dataesr/scientific-paragraphs-categorization huggingface dataset:
We have also found that by using individual subject-specific templates (IT, LIT, FS and SPM12), structure volume variability is decreased compared to the cross-sectional approaches like CS that use a single common template (e. g. , the ICBM152 model) for all subjects. Among the three longitudinal methods tested, the LIT and SPM12 demonstrated the least bias and the smallest variability in structure volumes which is expected since both methods apply a longitudinal regularization and therefore minimize the temporal variability. Experiments on ADNI data reveal increased stability in estimating individual changes over time compared to standard cross-sectional approaches. Indeed, the cross-sectional approach was chosen as a reference method and allowed us to show an important improvement in the measurement of longitudinal change thanks to the longitudinal pre-processing (IT) and temporal regularization constraint (LIT).
The proposed longitudinal analysis techniques will allow for better power to detect differences between groups, and thus will lead to the reduction of the number of subjects required for research and for clinical trials. Compared to the literature, where similar ADNI cohorts of AD and NC were used, our power analysis shows similar sample sizes required to detect treatment effects for the FS, KNBSI, QUARC and TBM approaches  [47]. The proposed temporal constraint (LIT), reduces the sample sized by a factor by approximately 50% for brain, 70% for the lateral ventricles and 50% for hippocampi when compared to the similar longitudinal pre-processing without spatio-temporal regularization (the ID approach). The temporal constraint from SPM12, developed to optimize longitudinal VBM, produces unbiased results on the scan-rescan dataset but might be over regularizing the longitudinal deformation to detect structural change on the ADNI cohort in this experiment.
We limited our comparison to publicly available methods and/or results on the ADNI-1 cohort, but other methods have been developed and applied on real longitudinal data. The complexity and/or the computational cost of these methods  [10, 14, 65]  may limit the application to large databases such as ADNI. Wu et al. [14]  aligned all longitudinal images of a population toward a hidden common space equivalent to a template and it can be applied to a single subject. The individual longitudinal deformations or "temporal fibers" are estimated without any priors but regularized with a Gaussian kernel to preserve the continuity of the longitudinal deformation field. Similarly, Lorenzi et al. [13]  proposed to fit a linear model to constrain the longitudinal velocity fields of the subjects time-points in the Demons' framework with the baseline image used as a reference.
Conclusion This study evaluated a longitudinal framework with spatio-temporal regularization of deformation fields and the creation of an individual 3D template through non-linear registration in the context of longitudinal neuroimaging studies. The experiments were carried out on scanrescan and ADNI datasets. In comparison with freely available and popular methods, the spatio-temporal regularization (LIT) shows competitive results in regard to robustness, power and stability while reducing the number of subjects required to show statistical differences between groups. In addition, the LIT approach showed promising results for longitudinal DBM analysis and can be easily adapted to investigate specific anatomical biomarkers.
Acknowledgments Canadian Institutes of Health Research  ( MOP-111169 & 84360 ), les  Fonds de Recherche Santé Québec  and the  MS Society of Canada  (BioMed PhD studentship, 691) and CBRAIN (http:// cbrain. mcgill. ca/,Principal Investigator:  Alan C. Evans ) [66], a Canada-wide platform for distributed processing, for computation. Data used in the preparation of this article were obtained from the  Alzheimer's Disease Neuroimaging Initiative  (ADNI) database (www. loni. ucla. edu/ADNI). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. Complete listing of ADNI investigators is available at http://adni. loni. ucla. edu/wp-content/uploads/how_to_apply/ADNI_Authorship_List.
We present a new integral-field spectroscopic dataset of the central part of the Orion Nebula (M 42), observed with the MUSE instrument at the ESO VLT. We reduced the data with the public MUSE pipeline. The output products are two FITS cubes with a spatial size of ∼ 5. 9 × 4. 9 (corresponding to ∼ 0. 76 × 0. 63 pc 2 ) and a contiguous wavelength coverage of 4595. 9366 Å, spatially sampled at 0. 2. We provide two versions with a sampling of 1. 25 Å and 0. 85 Å in dispersion direction. Together with variance cubes these files have a size of 75 and 110 GiB on disk. They represent one of the largest integral field mosaics to date in terms of information content. We make them available for use in the community. To validate this dataset, we compare world coordinates, reconstructed magnitudes, velocities, and absolute and relative emission line fluxes to the literature and find excellent agreement.
One of the best-studied Galactic H ii regions (and the closest) is the Orion Nebula (M 42), visible to the naked eye. It is often one of the first objects targeted with a new instrument; first, to Data products are available at http://muse-vlt. eu/science. Based on observations made with ESO telescopes at the La Silla Paranal Observatory under program ID 60. A-9100  (A). see if something new can be discovered, and second, to use the plethora of existing observations for comparison, to validate a new system. A review about the nebula and its stellar content can be found in  O'Dell (2001). Spectroscopic studies of the ionized gas, confined to one or several slit positions, have partially characterised the Orion's emission spectrum (e. g. Baldwin et al. 1991; Pogge et al. 1992; Osterbrock et al.
Some of these aspects (depth and spectral resolution) were improved in a new mosaic mapping a similar area  (Núñez-Díaz et al. 2013 ). However, the spatial resolution of these data were still relatively low. Also, at the moment, this improved dataset is not publicly available in reduced form. Additionally, there are several studies with very good data quality in terms of depth, spectral and spatial resolution, that were devoted to the study of invidiual targets within the Orion Nebula, and observed the interplay of gas and stars in proplyds and Herbig-Haro objects (e. g. Vasconcelos et al. 2005; Mesa-Delgado et al. 2011; Tsamis & Walsh 2011; Mesa-Delgado et al. 2012; Tsamis et al. 2013; Núñez-Díaz et al. 2012). Therefore, they only mapped very small (∼10 ) rectangular areas. None of these currently existing datasets satisfy all of the following requirements: i) large mapped area, ii) depth, iii) ample spectral coverage, and iv) good spatial and spectral resolution.
Here, we present what we call true imaging spectroscopy of the Huygens region of the Orion Nebula, observed with the MUSE integral-field spectrograph mounted to VLT UT4 "Yepun". MUSE comes close to producing the "perfect dataset" mentioned by  O'Dell (2001) : it samples the Huygens region with high spatial sampling (0. 2) and reasonable spectral resolution (R ∼ 3000), and covers a large dynamic range. Our aim in this work is twofold. On the one hand, from the technical point of view, this is one of the first sets of MUSE data and as such, it was taken with the main goal of testing offsets larger than the field of view and stress-test the data flow system related to the new instrument. On the other hand, from a scientific point of view, given the lack of a high-quality and science-ready set of spectrophotometric data of the whole Huygens region, we wanted to provide to the community with such data.
In this paper, we first describe the observations and the data reduction (Sect. 2), validate the new data against literature values (Sect. 3), describe a few unusual artifacts in the MUSE dataset (Sect. 4), and demonstrate how the MUSE datacube can be used for an analysis of both atomic and ionized gas (Sect. 5), before we conclude with a few general remarks (Sect. 6). We assume a distance of D = 440 pc (O'Dell & Henney 2008) for the Orion nebula. This implies a linear scale of 0. 0021 pc arcsec - 1. The field of view of the MUSE dataset then corresponds to ∼ 0. 76 × 0. 63 pc 2.
33 allowed a spectrophotometric calibration of The observing conditions were good, with photometric sky and DIMM seeing varying between 0. 67 and 1. 25. The M 42 mosaic was observed after transit, with airmass values ranging from 1. 067 to 1. 483. During the observations, the moon had an illumination of 95%, a distance of ∼ 87 • from the target, and rose from 10 • to 45 • in elevation. The reduction used the dedicated MUSE pipeline  (Weilbacher et al. 2012, Weilbacher et al. in prep. )  through the EsoRex program. We used a development version of the pipeline, but the code was very close to the 1. 0 release 1 (patches are available on request). For the basic calibration we followed the standard procedure to reduce MUSE data: combine 10 bias images to form a master bias, combine 5 lamp-flat exposures, and use one exposure of each arc lamp to derive the wavelength solution.
For datasets with longer exposure time and lower contrast, the pipeline usually manages to correct the zeroorder of the dispersion solution on a per-IFU 3  basis using Gaussian fits as centroiding of bright sky emission lines. In the case of the M 42 mosaic, extreme contrast differences in some exposures and IFUs and the low sky emission background made this process unreliable. We therefore used the following procedure: we assume that the line [O i] 5577 is dominated by telluric emission (see e. g. Baldwin et al. 2000) , so it was taken as baseline reference for each exposure and IFU. Since the shifts on the CCD are likely smoothly changing during the time of our observation, we iteratively fitted a linear relation to the MJD-OBS against the pipeline-computed wavelength offset, separately for each IFU.
All exposures were combined into a single cube. Since the observation strategy included rotation, the data were affected by the derotator wobble 5  , so that each exposure had to be repositioned slightly. Luckily, each pointing contained at least one star that was also listed in the 2MASS catalog  (Skrutskie et al. 2006 ), so we used the 2MASS positions as reference for the offsets that were applied when reconstructing the full cube. The effect is that the absolute astrometry of the final cube is tied to the 2MASS coordinates, similar to the HST mosaic of the Orion Nebula  (Robberto et al. 2013). We created a first full cube with the standard pipeline sampling of 0. 2 × 0. 2 × 1. 25 Å. However, as discussed below, we then chose a higher wavelength sampling for the final cube, to partially overcome the undersampling of MUSE data in the dispersion direction.
Several image extensions are available as well, averaging the cube either using known filter functions, or using constant weights across interesting wavelength ranges around some lines (see Table  1  for details). These image extensions are thought to be used only to locate interesting features in the cube, not for scientific analysis. The file size of the full dataset is 75 GiB (LR|1. 25) and 110 GiB (HR|0. 85). For the purpose of the demonstration in this paper, we finally decided to use the LR|1. 25 data for everything except the spatially resolved velocity analysis of the ionized gas, where HR|0. 85 gives much lower systematic structures (see Sect. 3. 4). However, the spatial calibration and the spectrophotometric accuracy is exactly the same for the HR|0. 85 data, so the values quoted for the data quality in sections 3.
Quality of the atmospheric refraction correction Since the atmospheric refraction present in the raw MUSE data was corrected by the pipeline reduction, compact sources in the field do not show strong gradients across several spatial pixels. Nevertheless, the formula to compute the refractive index of air (taken from  Filippenko 1982 ) is imperfect, so some residuals are left in the data. We test the residuals using the centers of four bright stars in the field. The centers of the stars were measured in each wavelength plane of the final cube by two methods: 1. by fitting a Moffat function and 2. by computing the marginal centroid as with imcentroid in IRAF. The results are shown in Fig. 2. The strongest deviations from the mean centroid position of each star occur in regions of high background (strong nebular emission lines) and low throughput (telluric absorption).
462 and 9068. 6 from the NIST database  Kramida et al. 2014). Indeed, taking the reference value of 9068. 9 Å as quoted by  Osterbrock et al. (1992)  for [S iii], we find a velocity of 14. 35 and 14. 97 km s -1 for our LR|1. 25 and HR|0. 85 data, respectively, perfectly in line with the general trend. We therefore conclude that in the range λ < 5250 Å the MUSE data likely shows a problem with the wavelength calibration, on the level of up to 0. 1 Å (less than 1/10th of a MUSE pixel), while no systematic deviations larger than ∼ 3 km s -1 were found for wavelengths λ > 5250 Å. We then compare maps of emission line velocities over the full field. These velocities were derived using single Gaussian profile fits to individual lines, and the maps show systematic patterns. These systematics are much more pronounced in the LR|1.
Absolute fluxes There are only few publications on the Orion Nebula which also quote absolute emission line fluxes; most rely on flux ratios. To check the flux calibration of our data, we extracted spectra at positions given in the literature. For this purpose, we used the regions functionality of DS9 which allowed easy, interactive placement of rectangular boxes onto the WCS positions, approximating the given slit lengths and widths. Then, the "3D plot" function was used to create spectra summed over these regions. Following the example of O'Dell & Harris (2010, hereafter ODH10), we first extracted a 96. 8 box corresponding to the corrected position (4 south of θ 1 Ori C as described in ODH10) for slits 10+11+12 of  Baldwin et al. (1991, hereafter B91). The positions of the slits reproduced on top of the MUSE data are displayed in Fig.
e. variations in seeing between exposures. Since the two exposures per position are interleaved in the final HR|0. 85 cube and -depending on the exact sampling in the cube -often contribute to alternating wavelength planes, any variations in seeing between exposures effectively causes the PSF to also vary between adjacent planes in the cube. When integrating the flux of a star in an aperture that is too small to integrate the whole flux in both seeing conditions, the output spectrum looks particularly 'wiggly', as displayed in Fig. 9. The problem is mitigated when using PSF-matched spectral extraction  (Kamann et al. 2013)  where the PSF is fitted to each wavelength plane separately instead of using simple aperture extraction. We confirmed this by testing extraction strategies in a different MUSE two-exposure dataset (of a globular cluster,  Kamann et al.
In the MUSE data, we detect a secondary (blueshifted) component in the velocity field of these emission lines in this region. Fig. 11  shows the same image but corrected for extinction using the Balmer decrement (see Sect. 5. 1). Fig. 12        Like the extraction regions from the cube, the line identification in Fig. 14  were taken from  Baldwin et al. (1991)  and  Osterbrock et al. (1992). We can identify lines down to a flux of about 0. 005 × F He i6678 listed in their reference tables. However, a few lines visible in our spectrum are not listed in these reference sources and are not known sky emission lines. They remain unidentified and are specially marked in our figure. As a first demonstration of what is possible with this new dataset, we analyze the nebular emission in a spatially resolved (pixel by pixel) manner.
Diagnostic maps With the amount of emission lines present in the MUSE data and the reddening correction derived in Sect. 5. 1, we can easily create flux ratio images, i. e. diagnostic maps. The diagnostic images (Fig. 20   The bright elongated region towards the outer south-west highlights the shocked wind region. Here the gas flows towards the low-density end in a so-called champagne flow  (Arthur & Hoare 2006). In addition, the bow shock connected to the T-Tauri star LL Ori (see spectrum in Fig. 3 ) sticks out to the outermost southwest. Furthermore, towards the west a loop structure pops up. Similar structures can be recognized as well in highly processed 20 cm-continuum images taken with the VLA (Yusef-Zadeh 1990). The Hα/[O i] 6300 image (Fig. 21 ) shows sharp extended structures in the outer (cooler) regions of the Orion Nebula.
This map can be compared to the Hα velocity map shown by  García-Díaz et al. (2008, their Fig. 13 ). In both datasets, the large scale features show up in a very similar way. Even smaller features, like the velocity dips south of the Trapezium (especially at 168-358 and 161-354) are visibly similar. The absolute velocity values are slightly different between our data and theirs, with their value ∼ 2. 5 km s -1 higher. This difference is within the combined error estimates of both datasets. 15 o highlight differences in velocity derived from our data for different ions, we also show the velocities derived for [N ii] 6584, subtracted from the Hα velocity field (Fig. 28 , middle panel). The velocity offset shown in this map is around -3. 5 ± 4. 8 km s -1. Prominent features in this map are HH 202 to the west of the Trapezium and HH 203 and HH 204 beyond the Bright Bar, but on careful investigation it shows a plethora of other features, like blueshifted compact features not related to prominent Herbig-Haro objects, fainter filamentary structures around the Orion-S region and smoother large-scale changes.
Conclusions We successfully demonstrated the capabilities of the integralfield spectrograph MUSE instrument with a new dataset representing imaging spectroscopy of the Huygens region of the Orion Nebula. The cubes we provide are among the largest 3D spectroscopic mosaics created so far. We showed that the MUSE data are of high quality in terms of positional accuracy, atmospheric refraction correction, V-band magnitude reconstruction, velocities, and flux calibration. We also pointed out artifacts in and imperfections of the data, and explained why two representations in cube form are necessary to cover all possible investigations. The ensemble of data presented here already allows to investigate a variety of science topics. In this paper, we restricted ourselved to only give a demonstration, with a simple analysis of the ionized gas in the nebula.
Until that time, the current dataset is of high quality and already maps the most interesting area of the Orion Nebula in the optical wavelength range. It can serve as reference for many follow-up studies. To enable the widest possible use of these exceptional legacy data for science questions from members of the community, we publicly release the complete, reduced cubes as well as the inferred reddening, density, and temperature maps on http://muse-vlt. eu/science.
Acknowledgements. The authors thank the (rest of) the  MUSE consortium , the teams that conducted first light and commissioning observations, and support from  ESO  during these activities. We also thank  C. R. O'Dell  and  G. Ferland  for helpful comments. We thank our referee,  W. Henney  for an insightful and detailed report, that enabled us to improve several critical points. PMW and SK received funding through  BMBF Verbundforschung  (project  MUSE-AO , grant  05A14BAC  and  05A14MGA ). AMI acknowledges support from  Agence Nationale de la Recherche  through the  STILISM  project ( ANR-12-BS05-0016-02 ). RB acknowledges support from the  ERC  advanced grant  339659-MUSICOS. We are grateful to the developers of software such as SAOImage  DS9  (developed by  Smithsonian Astrophysical Observatory , http://ds9.
This paper aims at illustrating the contribution of a 3D finite elements modeling of the rotor-stator contact interactions and consequently the limits of a simplified 1D model, by comparing the results of both models. Numerical examples are constructed to be consistent with industrial EDF turbines. However some data have been changed for confidentiality purposes. 1D and 3D simulations are carried out with the open source finite element software Code Aster  [19]. The paper is organized as follows. Firstly, the contact algorithms and the time integration techniques adapted to the problem are exposed. Then, the rotor-stator system is presented, and three application examples highlight the main contributions of a 3D model to rotor-stator contact problems.
Choosing the contact solution method A penalty contact method is the only solution technique proposed in 1D contact modeling in Code Aster. For the 3D model, Lagrange multipliers method  [24]  can be used. However, in Code Aster, this latter leads to an unaffordable computational cost. It also has convergence problems if the contact conditions are severe. Therefore, penalty contact algorithms are used in both 1D and 3D contact problems. Using the same method makes the two modeling techniques consistent and more appropriate to the objective of comparing their corresponding results (see  Section 5). The penalty contact method transforms the contact problem to a non-constrained optimization problem. The problem size is not increased by contact condition; however, its major drawback is that it allows interpenetration.
The EMCA method (energy momentum conserving algorithm) was introduced by Simo and Tarnow  [27]  and modified in Romero and Armero  [28]  by the introduction of a numerical dissipation, which lead to the EDMC method (energy dissipation momentum conserving). This latter is still one of the best for contact problems. However, standard finite element softwares have not yet integrated such integration schemes, since their formulation depends on each study case. A Newmark integration scheme is the unique choice for 3D contact problems in Code Aster. The Newmark integration scheme is not energy conservative for contact/friction problems  [29]. The energy conservation is achieved in a frictionless contact problem by a non-penetration kinematic condition expressed on the velocity  [30] , also called the persistence condition  [31].
Moreover, high frequency oscillations appear and may lead to divergence, when the Newmark scheme is used to solve contact problems. However, if the time step is small enough and numerical dissipation is introduced, the Newmark scheme is stable and conserves the angular momentum  [32, 33]  for contact problems. This was performed in this paper for 3D contact problems and resulted in a large computational cost. Moreover, the integration schemes used for 1D rotor-stator contact problems, and that for 3D contact problems cannot be the same on Code Aster. In fact, the integration scheme that offers good stability for 1D contact problems is an explicit non-damped Runge-Kutta integration scheme  [34]. It offers a good stability for contact problems and a time step adaption technique that enables us to use small time steps in the vicinity of severe contact conditions, and larger time steps for noncontacting conditions.
2 ). The dimensions of the stator as well as the rotor's and stator's materials are found in Table  1. A 6. 8 × 106 N unbalance force that follows the rotor's rotations is applied to the simply supported rotor at point N b. It is triggered by the loss of a 100 kg mass at a 2. 75 m distance from the rotating axis, when the rotational velocity of the latter is 1500 rpm. The rotor rotational velocity is a data of the problem. Its time evolution is governed by Eq. (  7 ) in Section 4. 2, which leads smoothly to a constant value. Due to the rotating unbalance, the rotor vibrations are amplified until a rotor-stator contact is detected. One current limitation of Code Aster is that the rotational velocity is a data of the dynamic problem. Its evolution law is not an unknown of the mechanical problem.