dataesr/scientific-paragraphs-categorization huggingface dataset:
b. Set 2: Normalized profiles (NP): The second data set is termed NP and is derived from the RP set using a homothetic transformation; all velocities are scaled by a factor of 800/V bedrock so that the (5) ζ i = 1 2Q i (6) Q Si = V i /SC Q bedrock velocity is equal to 800 m/s for each profile in this "normalized profile" set, while the thickness of each layer is also scaled with the same factor to maintain an unchanged transfer function. More specifically, for a site j with a bedrock velocity V bedrock,j , the scaling is applied to the velocities and thicknesses of all layers i (i = 1, N j ) as follows: For real sites with very hard bedrock, e. g. , V bedrock = 2500 m/s, the scaled velocities may become unrealistically small at shallow depths; for instance, if V 1 = 120 m/s, then, according to (7), V ′ 1 = 40 m/s.
Focus on short and intermediate period ("Borcherdt factors" F a and F v ) For a building code perspective, special attention is given to the short-and intermediate-period factors introduced    (bottom). Thin blue lines correspond to every site profile, the thick red line is the geometrical average over the whole profile set, and thick light blue lines are average ± one standard deviation by  Borcherdt (1994 Borcherdt ( , 2002) )  to specify the short-period level (acceleration plateau) and intermediate-period level (velocity response). In the absence of any consensual, widely accepted definition, we defined them as follows: • F a is taken as the geometrical mean of AF for peri- ods in the range [0. 1 s, 0. 2 s] • F v is taken as the geometrical mean of AF for periods in the range [0. 75 s, 1.
We will start with presenting the simple equations corresponding to the former and then briefly explain its implementation in the general framework of neural networks. Let (X j , Y j ) with j = 1, Q be the sample data set; X i is a vector with R components, which are here the site parameters (up to six) for each soil profile considered in either data set (RP, NP, or TP), and Y i is a scalar equal to the corresponding amplification factor at a given frequency (or F a or F v ). Let now x be a vector containing the same R site parameters, corresponding to a new soil profile, which has not been considered in the initial data set (RP, NP, or TP). The goal is to predict the corresponding amplification factor y. This is achieved with the following formula: with w j being the weights of each training data, estimated from their Euclidian distance to the point of interest with: The output y is thus simply estimated as a weighted average of the amplification factors of the training set, with the weighting derived from the distance between the considered site and site proxies from the training set; thereby, nearby sites contribute most heavily to the estimate.
Present implementation For the present application, the implementation is separately completed on the three profile sets of RP, NP, and TP. These databases are described in Sect. 2. 4. 1. The initial set of data to feed the neural network is constituted of n P profiles and their corresponding amplification factors (i. e. , AF m (P k , θ, T i ) or AF m (P k , θ , ν i )). The input vector consists of a subset of the six site parameters for the RP set, and five site parameters for the NP and TP sets, for which the bedrock velocity is constant. The output consists of the calculated AF values for a given period or normalized frequency (271 values), and the Borcherdt factors F a and F v. This output is labeled AF GRNN (P k , θ , T i ) and depends on the number of site proxies used. There is one GRNN model for each scalar output, i.
These soil profiles have been selected arbitrarily: SP1 is part of the initial RP profile set, SP2 is not. The corresponding site proxies, as also listed in the same Table  6 , fall within the "core" of the initial data set (see Fig. 3  and Additional Files 1, 2, and 3). As shown in Fig. 9a  for soil profile SP1 and Fig. 9b  for soil profile SP2, the predicted AF values are clearly different from the actual ones, especially when only a small number of site proxies are considered. The differences between predictions and actual amplification factors vary between soil profiles. This difference indicates the.
16  for pro- file sets of RP, NP, and TP. This distribution is rather uniform in the two latter cases, while there is a lack of data in the RP set in the lower left and upper right corners. Therefore, the RP-RF model is poorly constrained for high-frequency, low-velocity sites (typically f 0 > 5 Hz and V S30 < 350 m/s) and for low-frequency, high-veloc- ity sites (typically f 0 < 2 Hz and V S30 > 600 m/s). The behavior of F a and F v with f 0 and V S30 is expressed with the following explicit equation associated with the GRNN models: where w j are the weights of each training data, estimated from their Euclidian distance in the (log(f 0 ), log(V S30 )) plane (x 1 = log f 0 and x 2 = log(V S30 )) (29) log (F a ) = Q j=1 log F a,j w j / Q j=1 w j (30) w j = exp   - � b � � � log � f 0 � -log(f 0,j ) � 2 + � log � V S30 -log(V S30,j ) �� 2 �.
Many GRNN models were considered in each case, with all possible combinations of site proxies. This provided a mechanism for comparing the performances of every proxy to explain (and predict) site amplification. The results showed that the key characteristics of the frequency-dependent AF may be satisfactorily reproduced with a limited number of site proxies. The best performing site parameter is the overall impedance contrast between bedrock velocity and minimum surface velocity. Because it is one of the most difficult and expensive parameters to measure, especially for thick deposits, other more convenient parameters are preferred, among them, the couple V S30 , f 0 reduced the variance of resid- uals by at least 60%. From a code perspective, equations and plots were provided describing the dependence of the short-and mid-period amplification factors F a and F v on these two parameters.
Acknowledgements This work was partially supported by the project: " Prédiction du mouvement sismique et estimation du risque sismique lié aux effets de site "  13MDU901   Tassili CMEP between Universities of Tlemcen (Algeria)  and  Grenoble (France). The authors wish to express their acknowledgment for this support. They wish also to acknowledge the contribution of  C. Cornou  from  IsTerre (U. Grenoble ) and  D. Boore  from the  USA Geologic Survey  who provided data for the 858 soil profiles. We also thank  Dr. Sanjay Singh Bora  and an anonymous reviewer for their careful reading and helpful comments and suggestions that have greatly contributed to clarify several issues and improved the final version. The final editing largely benefitted from the  Earth, Planets , and Space journal services.
Conclusions For the first time, the capabilities of a Non-Ideal Computational Fluid Dynamics (NICFD) solver were assessed against experimental results regarding flows of fluid in a non-ideal regime. Experimental data used for comparison were collected using the TROVA facility at Politecnico di Milano. The NICFD solver from the SU2 open-source suite was assessed for a set of exemplary NICFD flow-field that are relevant to ORC applications. These are the supersonic flow in converging-diverging nozzle, representative of ORC supersonic stators; a diamond-shaped airfoil at zero incidence in a supersonic flow, which is used to investigate the physics of oblique shock-wall and shock-shock interactions in turbine cascades; a supersonic backward facing step, in which the formation of an oblique shock is observed experimentally at the reattachment point past the step, resembling the formation of fish-tail shock waves at the trailing edge of turbine blades.
software library, Multi-atlas label Propagation with expectation-Maximizationbased refinement inTrODUcTiOn Neuroimaging is widely used to investigate both pathological and non-pathological neural phenomena. Given the increasing focus on the reproducibility of MRI findings, it is important that investigators share experiences of the many MRI analysis techniques available in a move toward standardization and optimization of methods. Structural MRI is routinely used to investigate FigUre 1 | (a) An example of a gross failure on a Track-Huntington's disease (HD) scan when using Statistical Parametric Mapping (SPM) 8 Unified Segment. (B) An example of a gross failure on a Track-HD scan when using FMRIB's Software Library (FSL) Brain Extraction Tool (BET) brain extraction and FAST segmentation procedures.
The selection of an appropriate segmentation tool is a challenge facing any researcher aiming to measure gray matter (GM) volume. Many tools have been compared, yet there is currently no method that can be recommended above all others; in particular, there is a lack of validation in disease cohorts. This work utilizes a clinical dataset to conduct an extensive comparison of segmentation tools. Our results confirm that all tools have advantages and disadvantages, and we present a series of considerations that may be of use when selecting a GM segmentation method, rather than a ranking of these tools. Seven segmentation tools were compared using 3 T MRI data from 20 controls, 40 premanifest Huntington's disease (HD), and 40 early HD participants. Segmented volumes underwent detailed visual quality control.
Furthermore, greater anatomical variability is likely due to the presence of pathology in clinical cohorts leading to poor segmentation performance in software not designed to deal with pathological abnormalities  (11). These key factors could lead to inconsistent findings within clinical neuroimaging studies  (7). There is evidence that some GM segmentation tools are sensitive to volumetric change in clinical populations. SPM 8, SPM 12, FSL 4. 1. 9, and FreeSurfer 5. 1. 0, for example, are all sensitive to disease-related change in Alzheimer's disease, with SPM best for scans with increasing noise  (4) , but generally appear to perform with greater accuracy for cortical GM (CGM) than subcortical GM, as shown in MS patients  (13). SPM, FSL, and FreeSurfer have all shown significant bias in GM measurements when comparing participants with Autism Spectrum Disorder to control participants  (7) ; and SPM can overestimate group differences in healthy elderly participants with atypical anatomy-using a voxel-based technique  (14).
This guide acts as a primer aimed at the novice imaging analyst or non-technical imaging scientist providing recommendations on how best to select segmentation software for quantification of GM volume, in particular CGM, according to the nature of the cohort of interest. As there is no ground truth regarding cortical degeneration in HD per se, and therefore no one measure against which to compare the quality of segmentations, we do not provide a ranking of segmentation tools based on their performance, but instead guidelines on how to select the most appropriate segmentation tool according to the type of dataset being investigated. In addition to commonly used segmentation methods (SPM, FSL, and FreeSurfer), we have included two relatively new tools that have yet to be extensively validated, Advanced Normalization Tools (ANTs) and Multi-Atlas Label Propagation with Expectation-Maximization-based refinement (MALP-EM).
Software Packages A number of segmentation algorithms were considered for this investigation, with the final tools based on ease of access, frequency of use within the literature and usability of the software. Software packages selected were • SPM version 8 Unified Segment  (30, 31). • SPM version 8 New Segment. • SPM version 12 Segment. • ANTs Atropos version 2. 1. 0 (32, 33). • MALP-EM version 1. 2  (34, 35). • FSL FAST using FSL version 5. 0. 9  (36). • FreeSurfer version 5. 3. 0  (37). Segmentations were performed in the native (or individual) space in which the scans were acquired. All seven tools include brain extraction either as an additional step prior to segmentation or within the automated GM segmentation pipeline. In this study, the brain extraction procedure provided by each tool was used along with the segmentation method.
Quality control Following any manipulation of the images scans were visually examined for quality. For this study, processing was classed as a "fail" if there was gross failure in performing the extraction or segmentation (Figure  1 ), rather than for more minor errors. Gross failures at any stage were initially checked to rule out user error. Processing changes were made to rectify software-based gross errors in two cases. First, SPM 8 Unified Segment delineation of the GM may fail if the orientation of the brain deviates noticeably from the standard SPM templates (Figure  1A ). In a few cases, therefore, adjustments were performed to shift the brain orientation to achieve a better match. Second, prior to segmentation using FSL, the Brain Extraction Tool [BET  (38) ] was run on all data. Using standard parameters BET failed to extract brains satisfactorily on the Track-HD cohort (Figure  1B ) and optimized BET parameters were substituted, with these optimized parameters provided in the Supplementary Material.
During QC, the GM regions were overlaid on the original T1 scans. This enabled easy comparison between the boundaries of the segmented regions and the visible boundaries on the T1 scan. Over-and undersegmentation refers to regions whereby the boundary of the segmented region differed from the visible boundary on the T1. All segmentation tools also showed minor errors as discussed in the results section (Figure  2 ). No manual intervention was used, however, to avoid adding subjectivity to  The first slice shows the frontal and temporal regions, the second slice is toward the middle of the brain, and the last slice shows the occipital lobe. All figures show default probabilistic segmentation maps for each software except for FreeSurfer, which shows volumetric and surface-based regions. For the probabilistic segmentation maps, the brighter the yellow within a voxel, the more likely that the voxel contains GM.
Segmentation using all three versions of SPM, FSL, and MALP-EM were run with default settings in native space. Advanced Normalization Tools brain extraction and segmentation pipeline (Atropos) requires templates and priors. The recommended default pipeline was followed and study-specific templates and priors  (32)  were created using a subset of 25 Track-HD scans, 5 from each group following the process recommended in Tustison et al. (40). Templates were created for both of the back-to-back baseline datasets and for the final time point using the same participants. Following template creation, ANTs brain extraction was run on each participant using the studyspecific template brain mask and priors. The extracted brain for each participant was then used when running the segmentation pipeline, Atropos.
DiscUssiOn We compared seven segmentation tools in controls and HD participants. Our aim was to identify the key advantages and disadvantages of each tool and use this information to provide advice for the non-technical user on selecting the most appropriate method to use according to the nature of the cohort. The segmented data were examined qualitatively and quantitatively with a particular focus on CGM. Subcortical changes are already well characterized in HD but there is increasing recognition that the cortex plays an important role prior to disease onset and particularly around the time of conversion to manifest disease  (17). Moreover, delineation of the cortex is generally more problematic than subcortical segmentation due to its convoluted structure. Results showed while few segmentations were classified as a "gross" failure following visual examination many tools show poor delineation of the GM especially in temporal and occipital regions, with wide variation in the quality of segmentation performance across tools.
This result supports the work of Iscan et al. (6)  who found that by including scans which have poorly delineated FreeSurfer regions in an analysis, the sample size required to detect a true effect increases. It is possible that the results shown in the parietal and occipital lobe are more uniform across tools as this is a region that is thought to undergo the most atrophy within CGM in PreHD and early HD  (16, (45) (46) (47) , and so statistical sensitivity to change in these regions is more robust when segmentation quality is sub-optimal and variability is high. In comparison, regions that may have slower rates of change in HD (e. g. , frontal lobe) are more easily biased by poor segmentations and thus different techniques identify different patterns of atrophy. While this study is underpowered to draw conclusions on the true nature of lobular progression of GM atrophy in HD, the results provide a useful demonstration on the importance of selecting a segmentation tool that performs well on a particular dataset.
Which segmentation Tool Best answers Your Question? It is important to consider which software tools contain features that are most appropriate for addressing your question or hypothesis. For example, if regional GM volume is the main focus, considering software that includes the option to perform regional analysis and atlas optimization can potentially reduce errors otherwise introduced when applying a rough mask to your cohort. Some tools (for example, SPM, ANTs, FSL, MALP-EM) are suitable for extracting volumes from customized regions or atlases applied to volumetric maps, while others, such as FreeSurfer, recommend using default atlases. Furthermore, the intended use of other structural analyses such as cortical thickness or VBM should also be considered. More broadly speaking, if T1 weighted imaging is being considered for a study it is important to ensure that it is the most appropriate method for examining the expected clinically relevant pathology, as opposed to techniques for example the use of diffusion weighted imaging would likely be more appropriate for studying WM pathology.
In addition, a number of registration or segmentation tools require high levels of processing power and may not run locally on desktop/laptop machines. Access to a high-powered computer cluster or just a single laptop with limited processing resources might determine which tool you choose. Financial costs also warrant consideration. While all tools examined for this case study are freely available for academic purposes, SPM works on a MATLAB platform that is not freely available. In addition, some tools require a license for use in industry settings and if developing methodology for later use within clinical trials, industry costs of these tools should be considered.
Subtle regional differences were not detected by all tools, however. One of the most significant findings from this study is the importance of visual quality control of GM segmentations. Poorly segmented and inaccurate data can easily be included in neuroimaging research if visual QC is omitted. While time consuming, the results of research that uses visual quality control will be more sensitive and accurate than if it is not performed. No one tool is more appropriate for analysis of every type of dataset or cohort. We have identified several key considerations for the selection of the most appropriate GM segmentation tool. The scientific question, level of expertise and available resources are naturally paramount, while comparison of two or three different tools for ease and success of application is recommended and visual quality control essential.
We adapt the Bender-Wu algorithm to solve perturbatively but very efficiently the eigenvalue problem of "relativistic" quantum mechanical problems whose Hamiltonians are difference operators of the exponential-polynomial type. We implement the algorithm in the function BWDifference in the updated Mathematica package BenderWu. With the help of BWDifference, we survey quantum mirror curves of toric fano Calabi-Yau threefolds, and find strong evidence that not only are the perturbative eigenenergies of the associated 1d quantum mechanical problems Borel summable, but also that the Borel sums are exact.
This changed recently due to two parallel but distinct ideologies. On the one hand, Ünsal and Argyres  [24, 25]  conjectured that renormalon singularities have a semiclassical explanation if the problem is approached from the regime of weakly coupled theory via the idea of adiabatic continuity  [26] [27] [28]. Indeed in such regimes it was shown that renormalon singularities disappear  [29] , and resurgence is likely operative. However this is difficult to test as no access to high orders of perturbation theory is typically available in QFTs. Nevertheless certain 1+1D models, when dimensionally reduced to quantum mechanics via the special kind of compactification, has weakstrong coupling adiabaticity and resurgent structure  [30] [31] [32]. Resurgence is likewise useful in quantum field theories without renormalon singularities, for instance the Chern-Simons theory  [2, 33]  and certain supersymmetric field theories.
Relatedly resurgence also finds its use in topological string theories, where Borel resummation and resurgence techniques have been used to explore non-perturbative contributions and to turn the asymptotic series of topological string free energy into a finite function  [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] , culminating in  [44] [45] [46] [47] [48]. Since resurgence is tightly connected with high orders of perturbation theory, it is of immense practical use to have an efficient way to computer high orders of perturbation theory. Recently in  [49]  a Mathematica package called BenderWu was developed using the method originally used by C. M. Bender and T. T. Wu  [50]  for an anharmonic oscillator, which efficiently computes symbolic perturbative solutions to a generic one dimensional quantum mechanical problem with the Hamiltonian of the form H = - 2 2m ∂ 2 ∂x 2 + V (x) , (1.
To study these systems, we will generalise the algorithm presented in  [49]  to difference equations of type (1. 2) and study their spectrum. We added to the mathematica package BenderWu 2 of [49] a function called BWDifference, which computes efficiently perturbative solutions to one dimensional quantum mechanical problems whose Hamiltonian is a difference operator of the exponential-polynomial type given in  (1. 2). This allows us to study the spectral problem of quantum mirror curve perturbativelly to a very high order (≥ 100) in. When the toric Calabi-Yau threefold is fano, the Hamiltonian operator arising from the quantisation of mirror curve is unique. Y. Hatsuda  [85]  argued that in the case of one particular toric fano Calabi-Yau threefold, the local F 0 , the perturbative eigenenergies of the Hamiltonian operator are Borel summable and that the Borel sums of the perturbative eigenenergies agree well with the numerical spectrum.
Finally in Sec. 4 we conclude and discuss possible future directions. We relegate to the Appendix the derivation of the adapted Bender-Wu algorithm, as well as the explanation of the technical observation that all the Hamiltonians we have considered have a unique classical minimum. 2 The Bender-Wu method for difference equations and the BWDifference package In this section, we first describe the Bender-Wu algorithm adapted to solve the eigenvalue problems of Hamiltonian difference operators, and then explain how to use the function BWDifference in the BenderWu package which implements the adapted Bender-Wu algorithm.