dataesr/scientific-paragraphs-categorization huggingface dataset:
Eventually, the bifurcation law governs the relation between radii of the parent (inflow) and child vessels. The optimization criterion is the total volume of the bifurcation, which is minimized. The simulated vessel tree constructed for the purpose of this research was also designed based on a real CT angiogram of the human abdomen. Specifically, we used the CALIX data set from a publically available Osirix database  [38]  presenting the normal state of the abdominal arteries. However, this time the real image (right kidney) served only as a reference for choosing locations for the synthetic tree terminals. Moreover, the flow rates on the individual outlets of the tree model (hereafter called the CALIX model) were adjusted so that the inlet radius of the root vessel at the end of the optimization process matched the size of the right renal artery visible in the image.
Phase contrast angiography simulation Our framework for simulation of PCA sequences consists of two integral modules. The first one is responsible for modeling blood flow through the vasculature of an imaged organ. This part is accomplished with COMSOL Multiphysics. The blood flow dynamics is described by the Navier-Stokes equation and solved by assuming a laminar regime, rigid walls, constant viscosity and incompressibility of the fluid. The solution is represented in form of a velocity vector field and flow streamlines, i. e. , motion paths of virtual particles traversing the blood vessel system from the inflow to the outflow terminals. This information is then imported by the MRI simulation module. The import algorithm populates the streamlines along their entire length with particles corresponding to blood spin isochromats.
In case of the simulated tree (Fig. 7a ), the number of outlets was set to 14. The diameters of the vessels in this model range from 1. 5 mm (minimum outlet) to 5 mm (inlet). This model was used in a 2D experiment with objective to measure the blood velocity in the main renal artery. In relation to kidney location in the original CALIX dataset, the tree was rotated, so that the main feeding renal artery co-aligned with the Z axis. This operation has significantly simplified the imaging simulation and the post-processing stage. 2-dimensional PCA gives the most credible velocity estimates when the throughplane flow is maximized. Thus, without rotation, acquired cross-sections of the renal artery must have been selected in configuration with oblique slice orientation. Note, that current implementation of the used angiography simulator disallows oblique slices.
The experimentally found value was v AVG = 10 cm/s. Even- tually, in case of the CALIX phantom, the flow was forced by setting the pressure difference between the inlet and outlet branches. The inlet pressure was varied to achieve ten different velocity measurement levels. This range was determined in relation to the maximum velocity in the renal vasculature volume. Based on the data reported in the literature for healthy kidneys  [42]  the presumed velocity interval embraced values from 45 to 93 cm/s. The presented configuration of the blood flow simulation experiments assume a simplified model of the true renal hemodynamics. One such assumption refers to the blood material, which was treated as homogeneous, Newtonian and incompressible fluid. Moreover, the vessel walls were rigid and stationary.
(  5 ). Examples of the simulated magnitude images and reconstructed velocity maps (maximum intensity projections) are shown in Fig. 8a-h. In order to validate the performed measurements we compared the image-derived velocity magnitude values with the reference data simulated in the flow simulation software. The comparison procedure consisted in finding K nearest mesh elements of the model lattice processed in Comsol for every voxel belonging to an arterial tree in the reconstructed velocity map. In our experiments, we tested K = 5 and 10. Note, that velocity vector field-as it results from flow simulation-is determined on a lattice composed of approximately 75 × 10 3 up to 125 × 10 3 nodes. Thus, one voxel in a simulated PCA image roughly corresponds to 13-20 velocity vectors depending on the acquisition matrix size and slice spacing.
Conclusions Firstly, it must be underlined, that the proposed approach to modeling kidney vascular trees leads to constructing realistic renal arterial models, tractable by flow and MR imaging simulation software. Extraction of proper geometrical descriptions of vessel walls and usage of Comsol's built-in modeling tools facilitates design of the arterial trees which are free from common surface-and edge-related defects otherwise generated by automatic tools. Secondly, the presented simulation framework enables quantification of the measurement error committed by the PCA imaging sequences. The image-derived velocities can be compared against ground-truth data available from blood flow simulation on a voxel by voxel basis. The mean velocity measurement error for the reconstructed renal arterial trees range from 1.
Availability of data and materials The simulated PCA images along with the reconstructed velocity maps and geometrical models of the renal arterial trees that support the findings of this study are available from the corresponding author on request. The CALIX CT data set used for simulation of arterial tree growth is available for download from the OSIRIX DICOM Image Samples repository (http://www. osiri x-viewe r. com/resou rces/dicom -image -libra ry/). Further clinical data cannot be provided, since the informed consent did not cover sharing the data.
The data reduction is, however, not straightforward and involves removal of the elastic peak, normalization and Fourier-Log transformation. Furthermore, some of the quantities derived are highly sensitive to details in the baseline correction. A software package and several novel procedures to streamline and hopefully improve the reduction of the NRIXS data generated at sector 3ID of the Advanced Photon Source have been developed. The graphical user interface software is named SciPhon and runs as a Mathematica package. It is easily portable to other platforms and can be easily adapted for reducing data generated at other beamlines. Several tests and comparisons are presented that demonstrate the usefulness of this software, whose results have already been used in several publications. Here, the SciPhon software is used to reduce Kr, Sn, Eu and Dy NRIXS data, and potential implications for interpreting natural isotopic variations in those systems are discussed.
The analysis of NRIXS data is quite involved. To make most efficient use of precious synchrotron beam time, it is important to develop data processing software such as PHOENIX  (Sturhahn, 2000)  or DOS  (Kohn & Chumakov, 2000)  that allow beamline users to analyze the results concurrently with data acquisition so that they can assess if sufficient counts have been acquired or if the measurements suffer from biases that can be rapidly addressed. The software of choice for reducing NRIXS data at sector 3ID of the APS is PHOENIX  (Sturhahn, 2000) , which is written in Fortran90 and is a command-line based program. To streamline data reduction  (Blanchard et al. , 2015; Dauphas et al. , 2014) , we have developed a new software for NRIXS analysis to meet the following requirements: (i) It has a graphical user interface (GUI), which facilitates learning of the program and speeds up data processing for the most repetitive tasks.
(ii) It provides flexibility in the definition of the baseline. (iii) It allows the user to define the energy range used in data reduction. (iv) It propagates uncertainties not only from counting statistics but also from baseline subtraction and energy scaling. (v) It outputs all the parameters already given by PHOENIX. The program is named SciPhon (Science of Phonons) and is a package that can be run under Mathematica. The reason why Mathematica was used is that it makes it easy to develop a GUI that is portable from one operating system to another and from one software generation to another. The software is available from the corresponding author upon request, from scientists at sector 3ID of the APS, and from the website http:// originslab. uchicago. edu/Software-and-Facilities.
For samples that are too thick for X-rays to pass through, a resolution function measured during the same session as the samples should be used. The data and resolution files can be obtained using the 'padd' module, which is part of PHOENIX  (Sturhahn, 2000). Padd stacks the different scans that belong to a single sample and establishes the energy scale. A typical NRIXS scan would be from À130 to +150 meV in steps of 0. 25 meV. To minimize bias introduced by unaccounted drift (increase or decrease) in the instrument response with time, we alternate between low to high (À130 to +150 meV) and high to low (+150 to À130 meV) energy scans. The expectation is that by measuring an even number of scans the systematic effects associated with such a change in the instrument response can be minimized.
4a ). We then used this synthetic spectrum and associated resolution function as inputs in the SciPhon software to calculate the PDOS and all the atomic dynamics and thermodynamic properties that are derived from g(E) and S(E). We compared the results following (1) no deconvolution of the resolution function from the data, (2) deconvolution with 10 iterations, and (3) deconvolution with 100 iterations. Near the elastic peak, significant oscillations are present in the deconvoluted data, especially when 100 iterations are performed (Fig. 4b ). As is expected, the calculated PDOS after 10 or 100 iterations define sharper drops at the Debye energy than when no deconvolution is performed (Fig. 4c ). However, the deconvoluted data with either 10 or 100 iterations yield noisier PDOS. All the properties derived from the data (deconvoluted or not) are consistent within error bars.
Note that all sources of error are not well quantified and the default values adopted below are conservative. The user can easily change these uncertainties in SciPhon. (1) Counting statistics that follow a Poisson distribution. (2) Uncertainties in the baseline definition, which is given by the uncertainty in the interpolation between the truncated low-and high-energy ends. (3) Offset in energy scaling. The resonance energy is found automatically by the padd routine of the PHOENIX package by finding the maximum in SðEÞ corresponding to the elastic peak. The energy resolution of the scans is $ 1 meV but the scans are made with energy steps much smaller than that (typically 0. 25 meV). In a single scan, the maximum intensity in the spectrum, which sets zero in the energy scale, is not known to better than half of the energy step size (0.
Discussion The software most often used for reducing NRIXS data at sector 3ID of the APS is PHOENIX  (Sturhahn, 2000). The SciPhon software presented here presents several distinguishing features. Most notably, (1) it is a GUI software with interactive sliders and fill spaces that streamlines some tasks associated with the data reduction (Fig. 3 ), (2) it outputs all the parameters needed to calculate reduced partition function ratios that are used to predict equilibrium isotopic fractionation between coexisting phases in geochemistry, (3) it uses a different approach to remove the elastic peak based on an interpolation of the signal near the elastic peak, (4) it offers the option of running an iterative peak deconvolution algorithm, (5) it offers the option of truncating the energy range used in the data analysis, and (6) it streamlines the definition and removal of a non-constant baseline across the energy range, which is important for the determination of the parameters derived from the higher moments of gðEÞ and SðEÞ.
As discussed above in the context of 57 Fe NRIXS measurements, the critical temperature estimates agree between SciPhon and PHOENIX but there is no internal consistency between the critical temperature and resilience calculated by PHOENIX. Another difference concerns the vibrational entropy and vibrational specific heat, which differ by a factor of three (the output values of PHOENIX are higher than those of SciPhon). The values calculated by SciPhon are directional, meaning that they would have to be multiplied by a factor of three to account for the bulk material if it was isotropic. This factor of three is not the cause for the discrepancy between the two softwares for the resilience. Polyakov et al. (2005)  used previously published NRIXS data of SnO and SnO 2 to calculate the fractionation factors for those compounds.
For the 122 Sn / 116 Sn isotopic ratio, we use the three NRIXS data reported by  Polyakov et al. (2005)  to derive a one-parameter expression of the -factor, 1000 ln ' A 1 T 2 À 0:0062 A 2 1 T 4 þ 0:000052 A 3 1 T 6 : ð73Þ This formula will be refined as the database of NRIXS measurements continues to expand for Sn.
Conclusion The synchrotron radiation technique of nuclear resonant inelastic X-ray scattering is used across many fields, including material sciences, condensed matter physics, heme biochemistry, geophysics and isotopic geochemistry. Isotopic geochemistry requires accurate determination of the force constant of the chemical bonds, which depends on the third moment of the NRIXS spectrum and is prone to biases that had not been fully appreciated before. This prompted us to develop a new software called SciPhon to reduce NRIXS data for all applications. This software runs in Mathematica and is thus portable on Windows, MacOS, Linux and Raspbian platforms. It is also perennial as most Mathematica codes are portable in new versions of the software. A virtue of using the Mathematica platform is that a user-friendly GUI can be deployed on many operating systems.
The program runs rapidly, with each step in the data processing not taking more than a few seconds. The total data reduction can be done in a minute or two. NRIXS data for all Mo ¨ssbauer isotopes can be reduced with this software. The options offered to the user are those studied at the APS but this can easily be extended to include other Mo ¨ssbauer isotopes. SciPhon presents several features that make it an asset when reducing NRIXS data: (1) It has a GUI, which facilitates learning of the program and speeds up data processing for the most repetitive tasks. (2) It provides flexibility in the definition of the baseline/ background. (3) It allows the user to define the energy range used in data reduction. (4) It propagates uncertainties from counting statistics, as well as baseline subtraction and energy scaling.
(5) It outputs all the parameters that can be extracted from the NRIXS spectrum and partial PDOS. This includes a builtin function to calculate the Debye velocity from the PDOS as well as all data needed to calculate reduced partition function ratios used in isotope geochemistry. (6) It uses an original approach to remove the elastic peak using an interpolation that respects the detailed balance. Extensive testing was performed to ensure that the software performs as expected. SciPhon yields values that are most often consistent with the values derived by PHOENIX. The baseline subtraction procedure used in SciPhon has been proven to yield reproducible data. SciPhon is routinely used by our group and others and data generated by it have already been published in top journals  (Dauphas et al.
Gypsilab is a Matlab framework which aims at simplifying the development of numerical methods that apply to the resolution of problems in multiphysics, in particular, those involving FEM or BEM simulations. The peculiarities of the framework, with a focus on its ease of use, are shown together with the methodology that have been followed for its development. Example codes that are short though representative enough are given both for FEM and BEM applications. A performance comparison with FreeFem++ is provided, and a particular emphasis is made on problems in acoustics and electromagnetics solved using the BEM and for which compressed H-matrices are used.
Introduction The finite element method (FEM) is nowadays extremely developed and has been widely used in the numerical simulation of problems in continuum mechanics, both for linear and non-linear problems. Many software packages exist among which we may quote free ones (e. g. FreeFem++  [21] , FENICS  [13] , FireDrake  [14] , Xlife++  [27] , Feel++  [12] , GetDP  [17] , etc. ) or commercial ones (e. g. COMSOL  [9] ). The preceding list is far from being exhaustive as the method has known many developments and improvements and is still under active study and use. Numerically speaking, and without entering into too many details, let us say that the particularity of the method is that it is based on a weak formulation that leads to sparse matrices for which the footprint in memory is typically proportional to the number of unknowns.
In terms of software packages available for the simulation with this kind of methods, and probably due to the technicality sketched above, the list is much shorter than before. In the field of academic, freely available software packages, one can quote BEM++  [24] , or Xlife++  [27]. Commercial software packages using the method are for instance the ones distributed by ESI Group (VAone for acoustics  [26]  and E-Field  [11]  for electromagnetism), or Aseris  [6]. Again, the preceding list is certainly not exhaustive. Eventually, one can couple both methods, in particular to simulate multiphysics problems that involve different materials and for which none of the two methods apply directly. This increases again the complexity of the methodology as the user needs to solve coupled equations that are piecewise composed of matrices sparsely stored combined with other terms that contain dense operators or compressed ones.
How to express such a problem? Which format should be used for the matrix storage? Which solver applies to such cases, an iterative or a direct one? Eventually, the writing of the software still requires abilities that might be out of the user's field of expertise. The preceding considerations have led us to develop the framework Gypsilab which, in particular, aims at simplifying and generalizing the development of FEM-BEM coupling simulation algorithms and methods. Written as a full Matlab suite of routines, the toolbox can be used to describe and solve various problems that involve FEM and/or BEM techniques. We have also tried to make the finite element programming as simple as possible, using a syntax comparable to the one used in FreeFem++ or FENICS/FireDrake and very close to the mathematical formulation itself which is used to discretize the problems.
Let us emphasize that, to our best knowledge, the only freely available software package, which uses the BEM and for which the way of programming is comparable to FreeFem++, is BEM++ that has been interfaced into FEN-ICS. The software described in this paper thus provide the user with a Matlab alternative. Fairly easy to install since it is written in full Matlab without any piece of C code, the framework contains at the moment several toolboxes: • openMSH for the handling of meshes; • openDOM for the manipulation of quadrature formulas and weak formulations that involve integrals; • openFEM for the finite element and boundary element methods; • openHMX that contains the full H-matrix algebra  [20] , including the LU factorization and inversion. In what follows, we will assume that all the preceding librairies are in the user's path.
This could be done using the following commands, assuming that the librairies have been placed in the parent directory of the current one. % L i b r a r y p a t h s addpath ( '. / openMsh ' ) addpath ( '. / openDom ' ) addpath ( '. / openFem ' ) addpath ( '. / openHmx ' ) Eventually, although the main goal is not the performance, Gypsilab may handle, on classical computers, problems whose size reaches a few millions of unknowns for the FEM part and a few hundreds of thousands of unknowns for the BEM when one uses compression. For FEM applications, this performance is very much comparable to already proposed Matlab strategies  [10, 5, 23] , though Gypsilab presents a much higher generality and flexibility. The present paper explains in some details the capabilities of Gypsilab together with its use.
Explanations concerning the implementation are also provided that give an insight into the genericity of the approach. In order to simplify the exposition, we focus here on FEM or BEM applications, leaving coupled problems to a forthcoming paper. Due to its simplicity of use, we strongly believe that the software library described here could become a reference in the field. Indeed, applied mathematicians, interested in developing new FEM-BEM coupled algorithms need such tools in order to address problems of a significant size for real applications. Moreover, the library is also ideal for the quick prototyping of academic or industrial applications.
A Laplace problem with Neumann boundary conditions Let us start with the writing of a finite element program that solves the partial differential equation (PDE) -∆u + u = f on Ω , ∂u ∂n = 0 on ∂Ω , (1) where the right-hand side function f belongs to L 2 (Ω). Here Ω stands for a domain in R 2 or R 3. The variational formulation of this problem is very classical and reads: Find u ∈ H 1 (Ω) such that ∀v ∈ H 1 (Ω) Ω ∇v(x) • ∇u(x) dx + Ω v(x)u(x) dx = Ω f (x)v(x) dx. The finite element discretization is also straightforward and requires solving the same variational formulation where H 1 (Ω) is replaced by one of its finite dimensional subspaces (for instance the set of continuous and piecewise affine on a triangular mesh of Ω in the case of linear P 1 elements). We give hereafter the Gypsilab source code used to solve such a problem in the case where the domain under consideration is the unit disk in R 2 , and the function f is given by f (x, y) = x 2.
% Mesh o f t h e d i s k N = 1 0 0 0 ; mesh = mshDisk (N, 1 ) ; % I n t e g r a t i o n domain Omega = dom( mesh , 3 ) ; % F i n i t e e l e m e n t s Vh = fem ( mesh , ' P1 ' ) ; % Matrix and RHS f = @(X) X( : , 1 ). ˆ2 ; K = i n t e g r a l ( Omega , grad (Vh) , grad (Vh) ) + i n t e g r a l (Omega , Vh , Vh) ; F = i n t e g r a l (Omega , Vh , f ) ; % S o l v i n g uh = K \ F ; f i g u r e graph (Vh , uh ) ; We believe that the listing is very clear and almost self-explanatory. The disk is first meshed with 1000 vertices (lines 2-3), then one defines an integration domain (line 5), the finite element space (line 7), the weak formulation of the problem (lines 9-11) and the resolution (lines 13). Let us immediately insist on the fact that the operators constructed by the integral keyword are really matrix and vector Matlab objects so that one can use classical Matlab functionalities for the resolution (here the "backslash" operator \).
Fourier boundary conditions We now consider the problem -∆u + u = 0 on Ω , ∂u ∂n + u = g on ∂Ω , (2) Figure  1 : Numerical solution of (1) on a unit disk using Gypsilab. Again, the weak formulation of the problem is standard and reads as follows Find u ∈ H 1 (Ω) such that ∀v ∈ H 1 (Ω) Ω ∇v(x) • ∇u(x) dx + Ω v(x)u(x) dx + ∂Ω v(s)u(s) ds = ∂Ω g(s)v(s) ds. The preceding code is modified in the following way (we have taken the example where g(s) = 1). Figure  2 : Numerical solution of (2) on a unit disk using Gypsilab. quadratic (so-called P 2 ) element used (line 9) which leads to use more accurate integration formulas, respectively with 7 points for the triangles (line 6) and 3 points per segment for the boundary mesh (line 7). Again, the result obtained is plotted in Fig. 2.