dataesr/scientific-paragraphs-categorization huggingface dataset:
dE/dx resolution The other main goal of the HA-TPC is to perform particle identification by measuring the deposited energy per unit length (dE/dx) by charged particles crossing the gas. The TPC particle identification capability will depend on the dE/dx resolution that can be evaluated with the data from this test beam. The dE/dx was measured for horizontal and vertical tracks using the track projection on the pad side. For inclined tracks reconstructed with diagonal clustering the deposited energy was corrected for the track segment length in each cluster. Such correction accounts for the non-linear dependence of the charge with respect to the track length caused by the charge contribution from the neighbouring clusters for short track lengths. This procedure was described in  [22]. In the context of T2K it is particularly important to be able to distinguish electrons and muons.
Since δ varies along the track, an apparent inclination of the track is observed which can be evaluated with φ app : φ app = atan y L -y R X ERAM (11) where X ERAM is the width of the ERAM and y L and y R are the track vertical positions on the Left and Right edges. It follows from Eq. (  10 ) that the apparent inclination due to E×B effect is maximum for ωτ = µB = 1. In our case, where the electron mobility is To study this effect, we simulated the motion of drifting electrons with Garfield++ [35], under the proper electric and magnetic field conditions and the gas mixture used in the detector. For the magnetic field, we use the map based on previous measurements at DESY  [36]. From both data and simulation, we compute the inclination of tracks The E×B effect dependence on the magnetic field is shown in Fig.
Conclusions In this paper we present the performances of the prototype of the HA-TPCs for the T2K Near Detector upgrade obtained during a test beam at DESY performed in 2021. The TPC was instrumented with one of the ERAM detectors that will be installed in the HA-TPCs and the final HA-TPC readout electronics chain. The test beam data allowed spatial and dE/dx resolutions to be determined as a function of the angle of the track with respect to the ERAM plane for all the drift distances of interest for T2K. Spatial resolution better than 800 µm is obtained for all the angles and all the drift distances using a dedicated clustering algorithm which is adapted to the track angle. The dE/dx resolution better than 10% is obtained for all the angles. The data are compared with a simulation of the ERAM response, including the features of the resistive layer.
Acknowledgements The measurements leading to these results have been performed at the  Test Beam Facility at DESY Hamburg (Germany) , a member of the  Helmholtz Association. The authors would like to thank the technical team at the DESY II accelerator and test beam facility for the smooth operation of the test beam and the support during the test beam campaign. We also thank the T2K collaboration for the extensive use of the ND280 software. We acknowledge the support of  CEA  and  CNRS/IN2P3 , France;  DFG, Germany ;  INFN, Italy ;  National Science Centre (NCN)  and  Ministry of Science and Higher Education  (Grant No. DIR/WK/2017/05 ), Poland; the  Spanish Ministerio de Economía y Competitividad (SEIDI -MINECO)  under Grant No. PID2019-107564GB-I00  ( IFAE, Spain). IFAE is partially funded by the  CERCA program  of the  Generalitat de Catalunya.
In addition, the participation of individual researchers and institutions has been further supported by  H2020  Grant No. RISE-GA822070-JENNIFER2 2020 , MSCA-COFUND-2016 No. 754496 ,  ANR-19-CE31-0001 , RFBR grants # 19-32-90100 , the  Secretariat for Universities and Research of the Ministry of Business and Knowledge of the Government of Catalonia  and the  European Social Fund  ( 2022FI B 00336 ) and from the  program Plan de Doctora-.
Therefore, the accurate estimation of radial diffusion coefficients (D LL ) is crucial for detailed radiation belt modeling. In recent years several semi-empirical (SE) models have been developed for the estimation of radial diffusion coefficients which predominantly rely on parameterizations of the Kp index. However, several studies have suggested that the estimations derived from such models can have large deviations from actual (measurement derived) D LL values. In this work we have used the extensive D LL database created in the framework of the Horizon 2020 SafeSpace project which spans 9 years of hourly D LL calculations to develop a model which uses solely solar wind parameters for the derivation of D LL values. The Electric and MagnEtic RAdiaL Diffusion (EMERALD) model is able to derive simultaneously the magnetic and electric components (  D   and  D   , respectively) of the radial diffusion coefficient, and furthermore, provide realistic confidence levels on their estimation, which allows the transition from a deterministic paradigm to a robust probabilistic one.
Evaluations on the performance of the EMERALD model are shown by comparing its outputs to the D LL data, and examining the reproduction of various D LL characteristics. Finally, comparisons with widely used SE models are shown and discussed. Plain Language Summary The Earth's outer radiation belt consists of high energy electrons which are characterized by intense variability during solar eruptions and geomagnetic storms. These high energy electrons can cause moderate or severe damage to satellite electronics, therefore the accurate forecasting of their variability is of outmost importance. Radial diffusion, which is quantified by the radial diffusion coefficients, has been established as one of the key mechanisms for the prediction of the electron variability. In this work, we present a new machine learning model for the estimation of the radial diffusion coefficients.
To the best of our knowledge this has not been demonstrated before and it is a novel approach offering improved performance and capabilities. Regarding the operational aspect we aimed in developing a model which can be used with widely available historical SW parameters (hindcast), with real-time SW measurements (nowcast), as well as in conjunction with models which can forecast these SW variables with prediction horizons of up to a few days, see for example,  Samara et al. (2021)  and discussion therein. The core of the model consists of an ensemble of probabilistic NNs trained with the D LL dataset which was created in the framework of the Horizon 2020 SafeSpace project. Using the SW parameters the model provides expected (mean) values for both the electric and magnetic component of the D LL as well as uncertainties on the provided mean values themselves, in the form of standard deviations.
Data In this study we make use of the extended SafeSpace radial diffusion coefficients database  (Katsavrias et al. , 2022) , which is publicly available at https://synergasia. uoa. gr/modules/document/?course=PHYS120 and contains ∼79,000 hourly D LL values that span 9 years  (2011) (2012) (2013) (2014) (2015) (2016) (2017) (2018) (2019). These D LL have been calculated directly from in-situ magnetic and electric field measurements, exploiting the fluxgate magnetometers  (Auster et al. , 2008)  as well as the EFI instruments  (Bonnell et al. , 2008)   10. 1029/2022SW003283 3 of 17 been calculated separately, based on the theoretical approach by  Fei et al. (2006). We note that even though Fei's approach can lead to an underestimation of the total diffusion coefficient by a factor of two, due to the assumption of electric and magnetic field independence  (Lejosne, 2019) , it is still more widely used due to the fact that it is very difficult to separate the total measured electric field from single point measurements in space into its convective and inductive components  (Lejosne & Kollmann, 2020).
Furthermore, it has been shown that this discrepancy by a factor of 2 is minor relative to the large variability in the observed values  (Sandhu et al. , 2021). Here we use hourly measurements each of which contains data for L* values in the [3-7] range divided into 40 bins with dL* = 0. 1. As centroids we use the mean of the bin values, 3. 05, 3. 15 etc. The total D LL can be simply calculated as the sum of the two components as shown in Equation  2. 𝐷𝐷𝐿𝐿𝐿𝐿 = 𝐷𝐷 𝐵𝐵 𝐿𝐿𝐿𝐿 + 𝐷𝐷 𝐸𝐸 𝐿𝐿𝐿𝐿 (2) Moreover,  D   has been calculated for 36 values of the first adiabatic invariant (μ) in the [300-20,000] MeV/ Gauss range, corresponding to relativistic electrons with E > 400 keV at the aforementioned L* range (see also Figure  S1 ). This dataset is complemented with 1-hr resolution historical measurements of the SW speed (Vsw) and density (Nsw), the magnitude of the IMF and the Kp index (for the estimation of the D LL from semi-empirical [SE] models) as provided by the OMNIWeb service of the Space Physics Data Facility at the Goddard Space Flight Center (http://omniweb.
gsfc. nasa. gov/). For the calculation of the magnetic coordinates we have used the International Radiation Belt Environment Modeling (IRBEM) library  (Bourdarie & O'Brien, 2009)  and the Olson Pfitzer quiet external magnetospheric field model (OP77). The D LL and SW parameters from the SafeSpace database are used for the training of the NNs with the latter being used to define inputs and the former the outputs. We pre-process the D LL values by applying a moving mean window containing the current hour and the previous 23 hr. This is done in order to mitigate the uncertainties introduced by the partial azimuthal coverage in the D LL data derivation (see also Section 3 in  Katsavrias et al. , 2022)  as well as fill the gaps in L* which are inherently present due to the THEMIS spacecraft orbit.
Extension of Outputs in the μ Range As discussed the NNs are trained to output  D   values for μ = 1,000 MeV/G which is the geometric mean of the [300-20,000] MeV/G range of the dataset. In order to extend the  D   output of the NNs to the whole μ range of [300-20,000] MeV/G a simple but effective regression scheme is used here. For each L*, normalized  D   spectra are calculated by dividing the  D   dataset spectra with their respective values at μ = 1,000 MeV/G. As seen in Figure  2  the normalized spectra are very consistent for a given L* showing minimal divergences at the two ends of the μ range, effectively being all constrained within very narrow limits. We note this is fully expected as the  D   in the dataset is calculated as a function of μ, for details see the discussion in  Katsavrias et al.
This is a typical approach for evaluating a trained model on the entirety of a dataset without the need for additional reference data, see for example, Aminalragia-Giamini et al. (  2021 ) and is detailed in the steps below. We divide here the data in nine calendar years  (2011, 2012, …, 2019) , and for each year we train the model with the other 8 years and then test it with the one left out. We iterate this process over the 9 years of the dataset and train a different NN ensemble in each iteration which then provides D LL outputs for the left-out year. 1. The algorithm defines a specific calendar year and isolates the corresponding hourly D LL as well as the input parameters. 2. The training of the NNs is performed with the rest of the dataset. For example, if we consider the year 2011, the training will be made using the D LL values and SW parameters from the 2012-2019 time period.
3. The now trained model from the previous step is used to estimate the D LL values of the excluded year using the also excluded input parameters. 4. The process repeats iteratively for all the available years in the dataset. This way, in each iteration we test our model with data it has not been trained with and after all iterations we have derived outputs for the entirety of the dataset. Crucially, this approach ensures an objective and fair evaluation of the model performance. Figure  3  shows density plots for the electric and magnetic component at 1,000 MeV/G, as well as the total D LL , with comparisons of the data and the medians derived from the models outputs at all L* bins. For the density plots we have used 200 logarithmic bins, equality lines are in white, dark gray lines denote a factor of 3, and black lines a factor of 10.
The density plots also show metrics from the comparisons, where R 3 is the percentage of model values being within a factor of 3 of the dataset values, R 10 is the same for a factor of 10, and RMSE log10 is the root mean square error (RMSE) calculated for the log-base-10 values. The results show that the D LL and its components are estimated from the SW with a high degree of accuracy. In all three cases more than 50% of the values are within a factor of 3 while more than ∼88%, and up to ∼98%, of the values are within a factor of 10 the data. The highest densities appear along the equality lines with clear linear/log-linear trends seen across several orders of magnitude. It is noteworthy that the two D LL components are not equally well estimated, with.
For both     and     at 1,000 MeV/G, and total D LL , it can be seen that the model performs optimally for L* values roughly in the [4, 6] range, that is, for the core of the outer belt. This is primarily attributed to the correlation of the D LL components with the SW parameters we use as inputs, where the highest correlations for both D LL components occur roughly in the same [4, 6] L* range  (Katsavrias et al. , 2022). Therefore the peak performance of the model is indeed expected to be found in this range. An additional important reason is that the amount of available data at L* values lower than ∼4 is reduced in the dataset (see also Figure  S2 ) resulting in the model having less data in this region to be trained with. Data at lower L* values were originally removed from the dataset due to the effects of magnetic field gradients which make an accurate derivation of D LL coefficients very difficult (see also Section 2.
Comparisons of Total D LL With Semi-Empirical Models In this section we perform comparisons of the total D LL from the dataset with the outputs of the Electric and MagnEtic RAdiaL Diffusion (EMERALD) model and two established SE models, namely the Brautigam & Albert (B&A) model  (Brautigam & Albert, 2000) , and the Ozeke model  (Ozeke et al. , 2014). The parameterizations of AMINALRAGIA-GIAMINI ET AL. 10. 1029/2022SW003283 10 of 17 the models are seen in Equations 5-7 below. We have applied the previously discussed 24 hr moving mean on the SE D LL values so as the comparisons will be fair to the SE models. [] = 10 (0. 506⋅-9. 325) ⋅  10 (5)    [] = 6. 62 ⋅ 10 -13 ⋅ 10 (-0. 0327⋅ 2 +0. 625⋅-0. 0108⋅ 2 +0. 499⋅) ⋅  8 (6) 𝐷𝐷 𝐸𝐸 𝐿𝐿𝐿𝐿 [𝑂𝑂𝑂𝑂] = 2. 16 ⋅ 10 -8 ⋅ 10 (0. 217⋅𝐿𝐿+0. 461⋅𝐾𝐾𝐾𝐾) ⋅ 𝐿𝐿 6 (7) We present results for several values of μ in order to cover a wide range.
We note that as the NN ensemble outputs the     at 1,000 MeV/G these results at different μ values include the     regression scheme discussed previously. The comparisons are made for the whole dataset as well as for a time period of three consecutive geomagnetic storms which occurred during December 2013 and resulted in some of the highest D LL values of our dataset. Additionally we have examined a quiet period from December of 2012 to January of 2013. The quiet period was selected due to the absence of significant geomagnetic activity as well as both chorus and ULF wave activity  (Jaynes et al. , 2014). These two time periods are examined complementarily to the whole dataset comparisons in order to illustrate in more detail the model performance in shorter time scales.
Comparisons for All Values of the Dataset Figure  7  shows density cross-plots with comparisons at three μ values, 500, 3,000, and 10,000 MeV/G, of total D LL with the model's median output and D LL values calculated from the SE models. We note that as the latter ones do not include a μ dependence only the data they are compared with change. There are several observations to be made here. The first one is that similar to what was shown at Figure  3  for 1,000 MeV/G our model shows a consistent linear/log-linear relationship with the data for all μ values and across several orders of magnitude capturing the full L* range. Its performance, as quantified by the R 3 , R 10 , and RMSE metrics, is only slightly lower for 500 MeV/G than for 1,000 MeV/G whereas it improves for higher μ values as the magnetic component becomes more dominant in the total D LL.
We note there is a systematic overestimation at the lower extreme of the distribution at very low D LL values with the formation of a "background tail", for example, below 10 -3 days -1 at 3,000 MeV/G. This is primarily related to low L* values, which also have lower D LL values, and occurs for reasons previously discussed in Section 4. 1. 1. Apart from this, the overall model's performance remains consistently good for all cases. The high density areas are always clustered along the equality lines and the majority of values is within a factor of 3 of the data with the remaining cases being again predominantly within a factor of 10 while also achieving good RMSE scores. However, this is not the case with the D LL values from the SE models. As there is no μ dependence these models cannot capture this dependence of the D LL and show increasingly large deviations as μ also increases quantified in the shown metrics.
Furthermore there are clear trends which deviate from the ideal linear/log-linear relationship with the data; apart from the absolute magnitude of D LL , the SE models systematically underestimate the low and high values relative to values close to the mean. This results in a non-linear relationship with the data and a characteristic curve seen here. These findings on the SE models are in agreement with  Katsavrias et al. (2022)  and can be explained by the fact that these Kp-driven formulations have been derived from analytical fits to long-term averages. Due to this, the divergence of the lower and upper ends of the D LL distribution cannot be well taken into account and such fits will be dominated by the large majority of values that are closer to the mean or median. However, our model does not use such long-term averages and is able to capture optimally the behavior of the D LL using the SW parameters as input.
15%) of the estimations are within a factor of 3 of the data with the remaining cases being again predominantly within a factor of 10 (panel f). On the other hand, the two SE models exhibit very similar behavior between them, differing only by a small multiplying factor. Their behavior consistently underestimates the high D LL values on average by a factor of 10 or more (panel g). Furthermore, the SE models fail to capture the low D LL values, exhibiting a strong flattening behavior, which also contributes to the lower R 3 and higher RMSE values shown in Table  1. This comparison is in agreement with the results of  Katsavrias et al. (2022)  who illustrated, in the simulations of the March 2015 time period that the SafeSpace D LL produced a more realistic radial transport of 500 keV electrons than the one produced by the SE model of Boscher  Concerning the 5,000 MeV/G at L* = 4.
On the other hand, the two SE models fail to capture both the D LL dynamics and magnitude (panel g) estimating values in a relatively narrow range and exhibiting a pronounced flattening (panel h). This difference is also illustrated in the scores shown in Table  2 , where the SE models exhibit significantly higher RMSE values, compared to EMERALD, as well as lower R 3 and R 10 values. Concerning the 5,000 MeV/G at L* = 4. 45, here all three models fail to capture the magnitude and the dynamic evolution of the D LL values. The only exception is that EMERALD somewhat manages to reproduce the D LL evolution on the final week of the data (6-13 January). The SE models again produce D LL in a narrow range, following the very small variation of the Kp index (panel d), showing a mostly flat cross-plot (panel l), while they completely fail to capture the dynamics of the D LL values, especially at the second half (after 1 January) of the examined time period.
Their notably better scores (R 3 ∼ 88% and RMSE ∼ 0. 32 as shown in Table  2 ) stem mostly from the fact that their values are closer to the overall mean of the data during this period for this combination of μ and L*. The overestimation of the 5,000 MeV/G D LL values in this very quiet period, especially for the first 2 weeks, is in agreement with the results of Figure  7  and a fair representation of our model's performance is part of the reason we have made these comparisons. The 5,000 MeV/G D LL values in this period hover around 10 -3 days -1 which is at the lowest end of the distribution where the model tends to overestimate. We note however, that even here all the values are at most within a factor of 10. The above discussed results, combined with the results shown in Figure  7  for the whole dataset, show that EMER-ALD outperforms the SE models in a wide μ and L* range, and emphasize the importance of modeling the D LL μ dependence.
Conclusions In this work, we have used the SafeSpace database of radial diffusion coefficients, spanning 9 years (2011-2019), and we have developed EMERALD, a NN based model for the estimation of the D LL in the outer radiation belt, using solely SW parameters (Vsw, Nsw, IMF) and L* as an input. The approach we have employed is a significant departure from the common Kp-driven paradigm for the estimation of D LL. Rather than using as driver of the model an index which is a proxy of the effects of SW on the global magnetospheric activity, we have directly  connected SW characteristics to the evolution of the radial diffusion process. The use of these specific SW parameters is based on the correlation analysis by  Katsavrias et al. (2022). The latter authors discussed the correlation of the aforementioned parameters with the D LL components and linked them with the two main physical mechanisms that enhance the ULF wave power, that is, the Kelvin-Helmholtz instabilities and the SW pressure pulses.
Data Availability Statement The D LL dataset used for the training of EMERALD can be found in https://synergasia. uoa. gr/modules/document/index. php?course=PHYS120. The authors acknowledge the THEMIS/FGM and THEMIS/EFI teams for the use of the corresponding datasets which can be found online in http://themis. ssl. berkeley. edu/data_products/ index. php, the developers of the International Radiation Belt Environment Modeling (IRBEM) library and the NASA/GSFC's Space Physics Data Facility's OMNIWeb service in https://spdf. gsfc. nasa. gov/pub/data/omni/ high_res_omni/.
Ozeke et al. (2014)2022)e relationship of the two components is not broadly investigated in the literature with only a few recent works reporting on quantitative comparisons, such asSandhu et al. (2021)andKatsavrias et al. (2022). Moreover most established models directly estimate the total D LL making investigation of this relationship impossible in these cases. The modeling approaches ofAli et al. (2016)andOzeke et al. (2014)do estimate separately both 𝐴𝐴 𝐴𝐴 𝐸𝐸 𝐿𝐿𝐿𝐿 and 𝐴𝐴 𝐸𝐸 𝐿𝐿𝐿𝐿 , and 𝐴𝐴 𝐴𝐴 𝐴𝐴 𝐵𝐵 𝐿𝐿𝐿𝐿 as existing in the dataset. 𝐴𝐴 𝐴𝐴 𝐵𝐵 𝐿𝐿𝐿𝐿 allows us to investigate here whether the model 𝐴𝐴 𝐵𝐵 𝐴𝐴 𝐴𝐴 𝐸𝐸 𝐿𝐿𝐿𝐿 but, including these works, we cannot find in the literature any such investigations. Therefore, to the best of our knowl-outputs reproduces any relationship of 𝐴𝐴 𝐿𝐿𝐿𝐿 and edge this is the first time the 𝐴𝐴 𝐴𝐴 𝐵𝐵 𝐴𝐴 𝐴𝐴 𝐸𝐸 𝐿𝐿𝐿𝐿 relationship is demonstrated to be successfully modeled.
Statutory reasoning is the task of determining whether a given law -a part of a statute -applies to a given legal case. Previous work has shown that structured, logical representations of laws and cases can be leveraged to solve statutory reasoning, including on the StAtutory Reasoning Assessment dataset (SARA), but rely on costly human translation into structured representations. Here, we investigate a form of legal information extraction atop the SARA cases, illustrating how the task can be done with high performance. Further, we show how the performance of downstream symbolic reasoning directly correlates with the quality of the information extraction.