dataesr/scientific-paragraphs-categorization huggingface dataset:
These two representations are briefly described above, in Section 2. achieved the best performance when using a combination of keywords and language models, RULK KW+LM. The best correlation between the previously estimated gain and the actual gain was 0. 3164 against ALG and 0. 3192 against RPL. RULK mixed approaches. We also test a combination of our proposed instantiation RULK NE with the previous approaches RULK LM , RULK KW , and RULK KW+LM. In such combinations, each instantiation has the potential to contribute to the overall estimation of the knowledge gain by capturing some specific characteristics of the text documents. The mixed approach is defined by an interpolated estimator 𝜽 , parameterized by 𝛼 and 𝛽, defined as follows: 𝜃 RULK LM+KW+NE = 𝛼 𝐺 RULK LM + 𝛽 𝐺 RULK KW + (1 -𝛼 -𝛽) 𝐺 RULK NE , (4) where 𝐺 RULK is the estimated knowledge gain according to the respective RULK implementation.
CONCLUSION We have proposed an implementation of the RULK framework using named entities to represent the user's knowledge state and the contents of the documents. The knowledge gain -also said learning outcome -was estimated as the similarity between the tracked user's knowledge state and a target knowledge state expressing the learning objective. The estimated knowledge gain resulting from this framework was compared to the actual user's knowledge gain reported in a search-as-learning study. Our experiments suggest that such representation alone does not lead to an accurate estimate of the knowledge gains. However, by combining this approach to previously proposed ones (namely keyword and language model based), the results outperformed the state-of-the-art baseline by 10%. We proved that named entities representations are complementary to the other representations.
NMR Resonance Assignment, Solution Structure, and Intrinsic Dynamics The NMR resonance assignment (including full assignment of the [ 1 H, 15 N] HSQC spectra at 32 • C) as well as the solution structure of MAX60 have been published recently  [31, 32]  (BMRB: 34730; PDB: 7ZK0). The structure of MAX60 shares the global fold and a similar topology common to the MAX effectors  [5]  consisting of a ß-sandwich made of six antiparallel ß-strands (Figure  1 ). Also, the disulfide bridge characteristic of most MAX effector structures is present at a similar location in the structure of MAX60. Of interest, a helix turn (residues 77-79) replaces the ß5 strand that is present in the structure of most MAX effectors. In addition, the structure of MAX60 displays a long C-terminal extension that mainly comprises a well-defined α-helical conformation (residues 91-102).
Molecules 2023, 28, x FOR PEER REVIEW 3 of 24  [31, 32]  (BMRB: 34730; PDB: 7ZK0). The structure of MAX60 shares the global fold and a similar topology common to the MAX effectors  [5]  consisting of a ß-sandwich made of six antiparallel ß-strands (Figure  1 ). Also, the disulfide bridge characteristic of most MAX effector structures is present at a similar location in the structure of MAX60. Of interest, a helix turn (residues 77-79) replaces the ß5 strand that is present in the structure of most MAX effectors. In addition, the structure of MAX60 displays a long C-terminal extension that mainly comprises a well-defined α-helical conformation (residues 91-102). Residues colored in red correspond to identical residues in the two sequences (sequence identity ≈ 6%). Residues colored in green correspond to homologous residues between the two sequences (≈27% sequence homology).
The lower-bound limits were set to the sum of the Van der Waals radii between the two atoms. Repeating this process at each pressure step resulted in 25,250 potential restraint lists. After removing lists containing either no restraint (corresponding to random-coil unfolded conformers) or all the restraints (corresponding to the native conformers), the remaining lists were used to compute conformer ensembles by the torsion angle dynamics software Cyana3  [18] : 100 Cyana3 conformers were calculated for each list, and the conformer with the best target value was retained. These calculations were repeated four times, with four different random draws between lower-and upper-bound limit restraints, yielding four "best" conformers per restraint list and a final total set of 29,064 conformers. This total set of conformers was sorted according to the fraction of native constraints (Q), and to the r.
Discussion In comparison to the 3D structures of the M. oryzae MAX effectors AVR-Pia (PDB: 6Q76  [33] ) and AVR-Pib (PDB: 5Z1V  [6] ), whose folding pathways have been analyzed in a previous study  [17] , the structure of MAX60 presents two interesting differences. First, the ß5 strand, which is usually involved in the ß3ß4ß5 triple-stranded ß-sheet of the ß-sandwich, is replaced by a helix turn. Note that this strand is reduced to a maximum of only three residues in the crystal structure of AVR-Pia, and forms only few contacts with the ß4 strand, with a maximum of two H-bonds linking these two strands (ß4: E58 CO-HN T71: ß5 and, possibly, ß4: E60 NH-OC I69: ß5). Of course, the helix turn in the structure of MAX60 cannot make any H-bond with the ß4 strand, and thus does not contribute significantly to the stability of the core.
Sample Preparation Cloning of the MAX60 gene, overproduction, and purification of the protein were described in detail by Lahfa et al. [32]. In this construct, the N-terminal signal peptide has been removed from the original sequence, yielding a final protein of 89 residues, numbered from G19 to P107 (PDB: 7ZK0). Using this procedure, the 15 N-labeled MAX60 protein was prepared by using 15 NH 4 Cl in a minimal M9 medium and purified by employing affinity chromatography (HisTrap HP affinity column, Cytiva, Freiburg im Breisgau, Germany) and size exclusion chromatography (HiLoad 16/600 Superdex column (Cytiva). The protein was then concentrated to 0. 5 mM in the NMR buffer (25 mM Na Acetate, pH 4. 5) and stored at -20 • C. The purity was over 95%, as judged by SDS-PAGE.
Accordingly, a carefully optimized water flip-back pulse  [56]  was added before the last proton 90 • pulse in the experiment without saturation. A recycle time of 6 s between scans was used for obtaining a complete recovery of water magnetization and for reducing exchange effects. Moreover, the two experiments with and without proton saturation were acquired in an interleaved manner, FID by FID. A relaxation delay of 30 s was used before the FIDs of the experiment without saturation. For all these experiments, water suppression was achieved by using the WATERGATE scheme  [52, 57]. NMR spectra were processed with the Gifa 4. 22 software  [58]. Cross-peak intensities were determined from peak heights  [59]  using the Gifa peak-picking routine. The relaxation rate constants R 1 and the R 2 were obtained from nonlinear fits to mono-exponential functions  [60].
The square of the generalized order parameter S 2 , defined as S 2 f S 2 s , is a measure of the total amplitude of the internal motions. Note that S 2 equals S 2 f in Equation (2). Equation (4) assumes that the contribution of the fastest motion to the spectral density function is negligible. The values of the motional parameters of the individual residues can be derived from the fit of the 7 spectral densities obtained from the heteronuclear relaxation rate constants and NOEs measured at three different magnetic fields using equations  [2]  and  [4]  implemented in the software DYNAMOF  [69]  (https://bioserv. cbs. cnrs. fr/SITE/nmr_tools. html, accessed on 15 January 2022). An iterative non-linear least-squares algorithm  [60]  was employed to further minimize the error function. The "right" model was selected from χ 2 analysis.
∆G 0 f stands for the residue specific apparent free energy at atmospheric pressure or at 0 M urea. ∆V 0 f corresponds to the residue-specific apparent volume of folding for pressure denaturation, while m is related to the steepness of the unfolding transition for chemical denaturation. Half-denaturation pressure (P 1/2 ) or halfdenaturation concentration ([Urea] 1/2 ) were calculated as P 1/2 = ∆G 0 f /∆V 0 f and [Urea] 1/2 = ∆G 0 f /m. Native contact maps were obtained by using software CMView 1. 1  [41]  (http://www. bioinformatics. org/cmview/; accessed on 25 March 2020) with a threshold of 9 Å around the Cα of each residue, using the best structure obtained for GIPC1-GH2 among the 20 refined ones. The conformational landscape of MAX60 was obtained through a strategy described in detail in  [16].
html, downloaded 15 May 2019) software was used for the clustering of the 29064 conformers obtained through this procedure. The clustering must perform two goals: (i) global shape recognition and clustering at low Q values and (ii) more local r. m. s. d. clustering at high Q values. Accordingly, we adapted MaxCluster parameters that perform well with these two tasks. Since we performed 4 Cyana3 calculations for each constraint list, yielding 4 conformers per list, we choose the minimum number of conformers to form a cluster to be 5 (default value).
0 mmol L -1 nitric acid and 0. 75 mmol L -1 dipicolinic acid solution, with a flow rate of 0. 9 mL. min -1 , and an injection volume of 20 µL. MagIC Net is a control and database software for ion chromatography instruments that we used to perform all the calculations. Ca 2+ and Mg 2+ can also be determined by other methods, such as EDTA titration, atomic absorption spectrometry (AAS), and inductively coupled plasma optical emission spectrometry (IPC-MS). As known, the method of EDTA titration is used to determine the total hardness and therefore does not allow differentiating Ca 2+ cations from Mg 2+. Ion chromatography, AAS, and IPC-MS are the best techniques to determine the concentrations of Ca 2+ and Mg 2+. In our case, ion chromatography is the most suitable method because the concentrations are often quite high, far exceeding the maximum concentrations of the two other techniques, and therefore avoid dilution operations, sources of measurement errors, and time loss.
It is worth noting that the increase of calcium concentration contributes to maintaining the gradient concentration of calcium and magnesium high involving an improvement of cross-ion transfer. The optimal conditions determined according to the desirability function of the NEM-RODW software are 90 mg•L -1 for the concentration of magnesium, 80 mg•L -1 for the concentration of calcium, and 0. 68 mol•L -1 for the concentration of sodium, leading to a hardness removal efficiency of 90. 6 ± 5. 36%.
2016) , the North American Nanohertz Observatory for Gravitational Waves (NANOGrav;  Demorest et al. 2013) , and the Parkes Pulsar Timing Array (PPTA;  Manchester et al. 2013). Since the sensitivity of the GWB relies, among other things, on the number of pulsars and the length of the dataset, the three PTA collaborations came together to form the International Pulsar Timing Array (IPTA). The Indian Pulsar Timing Array (InPTA;  Tarafdar et al. 2022)  has recently also joined the IPTA. The three PTAs, along with the IPTA, have recently detected a common red signal (CRS) that shares many characteristics with the expected GWB  (Arzoumanian et al. 2020; Goncharov et al. 2021; Chen et al. 2021; Antoniadis et al. 2022). Although these measurements could be the first sign of the GWB emerging from noise, there was no definitive detection of the H-D correlation.
With simulated datasets,  Zic et al. (2022)  demonstrated how spurious evidence for CRS arises based on the choice of priors. Thus, robust modelling of the noise within each MSP dataset is critical given the possibility that the CRS may be a subset of the GWB signal. In addition to radio PTAs, an independent limit on the GWB was placed using gamma ray observations of MSPs  (Fermi-LAT Collaboration 2022). This not only provides an independent handle on the properties of the GWB but also, since gamma rays are immune to the effects of the ionised interstellar medium (IISM), it offers the possibility of testing the efficacy of current chromatic models through joint radio and gamma-ray analysis. Therefore, it is natural for such analyses to be integrated into future IPTA data releases. In this paper, we focus on the long-term timing noise budget of pulsars in the second data release of the EPTA  (hereafter, DR2full).
This contains ∼25 yr of data for 25 of the most precisely timed MSPs in the EPTA DR1. This new dataset will add significant sensitivity at the lowest Fourier frequencies of the GWB, owing to its long time span, and increased sensitivity at the higher Fourier frequencies due to improved observing cadence and an effective doubling of the observing bandwidth. We also combine low radio frequency pulsar timing data from the InPTA for 10 MSPs that are common to the EPTA DR2 (hereafter, DR2full+), to investigate the effects of the IISM and their impact on the total noise budget. For details on the EPTA and InPTA datasets, observing systems, and pulsar timing parameters, refer to EPTA  Collaboration (2023). The paper is structured as follows. In Sect. 2, we provide an overview of the noise budget, the descriptions of techniques used to estimate optimal Fourier frequency bins, and the selection of favoured noise models.
In Sect. 3, we present the estimated noise budget for the EPTA and InPTA datasets and highlight interesting cases. In Sect. 4, we interpret our results, compare them with previous analyses, and discuss implications for GWB searches. In Sect. 5, we discuss the efficacy of our noise models through additional tests, simulations, and cross-validation with independent software packages. In Sect. 6, we present conclusions and provide potential future trajectories to explore, especially by focussing on IPTA datasets. The customised noise models reported in this paper are applied directly to the EPTA's search for spatially correlated GWB signals  (EPTA Collaboration & InPTA Collaboration 2023).
Noise modelling techniques and noise budget The assumption that TOAs are only composed of a deterministic timing model plus time-uncorrelated instrumental noise is generally untrue in pulsar timing datasets. Stochastic processes, ranging from intrinsic spin noise in the neutron star to chromatic variations resulting from the IISM, contribute additional time-correlated noise in the observed TOAs  (Cordes & Shannon 2010). Unless this noise is accounted for, it can bias timing model parameter estimation and reduce the sensitivity to the GWB. The typical method to account for this noise is to solve for both the pulsar timing model and a stochastic Gaussian-process noise model simultaneously  (Lentati et al. 2013; van Haasteren & Vallisneri 2014). This is achieved by the use of Bayesian parameter estimation routines to find the posterior probability distribution of the noise model hyperparameters and the pulsar timing model parameters.
2010) , or spectral turnovers  (Parthasarathy et al. 2019 ) that may warrant additional terms beyond a single power law. However, the relatively small amplitudes of spin noise seen in MSPs is found to be relatively well-modelled by a power-law process  (Goncharov et al. 2020). The IISM introduces a wide range of chromatic noise processes into the TOAs that are dependent on the observing frequency. These include dispersive delays, scintillation, and pulse profile broadening due to multipath propagation  (Cordes et al. 2016; Shannon & Cordes 2017; Donner et al. 2020). Dispersive delays can become measurable on timescales of days to weeks and scale with the observing radio frequency as ν -2. DM variations are one of the biggest sources of unmodelled error, and although the wider bandwidths and higher cadence observations of recent PTA datasets significantly improves the ability to model the DM variations and separate them from achromatic signals, the inhomogeneity of the datasets means that it can be difficult to separate chromatic and achromatic noise on the longest timescales.
The best approach to account for DM variability depends on the underlying dataset. For EPTA, we currently favour using a stochastic power-law model for the DM variations, which assumes that there is a stationary smooth process that determines the DM. This allows for observations separated in both time and observing frequency to be used for constraining the DM. The theoretical expectation is that DM variations are caused by Kolmogorov turbulence in the IISM, and hence will have a power law index of γ DM = 8/3  (Foster & Cordes 1990). Alternative models (such as the use of DMX parameters;  Alam et al. 2021) , which typically make independent measurements of DM over discrete time intervals, avoid the assumption of smooth variation and stationary process, but require near-simultaneous observations at a wide range of frequencies to be effective.
This scales as ν -4 and therefore can be separated from DM given enough coverage in observing frequency. Variation in scattering timescale is modelled as a power law in the few cases where it is important for the pulsars in our current dataset. For each of our time-correlated noise processes, we model the noise of a process with chromatic index α for a TOA at time t and observing frequency ν (ν ref is the reference frequency set at 1400 MHz) with a Fourier basis of N coef coefficients as, y(t) = N coef j=1 Y j a j cos ( jωt) + b j sin ( jωt) ν ν ref -α , (1) where ω = 2π/T span for T span typically chosen to be the total observing time span, a j and b j are fit parameters with a Gaussian prior N(0, 1) and Y j determined by the noise model hyperparameters A and γ. Specifically, we define Y j as Y j = A 2 K scale s yr 3 T span f j f yr -γ , (2) where f yr = 1 yr -1 , s yr = 31557600 s yr -1 converts years to seconds with T span in seconds, and K scale is a scale that can adjust the units of A appropriately for the given noise process.
Parameter Prior A (s) log 10 U(10 -10 , 10 - 2  ) τ (days) log 10 U(1, 10 2. 5 ) t 0 (1st event)  [MJD]  U(54650, 54850) t 0 (2nd event)  [MJD]  U(57490, 57530) α (1st event) 4 (fixed value) α (2nd event) 1 (fixed value) adopted parameters 2 EFAC and EQUAD where the diagonals of the noise covariance matrix are scaled by σ 2 scaled = EFAC 2 × σ 2 original + EQUAD 2 , ( 3 ) where σ original is the measurement uncertainty of a TOA due to template-fitting errors. These parameters are applied for every observing backend and are tagged with the -group flag in the EPTA dataset. We use uniform priors on EFAC (0. 1 to 5) and log 10 (EQUAD) (-9 to -5).
The method implemented consists of including a real hyperparameter Ñcoef with a uniform prior U [ Ñmin , Ñmax + 1[ , and setting the number of frequency bins N coef as the integer floor value Ñcoef , thus ensuring an equal probability between all frequencies inside the prior range. The prior limits for the three stochastic signals considered in this work (red noise, DM, and scattering delay variations) are Ñmin = 10 and Ñmax = 150. The former is empirically chosen for statistical reasons. The maximum value of 150 allows testing for frequencies up to ∼33 days -1 and ∼60 days -1 for pulsars with the shortest and longest baselines, respectively, where white noise is expected to dominate over other signals. The value of the upper edge prior for the truncated dataset (DR2new; cf. Sect. 3) is Ñmax = 100 to cover frequencies up to 37-33 day -1 for all pulsars.
The six candidate noise models include any combination of achromatic red noise (RN), DM variations (DM), and scattering delay variations (SV). These are NONE (no time-correlated noise), RN, DM, RN+DM, DM+SV and RN+DM+SV (as reported in Tables  3  and 4. In this work, we do not consider models including SV but without DM, as they are physically unlikely at the observed radio frequencies in our dataset. We first evaluate the number of frequency bins that are the most preferred for each candidate noise model following the method described in Sect. 2. 4. In the second step, we select the most favoured model among the six candidates with a Bayes factor evaluation. Following the principle of Occam's razor, we select the simplest model (that is, the model with the lowest number of Gaussian process signals) in case of inconclusive results.
Estimated noise budget for the EPTA DR2 pulsars Here, we present the results of the noise model selection and parameter estimation for two EPTA datasets (to assist the reader, Table  5  provides a summary of the various datasets used in this paper), -The first is DR2full, containing data from the EPTA DR1 and the new instrumentation in DR2. -The second dataset consists only of the EPTA DR2 data from the new instrumentation (starting from ∼MJD 55611; hereafter, DR2new). -The third is DR2full+ which contains the data described as DR2full along with additional low-frequency data from the InPTA collaboration for 10 common MSPs. In principle, the combined EPTA+InPTA dataset (DR2full+) is much more sensitive for measuring the pulsar noise parameters as well as the GWB, with a total time span of 15-25 yr A49, page 5 of 20 Notes.
The second column lists the PTAs that contributed to the dataset for each pulsar. The third column reports the favoured model. Columns 4 to 9 report the estimated number of coefficients, amplitude, and slope (medians with 95% confidence intervals) for the achromatic and chromatic noise processes, respectively. The last column reports the total time span for each of the pulsars. for most pulsars. However, around half of these data are from instruments that were designed prior to the start of the PTA experiment, and in some cases lacked coherent dedispersion or were otherwise limited in time resolution on the fastest pulsars. Furthermore, in some cases the early data do not have good coverage in observing frequency, making it difficult to disentangle chromatic and achromatic noise processes.
Of Notes. The InPTA dataset extends the timing baseline of the EPTA dataset from MJD 59385 to 59644. It also provides consistent multifrequency coverage for a period of a few years, down to the low-end (∼300 MHz) of the frequency range whose coverage is very sparse with EPTA data only. the remaining nine pulsars, seven of them also include an achromatic red noise component in the favoured model, which could potentially impact the measurement of DM variations. We report a significant measurement of achromatic red noise for eleven pulsars, with six consistent with the predicted spectral index γ GWB = 13/3 from an idealistic GWB produced from GWdriven circular supermassive black hole binaries (SMBHBs). We find peculiar achromatic red noise for PSRs J0900-3144 and J1012+5307, with flat power-laws (resp.
γ RN = 1. 06 +0. 28 -0. 27 and γ RN = 1. 21 +0. 17 -0. 17 ), displaying short-term correlated noise, as shown in Fig. 1. For DR2new, we find significant achromatic noise only for seven pulsars, four of which are consistent with γ GWB = 13/3. The lower number of pulsars favouring RN as compared to DR2full+ can either be due to the shorter timing baselines which reduce the sensitivity for long-term red noise signals or due to unmodelled noise present in the first half of the dataset. Of the 22 pulsars with significant DM, sixteen are consistent with γ DM = 8/3. Of the remaining six, three pulsars have RN+DM as the favoured model. PSRs J1640+2224 and J1744-1134 display unusually low spectral indices at 0. 38 +0. 75  -0. 36 and 1. 13.
Comparison of EPTA Noise Models In this section, we compare the noise models between DR2full, DR2new, and the original models reported for the EPTA DR1 dataset from  Caballero et al. (2016). We find that the pulsars largely fall into three categories: -Category1: consistent noise models in the three datasets: Typically, DR2full improves over DR1 or DR2new, and both DR2full and DR2new do a better job of constraining chromatic noise than DR1. -Category2: DR2full and DR2new find chromatic noise: Several pulsars in DR1 found only achromatic noise or were unable to distinguish between achromatic and DM noise, but the DR2full and DR2new datasets prefer models with only DM variations. -Category3: complex noise models: In a handful of pulsars, including several of those with the best TOA precision, we find a more complex relationship between the noise models in the three datasets.