dataesr/scientific-paragraphs-categorization huggingface dataset:
The paper is organized as follows. After recalling the mathematical background we present five different approaches to address the non-linearity in the modal problem. For each approach, a variational formulation is derived. These formulations lead to five distinct EVPs: one rational EVP and four polynomial EVPs with various degrees (2, 3 or 4). In a second step, the corresponding discrete problems are numerically benchmarked using the state-of-the-art SLEPc  [22]  solvers. The issues inherent to the sign-changing coefficients and corners are discussed and the convergence of the fundamental mode of the structure is studied. A discussion on the respective strengths and limitations of all the proposed solutions is conducted. For the purpose of this study, an interface to SLEPc has been implemented in the FE code GetDP  [23].
6. 2, the mesh is globally unstructured and locally structured in order to be symmetric at the interface with the dispersive material. Finally, the mesh is periodic in the direction of periodicity of the grating. Figure  2 : Mesh of the computational domain for N = 5. The mesh size is set to a/N in Ω 2 (free-space), a/(2N ) in and around Ω d 1 (dispersive rod). First or second order edge elements (or Webb elements with interpolation order k = 1 or 2  [39, 40] ) are used in electric field cases (Aux-E, PEP-E, NEP-E, Lag-E) and first or second order nodal elements are used in the magnetic field case (PEP-h) depending on the study. The GetDP  [23]  software allows to handle the various required basis functions handily (details about the implementation are given in Appendix III). Finally, ONELAB is an open-source software bundle  [41] , containing both Gmsh and GetDP, which provides a lightweight graphical interface to these programs.
As for the polynomial eigenproblems (PEP-E, Lag-E, PEP-h) described in Eqs. (20, 23, 24) , the matrices corresponding to the various powers of ω (that is, in the reference example, 4 matrices for the electric field formulations and 5 for the magnetic electric field formulation) are assembled separately in GetDP and simply passed to SLEPc. SLEPc provides a PEP module for the solution of polynomial eigenvalue problems, either quadratic or of higher degree d. The user can choose among several solvers. Most of these solvers are based on linearization, meaning that internally a linear eigenvalue problem is built somehow and solved with more traditional linear eigensolvers. The linear eigenproblem produced by the linearization is of dimension d • n, where n is the size of the polynomial problem.
However, the number of terms to write with the NEP solvers remains "two plus the number of distinct dispersive media". We present both these twin approaches, but, from the practical point of view, the rational NEP solver class is clearly the best match for the purpose of this study. SLEPc's NEP module for general non-linear eigenproblems  [44]  can be used to compute a few eigenvalues (and corresponding eigenvectors) of any eigenproblem that is non-linear with respect to the eigenvalue (not the eigenvector). This includes the rational eigenvalue problem, for which SLEPc solvers provide specific support. The problem is expressed in the form -1 i=0 A i f i (λ)x = 0, (25) where A i are the matrix coefficients and f i (•) are non-linear functions. Again, SLEPc provides a collection of solvers from which the user can select the most appropriate one.
Conclusion In this paper, we have presented a framework to solve non-linear eigenvalue problems suitable for a Finite Element discretization. The implementation is based on the open-source FE software GetDP and the open-source library SLEPc. Several approaches aimed at the linearization of the eigenvalue problem arising from the consideration of frequency-dispersion in electromagnetic structures have been introduced, implemented and discussed. The relative permittivity was considered under the form of a rational function of the eigenvalue with arbitrary degrees for the denominator and numerator. Five formulations were derived in the frame of a typical multi-domain problem exhibiting several key features in electromagnetism: The mono-dimensional grating is a quasi-periodic problem with PMLs.
This is a 2D problem quite representative of 3D situations since the physics is as rich as in 3D (exhibiting surface plasmons) and the vector case with edge elements is tackled. We take advantage of the performance and versatility of the SLEPc library whose non-linear eigenvalue solvers were interfaced with the flexible GetDP FE GNU software for the purpose of this study. An open-source template model based on the ONELAB interface to Gmsh/GetDP is provided and can be freely downloaded from  [24]. It exhibits the various ways to set up nonlinear EVPs in the newly introduced GetDP syntax: One rational EVP and four polynomial EVPs with various degrees are shown. The first four formulations of the 2D grating problem concern the vector case and the choice of unknown is the electric field. First, physical auxiliary fields (Aux-E) allow to linearize of the problem by extending Maxwell's operator.
3(g ). Other higher bands appear below the first branch of the folded light line for higher values of the Bloch wavevector α. After the first folding of the light line at Re{ω}/η ≈ 0. 45, classical bands are retrieved but some discrepancy appears between the electric formulations and the magnetic one as detailed in Sec. 6. 1. The accumulation of flat bands in the range 0. 55 < Re{ω}/η < 1. 1 corresponds to plasmons and corner modes. Finally, the dispersion relation retrieves a more conventional behavior, with very leaky higher frequency modes such as mode h 8 in Fig. 3(i). This work has involved changes to GetDP in both the source code and the parser in order to call the relevant SLEPc solvers in a general manner. These changes now allow to solve a large class of non-linear (polynomial and rational) eigenvalue problems suitable for a FE discretization.
The processing cycle ends with the presentation of the results, using the PostOperation object. The major changes appear at Formulation and Resolution stages. A new Eig operator was introduced in the parser. It can be invoked to set up a polynomial EVP when combined with the keyword Order, or a rational EVP when combined with the keyword Rational. The Order or Rational keywords allow to define the dependence of the problem with the eigenvalue λ := iω. Depending on whether Order or Rational is set, GetDP internally calls the static functions _polynomialEVP or _-nonlinearEVP where the interface to SLEPc is written in practice. These functions can be found in the source code of GetDP in the C++ file Kernel/EigenSolve_SLEPC. cpp for further details. Note that in all GetDP eigenvalue solvers the eigenvalue has been chosen to be iω, consistently with the convention in this paper.
In the following GetDP listings, the dots (. ) represent a deliberate omission of some instructions that are unnecessary to the comprehension of the implemented syntax. The reader is invited to refer to the template example to see these GetDP code snippets in their global context. Then, at the Resolution step, each rational function expected as a factor of each Galerkin term is specified. The 6 th (respectively 7 th ) argument of the EigenSolve function is a list of polynomial numerators (resp. denominators), each polynomial numerator (resp. denominator) being itself given as a list of GetDP floats. The position of each numerator (resp. denominator) in the list of numerators (resp. denominators) corresponds to the tag following the Rational keyword. A polynomial numerator (resp. denominator), is represented by a list of (real) floats by decreasing power of λ.
For instance, the list -eps_oo_1,gam_1*eps_oo_1,-om_d_1^2,0 in Listing 3 represents the polynomial -ε ∞ λ 3 + γ d ε ∞ λ 2 -ω 2 d λ, numerator of λ 2 ε r,1 (λ). Likewise, the list 1,-gam_1 in Listing 3 represents the polynomial λ-γ d , denominator of λ 2 ε r,1 (λ). Note that the degrees of the numerators and denominators can be arbitrarily large. Listing 3: Syntax for the resolution of the rational eigenvalue problem iii Specifying the eigensolver The general SLEPc options for solving of non-linear problems are preset in the source code of GetDP (see Kernel/EigenSolve_SLEPC. cpp). Additional or alternative SLEPc options can be passed as command line argument when calling GetDP. There are particularly relevant options that can be passed to SLEPc: • Target: SLEPc eigensolvers will return nev eigenvalues closest to a given target value.
Acknowledgements The work was partly supported by the  French National Agency for Research (ANR)  under the project " Resonance"  ( ANR-16-CE24-0013 ). The authors acknowledge the members of the project " Resonance " for fruitful discussions. C. Campos  and  J. E. Roman  were supported by the  Spanish Agencia Estatal de Investigación (AEI)  under project  SLEPc-HS  ( TIN2016-75985-P ), which includes  European Commission ERDF  funds. C. Geuzaine was supported by  ARC grant for Concerted Research Actions  ( ARC WAVES 15/19-03 ), financed by the  Wallonia-Brussels Federation of Belgium. The authors thank  Christian Engström  from  Ume ȧ Universitet  for helpful comments. Maxence Cassier  from  Institut Fresnel  is acknowledged. Finally, the authors address special thanks to  Anne-Sophie Bonnet Ben-Dhia  and  Camille Carvalho  from  INRIA (POEMS)  for their motivating remarks and insights.
Spectrometer The experimental setup, as implemented in FairShip (the SHiP software framework), is shown in Fig. 1. A cylindrical SHiP-like 2  target (10 cm diameter and 154. 3 cm length) was followed by a hadron absorber made of iron blocks (240 × 240 × 240 cm 3 ) and surrounded by iron and concrete shielding blocks. The dimensions of the hadron absorber were optimised to stop pions and kaons while keeping a good p T acceptance of traversing muons. The SPS beam counters (XSCI. 022. 480/481, S0 in Fig. 1 ) and beam counter S1 were used to count the number of POT seen by the experiment. A spectrometer was placed downstream of the hadron absorber. It consisted of four drift-tube stations (T1-T4, modified from the OPERA experiment  [4] ) with two stations upstream and two stations downstream of the Goliath magnet  [5].
5 T, with 2. 81×10 11 raw S1 counts. After normalization 3 The centre of the Goliath magnet is 17. 86 cm above the beam line. (see Sect. 3. 1) this corresponds to (3. 25 ± 0. 07) × 10 11 POT. Additional data were taken with the magnetic field switched off for detector alignment and tracking efficiency measurement.
The statistical error is negligible. The efficiency of the trigger relies on the efficiency of detecting a muon signal in two scintillator planes S2a and S2b (see Fig. 1  and  [8] ). Each plane is equipped with two photo-multipliers (PMs), and the signal of each of the PMs is recorded for each event. The calculated trigger inefficiency is less than 1‰ and is hence neglected. Multiplying the number of reconstructed muons found in the 20128 spills by 710 we calculated that this data set corresponds to (3. 25 ± 0. 07) × 10 11 POT. Fig. 2  A two-muon event (most events are single-muon events) in the event display. The blue crosses are hits in Drift-tube stations T1 and T2, the red crosses are hits in T3 and T4. 3  Average of all drift-tube residuals. The fit is a double Gaussian and the resulting hit resolution (σ mean ) is the average of the two sigma's.
Comparison with the simulation A large sample of muons was generated (with Pythia6, Pythia8  [10]  and GEANT4  [11]  in FairShip) for the background studies of SHiP, corresponding to the number of POT as shown in Table  1. The energy cuts (E min ) of 1 GeV and 10 GeV were imposed to save computing time. The primary proton nucleon interactions are simulated by Pythia8 (using the default tune). The emerging particles are transported by GEANT4 through the target and hadron absorber producing a dataset of also referred to as "mbias" events. A special setting of GEANT4 was used to switch on muon interactions to produce rare dimuon decays of low-  mass resonances. Since GEANT4 does not have production of heavy flavour in particle interactions, an extra procedure was devised to simulate heavy-flavour production not only in the primary pN collision but also in collisions of secondary particles with the target nucleons.
The difference between data and simulation is probably caused by a different amount of muons from pion and kaon decays. It was seen that by increasing the contribution of muons from pion and kaon decays in the simulation the difference between data and simulation was reduced. The FLUKA  [13, 14]  generator is used to determine the radiation levels in the SHiP environment. To benchmark FLUKA with typical settings used for radiological estimates related to muons in the SHiP environment, the muon flux setup was implemented in FLUKA and the simulation with this setup was compared to that made with Pythia/GEANT4. The results of this comparison are given in Annex 1. This independent prediction provides additional support for the validity of the SHiP background simulation. We have measured the muon flux from 400 GeV/c protons impinging on a heavy tungsten/molybdenum target.
A3B07050649, 2018R1D1A1B07050701, 2017R1D1A1B03036042, 2017R1A6A3A01075752, 2016R1A2B4012302, and 2016R1A6A3 A11930680); the Russian Foundation for Basic Research (RFBR, Grant 17-02-00607) and the TAEK of Turkey. This work is supported by a Marie Sklodowska-Curie Innovative Training Network Fellowship of the European Commissions Horizon 2020 Programme under contract number 765710 INSIGHTS. We thank M. Al-Turany, F. Uhlig. S. Neubert and A. Gheata their assistance with FairRoot. We acknowledge G. Eulisse and P. A. Munkes for help with Alibuild. The measurements reported in this paper would not have been possible without a significant financial contribution from CERN. In addition, several member institutes made large financial and in-kind contributions to the construction of the target and the spectrometer sub detectors, as well as providing expert manpower for commissioning, data taking and analysis.
Data Availability Statement This manuscript has no associated data or the data will not be deposited. [Authors' comment: The raw datasets analysed during the current study are available from the corresponding author on reasonable request. ] Open Access This article is licensed under a Creative Commons Attribution 4. 0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
Another identified a common set of genes whose transcript abundance changed in both locations. And the third one was a more comprehensive network analysis using all of the sugar levels and the two locations. We chose two very similar sugar levels to determine the differential gene expression between the two locations, since sugar levels were not exactly the same at harvest. We identified 5528 differentially expressed genes (DEGs, at an FDR padj-value < 0. 05) between the using DESeq2  [27]  (Additional file 2). DEGs will refer to this set of differentially expressed genes throughout this manuscript. Gene set enrichment analysis using topGO determined the top gene ontology (GO) categories for biological processes for these 5528 genes (Additional file 3). Based on the number of genes identified, the top GO categories were cellular metabolic process (3126 genes, padj-value = 2.
The genes that had significantly different transcript abundance relative to control in at least one of the comparisons were identified in RNO and BOD. These gene lists were compared and the common gene set consisting of 1985 genes for both locations was determined (ap2 tab in Additional file 5). Comparing this common gene list (ap2) to the DEGs from approach 1 identified 907 genes that were common to both sets, indicating that this subset was differentially expressed between the locations at 22°Brix. The other 1078 genes did not differ significantly between locations. This 1078 gene subset list can be found in Additional file 5 (ap2-ap1 tab). The GO categories most enriched in this gene set included response to inorganic substance, response to abiotic stimulus and drug metabolic process. In approach 3, using a more powerful approach to finely distinguish the expression data for all sugar levels, Weighted Gene Coexpression Network Analysis (WGCNA) identified gene sets common to (based upon correlation) and different gene expression profiles between BOD and RNO.
All expressed genes for all °Brix levels (Additional file 1) were used in this analysis. Additional details of the analysis are described in the Materials and Methods section. Twenty-one modules or gene subnetworks were defined (Additional file 6) and a heat map was generated displaying the module-trait relationships (Additional file 7). The grey module is not a real module but a place to put all genes not fitting into a real module; thus, it was not counted as one of the twenty-one gene modules above. Eight modules had similar gene expression profiles for BOD and RNO (padj-value > 0. 05); these included cyan, midnightblue, pink, green yellow, salmon, blue, grey60, and royalblue. This gene set consisted of 8017 genes (see ap3 tab in Additional file 5 for the gene list). Comparing this common gene set from the WGCNA with the DEGs from approach 1 revealed that 524 genes in common were found in both sets.
This subset was removed from the WGCNA to produce a gene list of 7492 common to both locations and not differing in their transcript abundance at 22°Brix (ap2-ap1). This represents 25% of the total 29,929 genes in all of the modules. This gene set was compared with the ap2-ap1 gene set from approach 1 and 845 genes were found in common in both sets. The remainder from ap2-ap1 provided an additional 232 genes to the common set of genes from ap3-ap1 not affected by location giving a total number of 7724 genes, representing 25. 8% of the genes expressed. This gene set is listed in ap2-ap1_union_ ap3-ap1 tab in Additional file 5. The GO categories most enriched in this gene set included general categories such as Fig. 1  Principal component analysis of the transcriptomic data from berry skin samples at different °Brix levels from BOD and RNO organic substance biosynthetic process and organelle organization.
There were 785 enriched GO categories in total. In approach 3, further analysis of the gene modules using gene set enrichment analysis was performed with genes that had a kME > 0. 80 for each module in the WGCNA (Additional file 8). The similar gene sets in common with both locations with decreasing transcript abundance as sugar levels increased (negative correlation with °Brix) were enriched with the GO categories involving growth and water transport (blue module), and translation (grey60 module). The common gene sets with increasing transcript abundance as sugar levels increased were enriched with the GO categories involving gene silencing (cyan module), aromatic compound metabolism (midnight blue), organic substance catabolism (pink module), and DNA metabolism (salmon). Most modules were positively or negatively correlated with BOD and RNO berries (e.
The green (2287 genes) and brown (4147 genes) modules were also large modules that were most positively correlated with RNO (0. 92 and 0. 9, respectively). The green module was highly enriched in the GO category involving response to chemical. The brown module was highly enriched in GO categories involving multiple catabolic processes. Thus, the WGCNA results, which utilized all of the expressed genes from all °Brix levels were consistent with the DESeq2 results that only compared transcript abundances at 22°Brix or between locations. The WGCNA results were more comprehensive and complemented the results of approaches 1 and 2 by identifying hub genes and gene subnetworks. These subnetworks were linked and further defined by their highly correlated coexpression profiles and enriched GOs. Transcriptomic profiles dynamically changing with sugar levels DEGs with largest increases in transcript abundance between sugar levels As a first approach to examining the 5528 DEG dataset, differences between the transcript abundance in berries with the lowest and highest °Brix levels at the two locations were determined (Additional file 2).
Aroma-and flavor-associated DEGs Many aroma and flavor-associated compounds are synthesized in the late stages of berry ripening and sensitive to the environment. The major metabolic pathways affecting flavor and aromas in grapes and wines include the terpenoid, carotenoid, amino acid, and phenylpropanoid pathways  [6]. These pathways were identified by topGO to be highly enriched in the DEGs and the turquoise module. Some of the DEGs are involved in these pathways and will be presented in the following subsections. Terpene synthase genes with the greatest transcript abundance differences between BOD and RNO Cultivar differences in berries are often ascribed to differences in aroma compounds. One of the main classes of cultivar specific aroma compounds is the terpene group  [29]. The transcript abundance of a number of terpene synthases were higher in BOD berries as compared to RNO berries (Fig.
DEGs associated with abiotic stimuli Light-responsive genes In a previous analysis, WGCNA defined a circadian clock subnetwork that was highly connected to transcript abundance profiles in late ripening grapevine berries  [4]. To compare the response of the circadian clock in the two different locations, we plotted all of the genes of the model made earlier  [4]. Most core clock genes (Additional file 12) and light sensing and peripheral clock genes (Additional file 13) had significantly different transcript abundance in BOD berries than that in RNO berries at the same sugar level (profiles bracketed in a red box). All but one of these (PHYC, phytochrome C, g088040) had higher transcript abundance in BOD berries relative to RNO berries. The transcript abundance of other genes had nearly identical profiles (not bracketed in a red box).
Data collection and analysis The routine meat inspection abattoir case registry was used as a source of data. Variables collected were the type of animal, sex, year, the presence and type of parasitic infections and other signs of parasitic infection. Data were double entered directly into Microsoft Excel version 10. Annual numbers of slaughtered animals and the number of animals with echinococcosis and other zoonotic parasitic infection were computed to show the occurrence, proportion and trend over the last 14 years. Stata version 15 was used to show the trend over time graphically among three species of slaughtered animals.
Acknowledgements This research was conducted through the  Structured Operational Research and Training Initiative (SORT IT ), a global partnership coordinated by  TDR , the  Special Programme for Research and Training in Tropical Diseases  hosted at the  World Health Organization. The training model is based on a course developed jointly by the  International Union Against Tuberculosis and Lung Disease  and  Médecins Sans Frontières-Luxembourg (LuxOR). The specific SORT IT program that led to these publications included a joint implementing partnership between TDR, the  Institute of Tropical Medicine Antwerp, Belgium , the  University of Gondar, Ethiopia , the  WHO country office in Ethiopia ,  Médecins Sans Frontières, Luxembourg (LuxOR)  and the  International Union Against Tuberculosis and Lung Disease, Paris France.