dataesr/scientific-paragraphs-categorization huggingface dataset:
6) as the solid black line, and the 68. 7% and 95% confidence intervals as shaded dark and light gray regions. The bottom panels show the residuals of the median model. ature of T eff = 2988 ± 67 K and a metallicity of [Fe/H] = -0. 262 ± 0. 104 dex. These errors were estimated by considering on the one hand the machine-learning model error (precision errors of 17 K and 0. 03 dex, respectively), and on the other hand the mean absolute errors of the machine-learning models for the training dataset (65 K and 0. 10 dex for a resolution of 115 000 for the dataset grid, Antoniadis-Karnavas et al. 2020). Article number, page iv of xxii The SPOC pipeline aperture is overplotted with shaded red squares, and the Gaia DR2 catalog is also overlaid with symbol sizes proportional to the magnitude contrast with the target, marked with a white cross.
Evidence for a planet with a period of ∼80 days As reported in  Ment et al. (2019)  and confirmed in the new ESPRESSO dataset (see Sect. 2. 2 and Sect. 3. 1), the periodogram of the joint dataset shows a power excess between the first and second harmonic of the rotational period of the star; this  is between 65 and 131 days. These several signals have a maximum peak at around 80 days. We here explore the evidence for this third signal by studying different scenarios (different number of planets, from one planet to three planets; and different orbital configurations, eccentric or circular) and comparing the models using Bayesian analysis to unveil the significance of this signal. We explored each dataset separately (i. e. , HARPS and ESPRESSO), together with a final full radial velocity dataset analysis (i.
Based on the observed radial velocities, we set the η 1 and η 1,FWHM parameters to a uniform distribution with a maximum amplitude of 100 m/s. The timescale hyperparameter η 2 was set to a broad range of values between one and five times the stellar rotation period. The instrument systemic velocities were set up with uniform priors between -13. 4 and -13. 0 km/s, and the radial velocity jitter for each instrument was allowed to have values up to 20 m/s (based on our first model attempts). In total, 15 models (including zero to three planets and all combinations of circular and eccentric orbits for each of them) were tested for each of the three datasets (HARPS, ESPRESSO, and HARPS+ESPRESSO), that is, 45 models were tested in total. In order to statistically compare the different models and datasets, we estimated the Bayesian evidence (Z) of each model by using the perrakis 6 implementation.
Based on this Bayesian evidence, we can estimate the Bayes factor (B) between two models as the ratio between the evidence of each pair of models as B = ln Z iln Z j. The model with the strongest evidence has the highest statistical relevance, with B > 6 considered as a strong evidence for one model against the other. The three panels in Fig. A. 1 display this Bayesian evidence for all 15 models considered in each dataset. We find that the two-planet model with both planets on circular orbits has the strongest evidence in all datasets. This means that the current data are unable to provide evidence for eccentric architectures of the two known planets. We can only place upper limits of e b < 0. 096 and e c < 0. 274 (at 95% confidence level) based on the noncircular models. The median and 68.
7% confidence interval of the parameters for this two-planet model are presented in Table. B. 2. Although the evidence in the full dataset is weaker, all threeplanet models in the combined HARPS+ESPRESSO dataset converged to a planet candidate with a period of about 80 days, corresponding to the peak in the 1-periodogram described in Sect. 3. 1 and already seen in the classical periodogram presented in Sect. 2. 2 and Fig. 1. The three-planet model with all planets on circular orbits (labeled 3p1c2c3c) has the second strongest evi-dence, even above the eccentric two-planet cases. The median and 68. 7% confidence interval of the parameters for this circular three-planet model are presented in the last column of Table. B. 2, and the phase-folded radial velocity curve of this third planet candidate is shown in Fig.
8. It is important to note that this strong evidence is mainly due to the addition of the exquisite ESPRESSO data, which itself show clear signs for this threeplanet model. We performed a cumulative Bayesian analysis of the dataset by obtaining the Bayes factor for the two most likely models with two and three planets (i. e. , the circular case for all planets, labeled 2p1c2c and 3p1c2c3c in Fig. A. 1). We obtained the logevidence using up to N i data points in steps of five data points and starting with the first 20 measurements. The results are presented in Fig. 9  and show that the log-evidence of the threeplanet model, although the evidence is weaker than for the twoplanet model, increases progressively when more data points are added. This is an indication that additional data might clearly confirm this signal.
The jumps in the Bayes factor correspond to the addition of new data from a different instrument, which correspondingly adds new parameters (and so complexity) to the model. The evolution of the Bayesian evidence shows that about 50 new ESPRESSO measurements would be needed to clearly confirm this candidate signal. According to our three-planet model in the combined dataset, the third planet would have a minimum mass of m d sin i d = 4. 8 +1. 3  -1. 2 M ⊕ and an orbital period of P d = 79. 22 +0. 55 -0. 58 days. This describes a world in the rocky-gaseous frontier beyond the habitable zone. We note here that the detection of its radial velocity signal is at the ∼ 3. 8σ level (2. 21 +0. 59 -0. 57 ). According to the ephemeris found in this radial velocity solution, the TESS observations would have missed the transit of this small planet (in case of a coplanar orbit with the other known planets in the system, the estimated impact parameter is 0.
2018 ) on the HARPS+ESPRESSO dataset. We considered up to three Keplerian signals in addition to a GP model for the correlated noise. Broad and equal priors were assigned to the three sets of orbital parameters (i. e. , we did not use information from the transits). For the orbital periods we used a log-uniform distribution between 1 and 100 days, for the semiamplitudes a uniform prior between 0 and 20 m/s, and for the eccentricities a Kumaraswamy distribution with shape parameters a = 0. 867 and b = 3. 03  (Kipping 2013). The priors for the GP and remaining parameters were otherwise very similar to those in Table  B. 2. The results indicate a significant detection of only two signals, corresponding to the orbital periods of the two known transiting planets, and the orbital parameters are fully consistent with those found previously.
Limits on additional planets at different periods Because no additional planets can be confirmed with the current dataset, we explored the sensitivity of the HARPS and nals were injected in the GP-removed dataset 7. Then we proceed in the same manner as described in Section 3. 2 (but we now removed the GP part) to recover the injected planet signal. We considered the planet to be detected when the median of the posterior distribution for the radial velocity semiamplitude was more than five times the standard deviation away for zero. This analysis is shown in Fig. 10 , where we also add the detection limit assuming the scatter of the radial velocity data from the two-planet model in Section 3. 2. We conclude that we can discard planets with masses m > 1 M ⊕ for periods up to 10 days, m > 2 M ⊕ for periods below 100 days, and m > 5 M ⊕ for periods shorter than one year.
Exploring the TESS dataset The full analysis of the transit signal of LHS 1140 b and LHS 1140 c is presented in Section 6. Here, we explore the possibility of additional signals in the TESS dataset. We first analyzed the TESS dataset to search for transittiming variations (TTVs) of LHS 1140 c, for which five transits are present in the data. We used allesfitter  (Günther & Daylan 2020)  to model the photometric data alone. The priors on the parameters were set to Gaussian distributions according to the values published in  Ment et al. (2019) , with a broad width corresponding to ten times the published uncertainties. We also set uniform priors to the individual TTVs of each transit of ±3. 5 hours. The results for the inferred TTVs are shown in Table  2. All values are compatible with zero TTVs, except for the first transit, which occurs slightly earlier.
However, the TTV is still compatible with zero within 2σ. Additionally, the TESS transit times are also compatible within one minute with the Spitzer transit time obtained six months before by  Ment et al. (2019). We used the transit least-squares (TLS) software (tls, see  Heller et al. 2019)  to search for additional signals in the TESS dataset. We masked out the times of transit corresponding to planets LHS 1140 b and LHS 1140 c and performed a smooth detrending of the light curve using wōtan  (Hippke et al. 2019 ) with a window length of 0. 5 and using the biweight method. We then computed the TLS periodogram on this masked and detrended light curve over the period range calculated by the tls software based on the data sampling with a range spanning from 0. 6 to10 days. The result is shown in Fig.
Co-orbital analysis The long time span and high precision of the radial velocity dataset obtained for this target allows us to perform a detailed exploration for the possible presence of co-orbital planets (ex-otrojans). We explored this scenario for both planets in the system by applying the technique described in  Leleu et al. (2017)  (hereafter the α-test), a generalization of the technique proposed by  Ford & Gaudi (2006). The α-test has been applied to different planetary systems, for instance, by  Lillo-Box et al. (2018a,b) ,  Armstrong et al. (2020 ), or Toledo-Padrón et al. (2020). In this technique, the radial velocity induced by the co-orbital system corresponds the the sum of two Keplerians with the same orbital period, with at least one of the components transiting its host star (assumed to be the planet).
For the HARPS-only dataset, the evidence is stable throughout the entire dataset. However, in the case of the ESPRESSO-only dataset, the evidence for the co-orbital model progressively (although slowly) increases toward positive values as more data points are added. It therefore deserves additional attention. We also performed an independent test to confirm this signal by following the technique proposed by  Ford & Gaudi (2006)  to compare the time of conjunction measured from the transit signal (T 0 c,LC ) and from the radial velocity signal (T 0 c,RV ). In the case of a single planet in circular orbit, it is easy to see that the lag between both times is zero, ∆t = T 0 c,LC -T 0 c,RV = 0. However, in the presence of a co-orbital body at one of the Lagrangian points, the gravitational pull of the co-orbital will change T 0 c,RV (this occurs earlier if in L 4 and later if in L 5 ), while leaving the time of transit (T 0 c,LC ) unchanged.
We performed this test by analyzing both datasets independently. We modeled the TESS light curve with two planets and the radial velocity dataset with two Keplerian signals (details of the modeling of the photometric dataset are provided in Sect. 6). As a result, we obtain a time lag between the times of conjunction for LHS 1140 c measured from both techniques of ∆t = 2. 04 ± 1. 27 hours. This value is again 1. 6σ away from zero and provides consistent results with the αtest, an indication for a co-orbital body in L 4 of LHS 1140 c. We note that this time lag can also be explained by a single planet with e cos ω ∼ 0. 15, which is within the confidence interval of the eccentric two-planet model we showed in Sect. 3. 2. We further investigated this co-orbital candidate by inspecting the TESS light curve in this Lagrangian point.
Five transits are observed with TESS of LHS 1140 c, but only four passages of its L 4 in front of the star because the third Lagrangian point lies inside the mid-sector gap. We explored the TESS light curve  in the region of the Lagrangian point after removing the data points inside the transit of planet LHS 1140 b which occurs close to the L 4 location of transit 4 of LHS 1140 c. The phase-folded light curve in this regime shows a shallow dimming at the location of the L 4 Lagrangian point (slightly shifted by 0. 006 in phase, or equivalently, ∼32 minutes, but perfectly compatible with a dynamically stable libration orbit), see the middle panel in Fig. 12. Interestingly, the duration of the dimming is perfectly compatible with the transit duration of the planet LHS 1140 c, expected for a co-orbital in the coplanar case.
Joint photometric and radial velocity model Based on the analysis performed in the previous section, we proceeded with a joint simultaneous analysis of the HARPS and ESPRESSO radial velocities and the TESS photometric time series to estimate the physical and orbital parameters of the system. To this end, we modeled the the radial velocities as explained in Sect. 3. 2, but with a slightly different parameterization that now explicitly included the individual contributions of the planet mass and orbital inclination for each planet (instead of using the radial velocity semiamplitude). We also included the GPs in the modeling and constrained them by simultaneously modeling the FWHM of the CCF of the ESPRESSO and HARPS data (see Sect. 3. 2). The TESS photometry was modeled with the batman code  (Kreidberg 2015)  to retrieve the transit models.
We finally removed the first half of each chain and combined all chains (1. 68 × 10 6 steps in total) to compute the final posterior distributions. Table  B. 3 shows the prior and posterior distributions for each parameter. The final models and confidence intervals for the planet transits are shown in Fig. 5 , and the corresponding modeling of the radial velocity dataset is shown in Fig. 2  (full time series) and Fig. 3  (phasefolded dataset). In Fig. 7  we additionally show the joint modeling of the FWHM of the CCF sampling the stellar activity. The variations seen in this parameter mimic the variations seen in the radial velocity dataset, showing the correspondence between both measurements coupled by the activity of the star (see also Suárez Mascareño et al. 2020 for a similar analysis on Proxima b).
The inferred masses are compatible with the minimum masses obtained in the radial velocity analysis (Sect. 3. 2). We find masses for the two planets that correspond to m b = 6. 38 ± 0. 45 M ⊕ and m c = 1. 76 ± 0. 17 M ⊕ , slightly lower than the previously reported values. We also find slightly smaller radii for the two planets with the TESS data (R b = 1. 635 ± 0. 46 R ⊕ , R c = 1. 169 ± 0. 038 R ⊕ ) than the values found by  Ment et al. (2019)  using Spitzer data (R b = 1. 727 +0. 032 -0. 032 R ⊕ , R c = 1. 282 ± 0. 024 R ⊕ ); they are different by about 1. 5σ for LHS 1140 b and by 2σ for LHS 1140 c. We also performed a three-planet modeling of the full radial velocity and TESS dataset to extract better constraints on the ephemeris of the third planet candidate. The resulting phasefolded radial velocity curve of the third planet is shown in Fig.
Conclusions We have revisited the planetary system LHS 1140 with its two known Earth-like transiting planets by analyzing an intensive campaign taken with the new ultra-stable high-resolution spectrograph ESPRESSO and observations from Sector 3 of the TESS mission. We have searched for additional signals in the radial velocity data including HARPS and ESPRESSO measurements. The results show additional evidence for the signal of a third planet candidate at ∼78 days. Our analysis of the joint radial velocity dataset, including a modeling of the stellar activity using the FWHM of the CCF as an activity indicator, shows positive evidence that this signal isof planetary nature (i. e. , not caused by activity). We find a ∼ 4σ significance in the semiamplitude of the radial velocity of this signal.
This is supported by our statistical analysis with kima and the l1-periodogram (see Sect. 3. 2). The Bayesian evidence of the two-planet model against the three-planet model, however, is still not enough to claim a confirmation, but its evolution when the dataset was increased points toward the planetary scenario. This evolution shows that ∼50 more ESPRESSO measurements are required to unambiguously confirm the planet signal based on radial velocity data alone. The corresponding planet mass of the candidate planet is 3. 9 ± 1. 1 M ⊕. Unfortunately, no transit signal is present in Sector 3 of the TESS data, as expected from the ephemeris of our joint LC+RV analysis. This ephemeris also suggest that the extended TESS mission will not catch the planet transit when the mission revisits this field in Sector 30 between 22 September 2020 and 21 October 2020.
If the system is coplanar (as the two known planet inclinations strongly suggest), the impact parameter of this planet candidate would certainly mean that it transits the host star. The expected total transit duration (assuming circular orbit) is about three hours. Further ground-based photometry to search for this transit would therefore be extremely useful and efficient to confirm this signal. We caution about the relatively large uncertainties of the ephemeris, however, which would imply a dedicated campaign of about five consecutive nights on the same target. We also explored the possibility of co-orbital planets in the two known transiting planets through a dedicated study of the radial velocity data and light curve. For LHS 1140 b, the radial velocity data allowed us to constrain the mass of any tadpole and horseshoe co-orbitals up to 2.
1 M ⊕ in L 4 and 1. 8 M ⊕ in L 5 (95% confidence levels). Similarly, the TESS data discard nearly coplanar co-orbitals around the Lagrangian point regions larger than ∼3 R ⊕. On the other hand, for LHS 1140 c, the radial velocity analysis unveils a 2σ signal in its L 4 region that would correspond to a sub-Earth co-orbital planet with a 0. 26±0. 18 M ⊕. The Bayesian evidence of this model still does not support this scenario against the null hypothesis, however, and several hundred additional measurements with ESPRESSO-like precision are required to confirm the signal with radial velocity data alone. However, the analysis of the TESS light curve indicates a shallow dimming very close to this Lagrangian point with the same duration as the transit of LHS 1140 c (as expected in the coplanar case).
If real, this dimming would correspond to a 0. 44 ± 0. 08 R ⊕ sub-Earth size body. Unfortunately, the significance of the signal is not strong enough to ensure that this dimming is not caused by systematics of the TESS light curve, and only additional data will shed more light on this co-orbital candidate. Finally, we performed a joint analysis including the radial velocity and light curve datasets assuming the two-planet scenario to derive precise properties of the known transiting planets. We used the largest evidence model from the radial velocityonly analysis, corresponding to the two-planet case with circular orbits for both planets (this is favored by the Bayesian evidence with a Bayes factor larger than B > 68 compared to the eccentric case). The results of this analysis show slightly less massive and smaller planets than previously reported values.
Acknowledgements. This research has been funded by the  Spanish State Research Agency (AEI)  Projects No. ESP2017-87676-C5-1-R  and No. MDM-2017-0737  Unidad de Excelencia "María de Maeztu"-Centro de Astrobiología (INTA-CSIC ). This work was supported by  FCT -Fundação para a Ciência e a Tecnologia  through national funds and by  FEDER  through  COMPETE2020 -Programa Operacional  Competitividade e Internacionalização by these grants:  UID/FIS/04434/2019 ;  UIDB/04434/2020 ;  UIDP/04434/2020; PTDC/FIS-AST/32113/2017 & POCI-01-0145-FEDER-032113; PTDC/FIS-AST/28953/2017 & POCI-01-0145-FEDER-028953. N. A. -D. acknowledges the support of  FONDECYT  project  3180063. XB and JMA acknowledge funding from the  European Research Council  under the  ERC Grant  Agreement n. 337591-ExTrA. A. C. acknowledges support by  CFisUC projects  ( UIDB/04564/2020  and  UIDP/04564/2020 ),  ENGAGE SKA  ( POCI-01-0145 -Article number, page xiv of xxii Lillo-Box et al.
More precisely, while the designers' lower bound on the probability of differential for 9 and 10 rounds of the cipher are least 2 -54. 67 and 2 -62. 61 , respectively, we are able to present 9, 10, 11, 12, 13, and 14 rounds of the differential in single-tweak model with the probabilities of at least 2 -40. 20 , 2 -44. 89 , 2 -49. 79 , 2 -54. 48 , 2 -59. 13 , and 2 -63. 80 , respectively, that improve the previous lower bounds significantly. We make our implementations of the attacks and our modeling of algorithms in MILP and SAT freely available at: https://github. com/hadipourh/craftanalysis. 4. We also show some typos in the designers' analysis which could be useful for later studies. For example, we show that two out of 12 zero-correlation masks for 13 rounds of CRAFT, that are provided by the designers, are not valid.
3. Based on the found trail, develop the constraints for CryptoSMT, to limit the search to the truncated pattern with fixed input/output in the previous step. CryptoSMT, supports primitives with S-boxes  [AK18] , but it uses a naive approach to encode S-boxes. In the SMT model generated by CryptoSMT, input and output differences of each n-bit S-box, are represented by n binary variables x = (x 0 ,. , x n-1 ), and y = (y 0 ,. , y n-1 ), respectively. It also introduces additional variables p = (p 0 ,. , p n-1 ) for each S-box S, representing the probability of the transition x S -→ y, which are linked to the Pr{x S -→ y}, by the following relation: wt(p 0 ,. , p n-1 ) = -log 2 (Pr{x S -→ y}), where wt(p 0 ,. , p n-1 ) denotes the Hamming weight of binary code p 0. p 3 , and is called the weight of the transition x → y.
For example, if (1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0), is an invalid assignment for the variables (x 0 ,. , x 3 , y 0 ,. , y 3 , p 0 ,. , p 3 ), then the following clause is added to the CNF of the S-box in the SMT model. (¬x 0 ∨ x 1 ∨ ¬x 2 ∨ ¬x 3 ∨ y 0 ∨ y 1 ∨ y 2 ∨ y 3 ∨ p 0 ∨ p 1 ∨ p 2 ∨ p 3 ). By considering all invalid assignments, the CNF modeling the differential behaviour of a n-bit S-box is as follows: m i=1   n-1 j=0 L j (s i , t i )  . The entries in the DDT of a 4-bit S-box with differential uniformity 4, including CRAFT's S-box, only take four possible values, which are 0, 2, 4, and 16; therefore, the possible differential probabilities are 0, 2 -3 , 2 -2 , and 1, respectively. In contrast to the CryptoSMT's encoding, which always uses four variables to encode the probabilities of a given 4-bit S-box, the CRAFT's S-box probabilities can be encoded via only three binary variables denoted as p 0 , p 1 , p 2 , such that wt(p 0 , p 1 , p 2 ) = -log 2 (p).
With the aim of optimizing the CryptoSMT's method for encoding the differential behavior of the CRAFT's S-box, we use a different method than the CryptoSMT's original method, which can be easily generalized for an arbitrary n-bit S-box. We first generate the truth table of the following 11-bit boolean function [SWW18]: f (x, y, p) = 0 if Pr{x → y} = 0, f (x, y, p) = 1 p = (1, 1, 1) 0 o. w if Pr{x → y} = 2 -3 , f (x, y, p) = 1 p = (0, 1, 1) 0 o. w if Pr{x → y} = 2 -2 , f (x, y, p) = 1 p = (0, 0, 0) 0 o. w if Pr{x → y} = 1, where x = (x 0 ,. , x 3 ), and y = (y 0 ,. y 3 ) denote the input and the output differences, and p = (p 0 , p 1 , p 2 ) is used to encode Pr{x → y} = 2 -wt(p). To generate the constraints that model the differential behavior of S-box, we use the minimized product-of-sum representation of the above boolean function, which can be obtained via the Quine-McCluskey[Qui52, Qui55, MJ56], and Espresso algorithm  [BHMSV84]  implemented at the off-the-shelf program Logic Friday  [Log19].