dataesr/scientific-paragraphs-categorization huggingface dataset:
ACKNOWLEDGEMENTS This work has been carried out within the framework of the  EUROfusion  Consortium, funded by the  European Union  via the  Euratom Research and Training Programme  (Grant Agreement No  101052200 -EUROfusion ). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the  European Commission. Neither the  European Union  nor the European Commission can be held responsible for them. The involved teams have operated within the framework of the Enabling Research Project:  ENR-IFE. 01. CEA " Advancing shock ignition for direct-drive inertial fusion ". This work was also done with the support and under the auspices of the  NIFS Collaboration Research program  ( 2021NIFS18KUGK123 ).
Acknowledgements We express our sincere gratitude to  G. Arwas ,  B. Beradze ,  M. Capone ,  I. Carusotto ,  C. Ciuti ,  D. De Bernardis ,  O. Di Stefano ,  D. Fausti ,  G. Mazza ,  A. Mercurio ,  C. Mora ,  A. Nersesyan ,  F. M. D Pellegrino ,  M. Polini  and  S. Savasta. for useful discussions. We are particularly grateful to the organizers of Shedding Quantum Light on Strongly Correlated Materials (QLCM22) where this collaboration took its first steps. Z. B. and M. D. acknowledge PNRR MUR project  PE0000023-NQSTI  for financial support.
Funding information The work of G. C. and M. D. was partly supported by the  ERC  under grant number  758329  (AGEnTh), and by the  MIUR Programme FARE (MEPH). T. C. acknowledges the support of PL-Grid Infrastructure for providing high-performance computing facility for a part of the numerical simulations reported here. G. M. A. and M. S. acknwoledge funding from the  European Research Council (ERC)  under the  European Union 's  Horizon 2020 research and innovation programme  (Grant agreement No. 101002955 -CONQUER ).
The first class of approaches focuses on inferring coefficients from known data (e. g. ,  [7, 10, 12, 15, 18, 19] ). An example of this is the widely known PINN (Physics-informed Neural Networks) method  [10] , which uses PDEs in the loss function of neural networks to incorporate scientific knowledge. Ref. [7]  improved the efficiency of PINNs with the residual-based adaptive refinement (RAR) method and created a library of open-source codes for solving various PDEs, including those with complex geometry. However, this method is only capable of estimating coefficients for fixed known terms in PDEs, and may not work well for discovering hidden PDE models. Although  [9]  extended the PINN method to find unknown dynamic systems, the nonlinear learner function remains a blackbox and no explicit expressions of the discovered terms in the predicted PDE are available, making it difficult to interpret their physical meaning.
Optimizing Hyperparameters In this section, we will explain the process of tuning hyperparameters λ M and λ S in the loss function  (7). Firstly, the range of spatial and temporal variables in the training set are defined as [-L, L] and [0, T], respectively. Then, using the finite difference method, we generate a dataset that acts as the "true data". Additionally, we consider M initial conditions. The time interval is determined by dt/ dt, where dt is the time step size for computing the "true data" and dt represents the time step size for selecting the "observational data". Typically, dt is chosen to be much smaller than dt. The solution corresponding to the mth initial condition is denoted as u m (•, •), where the first "•" refers to the spatial variable and the second "•" represents the temporal variable.
Frac-PDE-Net We have noted that mPDE-Net accurately fits data and recovers terms, but it may not always simplify the learned PDE, making it challenging to interpret. To address this, we implement sparsity-encouraging methods such as the Lasso approach. However, even with Lasso and hyperparameters chosen from the validation sets, the predicted equation still had redundant terms. This is likely due to correlated data and linear dependencies in the data, which prevent Lasso from fully shrinking the extra coefficients to zero. To overcome this, we employ two approaches. The first, called the L 2 norm-based term selection criterion, weakens or eliminates linear dependencies in the data. The second, called sequential threshold ridge regression (STRidge), creates concise models through strong thresholding.
Numerical Studies: Convection-Diffusion Equations with the Neumman Boundary Condition In this section, we showcase numerical examples to demonstrate the efficacy of Frac-PDE-Net, our proposed method. The training, validation, and testing data are generated based on the underlying governing equation. Our aim is to use Frac-PDE-Net on these data to obtain a concise and interpretable model for the PDE. The governing PDEs under consideration in this paper are of the following form: ∂ t u = F 1 (u, v), ∂ t v = F 2 (u, v), (14) where F 1 (u, v) = d 1 ∆u + P 1 (u, v) + R 1 (u, v), F 2 (u, v) = d 2 ∆v + P 2 (u, v) + R 2 (u, v). (15) Here, d 1 and d 2 are positive diffusion coefficients, R 1 and R 2 represent fractional functions of (u, v), and P 1 and P 2 denote combinations of power functions and integration operators of (u, v) through addition and multiplication.
3(∂ 2 x u + ∂ 2 y u) + 1 -u - 1 2 uv u 2 + 0. 25u + 0. 25 , F 2 (u, v) = 0. 4(∂ 2 x v + ∂ 2 y v) + 0. 4 -0. 2v - 1 2 uv u 2 + 0. 25u + 0. 25 x + ∂ 2 y , and with a temporal discretization of second-order Runge-Kutta (see  [16] ), using a time step size of 1  1600. In addition, the observations are obtained from various initial values: this implies an extra variability in the datasets, that is necessary if we want to be able to generalize well to any initial conditions. We assume that we have N Init = 12 different solutions, coming from different initial values w 0. The functions are random, defined through random parameters a i,j , b i,j , c i,j , d i,j , a k,l , b k,l , c k,l and d k,l , which follow from the standard normal distribution N (0, 1), c 1 and c 2 , which follow from uniform distributions: c 1 ∼ U (-0.
) is the standard deviation of the true data u * (or v * resp. ). Since the time is from 0 to 0. 15, there are 15 time blocks and we denote N Time = 15. For spatial variables, we have N Space = 64, where N Space represents the number of space grids. Therefore, the dataset is (u t,k , v t,k ) : 1 ≤ t ≤ N Time , 1 ≤ k ≤ N Init , where both u t,k and v t,k are matrices in R N Space ×N Space. The following Tables  1  and 2  show a summary of parameters for Frac-PDE-Net. Our goal is to discover the terms F 1 (u, v) and F 2 (u, v) on the right hand side of (  16 ) and the true expressions are given by  (17). For convenience of notation, we denote F 1 and F 2 to be our predicted operators for F 1 and F 2. Based on some existing models (see, e. g. , Section 2. 2 in  [2] ), we adopt some assumptions before discovering F 1 and F 2.
4. Finally, to verify that no further terms can be eliminated after Frac-PDE-Net, we compare two models: Model 1, generated by Frac-PDE-Net; and Model 2, which is identical to Model 1 but removes the term with the smallest L 2 norm from F 1 and F 2. The coefficients in Model 2 are retrained, and the resulting model is referred to as F PHrsmPDE-Net i. "PH" in F PHrsmPDE-Net i represents the Post-hoc selection in Model 2. The comparison between Model 1 and Model 2 will be conducted using the Kolmogorov-Smirnov test as outlined in Section 2. 5. For this case, we added 5% noise to the generated data to form the observational data. The results are displayed in Table  3. Table  3  shows that F mPDE-Net i (modified PDE-Net framework) accurately identifies the terms in Example 1 and estimates their corresponding coefficients.
) is the standard deviation of u * (or v * resp. ). The reason of imposing the absolute value sign is to avoid negative values, which may cause trouble to evaluate power functions with non-integer power, such as u 1. 5. We choose 15 blocks for the time on the interval [0, 0. 75] and denote N Time = 15. For spatial variables, we set N Space = 200, where N Space represents the number of space grids. Therefore, the dataset is (u t,k , v t,k ) : 1 ≤ t ≤ N Time , 1 ≤ k ≤ N Init , where both u t,k and v t,k are matrices in R N Space ×N Space. The following Tables  5  and 6  show a summary of parameters for Frac-PDE-Net. In  [6] , some assumptions are made on the model based on existing experimental knowledge of the biological behavior. For example, it is assumed that the operator F 2 (u, v) is linear in both u and v, while F 1 (u, v) is nonlinear in both u and v.
06475 + 0. 01 sin(3x). We use finite difference method to generate the "true" data in the forward direction using the known coefficients and terms in  (20)  and  (21). The spatial step sizes (dx and dy) are set to 5π 200 and the time step size (dt) is 5 100. The time interval considered is t ∈ [0, 10]. We then simulate the data using the trained model from Table  7  over the time period [0, 10]. In Figure  10 , both the true solution and the predicted solution of the trained model by Frac-PDE-Net are plotted for t ∈ [0, 10]. One can see from Figure  10  that the predicted solution is very close to the true one. The results of the comparison between Frac-PDE-Net and PDE-Net 2. 0 are presented in both graphical and quantitative form. The model discovered by PDE-Net 2. 0 is shown in Table  10 , while the predicted solutions are displayed in Figure  11.
Confocal microscopy Confocal microscopy was conducted using a Zeiss LSM-T-PMT 880 instrument coupled to an Airyscan detector. Membranes were visualised using the hydrophobic dye Rhodamine 6G. 0. 5 µL of a 100 µM dye solution was added to a heated (70 °C) microscope slide. The vesicle solution was vortexed, and a 5 µL aliquot was added to the slide, mixed with the dye. The aliquot was covered with a #1. 5, 16 mm diameter coverslip and positioned on the microscope stage. The dye was excited using an Ar laser operating at 514 nm and observed through a 63x oil objective with a 488 nm filter. Images were captured using Zeiss Zen microscopy software, and final processing was conducted using the FIJI (Fiji is just ImageJ) software package.
Negative Staining -Transmission Electron Microscopy (NS-TEM) NS-TEM was performed using a JEOL 1010 TEM (JEOL, Japan). Samples were applied to a Cu 100 mesh grid and allowed to incubate for 30 seconds. Excess sample was then removed by blotting with filter paper, and a portion of aqueous uranyl acetate (1. 5%) was added to the grid. After standing for 30 seconds, the excess liquid was blotted. Grids were immediately analysed under vacuum. Image processing was carried out using the FIJI software package.
Acknowledgements We thank  Mark Turmaine  and  Andrew M. Hartley  for assistance with NS-TEM and Cryo-EM experiments, respectively. S. F. J. acknowledges support from  "la Caixa" Foundation  ( ID 100010434 ) and from the  European Union 's  Horizon 2020 research and innovation programme  under the  Marie Skłodowska Curie  grant agreement No  847648. The fellowship code is " LCF/BQ/PI21/11830015 ". Centro de Química Estrutural  acknowledges the financial support of  Fundação para a Ciência e Tecnologia (FCT)  through projects  UIDB/00100/2020  and  UIDP/00100/2020. Institute of Molecular Sciences  acknowledges the financial support of  FCT  through project  LA/P/0056/2020. Z. M. acknowledges funding from  Fundação para a Ciência a Tecnologia (FCT)  grant number  2022. 05284. PTDC.
Results As shown in figure  1 , electron beams with different energy γ should emit the same X-ray energy ω if the scattering pulse arrives at an angle (in radians) ϕ = 2 arcsin ⎛ ⎝ 1 2γ ω ω 0 ⎞ ⎠ ≈ 1 γ ω ω 0. (2. 1) Taking a target energy of 100 keV, which corresponds to an upshift of approximately 64 500 compared with the laser energy ω 0 = 1. 55 eV, we find that the scattering angle is approximately given as ϕ ≈ 75 • /E[100 MeV]. In the following we will thus analyse several different combinations of electron energy and scattering angles that should, in theory, yield to X-ray emission at the same energy. (e) ( g) ( h) (b) (a) ( c) ( d ) ( f ) We have simulated four different scattering cases by reconstructing electron trajectories in a laser pulse with the Gaussian temporal and spatial profiles using an implicit fifth order Radau IIA family Runge-Kutta method and calculating the emitted radiation field using the SynchRad software  (Andriyash 2018 ).
The latter are artifacts that originate from unequal absorption of different X-ray energies in a sample. We can briefly estimate to which extend the beams simulated in the previous sections would produce such artifacts and compare this with synthetic tomograms based on monochromatic sources and broadband spectra from laser-driven betatron radiation as used in  Cole et al. (2015)  or  Döpp et al. (2018). To do so, we generate synthetic tomograms based on the 'Doga's Circles' phantom from the TomoBank database FIGURE 6. Simulated tomography to estimate the extend of beam hardening artifacts given different X-ray spectra. The ground truth, a slice through an aluminium rod array, is shown on the very left-hand side. What follows from left to right are input spectra and reconstructions for a monoenergetic 70 keV source, a betatron spectrum with 40 keV critical energy and the simulated on-axis Compton spectrum from figure  4.
Rare meson decays are among the most sensitive probes of both heavy and light new physics. Among them, new physics searches using kaons benefit from their small total decay widths and the availability of very large datasets. On the other hand, useful complementary information is provided by hyperon decay measurements. We summarize the relevant phenomenological models and the status of the searches in a comprehensive list of kaon and hyperon decay channels. We identify new search strategies for under-explored signatures, and demonstrate that the improved sensitivities from current and nextgeneration experiments could lead to a qualitative leap in the exploration of light dark sectors. m a = 0 (Standard QCD Axion).
[130] ). comes from the ISTRA+ experiment  [119] : B(K -→ π -π 0 a) < 0. 9 × 10 -5 ⇒ 2f a /C A sd > 3. 6 × 10 7 GeV. ( 25 ) This is expected to be improved with the NA62 Run 1 dataset. The projected NA62 reach would still be below the nominal bounds from the SN cooling due to hyperon decays  [96]  (Fig. 5 ). However the SN cooling bounds carry an important caveat that they are likely affected by large systematic uncertainties related to the SN modeling (it is even possible to argue that the bound may be completely absent  [131] ). In addition to the above bound on the K -decay, there is a phenomenologically interesting experimental bound on B(K L → π 0 π 0 a) from the E391a experiment  [120] , which is set to be improved by KOTO. This bound does not cover the massless ALP (see Section 4. 2), while it leads to 2f a /C A sd 1.
When considering a three-light-two-heavy-neutrino scenario (the minimum required to explain oscillation results in a seesaw mechanism), additional mixing parameters break the simple dependence between light-neutrino masses, heavy-neutrino masses, and mixing, making this target broader. Experimental details and future prospects of the K + → + N measurements are discussed in Section 4. 14. Depending on the HNL mass, the branching ratio of the K + → π 0 + N decay can be comparable to that of the K + → + N decay, both of which are proportional to |U N | 2. This is particularly true for the electron-coupled final state with m N 20 MeV  [173] [174] [175]. If experiments can constrain B(K + → π 0 e + N ) at comparable levels as B(K + → e + N ), then smaller |U eN | 2 can be probed. However the currently available datasets only offer a limited sensitivity (Section 4.
The pion dataset is collected from identified kaon decays (e. g. K ± → π ± π 0 , K ± → π 0 µ + ν and the dark photon yield is controlled by the mixing squared ∼ ε 2. Similarly, one could hunt for the dark photon at NA62 in all the channels containing SM photons, performing a bump hunt on the dielectron spectrum of the collected data. For instance one could estimate B(K + → µ + νA (e + e -)) ∼ 10 -3 × ε 2 , (40) which should yield a competitive bound on the dark photon mixing angle.
The coupling between φ and the SM neutrinos can be generated from the φ interactions with sterile neutrinos, L = -g D φν D ν D +. , if the sterile neutrinos mixes with the lighter SM neutrinos. The phenomenology can be more involved, if φ mixes channel  [224]. After 15 years of data taking the MiniBoone dataset itself now shows a 4. 8σ excess in the low energy part of electron spectra in both the neutrino and antineutrino channels  [225] , possibly not inconsistent with the LSND anomaly. with the Higgs, and resembles the phenomenology of the Higgs portal scalar in Section 2. 1, but with the large couplings of φ to neutrinos allowed. In particular, the B(K → ν φ) can be followed by decays to visible SM particles as well as by decays to neutrinos, with the relative branching ratios controlled by the size of g D and the mixing angles.
The NA62 experiment at CERN The main goal of the NA62 experiment at CERN is the measurement of the K + → π + ν ν decay rate to a 10% precision using the decay in flight technique. The experiment operates a high-intensity K + beam with a momentum of 75 GeV/c derived from primary 400 GeV/c protons extracted from the SPS accelerator, and kaon decays in a long vacuum tank are detected  [344]. The NA62 Run 1 dataset collected in 2016-2018, corresponding to 2. 2 × 10 18 protons on target, has led to the first observation of the K + → π + ν ν decay based on 20 candidate events  [109]. Several auxiliary trigger lines were in operation during Run 1 in addition to the main K + → π + ν ν trigger line, with downscaling factors applied due to the overall trigger bandwidth limitation. The principal NA62 Run 1 kaon decay datasets correspond approximately to the following numbers of K + decays in the fiducial decay region  [345] : -the main K + → π + ν ν trigger line: N K ≈ 6 × 10 12 ; -the di-muon trigger line: N K ≈ 3 × 10 12 ; -di-electron and electron-muon pair trigger lines: N K ≈ 10 12 each; -the minimum bias trigger providing a suitable dataset for all searches: N K ≈ few × 10 10.
NA62 Run 2 started in July 2021, and is approved until Long Shutdown 3 (LS3). The goal of Run 2 is to increase the total dataset to an equivalent of 100 SM candidate K + → π + ν ν events  [346]. One can expect the auxiliary trigger lines listed above to be in operation throughout Run 2, with similar downscaling factors to those employed during Run 1. The proposed future K + decay program at CERN is discussed in Section 3. 2. In 2003-2004, the NA48/2 experiment at CERN collected a dataset corresponding to 2 × 10 11 decays of 60-GeV charged kaons (K ± ) with the main trigger designed for collection of three-track vertices  [347]. Due to the smaller longitudinal extent of the apparatus with respect to NA62 and the absence of three-track trigger downscaling, NA48/2 offers comparable or better sensitivity with respect to the NA62 Run 1 dataset for certain K + decays to multiple charged tracks.
8 × 10 -10 with the data collected in 2016-2018  [240]. The target single event sensitivity of the KOTO experiment is O(10 -11 ), to be achieved by 2025. The next generation KOTO step-2 experiment with a target single event sensitivity of O(10 -13 ) has been discussed in Ref. [5, 6]. Higher K L flux and harder momentum spectrum for step-2 will be provided by a new beam line with a 5 • extraction angle. A longer decay region and a larger diameter calorimeter will be used to increase the data sample.
The LHCb experiment at CERN The LHCb experiment has collected a dataset corresponding to an integrated luminosity of about 9 fb -1 during Run 1 in 2010-2012 and Run 2 in 2015-2018. This dataset provides the leading sensitivity for decays of short-lived strange particles, i. e. K S and hyperon decays. Therefore LHCb is complementary to the dedicated K + and K L decay experiments described in Sections 3. 1, 3. 2, 3. 3. The biggest potential of LHCb in kaon and hyperon physics lies in the measurement of rare decays into opposite-sign muon pairs (K S → µ + µ -, Σ → pµ + µ -). This owes to the dedicated trigger, which had an efficiency of about 15% during Run 2, and is expected to reach an efficiency close to 100% from Run 3 onward. The experiment is set to collect large datasets in future. The timeline for operation and upgrades of the LHCb experiment in the coming years, including the proposed Phase-II upgrade, is presented in Table  5.
The BESIII experiment The BEPCII e + e -collider is a charm-tau factory with a peak luminosity of 1. 0 × 10 33 cm -2 s -1 running at the center of mass energy in the 2-5 GeV range, the unique features of which allow for a rich physics program  [350]. BESIII is a hermetic detector with a geometrical acceptance of 93% (out of the complete 4π) in a 1 T solenoid  [351]. It has accumulated world's largest datasets of (10087 ± 44) × 10 6 J/ψ events (corresponding to 3. 1 fb -1 integrated luminosity)  [7] , 3 × 10 9 ψ(3686) events, and 2. 9 fb -1 integrated luminosity at ψ(3773), all of which are produced directly from the e + e -collisions. A number of searches for rare decays and physics beyond the SM have been performed by BESIII, utilizing the clean experimental environment  [352, 353]. Hyperons are mainly produced at BESIII via ψ → B B, where B B denotes a polarized, quantumentangled hyperon pair.
The ψ mesons are produced in the annihilation of unpolarized electron-positron beams and therefore the spin-density matrix of the ψ depends only on the scattering angle θ B between the electron beam direction and the hyperon momentum. The coherent production of B B pairs from the decay, with the subsequent weak decays of the B and B, therefore constitute a spin-entangled quantum system where the final state is specified by two global real parameters. These features add an exciting new dimension to the study of CP violations and could enhance the related new physics search sensitivity with relatively modest statistics compared with the other hyperon sources. The projections for BESIII reach for rare and forbidden hyperon decays are reported in Ref. [354]. BESIII is optimizing its data-taking plans over the coming years to accumulate even larger data sets with an ever-improving understanding of the detector performance.
Models leading to enhanced K L → π 0 X inv with little or no effect on K + → π + X inv are discussed in Section 2. 7. The SM decay K → πν ν is theoretically clean, and represents a well-known probe for heavy new physics (Section 2. 11). Using the complete Run 1 dataset, the NA62 experiment established upper limits on B(K + → π + X), with X invisible, at the level of O(10 -11 ) in the mass ranges 0-110 MeV and 154-260 MeV  [109, 361] , improving on the previous limits from the BNL E949 experiment  [111]. The search represents a direct extension of the K + → π + ν ν measurement, which determines the m X range scanned. The event selection requires a K + from an incoming beam and a π + in the final state, in the absence of any other in-time activity in the detector. The largest (and irreducible) background is due to the K + → π + ν ν decay.
1  and 4 , respectively. Above the di-muon threshold, large values of the Higgs-scalar mixing angle θ are not excluded since the dark scalar decay length becomes comparable to the length of the experimental setup. The above search for K + → π + X with the NA62 Run 1 dataset is almost background-free: the background is O(1) events in each X mass hypothesis (determined by the experimental resolution), and decreases as a function of m X. However the background is expected to become significant for the large future datasets (Sections 3. 1, 3. 2). The sensitivity to the decay branching fraction can be expected to improve by up to a factor of four with the NA62 Run 2 data, and by at least another factor of two at the future CERN high-intensity kaon beam facility. The sensitivity to the Higgs portal and ALP parameters is determined from the scaling B(K + → π + X) ∝ θ 2 and B(K + → π + X) ∝ 1/f 2 a.