dataesr/scientific-paragraphs-categorization huggingface dataset:
This is indicated by a comma-separated list for the kinematic quantities used in the corresponding analysis. In addition, the year of the data release and the number of bins (N Bins ) for each dataset are specified. The details on the analysis requirements for MiniBooNE, T2K ND280, MINERνA and MicroBooNE datasets as well as comparisons of the G18_10_02_11b predictions to the data are presented in Appendix B. The main observations from Appendix B are summarized in Sec. II B. For completeness, Table  II  includes measurements from SciBooNE and NOMAD which are not discussed further in this paper as their analysis strategy is limited with respect to the other measurements discussed in this work. There is a now large body of CC0π data in the literature. This work focuses on the tuning of double-differential fluxintegrated CC0π and CC0p0π cross-section measurements on carbon from MiniBooNE, T2K ND280 and MINERνA.
This is sufficient for an initial study. Additional singleand triple-differential CCNp0π datasets are not considered in the first iteration of this work; these will be included in future iterations. However, some comparisons are given in this paper. It is important to note the differences between the measurements considered in this work. These are highlighted in Appendix B. A significant difference is the treatment of uncertainties. Bin-to-bin correlation are not reported by MiniBooNE for many of their cross-section measurements (including the data used in this work). In addition, flux uncertainty is given as a single normalization uncertainty of 10. 7% and 17. 2% for neutrino and antineutrino measurements on carbon respectively. These treatments involve approximations from modern treatments and do not fully incorporate MiniBooNE uncertainties  [39].
B. Dataset overview and initial considerations The need for a tuning exercise for GENIE is clear. A few comparisons of G18_10a_02_11b against the available nuclear data are shown here. The remaining plots are in Appendix A. We observe in Figs. 2-4 that CC0π and CC0p0π datasets are under-predicted, whilst the CCNp0π datasets are in quite good agreement with the G18_10a_02_11b predictions. As a consequence, a coherent global tune of CC0π and CCNp0π datasets is not possible. Hence, the analysis is mostly focused on CC0π and CC0p0π datasets. Nonetheless, understanding the tension is essential for future tuning efforts. This tension is further explored in this paper. MiniBooNE CC0π (Fig. 2 ) and T2K ND280 CC0p0π data are both underpredicted at muon backward angles, where the contribution to the prediction is mostly from CCQEL events.
A. Construction of the GENIE prediction In order to build the prediction associated with each dataset specified in Sec. II, we generate ν μ and νμ CC events for the experiment target using the neutrino fluxes from Fig. 1. In this work, the events are generated with the G18_10a_02_11b tune  [5]. To compute the prediction associated with the ith dataset, we generate N TOT i events. Events that do not satisfy the corresponding selection criteria specified in Sec. II are rejected. The number of accepted events in the jth bin is N i j ðθÞ. θ is the vector of tunable parameters specified in Table  III. We build the corresponding n-differential flux-integrated cross-section prediction for a given set of observables, O, as ∂ n σ th ðθÞ ∂O n i j ¼ N i j ðθÞ Φ i N TOT i ΔO i j × Z dE ν dϕ i dE ν X T i R T i σ T i ðE ν ; θÞ; where Φ i is the integrated flux for the ith dataset, ΔO i k corresponds to the jth n-dimensional bin volume for the quantities used in the differential cross-section calculation, and dϕ=dE ν is the expected flux at a given neutrino energy.
B. Avoiding the Peele's pertinent puzzle The bin-to-bin covariance matrix provided by each experiment is considered in the evaluation of the χ 2. The T2K ND280, MicroBooNE and MINERνA datasets have highly correlated bin-to-bin covariance matrices. Previous attempts to fit neutrino-nucleus data using the full covariance matrices result in a significant reduction of the cross section  [10, 51, 52]. These results are not surprising in highly-correlated bins (ρ > 60%) in the Gaussian approximation  [53]. This is known as Peele's pertinent puzzle (PPP)  [53, 54]. To avoid PPP, we change our variables in order to reduce the correlation for the ith dataset using the following prescription, Z i j ≡ 8 > > < > > : P k D i k j ¼ 0; D i j P k D i k 0 < j < N i : D i j corresponds to the ith dataset mean value at the jth bin.
The jth and kth indices run over the number of bins associated with the ith dataset. This is known as the Norm-Shape (NS) transformation. After the NS transformation, the integral is moved into the first bin of the ith dataset, whilst the rest describes the shape distribution. This transformation is applied to both data and predictions. The bin-to-bin covariance associated with the ith dataset, Σ D ðDÞ i jk , transforms as follows: Σ NS ðZÞ i jk ≡ dZ dD Σ D ðDÞ dZ dD T i jk ; where dZ dD i ja ¼ 8 < : 1 j ¼ 0 δ ja ð P k D i k Þ-D i j ð P k D i k Þ 2 0 < j < N i : After the NS transformation the relative uncertainties are constant when the normalization changes. The same transformation is applied to the prediction mean values and covariance. Before the NS transformation, the prediction covariance only has diagonal elements.
E. Evaluation of the χ 2 The complete form for our χ 2 is χ 2 ðθÞ ¼ X N i X N i j;k ffiffiffiffiffi w i j q Δ Ỹi j ðθÞðΣ i NS;jk Þ -1 Δ Ỹi k ðθÞ ffiffiffiffiffi ffi w i k q þ ðθ -θ 0 Þ T Σ -1 θ ðθ -θ 0 Þ; ð1Þ being i the index that runs over the N datasets considered in the fit. Δ Ỹi j is the difference between the NS parametrization prediction and the ith dataset at the jth bin, Δ Ỹi j ðθÞ ≡ Ỹi j ðθÞ -Z i j. The ω ij is the weight applied to jth bin from the ith dataset. In this work, weights are used to include or exclude data from the analysis. In other words, they are either 1 or 0. The prediction errors, δ Ỹi j ðθÞ, are added in quadrature to Σ NS. The second term takes care of correlated priors in our fit. θ 0 and Σ θ are the central values vector and the covariance matrix of the priors for the M QEL A S RES (b) M QEL A 1.
Here G is a capital letter that stands for GENIE, highlighting the authorship of the tunes. xx is a number assigned to each experiment, i. e. , MiniBooNE  (10) , T2K ND280  (20)  or MINERνA  (30). When using antineutrino datasets, xx is increased by one unit. For CCNp0π datasets, xx is increased by five units. Note that this is different from the standard naming scheme used for the tunes released through the GENIE platform. The standard naming convention from Ref. [5]  will be used if one or more of the tunes produced in this work or future iterations is prepared for release in GENIE. In total, six partial tunes are performed: three tunes on neutrino CC0π data, two tunes using antineutrino CC0π data and one tune using ν μ CCNp0π data. The tunes on CC0π data aim to explore avenues for improving the agreement between GENIE and data, consolidate the main elements of the GENIE CC0π tuning methodology and provide a common ground for the discussion of tensions.
The tune on CCNp0π data aims to highlight tensions between CC0π and CCNp0π datasets. All of the tunes presented in this work consider carbon datasets only. Joint fits to all available data will be performed at a future iteration of this work, aiming to produce the tunes that will be publicly released through the GENIE platform. In all CC0π tunes, the analyses are carried out using double-differential CC0π data as a function of muon kinematics. Preference is given to datasets that do not require a minimum number of protons above detection threshold in the final state. Whenever CC0π datasets are not available for a particular experiment, the tune is performed using CC0p0π datasets instead. G18_10a_02_11b is the starting point for all these tunes and provides the nominal predictions. The corresponding names assigned to each tune prepared for the purposes of this paper are the following: [G10a Tune]: GENIE tune to MiniBooNE ν μ CC0π data  [25].
Each Nominal ¼ 626=144 DoF. After the tune, χ 2 Nominal ¼ 151=144 DoF. This is mainly a consequence of an improvement in the overall normalization for each partial tune. All carbon tunes show similar trends; whilst the tunes are in good agreement with the priors on M QEL A and S RES , the other parameters differ from the nominal parameter values. There is also a clear preference for QEL with RPA corrections. In addition, the tunes prefer a higher QEL, i. e. , ω RPA þ ω RPA > 1, and 2p2h cross section. Finally, the FIG. 12. Comparison of the G18_10a_02_11b and G10a tunes against MiniBooNE ν μ CC0π double differential data  [25]. The comparisons are restricted to the 0. 2 < T μ < 1. 0 GeV phase space. The predictions are computed using the parameters specified in Table  V. The total χ 2 associated with this dataset before and after the tune are reported in Table  VI.
FIG. 13. Comparison of the G18_10a_02_11b and G11a tunes against MiniBooNE νμ CC0π double-differential data  [26]. The comparisons are restricted to the 0. 2 < T μ < 1. 0 GeV phase space. The predictions are computed using the parameters specified in Table  V. The total χ 2 associated with this dataset before and after the tune are reported in Table  VI. different tunes suggest an underlying energy dependence on the 2p2h cross section strength and shape; the G10a, G11a, and G20a tunes enhance (suppress) the Valencia 2p2h cross section at the nucleon (Δ) region. Alternatively, the G30a and G31a tunes enhance the cross section at the nucleon and Δ region, with S 2p2h Δ > S 2p2h N. A hint of an underlying energy dependence was also observed in Ref. [56]. The enhancement of the QEL cross section is crucial for the description of MiniBooNE CC0π data at cos θ μ < 0.
FIG. 14. Comparison of the G18_10a_02_11b and G20a Tune against T2K ND280 ν μ CC0p0π double differential data  [27]. The comparisons are restricted to the -1. 0 < cos θ μ < 0. 94 phase space. The predictions are computed using the parameters specified in Table  V. The total χ 2 associated with this dataset before and after the tune are reported in Table  VI. FIG. 15. Comparison of the G18_10a_02_11b and G30a tunes against MINERνA ν μ CC0π double-differential data  [28]. The comparisons are restricted to the 0. 25 < p T < 0. 85 GeV=c phase space. The predictions are computed using the parameters specified in Table  V. The total χ 2 associated with this dataset before and after the tune are reported in Table  VI. Particularly, the G10a and G11a tunes suggest an increase of the QEL cross section of about 20%.
The total χ 2 associated with this dataset before (after) the tune reported in Table  VI. TABLE VI. Summary of χ 2 values associated the CC0π datasets specified in each row. The χ 2 values are calculated using the NS method for seven different GENIE predictions: G18_10a_02_11b, G10a, G11a, G20a, G30a, G31a, and G35a. The values highlighted in bold correspond to the best-fit χ 2 for the partial tune predictions.
B. Tension between CC0π partial tunes Tensions between datasets can be explored by comparing the different tunes. Figure  20  compares the G10a, G20a and G30a predictions against MiniBooNE ν μ CC0π data. Even though the normalization of the three tunes is similar, differences in the predicted cross-section shape exist. The G10a tune is the only one out of the three that successfully describes the shape of the data, as it can be seen in Fig. 20  (left). The other tunes underestimate the cross section at backward muon angles. In addition, the G30a Tune overpredicts the cross section at forward angles as a consequence of the enhancement of the 2p2h cross section at the Δ region. All tunes overestimate the cross section at forward muon angles and low muon kinetic energies, as demonstrated in Fig.
20 (right). The G31a tune is in clear tension with all the rest, including partial tunes performed with MINERνA neutrino FIG. 17. Comparison of the G18_10a_02_11b and G30a tunes against MINERνA ν μ CC0p0π single-differential data  [28]. The predictions are computed using the parameters specified in Table  V. [26, 28]. The predictions are computed using the parameters specified in Table  V. data. In comparison with the rest of the tunes, the G31a tune prefers higher QEL and 2p2h cross sections. This leads to the over-prediction of all the other datasets. The comparison of G30a and G31a against MINERνA and MiniBooNE ν μ CC0π data are shown in Fig. 21. The effect of this tension on the χ 2 is reported in Table  VI. The tension between the G31a tune and the rest can have different origins. A possibility is that the model does not fully characterize the difference between neutrino and antineutrino fluxes.
This is investigated comparing the G20a tune to the T2K WAGASCI antineutrino data. Both the T2K WAGASCI and T2K ND280 analysis explore the νμ CC0p0π topology, but these are exposed to different neutrino fluxes (see Appendix B 2). The impact of the G20a tune to these predictions is shown in Fig. 22. It is observed that the G20a tune has little impact on the T2K WAGASCI predictions. This indicates than an additional neutrino/antineutrino modeling uncertainty should be considered in a global tune of neutrino and antineutrino data. Another possible source of uncertainty is the different topology definition for MINERνA's νμ dataset, with FIG. 20. Comparison of the G18_10a_02_11b, G10a, G20a and G30a tunes against MiniBooNE ν μ CC0p0π integrated crosssection data  [25]. The predictions are computed using the parameters specified in Table  V.
C. Tensions between ν μ CC0π and ν μ CCNp0π datasets T2K ND280, MINERνA and MicroBooNE are the only experiments that released cross-section measurements for different proton multiplicities. As discussed in Sec. II B, CC0π and CC0p0π datasets are underpredicted, whilst the CCNp0π datasets are slightly overpredicted by the nominal G18_10a_02_11b prediction. This modeling limitation is also observed in Refs. [27, 56, 58]. After the partial tunes using ν μ CC0π data, the agreement with CCNp0π data deteriorates. This is highlighted in Table  VII , which summarizes the postfit χ 2 values associated with CCNp0π datasets. In all cases, the χ 2 computed with each partial tune prediction increases with respect to the χ 2 computed with the nominal G18_10a_02_11b tune. All G10a, G20a and G30a tunes overpredict ν μ CCNp0π data.
In addition, the tune suppresses the Valencia cross-section peak prediction at W ¼ M N and shifts the Δ peak to W > M Δ. This result contradicts the rest of the partial tunes presented in this article, reinforcing the fact that there is a strong tension between CC0π and CCNp0π datasets. The summary of χ 2 is reported in Tables  VI  and VII. An important observation is that the G35a tune also improves the agreement with MicroBooNE CCNp0π data, suggesting that a possible A dependency on the parameters does not play an important role. The tension between CC0π and CCNp0π datasets needs to be resolved before attempting a global tune of CC0π data that can describe all data available to date. Some modeling aspects that may contribute to this tension are investigated in Sec. VI.
VI. INVESTIGATION OF TENSIONS BETWEEN CC0π AND CCNP0π DATASETS This section offers an insight into possible modeling implementations that may contribute to the tension between TABLE VII. Summary of χ 2 values associated the CCNp0π datasets specified in each row. The χ 2 values are calculated using the NS method for seven different tunes: G18_10a_02_11b, G10a, G11a, G20a, G30a, and G31a. The values highlighted in bold correspond to the best-fit χ 2 G35a for the partial tune using the specified dataset. CC0π and CCNp0π datasets and explores avenues of accommodating both within future joint tunes. None of the uncertainties described in this section has a big impact on CC0π datasets.
This analysis is based on the G18_10a_02_11b CMC, which was previously tuned against free nucleon data  [5]. This tune confronted a number of new challenges with respect to previous GENIE free nucleon tuning efforts. This led to important changes in the GENIE tuning software. In particular, modern nuclear data provide the full correlation between the data release bins due to systematic uncertainties. In order to incorporate this information in the analysis, the definition of the χ 2 is modified to avoid the Peele's pertinent puzzle, which leads to nonphysical normalization factors. This analysis considers a total of seven parameters which attempt to capture the basic features of the component interactions-QEL, 2p2h, and RES as implemented in the G18_10a_02_11b model set. Some of the parameters used in this work affect the simulation of neutrino interactions on free nucleon.
For this reason, no requirements based on the recoil proton are considered in the MiniBooNE analyses. The analysis considers further model-dependent cuts to correct for backgrounds and extract the CCQEL crosssection from the CC0π sample. In the original publication, these are referred to as irreducible backgrounds. An example of irreducible background is CC1π events that were not removed by the cut on the pion subevent topology or pion production events in which the pion is absorbed. This is corrected using a MC simulation tuned to ν μ CC1π MiniBooNE data. Information on ν μ CC1π þ sample is used to characterize this background and correct for single-pion events which were not removed by the CC0π selection criteria in the neutrino and antineutrino analyses. This procedure is one of the main limitations of this dataset as it incorporates strong biases in the reported measurement.
The contribution to the cross-section measurement from irreducible backgrounds is also reported, allowing the comparison against CC0π data. The quality of the MiniBooNE CC0π data release is poor in comparison with the rest. The MiniBooNE Collaboration provided measurements in bins of T μ and cos θ μ , but did not provide the bin-to-bin covariances for either of the two measurements. Instead, they quoted a normalization systematic uncertainty of ∼10. 7% (17. 2%) for the neutrino (antineutrino) measurement. As suggested by Ref. [25] , this error is added as a systematic in our database, effectively including a correlation between the bins. In Figs. 2 and 33, the flux-integrated double differential ν μ and νμ CC0π cross-section data as a function of p μ and T μ are compared against GENIE. The main observation is that the GENIE tune underpredicts the data.
This disagreement in the overall normalization is also observed in Fig. 5 , which compares GENIE against the cross-section as a function of the proton multiplicity. This observation conflicts with ν μ CC1p0π data, which is not underpredicted. There are some outstanding differences between the GENIE predictions for CC0p0π and CC1p0π data. Whilst the total contribution from 2p2h events is similar, the main 2p2h contribution comes from 2p2h events with W > W Dip. In addition, the fraction from RES events is higher with respect to the CC0p0π one. Fig. 35  provides comparisons against ν μ CCNp0π data as a function of the STKI variables, concluding that non-QEL interactions are essential to describe this data within regions of high-transverse kinematic imbalance. Antineutrino CC0π cross-section measurements are also available: νμ and νμ þ ν μ CC0π on water  [35]  and hydrocarbon at T2K ND280  [36] , and νμ and νμ þ ν μ CC0p0π at the T2K WAGASCI, INGRID, and Proton Module detectors  [37].
Summary of CC0π analyses of ν μ and νμ interactions on nuclei. For each analysis, information on the neutrino flux mean energy, target type and event topology is provided. The kinematic quantity column specifies the list of kinematic quantities used in the cross-section measurement. Integrated cross-section measurements are denoted with a "-". All kinematic quantities are defined in Appendix. A. The last column specifies whether the dataset is considered in the analysis. Δp p , cos θ μ , p μ 49 jΔp p j, cos θ μ , p μ 49 Δθ p , cos θ μ , p μ 35.
tune's best-fit parameter values and the χ 2 calculated with the Professor parametrization at the best-fit point are summarized in Table V. The nominal and best-fit predictions are shown in Figs. 12-18. Table VI provides the χ 2 values computed with each tune's GENIE prediction and corresponding dataset. In this case, the χ 2 values are calculated with the NS transformation with the GENIE predictions. Notice that the χ 2 values from Table VI are different to the ones provided in Table V. This is a consequence of the Professor parametrization not being exact.
ACKNOWLEDGMENTS We would like to thank  Andy Buckley  ( University of Glasgow, United Kingdom ) and  Holger Schultz  ( Institute of Particle Physics Phenomenology, University of Durham, United Kingdom ) for their support interfacing the Professor tool with the software products that underpin the GENIE global analyses. We would like to thank the  CC-IN2P3  Computing Center, as well as the  Particle Physics Department at Rutherford Appleton Laboratory  for providing computing resources and for their support. This work, as well as the ongoing development of several other GENIE physics tunes was enabled through a PhD studentship funded by  STFC  through LIV. DAT, the  Liverpool Big Data Science Centre for Doctoral Training (Project Ref. No. 2021488 ). The initial conceptual and prototyping work for the development of the GENIE/Professor interfaces, as well as for the development of the GENIE global analyses framework that, currently, underpins several analyses, was supported in part through an  Associateship Award  by the  Institute of Particle Physics Phenomenology, University of Durham.
Problem formulation Let be an input u(t) and its noise-free output y(t) related by equation (  6 ), where A(s) and B(s) are assumed coprime and the system stable. Data are collected at regular samples from t = 0 to current time t = T f with the sampling time T s. Furthermore, the number of data sample is assumed to be large enough so that the convergence of the estimated parameters to the true ones is guaranteed. Moreover, the quasi-stationary input signal {u(t), 0 ≤ t ≤ T f } applied to the system is persistently exciting, and gives rise to an output signal {y(t), 0 ≤ t ≤ T f }. The output data is corrupted by an additive white measurement noise ξ(t) due to experiment and sensor imperfections, normally distributed with a zero mean and σ 2 variance, considered at discrete instants. The complete equation can be written as: S : y(t) = G(p)u(t) y * (t k ) = y(t k ) + ξ(t k ), (10) where y * (t k ) is the noisy sampled value of the unobserved noise free output y(t).
01s. All simulations are initialized with θ T = [1, 0. 5, 2. 5] and ν = 0. 5 such as the true system  (39). Fig. 2  shows the input used for simulations, as well as the noise-free output and the noisy output with a SN R = 15dB. All simulations have been carried out with the CRONE toolbox developed in Matlab®, which is dedicated to fractional calculus, fractional system simulation and system identification with fractional models 2.
In noiseless conditions, the hybrid LMRPEM Alg. 1 has converged to the true commensurate order, and therefore the coefficient estimations is pretty accurate in mean. As the noise level increases, Hybrid LMRPEM Alg. 1 presents consistent estimates, with minimum variance and without bias. The present work shows parameter estimation within a finite data length. In practice, realistic applications may require much longer datasets. One main issue regarding longer datasets lies on the computation time. Grünwald-Letnikov's derivative is longer to calculate at each iteration when the dataset gets long enough, as the whole past of the signal is used for its computation. If the dataset gets even longer, the computation time will definitely be affected. Therefore, an extremely long dataset would require an extremely long calculation time by the end of the simulation, which would be impossible to implement in a real-time scenario.