dataesr/scientific-paragraphs-categorization huggingface dataset:
AlterBBN also contains models of weakly-interacting massive particles (WIMPs) decaying at the time of BBN, as exemplified by the alter_wimps. c program, which can affect the abundance of the elements. A special feature of AlterBBN is the possibility to use larger nuclear networks and heavier elements via an interface with the JINA REACLIB database  [14] , which is usually used for thermonuclear modelling of supernovae. In AlterBBN, the user can choose the heaviest elements to be considered for the calculation of the primordial abundances. This is particularly useful in the context of inhomogeneous BBN  [15] , where local baryon densities at BBN time can be much larger than in standard BBN.
Conclusion and perspectives AlterBBN is a public tool for computing the abundance of the elements from Big-Bang nucleosynthesis. It is flexible, easy to use and to modify, and features different cosmological scenarios which can be constrained using observations. For the near future, updates of the nuclear network are planned, together with the implementation of more cosmological scenarios, with in particular the possibility to directly input the scale factor and temperature evolution as a function of time, and the implementation of a scenario in which primordial black holes inject radiation at BBN time, via an interface with the BlackHawk code  [16].
Connection between topology and dynamics For a given topology one can have several reduced models, depending on the kinetic orders. Each reduction corresponds to a particular qualitative dynamics. In order to illustrate the connection between network topology and its dynamics in the limit of well-separated rate constants, we made a number of experiments on fragments of real-life transcription networks extracted from Dorothea database (https://saezlab. github. io/dorothea/), for the edges of which we assigned sequential and distinct kinetic orders. For example, we extracted all network neighbours of MYCN transcription factor (see Figure  2,A,  and randomly  assigned kinetic orders from 0 to 9, to network reactions. Application of LNetReduce to 10000 random kinetic order assignments led to 51 topologically distinct (topologically isomorphic with node identity kept) model reductions, where some reductions were much more frequent than others.
Of note, in approximately 7% cases, LNetReduce met a conflict in the reduction algorithm. In these cases, two kinetic rates of the same order in the outgoing reaction fork happened at a stage of reduction process. Interestingly, rare reductions (Figure  2C, D ) were typically characterized by the presence of reactions with effectively opposite direction compared to the initial network, and inefficient, leaky dynamics of MYCN, with small probability of visiting it by a random walk at longer timescales (as opposed to the activating and efficient dynamics of the most frequent reductions, Figure  2A, B ). Other computation experiments with fragments of the transcripnetwork are described at the LNetReduce web-site as Python notebooks.
Transport Tests The proposed method is implemented into the interfacial solver of the in-house code CIAO, which has been successfully used for many multi-physics simulations  [2, 6]. The new method is verified using a 2D and a 3D transport test. In both tests, a periodic velocity field is prescribed to transport the interface instead of using a velocity field from a Navier-Stokes solver. The performance of the scheme is evaluated according to E mass = | k V E k F k ) -k V E k F 0 k | k V E k F 0 k and E shape = k V E k |F k (T ) -F 0 k | k V E k F 0 k , (7) where F 0 k indicates the initial volume fraction and T the period of the flow. While the first metric, E mass , measures the change of liquid volume after one period, the second metric, E shape , quantifies unphysical interface deformations after one period.
Mode-S/EHS are gathered by the ATC means (where a precise aircraft position is given by the radar) whereas Mode-S/ADS-B are collected by ADS-B antennas which lead to less accurate aircraft locations from emitted ADS-B messages that are not synchronous with other BDS registers used to compute wind components (Table  1 ). A first dataset of Mode-S/ADS-B winds over 20 days is considered to describe and evaluate the bias correction method. Then a second period of one month is examined to tune more precisely the methodology. Such data have been collected in real time, by a semi-operational ADS-B antenna network set-up by M et eo-France. The wind vector Ṽ can be derived from the difference between the aircraft motion relative to the ground and its motion relative to the air (Figure  1 ). Thus V ! is the difference in heading vector Ṽa defined by its module j Ṽa j and heading a, and the ground track vector Ṽg , defined by ground speed j Ṽg j, and track angle a g : Ṽ ¼ Ṽg À Ṽa : In this equation, both angles a and a g are defined in the same reference framework.
For Mode-S wind data (u and v), r o is taken equal to the AMDAR values since de Haan (2011) has shown that errors for both sources are comparable. This observation error has a vertical dependency and r b is provided by the ARPEGE Ensemble Data Assimilation System. The same spatial sampling used for AMDAR data has been chosen in a first stage for Mode-S data. For each aircraft only one active observation by 25 Â 25 km 2 box model level is selected. When AMDAR and Mode-S data are available within the same selection box, priority is given to AMDAR. The so-called 'passive observations' have passed the quality controls but have been flagged by the spatial thinning. There is between 10 to 20 times more Mode-S passive data than active ones. In practice, passive observations are used in the 3D-Var system in such a way that they have no impact on the result of the minimization but contribute to the convergence of the VarBC coefficients.
Indeed, in the 3D-Var system, data not bias corrected by VarBC, like radiosoundings and AMDAR reports (called 'anchoring data'), still contribute to the cost function and act as a constraint on the assessment of the control variable and, in particular, of the VarBC bias parameters. As explained above, it is possible to distinguish between so-called passive and active observations in the AROME 3D-Var. The active data are those that are used in the minimization to find the analysis state x a. Passive ones are only considered in addition to the active ones, to estimate the bias parameters. So, data that have not been selected during the thinning process are nevertheless used to compute the bias (increasing the data sampling and therefore improving the convergence of the predictor bias parameters).
P u1 and P v1 are named 'heading bias predictors' and P u2 and P v2 'airspeed bias predictors'. It is important to notice that heading a m is given with 1 resolution. The more observations are available for a given aircraft in an assimilation window, the more accurate the bias assessment will be. The VarBC method uses reduced centred predictors. All predictors are by definition centred. Standard deviations are the same for P u1 and P v1 (given by the dataset statistics from 5 to 24 April 2018, that is 150 m/s), on one hand, and for P u2 and P v2 (known sin and cos standard deviations, that is 0. 707), on the other hand. Therefore, the VarBC method has been implemented in AROME using the above predictors where airspeed (resp. heading) predictors have been divided by 0. 707 (resp. 150 m/s).
During this period, we compare different sources of aircraft wind data: AMDAR (assimilated, cycled), MF Mode-S/ADS-B (assimilated to compute bias, not cycled) and KNMI Mode-S/EHS (monitored). It is important to stress that VarBC Mode-S and MUAC data have been processed independently. Potentially, data from a given aircraft can be quasi collocated for each of the three datasets. If all of them were assimilated, such thinning would not be optimal, but in a VarBC context, AMDAR data will be used as anchoring observations for the VarBC MF Mode-S/ADS-B data. 4. 1. 1. Global behaviour. Table  4  presents global BGD mean and SD values of u and v wind components for raw MF Mode-S/ADS-B, VarBC MF Mode-S/ADS-B, KNMI unbiased Mode-S/EHS and AMDAR data over the 20-day period. Note that the comparison is done with different samples over the period of interest (see Section 2.
AMDAR and KNMI unbiased Mode-S/EHS winds have similar values with the lowest BGD mean and SD values. Results with VarBC Mode-S/ADS-B winds are very similar. Due to on-board computations AMDAR winds have a better quality than Mode-S ones. Mode-S/EHS data have better statistics than those from Mode-S/ADS-B that is explained by a better precision of aircraft locations. Other differences can be explained by different quality controls applied by each data producer.
Behaviour of an individual aircraft (aircraft A1). The behaviour of the VarBC is assessed more precisely by examining an individual aircraft. We have selected an aircraft having one of the largest amount of Mode-S data during the period (4583 active data) with high BGD values on raw wind components. Figure  7  shows the improvement on BGD statistics by the VarBC method. The bias correction narrows the sample distribution and centers it around its median with mean values close to zero. Moreover, the u (resp. v) component BGD standard deviation decreases from 10 m/s to 2. 5 m/s (resp. 6. 9 m/s to 2. 6 m/s). Figure  8  (top panel) displays the time evolution of the zonal wind component BGD values. The large positive and negative periodic biases present in raw data are almost suppressed by the VarBC method.
Global behaviour. Figure  10  shows the evolution of main BGD statistics after the use of VarBC with two predictors for both u and v parameters to unbiase Mode-S data as described above. These results are compared to similar statistics for AMDAR winds. Aircraft with more than 200 active Mode-S and AMDAR data over the period have been considered to provide reliable BGD statistics, representing 6025 (resp. 738) aircraft over the 7603 (resp. 1110) available after quality controls during the period for Mode-S (resp. AMDAR) data. It is important to stress that u and v raw Mode-S/ADS-B BGD mean and SD values can be very different from an aircraft to another. Therefore, even if half of the aircraft have BGD means close to zero for raw data, the remaining ones exhibit mean differences reaching up to 10 m/s.
For the same sample, after bias correction, the spread of BGD mean values around zero has been reduced, with maximum values around 2. 4 m/s. Among the raw Mode-S/ ADS-B dataset, 75% of both wind components BGD SD values are above 3 m/s and can reach values above 15 m/s. The VarBC allows to reduce significantly BGD SD values. Results are better than for the first period mainly because a number of aircraft have been blacklisted. The global BGD SD value is around 2. 2 m/s for u and v Mode-S/ADS-B data. These results can be directly compared to those of AMDAR data (2. 4 m/s for u and 2. 45 m/s for v). This comparison confirms the good behaviour of the VarBC. Complementary information on random and systematic errors of Mode-S winds can be obtained using the triple collocation method  (Stoffelen, 1998)  with additional datasets from AMDAR aircrafts and AROME 1 h forecasts.
This method allows to estimate simultaneously modelling and calibration errors in order to avoid pseudo biases that could be introduced by other intercomparisons. Results are shown in Appendix A. Collocated AMDAR and VarBC Mode-S u and v data differences are much lower than those between AMDAR and AROME and those between VarBC Mode-S and AROME. This result indicates that the variational scheme, constrained by all other non-corrected assimilated data, shows significant skill in distinguishing between the sources of biases. It also allows to assess random observation errors (without representativeness error) for both AMDAR and VarBC Mode-S (resp. $1 and $0. 77 m/s) and 1 h AROME forecast error ($1. 74 m/s). From Equation (1), we define the following quantities: representing the u and v mean absolute weights in percent of the absolute bias amplitude explained by predictor i for all Mode-S observations from aircraft p.
Discussion Model errors (linked to unresolved scales, parametrisations and initial conditions) can be persistent and/or of large scale. Depending on the available aircraft data, they can have an impact on both static and dynamic unbiasing methods. The VarBC method, being dynamic, could, if it was not able to distinguish the origin of the bias, convert any model error into an observational bias as shown by Aulign e et al. (2007). The VarBC method applied to Mode-S data avoids this pitfall for the following reasons: It relies on AMDAR data (in addition to other wind measurements: AMVs, radiosoundings, surface weather stations, radar Doppler winds, etc. ) as anchoring data. The AMDAR data are of the same type, at the same levels as Mode-S data and are also measured by the same aircraft. It uses a large amount of Mode-S data per hourly analysis window.
Conclusions and perspectives The main objective of the study described in this paper was to apply the VarBC correction method to reduce, within a NWP DA system, the biases on horizontal wind components derived from Mode-S/ADS-B messages. This is, to our knowledge, the first time that such method is applied to Mode-S derived winds. For that purpose, we have considered the 3D-Var DA system of the M et eo-France convective scale model AROME and Mode-S/ ADS-B data gathered by a network of 8 antennas installed by M et eo-France over the French metropole. To set-up the VarBC method, two trivial predictors related to known biases of Mode-S/ADS-B wind data have been chosen. For a given aircraft, the first one is linked to the heading whereas the second one is linked to the airspeed. When sufficient wind Mode-S/ADS-B data are available for a specific aircraft, the airspeed and heading biases can be efficiently estimated by the VarBC method for both wind components.
To insure that the VarBC method does not absorb significant NWP model errors, nearby 'anchoring' observations  (Eyre, 2016)  are necessary. This is the case for Mode-S data that often sample the same surrounding atmosphere as other good quality aircraft data (AMDAR, AIREP). To prevent bias parameters from changing significantly from one analysis to another, their associated inertia could be increased. We have verified with triple collocation method  (Stoffelen, 1998)  using 1844 AMDAR, Mode-S and AROME data that VarBC Mode-S u and v data are much closer to AMDAR data than to AROME ones. It tends to prove that the variational scheme, constrained by all other noncorrected assimilated data, shows significant skill in distinguishing between the bias sources. However, we have also demonstrated the capacity of the VarBC method to rapidly modify the bias parameters (few hours) to changes in the raw data due for example to aircraft maintenance.
has to be defined. Preliminary results tend to prove that rejected aircraft represent a small fraction of the total amount of Mode-S data. An important aspect to examine in the context of DA studies is the sampling of Mode-S data given their availability at high temporal and spatial densities, compared to AMDAR data. A number of encouraging preliminary studies have been already undertaken (data selection within boxes of various sizes both on the horizontal and on the vertical, superobbing with revised observation errors, … ), but work still remains to sample en-route phase of flights, to better handle nearby Mode-S data and to specify the inertia of the bias predictor parameters to reach the best compromise between noise reduction and freedom to change. The VarBC method is very useful and efficient on its own to bias correct data.
A. 1. Triple collocation The method was carried out over a one-month period (6/ 10/2018 to 6/11/2018). The collocation parameters in terms of altitude, horizontal distance and time where setup to 1 hPa, 2 km and 5 min respectively. AROME 1 h forecasts data are projected to Mode-S locations. These criteria led to a sample of 1,844 of collocated values. Even though it is possible that collocated AMDAR and Mode-S data could correspond to the same aircraft, their observation errors are assumed to be uncorrelated. Indeed such measurements, obtained from different acquisition systems, are not taken at the same place and time.
A. 2. Error modelling We consider three observing systems measuring values x i , i ¼ 1, 2, 3 of the same quantity t (true value). Following  Stoffelen (1998) , each measurement x i is decomposed as follows: x i ¼ a i ðt þ e i Þ þ b i (9) where a i is the trend, b i the bias and e i a random error. The mean < e i > is supposed to be zero and the variance < e i 2 > noted r i 2 is supposed not to depend on t. Four different systems are examined: AMDAR (1), Mode-S (2), Mode-S without bias correction (2b) and AROME (3). Afterwards, the triple collocation involving systems 1, 2 and 3 is noted TC, whereas the one involving 1, 2b and 3 is noted TC b. AMDAR data are chosen to be the reference for calibration (a 1 ¼ 1 and b 1 ¼ 0). AMDAR and Mode-S data can represent smaller scales that are not described by the AROME model.
By assuming that the true signal t is at the AROME model scales, the variances resolved by AMDAR and Mode-S data and not by AROME are integrated into e 1 and e 2 as random errors. AMDAR and scaled Mode-S data resolving the same scales can have correlated errors: < e 1 e 2 >¼ r 2 : We can notice than e 1 also contains collocation errors due to the fact that AROME 1 h forecasts data are projected to Mode-S locations. For this study, we have considered AMDAR and Mode-S data that have been assimilated in the AROME model. Moreover, we assume that AROME forecast errors are uncorrelated with observation errors (< e 3 e 2 >¼ 0 and < e 1 e 3 >¼ 0). With the above hypotheses, the first and second order statistical moments can be deduced using Equation (  9 ): a 2 ¼ c 23 c 31 and a 3 ¼ c 23 c 12 À a 2 r 2 (10) b 2 ¼ M 2 À a 2 M 1 and b 3 ¼ M 3 À a 3 M 1 (11) r 1 2 ¼ c 11 À c 31 c 12 c 23 þ r 2 (12) r 2 2 ¼ c 22 =a 2 2 À c 31 c 12 c 23 þ r 2 (13) r 3 2 ¼ ðc 33 À a 3 c 31 Þ=a 2 3 ( 14 ) where M i ¼< x i > , M ij ¼< x i x j > and c ij ¼ M ij À M i M j (15) Knowing the representativeness error r, all above other parameters can be estimated from the statistics of collocated data.
Observations errors can be also estimated using the a posteriori diagnostics proposed by  Desroziers et al. (2005). These estimates r id also contain a representativeness such as: r id 2 ¼ a 2 i r i 2 , i ¼ 1,2 (16 ) where r i 2 are given from Equations (  12 ) and (13). It is therefore possible to estimate r 2 : The Desroziers method also provides an estimate of the forecast error r 3d that can be compared to a 3 r 3 deduced from Equation (  14 ). Quality of the collocation can be estimated using differences of AROME data at each AMDAR (a) and Mode-S (b) collocated different points. < ðx 3a Àx 3b Þ 2 >¼ a 3 2 ð< t a À t b ð Þ 2 > þ2r 3 2 À 2 < ðe 3a e 3b Þ.
A. 3. Results A. 3. 1. Global statistics Figure  A1  shows that the VarBC method allows Mode-S data to be more consistent with AMDAR data by reducing significantly the differences in terms of standard deviation values for u (resp. v) from 3. 79 m/s (resp. 3. 13 m/s) to 1. 21 m/s (resp. 1. 25 m/s). In addition, Mode-S VarBC and AMDAR data have very close statistics when compared to AROME. Moreover, Mode-S VarBC data are closer to AMDAR data than to AROME data. AMDAR data selected for the triple collocation have been used to anchor the VarBC method. However, due to their reduced number, they represent only a fraction of the total observations (other distant aircraft, AMV, soundings … ) that steered the bias correction for these aircraft.
3 m/s respectively 1. 1 m/s. The small difference in favour of Mode-S data can partly be explained by their number. Indeed, the same thinning is applied in the analysis to both data sources (1 aircraft data per 25 km box size, per model level, per analysis, by choosing the time closest to the analysis date). Since there are many more Mode-S data per analysis than AMDAR data, those selected for assimilation will be on average closer to the analysis date and potentially of better quality (by an improved time, and therefore position consistency). Moreover, the temporal accuracy of AMDAR and Mode-S data acquisition is 1 min and 1 s, respectively. This leads to a less accurate collocation of AMDAR data inducing an additional positioning error. Finally, we can estimate the quality of the collocation using AROME data at AMDAR (a) and Mode-S (b) collocations from Equation (17), and for both u and v parameters:     12 ) and (  16 )) Mode-S VarBC (Equations (  13 ) and (  16.
Acknowledgments The technical support from  F. Guillaume  (M et eo-France/ CNRS) has been very useful during the course of the study. Olivier Henry (M et eo-France) provided the plots of magnetic declination difference (Figure 2). S. de Haan (KNMI)  is acknowledged for his pionnering work on Mode-S data in the NWP context and for providing a MUAC dataset for our own evaluations. Finally, the UKMO software has been essential to compute derived winds from BDS registers collected by M et eo-France antennas with the help of Olivier Traull e,  Guillaume Gamelin , and  Jean-Marc Lef  evre (M et eo-France) to insure data production.
End-to-end microscopic simulation The first simulation chain consists of four independent steps: (i) We produce a fixed number of tau decays induced by cosmic tauneutrinos (ν τ ) interacting in a spherical Earth. This is done for two neutrino energies (E ν = 10 9 and 10 10 GeV) with a dedicated Monte-Carlo engine: DANTON  [19, 20] , further described in section 3. 1. (ii) We compute the electromagnetic field induced at the location of the detection units by the showers generated by these tau decays. This is done through a full microscopic simulation of the particles in the EAS and of the associated electromagnetic radiation using the ZHAireS  [21]  simulation code (see section 3. 2. 1 for details). (iii) The voltage induced by the radio wave at the antenna output is then computed using a modelling of the GRAND HorizonAntenna  [2]  performed with the NEC4  [22]  code.
Production of the shower progenitors The production of the shower progenitors was performed with the DAN-TON software package  [19, 20]. DANTON simulates interactions of tau neutrinos and tau energy losses. It produces results compatible with similar codes  [25]. Additionally DANTON offers the possibility to run simulations in backward mode (i. e. from tau decay upwards, with appropriate event weight computations), an attractive feature for massive simulations, and it also allows us to take into account the exact topography of the Earth surface  [26]. It is however operated here in forward mode, i. e. as a classical Monte-Carlo. The primary neutrino source is set as mono-energetic and isotropic. A spherical Earth is used with a density profile given by the Preliminary Reference Earth Model (PREM)  [27] , but with the sea layer replaced by Standard Rock  [28].
Simulation of the electric field 3. 2. 1. Microscopic method In the microscopic method, the extensive air showers initiated by the byproducts of the tau decay, and the impulsive electric field induced at the antenna locations were simulated using the ZHAireS software  [21] , an implementation of the ZHS formalism  [29]  in the AIRES  [30]  cascade simulation software. To allow for geometries where cascades are up-going and initiated by multiple decay products, we implemented a dedicated module called RAS-PASS (Radio Aires Special Primary for Atmospheric Skimming Showers) in the ZHAireS software.