dataesr/scientific-paragraphs-categorization huggingface dataset:
Results. Despite the Orion B molecular cloud being highly supersonic (mean Mach number ∼ 6), the fractions of motion in each mode diverge significantly from equipartition. The cloud's motions are on average mostly solenoidal (excess > 8% with respect to equipartition), which is consistent with its low star formation rate. On the other hand, the motions around the main star-forming regions (NGC 2023 and NGC 2024)  prove to be strongly compressive. Conclusions. We have successfully applied to observational data a method that was so far only tested on simulations, and have shown that there can be a strong intra-cloud variability of the compressive and solenoidal fractions, these fractions being in turn related to the star formation efficiency. This opens a new possibility for star-formation diagnostics in galactic molecular clouds.
The reflection nebula NGC 2023 is a quieter counterpart of NGC 2024, hosting young B-type stars. It lies North-East of the Horsehead nebula. The rest of the cloud contains extended and quieter areas with strong filamentary structures (Fig. 1 ). This area has been extensively observed in the 3 mm range with the IRAM-30m telescope (PI: J. Pety). This survey has led to a series of papers  (Liszt & Pety (2016) ;  Pety et al. (accepted) ;  Gratier et al. (subm. ) ) to which this article belongs. The paper is organised as follows. We briefly describe in Section 2 the observations by the ORION-B (Oustanding Radio Imaging of OrioN B) collaboration, and the data we use here. In Section 3, we present the concepts and equations of the statistical method and the details of its implementation, from noise filtering to the computation of power spectra and the estimation of velocity-density correlations.
The Orion B project dataset The Orion B project (PI: J. Pety) has already mapped with the IRAM-30m telescope the south-western edge of the Orion B molecular cloud over a field of view of 1. 5 square degrees in the full frequency range from 84 to 116 GHz at 200 kHz spectral resolution  (Pety et al. accepted). The red rectangle in Fig. 1  shows the field of view observed up to now, over an H 2 column density map produced by the Herschel Gould Belt Survey consortium  (André et al. 2010; Schneider et al. 2013). The mapped area covers 56 × 98 arcminutes (about 6 × 11 parsecs at the assumed distance of Orion B, 400 pc) in size. So far, the observations provided about 250 000 spectra over a 32 GHz bandwidth, yielding a position-position-frequency cube of 370 × 650 × 160000 pixels, each pixel covering 9 ′′ × 9 ′′ × 0.
5 km s -1 (at Nyquist sampling). The reduced dataset amounts to 100 GB of data. The data reduction is described in details in  Pety et al. (accepted). This dataset is unique for its extensive coverage, both spatially and spectrally, at a typical resolution of 25 ′′ and a median noise of 0. 1 K [T mb ] per channel over a 32 GHz spectral range. From the spatial point of view, the survey gives us access to a large range of scales in the molecular cloud, from 50 mpc to 10 pc. For the analysis of turbulence properties (see  Sect. 4. 3) , it means that we are able to study a large fraction of the inertial range of the turbulence, with a potential view on the injection scale. The dissipation scale, on the other hand, is of the order of a milli-parsec  (Hennebelle & Falgarone 2012; Miville-Deschênes et al.
The 13 CO spectral data cube Most of the work presented here was performed on the 13 CO(J = 1 -0) datacube, which covers a velocity range of 40 km s -1 centred around the source systemic velocity of 10. 5 km s -1 and a rest frequency of 110. 201 354 GHz. The datacube presents an RMS noise of σ = 0. 17 K, and a median signal-to-noise ratio of T peak /σ = 7. 9. The 13 CO(J = 1 -0) line was chosen because it offers one of the highest signal-to-noise ratios over the whole map, but it does not feature as much saturation as the 12 CO(J = 1 -0) line. Signal is present at a signal-to-noise ratio greater than 5 in the whole map, except in the Hii regions around σ Ori and HD 38087 where molecular gas is photodissociated. The brightest regions are the NGC 2023 nebula, the center of the NGC 2024 nebula, and its northern edge (Fig.
In that case, the next main tool to retrieve 3-dimensional properties is the Helmholtz theorem, which allows to decompose any vector field in its divergence-free (solenoidal) and curl-free (compressive) components, F ⊥ and F ||. These components are related via a local orthogonality in Fourier space, F⊥ (k) ⊥ F|| (k). Solenoidal modes can be pictured as the modes of a turbulent incompressible field, made of vertices and eddies. On the other hand, compressive modes, made of compression and expansion motions, are more likely to be generated by phenomena linked to star formation. The application of these methods implies several requirements on the studied dataset. As mentioned earlier, the statistical isotropy of the cloud is the first necessary point, and enables the use of 2-dimensional averages as a means to estimate 3-dimensional properties.
It means that the method cannot be applied to individual filaments, or to clouds where a strong anisotropy is suspected, e. g. , due to the presence of a strong magnetic field at low Mach numbers. Second, the field is required to go smoothly to zero on its borders. This property is needed to ensure that the decomposition of the field is unique, since the Helmholtz decomposition is, in theory, defined up to a vector constant. It is also a necessary condition for good behaviours of the Fourier transform, since actual observational data are not periodic fields, unlike hydrodynamical simulations (see discussion in  Brunt et al. 2010). This implies that the studied field should be bounded in space, like for example a gravitationally bound cloud. In the case where the signal extends up to the edge of the observed field, the dataset has to be apodized.
The coordinates of the various lines of sights are given in arc-minutes in our custom set of coordinates (δx, δy). The average spectrum for the whole field, normalized to have the same peak temperature, is superimposed with a dashed line for comparison. The position of the spectra on the map are shown by white squares in the first panel of Fig. 2. Finally, from a practical viewpoint,  Brunt et al. (2010)  have shown that their method works best for fields with power spectra that are not too steep. Steep power spectra give measurements that are very sensitive to the low spatial frequencies, which are usually uncertain due to poor statistics. The compliance of our dataset with these requirements is discussed in detail in Sect. 5. 1.
The choice of fitting the power spectrum with a modified power law implies that the underlying physical processes should produce a power law. This is indeed the case for the inertial range of scales in Kolmogorov turbulence, and can be applied as well to Burgers turbulence (see, e. g. , Federrath 2013). However, the power spectrum of turbulence starts to deviate from a power law at scales where the energy is injected (low spatial frequencies) or dissipated (high spatial frequencies). The power spectra computed from our dataset somewhat deviates from a power law at low spatial frequencies (see Fig. 5 ). The power law can therefore only be fitted and then used above a given spatial frequency. The power-law range starts around ∼ 5. 5 ′. At high spatial frequencies, no deviations from the power law are detected (the fits render the observations very well).
Compliance with the method's assumptions In order to apply the Brunt & Federrath method to real observational data, we were able to overcome several difficulties and sources of uncertainty. First, the compliance of the dataset with the requirements of the method must be checked, namely the isotropy of the studied cloud, and its isolation. The whole field and the zooms present two opposite situations. The isolation criterion is well met in the case of the whole field: we have almost no signal to the West and to the South of the field, and very diffuse regions to the North and to the East (see Fig. 4 , first column), so that there is almost no need for apodization in order to have the signal going down to zero on the edges of the field. For the zooms, on the other hand, we are well into the cloud, so that there is signal all the way to the edges of the field.
In the case of a zoom on a bright region embedded in a diffuse one, the signal, and therefore the dimension on which it is emitted along the line of sight, is dominated by the bright gas. Therefore, since the zooms are centred on a bright region, the corresponding datacube behaves almost as if the bright region was isolated and isotropic. Besides, the non-angle-averaged power spectra of W 0 and W 1 do not show any apparent anisotropy at any scale (except for the windowing effects). If the power spectra are isotropic in two dimensions, then statistically we can expect the third dimension to follow this isotropy as well. Therefore, the isotropy requirement seems to be fulfilled by our dataset and the method can be applied. Second, as was mentioned by  Brunt & Federrath (2014) , the method is sensitive to values of the power spectra at large spatial scales (low frequencies of the power spectra) due to the characteristics of the sums in the parameters A and B.
Physical interpretation To our knowledge, this work is the first attempt at applying the Brunt & Federrath method to actual observational data  (Brunt & Federrath 2014; Lomax et al. 2015). The results need to be compared with what was done so far on numerical simulations. Both  Schneider et al. (2013)  and our calculations (see Sect. 4. 1 and Appendix) show that we are in a context of highly Fig. 8. Solenoidal turbulence fraction for zooms on the NGC 2023 and NGC 2024 star-forming regions. The shaded area corresponds to the g 21 uncertainty, while the error bars show the experimental uncertainties due to observational noise. The upper limit of the plots marks the equipartition limit. The map on the left presents the areas for which the calculations were performed (solid squares: NGC 2024, dashed squares: NGC 2023), superimposed on the 13 CO(J = 1 -0) T peak map.
Fig. 9. Comparison of the calculation results in the case of the zoom on NGC 2024 with three different methods of computing the power spectra: either the power spectra resulting from Fourier-transformed data are used directly, with a linear interpolation between the points (data only, blue), or the result of the power law fit at high frequencies is extrapolated to low frequencies to provide a power law throughout the whole range of frequencies (fit only, green), or a composite version of the power spectrum is built using the raw data at low frequencies, and the fit result at high frequencies (data + fit, red). The error bars account for the observational noise as well as for the g 21 uncertainty. The horizontal line marks the equipartition limit. supersonic turbulence, with a mean Mach number of about 6.
Conclusion From a practical point of view, our work has shown that it is possible to apply the numerical method of  Brunt & Federrath (2014)  to observational data, in order to determine the fraction of solenoidal and compressive motions in a molecular cloud, using molecular lines as tracers of the density and velocity fields. We were able to pinpoint the observational requirements to apply this method to a dataset. The spatial dynamic range is an important element, mostly in order to provide good quality power spectra. The field must be large enough to provide good statistics at low spatial frequencies, but it must also have a good spatial resolution, so that the power spectra have enough points to correct properly for the beam and noise effects. We found our minimum field size to be of at least 50 independent pixels.
Since infrared spectra are highly complex, with many overlapping signals, multivariate data analysis is required to gain useful information  [17, 22]. The aim of this study was to introduce the Duetz microtiter plate system (Duetz-MTPS) combined with HTS-FTIR spectroscopy as a high-throughput analytical platform for screening and monitoring of oleaginous fungi. In order to demonstrate the suitability of the system, we have used three fungal species and incubated them for 12 days under different temperatures. We have monitored lipogenesis of the fungal fermentations in microplates by high-throughput FTIR spectroscopy and GC reference analysis.
The preprocessed FTIR spectra (2nd derivative and EMSC) were used in the 3100-2800 cm -1 region, while the GC fatty acid data were autoscaled. Partial least square regression (PLSR) was used to establish calibration models for fatty acid parameters of fungal biomass. In order to establish such models a data set of GC reference measurements (responses) were used as a Y matrix, which was regressed onto an X matrix containing FTIR measurements of fungal biomass (predictors). Fatty acid parameters included total lipid content of biomass and fatty acid compositional data such as saturated fatty acids (SAT), monounsaturated fatty acids (MUFA), polyunsaturated fatty acids (PUFA), unsaturation index and relevant single fatty acids. From a total of 210 averaged FTIR spectra, nine samples belonging to early growth phase of the fungi were excluded (3 biological replicates each of M.
circinelloides 20 °C on day 1, P. glabrum 20 °C on day 2, and P. glabrum 30 °C on day 1). The remaining 201 average FTIR spectra were used for the PLSR. Reference GC fatty acid dataset was built on the measurement of 67 fungal samples, each of them measured in three technical replicates and then results were averaged. Therefore, one averaged GC fatty acid composition was used in the regression for three corresponding biological replicate FTIR spectra. In order to optimize the number of PLSR principal components (PCs), cross-validation (CV) was performed, where cross validation segments were defined by days. All spectra from samples obtained on the same day were removed in turn and used for validating the model established on the rest of the data. A root-mean-square error (RMSE) was calculated for models with 1-25 components.
4 ) and the C-O stretching peak around 1033 cm -1 (Nº 14) increased as well with the cultivation time for all studied fungi. Such changes in the polysaccharide region of IR spectra show that the cell wall composition changes during lipid accumulation. We can hypothesize that an increase of β (1,3)-glucan peaks corresponds to an increase in the cell wall thickness which goes along with lipid accumulation. Indeed, the homogenization of lipid-rich fungal biomass used for FTIR required long time, while that used for GC analysis required the use of hydrochloric acid and harsh mechanical pretreatment (bead beating)  [34]. Ami et al. [8]  and Signori et al. [10]  observed similar cell wall changes in FTIR spectra during oleaginous yeast lipogenesis. PCA was performed on FTIR spectra and GC fatty acid data to evaluate temporal-, species-and cultivation temperature specific differences related to lipid production.
In general, the lipid accumulation curves on the basis of the FTIR C=O ester peak showed smaller day-to-day variations and thus are more plausible. For quantitative purposes, the FTIR spectral data of biomass were calibrated versus GC fatty acid data. Summed fatty acid parameters (SAT, MUFA, PUFA, total fat, unsaturation index) and main individual fatty acids were predicted with high precision (R 2 between 0. 86 and 0. 96, RPD CV between 2. 6 and 5. 1). Sample preparation for HTS-FTIR measurement can be fully automated by robotics to further increase precision and throughput. We therefore conclude that HTS-FTIR spectroscopy is a simple, rapid tool for screening or at-line monitoring the cultivation of oleaginous species.
Molecular identification of microorganisms Molecular identification was done by amplifying and sequencing a 1. 3 kb fragment of the 16S rRNA gene. PCR reactions were carried out with primers 63F and 1387R  (Marchesi et al. , 1998)  on a Veriti TM 96-well thermal cycler (Applied Biosystems, Foster City, USA) using OneTaq Hot Start DNA Polymerase (New England Biolabs). Sequencing of both strands was done at Macrogen USA Corp. Consensus sequences (Supplemental Information) were generated with the CLC Main Workbench 5. 5 software package (CLCBio, Aarhus, Denmark) and compared to recorded sequences from GenBank database using the BLASTn algorithm.
FOX (Free Objects for Xtallography) is a computer program for solving crystal structures of all types of compounds using the powder data (but also the single crystal data) measured using X-ray, neutron and electron diffraction. It works in direct space using the reversed Monte Carlo algorithm of global optimization. Since its release fifteen years ago, it has developed into a powerful tool, simplifying the powder pattern analysis starting from the background determination, indexing and space group selection over the structure modelling using various pre-programmed structural fragments up to the validation of the proposed structural model.
Introduction FOX, 'Free Objects for Xtallography' is a free, open-source program for windows and Linux written for ab-initio structure determination from powder diffraction. It performs direct-space structure determination, allowing a modular description of the structure as a combination of atoms, polyhedra and molecules. Since the first release of FOX in 2001  [1] , many features have been added in order to enhance all steps required for a successful structure determination from powder diffraction (SDPD), along with various useful tools to explore crystal structures and powder diffraction patterns. Some of the developments have been reported in previous publications on FOX  [2] [3] [4] [5] [6]. Here, we complete the information on existing and new features, and give two examples of solving inorganic and organic crystal structures assisted with specific FOX tools.
Distributed Computing An extension with simple grid-computing capabilities (FOXGrid) has been added  [6]. This allows the use of the full processing power of the working PC, or adding other computers in the network to the computation process. It is embedded directly in the FOX program, and no additional software is required. The code works so that one instance (the server) is sending jobs to multiple FOX instances (clients) running on computers in the network or on other cores of the same multi-core computer, see Figure  2. When the job is solved, the clients send the result back to the server and request new work; therefore, the structure is solved in parallel. It is clear that adding more computing units to the calculation process further accelerates the structure solution process. Crystals 2017, 7, 322 4 of 9 depending on the desired average atomic displacement.
Distributed Computing An extension with simple grid-computing capabilities (FOXGrid) has been added  [6]. This allows the use of the full processing power of the working PC, or adding other computers in the network to the computation process. It is embedded directly in the FOX program, and no additional software is required. The code works so that one instance (the server) is sending jobs to multiple FOX instances (clients) running on computers in the network or on other cores of the same multi-core computer, see Figure  2. When the job is solved, the clients send the result back to the server and request new work; therefore, the structure is solved in parallel. It is clear that adding more computing units to the calculation process further accelerates the structure solution process. This approach allows solving more complex crystal structures in less time, as well as using the brute-force approach by defining a list of slightly different jobs, e.
g. , to test several possible space groups or different content of the asymmetric part of the unit cell. However, it is important to note at this point that correctly defining the problem at the beginning (correct description of the structure, unit cell and space group) is much more efficient than adding a large number of computing units. A similar approach was previously reported for the commercial software DASH  [20] , with its grid module GDASH  [27] , and was also reported using a cloud computing approach  [28]. This approach allows solving more complex crystal structures in less time, as well as using the brute-force approach by defining a list of slightly different jobs, e. g. , to test several possible space groups Crystals 2017, 7, 322 5 of 10 or different content of the asymmetric part of the unit cell.
Import and Export, CIF and Crystallography Open Database Since the first version, FOX has improved its support for the Crystallographic Information File (CIF) format; it is possible to load both crystal structures and diffraction data (single crystal and powder patterns) from CIF files. Note that, since the wavelength is not listed in powder pattern CIFs, the wavelength loaded in the previous CIF loaded is used instead. Crystal structures can be exported from FOX as CIF files, in order to be used in other software. It is also possible to export files (crystal description and powder pattern) directly for the FULLPROF software  [29]. One additional feature of FOX is the ability to query the Crystallographic Open Database (COD)  [30]  by giving constraints like a name or keyword, name of authors, list and number of elements, unit cell volume.
Availability of FOX FOX, 'Free Objects for Xtallography' is open-source software, available for free for Linux, Windows and MacOS from http://fox. vincefn. net. The source code is available directly from Sourceforge (https://sourceforge. net/projects/objcryst/) and GitHub (https://github. com/vincefn/ objcryst/releases). The underlying library can also be used with Python using the pyobjcryst project (http://www. diffpy. org/pyobjcryst/). Supplementary Materials: Powder diffraction data, FOX files and files containing Z-matrix description of molecules and rigid bodies are available as ZIP files at: www. mdpi. com/2073-4352/7/10/322/s1.
In this study, we propose a novel computational framework named general MSS transformation framework (GMSSTF) between two MSSs without the assistance of union of balls. To evaluate the effectiveness of GMSSTF, we applied it on a popular public database PDB (Protein Data Bank) and compared the existing MSS algorithms with and without GMSSTF. The simulation results show that the proposed GMSSTF effectively improves the computational efficiency and is potentially useful for macromolecular dynamic simulations.
Introduction Physically understanding the protein-protein or protein-RNA interactions involved in the biological processes is essential for new drug design in biomedical research  [1, 2]. Biological macromolecular surface visualization in 3D space helps us to focus on the spatial and structural information of proteins at atomic level and further explains the dynamic changes of molecular structure timely. Biological macromolecule (such as proteins) surface representation has been an important subject in the field of molecular visualization since 1964  [3] , where atoms are represented by 3-dimensional spherical structures with the sphere centers at actual atom positions and radii representing the electron fields. For example, the public database PDB (Protein Data Bank)  [4]  provides the spatial information about the amino acids in each protein in 3D space.