dataesr/scientific-paragraphs-categorization huggingface dataset:
Parameter Constraints for WWI Parameters WWI-A WWI-B WWI-C WWI-D WWI ∆ DOF = 4 ∆ DOF = 4 ∆ DOF = 4 ∆ DOF = 4 ∆ DOF = 2 Ω b h 2 2. In table  1 , we list the constraints for CORE in the WWI case. We stress again that within the WWI potential, A, B, C, D represent the best fits that we obtained using Planck 2015 data in  [9]. Since our objective is to predict at which significance level CORE data can constrain these favored models, should they be the real underlying model of the Universe, we have used the local best fits to the Planck TTTEEE + lowTEB + BKP datasets †. For the WWI potential it generates one single class of features with only two parameters, this class improves the fit to both Planck temperature and polarization data compared to power law PPS. In the different rows of the table 1 we provide the background and inflationary parameter constraints, the columns represent the cases where WWI-A, B, C, D and WWI best fits are used as fiducial cosmologies for our simulations.
We stress that different features provide different best fits to the Planck 2015 and therefore in the CORE simulated data have different fiducial values for the cosmological parameters. The results show that while with Planck data all the different background parameter best fits fall within the uncertainties of the power law constraints, making it impossible to distinguish one from the other, with CORE it is possible not only to constrain some of the parameters which characterize the features but also distinguish among the different cosmological parameters associated with different features themselves increasing the possibility to distinguish among the possible models. For example, for baryon and CDM densities, the posterior peaks for WWI-A and C are quite off with respect to the power law.
z re denotes the redshift where the free electron fraction from hydrogen is 0. 5. Defining the reionization history in this way, CAMB does a search in the z re and find the redshift of reionization for a given optical depth τ which is one of the baseline parameter in the Markov-Chain Monte Carlo analysis code COSMOMC  [52, 53]. In order to allow for more freedom in the reionization history, and be compatible with current observations, we use a model characterized by one additional parameter (hereafter addressed as Poly-Reion) defined as: x e (z) = (1 + F He )f (z), (4. 2) where f (z) is a polynomial. f (z) is a Piecewise Cubic Hermite Interpolating Polynomial (PCHIP). The polynomial is determined by the electron fraction at four redshifts (the nodes in the polynomial): z = 0, 5. 5, 7 and z xe=0.
Constraints on Reionization history As already been mentioned, the Tanh-Reion is not nested within the more general Poly-Reion. However, since we aim to propose Poly-Reion as an alternative model for reionization history, we will present and discuss the results of the constraints on cosmological parameters using the two models. The best fit -2 ln L obtained from Powell's BOBYQA method ¶ for Planck TTTEEE + lowTEB + lensing when Tanh-Reion is used is 12947. 2. For Poly-Reion we find -2 ln L max = 12944. 6. Hence we find roughly an improvement of 2. 6, with an extra parameter, compared to the Tanh reionization histories. In table 2 we provide the bounds on the cosmological parameters when Poly-Reion is used for the reionization history for both Planck real data and CORE forecasts. Instead of presenting the results for z xe=0 we prefer to use the duration of reionization ∆ Reion z which is defined as the difference between the redshift when the reionization is 10% complete and the redshift when it is 99% complete.
Conclusions In this paper, we address three important aspects of cosmological parameter estimation with next generation space based CMB surveys, namely, features in the primordial power spectra, non-instantaneous reionization histories and the possible degeneracies between these two aspects. For the first part, to avoid the use of different models of features, we use the more general Wiggly Whipped Inflation that provides different feature models within the same framework. WWI includes inflationary phase transitions with discontinuities in potential or in its derivative. In our earlier analysis  [9] , we had demonstrated that using only one potential with 2-4 extra parameters, we can generate multitudes of inflationary features that are discussed in literature using different potentials. The advantage of using WWI is that with the same potential or same framework we can locate the existence of features that are supported by the data in one step.
In this paper we addressed the possibility that future space CMB observations will detect features in the inflaton potential if they represent the true model of the Early Universe. We take CORE as an example for a future CMB space satellite concept and we tested WWI framework against simulated data for temperature, polarization and lensing potential. The results show that broadly we have a moderate significance to features in the inflaton potential leading to features in the primordial power spectrum that are localized to certain cosmological scales. While for WWI-A and WWI-B, we find 2 -3σ significance of rejection of featureless PPS, wiggles in WWI-C and WWI show just 3σ C. L. WWI-D on the other hand has highest probability of detection where the amplitude of wiggles reject zero amplitude at much more than 3σ.
Since WWI-D has oscillations continuing to small scales, CORE is expected to capture its fine oscillations at high significance with better small scale measurements. In all the cases we find < 2σ significance for the suppression at large scale primordial power since cosmic variance is expected to limit our ability to detect such large scale signals. However, we must mention that, here we are only considering the local best fits to the Planck 2015 data obtained in the WWI framework. It is entirely possible that even within this framework there are wide features with higher amplitude that are still allowed by the Planck data and which would be probed at higher significance with CORE. Our analysis does not rule out such possibilities. We have observed a consistent reduction of the capability of future CMB polarization data to probe features at large scales with respect to previous literature, as also noticed in  [60].
This is a more economic extension of the instantaneous reionization history than the PCA  [32]  approach which might be useful given the decrement in the value of the optical depth with Planck  [2, 58]. Assuming completion of hydrogen reionization by z < 5. 5, in agreement with current astrophysical observations, and a monotonic decrease of the electron fraction, we confront this model against Planck 2015 data with one extra parameter compared to the Tanh-Reion case. Although Poly-Reion does not encompass the Tanh-Reion for all optical depth values, we find marginal improvement in fit compared to the standard case. In this parametrization we could constrain the duration of reionization (redshifts between 10% to 99% reionization) within 1 to 15 redshifts with Planck data at 2σ C. L. CORE spectra is expected to improve the constrain three times compared to Planck data.
Acknowledgments The authors would like to acknowledge the use of APC cluster (https://www. apc. univ-paris7. fr/FACeWiki/pmwiki. php?n=Apc-cluster. Apc-cluster). DKH and  GFS acknowledge Laboratoire APC-PCCP, Université Paris Diderot and Sorbonne Paris Cité (DXCACHEXGS)  and also the financial support of the  UnivEarthS Labex program at Sorbonne Paris Cité  ( ANR-10-LABX-0023  and  ANR-11-IDEX-0005-02 ). DP, MB and FF acknowledge financial support by  ASI  Grant  2016-24-H. 0and  partial financial support by the  ASI/INAF Agreement I/072/09/0  for the  Planck LFI Activity of Phase E2. MB acknowledge the support from the  South African SKA Project. AS would like to acknowledge the support of the  National Research Foundation of Korea  ( NRF-2016R1C1B2016478 ). AAS was partially supported by the grant  RFBR 17-02-01008  and by the  Russian Government Program of Competitive Growth  of  Kazan Federal University.
Observational data The g magnitude of Pisces II 10694 is 19. 9. This very faint star was observed in service mode with Kueyen (ESO-VLT, UT2) and the high-efficiency spectrograph X-Shooter  (D´Odorico et al. 2006; Vernet et al. 2011). The observations were performed in staring mode with 1x1 binning and the integral field unit  (Guinouard et al. 2006). The stellar light is divided in three arms by X-Shooter; we analysed here only the UVB spectra (from 400 to 560 nm with a resolving power R = 7900) and the visual (VIS) spectra (from 560 to 1000 nm with R = 12600). The signal-to-noise ratio (S/N) of the infrared spectrum (λ > 1000 nm) is too low to allow the analysis. The spectra were reduced using the same procedure as in  Caffau et al. (2013). The total exposure time was 11 hours divided in thirteen 3000 s spectra.
Acknowledgements. This work has made use of data from the  European Space Agency (ESA) mission Gaia  (https://www. cosmos. esa. int/gaia),processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www. cosmos. esa. int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the  Gaia Multilateral Agreement. Stefania Salvadori  is supported by the  Italian Ministry of Education, University, and Research (MIUR)  through a  Rita Levi Montalcini Fellowship.
Following  Berner et al. [2013]  we agree that "stochasticity must be incorporated at a very basic level within the design of physical process parameterizations and improvements to the dynamical core. " The purpose of this paper is to offer new approaches at this basic level. However, it is beyond the scope of the present paper to analyse the large dataset of drifter trajectories that has inspired our investigation. The work is in progress to fully analyse the drifter dataset and will be discussed elsewhere. Here we will discuss both 2D and 3D stochastic fluid dynamics models. How to do it? How does one use stochasticity to improve the physical and mathematical basis for designing statistical model uncertainty schemes? Recently, this question was answered by using Hamilton's principle to derive a new class of mathematical models of stochastic transport in fluid dynamics  Holm [2015].
The associated Lie algebra action of divergence free vector fields u ∈ g is given by the Lie derivative as q ∈ V → £ u q := d dε ε=0 g * ε q ∈ V, where g ε is the flow of u. We fix a space V * of tensor fields in nondegenerate duality with V relative to the L 2 pairing p, q V = D p(x), q(x) d n x. Remark 2. 1 (Determining the correlation eigenvectors ξ i (x)). How may the eigenvectors ξ i (x) be found in practice? One approach for determining them would be based on running an ensemble of computer simulations of the flow started with observed initial velocity data measured in the NOAA data base at each grid point X on a computational mesh erected in the flow domain. This computational mesh would be significantly coarser that the resolution of the data. An ensemble of these computer runs would produce a distribution of simulated end points X r = U r dt on the coarse mesh, where r labels the ensemble member.
Acknowledgements. We are very grateful to  C. J. Cotter ,  D. Crisan ,  E. Mémin ,  S. Olhede ,  W. Pan ,  V. Resseguier ,  I. Shevshenko , and  A. Sykulski  for valuable discussions and presentations during the course of this work. During this work, FGB was partially supported by the  ANR  project  GEOMFLUID   14-CE23-0002-01  and DDH was partially supported by the  European Research Council  Advanced Grant  267382 FCCA  and  EPSRC Standard Grant   EP/N023781/1.
The reference phase (which randomly changes when both f 1 and f 2 are varied in measurements) was found using similar processing of the low-noise signal provided by mixer M2 and digitized by the second channel of the ADC. Excitation of the modes resulted in a change of the ladder impedance  [22] ; this change was registered as a shift of the resonance of the readout resonator probed at f 1. The low-energy modes were measured as a function of the flux in the ladder's unit cells within the frequency range of our microwave setup 0. 5 -20GHz. the time-domain experiments, we have observed Rabi oscillations for a "qubit" formed by the ladder and a shunting capacitance C K. The ladder modes were excited by a short (∼ 0. 02 -10µs) MW pulse at the second-tone frequency f S and the population of the excited level was recorded at the end of each pulse; the data were averaged over many repetitive measurements.
Density-dependent atom losses are an important limiting factor in BEC spin squeezing  [3, 32]. While the background-limited lifetime of state |1 is much longer than the oscillation period, state |2 has additional loss channels which reduce its lifetime. To measure the relevant loss parameters, we prepare a BEC in |1 , |2 or an equal superposition of both states, and measure the remaining populations in the interrogation trap after different trapping times. The results are displayed on Fig. 3  (points). An exponential fit to the |1 data yields a 5 s background-limited lifetime. The other curves in Fig. 3 (a) are not fits but predictions without adjustable parameters as described in the caption. They reproduce the data well, as does the simulation using coupled GPEs (Fig. 3(b) ). In our experiments, number densities in the |2 state range from 1 × 10 12 to 8 × 10 12 cm -3 , corresponding to two-body loss limited lifetimes ranging from 12 s to as short as 1.
Acknowledgments We thank  Markus Oberthaler ,  Philipp Treutlein  and  Christian Gross  for inspiring discussions. This work was supported by the  Délégation Générale de l'Armement (DGA)  through the  ANR ASTRID program  (contract no. ANR-14-ASTR-0010 , project "eeTACC"), the  European Research Council (ERC) , ( GA 671133, Advance Grant "EQUEMI "), and the  Institut Francilien pour la Recherche sur les Atomes Froids (IFRAF). nonlinearity is large and the squeezing generation is fast with respect to the losses, so that the squeezing factor gets very small which makes a good test for the projected Wigner method. As shown in Fig. B1, we find a good agreement between the two methods.
This work is structured as follows: in Section 2 we briefly describe the SHARDS survey and the Rainbow Cosmological Surveys Database and explain the process used to carry out our candidates selection, as well as to eliminate interlopers; in Section 3 we calculate several physical parameters; in Section 4 we present the relevant results and compare them with previous studies; finally, in Section 5 we summarize the main conclusions. In what follows all calculations were made adopting a Λ-dominated flat universe with H 0 = 68 km s -1 Mpc -1 , Ω M = 0. 3 and Ω Λ = 0. 7  (Planck Collaboration et al. 2016). All magnitudes are expressed in the AB system and all physical distances refer to comoving distances.
The SHARDS survey and the Rainbow Cosmological Surveys Database SHARDS is an ESO/GTC deep optical spectro-photometric survey of the GOODS-N field acquired with 200 hours of observing time with the OSIRIS instrument on the 10. 4 m Gran Telescopio Canarias (GTC). The surveyed area is ∼ 130 arcmin 2 , split into two pointings. This survey provides very deep photometry (m 26. 5 -27. 0 AB mag, at the 3σ level) in 25 medium-band filters, from 500 nm to 941 nm. The first 22 filters have ∼ 17 nm FWHM, while the last three have a FWHM of 35, 25 and 33 nm, respectively. The main purpose of SHARDS was to provide SEDs with good enough spectral resolution to study red and passive galaxies up to redshift z ∼ 2. Nonetheless, they can be used to detect line emitting sources that otherwise would not be detected using broader filters  (Cava et al.
2004) , Subaru/MOIRCS  (Kajisawa et al. 2011) , CFHT /WIRCam  (Lin et al. 2012) , Spitzer /IRAC  (Fazio et al. 2004; Pérez-González et al. 2005 , 2008; Ashby et al. 2015)  and GALEX  (Bianchi et al. 2014)  as compiled in the Rainbow Cosmological Surveys Database 1   (Barro et al. 2011 (Barro et al. ,b, 2018, in prep. ), in prep. ). We have therefore added valuable data in wavelengths beyond the SHARDS range. This is important to ensure that our candidates do not present significant emission bluewards of the Lyman break, and in general to discard interlopers.
Data processing We start by limiting our search field to the common area of all the SHARDS images, for each pointing, as each SHARDS image samples a slightly displaced area. Thus the detection code only takes into account sources that are inside a resulting effective area of 128. 4 arcmin 2 (otherwise we get many spurious detections near the borders of the frames). We also need to take into consideration the effective central wavelength (CWL) within each filter, which depends on the particular position of each source in the field of view. This is a pure geometrical effect, as a result of the angle of incidence of the GTC/OSIRIS light beam on the filter. Objects in the same SHARDS image are detected with similar effective wavelengths but not exactly the same, depending on their precise position in the image.
Sample selection Here we explain in detail the process used to search for the candidate sources in the SHARDS catalogue. SHARDS contains 44,752 sources in the GOODS-N field, and for each object there is information on its flux in the SHARDS filters, plus the ancillary data available in Rainbow (see Section 2. 1). A first selection was made taking advantage of the photometric redshifts available in the Rainbow Database for 35,445 of the SHARDS objects in the CANDELS/GOODS-N field. These redshifts were obtained by  Barro et al. (2018, in prep. ) , hereinafter Ba18, through SED fitting with EAZY  (Brammer et al. 2008) , using SHARDS combined with the WFC3 102 and 141 grisms and additional data from HST, Subaru, Spitzer and others. This results in a very well detailed SED characterization and redshift calculation, reaching an accuracy better than ∆z ∼ 0.
In this process we used images mainly from GTC /SHARDS, HST /ACS, and HST /WFC3, though we also used other images available in the Rainbow Database from Subaru/Suprime-Cam and Spitzer /IRAC. The SEDs were further completed with useful data at other wavelengths available in Rainbow (see Section 2. 1). Finally, we visually discarded those objects which were deemed either spurious or presented strong emission blueward of their supposed Lyman break wavelength. This check is necessary since lower z objects with a high slope SED could match our SHARDS preselection criteria when their emission in one of the redder filters is substantially higher than the average emission in the filters blueward of that one. The whole process was iterated many times, identifying the wavelength where the Lyman break appears for each object, paying special attention to galaxies with photometric redshift estimations from previous authors, making sure we did not skip possible candidates while not including unwanted objects.
Interloper rejection Once the selection was finished, we carried out some additional theoretical models fits to our SEDs to make a further test on those objects that had met our selection criteria but could still be lower z interlopers. In the search for high-z LBGs the main interlopers are lower z galaxies where the D4000 break is wrongly identified as the Lyman break. Additionally, M, L, and T dwarf stars with a very steep slope can be mistakenly taken as drop outs. In these, it is possible to measure an abrupt flux change, specially with broad band filters. However, these last cases are in general easily recognizable when using many filters. So we did not expect an important number of them among our interlopers. The fitting process was made with the code Le Phare To make this SED we made use of all the data available in the Rainbow Database with reliable information on this galaxy.
7 Å at high redshifts  (Rauch 1998; Fan et al. 2006b ). To prove the goodness of our photometric redshifts we check every case where a spectroscopic redshift was available either in the Rainbow Database or in the NASA/IPAC Extragalactic Database (NED) 2  (from  Steidel et al. 2003; Kakazu et al. 2007; Barger et al. 2008; Kajino et al. 2009; Adams et al. 2011; Conselice et al. 2011; Shim et al. 2011; Stark et al. 2011 Stark et al. , 2013;; Schenker et al. 2013, among others)  and compare them with our photometric redshifts (see Fig. 5 ). The excellent correlation obtained indicates that we can trust the calculated redshifts for our candidates with an average error of around ∆z = 0. 07 (0. 14 for objects above z ∼ 6. 2, where the filters measuring the Lyman break are wider). The redshift distribution of our LAE and LBG candidates is shown in Fig.
DISCUSSION We have selected a high-z star forming galaxy sample using the SHARDS survey as described in Section 2. As shown before, our sample consists of 1434 LBGs and 124 pure LAEs, 202 of them forming pairs or close groups. Using the SHARDS data and all the extra information available in the Rainbow Database we have calculated redshifts, SFRs, comoving distances, Lyα EWs and X Lyα (Section 3). In this section we discuss the main results of our study.
Redshift distribution of the objects in the B15 sample that appear as interlopers according to both our selection criteria and the photometric fits with SHARDS data from Ba18. On the left, different colours correspond to different m 1500 limits with a fixed isolating distance (0. 9 arcsec). On the right, different isolating distances with a fixed m 1500 limit of 25. 87 AB mag, corresponding to our 90% completeness. The shape of the distribution is practically the same in all cases. The peak around z ∼ 0. 5 suggests a wrong identification of the Balmer break as the Lyman break. F ν (AB mag) Figure  14. SED of the object SHARDS J123659. 36+621518. 7, wrongly selected as a z ∼ 4. 54 LBG using broad band criteria. The information as given by the green triangles (ACS and WFC3 data) can lead to an incorrect Lyman break detection.
Luminosity Functions We proceed now to build the LBGs LFs, which are shown in Fig. 18. Our 90% completeness absolute magnitude limit for each redshift is marked with a dashed vertical line. A correction for those objects that we miss, either because of non-detection in the SHARDS images or because of neighbouring light contamination of their SEDs, is considered for each z range, based on their m 1500 distribution (see Fig. 12 ). The magnitude values are measured using HST photometry. To correct our data in the faint region of the LF, we use the V/V max correction to adequately consider the effective volume sampled by each detected source. We divide our sample in three main redshift bins to facilitate comparing with the literature, namely z ∼ 4 (3. 5 ≤ z < 4. 5), z ∼ 5 (4. 5 ≤ z < 5. 5) and z ∼ 6 (5.
We find similar tail-like morphologies in most of our groups (e. g. , the westernmost object of G6 shown in Fig. 11 ). These structures support the hypothesis that our groups are gravitationally bounded systems. In addition to the tidal tails we also notice some other little spots near the trios and one more near G6 in the HST /ACS images that could be additional members of their respective groups. However, these extra objects do not appear either in the SHARDS or the ACS catalogues nor in the Rainbow database, and they cannot be resolved in the GTC images, so we do not have conclusive photometric information for them. In fact, some of the objects forming these groups seem to be more than one unresolved source. Note that the number of groups found, though significant, is not large enough to warrant studies of their dependence on redshift.