dataesr/scientific-paragraphs-categorization huggingface dataset:
But typing ltNotGt requires typing gt and thus typing lt and eq. Hence, ltNotGt has decl-dependencies on lt and eq, coming from the def-dependency on gt. So, lt and eq must be λ -lifted in ltNotGt, to build the value of abst gt by applying the method generator gt found in the module OrdData to its three arguments. Note that only the types of lt and eq are used by ltNotGt: these methods can be redefined without impacting this theorem. As illustrated by this example, the dependency calculus cannot be reduced to a simple "grep". For any method, the analysis must compute the sets of methods of the species and of the parameters which are needed to elaborate the type and the value of its logical code (in Coq, they are called visible universe and minimal typing environment). This is the price to pay for having no errors in target codes.
Example ended We continue the example of 2. 2 by completing the module TheInt with the collection generator and its record type. The type of each method of the species is recorded into a record field labeled rf , its value local (obtained by a future application of the collection generator to all the param-arguments) has no more λ -lift. Here, as this collection has no parameter, there is no λ -lifting on the record itself. The value of local gt for example is obtained by applying the method generator coming from OrdData to its specarguments, whose values have already been generated, thanks to the absence of cycles in dependencies. The function mk record builds the record out of these values. Generating code for species IsIn. The types of the fields are translations of the types of the methods of the collection.
Conclusion Building FoCaLiZe, a lot of questions, choice points, etc. arose from the will to avoid dissociating the computational and logical aspects in a formal development while keeping the FIDE palatable. The mix of inheritance, late binding, encapsulation, inductive data types and unfolding of definitions in proofs creates complex dependencies, which have to be analyzed to ensure development correctness. This analysis gives the basis of the compilation process through the notions of method and collection generators, that we introduced to allow code sharing. The code generation model producing computable and logical target codes is outlined through an example. The formal computation of dependencies was presented with an short summary of their usage in the λ -lifting process. Several other FIDEs mentioned in the introduction have followed other choices.
It should be very interesting to compare their compilation models with ours, particularly on the method used to establish correspondence between runnable and logical code and on their semi-automation of proofs. Zenon greatly contributes to FoCaLiZe since it brings proof automation. This point is especially crucial to keep proofs simpler. We plan to extend it to handle recursion termination, arithmetic, temporal properties and, as it targets other provers than Coq, to experiment with other target type theories.
We present Keck/LRIS follow-up spectroscopy for 13 photometric candidates of extremely metal poor galaxies (EMPGs) selected by a machine-learning technique applied to the deep (∼ 26 AB mag) optical and wide-area (∼ 500 deg 2 ) Subaru imaging data in the EMPRESS survey. Nine out of the 13 candidates are EMPGs with an oxygen abundance (O/H) less than ∼ 10% solar value (O/H) , and four sources are contaminants of moderately metal-rich galaxies or no emission-line objects. Notably, two out of the nine EMPGs have extremely-low stellar masses and oxygen abundances of 5×10 4 -7×10 5 M and 2-3% (O/H) , respectively. With a sample of five EMPGs with (Fe/O) measurements, two (three) of which are taken from this study (the literature), we confirm that two EMPGs with the lowest.
SAMPLE We use a photometric sample of EMPG candidates selected by Paper I. The Paper-I photometric sample consists of EMPG candidates identified from the data of HSC and SDSS, which we refer to as HSC EMPG candidates and SDSS EMPG candidates, respectively. In this paper, we do not use SDSS EMPG candidates, because the SDSS EMPG candidates include more contaminants than the HSC EMPG candidates (Paper I). 1 More precisely, Paper II predicts super-massive stars beyond 300 M. However, such massive stars are not likely to contribute to the Fe/O enhancements of EMPGs unless the stars rotate very fast  (Shibata & Shapiro 2002). The catalog of the HSC EMPG candidates is developed with the HSC-SSP S17A and S18A data  (Aihara et al. 2019) , which are wide and deep enough to search for rare and faint EMPGs.
g -r, Paper I constructs a machine-learning classifier based on a deep neural network (DNN) with a training data set. The training data set is composed of mock photometric measurements for model spectra of EMPGs and the contaminants of other types of galaxies, Galactic stars, and QSOs. The DNN allows us to isolate EMPGs from the contaminants with non-linear boundaries in the multi-dimensional color space. Paper I finally obtains 27 HSC EMPG candidates from the HSC source catalog. Paper I conducts spectroscopic follow-up observations with Magellan/LDSS-3, Magellan/MagE, Keck/DEIMOS, and Subaru/FOCAS for 4 out of the 27 HSC EMPG candidates, and confirm that all of the 4 HSC EMPG candidates are truly emission-line galaxies with the low metallicity of 12 + log (O/H) = 6. 90-8. 27 (i. e. , 1. 6-38% Z ).
Data Reduction To reduce and calibrate the data taken with LRIS, we use the iraf package. The reduction and calibration processes include the bias subtraction, flat fielding, cosmic ray cleaning, sky subtraction, wavelength calibration, one-dimensional (1D) spectrum extraction, flux calibration, atmospheric-absorption correction, and Galactic-reddening correction. The 1D spectra are derived from apertures centered on the blue compact component of the HSC photomeric EMPGs. We use the standard star Feige 110 for the flux calibration. The wavelengths are calibrated with the HgNeArCdZnKrXe lamp. We correct the atmospheric absorption with the extinction curve at Mauna Kea Observatories  (Bèland et al. 1988 ). The Galactic-reddening value for each target is drawn from the NASA/IPAC Infrared Science Archive (IRSA) 2 based on the  Schlafly & Finkbeiner (2011)  estimates.
All of the LRIS EMPG candidates have [O iii]λ4363 detections, which allows us to derive metallicities and other element abundances with the direct-T e method (e. g. ,  Izotov et al. 2006 ) as described below. The electron temperature T e is calculated from two collisional excitation lines of the same ion such as O 2+ , because the collisional excitation rate is determined by T e. Using the PyNeb package getCrossTemDen with the latest atomic data and temperature relationship listed in Table  3 , we derive T e of O 2+ (T e (O iii)) and n e from emission-line ratios of is not available, we calculate T e with a fixed n e of 100 cm -3 , which is roughly consistent with those of EMPGs (e. g. , Paper I). We summarize results of T e and n e in Table  5. Again, our iterative calculations provide selfconsistent values of E(B -V ), T e (O iii), and n e (cf.
ACKNOWLEDGMENTS This paper includes data gathered with the 10-meter  Keck Telescope located at W. M. Keck Observatory, Hawaii. We thank the staff of  Keck Observatory  for their help with the observations. The  Hyper Suprime-Cam (HSC) collaboration includes the astronomical communities of Japan and Taiwan , and  Princeton University. The HSC instrumentation and software were developed by the  National Astronomical Observatory of Japan (NAOJ) , the  Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU) , the  University of Tokyo , the  High Energy Accelerator Research Organization (KEK) , the  Academia Sinica Institute for Astronomy and Astrophysics in Taiwan (ASIAA) , and  Princeton University. Based on data collected at the  Subaru Telescope  and retrieved from the HSC data archive system, which is operated by  Subaru Telescope  and  Astronomy Data Center at NAOJ.
This work was supported by the  joint research program  of the  Institute for Cosmic Ray Research (ICRR) ,  University of Tokyo. The Cosmic Dawn Center is funded by the  Danish National Research Foundation  under grant No. 140. S. F. acknowledges support from the  European Research Council (ERC)   Consolidator Grant funding scheme  (project  ConTExt , grant No. 648179 ). This project has received funding from the  European Union 's  Horizon 2020 research and innovation program  under the  Marie Sklodowska-Curie  grant agreement No. 847523  "INTERACTIONS". This work is supported by  World Premier International Research Center Initiative  ( WPI Initiative ),  MEXT, Japan , as well as KAKENHI  Grant-in-Aid for Scientific Research (A)  ( 15H02064 ,  17H01110 ,  17H01114 ,  20H00180 , and  21H04467 ) through  Japan Society for the Promotion of Science (JSPS).
Towards that end, we extract the dE/dx value from each SVD hit for these particles. In order to combine the hit-level dE/dx information for reconstructing the track-level dE/dx value, we find a simple arithmetic mean to be insufficient since the hit-level distribution follows a Landau function  [3]  for which the mean is undefined. Thus, a truncation is applied while combining the individual hit-level dE/dx measurements; basically the energy of all clusters except for the two highest ones are used in the calculation. Later we check the impact of dE/dx information on overall PID performance using the above two decay channels. We have also verified the dE/dx values to be independent of the mass of traversing particles, depending only on their βγ values  [4]. The study is based on e + e -collision data recorded at the Υ(4S ) peak by Belle II and the results are compared with that of a Monte Carlo (MC) sample.
The two-dimensional distributions of dE/dx vs. momentum (see Figs. 3  and 4 ) show a clear separation between different particles in the low momentum region, and are uploaded to the calibration database. As the specific ionisation depends only on the velocity (β) of traversing particles, we check the βγ universality of dE/dx values (Fig. 5 ) obtained from D * and Λ samples. The minimum energy loss occurs at βγ ≈ 3 regardless of the particle type. We get a flat curve beyond that threshold, as the relativistic rise of energy loss is suppressed by the density effect in silicon.
Acknowledgment This project has received funding from the  European Union 's  Horizon 2020 research and innovation programme  under the  Marie Sklodowska-Curie  grant agreements No  644294  and  822070. This work is supported by  MEXT ,  WPI , and  JSPS (Japan) ;  ARC (Australia) ;  BMWFW (Austria) ;  MSMT (Czechia) ;  CNRS/IN2P3  (France);  AIDA-2020 (Germany) ;  DAE  and  DST (India) ;  INFN (Italy) ;  NRF-2016K1A3A7A09005605  and  RSRI (Korea) ; and  MNiSW (Poland).
In the future, it will be interesting to further generalize our method to probe even higher-dimensional extensions or other classes of topological models. In 4D, for example, a non-zero second Chern number may arise in systems featuring timereversal symmetry, e. g. with spin-dependent gauge fields, in which all first Chern numbers vanish  [20, 21, 23, 26]. In our implementation, the role of spin may be played by the polarization degree of freedom of the light beam. (ANR-PRC-CES47  The experiment has been realized by studying the farfield diffraction patterns of a He-Ne laser beam (operating wavelength: λ = 632. 8 nm) impinging on a spatial light modulator (SLM). The SLM is a liquid-crystal (LC) device where the extraordinary refractive index has an inhomogeneous distribution that can be controlled and dynamically changed with a computer.
ACKNOWLEDGEMENTS We wish to thank  E. Prodan  for very insightful discussions. FDC, ADE, LM and FC acknowledge support from the  EU  ( Horizon 2020 program , under  ERC PHOSPhOR 694683 ). MM acknowledges support from the  Foundational Questions Institute Fund  (Grant number  FQXi-IAF19-05 ), and from the  ANR   Research Collaborative Project  " Qu-DICE ".
The lower- 2 NC data constrain the low- sea-quark distribution but are not able to distinguish between quark flavours in the sea at low , or between the down-type quarks, d and s at any. The difference between the NC  +  and  - cross sections at high  2 , together with the high- 2 CC data, constrains the valence distributions. The  2 dependence measured in the data constrains the gluon distribution. Additional information about the gluon comes from using HERA cross sections measured at various centre-of-mass energies ( √ ) through the contribution of the longitudinal structure function  [6] [7] [8]. Diverse ATLAS data sets can be used in addition to the HERA data to constrain the PDFs better. In Ref. [9] , high precision measurements of the inclusive differential  ± and / * boson cross sections at 7 TeV were added to the HERA data, resulting in the PDF set ATLASepWZ16, which improved on the HERAPDF2.
0 set in various respects. Firstly, the strange content of the sea was determined rather than assumed to be a fixed fraction of the light sea. Indeed, compared to previous determinations, the strange sea was found to be enhanced at low. Secondly, the accuracy of the valence quark distributions for  < 0. 1 was improved. The effect of adding differential  t distributions, in the lepton + jets and dilepton channels at 8 TeV, to the HERA data and the inclusive , / * data was studied in Ref. [10]. These  t data are complementary to the , / * data in their power to constrain PDFs because they are sensitive to the high- gluon distribution. The resulting PDF set was called ATLASepWZtop18. In Ref. [11] , data on the production of  and  bosons in association with jets (+ jets) were added to the HERA data and inclusive , / * data, resulting in the ATLASepWZVjets20 PDF set.
The + jets data are sensitive to partons at higher  than can be accessed by inclusive  and / * data and, in particular, they constrain the d and s quarks at higher. It would clearly be advantageous to combine ATLAS , / * data,  t data and + jets data in a single QCD fit. This is done in the present paper, and additional ATLAS data sets are also included. This paper presents the first comprehensive and comparative NNLO perturbative QCD analysis of a number of ATLAS data sets with potential sensitivity to parton distributions. The additional ATLAS data sets are described in the following. Firstly, the data on   [12]  production and / *  [13]  production with 20. 2 fb -1 at 8 TeV are added, providing further constraints on the valence PDFs and on the composition of the light-quark sea. Secondly, the direct photon production differential cross sections with 20.
2 fb -1 at 8 TeV and 3. 2 fb -1 at 13 TeV are added in the form of their ratios  [14] , whereby many systematic uncertainties cancel out. Thirdly, the  t differential cross sections in the lepton + jets channel from 3. 2 fb -1 at 13 TeV  [15]  are added and, fourthly, inclusive jet production cross sections with 4. 5 fb -1 at 7 TeV  [16] , 3. 2 fb -1 at 8 TeV  [17]  and 3. 2 fb -1 at 13 TeV  [18]  are considered. These direct photon data,  t data and inclusive jet data all have impact on the gluon PDF at medium to high. All ATLAS data sets considered in this study have full information about correlated systematic uncertainties. The analysis considers systematic uncertainty correlations between, as well as within, data sets. This is important now that several of the input data sets have systematic uncertainties deriving from jet measurements, since these uncertainties are larger than those from the lepton measurements.
Theoretical uncertainties, such as scale uncertainties, are also considered, including their correlations between data sets. The resultant PDF set is called ATLASpdf21. The structure of the paper is as follows. Section 2 presents the input data sets. Section 3 describes the theoretical framework of the fit. Section 4 presents the fitting methodology, including the definition of the fit  2 and details of the parameterisation. Section 5 presents ATLASpdf21 PDFs and then compares them with a fit in which correlations between data sets are not implemented. The impact of each data set is considered and then model uncertainties and further theoretical uncertainties, including scale uncertainties, are considered. Section 6 presents a study of the  2 tolerance and a comparison with other modern PDF sets.
4% for c-c rapidity and 2. 3% for c-f rapidity. There are 131 sources of correlated systematic uncertainty. The low-mass off-peak / * data are not used in the present analysis because they are subject to much larger corrections for non-fixed order, parton shower  T -resummation effects than the other , / * data  [21]. These low-mass data had little impact on the ATLASepWZ16 PDFs. ATLAS has published differential cross sections and forward-backward asymmetries for / * production at √  = 8 TeV, based on 20. 2 fb -1 of data  [13]. The measurement is presented in terms of three variables for both the c-c and c-f regions of the dilepton rapidity,  ℓℓ. For the c-c region, there are 12 bins of absolute rapidity ranging from 0. 0 to 2. 4, in intervals of 0. 2, divided into 7 bins of the dilepton mass  ℓℓ ranging from 46 to 200 GeV and 6 bins of the polar angle, , of the decay lepton in the Collins-Soper frame  [22].
Acknowledgements We thank  CERN  for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently. We acknowledge the support of  ANPCyT , Argentina; YerPhI, Armenia;  ARC, Australia ;  BMWFW  and  FWF , Austria; ANAS, Azerbaĳan; SSTC, Belarus;  CNPq  and  FAPESP, Brazil ;  NSERC ,  NRC  and  CFI ,.
Method The measured Love and Rayleigh wave dispersion curves were inverted jointly to obtain one-dimensional (1-D) V SV and V SH models representing the average structure between the station and the quake. The V SH and V SV model distributions were then combined to calculate radial anisotropy ξ. We used the Computer Programs in Seismology  (Herrmann, 2013)  code package to generate the synthetic group velocity, and a Niche Genetic Algorithm for the inversion  (Koper et al. , 1999; Li et al. , 2021)  together with a B-spline parameterization, as described below. The results obtained with this approach, hereafter referred to as Method 1, were compared against results from two other techniques (Method 2 and Method 3). Method 2 is a fully non-linear transdimensional hierarchical Bayesian approach using a reversible jump Monte Carlo Markov Chain (MCMC) algorithm and a layered parameterization that is allowed to vary at each iteration  (Weidner et al.
Conclusion We analyzed the Rayleigh and Love waves generated by the largest event ever recorded on Mars. The waveforms contain surface wave energy on all three components of the seismogram at periods between 15 s and 40 s. We measured the group velocity dispersion of these waves on the vertical, radial, and transverse components of the seismogram using a multiple filter analysis. We found that Rayleigh waves group velocities increase continuously up to about 3 km/s between 15 s and 40 s period. Love wave group velocities are systematically larger, between about 3. 2 km/s and 3. 5 km/s in the 15 -40 s period range. Because of a discrepancy between the Rayleigh wave group velocities in the transverse and vertical directions at periods greater than 30 s, we only used data up to 30 s. Isotropic inversions of the Love wave data were unable to explain the Rayleigh wave data and vice versa.
Acknowledgments We thank  Dr. Caroline Eakin  and  Dr. Joshua Russell  for their constructive reviews of our manuscript. C. B. also wishes to thank  Dr. Jeremy W. Boyce  for the discussions that helped with the interpretation of our results. We acknowledge  NASA ,  CNES , their partner agencies and Institutions (UKSA,  SSO ,  DLR ,  JPL ,  IPGP-CNRS, ETHZ, IC, MPS-MPG ) and the flight operations team at  JPL, SISMOC, MSDS, IRIS-DMC  and  PDS  for providing SEED SEIS data. This is ICN 271. This research was carried out in part at the  Jet Propulsion Laboratory, California Institute of Technology , under a contract with the  National Aeronautics and Space Administration  ( 80NM0018D0004 ). C. B. , J. L. , and E. W. were funded by  NASA InSight PSP  grant # 80NSSC18K1679. J. W. was funded by  UKSA Aurora  grant  ST/T002972/1.
Data and materials availability : The InSight event catalogue  (Clinton et al. , 2021; Ceylan et al. , 2022;  InSight Marsquake Service, 2022a, 2022b)  and waveform data are available from the IRIS-DMC, NASA-PDS (InSight Mars SEIS Data Service, 2019a) and IPGP data center (InSight Mars SEIS Data Service, 2019b).
Details of the aperture photometry are described in Appendix A. The light curves of the SAP fluxes in S40 and S41 have no obvious systematic trends. Without further corrections done, the SAP fluxes are used for the frequency analysis. The two light-curve files in S40 and S41 are combined to one light curve because of the same exposure time and the almost continuous time span. In the TESS data, the data set of S14 contains 757 points covering a time span of 26. 8 days, and the whole data set of S40 and S41 contains 7475 points covering a time span of 55. 9 days. The detailed time spans of the Kepler and TESS data are given in Table  2. We used the normalized fluxes for the subsequent analysis of KIC 3440495, in units of intensity (ppm). The corrected light curves constructed from the Kepler and TESS short-and longcadence data are shown in Figure  1.
The PYTHON package Lightkurve is a useful tool to analyse archive data Kepler and TESS data  (Lightkurve Collaboration et al. 2018). We used the package to access, check, and combine multiple quarters of data from MAST. The Lightkurve package is also used to remove outliers and to detrend and normalize the light curve. In addition, the aperture photometry for TPFs is done with the Lightkurve package.
Frequency Analysis In order to analyse the pulsation content, we use a discrete Fourier transform (FT) to calculate the amplitude spectra of the Kepler and TESS data  (Kurtz 1985). The amplitude spectra are in the range of zero to the Nyquist frequency. The Nyquist frequency, f Nyq = 1/(2 Δt), where Δt is the time interval of a discrete data set, is the highest frequency that is not undersampled for a given sampling frequency. The Nyquist frequencies have values of 24. 47 day -1 and 694. 06 day -1 for the KLC and KSC data, and 23. 99 day -1 and 71. 99 day -1 for the TLC and TSC, respectively. The peaks in the amplitude spectra were extracted with the software PERIOD04  (Lenz & Breger 2005) , using a multifrequency nonlinear least-squares fit to calculate and optimize the frequency parameters with the following equation: ( ( )) ( ) L A ft sin 2 , 1 i N i i i 1 å p f D = + = where A i , f i , and f i are the amplitude, frequency, and phase of each peak, respectively.
The resolution frequencies are values of 0. 001020 day -1 and 0. 04950 day -1 for the KLC and KSC data, and 0. 056 day -1 and 0. 0268 day -1 for the TLC and TSC data, respectively. The KLC data therefore have the best frequency resolution and afford the greatest precision. In what follows, we will primarily use the KLC data set. We first used the KSC data to check for Nyquist aliases  (Murphy 2012) ; these data reveal that all of the real frequencies lie below the KLC Nyquist frequency of 24. 49 day -1. We present all the amplitude spectra of the Kepler and TESS data in Figure  2. It can be seen that the significant frequencies in the KLC amplitude spectrum are concentrated in the low-and highfrequency regions. The significant frequencies in the lowfrequency region include pulsation frequencies, as well as frequencies related to modulation.