dataesr/scientific-paragraphs-categorization huggingface dataset:
Therefore, the rotation frequency f rot can be 2. 322909(2) day -1 (P rot = 0. 430495(1) day). Besides the frequency f l1 , another dominant frequency ( f l ) at low frequencies is detected at 0. 0379 day -1 in the KSC data. The frequency f l corresponds to one modulation with a period of about 26 days for the light curve made from the KSC data, which can be seen in the top panel of Figure  1. The frequency f l is detected only in the KSC data, and its authenticity cannot be determined based on the 30. 3 day Kepler short-cadence observations. Since this peak is not present in the KLC data, it is probably an artifact. Considering the resolution frequency of KSC, the frequency f l1 is the same as an artifact of the known Kepler's artifacts, f downlink = 0. 031 day -1  (Yang et al. 2018). The data downlink process produces a break lasting 24 hr every 32 days, which leads to the artifact f downlink.
There is a data gap of approximately 24 hr in the KSC data that can be seen in the top panel of Figure  1. Therefore, we speculate that the appearance of f l1 in the KSC spectrum can be attributed to the failure of the de-trending operation of the PDC_SAP fluxes in the KSC observations. There are many side peaks around the rotational frequency and its four harmonics. It is no surprise because intrinsically the power spectrum is dense around the frequencies of gravitoinertial modes or pure inertial modes  (Dintrans & Rieutord 2000; Rieutord & Valdettaro 2018). By using frequency separations larger than f res = 0. 001020 day -1 and a S/N higher than 5, 24 side peaks are retained and listed in Table  3. Fewer frequencies are detected in the TSC and TLC data. The two dominant peaks ( f h1 , f h2 ) at high frequencies and the modulation frequencies associated with rotation are also detected in the TESS data.
A δ Sct-γ Dor Hybrid Pulsator in A Binary System A pulsator in a binary system would exhibit pulsational phase variations caused by the orbital motion. The pulsational phase variations of KIC 3440495 have been found by  Murphy et al. (2018) , which suggest that the star is in a binary system with a period longer than the time span of the KLC data. We analysed the pulsational phase modulations of the star in detail to obtain more information about the binary system. The light curve made from the KLC data is divided in multiple 10 day segments. These segments are used to calculate the phase shifts of the pulsations, which are converted into light arrival-time delays  (Murphy et al. 2014 (Murphy et al. , 2016;; Murphy & Shibahashi 2015; Hey et al. 2020 Hey et al. , 2022)). The four high frequencies with amplitudes greater than 20 ppm in the KLC spectrum are chosen to measure their phase shifts in each segment, and they show the same time-delay signal with a period of more than 1400 days, as shown in Figure  3.
The result suggests that KIC 3440495 is a pulsator in a binary system with an orbital period longer than the time span of the KLC data. The asymmetric time-delay curve implies that the orbit of the binary system has high eccentricity  (Murphy & Shibahashi 2015; Murphy et al. 2016). KIC 3440495 was observed by both the Kepler and TESS missions. There are expected to be phase shifts of the pulsations between the Kepler and TESS data due to the different passbands of the observations used by the two missions. Even in the absence of binarity, the pulsation phases in the Kepler and TESS data would not be identical. It is therefore non-trivial to combine the two data sets for a phase modulation analysis, and we do not attempt that here. We tried to determine the possible orbital parameters of the binary system based on these segments of the KLC data by using a Markov Chain Monte Carlo (MCMC) software program  (Murphy et al.
Despite the oblateness, the star should remain axisymmetric, which should not give rise to any modulation by rotation. So there should be other reasons for the rotation modulation. In the frequency analysis of the Kepler and TESS data, the star shows rotation modulation for a long time. The brightness variations of the star should be further analysed after excluding the disturbance of the pulsations. The KSC and KLC data will be used simultaneously to explore causes of the rotation modulation. First, we filter out all the pulsation frequencies independent of rotation with a S/N higher than 5 from the light curve of the KSC data, and fold the residuals of the light curve with the rotation frequency f rot = 2. 322909(2) day -1. The folded phase light curve is binned every 0. 002 phase, and showed in Figure  5.
A Potential Sister of Altair In the literature, it is found that KIC 3440495 is very similar to the widely studied star Altair  (Suárez et al. 2005; Bouchaud et al. 2020; Le Dizès et al. 2021). Interestingly, the oscillation spectrum of KIC 3440495 shows many similarities with that of Altair. The amplitude spectra of KIC 3440495 and Altair are presented as a comparison in Figure  11. The data of Altair's spectrum are from the Microvariability and Oscillations of STars (MOST) satellite from 2012 (see Le  Dizès et al. 2021). The two stars coincidentally exhibit very close excited modes at low and high frequencies. The three frequencies with the highest amplitude are 15. 9733 day -1 , 0. 6364 day -1 , and 20. 29943322 day -1 in the KIC 3440495 spectrum, and 15. 7679 day -1 , 0. 57 day -1 , and 20.
The ordering tendencies and geometry of the pathways are shown to be controllable by the strength of further neighbor interactions. The  where the elastic contribution is separated by a pseudostatistical chopper  [38]. The crystal was rotated through 180 degrees with the step of 5 degrees horizontally with the vertical angular coverage of ±8 degree (limited by the magnet vertical opening) for survey on the elastic and diffuse peaks in reciprocal space. The dilution refrigerator insert and cryomagnet were used to enable the measurements down 100 mK and fields up to 1. 4 T. The data were reduced using Mantid  [39]  and Python script available at Corelli. Background runs at 1. 4 Tesla were made to remove all diffuse signals. The extra scattering at Bragg peak positions due to the polarized spin contribution was accounted for using zero-field intensities.
S1. Data were collected then converted into 3D reciprocal space using the instrument's TVnexus software. A measurement at saturated field was subtracted (with Bragg peaks in the background being replaced by a suitable region of the scattering in Q-space) to reduce background contamination of the diffuse scattering. The scattering measurements after a quench from 3 K down to temperature of 50 mK is shown in Fig. S2 (a). The scattering cross-sections after annealing down to the same temperature is shown in Fig. S2(b). No difference was found between the annealed and quenched diffuse scattering patterns, as shown in Figs. S2(c ).
In particular, N 0 Betti stands for the number of connected components. The sequence of Betti numbers {N 0 Betti , N 1 Betti ,. , N k Betti } characterize an n-dimensional complex. For example, it is {1, 0, 0} for a single point, {1, 1, 0} for a circle and {1, 2, 1} for a torus. In the context of monopoles, a pathway is generated by a sequential 1D walk in 3D space. As shown in Fig. 3B , a monopole could have multiple loops as it progresses in a certain direction. The looping in the pathways indicates the complexity of the local energy landscape the monopole experiences. To analyze this phenomenon, we calculated the 1st Betti number (N 1 Betti = N Betti ) for traced pathways using the jPlex package for applied topology  [43]. The averaged value over all the monopoles as a function of temperature is shown in Fig.
DE-AC05-00OR22725. SAG thanks Agencia Nacional de Promoción Científica y Tecnológica through PICT 2017- 2347. This work was partly supported by the Deutsche Forschungsgemeinschaft under grants SFB 1143 (project- id 247310070) and the cluster of excellence ct. qmat (EXC 2147, project-id 390858490), by the Helmholtz Vir- tual Institute "New States of Matter and their Excita- tions", and by the Engineering and Physical Sciences Research Council (EPSRC) Grants No. EP/K028960/1, No. EP/P034616/1, and No. EP/T028580/1 (CC). Part of this work was carried out within the framework of a.
Sloan foundation, and Maryland Center for Fundamental Physics at the University of Maryland, College Park. A. E. acknowledges support from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant agreement No. 758027) and the Swedish Research Council project grant (Grant agreement No. 2020-05127). J. D. H. acknowledges support from the Natural Sciences and Engineering Research Council of Canada uunder grants SAPIN-2018-00027, RGPAS-2018-522453, and the Arthur B. McDonald Canadian Astroparticle Physics Research Institute. I. T. was supported by the U. S. Department of Energy, Office of Science, Office of Nuclear Physics, under contract No. DE-AC52-06NA25396, and by the U. S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Scientific Discovery through Advanced Computing (SciDAC) NUCLEI program.
Acknowledgements: This work was supported by the  U. S. National Science Foundation  ( PHY-1913728 ) and benefitted from computing resources provided by the  National Energy Research Scientific Computing Center NERSC  (under Contract No. DE-AC02-05CH11231 ), Frontera computing project at the  Texas Advanced Computing Center (under National Science Foundation  award  OAC-1818253 ) and  LSU  (www. hpc. lsu. edu). Acknowledgments: We thank  Benjamin Bally  and  Zohreh Davoudi  for useful discussions on opensource collaborations. This work was supported in part by the  US Department of Energy  under contracts DE-SC0015393 (H. W. G. ),  DE-SC0017887  (H. H. ), and  DE-SC0018083  (NUCLEI SciDAC-4 Collaboration, H. H. ), by the  Deutsche Forschungsgemeinschaft (DFG, German Research Foundation ) -Projektnummer 279384907 -SFB (M.
H. , A. T. ), and by the  BMBF  Contract No. 05P18RDFN1  (M. H. , A. T. ). Acknowledgements: We thank  R. J. Furnstahl ,  A. J. Garcia ,  P. Giuliani ,  A. E. Lovell ,  J. A. Melendez ,  F. M. Nunes , and  M. Quinonez  for sharing their invaluable insights with us. We are also grateful to the organizers of the (virtual)  INT program  " Nuclear Forces for Precision Nuclear Physics " ( INT-21-1b ) for creating a stimulating environment to discuss eigenvector continuation and variational principles. This material is based upon work supported by the  U. S. Department of Energy, Office of Science, Office of Nuclear Physics , under the  FRIB Theory Alliance award   DE-SC0013617. Xilin Zhang  was also supported by the  National Science Foundation  under Grant No. PHY-1913069  and by the  NUCLEI SciDAC Collaboration under Department of Energy MSU  subcontract  RC107839-OSU.
Acknowledgements: This work was supported in part by  BMBF  (Grant No. 05P18PCFP1 ), by  DFG  and  NSFC  through funds provided to the  Sino-German CRC 110  "Symmetries and the  Emergence of Structure in QCD" (NSFC  Grant No. 12070131001 , Project-ID  196253076 -TRR 110 ), by  Collaborative Research Center  "The  Low-Energy Frontier of the Standard Model " (DFG, Project No. 204404729 -SFB 1044 ), by the  Cluster of Excellence "Precision Physics, Fundamental Interactions, and Structure of Matter" (PRISMA +  ,  EXC 2118/1 ) within the  German Excellence Strategy  (Project  ID   39083149 ), by the  Georgian Shota Rustaveli National Science Foundation  (Grant No. FR17-354 ). Acknowledgements: It is a pleasure to thank  Zohreh Davoudi ,  Andreas Ekström ,  Jason Holt  and  Ingo Tews  for making this wonderful INT program possible.
S. Department of Energy  grant No. DE-FG02-00ER41132. This material is based upon work supported by the  U. S. Department of Energy, Office of Science, Office of Nuclear Physics , under Award Numbers  DE-SC0019647  (TRR and MRS) and  DE-FG02-05ER41368  (RPS). Acknowledgements: We are grateful to the former and current members of the  NPLQCD Collaboration , especially  Martin Savage , for many insightful discussions and valuable collaborations around the topics discussed in this piece. ZD acknowledges support from the  Alfred P. Sloan fellowship, Maryland Center for Fundamental Physics at the University of Maryland, College Park , and the  U. S. Department of Energy's (DOE's) Office of Science Early Career Award   DE-SC0020271. WD and PES are supported in part by the  U. S. DOE's Office of Science, Office of Nuclear Physics  under grant Contract  DE-SC0011090.
S. Department of Energy, Office of Science, Office of Nuclear Physics, InQubator for Quantum Simulation (IQuS)  through the  Quantum Horizons: QIS Research and Innovation for Nuclear Science, under Award Number DOE (NP)  Award  DE-SC0020970. AP acknowledges financial support from the  State Agency for Research of the Spanish Ministry of Science and Innovation through the "Unit of Excellence María de Maeztu   2020-2023 " award to the  Institute of Cosmos Sciences  ( CEX2019-000918-M ), the  European FEDER  funds under the contract  PID2020-118758GB-I00 , and from the  EU   STRONG-2020  project under the program  H2020-INFRAIA-2018-1 , grant agreement No. 824093. This piece has been authored by  Fermi Research Alliance, LLC  under Contract No. DE-AC02-07CH11359  with the  U. S. Department of Energy, Office of Science, Office of High Energy Physics.
Acknowledgements JRG acknowledges support from the  Simons Foundation  through the  Simons Bridge for Postdoctoral Fellowships scheme. ADH is supported by the  U. S. Department of Energy, Office of Science, Office of Nuclear Physics  through the Contract No. DE-SC0012704  and within the framework of  Scientific Discovery through Advance Computing (SciDAC)  award "Computing the Properties of Matter with Leadership Computing Resources. "RAB is supported in part by  U. S. Department of Energy  Contract No. DE-AC05-06OR23177 , under which  Jefferson Science Associates, LLC , manages and operates  Jefferson Lab , and is partly supported by the  U. S. Department of Energy  Contract No. DE-SC0019229. ANN is supported by the  U. S. National Science Foundation CAREER  Award  PHY-2047185. The work of AWL is supported in part by  U.
Beyond EBs, it is also possible to determine the masses of stars belonging to visual multiple-systems, where individual components are spatially resolved, which allows retrieval of their projected orbits, provided radial velocities are available too. So far, very few of such systems include solar-like pulsators  (Marcadon et al. 2018; Metcalfe et al. 2020). The drawback of such systems is that the orbits are long and getting accurate orbital parameters can take decades and rely on heterogeneous datasets. Finally, hierarchical triple systems are promising types of benchmarks; they are composed of a close binary with a relatively distant companion (e. g. ,  Tokovinin 1997; Ford et al. 2000; Borkovits et al. 2003). Depending on their orbital configurations, the presence of eclipses and significant eclipse timing variations (ETVs), it can be possible to determine the masses of their components  (Derekas et al.
The Kepler light curve We worked with the Kepler public light curves that are available on the Mikulski Archive for Space Telescopes (MAST) 1. Two types of time series are available: the Simple Aperture Photometry (SAP) and the Pre-search Data Conditioning Simple Aperture Photometry (PDC-SAP) light curves. The latter consists of time series that were corrected for discontinuities, systematic errors and excess flux due to aperture crowding  (Twicken et al. 2010). They do not meet our requirements for monitoring possible rotational modulation or eclipse depth, which are often altered during the process (e. g. ,  García et al. 2014; Gaulme et al. 2014). We thus made use of the SAP data to preserve any possible long-term signal. This choice entails our own detrending and stitching operation on the light curves while ensuring that the rotational modulation is preserved after each interruption of the time series.
Such a choice actually also helps the deconvolution of the RG spectrum because the large number of absorption lines in RG spectra tends to increase the noise in the BF profiles when the original spectra do not have an excellent S/N, which is our case. We computed the BF by making use of the wavelength range 4500 and 5800 Å. Our final RV data were obtained after correcting the BF profiles from the barycentric corrections, which account for the rotation and revolution of the Earth with respect to the target. We computed the barycentric corrections with the PyAstronomy 2 routine helcorr, which is based on the  Piskunov & Valenti (2002)  algorithm. All the radial velocities we produced in this work are compiled in Table  A. 1 and displayed in Fig. 2  together with the series of BF profiles. For illustration purposes we overplot data points with a fit performed with a simple Keplerian orbit.
This allows us to estimate the standard deviation of the measurements to be about 0. 70 km s -1. We note that employing a Keplerian orbit is a very simplistic approach as KIC 7955301 is a triple system. In Sect. 5 we show that the argument of periastron of the outer orbit changed by about 20 • during the four years of Kepler observations, meaning that a simple Keplerian orbit is not sufficient to accurately model the RG orbit. 2 https://github. com/sczesla/PyAstronomy.
Stellar atmospheric parameters For the analysis of the disentangled spectra of all three components of the KIC 7955301 system, we employed the Grid Search in Stellar Parameters 3  (gssp Tkachenko 2015) software package, specifically its gssp_single module. It is a grid searchbased spectrum analysis algorithm that (on the fly) generates synthetic spectra in an arbitrary wavelength range based on a pre-computed grid of model atmospheres, and performs a comparison between the observed spectrum and each synthetic spectrum from the grid in the χ 2 statistical framework. The reported 1-σ uncertainties are computed from the χ 2 -statistics and taking into account possible correlations between the free parameters. The gssp algorithm allows for the simultaneous optimization of the effective temperature, surface gravity, micro-and macroturbulent velocities, projected rotational velocity, and metallicity of the star.
Detailed analytical investigations of third-body perturbed ETVs  (Borkovits et al. 2011 (Borkovits et al. , 2016) )  have shown that such curves tightly constrain almost all of the orbital elements of both the inner and outer orbits, together with the mutual inclination of the two orbital planes. Their amplitude is related to the outer mass ratio as A dyn ∝ 1 1 + q out. (11) Finally, the variation of the eclipse depth and duration of the inner eclipsing binary offer a very precise determination of the varying inclination of both the inner orbit of the eclipsing pair and the outer orbit. The combined photodynamical analysis was carried out with the software package Lightcurvefactory (see, e. g. Borkovits et al. 2019, and further references therein). This code contains a built-in numerical integrator to calculate the three-body perturbed coordinates and velocities of the three bodies, a multiband light curve, ETV and RV curve emulators, and an MCMCbased parameter search routine for the inverse problem.
Regarding other smaller effects that are mainly light-curve related, we used a logarithmic limb-darkening law. The corresponding parameters were calculated internally at each trial step with the use of the publicly available passband-dependent tables of the Phoebe software (Prša & Zwitter 2005) 5. For the well detached nature of both the inner and the outer binaries and, therefore, for the practically spherical shape of the stars, the gravity darkening coefficients have no detectable effect on the light curve solution. Therefore, we did not consider the results of the recent, more sophisticated study of  Claret & Bloemen (2011) , but simply adopted the fixed value of g = 0. 32, which is based on the seminal model of  Lucy (1967). Finally, we neglected both the reradiation/illumination and the Doppler-boosting effects  (Loeb & Gaudi 2003; van Kerkwijk et al.
To supplement these seismic constraints, we used the spectroscopic constraints from scenario C ([M/H] and T eff ). These were used to compute log-likelihood functions as χ 2 = χ 2 spec + χ 2 + χ 2 ∆Π 1 / f, ( 12 ) where f is initially set to 1 when performing the optimization. Optimization was performed using the differential-evolution algorithm as implemented in the yabox package  (Mier 2017) , using the initial mass M, initial helium and metal mass fractions Y i and Z i , and the mixing-length efficiency parameter α MLT as the independent variables for this optimization. After the optimization was complete, f is set to the minimum value of χ 2 seis along the optimization trajectory, in order to ensure that the reported results are not entirely dominated by the seismic quantities, which are significantly more precisely constrained than the spectroscopic ones.
Overall system model based on classical parameters We have compared the classical parameters of the three components of the system with the isochrones and tracks from the YaPSI database (Spada et al. 2017); the results are summarized in Figure  13. In the two panels on the left of the Figure, the measured masses and radii are compared with several isochrones of appropriate metallicity, generated by interpolation from the YaPSI database. The best fit is obtained for an age of 4. 5 ± 0. 2 Gyr for the primary component (top left panel); the components of the inner binary are marginally compatible with this isochrone (bottom left). In the right panel of Figure  13 , we show the bestfitting isochrone, together with evolutionary tracks constructed with the same code and input physics used for the YaPSI models (see Spada et al.
Model based on isochrones and SED We carried out a second spectro-photodynamical study with the software package Lightcurvefactory that includes the lightcurve, ETVs and RVs, as earlier, but also the stellar energy distribution (SED), a stellar evolution code (PARSEC, Bressan et al. 2012), and the Gaia-based accurate trigonometric distance. The cumulative SED, which consists of pass-band magnitudes, drives the temperature of sources, or at least of the dominant one. That way, effective temperatures together with stellar masses and radii determine the locations of the stars on co-eval PARSEC evolutionary tracks. Besides the lightcurve, RVs, and ETVs, the publicly available multipassband magnitudes (see Table  1 ) were simultaneously fitted against the theoretical passband magnitudes interpolated from theoretical PARSEC isochrone tables.
(2021). However, we keep in mind that Gaia EDR3 data are not corrected for binarity and, might suffer from systematic errors for such a triple system. About the dynamical evolution of the system, the small outer-to-inner period ratio P 2 /P 1 ≈ 13. 8 puts the system among the category of compact hierarchical triple systems. That being said, the small mutual inclination of i m = 6 •. 2 ± 0 •. 3 and almost circular inner orbit (e 1 = 0. 0276 ± 0. 0001), the orbital config-uration of the system is stable in dynamical timescale. Consequently, the dynamical evolution of the system will be driven by the stellar evolution of the evolved RG component. Therefore, here we restrict our discussion for some short term effects, and their observational consequences. In Fig. 14  we plot the variations of the observable arguments of periastrons (ω 1,2 ) and inclinations (i 1,2 ) of the inner and outer orbits during the present century.