dataesr/scientific-paragraphs-categorization huggingface dataset:
Linguistic Acceptability Acceptability judgments have been broadly used to investigate whether LMs learn grammatical concepts central to human linguistic competence. However, this approach has several methodological limitations. (i) The judgments may display low reproducibility in multiple languages  (Linzen and Oseki, 2018) , and (ii) be influenced by an individual's exposure to ungrammatical language use  (D ąbrowska, 2010). (iii) Distribution shifts between LMs' pretraining corpora and LA datasets may introduce bias in the evaluation since LMs tend to assign higher probabilities to frequent patterns and treat them as acceptable in contrast to rare ones  (Marvin and Linzen, 2018; Linzen and Baroni, 2021).
Instead of H 1 , the higher-order homology groups (e. g. , H 2 , H 3 ) can be considered. However, the preliminary experiments have shown that they are less helpful for LA tasks. 3. RTD(G a , G b ) is calculated as the sum of bar lengths in the barcode from the previous step. It should be noted that this procedure is asymmetric on G a and G b , and for non-equal graphs holds RTD(G a , G b ) ̸ = RTD(G b , G a ). To compute barcodes, we use the Ripser++ toolkit, which cannot work with asymmetric graphs. Hence, we represent the asymmetric attention maps as the distance matrices to obtain the symmetric graphs G a and G b as described in §3. 2. We consider only the forward-looking part of attention, i. e. , how each token affects the rest of the sentence. The majority of the BLIMP minimal pairs are of equal length in the BERT/RoBERTa tokens.
D Attention Head Selection D. 1 Head Selection Procedure We use publicly available scripts 5 to generate up to 100 minimal pairs per each of 67 types, ensuring no overlap with the BLIMP pairs. We select the best-performing individual heads and head ensembles by estimating their scoring performance on the generated data and further evaluate them on BLIMP. Algorithms 1-2 describe the Top Head and Phenomenon Head selection procedures using a brute force search, while Algorithm 3 presents the process of selecting the Head Ensembles via beam search.
Experimental tests First, a series of experimental tests were carried out on the experimental fixture presented in the Figure  1. This series of experimental tests is automated through a program written on Matlab that allows the acquisition system (NetdB) to be driven directly through the TCP/IP communication mode. This acquisition system has twelve synchronous acquisition channels and two signal generation channels with a sampling frequency fixed for all experiments at 12. 8 kHz. The setup allows the tube to be excited by a harmonic acoustic field through a loudspeaker. The loudspeaker is fed through a TIRA 120BBA amplifier whose input signal is provided by the NetdB acquisition system. A low-pass filter with a bandwidth of [0,1000] Hz filters the output signal of NetdB in order to avoid polluting the excitation signals with noise.
The blue curve is the ground-truth signal, representing an unfiltered signal. The red curve represents the filtered DIC signal of a 17 pixels subset DIC code using a first-order shape function. The DIC filtering is calculated using a first order Savitzky-Golay (SG) filter with a width of 17 pixels (see appendix for more details)  [2]. The progressive attenuation of the signals, from no attenuation in (b) to a highly attenuated signal in (g) clearly illustrates the low-pass filtering effect of the DIC calculation. The peak-to-peak attenuation amount is shown in the figure title as a percent of the ground-truth value. The lower frequency (Mode 1) exhibits almost no attenuation at 5%, while the highest frequency (Mode 11) exhibits 92% attenuation. This filtering effect is what causes the sharp displacement change in the GT (Figure  1 (a)) to exhibit a rounded transition in the SG filter data.
This calculation varies depending on the implementation of the code, but for many methods, the strain calculation functions as a second low-pass filter. It is worth noting that DIC deals with images that are always impaired with pixelwise acquisition noise. DIC spatial filtering does have the benefit of reducing the propagation of this noise to the kinematic measurement but may create biases as just discussed. The ability of DIC to resolve ever smaller periods of the QOI is, therefore, in competition with the measurement resolution also called displacement or strain noise. Indeed, more filtering of the DIC data results in a lower overall noise of the QOI, but at the expense of decreased spatial resolution. It is thus of great interest to understand the relationship between the spatial resolution, bias, and the measurement resolution or QOI noise.
2 "Image generation -the Boolean model"). The inset figure for Star 1 (Table  1 ) illustrates the frequency variation across the image. The left of the image has a period of 10 pixels for the sinusoid decreasing towards the right hand of the image to a period of 150 pixels 1. Period, defined as 1/frequency, is more natural to use for discussing the variation of the displacement gradients in the image as it gives the distance between points that can be measured, i. e. , spatial resolution. The Star 1 data set contains only a reference and a deformed image. Star 2 is the same. This is constructed specifically using the noise profile on data from a PointGrey Grasshopper 5 megapixel, 8-bit, monochrome CCD camera. The left axis shows the grey level variance superimposed for each pixel value found in an image, while on the right axis the variance is normalized by the signal intensity (i.
An integration is then performed from this infinite spatial resolution image to the pixelwise image. A Monte Carlo scheme is introduced, with a number of realizations ensuring that integration error is lower than the rounding error that corresponds to the gray value truncation when converting to 8-bit images. The code used for the generation of the data set is available here: https://members. loria. fr/FSur/software/BSpeckleRender/ [15]. The parameters used for defining the Boolean model and its generation are given in.
Participation The DIC challenge was open to all participants with the goal to ensure that the commercial DIC codes were well represented as well as open source (e. g. , DICe and Ncorr  [16] ), university codes (e. g. , ALDIC  [17] ), and global codes (e. g. , Correli). In addition to the variety of code implementations, there were variations on the analysis that were used, including subset weighting and higher-ordered shape functions, that are listed without attribution. These variations are important to include as they influence the DIC results.
This vague direction was required because of the wide variety of strain calculation implementations that were employed by the participating codes. The results were created by the respective code owners/experts and submitted to the DIC Challenge committee via a comma separated file (. csv). The analyzed results were selected from the center row (referred to here as a line-cut) of the DIC image results and reported with a 1 pixel horizontal spacing for both the noisy undeformed image and the noisy deformed image. The file starts with a short header that contains information on the subset, element size, VSG size or other parameters deemed important by the participant. The code output was arranged in columns of data with the first row indicating the horizontal pixel position with 1 pixel spacing for both the noise floor image and for the deformed image.
Illustration of full-field results All participants submitted a line slice in the horizontal direction of the vertical displacement obtained for both the deformed image and the noise image. These are shown in Figure  4 (a) for a typical local DIC code for the 5 subset sizes. This plot illustrates the tradeoff between filtering of the DIC code and measurement resolution. That is, results with the highest spatial resolution also have the highest measurement resolution, and vice versa for the largest subset size. Figure  4 (b) similarly shows typical results for a global DIC code for a variety of length parameters (element sizes). Figure  5  shows the strain results for a local DIC code. These results are representative of nearly all the submitted results. Figure  5  provides results from a typical local DIC approach, for several subset choices, with the attenuated strain fields shown on the left and the corresponding noise field on the right.
Since the theoretical solution does not exist for global and miscellaneous approaches, the red line corresponds to the local closed-form best fit, in the least square sense. seemed prudent to choose a polynomial fit that reasonably matches the data while also reproducing the correct theoretical fit for the local affine solution shown Figure  7 (a-b ). Figure  7 (c-d ) illustrates the fitting results when the proposed fits are applied to data provided from Global. A with elements of 75 pixels width (c) and Misc. B with length parameter set to 9 pixels (d). A fit is proposed, which best identifies the coefficients of the theoretical solution, in the least square sense. As expected, the theoretical fit, relevant for the local affine version of DIC, fails to describe the alternate DIC measurement techniques.
" Because of the variety of codes used, the actual VSG size is not reported. The results, however, do include the smallest feasible VSG for that code implementation. For this evaluation, knowing the VSG size is not important. Instead, like the displacement, the strain noise (measurement resolution) and spatial resolution can be plotted as in Figure  12. Nevertheless the MEI for the strain is defined as the squared of the spatial resolution times the measurement resolution. There is a larger spread in the results due to the extra choices that can be made in the strain calculation, however, the same trends occur, with the same tradeoff in spatial resolution and measurement resolution. The curves are not smooth and not all are monotonically decreasing, because multiple parameters can be changed at the same time causing jumps in either the spatial resolution or the measurement resolution.
Nevertheless, almost all curves have a slope of -2. This indicates that the spatial resolution is proportional to the square of the measurement resolution. B C D E F G A B C D E F G H A B C D A B C D E F 0 5 10 15 Fig. 13 : MEI for the strain (lower is better). Order of codes the same as in Figure  11  and broken up by code type. Bar colors correspond to the same as in Figures  8, 9 , 10 or 12. Percentage are calculated here with respect to the mean value. The MEI for the strain is summarized in Figure  13 , where Local. Affine. C and Local. Affine. G are not included because they were not submitted. In the figure, both the mean value and the standard deviation obtained with all the codes are shown in the red text and background. Relative percentages of the MEI with respect to the mean value are also shown for each code.
Conclusions Rather than functioning as a competition, it has always been the mission of the DIC Challenge board to encourage a healthy code development environment by sharing how the various codes compare with each other. Furthermore, each participant is given the code letter for their code, allowing them to see where they sit relative to all other codes, and allowing them to improve their code, or implement new approaches as needed. An important link between the measurement resolution and the spatial resolution has been highlighted in this work and is quantified via the MEI, emphasizing its relevancy. This clearly shows the direct tradeoff between spatial resolution and the measurement resolution for the displacement results. Tuning DIC parameters for improving the measurement resolution may impair the spatial resolution depending on the gradients of the measured QOI.
The results also show a much wider variation in the strain MEI, indicating that the method of calculation of the strain can have a very large impact on the results. While it seems that 2D-DIC is well understood, there is clearly a substantial amount of variation in the performance among the different codes. While spatial resolution is important, it is not the only criterion for deciding what methods to implement in a code. For example, analysis speed may be more important than bias, or tying directly to model results in the case of global DIC. However, when looking at full-field spatially varying data, this tradeoff between the measurement resolution and the spatial resolution is key. This work provides a useful framework for understanding the tradeoff and analyzing the performance of the DIC software using the provided images.
Acknowledgements The 2D-DIC Challenge is dedicated to  Dr. Laurent Robert. An active and important board member in the early years of the project, who passed away in 2016. He has been sorely missed in the experimental mechanics community. Sandia National Laboratories  is a multimission laboratory managed and operated by  National Technology and Engineering Solutions of Sandia, LLC. , a wholly owned subsidiary of  Honeywell International, Inc. , for the  U. S. Department of Energy's National Nuclear Security Administration  under contract  DE-NA-0003525. B. Blaysat is grateful to the  French National Research Agency (ANR)  and to the  French research program  " Investissements d'Avenir " for their financial support ( ICAReS  project , N•   ANR-18-CE08-0028-01 & IDEX-ISITE initiative 16-IDEX-0001 ,  CAP 20-25 ).
M is the number of compounds and N the number of reactions in the chemical system. D is oxygen diffusivity. An algorithm was developed that make it possible to consider: (1) a large number of reactions, (2) variations of different magnitudes in the different terms of the system of equations connected to the diffusion or to the rate constants of the reactions. A robust numerical model, written in MATLAB, was used to solve the reaction-diffusion system of equations. The resolution of this system included two loops. The first loop solves the diffusion of oxygen into the muscle tissue by discretizing the diffusion equation using a second-order Crank-Nicolson finite difference method that has the advantage of being numerically stable and accurate  ( Özis ¸ik, 1994; Kondjoyan et al. , 2006a , Kondjoyan et al.
, 2006b). At each time-step, the reaction system made up of ordinary differential equations was solved only in the numerical meshes where the oxygen had actually diffused. The algorithm used to solve the ordinary differential equations was the MATLAB ode15s solver. This solver applies to stiff systems, which was important in our case because of the order-ofmagnitude differences in the rate constants of the different chemical reactions. The model was applied on an infinite flat plate geometry of cm thickness (one-dimensional geometry). A Dirichlet boundary condition was used at the meat surface exposed to oxygen, with oxygen concentration being that of the oxygen-soluble content in the meat at the given temperature and packaging oxygen content. An Excel interface was used to easily change the group of reactions and rate constants considered.
To test the impact of numerical meshing on the results, we ran a set of preliminary calculations using 80, 100, 200 or 400 meshes. The time needed for the MATLAB code to simulate an 8-h period in storage at 20 • C on a desktop PC (Windows 10, Intel® Core™ i7-4790S 3. 2GHz CPU) was 11 min, 18 min, 4 h, and 18 h for 80, 100, 200 and 400 meshes, respectively. The average difference between the 400-mesh solution and the 200-mesh solution over the first 0. 5 mm from the surface was 5% of the 400-mesh solution for MbO 2 and 8% for MMb. These differences became 8% and 14% when the 100-mesh solution was compared to the 400-mesh solution. These differences were mainly localized in the first mesh at the surface of the meat. The spatial locations of the maximum and minimum values in the MbO 2 and MMb profiles were slightly affected by refining the mesh, especially when using a 200-mesh resolution.
Model application on the initial reaction-scheme As a first modelling stage in the work, some simulations were carried out at homogeneous oxygen concentrations to study the sensitivity of myoglobin oxygenation, and oxidation, to each of the 44 reactions Table  3  Oxygen consumption rates (OCR) measured by different authors on extracted mitochondria or on meat tissue at ambient temperature and at pH 5. 6. This data was selected from the literature as it was measured without additional reactants or enzymes in the case of meat tissue or with a little substrate and no added ADP in the case of extracted mitochondria. OCR values for meat were directly measured on the tissue in  Tang et al. (2005)  but calculated by us from the mitochondrial rates in  Ke et al. (2017).
Comparison with myoglobin profiles in meat Calculated effects of MAP, NHI, AO* & respiration Fig. 1. Representation of the approach followed in this paper. *MAP, NHI and AO refer to modified atmosphere packaging, non-heme iron (Fenton reactions), and water-soluble antioxidants respectively. making up our initial reaction scheme (Fig. 1 ). For this first sensitivity analysis, performed using the previously-developed  (Oueslati et al. , 2018)  SIMULOX software, the diffusion term was set to nil and only the rate constants connected to myoglobin reactions were made to vary, as the rate constants of the Fenton chemistry and antioxidant reactions were known from the previous study  (Oueslati et al. , 2018). The sensitivity calculations were performed using different methods: (1) determination of the contribution of each reaction of the scheme to the rate of formation of the targeted compounds, (2) effect of a variation in the rate constants of the reactions on the formation/consumption of targeted compounds, or (3) removing the studied reactions from the system and looking at the impact on the targeted compounds.
The treatment of chemical mixing in the radiative envelopes of intermediate-mass stars has hardly been calibrated so far. Recent asteroseismic studies demonstrated that a constant diffusion coefficient in the radiative envelope is not able to explain the periods of trapped gravity modes in the oscillation spectra of γ Doradus pulsators. We present a new generation of MESA stellar models with two major improvements. First, we present a new implementation for computing radiative accelerations and Rosseland mean opacities that requires significantly less CPU time. Second, the inclusion of shear mixing based on rotation profiles computed with the 2D stellar structure code ESTER is considered. We show predictions for the mode periods of these models covering stellar masses from 1. 4 to 3. 0 M across the main sequence (MS), computed for different metallicities.
We make use of the open-source stellar structure and evolution code MESA, r11701  (Paxton et al. 2011 (Paxton et al. , 2013 (Paxton et al. , 2015 (Paxton et al. , 2018 (Paxton et al. , 2019)) , where the default routines for computing radiative accelerations are based on the work by  Hu et al. (2011). The diffusion velocity of a species i is determined in MESA by solving the Burgers' equations  (Burgers 1969). We refer to  Mombarg et al. (2020)  and references therein for details on the numerical implementation. The effectiveness of radiative acceleration enters Burgers' equations via the local acceleration induced by momentum absorption of photons generated in the stellar core  (Hu et al. 2011) , g rad,i (r) = µκ R µ i c F(r)γ i (r), (2) where µ i and µ are the molecular weights of species i and the mean molecular weight, respectively, κ R is the Rosseland mean opacity, F(r) is the local radiative flux, c is the speed of light, and γ i (r) = ∞ 0 σ i (u)[1 -e -u ] -a i (u) k f k (r)σ k (u) du, (3) where u = hν/k B T (with h the Planck constant and k B the Boltzmann constant).
This integral depends on the local mixture which is given by the fractional abundances f k , with k f k = 1, and its computation requires the monochromatic cross sections σ i , and correction terms a i. MESA relies on the tables provided by the OP project  (Seaton 2005 ) for these quantities. These OP monochromatic tables provide data for H, He 1  , C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Cr, Mn, Fe, and Ni, which are equally spaced in v(u ) ≡ 15 4π 4 u 0 u 4 e -u du (1 -e -u ) 3 , (4) where u ranges from 10 -3 to 20. As a result of atomic diffusion, the Rosseland mean opacity can no longer be evaluated for the same mixture in each cell of the model since, κ R (r) = 1 µ 1 k f k (r)σ k (u) du -1 , (5) where the factors f k (r) for the metals are no longer constant throughout the star. Consistently computing κ R requires a lot of additional computation time compared to when the fractional metal abundances are constant throughout the star.
As a first step to reduce the number of redundant computations, we pre-process the OP mono tables where we compute the cross section for momentum transfer to an atom (i. e. the numerator in Eq. 3). The data from the OP project are tabulated in temperature T and electron number density N e. The latter has to be converted to a mass density as per, log ρ = log N e + log µ -log Ξ -log N A , (6) where Ξ = k f k Ξ k the average number of electrons per atom, and N A is Avogadro's number. For the temperature T (r) and density ρ(r) in each cell κ R and γ are computed by means of a bicubic interpolation, where we use the following scheme to select the 16 points on which the interpolation is done. First, select the closest point in the table by minimizing ∆ = (log T (t) -log T (r)) 2 0. 0025 + (log ρ (t) -log ρ(r)) 2 0.
7-M model starting at the pre-MS to a core-hydrogen mass fraction of X c = 0. 005, including radiative levitation for all elements for which OP mono data are available, takes 30 min on 36 CPUs with the routine presented here. In comparison, this takes 130 min with the current routines in MESA. Additionally, models computed in this work experience almost no failures to converge on the pre-MS, which was until now, besides the long wall times, also a bottleneck for us to compute grids of models with radiative levitation included. Fig. A. 1 in the appendix shows the difference in the predicted radiative accelerations and Rosseland mean opacity between the method presented in this paper and those of  Hu et al. (2011). Overall, the differences are small and the differences in the surface temperature and luminosity are well within typical precisions that can be achieved observationally.
IMPLEMENTATION OF SHEAR MIXING IN MESA In this work, we focus on macroscopic mixing from rotation-induced turbulence, henceforth referred to as shear mixing. It should be noted that this does not refer to the various forms of shear instabilities implemented in MESA (cf. Heger et al. 2000) , which cause very spiky mixing profiles, and as such, are not suitable for gmode asteroseismology  (Truyeart 2016). We follow the formalism by  Zahn (1992, Eq. 2. 14) , where we scale the local diffusive mixing coefficient as per D macro (r, t) = ηK r N dΩ dr 2 , ( 13 ) where η is a free parameter, N is the (weighted) Brunt-Väisälä frequency, and K the thermal diffusivity, K = 16σ SB T 3 3κ R ρ 2 C P , (14) with σ SB the Stefan-Boltzmann constant, and C P the heat capacity. The radial derivative of the rotation frequency, Ω, is computed using the 2D ESTER code (Espinosa Lara & Rieutord 2013;  Rieutord et al.