dataesr/scientific-paragraphs-categorization huggingface dataset:
2. DATA PS1 has produced an ideal catalog to study stellar densities in the Monoceros Ring. Like SDSS, PS1 has sufficient optical depth in the g and r filters to measure the magnitudes and colors of main sequence stars at MR distances of roughly 10 kpc. Unlike SDSS, PS1 does not avoid the Milky Way disk. Instead it covers the entire 30,000 deg 2 above declination -30 •. This includes roughly 75% of the plane of the Milky Way. At very low latitudes, PS1's depth is limited by dust and the light from foreground stars. But PS1 can make reliable measurements of MR stars down to Galactic latitudes of ±4 • while SDSS was mainly restricted to be more than 30 • from the plane. The PS1 g P1 r P1 i P1 z P1 filters (described in  Tonry et al. (2012) ) are fairly similar to the analogously named SDSS filters, although the g P1 filter (including the camera sensitivity) is a bit redder than the SDSS g filter and the z P1 filter has a sharper red cutoff than the SDSS z filter.
PS1 Spatial Completeness In order to accurately estimate the density of stars in the Monoceros Ring, we must accurately account for the spatial completeness of the PS1 survey. PS1 does not cover the sky uniformly. Gaps between chips in the camera and between exposures combine with bad weather to produce small holes in the PS1 survey. To measure the fraction of the sky covered by PS1, we cross-match our PS1 data with the 2MASS point source catalog  (Skrutskie et al. 2006 ) and calculate the fraction of stars in 2MASS that are detected in the g P1 and r P1 bands. We use the fraction of 2MASS stars we detect in each 2 × 2 degree pixel as a proxy for the spatial completeness in PS1 in that pixel. In order for the fraction of 2MASS stars detected by PS1 to accurately represent the spatial completeness of PS1, we must ensure that our 2MASS stars are real stars.
2 0. 2 0. 05 TABLE 2 A summary of the MATCH settings we use. The exact metallicity binning is described in the text. We automatically correct for dust extinction with SFD, but also allow MATCH's de-reddening tool to correct errors in SFD where the SFD g P1 extinction is greater than 0. 9 mags. at the fainter g P1, 0 which probe exponentially more volume than the brighter g P1, 0. Converting this qualitative description of MR densities along the line of sight into a quantitative one is one of our main challenges in this paper. 4. FITTING LINE OF SIGHT DENSITIES To convert our CMDs (Fig. 5 ) from densities in g P1, 0 , g P1, 0 -r P1, 0 space into line of sight stellar mass density estimates, we use a program called MATCH  (Dolphin 2002). With significant fine-tuning, MATCH can fit not only the line of sight densities, but also metallicities for large volumes of the Milky Way.
The MATCH Software The MATCH software matches color magnitude diagrams to fit stellar age, metallicity and density as a linear combination of model isochrones (we use those from  Cioni et al. (2006a,b) ) with fixed age, metallicity and distance. While it was initially used to probe the metallicity and age of stars in nearby dwarf galaxies or other localized structures with essentially fixed distances, it was adapted to model stellar mass densities with a smaller set of fixed age and metallicity combinations. Since we are concerned with the outer Milky Way, which has a relatively old stellar populations, we use 4 isochrones of stars of age 13. 3 billion years (10 10. 1 -10 10. 15 years in the settings file) with median metallicities ([Fe/H]) of -0. 3, -0. 8, -1. 4 and -2. 1 (in log 10 units relative to Z ).
Unlike Fig. 5 , the data here is not normalized in any way. Each bin is contain the total number of stars in that bin. We fit the data with a combined Milky Way and Monoceros Ring radial density described by: ρ(d) = MW (d) + MR(d) (11) MW (d) = ρ 0 1 + d/d 0 γ MR(d) = δρ(1kpc) 2πW 2 MR 1/2 exp (d -d MR ) 2 2W 2 MR. Here, d is distance along the line of sight from the Sun. MW (d), the main Milky Way density, as a function of distance, is fit as a modified power law with distance scale, d 0 , and exponent, γ, as free parameters. This profile performed slightly better (produced lower χ 2 's) than the more traditional Sérsic profile  (Sérsic 1963)   Eq. 11 fails in the direction of the Galactic Center, where a more sophisticated, global MW model is needed. Specifically, it uses the "MR" component to fit the bulge.
8. DISCUSSION Using the PS1 dataset that covers the MW plane, new modeling techniques and novel maps, we have produced a three dimensional and quantitative analysis of the Monoceros Ring. At the root of this work is the Pan-STARRS1 catalog. PS1 is the first optical dataset to examine the large areas of the Milky Way plane with the photometric precision necessary to perform isochrone fitting. Particularly, PS1 observed almost the entire 120 • < l < 240 • , -30 • < b < +40 • region where the MR is most visible. Our construction of depth and completeness maps was essential for precise measurements of stellar mass density. We fit line of sight densities from the MATCH program with a combined Milky Way and Monoceros Ring model to obtain quantitative stellar mass and distance estimates to the Monoceros Ring across PS1.
In addition to utilizing new data products and applying MATCH across three quarters of the sky, we have developed several new maps of the Milky Way and Monoceros Ring. In Section 5, we show Heliocentric maps of total stellar mass density and rediscover familiar features from  Newberg et al. (2002) ,  Grillmair (2006)  and  Slater et al. (2014). In Section 6. 1, we map our estimated MR mass and distance in this same projection. We see that the MR is at Heliocentric d = 6 kpc in the South but d = 9 kpc in the North. In Section 6. 2, we produce meridional cross-sections of the Milky that suggest that the Southern MR is contiguous with the Galactic plane while the Northern MR is elevated above the plane. Finally in Section 6. 3, we produce planar cross sections that show that the Northern MR is most consistent with a 13 kpc circle centered 4 kpc from the Galactic Center in the Anticenter (solar) direction.
Peñarrubia et al. (2005)  simulates the MR as a tidal dwarf stream that includes several wraps around the Milky Way. It is conceivable that this dwarf could have passed by the Galactic Anticenter at 6 kpc in the South on one pass and 9 kpc in the North on the second pass. It would be difficult to model both the Northern and Southern MR as a traditional warp or flare, but a disrupted flare (as per  Kazantzidis et al. (2009) ) provides a mechanism for creating the observed asymmetry. Deeper data and an improved understanding of Milky Way dust extinction will allow us to constrain the MR further. But even with no improvement in data or analysis, we have shown that any successful model of the Monoceros Ring must include a Northern feature at 9 kpc (Heliocentric), a Southern feature at 6 kpc and a total stellar mass of at least 10 7 M.
9. ACKNOWLEDGMENTS The PS1 Surveys have been made possible through contributions of the  Institute for Astronomy , the  University of Hawaii , the Pan- STARRS  Project Office, the  Max-Planck Society , and its participating institutes, the  Max Planck Institute for Astronomy, Heidelberg , and the  Max Planck Institute for Extraterrestrial Physics, Garching , The  Johns Hopkins University, Durham University , the  University of Edinburgh, Queen's University Belfast , the  Harvard-Smithsonian Center for Astrophysics , and the  Las Cumbres Observatory Global Telescope Network, Incorporated , the  National Central University of Taiwan , the  National Aeronautics and Space Administration  under Grant No. NNX08AR22G  issued through the planetary  Science Division of the NASA Science Mission Directorate , the  National Science Foundation  under Grant No.
Numerical aspects From the numerical point of view, an advanced numerical procedure is presented. The finite element code that is used to implement the micromorphic model is developed in ABAQUS®. The numerical integration in mixed one/four quadrature(s) (or Gauss) point for all the coupled constitutive equations is necessary in order to compute the stress tensor and the overall stress-like internal variables which appear in the weak forms associated to the balance equations. For the time discretization of the equations of our behaviour model, the fully implicit (iterative) Euler scheme in combination with an asymptotic one applied to the hardening equations are used. The overall constitutive equations are then reduced to two nonlinear and coupled algebraic equations (for the isotropic plasticity) with two unknowns: O ' and 1 n d.
Acknowledgements The authors acknowledge the financial support of the  National Research Agency (ANR)  as well as the contribution of their partners from  LRM/UTC and CdM/Ecole des Mines  in the project " MICROMORFING ". Also  Prof. M. François  ( UTT/LASMIS ) and  Ph. D C. Bao  ( UTT/LASMIS ) are gratefully acknowledged for the experimental work.
Multiobjective optimization-based embodiment design framework This section details the multiobjective optimization framework we developed to support the embodiment design process of mechatronic systems based on the morphological matrix and the design structure matrix used to formalize the compatibility and dependency relationships between the solution principles. These matrices should be used within a mathematical to formulate the multiobjective optimization framework. The objectives of the multiobjective optimization-based embodiment design framework detailed in this section. For each technical function expressed in the functional architecture, solution principles or technical solutions are extracted from solution databases. These solution principles shape the morphological matrix (see Table  1 ).
A compatibility analysis is then performed to identify incompatibility and dependency relationships between each pair of solution principles. This analysis is synthetized using the design structure matrix. The objective of the multiobjective optimization-based embodiment design framework is then to combine some solution principles in order to build mechatronic products that concretize all technical functions. Input data from our framework is then the morphological matrix summarizing the solution principles that can be considered to realize a given technical function, and the output data are possible architectures for the mechatronic system.
Application of the optimization framework on the case study We obtained the following optimization problem according to the design problem expressed in subsection 1. 1  (9)  The optimization process therefore aims to identify, for each technical function exposed in Table  1 , the best technical solution to obtain the best combinations of optimal solutions for the wind turbine. We implemented the equations (3) to  (9)  in Matlab in order to computerize the evaluation and the optimization process. Matlab is then integrated into ModeFrontier software that has been used to solve that problem. We considered the following parameters for the optimization problem solving: 1) Algorithm: NSGA II  [31] ; 2) Number of generations: 100; 3) Population size: 100; 4) Crossover probability: 0. 2; Mutation probability: 0.
Conclusion This paper dealt with the embodiment design of mechatronic devices. In this paper we proposed a multiobjective optimization framework intended to computerize the process for combining and selecting solution architectures built by aggregating solution principles from the morphological matrix. In a first part, we described the morphological matrix as a multiobjective optimization problem and use the design structure matrix to analyze the compatibilities between the solution principles. Then, in a second part, we presented the optimization framework showing how the proposed mathematical formulation can be integrated within the embodiment design process. And, in a third part, we exposed how this optimization can be implemented. Finally, in a final part, we successfully showed how the proposed framework could be used to solve a case study aiming to design a wind turbine and using Matlab and ModeFrontier.
Second, it introduces the flexible finite element framework GetDDM ("a General environment for the treatment of Domain Decomposition Methods") to test and compare them, based on the open source software GetDP 1  [21, 22, 35]  and Gmsh 2  [39, 40]. While GetDDM is written in C++, all the problem-specific data (geometry description, finite element formulation with appropriate transmission condition, domain decomposition algorithm) are directly written in input ASCII text files, using the code's built-in language. This general implementation allows to solve a wide variety of problems with the same software, and hides all the complexities of the finite element implementation from the end-user (in particular the MPI-based parallelization). Moreover, the software is designed to work both on small-and medium-scale problems (on a workstation, a laptop, a tablet or even a mobile phone) and on large-scale problems on high-performance computing clusters, without changing the input files.
The complete implementation of all the techniques reviewed in this paper is freely available online on the web site of the ONELAB project 3  [36, 37] , together with various 2D and 3D sample geometries, for both Helmholtz and Maxwell's equations. While other open source codes provide facilities for domain decomposition methods, either linked to finite element kernels (e. g. FreeFem++  [43]  or Feel++  [53]  via the HPDDM framework), or from a purely algebraic perspective (e. g. PETSc  [3] ), GetDDM adopts a complementary point of view. It focuses on Schwarz methods where the transmission conditions play a central role and provides a simple, flexible and ready-to-use software environment where the weak formulations of these transmission conditions can be automatically transcribed at the discrete level, with a direct link to their symbolic mathematical and physical structure.
The authors hope that this approach will help the scientific community to test and compare different optimized Schwarz domain decomposition techniques by focusing on the mathematics of the transmission conditions, while not having to worry (too much) about the implementation. The paper is organized as follows. The first section describes the acoustic and the electromagnetic scattering problems and the associated optimized Schwarz methods; the main transmission operators and the weak formulations are given, in view of their transcription in GetDDM. The next section describes the main features of GetDDM and provides code samples for the implementation of domain decomposition problems. Finally, the article concludes with some illustrative numerical results and perspectives for further development.
Implementation in GetDDM GetDDM is based on the open source finite element solver GetDP (http://getdp. info) and the open source mesh generator Gmsh (http://gmsh. info). The complete implementation of all the techniques reviewed in this paper is freely available online on the web site of the ONELAB project  [36, 37] , at the following address: http://onelab. info/wiki/GetDDM. Various 2D and 3D test-cases are provided online (see also Section 4) for both Helmholtz and Maxwell's equations, as well as detailed instructions on how to build the software for parallel computer architectures. Pre-compiled, serial versions of the software for Windows, MacOS and Linux are also available for development and testing. By default, GetDDM uses Gmsh  [39, 40]  for geometry description, mesh generation and data visualization.
Its main feature is the closeness between the input data defining discrete problems and the symbolic mathematical expressions of these problems, translated into ten inter-dependent objects. As mentioned in the introduction, while GetDP is written in C++, the problem definition is directly written in input ASCII text files (. pro files), using GetDP's own problem definition language. This allows for example to write weak forms of (28) together with either (  32 ),  (33)  or  (34)  directly in the input data files, and use the natural mixed finite element spaces suitable for discretization  [34, 23]. In practice, a problem definition written in. pro input files is usually split between the objects defining data particular to a given problem, such as geometry, physical characteristics and boundary conditions (i.
g. waveguide3d. pro or marmousi. pro). Of particular significance is that the input. pro files are not interpreted at run-time: they are analyzed once before the computation is run; then the computation (finite element assembly, system solution, etc. ) is carried out fully automatically in compiled code, the parallel linear algebra being handled by the open-source PETSc solvers  [3, 4, 5]. The remainder of this section covers in detail the implementation in the GetDP language (in. pro files) of the domain decomposition algorithms presented in Section 2, from the weak formulations to the parallel iterative solution of the resulting linear systems. The focus is on advanced techniques required to implement the domain decomposition algorithms efficiently; for an introduction to GetDP and its various more elementary features, the reader is referred to the GetDP reference manual  [20]  and is encouraged to explore the numerous examples available on the website of the ONELAB project (http://onelab.
g. i th process would send the field g ki to process j instead of only g ji , for j, k ∈ D i , j = k). A general implementation for layered decomposition is provided in Listing 12, taken from the file Decomposition. pro. This code is again written for an arbitrary number of MPI processes. Note that, to be used in the weak formulations, a Field must be called through the command ComplexScalarField or ComplexVectorField, depending on its nature. In Listing 12 and to simplify, the connected Fields are stored in the quantities g_in (see also Listing 4).
Other Features As seen above, GetDDM provides quite a general environment for the solution of Schwarz-type domain decomposition problems: the flexibility in the specification of discrete function spaces and weak formulations allows to handle a variety of physical problems and geometrical configurations; and the generic linear algebra (through IterativeLinearSolver) and communication mechanism (using Fields) permits to implement different variants of Schwarz methods. In addition to the basic functionality described above, the following features are also available: Coarse grids and preconditioning. The IterativeLinear solver can handle both left and right preconditioners: they can be specified in between a second pair of braces after the operations implementing the main matrix-vector product-see Listing  (Code extracted from the file SchwarzMacros.
Complete Examples Several complete examples for both Helmholtz and Maxwell problems are available online. Here are the simple steps to run these examples interactively in serial mode (see Figure  1 ): 1. Download and uncompress the pre-compiled GetDDM code bundle: • Windows: http://onelab. info/files/gmsh-getdp-Windows64. zip • MacOS: http://onelab. info/files/gmsh-getdp-MacOSX. zip • Linux: http://onelab. info/files/gmsh-getdp-Linux64. zip 2. Launch Gmsh (e. g. double-click on the gmsh. exe executable on Windows). 3. Open the models/ddm_waves/main. pro file with the File>Open menu.
Click on Run. Different test-cases can be chosen by selecting the appropriate Problem in the menu to the left of the graphics window. Top-level parameters (type of transmission condition, number of subdomains, frequency, etc. ) can be changed interactively in the menu as well. This interactive use of GetDDM is useful for testing, demonstration and visualization purposes. For actual, parallel computations, you will need to recompile the GetDDM source code for your particular computer architecture and MPI implementation. Detailed installation instructions are available on the website of the GetDDM project, at the address: http: //onelab. info/wiki/GetDDM. Once compiled, GetDDM is then called from the command  with concentric or radial subdomains  [13, 25]. e. , f. : guided acoustic or electromagnetic waves in rectangular waveguides  [57].
g. : guided acoustic or electromagnetic waves in the COBRA benchmark defined by the JINA98 workgroup  [58]. h. : acoustic waves in the underground Marmousi model  [54]. line, using (depending on your MPI setup), commands similar to the following (here for the waveguide3d test-case, on 100 CPUs): mpirun -np 100 gmsh -setnumber N_DOM 100 waveguide3d. geompirun -np 100 getdp -setnumber N_DOM 100 waveguide3d. pro -solve DDM Sample scripts for running large scale computations on computer clusters using the SLURM or PBS job schedulers are also provided in the models/ddm_waves directory. In all cases (interactive, serial or parallel), the input files and the workflow are the same: a geometry (file. geo) is constructed, meshed and partitioned into subdomains using Gmsh; then the problem definition (file.
Conclusion This article introduced a new open source software, called GetDDM, for testing optimized Schwarz domain decomposition methods for time-harmonic wave problems. The software aims to provide a simple, flexible and ready-to-use environment where the weak formulations of the wave propagation problems and associated transmission conditions for the Schwarz methods are transcribed naturally, with a direct link to their symbolic mathematical representation. The code and a variety of examples for both Helmholtz and Maxwell problems are freely available online for further testing, at the address: http://onelab. info/wiki/GetDDM. Depending on the chosen parameters (frequency, mesh refinement, number of subdomains, etc. ) the same files can run with a few thousands of unknowns on laptop computers or even tablets; or with billions of unknowns on massively parallel computer clusters.
Acknowledgements This work was supported in part by the  Belgian Science Policy  ( PAI grant   P7/02 ), the  Walloon Region  (WIST3 grants ONELAB and ALIZEES), the  French ANR  (grant MicroWave  NT09 460489  " Programme Blanc ") and the  "EADS Foundation " ( High-BRID  project, grant  089-1009-1006 ). Computational resources have been provided by  CÉCI , funded by  F. R. S. -FNRS (Fonds de la Recherche Scientifique)  under grant n  • 2. 5020. 11 ,and the Tier-1 supercomputer of the  Fédération Wallonie-Bruxelles , funded by the  Walloon Region  under grant n  • 1117545.
In this study, we characterized FSGS using the kinship relatedness coefficient (F ij )  (Hardy and Vekemans 1999 ) and the autocorrelation coefficient (r)  (Peakall et al. 2003). Analyses were based upon genetic and geographic distance matrices calculated using data from the six microsatellite markers and field GPS records of the plants sampled. Distance class sizes (20, 40, 80, 160, 300, 500 and 850 m) were specified such that the first distance interval would calculate relatedness coefficients based on all pairwise comparisons within a distance of 0-20 m, the second analysis for 20-40 m, and so on until the total spatial distance was covered. We used the same distance classes in both populations and both cohorts to be able to compare the results between the two sites and between the two cohorts within a population.
Acknowledgments This study was financially supported by  Netherlands Fellowship program (NUFFIC) , the  Netherlands. The field research was partly supported by  Abdou-Salam Ouédraogo Fellowship through Bioversity International (Rome, Italy) , the  CGIAR Research Programme on Forests, Trees and Agroforestry  and by  CGIAR  Fund Donors <http://www. cgiar. org/about-us/governing-2010-june-2016/cgiar-fund/fund-donors-2/>.