 0. 36 × 10 -10 erg/s/cm -2 , which is within the reported values in previous works within the uncertainties. Using equations  C. 3 and C. 4, we estimate an accretion rate of 9. 8 × 10 -8 M ⊙ /yr. If we consider the minimum and maximum H α line fluxes estimated for the object, and the updated stellar parameters included in Table  1 , the accretion rate can vary between 0.
Acknowledgements. This research has been partially funded by the  Spanish   MCIN/AEI/10. 13039/501100011033grant PID2019-107061GB-C61  and MDM-2017-0737  Unidad de Excelencia María de Maeztu -Centro de Astrobiología (CSIC-INTA ). N. H. is very grateful to the Paranal staff that performed the service observations, and to the  ESO USD , in particular,  Henri Boffin. Part of this work has been carried out within the framework of the  National Centre for Competence in Research PlanetS  supported by the  Swiss National Science Foundation. I. M. is funded by a  RyC2019-026992-I grant  by  MCIN/AEI /10. 13039/501100011033. J. M. A. acknowledges financial support from the project  PRIN-INAF 2019 Spectroscopically Tracing the Disk Dispersal Evolution. G. C. thanks the  Swiss National Science Foundation  for financial support under grant number  200021_169131.
That approach has been limited to the lowest few moments by the reduced rotational symmetry of the Euclidean lattice, and generally provides weaker constraints on PDFs than methods that give access to the x dependence directly  [74] [75] [76]. In the present analysis, we make use of new data from lattice QCD simulations of pion matrix elements with space-separated quark-quark and current-current (CC) correlators, which have well-defined continuum limits, and can be factorized to the standard light-cone PDFs with perturbatively calculable matching coefficients. The lattice data on matrix elements of quark-quark correlators are presented in the form of reduced Ioffe time pseudodistributions (Rp-ITDs)  [55, 77]. In this analysis lattice data on both Rp-ITDs and matrix elements of CC correlators are treated on the same footing as experimental data, and are analyzed simultaneously.
Such tools allow us to build theoretical observables describing processes involving partons, and to compare them with the available data. Much in the same way as different experimental datasets are used in phenomenological extractions of PDFs, the universality of the PDFs in different lattice observables can also be tested. Here, we treat lattice QCD data on the same footing as experimental data. We use factorization theorems for lattice observables to describe the results in terms of convolutions of hard coefficients with PDFs, and the approach to the extraction of PDFs from lattice data is analogous to the methods used in global QCD analysis of experimental data. In practice, in our analysis we include DY and LN electroproduction observables in conjunction with Rp-ITD and CC correlator lattice QCD data to extract the PDFs in the pion.
To obtain a meaningful description of the valence quark distribution in the pion, q v ðxÞ ¼ qðxÞ -qðxÞ, we take the real component of the factorized Rp-ITD Mðν; z 2 Þ  [49]. The imaginary component of Mðν; z 2 Þ computed in these datasets cannot be expressed in terms of the physical pion sea quark distribution, because the calculation does not at present include the disconnected contributions. The Rp-ITD takes the form of a convolution of the PDF with a hard coefficient function, to which correction terms are added to account for systematic uncertainties. The real part of M can be expressed as ReMðν; z 2 Þ ¼ Z 1 0 dxq v ðx; μ lat ÞC Rp-ITD ðxν; z 2 ; μ lat Þ þ z 2 B 1 ðνÞ þ a jzj P 1 ðνÞ þ e -m π ðL-zÞ F 1 ðνÞ þ …; ð8Þ where q v ≡ u -ū ¼ d -d in π þ , and the C Rp-ITD is the cosine transformation of the coefficient function, as discussed in Refs.
In this analysis, we include a and b in the set of fit parameters. By construction, Mð0; z 2 Þ ¼ 1, and the leading twist contribution satisfies this condition through the valence quark number sum rule. At ν ¼ 0 the systematic corrections must therefore vanish. For this reason, we do not include the n ¼ 0 term in the series in Eqs. (  9 ), since these are not guaranteed to vanish at ðn; νÞ ¼ ð0; 0Þ. Instead, we begin the expansion at n ¼ 1 and take up to the n ¼ 2 term, since both terms vanish at ν ¼ 0. We use the available Rp-ITD data from the Jefferson Lab HadStruc group  [49] , calculated on the ensembles labeled a127m413 and a127m413L, whose parameters are given in Table  I. The two datasets each have the same lattice spacing a ≈ 0. 127 fm and pion mass m π ≈ 413 MeV, but different lattice volumes, with the larger volume dataset a127m413L having L ¼ 32a and the smaller volume dataset a127m413 having L ¼ 24a.
Each dataset includes the momentum values of p i ¼ i × ð2π=LaÞ, where i ∈ f1; 2; 3g, and each features discrete separations z up to 6a, with a127m413L including z up to 8a. The signal-tonoise ratio of the lattice points decays exponentially with momentum, making the calculation of the p 3 points in the a127m413 ensemble incompatible with statistical fluctuations. For this reason, we exclude these points. We also cut the z ≤ 2a data points to avoid discretization errors and contact terms arising from the chosen discretization of the quark action.
(  12 ) are the power correction z 2 B 1 ðνÞ and discretization correction aR 1 ðνÞ, with the ellipsis representing other potential systematic correction terms. Attempts were made to fit systematic corrections such as lattice spacing, pion mass, and finite volume, but because the data have such large statistical uncertainties, it was difficult to separate the systematic effects beyond what is included in Eq. (12). We parametrize function B 1 ðνÞ as in Eq. (  9 ), and the discretization term R 1 ðνÞ is similarly parametrized as where σ 0;n is given in Eq. (10). Unlike in the Rp-ITD case, here we expand Eqs. (  9 ) and (  13 ) in n from 0 to 2 because the quantity T 1 ðν; z 2 Þ does not have a specified normalization given by the leading twist term at ν ¼ 0. Four datasets were included in our analysis of the HadStruc data  [51] , with the parameters given in Table  I.
We refer to the datasets as {a127m413, a127m413L, a94m358, a94m278}, which have lattice spacings of {0. 127, 0. 127, 0. 094, 0. 094} fm and pion masses of {413, 413, 358, 278} MeV, respectively. Each ensemble has a total lattice size of L ¼ 32a, with the exception of the a127m413 set, which has L ¼ 24a. Each dataset spans the range 2a ≤ z ≤ 4a, and the a94m358 and a94m278 ensembles further include z ¼ 5a and 6a. The momentum of the generated lattice data include p i ¼ i × ð2π=LaÞ, where i ∈ f1; 2; 3; 4g. No kinematic cuts were made on the CC observables. R 1 ðνÞ ¼ X n σ 0;n ðνÞr n ; ð13Þ.
As in previous JAM global QCD analyses of pion PDFs  [12] [13] [14] , we employ Bayesian statistics to sample the posterior distribution according to PðajdataÞ ∼ LðdatajaÞπðaÞ; ð15Þ where πðaÞ is the prior distribution, which sets the boundaries of the fit parameters a, L is the likelihood function, LðdatajaÞ ¼ exp - 1 2 χ 2 ða; dataÞ ; ð16Þ which is a Gaussian with the argument χ 2. In practice, maximizing the likelihood function is done by minimizing the χ 2 function, which for a given experimental dataset e is defined by χ 2 e ða; dataÞ ¼ X i d e i - P k r e k β e k;i -t e i ðaÞ=n e α e i 2 þ 1 -n e δn e 2 þ X k ðr e k Þ 2 ; ð17Þ where the sum is over i data points up to N e dat , with k types of correlated uncertainties. The data points are represented by d e i , while the parameter-dependent theory, t e i ðaÞ, is divided by the fitted normalization parameter n e for each experiment and added with the correlated shift, which includes the nuisance parameters r e k and point-to-point correlated uncertainties β e k;i.
A. Analysis with reduced Ioffe time pseudo-distributions As baseline fits for our analysis, we consider first as "scenario A" the analysis of DY and LN data determined using the NLO or NLO þ NLL DY methods for the DY cross sections  [12, 14] , without inclusion of lattice data. A good overall fit to the DY and LN data is obtained, similar to that in the recent JAM analysis  [14]. As illustrated in Table  II , which summarizes the goodness of fit for each scenario, the number of points in each dataset and the corresponding reduced χ 2 , a total reduced χ2 of ≈0. 8 is found for both the NLO and NLO þ NLL DY baseline fits to the experimental data. In a first attempt to fit the Rp-ITD data simultaneously with the experimental data, in "scenario B" we include the lattice data in a simplified way, excluding the systematic effects and only fitting to the leading twist terms in Eq.
(  8 ). While the DY and LN data were described almost the same as the fits to only experimental data, we found the fit to the smaller lattice volume data, a127m413, was unacceptably large, with a χ2 of 1. 98 and 2. 63 for the NLO and NLO þ NLL DY methods, respectively. This lack of agreement with the data is an indication that the leading twist convolution term alone is not sufficient to describe the available Rp-ITD data. Consequently, we consider a further "scenario C," which includes all of the available types of systematic terms as shown in Eq. (8). With the inclusion of the systematic corrections in scenario C, the resulting χ2 are acceptable for all datasets, with a global χ2 ≈ 0. 85. Importantly, the χ2 e values do not change much among the scenarios, indicating compatibility of the experimental and lattice data.
Interestingly, the agreement of the results with the large lattice volume data, a127m413L, does not change with the inclusion of systematic corrections, and the effect is largely seen in the smaller lattice volume ensemble, a127m413. By performing Monte Carlo inference of all PDF shape parameters and lattice systematic parameters, in the following we investigate the relationship between the PDFs and the systematic uncertainties, including their overall contributions. To assess the significance of the χ2 values in Table  II , we perform the Z-sigma level statistical test on each of the datasets analyzed in the global analysis. In this test, the null hypothesis is the expected χ 2 distribution assuming the number of degrees of freedom to be the number of points in the data set, and the resulting χ 2 samples from the Monte Carlo (MC) analyses from scenario C are the alternative hypotheses.
We compute the p value using the peak of the resulting MC χ 2 distributions, and the Z-sigma level is the inverse of the normal cumulative distribution function, Z ¼ Φ -1 ðpÞ ≡ ffiffi ffi 2 p erf -1 ð2p -1Þ. These values are given in Table  III  for each of the datasets and represent the number of normal standard deviations from the expected χ 2. The "-" or "þ" superscript on the values indicates their positions below or above the expected χ 2 distribution's mean value, respectively. A large negative value may imply a non-Gaussian χ 2 function is needed to treat the systematic uncertainties. Nevertheless, none of the values are outside of 5σ, indicating a reasonable probability that our results are achieved with the given data. Notably, the NLO and NLO þ NLL DY are not in tension for the Rp-ITD data.
Which lattice data have maximal impact? When studying the impact of adding lattice data to global phenomenological extractions of PDFs, it is pertinent to ask which lattice datasets have the most impact. In lattice calculations, all hadrons suffer from an exponential growth of the signal-to-noise ratio as energy increases, but the effect on the pion, as the lightest hadron, is most significant. This signal-to-noise ratio of lattice correlation functions decays exponentially as ∼ exp½-ðE h -1 2 m π n q ÞT, where E h is the energy of the hadron, n q is the number of valence quarks, and T is the Euclidean time separation of the operators  [109, 115]. Excited state contamination is lessened at large time separations, where the pion has a larger signal-to-noise ratio than the nucleon at a fixed low momentum.
In the datasets used here, the relative uncertainty of the lowest momentum state data having p ¼ 1 (hereafter referred in units of 2π=La) is an order of magnitude smaller than the p ¼ 2 data, even though all momenta were calculated with equal computational cost. As such, we expect the lowest momentum state to drive the impact from the lattice data overall. This feature also means that utilizing factorization methods that limit power corrections at low momentum is crucial for efficient and precise numerical calculations of parton structure, particularly for the pion, where the effects can be rather dramatic. As demonstrated with mock data in Ref. [116] , the range of Ioffe time can dramatically change the quality of the resulting PDF, specifically in the low-x region. However, in this combined analysis, the LN data provide constraints at low-x such that an improvement is possible across the whole range of x.
For each value of z, the smallest ν values correspond to the p ¼ 1 points. As seen in Fig. 3 , the leading twist terms generally agree the best with the total results when ν is small, so that the systematic corrections do not compete with the leading twist contribution. We performed a Monte Carlo analysis of the experimental data combined with the p ¼ 1 lattice points with the same systematic corrections included above, again using both NLO and NLO þ NLL DY coefficients. These analyses included 6 and 4 data points from the a127m413L and a127m413 ensembles, respectively. The resulting χ2 e are almost identical to scenario C in Table  II , with the NLO analysis producing χ2 λ ¼ 0. 80 and 1. 02 for a127m413L and a127m413, respectively, and the NLO þ NLL DY giving χ2 λ ¼ 0. 82 and 1. 05 for the same datasets.
The ratios of the p ¼ 1 data to the mean values of the theory are shown in Fig. 6  for each of the Rp-ITD datasets. Since all data points have the same momentum p, the increase in ν is directly proportional to the increase in the z spatial separation. Each of these points is close to unity within the uncertainties of the theory, indicating a good agreement in the analysis. The datasets agree best with the theory at small ν, and deviate in opposite directions at large ν. The theory slightly underpredicts the a127m413L data, while marginally overpredicting the a127m413 data. The difference between NLO and NLO þ NLL DY is minimal, with a modest preference for the NLO analysis from the a127m413 dataset, evident at large ν. In comparison with Fig. 4 , which showed the PDFs when taking into account all of the momentum values in a127m413L and p ¼ 1; 2 in a127m413, in Fig.
Importantly, each of the central values lie within the FIG. 6. Data to theory ratios for the Rp-ITD datasets a127m413L (red circles) and a127m413 (blue triangles) resulting from fits including only the p ¼ 1 data points for the NLO (top) and NLO þ NLL DY (bottom) methods. The bands represent 1σ uncertainties. 1σ uncertainty band from the μ lat ¼ 2 GeV result. This suggests that the uncertainty band associated with the valence quark PDF has not been underestimated due to scale variation effects, and demonstrates that these effects for the Rp-ITD are largely insignificant.
We use the systematic correction terms associated with the power corrections and lattice spacing errors, as shown in Eq. (11). We found that by excluding all systematic effects, there was tension between the experimental and lattice data, evident in the resulting PDFs, which accepted a small set of solutions that were noticeably different from the experimental-only analysis. Additionally, including more systematic corrections increased the uncertainties on the Drell-Yan predictions generated from the experimental-only analysis. These inconsistencies led us to consider various systematic effects, and incorporating power and discretization corrections tamed both the uncertainties on the Drell-Yan predictions and tensions in the PDFs. In Table  IV  we show the reduced χ 2 for each of the datasets in the analysis.