dataesr/scientific-paragraphs-categorization huggingface dataset:
We compared the models using the Akaike Information Criterion (AIC) and found the second-order polynomial fit to be best (AIC, first: 334. 30, second: 249. 62, third: 250. 07). The parameter fit confirms that for overall low performance (i. e. , slope ABS + slope REL < 8. 12) human behavior significantly aligns to relative timing  (Fig 2C). Furthermore, the model fits the data remarkably well (adj. R-square = 0. 71).
We found that this modified version of the classic oscillator, the Adaptive Frequency Oscillator (AFO), well mimics human behavior. Simulations run with this model (see Methods) showed that the phase of the AFO better predicted early or late according to absolute timing for the 1. 2 Hz condition (Wilcoxon signed-rank test, two-sided p < 0. 001) and to relative timing for 4 Hz (Wilcoxon signed-rank test, two-sided p = 0. 015). No significant difference between timing algorithms was found for 2 Hz (Wilcoxon signed-rank test, two-sided p = 0. 81). Also, the AFO yields a similar relationship between timing mechanism alignment and overall performance (Fig 3C ) as the experimental dataset. Here, as well as for the behavioral data, we fit the simulations across experimental conditions with polynomial functions of 1, 2, and 3 degrees.
The main difference between these algorithms is whether you should allow for drift in the expected locations. In that sense, for the relative timing algorithm the time of the incoming tone is predicted by computing the overall temporal regularity in the preceding sequence. In contrast, for the absolute timing algorithm it is the absolute time that goes by between tones that drives prediction. A primary question for our study was to uncover, given a tone sequence, how do participants navigate this distinction and deal with the lack of a ground truth to generate a response. To answer this, we score participant data by both algorithms to help us identify which one the participants behavior most closely resembles. To do so, probe tones are coded by their deviation from either the relative prediction or the absolute algorithm prediction.
Logistic regressions on each participant's responses were fitted using the fitglm matlab function, which returns a generalized linear model fit. Participants with a noisy response pattern (χ 2 statistics against constant model, p>0. 05) were excluded from the follow up analyses. The number of participants excluded for each experiment are: 14 from a total of 65 for the 4 Hz experiment, 15 from a total of 78 for the 2 Hz, and 1 from a total of 72 for the 1. 2 Hz experiments (including both 1. 2 Hz and 1. 2 LJ). ii. Statistics. All between-and within-subject comparisons were assessed by nonparametric Mann-Whitney-Wilcoxon and Wilcoxon signed-rank tests, respectively. The precision of absolute and relative algorithms were first plotted against each other. Then, to optimize analysis, the axes were rotated to highlight algorithm dominance (absolute-relative) and overall precision (absolute + relative).
We then ran polynomial fits on this rotated version to estimate regions of absolute and relative algorithm dominance. We fit polynomials from first to third order and compared the fits using Akaike Information Criterion (AIC) to estimate how overall performance relates to method behavior. The model is fitted using a least-squares estimation using the matlab fitglm function. 95% confidence intervals of the model predictions were extracted from the model fit and compared against 0 to assess when the function is significantly above or below 0. The overall goodness of the fit was estimated by means of the adjusted R-square, penalizing the variables addition to the model.
Higher concentration infers that the phase is synchronized to this expected timing. Phase concentration is assessed using the following equation: PC X ¼ j P T i¼1 e iy X j T All simulations were run in MATLAB using a standard Euler solver with a time step of 0. 0001 sec. The Phase Response Curve in S2F Fig was analyzed by freezing the oscillator start point and running it for four cycles (1 s) as a reference. Then we simulated the Wilson-Cowan model again with the same start point but adding a tone stimulus identical to the one used in task simulation but roving its onset from the beginning to the end of the second cycle using 1 ms step size. Then we averaged the phase difference between perturbed and reference oscillators in the fourth cycle. This phase difference as a function of phase of stimulus onset is plotted S2F Fig at coupling constants of 0.
Treatment interruptions (for ≤ 4 weeks for adverse events considered related to trial medication or ≤ 8 weeks for other adverse events) and dose reductions to 100 mg bid were used to manage adverse events. The trial consisted of two parts. Part A comprised 52 weeks of treatment. Part B was a variable period during which subjects continued to receive blinded treatment until all the subjects had completed the trial. The final database lock took place after all subjects had completed the follow-up visit or had entered the open-label extension study, INBUILD-ON (NCT03820726); the data available at this point are referred to as data from the whole trial.
Acknowledgements We thank the INBUILD trial investigators. We thank the patients who participated in the INBUILD trial. The INBUILD trial was supported by  Boehringer Ingelheim International GmbH (BI). The authors meet criteria for authorship as recommended by the  International Committee of Medical Journal Editors (ICMJE). The authors did not receive payment for development of this manuscript. Writing assistance was provided by  Elizabeth Ng  and  Wendy Morris  of  FleishmanHillard, London, UK , which was contracted and funded by BI. BI was given the opportunity to review the manuscript for medical and scientific accuracy as well as intellectual property considerations.
The interaction of strong-field laser with FLU results in the production of electrons and multiple ions, which were measured using a double-sided velocity map imaging (VMI) spectrometer. VMI enabled the disentangling of the various photodissociation fragmentation pathways on the basis of momentum. In addition, the time-of-flight (TOF) mass spectra (MS) of the ions were measured. This multi-channel data accumulation allowed for a detailed and comprehensive decomposition of the strong-field-induced dynamics of FLU. In this manuscript, we describe the experimental details, data analysis, and theoretical calculations. This is followed by pump-probe independent results, dynamical observations, and conclusions.
Three types of data obtained from the experiments have been used for the analysis, namely, the TOF-MS, the electron VMI, and the ion VMI. Each ion and electron dataset were acquired using a combination of microchannel plate (MCP) in chevron configuration and phosphor screens, P47 and P20, respectively. The TOF-MS were obtained directly from the MCP readout with the help of a 2 GHz analog-to-digital-converter (ADQ412AC-4G-MTCA). The velocity map images of the ionic species, together with lowerresolution TOF-MS, were obtained using a Pixel Imaging Mass Spectrometry (PImMS2) sensor. 27, 28  Lastly, the electron data was obtained directly from a CCD (in 2018) or CMOS (in 2023) camera readout.
Data analysis Data extraction and analysis were performed using home-written scripts. To retrieve and analyze the data from the TOF-MS and electron VMI data, a combination of the BeamtimeDAQAccess 29 and CAMPFancyAnalysis  30  Python libraries was used. For the analysis of the PImMS data, a home-written set of LabView scripts and the CAMPFancyAnalysis library were employed. A detailed description of the recoil-frame covariance analysis for the ion VMI data can be found elsewhere. 13, [31] [32] [33] [34] [35]  The photoelectron-photoion covariance analysis (PEPICOV) was performed in the following way:  36, 37  first, each single-shot electron image was converted into the radial distribution function (RDF), and each single-shot TOF-MS was converted into the mass-overcharge (m/z) MS. The centers of the images and the momentum calibration were determined based on the helium II photoelectron data, which was obtained in pre-and post-measurements for the same molecular beam with 41 eV XUV radiation from FLASH, pub-lished in Refs.
13,15. Then, the covariance map was obtained as cov(IY, PEY) = ⟨IY • PEY⟩ -⟨IY⟩ • ⟨PEY⟩ , where "IY" denotes ion yield at a given m/z value, "PEY" denotes photoelectron yield at a given image radius value, and ⟨. ⟩ denotes averaging over all shots. A partial covariance correction for fluctuations in the pressure in the chamber was also applied. 38  Then, along the image radius axis of the map, a direct Abel inversion transformation was performed, as implemented in the PyAbel package. 39, 40  The observed dependencies of the ion and electron yields as a function of pump-probe delay time were fit with standard expressions  13, 41  using the MC 3 Fitting software  42  with a previously described algorithm. 13  A simultaneous fitting was done for the multiple channel data for the parent ions (from the high-resolution TOF-MS), momentum-disentangled fragment ion yields (from the ion VMI), and photoelectron yields (from the electron VMI).
Fitting was done for 40 datasets of ion yield versus pump-probe delay time, which comprise momentum-resolved fragment ion yields of ions having 5 to 13 carbon atoms, the parent monocation, dication and trication, dehydrogenated parent monocation, momentumresolved dications of fragment ions having 5, 7, and 11 carbon atoms and electron yields corresponding to five photoelectron bands. Fitting multiple datasets together enabled an estimation of the overlapping time of the pump and probe pulses (t 0 ). Using this t 0 , five momentum-resolved fragment ions with more than one transient feature were also fitted, giving out 15 datasets. The results of the data analysis are given in the Electronic Supporting Information (ESI).
Computational details To calculate the MS of FLU, augmented Born-Oppenheimer molecular dynamics (aBOMD) simulations of the fragmentation of FLU were done using the DissMD script from the PyRAMD software. 43  The algorithm was based on the QCEIMS idea,  44, 45  and the modifications are described in detail in Refs. 14,46. The forces for aBOMD were computed with the xTB software  47  at the semiempirical GFN2-xTB level of theory  48  that was shown to be suitable for the fragmentation pattern predictions. 49  To emulate the high-energy excitation regime, the excitation energy was represented as n • hν, where n is the number of photons, and hν is the photon energy, which was taken to be 1. 5 eV (corresponding to a wavelength of 810 nm). The parameter n was sampled from the Poisson distribution with a mean number of photons ⟨n⟩ = 40, and the result was adjusted to fit in the interval of 6 ≤ n ≤ 100 by setting the outlier n value to the closest value of n = 6 or n = 100.
The energetics of the reaction C 2+ 2 --→ 2C + , discussed later in section 3. 2. 5, were computed at CCSD(T)/aug-cc-pVTZ 50-52 using the ORCA 5 software. 53  The geometries of C 2+ 2 were optimized for the singlet, triplet, and quintet multiplicities, with the triplet being the lowest energy state. For the carbon monocation, doublet and quadruplet states were computed, with the doublet found to be the lowest in energy. All the geometries and energies are given in the ESI.
Recoil-frame covariance Recoil-frame covariance analysis was performed on the massresolved VMI data to distinguish the various measured fragmentation channels. This approach was shown to be very effective in disentangling the fragmentation pathways of complex PAH molecules. [13] [14] [15]  In brief, this method correlates the relative positions of two ions (the reference ion and the ion of interest) on the imaging detector. If the ion of interest is produced simultaneously with the reference ion, we see a recoil feature, a positive covariance in the opposite direction to that defined by the reference ion, which we choose to be upwards. More information on this technique can be found in Ref. 31. When we look at the covariance images obtained from the strong-field excitation (Figure  3 ), we see a major difference from the results observed upon the ionization and fragmentation induced with the single-photon XUV.
The strong-field excitation also opens new channels that were not observed in the XUV ionization. First of all, this is the dynamics of the near-threshold neutral molecule, which produces previously unobserved features appearing from the presence of the excited neutral molecule. The second new observation is the tetracation formation, which was observed via the (2,2) channel of the dicationic fragments C 7 H 2+ x and C 11 H 2+ x. All the observed time-dependent channels in photoion and photoelectron spectra were included in a global fit. This fitting dataset consisted of four parent ions extracted from the mass spectra, 15 kinetic-energy resolved ionic fragments extracted from ion-velocity-map imaging, and five photoelectron channels obtained from electron-velocity-map imaging. From this analysis, we extracted 60 transient lifetimes corresponding to different photoinduced intermediates.
This extensive dataset of the transient species' lifetimes of a prototypical polycyclic aromatic hydrocarbon provides new insights into the rich photochemistry of PAHs under the influence of intense electric fields. velopment and the initial operation of the CAMP end-station within the Max Planck Advanced Study Group at CFEL and for providing this equipment for CAMP@FLASH. The installation of CAMP@FLASH was partially funded by the BMBF grants 05K10KT2, 05K13KT2, 05K16KT3, and 05K10KTB from FSP-302. MBr and CV gratefully acknowledge support from the UK EPSRC EP/T021675/1, EP/V026690/1. MBu, EJ, ZL, and JM gratefully acknowledge support from the UK EPSRC (EP/S028617/1). EJ, ZL, and JM additionally thank Lincoln College, Oriel College, and University College, Oxford, for their respective travel funding.
Acknowledgements This work was supported by the  ERC   Starting Grant ASTROROT , grant number  638027 , and the project  CALIPSOplus  under grant agreement  730872  from the  EU Framework Programme for Research and Innovation HORIZON 2020. We acknowledge  DESY (Hamburg, Germany ), a member of the  Helmholtz Association HGF , for providing experimental facilities. Parts of this research were carried out at  FLASH. Beamtime  was allocated for proposals F-20170540 and  F-20211752. This research was also supported through the Maxwell computational resources operated at  Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany. We acknowledge the  Max Planck Society  for funding the de-.
In other words, atoms k must share the available momentum at frequency ν between them. Therefore, g rad k (average acceleration of each atom k) decreases when C k increases. For stellar interiors, there is an equivalent form of Equation (  6 ) in expressing the radiative acceleration of element k that is much more convenient for stellar modeling: g rad k = 15 16π 5 r 2 L rad r c κ R X k ∞ 0 κ u,k κ u,all P(u)du (7) with P(u)=u 4 e u (e u -1) 2 and u= hν kT where L r is the luminosity of the star, X k is the mass fraction of element k, κ R the Rosseland opacity, κ u,k the monochromatic opacity of the element, κ u,all the total monochromatic opacity, all these quantities being estimated at radius r. With this expression, one could take benefit from several numerical opacity databases (for instance, OP, OPAL), where the sum of all contributing atomic transitions is already performed, provided that monochromatic opacity for each element separately is available.
This method is most often used for atmospheres  [45, 46] , and no more for interiors after large atomic or opacity data banks became available. With no surprise, this method is the most CPU time-consuming. However, it is, in principle, the most precise one as much as atomic data are accurate and complete. -Opacity sampling in stellar evolution. Here, the radiative acceleration is computed using Equation (  7 ), the method was developed by Richer et al. (1998)  [10]  and was based on the OPAL database. One of the difficulties of this method is that calculation is performed on a fixed frequency grid, which is most often equally spaced in u, which needs to pay particular attention to the grid resolution. On another hand, this method applies to average atoms (with averaged ionization degree). Notice also that there is a limited number of elements in the databases (mostly elements lighter than Fe), generally elements contributing to the Rosseland average.
This implies that studies needing to consider the atomic diffusion of these missing elements cannot be addressed. -Interpolation method. This method was proposed by M. Seaton in 1997  [47]. He was the initiator and the main architect of the Opacity Project (OP). The OP project first consists of computing ab initio numerically a large number of atomic transitions for many metals (presently lighter than iron). From these atomic data, the OP team computes tables of opacities (Rosseland average, monochromatic opacities of each element), and the numerical codes allowing interpolation from these tables for any chemical composition and position inside the stars. Since all the necessary data for radiative accelerations are already in the OP database, M. Seaton understood the potential importance of also providing radiative accelerations.
He therefore added the codes to compute them with interpolations (as performed for opacities) in a specific table of a function built from Equation  (7). This method is accurate and fast compared to the previous ones since all the necessary tables are already computed by the OP team. The method is easy to implement in existing codes. The limit of this method, as previously, is imposed by the list of elements in the database. -Semi-analytic or parametric approximation. The SVP (Single-Valued Parameters) method gives radiative accelerations in stellar interiors without having to explicitly handle large amounts of atomic data or opacity tables. A preliminary version was first proposed by G. Alecian (1985)   [48]. In developing Equation (  6 ), one obtains an expression where the atomic data and the concentration of the considered element are mixed, with a non-linear dependence on the concentration.
Actually, one knows that what happens in the atmosphere does not generally significantly affect the star structure. However, understanding the main trends is important for making various diagnostics since the stellar chemical composition is essentially estimated (from observed spectra) through abundances in atmospheres. Therefore, one needs to be careful when these abundances are considered to be those in deeper layers of the star. The problem is different for stellar interiors for which macroscopic motions are better constrained in models, and numerical modeling of atomic diffusion is easier since radiative accelerations may be computed from large opacity databases. The recent asteroseismology surveys such as CoRoT, Kepler, TESS, and in the future, PLATO have emphasized the need for accurate stellar evolution models for the accurate determination of stellar systems.
The present study aimed to increase the accuracy of SOC content predictions using two complementary mechanisms: (i) Enriching the information considered by combining remote sensing time series and laboratory spectral measurements; (ii) Improving model accuracy using machine-learning algorithms. To this end, we used Sentinel-2 remote sensing data of bare soil and combined them with Sentinel-1 SAR-derived data and indices derived from Vis-NIR laboratory spectra to predict SOC content in an agricultural study area. We also compared the performance of PLS regression, RF, and DNN models in predicting SOC content.
Laboratory Reflectance Measurements Soil spectra were measured under laboratory conditions. The 2 mm sieved soil samples were oven-dried at 40°C for 24 h. Their spectra were then measured using a full range spectroradiometer (ASD FieldSpec ® 3, Malvern Panalytical Ltd. , London, UK). For each sample, the instrument was calibrated using the white reference standard (Spectralon ® , North Sutton, NH, USA) before scanning the soil four times at different positions with the contact probe. Since the spectrometer is equipped with three different detectors  [66] , the spectra were splice-corrected using ViewSpecPro software to eliminate signal jumps that can occur when changing detector ranges  [67]. The mean of the four reflectance spectra in the 400-2450 nm range was used to maximize the signal-to-noise ratio.
Laboratory Reflectance Measurements Soil spectra were measured under laboratory conditions. The 2 mm sieved soil samples were oven-dried at 40 • C for 24 h. Their spectra were then measured using a full range spectroradiometer (ASD FieldSpec ® 3, Malvern Panalytical Ltd. , London, UK). For each sample, the instrument was calibrated using the white reference standard (Spectralon ® , North Sutton, NH, USA) before scanning the soil four times at different positions with the contact probe. Since the spectrometer is equipped with three different detectors  [66] , the spectra were splice-corrected using ViewSpecPro software to eliminate signal jumps that can occur when changing detector ranges  [67]. The mean of the four reflectance spectra in the 400-2450 nm range was used to maximize the signal-to-noise ratio.
Retrieval and Analysis of Spectral Indices In addition to the spectral bands, spectral indices have been developed and used to analyze remote sensing images. These indices are calculated using common equations and enhance some spectral features by minimizing effects of illumination and reducing noise  [76, 77]. In this study, we used the bare-soil reflectance extracted from the Sentinel-2 images to calculate 40 spectral indices (Appendix A). Based on their application in previous studies, these indices can be grouped into four categories: vegetation, soil, geology, and water. To identify the indices that improved detection of soil variability in space and time, we performed multiple factor analysis (MFA) of the time series of indices for the 58 points of bare soil. This multivariate method, MFA  [78]  is based on principal component analysis (PCA) and used to summarize data described by several sets of variables organized into groups.
Partial Least Squares Regression PLS regression is the most common linear regression used to predict soil properties. Developed by Wold  [92] , it maximizes the variance of spectral variables by reducing the original dimension of the spectra into latent variables. It extracts useful components that are strongly correlated with the dependent variables and overcomes problems of multicollinearity between spectral variables  [93]. PLS regression performs better than other linear regression methods because of the stability of its latent variables. However, it is sensitive to outliers in the dataset  [94]  and forces predictions towards the center of the calibration dataset. Thus, for samples with high leverage, prediction uncertainty increases  [95]. Non-linear iterative PLS (NIPALS) and statistically inspired modified PLS are the two most common optimization algorithms of PLS regression.
In this study, we used the NI-PALS algorithm implemented in the scikit-learn 1. 0. 2 package (Python 3. 7. 4), which aims to linearize models that have non-linear parameters  [92, 96]. The optimal number of components was selected using both the coefficient of determination (R 2 ) and the RMSE of a 5-fold cross-validation (RMSECV) and relying on the grid search method (Table  A2  in Appendix B). This method allows models parameters to be adjusted by searching a grid of all possible combinations and evaluating them using cross-validation (Figure  3 )  [97, 98]. 2  for definitions of the spectral indices. PLS: partial least squares, RF: random forest, DNN: Deep neural network, R 2 : coefficient of determination, RMSE: root mean square error, RPD: ratio of performance to deviation, RPIQ: ratio of performance to interquartile distance.