dataesr/scientific-paragraphs-categorization huggingface dataset:
Account Political Orientation We consider the algorithmic amplification of friends'tweets as a function of the political leaning of their authors. The estimation of political orientations was conducted using the Politoscope database  15, 16  , which has collect all tweets containing French political keywords or authored by French political figures since 2016, gathering more than 700 million tweets. Shortly, the French political landscape is characterized by a multipolar structure, with the current French president occupying a centrist position, as displayed in the Supplementary Information. The opposition consists of a broad left coalition on one side and a far-right group on the other. Notably, anti-system activists play a role in bridging the divide between far-left and far-right militants, resulting in a circular political landscape  17.
For instance, an account with a far-left leaning may exhibit stronger affinities with far-right content rather than with centrist content, it is then crucial to consider this circularity when analyzing potential patterns of amplification. To determine the political leanings of Twitter accounts, we leveraged the retweet graph associated with political tweets published in 2022 (during which the French presidential and legislative elections occurred). The network of retweet is made of 1. 2 millions nodes, 26 millions edges, where two nodes are tied if one retweeted the other -in a political context-at least twice. The collection procedures for this dataset are detailed in Gaumont et al  16  , retweets were shown to be reliable indicators of ideological alignment. We employed the node2vec algorithm  11  to generate embeddings of the nodes, capturing the underlying structure of the retweet network.
A blank space means that the computation took more than 1000 seconds. We observe empirically that the degree in 𝑥 is 𝑑𝑟 (𝑟 + 1)(2𝑟 -1)/2 -𝑟 (𝑟 -1) while its degree in 𝑛 is (𝑟 -1)(𝑟 + 2)/2; this is expected asymptotically by  [2, Thm. 25]  and Lemma 3. 4, because deg 𝑦 𝑄 (𝑥, 𝑦) = 𝑟 and deg 𝑥 𝑄 (𝑥, 𝑦) = 𝑑𝑟. The tested implementations are • in Maple: redct  [4] ; HermiteTelescoping (HT)  [8] ; Zeilberger (ZB)  [1]  in DEtools; creative_telescoping (c_t)  [13] ; • in SageMath: creative telescoping (ct) from the ore_algebra package  [25] ; • In Mathematica: FindCreativeTelescoping (FCT), CreativeTelescoping (CT), and HermiteTelescoping (HCT), see  [28]. Table  2 : Timings in seconds, using the C++ library NTL  [33]  and PML  [24] , for computing the top-right entry of the 𝑁 th power of a randomly chosen matrix in F 𝑝 [𝑥] 𝑟 ×𝑟 of degree 𝑑, for a 50-bit prime 𝑝.
The authors thank  Bruno Salvy  for his remarks, and the anonymous referees for their reports. The authors are supported by the  French  project  De Rerum Natura  ( ANR-19-CE40-0018 ) and by the  joint French-Austrian  project  EAGLES  ( ANR-22-CE91-0007  &  FWF I6130-N ). The third author was supported by the  ÖAW DOC  fellowship  P-26101.
Finally, phases 10-12 (Early Neolithic, Recent Neolithic and Copper Age) could be related to the burial activities documented for these periods. These activities include the deposition of human skeletal remains, ceramics and/or personal ornaments  11, 46. In this paper, we provide new chronological data on these incursions, which run from the Early Neolithic to the Copper Age, as well as information on their topographical distribution, preferably linked to the Lower Galleries, although two specific explorations of the upper parts of the cave were also identified (samples 12, 19). In other words, the visits concerning Recent Prehistory are not restricted to burial activities in the Lower Galleries, but are also due to exploratory actions, not to mention the execution of cave art linked to these dates and present in one of the external rooms (specifically, the schematic anthropomorphs in the Torca room).
pinea-pinaster, Juniperus sp. )  12, 54  , but also that it is not exclusive to a specific Palaeolithic phase or cultural period, but is a multiphasic selection. Specifically, the choice of this woody resource for lighting was recorded in 8 of the 9 Palaeolithic occupation phases documented in this work, between phases 2-9 (Gravettian-Upper Magdalenian) inclusive. Likewise, the repeated use over time of Pinus sylvestris for lighting has been previously proposed for the Chauvet cave, and for two different periods of occupation referring to the Aurignacian and Gravettian  56, 57. The anthracological data from this study further reinforce this idea of a preferential and cross-cultural choice of Pinus tp. sylvestris-nigra for lighting activities inside caves during the Upper Palaeolithic.
Acknowledgements This work is part of  M. Medina 's postdoctoral research project funded by the  FYSSEN FOUNDATION  ( 2021FOUNDATION ( -2022 )). This research is also part of the " Proyecto General de Investigación aplicada a la conservación de Cueva de Nerja " authorised by the  Junta de Andalucía  and financed by the  Fundación de Servicios Cueva de Nerja. This paper is also part of the following projects: a) A- Light  project (PI M. Medina) ( 2022-2024 ), within the framework of  HORIZON-MSCA-2021-PF-01-01  (project number  101066376 ), funded by the  European Union. Views and opinions expressed are however those of the author(s) onlyand do not necessarily reflect those of the European Union or REA. Neither the  European Union  nor the granting authority can be held responsible for them.
This validation was performed against the corresponding N-body measurements, estimated from 50 simulations. We found the method to be valid up to k ∼ 0. 2h Mpc -1 for the power spectrum and down to r ∼ 20 Mpc h -1 for the correlation function. Then, we extended the method by proposing a new modelling of the peculiar velocity distribution, aimed at reproducing the redshift-space distortions both in the linear and mildly non-linear regimes. After validating this prescription, we finally compared and validated the resulting redshift-space two-point statistics covariance matrices in the same range of scales. We released the Python code associated with this method on a public repository, which allows for the production of tens of thousands of realisations in record time. In particular, COVMOS is intended for any study involving large-scale galaxy-survey science that requires a large number of mock realisations.
Theoretical pipeline in real space In this section, we recall the basics of the pipeline that enables the generation of a discrete set of objects defined by a given, arbitrary one-point PDF and density power spectrum. For a more detailed description of the method, we refer to  Baratta et al. (2020). In the first stage, we focus on the generation of the continuous density field. Then we discuss how to circumvent the limit of the method, that is, the production of negative, non-physical power spectra, when the target power spectrum is the non-linear 1 Publicly available in github. com/PhilippeBaratta/COVMOS one. Finally, we describe how to discretise the field into pointlike tracers.
They have been produced on various high-performance computing (HPC) machines provided by the super computing centre CINECA 7  , Italy, by exploiting the GADGET-3 code of  Springel (2005) , further developed by  Viel et al. (2010)  for the inclusion of massive neutrino particles. All the simulations of the DEMNUni have in common the following cosmological parameters: Ω k = 0, Ω m = 0. 32, Ω b = 0. 05, h = 0. 67, n s = 0. 96, A s = 2. 1265 × 10 -9. The initial conditions have been set at redshift z = 99 using the Zeldovich approximation  (Zeldovich 1970 ) and the public code described in  Zennaro et al. (2016 Zennaro et al. ( , 2018 Zennaro et al. ( , 2019)). The evolution of cosmic structures is simulated down to redshift z = 0, while outputting 63 particle snapshots with equally spaced logarithmic scale factor intervals.
In this way, they offer the possibility of estimating the covariance matrices to some extent. Each simulation consists of 1024 3 dark matter particles of mass m p 8 × 10 10 M h -1 , and 1024 3 massive neutrino particles (in the case of the massive neutrino cosmology) of a mass m ν p 1 × 10 9 M h -1 in a cubical volume of size L = 1000 Mpc h -1 with periodic boundary conditions. For each snapshot of each realisation, we estimated the PDF and the power spectrum of the matter field using a PCS MAS on a grid of sampling parameter N s = 1024. The power spectrum was estimated using the NBodyKit 9  (Hand et al. 2018 ) software, applying the interlacing method to reduce the aliasing  (Sefusatti et al. 2016). The averaged PDF and filtered power spectra (following the prescription in Eq. (  6 )) of the 50 simulations can then be directly used as targets for the Monte Carlo code.
4 GHz. We note that reducing the precision of the COVMOS grids to N s = 512, three days are necessary to simulate and estimate the power spectrum of 100 000 catalogues. In Figs. 6 and 7, we compare the power spectra of COVMOS to those estimated in the reference DEMNUni_cov, N-body simulations. An initial observation of Fig. 6  leads us to the very same conclusions as those drawn for its real-space equivalent Fig. 2. The ratios PCOVMOS (k)/ PDEMNUni (k) in both spaces do indeed seem similar. The maximal wave-mode at which the power spectra are reliably simulated are conserved. We can, however, note a gain in power of the redshift-space power spectrum at z = 0, with respect to its real-space equivalent. Such effects can be due to an overestimation of the β parameter in Eq. (  22 ), which, in our code implementation, is averaged over a tens of realisations before becoming constant for the whole set of simulations.
Conclusion and discussion Although it is apparently straightforward, the reliance on covariance matrices for two-point statistics estimators evaluated from mock catalogues generally leads to two main issues. The first is the sampling noise that propagates down to the parameter constraints and turns out to be difficult to correct without making any assumption on the posterior distribution of parameters  (Gouyou Beauchamps et al. in prep. , Dodelson & Schneider 2013; Percival et al. 2014; Taylor et al. 2013; Taylor & Joachimi 2014). The second (and less investigated) concern is the computational cost of evaluating a covariance matrix for various set of cosmological parameters in order to study potential biases due to the fiducial choice of the cosmology when analysing data. In this context, we propose a method implemented in the public code named COVMOS, allowing the fast production of a large number of catalogues.
25 h Mpc -1 (down to r = 10h -1 Mpc for the two-point correlation function). We extended the validation of the method to 4-point statistics in Fourier space. More precisely, we verified that the shell-averaged trispectrum, T , which enters the power spectrum covariance, is in good agreement with the one obtained from 50 N-body simulations. This results in an accurate reproduction of the power spectrum covariance matrices. Although it is slightly over-estimated in real space for k ∼ 0. 15 h Mpc -1 , it turns out that in the redshift space, we can reach k ∼ 0. 2 h Mpc -1 for the monopole power spectrum. Having validated the method against N-body simulation, a major advantage of the code is its numerical efficiency in terms of computational cost. As an example, for this work, we generated 5 × 5000 catalogues of 10 8 objects in 20 days on a HPC cluster 10  , using 940 processors of 2.
A scale limitation is therefore to be expected and would require further inspection to be carefully determined. However, the associated public code can already be useful for a broad variety of applications. Indeed, its ability to simulate a wide variety of cosmolog-ical models and to achieve almost no sampling noise in the produced covariance matrices makes this method particularly relevant for testing likelihood pipelines (see Gouyou Beauchamps A1, page 18 of 21 et al. in prep. , for a first application) aimed at constraining cosmological parameters. Finally, we recall that the COVMOS code is public 11 , fully written in Python, ready to be used and adapted to receive the needed inputs either from theory or simulations. This is a method specialised in producing two-point statistics and associated by-products (covariance matrices) that may produces unrealistic outputs when considering other statistics.
Acknowledgements. PB and SGB were supported by  CNES , focused on Euclid mission. The project leading to this publication has received funding from  Excellence Initiative of Aix-Marseille University  -A*MIDEX, a  French "Investissements d'Avenir" programme  ( AMX-19-IET-008 -IPhU ). The DEMNUni simulations were carried out in the framework of "The  Dark Energy and Massive-Neutrino Universe " project, using the Tier-0  IBM BG/Q Fermi machine and the Tier-0 Intel OmniPath Cluster Marconi-A1 of the Centro Interuniversitario del Nord-Est per il Calcolo Elettronico (CINECA ). We acknowledge a generous  CPU  and storage allocation by the  Italian Super-Computing Resource Allocation (ISCRA) as well as from the coordination of the "Accordo Quadro MoU per lo svolgimento di attività congiunta di ricerca Nuove frontiere in Astrofisica: HPC e Data Exploration di nuova generazione ", together with storage from.
Observations and data reduction AB Pic b has been the focus of many studies since its discovery by  Chauvin et al. (2005). A rich set of literature observations is available. Among them are (i) photometry points on the visible (0. 53-0. 92 µm) taken by the HST/WFC3  (Bonnefoy et al. 2014 ), (ii) medium-resolution SINFONI spectra (R λ = 1500-2000) in the J and H bands  (Bonnefoy et al. 2014), (iii)  an Lp band spectrum (R λ ∼ 300) from the Magellan-AO/CLIO2  (Stone et al. 2016) , and (iv) Spitzer IRAC photometry points at 3. 6, 4. 5, 5. 8, and 8 µm  (Martinez & Kraus 2022). Mining into unpublished archived datasets, we found medium-resolution SINFONI/VLT spectroscopic observations at K band from December 2013 (program 092. C -0809 (A); PI J. Patience), which complement the spectral information at J and H bands.
SPHERE observations and data processing AB Pic was observed during the SpHere INfrared survey for Exoplanets (SHINE, Guaranteed Time Observations;  Chauvin et al. 2017; Desidera et al. 2021; Langlois et al. 2021; Vigan et al. 2021)  on February 6, 2015, using the VLT/SPHERE high-contrast instrument  (Beuzit et al. 2019 ). The observations were obtained with the IRDIFS mode, which combines the IRDIS  (Dohlen et al. 2008 ) and IFS instruments  (Claudi et al. 2008)  simultaneously. IRDIFS combines IRDIS in dual band imaging (DBI,  Vigan et al. 2010 ) with H2H3 filters (λ H2 = 1. 593 ± 0. 055 µm, λ H3 = 1. 667 ± 0. 056 µm), and IFS in the YJ (0. 95-1. 35 µm) setting. All IRDIS and IFS datasets were reduced using the SPHERE Data Reduction and Handling (DRH) automated pipeline  (Pavlov et al. 2008 ) at the SPHERE Data Center (SPHERE-DC) to correct each datacube for bad pixels, dark current, flat field, and sky background.
After combining all datacubes with an adequate calculation of the parallactic angle for each frame of the deep coronagraphic sequence, all frames are shifted at the position of the stellar centroid calculated from the initial star center position. To calibrate the IRDIS and IFS datasets on sky, the astrometric field 47 Tuc was observed. The platescale and true north solution were extracted from the long-term analysis of the GTO astrometric calibration described by  Maire et al. (2021). The rotation correction considered to align the images to the detector vertical in pupil-tracking observations is -135. 99 ± 0. 11 deg. The anamorphism correction was obtained by stretching the image Y-direction by a factor of 1. 0060 ± 0. 0002 (inducing an error of 1. 1 mas at the separation of AB Pic b, 440 pixels).
SINFONI cube building and spectral extraction We initially reduced the data with the ESO SINFONI data handling pipeline v3. 0. 0 3 through the EsoReflex 4 environment. The 3 SINFONI Pipeline 4 EsoReflex Software pipeline uses calibration frames to perform basic adjustments to the raw science frames and correct them for distortion. The slitlet positions on the frames at each wavelength are identified before building a datacube for each exposure. Further corrections on top of the ESO reduction steps were performed based on the Toolkit for Exoplanet deTection and chaRacterization with IfS (TEx-TRIS;  Petrus et al. 2021; Bonnefoy et al. , in prep. ). A detailed description of these methods is given below. Wavelength calibration. As implemented by  Petrus et al. (2021) , this method identifies a constant wavelength shift with respect to the telluric absorption lines.
It is known to affect the K band data and we corrected it by fitting a one-dimensional polynomial from 2. 14 to 2. 15 µm. Next, we corrected the NIR hydrogen lines from the STD spectrum by fitting a Voigt profile. The function corrects for specific lines of the Paschen (Pa β ) and Brackett (Br 16 , Br 14 , Br 12 , Br 11 , Br 10 , and Br γ ) series that may be observable in the NIR. We inspected these corrections, and using the spectral type of the STD star, we computed its corresponding theoretical black-body curve. Each STD spectrum was divided by the computed black body to recover the atmospheric transmission of each night. Finally, each spectrum of AB Pic b was corrected by dividing the atmospheric transmission spectrum. Final spectrum. We mean-combined all observations, obtaining a final spectrum for AB Pic b with the corresponding errors, which were computed by mean-combining the errors of each spectrum and dividing this by the root of the number of datacubes considered.
Orbital properties The combination of NaCo observations from  March 2003 , March 2004 , and September 2004 (Chauvin et al. 2005)  with the SPHERE observation from February 2015 offers the time needed to partially resolve the orbital motion of AB Pic b. The motion is mainly resolved in separation (nothing significant is observed in position angle), which indicates a highly inclined orbit for the planet. We used the Orbits for the Impatient (OFTI) tool -a Bayesian rejection sampling method for quickly fitting the orbits of long-period exoplanets  (Blunt et al. 2017 ) -to explore the solutions. We adopted the default priors detailed in the 'orbitize!' Python package  (Blunt et al. 2020) , which is logarithmic for the semi-major axis and flat for the eccentricity. We set an upper bound of 1000 au for the semi-major axis because solutions greater than 1000 au have a probability that is 100 times lower than the most likely value.
The best orbital solution is observable in Fig. 3  and detailed in Table  2. We note that AB Pic b was directly detected by Gaia, but we decided to not use the Gaia eDR3 data point given the poor astrometric fitting solution due to the faintness of AB Pic b in the optical and its close separation. The corner plot of the orbital parameters is shown in Fig. A. 1. The solution confirms that the exoplanet AB Pic b is likely to be orbiting at a semi-major axis of a = 190 +200 -50 au on a highly inclined orbit (i = 90 ± 12 deg), with a potentially moderate to high-eccentricity, albeit poorly constrained. As expected by the north-south orientation of the orbit, the longitude of the ascending node (Ω) is close to ∼0 deg (±180 deg).
Atmospheric models BT-SETTL13. This model is part of a family of atmospheric models by  Allard et al. (2013)  that include 1D clouds where the abundance and size distribution of 55 types of grain are determined by comparing the timescale of condensation, coalescence, gravitational settling, and mixing of solids, with these latter assumed to be spherical. The details of each solid and chemical element are described in  Rajpurohit et al. (2018). The opacities are calculated for each line and the radiative transfer simulations are carried on by the PHOENIX code  (Hauschildt et al. 1997; Allard et al. 2001 ). The convection is handled following mixinglength theory and works at hydrostatic and chemical equilibrium. The model also accounts for non-equilibrium chemistry between CO, CH 4 , CO 2 , N 2 , and NH 3.
A possible second, inner planet To explore the possible presence of additional inner planets in the system, we explored the completeness of the new SPHERE highcontrast imaging observation using the MESS2 code  (Lannier et al. 2017) , an evolution of the Multi-purpose Exoplanet Simulation System (MESS), a Monte Carlo tool for the statistical analysis of direct imaging survey results  (Bonavita et al. 2012 ). MESS2 combines the information on the star with the instrument detection limits to estimate the probability of detection of a given synthetic planet population, ultimately generating detection probability maps. The code generates a grid of masses and physical separations of synthetic companions, and then estimates the probability of detection given the provided detection limits. By default, all the orbital parameters are uniformly distributed except for the eccentricity, which is generated using a Gaussian eccentricity distribution with µ = 0 and σ = 0.
3 (constraint: e ≥ 0), following the approach by  Hogg et al. (2010). This allows us to properly take into account the effects of projection when estimating the detection probability using the contrast limits. The result for the case without any prior regarding the system configuration is reported as blue probability areas labeled "DI" (direct imaging) in Fig. 11. To further explore the presence of additional planets in the system, we searched for the existence of a proper motion anomaly (PMa) based on the compilation of  Kervella et al. (2022). The long time baseline of 24. 75 yr between the HIP-PARCOS and Gaia Early Data Release 3 (eDR3) position measurements is exploited to pinpoint the presence of a secondary orbiting body in the system. For AB Pic, the tangential velocity anomaly is ∆v tan = 65.
Our results suggest that AB Pic b was potentially formed through gravitational instability or core accretion closer to the star before being scattered to a wide orbit by a planet-planet scattering dynamical interaction with the inner companion currently indicated by the HIPPARCOS-Gaia proper-motion anomaly of the stellar host. The confirmation of AB Pic c, along with access to broad wavelength coverage and high-resolution data for AB Pic b could position this system as an ideal benchmark for comparison when studying the formation and evolution histories of planetary systems.
Acknowledgements. To the memory of  Dr. France Allard  and her contributions to the domain of atmospheric physics of stars, brown dwarfs, and exoplanets. P. P. B. acknowledges support from the visiting program of the  CNRS French-Chilean Laboratory for Astrophysics  (FCLA,  IRL-3386 ), under contract number  14177/2021. PMR acknowledges support from the  ANID BASAL  project  ACE210002. I. S. and Y. Z. acknowledge funding from the  European Research Council (ERC)  under the European Union's  Horizon 2020 research and innovation programme  under grant agreement no. 694513. We acknowledge in France from the  French National Research Agency (ANR)  through project Grant  ANR-20-CE31-0012  and the  Programmes Nationaux de Planétologie et de Physique Stellaire  (PNP and PNPS). This project has received funding from the  European Research Council (ERC)  under the  European Union 's  Horizon 2020 research and innovation programme  ( COBREX ; Grant agreement  885 593 ).
This publication used the SIMBAD and VizieR databases operated at the  CDS, Strasbourg, France. This work is partly based on data products from the SPHERE GTO processed at the  SPHERE Data Centre  hosted at  OSUG/IPAG, Grenoble. SPHERE is an instrument designed and built by a consortium consisting of  IPAG (Grenoble, France) ,  MPIA (Heidelberg, Germany) ,  LAM (Marseille, France) ,  LESIA (Paris, France) ,  Laboratoire Lagrange (Nice, France) ,  INAF-Osservatorio di Padova (Italy) ,  Observatoire de Genève (Switzerland) ,  ETH Zurich (Switzerland) ,  NOVA (Netherlands) ,  ONERA (France)  and  ASTRON (Netherlands)  in collaboration with ESO. SPHERE was funded by  ESO , with additional contributions from  CNRS (France) ,  MPIA (Germany) ,  INAF (Italy) ,  FINES (Switzerland) , and  NOVA (Netherlands).