dataesr/scientific-paragraphs-categorization huggingface dataset:
( 5 ) For each projection matrix (each generation in each condition), σ i (for i > 1) values were calculated from survival curves established during the experiment, and σ 1 (proportion of surviving embryos) corresponds to the ratio between the number of embryos and oocytes. The duration of the size class i (d i ) was calculated based on growth curves. Regarding the calculation of the fertility F i , the sex ratio was set at 0. 5. Given the experimental temperature of 16 • C, the duration of the reproductive cycle (d c ) was set at 3 weeks  [36]. The proportion of reproductive females was determined from puberty monitoring data. The average number of oocytes per female of each size class was estimated from reproductive data recorded in the different conditions for F1 and F2 generations. An extrapolation of recorded measurements to the different size classes was operated, based on the mean size of each class, and a linear relationship was established between the oocyte number and body size of females.
This is accomplished by using synthetic examples and field cases, and comparing the quality, plausibility and uncertainty of the inverted models obtained with a single coincident loop (COIL) acquisition sequence with those obtained with a central-loop (CL) and a multi-central-loop (MCL) dataset. Various inversion methods and uncertainty estimation strategies are used, as well as a new stochastic method developed to interpret 1D SNMR data, referred to as the Bayesian Evidential Learning 1D imaging (BEL1D), originally presented by  Michel (2018).
Data processing Most of the forward modeling and inversion operations were performed with the software MRSMatlab  (Müller-Petke et al. , 2016) , an open-source GUI based on Matlab programming. MRSMatlab provides the possibility to perform forward modeling with different loop configurations (coincident loops, central-loop, figure-of-eight) while controlling the resistivity, water content and relaxation time for multi-layered models. The software also provides tools to import field data, process raw recordings, and extract the FID envelopes in order to subsequently invert it. All of the inversions strategies proposed are based on the QT inversion scheme  (Müller-Petke & Yaramanci, 2010) , with different ways of handling the data, using different model discretization approaches and solvers. For more details about the specific design and functioning of MRSMatlab, the reader is referred to  Müller-Petke et al.
2008 ), which supports acquisition of multi-channel data surveys and recording noise reference loops during the experiment. Due to the low level of noise expected, only one channel was used for the reference loop, which was circular shaped, 40 m diameter, and placed about 50 m from the closest emitting loop edge, ensuring that the reference loop should not be contaminated by the NMR signal measured in the acquisition loop  (Walsh et al. 2008 , Dlugosch et al. 2011). After a few measurements and a quick processing (quadrature detection associated with bandwidth filtering), the Larmor frequency value was estimated to be 2103. 6 Hz. During the experiment, 44 stacks were acquired, and the pulse length was set to be 20 ms. All data were processed for harmonic noise and spikes, followed by stacking, and the extracted FID envelopes were then used for inversion.
Multi-central-loop (MCL) configuration The MCL configuration consists of deploying two, three (or more) loops concentrically with different diameters. By transmitting the excitation magnetic field using the largest loop, one can simultaneously record three different data sets: the transmitter loop that can also act as a receiver (classical COIL measurements) and the two smaller loops (CL configurations). Each of these data sets is associated with a different sensitivity distribution, that all provide a different illumination of the subsurface. Modest diameter variations lead to significantly different sensitivity distributions. Figure  2b  shows an example of the three sensitivity distributions associated with a MCL configuration where the transmitter/receiver (Tx/Rx) loop is 100 m in diameter (1 turn), and the two smaller receiver loops are respectively 50 m diameter (1 turn) and 20 m diameter (3 turns).
Data interpretation and uncertainty estimation To perform this study, various methods are alternatively being used to interpret the data and estimate the uncertainties associated with the inverted subsurface models, so as to accumulate arguments for or against the use of the MCL configuration. The data set is handled under its complex form, which is the most complete representation of the signal since it takes in account the phase effect of the electrical conductive properties of the subsurface. When successful, complex inversion results in reduced model ambiguity and improved depth resolution  (Braun et al. , 2005 , Irons & Li, 2014). Three different inversion methods are being used: the so-called mono-exponential and multi-exponential inversions  (Müller-Petke et al. , 2016). They both use a smooth discretization of the subsurface, but the first one only allows a mono-exponential relaxation time within each layer  (Dlugosch et al.
, 2014) , while the second one allows for multi-exponential decay times  (Müeller-Petke et al. , 2010). In order to compare the COIL configuration results with the results of MCL strategy, the shape of the resulting inverted models is compared to the expected results (synthetic model or lithologic log information) and the uncertainties associated with those models are estimated. In the case of the mono-exponential inversion, the uncertainty estimation feature of MRSMatlab is used, which is based on the bootstrapping strategy proposed by  Parsekian & Grombacher (2015). After the first inversion, a portion of the QT data set is randomly removed, and the inversion is performed again on the remaining reduced data set. Parsekian & Grombacher (2015)  showed empirically that resampling the data set while keeping 90% of the time samples and 50% of the pulse moments provides the best balance between water content uncertainty and relaxation time uncertainty estimation.
, 2015) , and was then adapted for the first time to the interpretation of geophysical data by  Hermans et al. (2016)  in the context of timelapse electrical resistivity monitoring. Recently,  Michel (2018)  adapted the method to the interpretation of 1D SNMR data, and provided a dedicated Matlab GUI that allows for the processing of SNMR  (Michel et al. 2019). The main interest of applying this innovative methodology to the present study comes from the fact that the output of the BEL1D process is a statistical distribution of models which all explain the data set, allowing for a direct quantitative comparison of the uncertainty associated with the COIL and the MCL data sets interpretation, under the form of probability density distributions. For more details about the method and the different steps of the process, the reader is referred to  Michel et al.
The results show that different behaviors can be observed depending on the noise level. For low noise levels (10 nV), it seems that most of the improvement brought by the MCL configuration concerns the shallow part of the model. Looking at the resolution matrices (Fig. 4a ), we see that for both the CL and COIL configuration, the red curve representing maximum values is quite far from the diagonal in the shallowest layer (0-10 m depth), which indicates strong uncertainty at these depths. This is not visible for the MCL configuration for which the maximum value curve is very well located on the diagonal. Figure  5a. Since the noise level is not always predictable, this yields an ambiguity as to which is the optimal choice. Therefore, as a general recommendation, we propose to use in the field a three loops MCL, with central receivers of 50 % and 20%-30% of the main diameter, and to either invert the whole data set, or select the data from one of the two central receivers once the noise level is known.
Although Fig. 6  shows that the three loops MCL provides similar but not better resolution improvements than the two loops MCL, the slight effort of placing an extra loop will provide adaptability to the noise level, a more robust data set and a more complete global sensitivity distribution. slightly misplaces the aquifer boundaries. With the COIL, the aquifer boundaries are also misplaced, but the total water content is largely underestimated (maximum total value of 5%).
Mono-exponential inversion In order to make a second comparison between the three loop configurations, the mono-exponential inversion scheme was applied to the three datasets. Fig. 8  displays for each loop configuration: the initial synthetic model, the main inverted model (complete data set) and all the secondary models resulting from the inversion of resampled data sets. The misfit between the final simulated data and observed data was computed as a χ² value and was about 1. 5 in all cases, which is acceptable given the relatively low S/N ratio associated with the simulated data. The mono-exponential scheme leads to similar conclusions as the multi-exponential inversions: the MCL model provides equivalent or better estimation of the different layers limits and water content values compared with the CL and COIL configurations.
The additional parameter to be examined here is the uncertainty associated with those inverted models, which is represented by the distribution of resampled bootstrapped models. In the shallow part of the model [0 -20m], the uncertainties have a higher magnitude for the CL and the MCL data sets than for the COIL data set (the resampled models distribution is wider). For the intermediate aquifer, the uncertainties have globally equivalent magnitude for the three configurations (the resampled models distribution have the same width), but the resampled distribution of the MCL is centered around the inverted model, hence confirming the presence of this intermediate aquifer. For the CL and COIL configurations most of the resampled models do not show the intermediate aquifer, which would cast significant doubt on its existence if one was interpreting a real field case.
Uncertainty estimation with Bayesian framework Finally, a novel method called Bayesian Evidential Learning 1D imaging (BEL1D,  Michel 2018 , Michel et al. 2020 ) has been used to estimate the effect of using the MCL configuration upon the interpreted model uncertainties, using a stochastic process. This time, a 5 layers model has been used to respect some current limitations of the method. The previous synthetic 8 layers subsurface model was modified by merging layers three and four together, and layers five, six and seven together. The water contents and decay times for those merged layers are the average of the initial values, hence resulting in a less-complex, yet similar model (Table  1 ). BEL1D was then applied to the COIL and MCL dataset for comparison. The method is based on a blocky discretization of the subsurface.
Field experiment This section presents the results of a field SNMR survey conducted at the Schillerslage test site. A MCL configuration was displayed at the surface, with a 50 m diameter circular loop used as transmitter/receiver and a concentric 30 m diameter circular loop as a separated receiver. Compared to the previous synthetic case, this is a 2 coils MCL configuration. Our goal in this section is to compare the inversion obtained with 3 different loop configurations: the classical COIL configuration (Tx50m Rx50m), the CL configuration (Tx50m Rx30m) and the MCL configuration (Tx50m Rx50m & Rx 30m), which in this case consists of merging together the COIL and CL datasets. Fig. 10  shows the results of inverting these three datasets using the mono-exponential scheme and applying 100 realizations of the bootstrap algorithm for uncertainty estimation.
2008 (Cordua et al. , 2009 ; ; Dosso et al. 2006 ). In the context of a MCL acquisition, correlation within the data error vector may originate from the fact that, for one pulse moment emission, several NMR signals are recorded simultaneously through the different receiver loops. This simultaneity implies that the electromagnetic (EM) noise spatial distribution affecting these NMR signals at the time of the recording is the same, and hence that some correlation may exist between the data error estimated values, since they directly depend on the noise magnitude and characteristics. This issue was investigated by examining the results of two MCL experiments where noise-only signals were recorded. The first one was performed in low-noise conditions, at the Schillerslage test-site, using three circular loops with respective diameter of 50m, 30m and 10m (5 turns), and the second one was performed near the castle of Hodoumont, in Belgium, where the noise level is very important, using three circular loops with respective diameter 78m, 40m and 20m.
Fig. 11  shows, for the Schillerslage and the Hodoumont experiment, the MSC functions computed between the different loops composing the MCL configuration, before and after the application of classical noise processing techniques. For the Schillerslage case, the noise processing procedure consisted of despiking, model-based harmonic removal  (Larsen et al. , 2013) , bandpass filtering and stacking of 40 records. For the Hodoumont experiment, the most efficient processing was obtained using despiking, global reference noise cancellation  (Müller-Petke et al. , 2016) , bandpass filtering and stacking of 16 records. For raw signals in both experiments, only bandpass filtering and stacking were applied. These results suggest that most of the correlation existing between the MCL signals originate from the spike and the harmonic components of the noise, and that appropriately and efficiently removing them will eliminate the risk of correlation within the MCL data errors.
Model plausibility The main question when looking at a physical model of the subsurface which results from the interpretation of a geophysical data set concerns the model coherence and plausibility, that is, how close is it to reality? It is of course not possible to provide a definite answer to this question, because the inverted model is by nature uncertain and results from solving a problem characterized by the non-uniqueness of the solution. In this case different methods have been chosen to try to evaluate the benefit of using the so-called MCL configuration instead of a classical COIL data set, and improvements both in model accuracy and uncertainty reduction have been observed. However, it should be understood that in some situations, the MCL may very well produce results much similar to those obtained with a COIL configuration, and not necessarily superior.
Mostly because the additional benefits from the MCL come from 1) the sensitivity and resolution improvements brought by integrating the CL datasets within the inversion and 2) the "robustness" of the data set due to the merging of different sensitivity distributions. For the first point, the analysis of the resolution matrices in section 3 clearly show that the improvements provided by the MCL dataset may concern different part of the subsurface depending on the noise level. As a rough, first approximation, it seems that with low noise levels, most benefits will occur in the shallow part of the model, whereas for higher noise levels the benefits extend to deeper layers. Hence, depending on the noise level, it is possible that some aquifers be located in a part of the model where no improvement occurs, in which case all uncertainty assessments and synthetic modeling tests will provide similar results, whichever configuration is used.
Nevertheless, note that the MCL configuration still provides the advantage of adaptability depending the objectives of the survey. For example, assuming a given number of pulse moments, one could decide to take advantage of the resolution benefits of the MCL close to the surface to reduce the number of low value pulse moments while conserving the same resolution as with the COIL configuration. Then, increasing the number of high value pulse moments would improve resolution at depth, while keeping the same acquisition time. Second, the possibility of merging and inverting together data sets with different sensitivity distributions provides a more complete illumination of the subsurface, and hence a more robust data set in the sense that if a particular signal associated with one pulse moment value shows a very low S/N ratio compared with the others, it could be removed without a significant loss of sensitivity or, if conserved, its effect on the inversion results would be smoothed thanks to the presence of the other data sets.
This robustness also implies that the MCL configuration probably exhibits some averaging/integrating properties, which result in a model that seems to incorporate different features that could be observed independently in the inverted models obtained by the single COIL or CL data sets (Fig. 10 ). Finally, given the fact that applying a MCL acquisition strategy only requires the additional time corresponding to the layout of the centered loop, and no other additional measurements than a classical acquisition, it can be easily implemented, hence providing additional geophysical information for a minimum additional effort.
CONCLUSIONS Inverting the MCL dataset leads to at least equivalent and generally more accurate models with regard to the real water spatial distribution than using the single COIL data set or the CL data set. For the synthetic cases studied here, the water content values are better determined and the aquifer boundaries are delineated more precisely. For field cases, the resulting model appears to better match our lithological knowledge of the area. It was also shown that using the MCL data set reduces the uncertainties weighing on the inverted models. These improvements are achieved thanks to the conjoint use of data sets characterized by different sensitivity distributions. Maximum improvement is obtained when central receivers have a diameter equal or lower than the transmitting loop diameter, and using two central receivers instead of one ensures adaptability to various noise conditions, although great improvement can still be reached with only one central receiver.
The bootstrap algorithm results are globally equivalent for each case indicating an uncertainty on the water content estimation of about ± 4% in most part of the aquifer models. Yet differences exist between the three situations. First, in the very shallow part of the model the classical COIL configuration shows that the water content at depth " = 0 m is directly 15 %, and the presence of the 2 m thick unsaturated layer is not visible, as if the aquifer was reaching the surface. However, the CL results(Fig 10b)  clearly show this known unsaturated layer, which is also retrieved using the MCL dataset (Fig10c). Then, regarding the aquifer itself, the COIL model shows that the water content oscillates between 0 m and 10 m depth and then progressively decreases between 10 m and 20 m depth. Although oscillations are not unrealistic due to the changing lithology, a progressive water content decrease is not really consistent with the sudden transition at 22 m depth between medium sand and the marl bedrock.
g. Mészáros et al. 2015 Mészáros et al. , 2020a)). Thus, such a search in other Galactic environments provides strong evidence either for or against the uniqueness of the progenitor stars to GCs evolution. This paper is outlined as follows. In Section 2, we present details and information regarding the APOGEE-2 data set and the incremental data used in this work. In Section 3, we describe our sample selection, the adopted stellar parameters, and the methodology employed to determine the elemental abundances. In Section 4, we present the newly identified Si-rich stars. In Section 5, we present the statistical significance of the Jurassic structure. In Section 6, we present details regarding the elemental abundances of the stars in the Jurassic structure. In Section 7, we present a dynamical study of the stars in the Jurassic structure.
The APOGEE H-band Spectroscopic survey The dataset analysed in this work comes primarly from the Apache Point Observatory Galactic Evolution Experiment (APOGEE:  Zasowski et al. 2013; Majewski et al. 2017 ) and its successor APOGEE-2  (Zasowski et al. 2017) , which have collected high-resolution (R ∼22,500) H-band spectra (near-IR, ∼15,145 Å to 16,960 Å, vacuum wavelengths) for almost 430,000 sources in their sixteenth data release (DR16,  Ahumada et al. 2020) , as part of the Sloan Digital Sky Survey IV  (Blanton et al. 2017 ). Here we take advantage of new data taken subsequent to the DR16 release, which were reduced with the same pipeline as the DR16 stars. This new incremental data set provides to the scientific community spectra of more than 680,000 stars; we refer to these data as the incremental APOGEE-2 DR16 plus (hereafter APOGEE-2+).
(2020). We also refer the reader to  Nidever et al. (2015)  for further details regarding the data reduction pipeline for APOGEE2+. The model grids for APOGEE-2+ are based on a complete set of MARCS  (Gustafsson et al. 2008 ) stellar atmospheres, which now extend to effective temperatures as low as 3200 K, and spectral synthesis using the Turbospectrum code  (Plez 2012).
Data Since we are primarily interested in the detection and mapping of Si-rich metal-poor stars, our focus in this work is on giants in the metallicity range between [Fe/H] = -1. 8 and -0. 7. The Si-rich stars were first discovered in  Fernández-Trincado et al. (2019a) , and were hypothesized to belong to a new sub-population of the inner stellar halo. Here, we conduct a large search for such stars in the APOGEE-2+ catalogue. By imposing a lower limit on metallicity, [Fe/H] > -1. 8, we include stars with high-quality spectra and reliable parameters and abundances. The requirement of an upper limit of [Fe/H] < -0. 7 minimizes the presence of stars belonging to the disk system. Thus, we selected a sample of giant stars, adopting conservative cuts on the columns of the APOGEE-2+ catalogue in the following way: (i) S/N > 60 pixel -1.
(2019a)  analyzed in previous data releases. After the internal release of the APOGEE-2+ catalogue, we discovered many more stars belonging to the Si-rich sample, which we report here as part of a larger homogeneous census. We have added these new stars to the sample, derived new atmospheric parameters, and ran our abundance determination pipeline BACCHUS  (Masseron et al. 2016)  with the same setup used in  Fernández-Trincado et al. (2019a). Here, we proceed with a detailed re-analysis of the newly discovered Si-rich stars with the BACCHUS code, as ASPCAP introduce its own set of problems for the effective temperatures and [X/Fe] at low metallicities, [Fe/H]< -0. 7 dex (see, e. g. Fernández-Trincado et al. 2019c,b,a; Nataf et al. 2019; Mészáros et al. 2015 Mészáros et al. , 2020a;; Fernández-Trincado et al.
Stellar Parameters and Abundance Determinations Since the method of deriving atmospheric parameters and abundances is identical to that as described in  Fernández-Trincado et al. (2019a) , we only provide a short overview of it in this paper. As before  (Fernández-Trincado et al. 2016a , 2017 , 2019d,c,b,a) , we use the uncalibrated stellar parameters for T AS PCAP eff (FPARAM_1) and log g AS PCAP (FPARAM_2). First, we made a careful inspection of each H-band spectrum with the BACCHUS code to derive the metallicity, broadening parameters, and chemical abundances, based on a line-by-line approach in the same manner as in  Fernández-Trincado et al. (2019a) , and summarized here for guidance. The BACCHUS code relies on the radiative transfer code Turbospectrum  (Alvarez & Plez 1998; Plez 2012 ) and the MARCS model atmosphere grid  (Gustafsson et al.