dataesr/scientific-paragraphs-categorization huggingface dataset:
They are up to ten times faster than Qhull, but for ten millions of points. For sets with less than 500K points, the GPU program is much slower. Note also that these GPU implementations are limited to 2D and 3D. We propose thus a new implementation of quickhull algorithm dedicated to lattice points (or rational points), as a DGtal package. 3  Lattice points may have fixed-sized integer coordinates (int32, int64) or even arbitrary size integer coordinates (using GMP library 4  ). In order to have correct geometric computations (inside/outside tests and determinant computations to get the normal vector), the user can choose also the type of integer numbers for the geometric computations. The table below shows the maximum width of the bounding box containing all lattice points in order to get exact convex hull computations in all cases when choosing int64 both for coordinates and geometry computations.
If your width exceeds this bound (which depends on the dimension), then you have to use GMP arbitrary size integers, with an approximate 25 times slow-down factor. dimension 2 3 4 5 6 max. width 2e9 1. 5e6 4e4 5e3 1. 2e3 Experiments show that our implementation is as fast as qhull but with correct results, and is generally two times faster than CGAL version. See the package documentation 5  for more details. Since each cell e i touches CvxH (X), then there exists for each one a point x i ∈ ēi with x i ∈ CvxH (X). By convexity, CvxH {x i } i=1,. ,n ⊂ CvxH (X). But c is at the center of its surrounding d-cells (e i ), so according to Lemma 23 (in Appendix), we have CvxH {x i } i=1,. ,n ∩ c ̸ = ∅. We have just found a common real point between CvxH (X) and c, so c ∈ C d [CvxH (X)]. □ Since Lemma 12 tells that a digital set X is fully convex iff Star (X) = Star (CvxH (X)), then Theorem 5 above states that Star (CvxH (X)) can be computed directly from CvxH (U I d (X)) ∩ Z d , which involves only one convex hull computation and lattice point enumeration within the polytope.
TDISim was a prototype TDI simulation tool programmed in MATLAB. The simulation fully operated in the time domain and performed both data generation and TDI, including for the first time the updated split-interferometry optical bench design and a simplified state-space model for the motion of the test mass and the spacecraft  [20]. We based our simulation efforts on LISACode, which was initiated with the similar ambition to include most of the ingredients that were thought to influence LISA's performance at the time  [21]. Since then, developments in the instrument and mission design revealed new important effects that must be included in the simulations. The model that we propose in this paper is an attempt to extend LISACode's model to capture those effects. Section II introduces the conventions we use, and, for the first time, a description of the time frames relevant for LISA Instrument simulations.
A. LISA Instrument LISA Instrument  [38]  is a Python-based implementation of the simulation model described in this paper. It is designed to facilitate fast exploratory studies, run quick or partial simulations (instrumental effects and noises can easily be toggled on and off), and prototype new features. LISA Instrument ships as a standalone Python package. As a consequence, it is easy to install, use, and integrate in traditional workflows, such as Jupyter Notebooks. LISA Instrument does not require a custom installation and can be used out-of-the-box on most computing clusters. LISA Instrument relies strongly on traditional numerical libraries, such as NumPy and SciPy  [39, 40] , and therefore benefits from fast optimized vectorized operations as it handles large arrays of data. Its runtime performance is studied and compared to that of LISANode in Fig.
B. LISANode LISANode  [42, 43]  is a simulation framework that allows the user to build modular simulation graphs out of atomic computational units, called nodes. This is realized using a mix of Python and C++, where the Python code is responsible for defining the graph structure and interconnecting the different nodes. The nodes themselves are implemented in C++, such that the final executable is a C++ command line program. Using C++ offers the advantage that compiler optimizations produce a fast executable, and allows us to reuse legacy code from previous C++ LISA simulators, such as LISACode  [21]. Naturally, the cost is reduced readability, usability, and slower development times. Another consequence is that LISANode needs to be compiled on each machine it runs. To work around this last difficulty, we offer containerization solutions, in the form of Docker and Singularity images that contain optimized compiled versions of LISANode along with the software environment necessary to run them.
These images can be downloaded and used on local machines and on most computing infrastructures, and do not hinder the runtime performance of the simulations. In LISA Instrument, data is generated for the whole simulation length. On the contrary, LISANode creates data one step at a time: a sample at time t n is computed for all quantities before repeating the same instructions for the next samples t nþ1. New samples are therefore simulated on the fly, keeping only in memory the data that is required for the current and future samples. This way, memory usage remains roughly constant regardless of the simulation length (see Sec. VIII C). This allows long simulations to run on memory-constrained machines.
We run simulations of increasing durations, ranging from 1 h (1. 4 × 10 4 telemetered samples at 4 Hz for each channel) to 6 months (6. 2 × 10 7 samples). Missing points indicates that the simulation did not complete on our test machine (MacBook Pro M1, 2021, 64 GB of RAM) because of excessive memory pressure or runtime. We extrapolate the results to 1 year (dashed lines) using a linear (LISANode) or quadratic (LISA Instrument) fit to the existing data points. We used the latest version of LISA Instrument and LISANode, and compiled three different LISANode executables to study the impact of optimizations; one with no compiler optimization (compiler flag -O0), one with some optimizations (-O1), and one with most optimizations (-O2) enabled. In each case, we measure the runtime and peak memory usage.
LISA Instrument is a Python implementation that is easy to use, and very efficient for short simulations (a few months or less), while we recommend LISANode for longer and more complex simulations. Some results obtained with LISA Instrument are presented to demonstrate the correctness of the implementation. In particular, we check that the beatnote measurements exhibit the expected behavior, in terms of total frequency or frequency fluctuations. For the latter, we show that our model keeps numerical noise to acceptable levels for the study of instrumental noises and gravitational-wave signals. We also check that laser and clock noise reduction by TDI performs as expected by computing the secondgeneration Michelson combinations. We confirm that the residual noises in these channels matches their expected levels, and that a typical gravitational signal hidden in the raw telemetry data becomes clearly apparent at the expected frequency and magnitude.
ACKNOWLEDGMENTS The authors thank the  LISA Simulation Working Group  and the  LISA Simulation Expert Group  for the lively discussions on all simulation-related activities. They would like to personally thank  A. Petiteau ,  G. Heinzel ,  V. Müller ,  A. Hees ,  M. Staab , and  J. N. Reinhardt  for their insightful feedbacks. J. B. B. gratefully acknowledges support from  UK Space Agency  (Grant No. ST/X002136/1 ), the  Centre National d'Études Spatiales (CNES) , the  Central National pour la Recherche Scientifique (CNRS)  and the  Université Paris-Diderot. J. B. B. has been supported by an appointment to the  NASA   Postdoctoral Program  at the  Jet Propulsion Laboratory, California Institute of Technology , administered by  Universities Space Research Association  under contract with  NASA.
Part of this research was carried out at the  Jet Propulsion Laboratory, California Institute of Technology , under a contract with the  National Aeronautics and Space Administration  ( 80NM0018D0004 ). O. H. gratefully acknowledges support by  Centre National d'Études Spatiales (CNES)  and by the  Deutsches Zentrum für Luft-und Raumfahrt (DLR, German Space Agency)  with funding from the  Federal Ministry for Economic Affairs and Energy  based on a resolution of the  German Bundestag (Projects Ref. No. 50OQ1601  and No. 50OQ1801 ). This work was supported by the  Programme National GRAM of CNRS/ INSU  with  INP  and  IN2P3  cofunded by  CNES.
SNP Calling According to the initial parameters indicated in the Section 3, the TASSEL software identified 22,326 di-allelic SNPs. We then filtered the positions where all replicates of the parents were identical, with at least one of the parents being heterozygous; other filters included those with less than 15% missing data, and with at least 10% minor allele frequency. This resulted in the selection of 6444 SNPs.
Phenotypes Among the 61 genotyped hybrids, 53 flowered during the three-year experiment, 52 of them produced fruits, and in 32 of these, the fruits contained seeds. Data obtained for the phenotyped traits NPGA and APF, as well as the polyembryony of each hybrid, are displayed in Supplementary Table  S4. Male sterility phenotyping was performed based on NPGA and APF. The ANOVA analysis showed significant differences between genotypes for NPGA, while no differences were observed between genotypes for APF (Table  2 ). As shown in Figure  1 , great differences, particularly for APF, were observed within several genotypes, while the data obtained for NPGA were more homogeneous within genotypes. Taking both parameters together, some genotypes showed high APF, but very low NPGA values. For example, for KM-1 and KM-2 with similar APF averages of 73% and 82%, respectively, the average NPGA values were 1950 and 81, respectively.
Marker-Trait Association Through a general linear model (GLM) using default parameters in the TASSEL 5 software, polyembryony and male sterility marker-trait association studies were separately evaluated in both 'Kiyomi' and 'Murcott' tangors maps. The statistical significance of the genetic and phenotypic associations was calculated with a 0. 05 probability threshold, as well as applying the Bonferroni correction for multiple testing. For theMurcott' tangor, the probability threshold was p ≤ 7. 5 × 10 -5 (0. 05/670) or -log(p) >= 4. 01, whereas for `Kiyomi´, it was p ≤ 3. 7 × 10 -5 (0. 05/1346) or -log(p) >= 4. 43. The TASSEL software was designed to evaluate trait associations, evolutionary patterns, and linkage disequilibrium using GWAS. It has been successfully used for markertrait association studies using bi-parental progenies.
Marker-Trait Association Through a general linear model (GLM) using default parameters in the TASSEL 5 software, polyembryony and male sterility marker-trait association studies were separately evaluated in both 'Kiyomi' and 'Murcott' tangors maps. The statistical significance of the genetic and phenotypic associations was calculated with a 0. 05 probability threshold, as well as applying the Bonferroni correction for multiple testing. For the 'Murcott' tangor, the probability threshold was p ≤ 7. 5 × 10 -5 (0. 05/670) or -log(p) >= 4. 01, whereas for 'Kiyomi , it was p ≤ 3. 7 × 10 -5 (0. 05/1346) or -log(p) >= 4. 43. The TASSEL software was designed to evaluate trait associations, evolutionary patterns, and linkage disequilibrium using GWAS. It has been successfully used for markertrait association studies using bi-parental progenies.
For each library, ligated samples were pooled (i. e. , 2 multiplex libraries of 96 samples) and PCR-amplified in a single tube. Complexity was further reduced using PCR primers with one selective base (A), as described by  Sonah et al. [80]. Single-end sequencing was performed on a single lane of an Illumina HiSeq4000. Keygene N. V. (Keygene, Wageningen, The Netherlands) owns the patents and patent applications protecting its sequence-based genotyping technologies. SNP genotype calling was performed using data from the DNA sequence reads with the TASSEL 5 GBS v2 pipeline  [31]  available at https://bitbucket. org/tasseladmin/tassel-5-source/wiki/Tassel5 GBSv2Pipeline (accessed on 7 June 2022) with default parameters, to identify good quality, unique, sequence reads with barcodes. These sequences were aligned on the C.
Linkage Analysis and Genetic Mapping The two-way pseudo-testcross mapping strategy implemented for genetic mapping from progenies, resulting from crosses between two heterozygous parents  [81]  and used in previous high-density mapping studies in citrus  [35, [37] [38] [39] 41] , was applied to establish the 'Kiyomi' and 'Murcott' genetic maps. For each map, SNP markers were selected according to their respective heterozygosity for the mapped parent and homozygosity for the other one. Each set of data for the 61 hybrids was filtered to retain markers and hybrids with less than 15% of missing data. Linkage analysis and genetic mapping were then performed using JoinMap5 (https://www. kyazma. nl/index. php/JoinMap/; accessed 7 June 2022). Linkage mapping was performed in the «Hap» option for both 'Kiyomi' and 'Murcott' tangors.
Drops were photographed (Figure  5a ) with a Leica DMLS microscope, and the number of pollen grains per drop was counted with the ImageJ 2. 0. 0-rc-61/1. 52n software  [87]. with less than 15% of missing data. Linkage analysis and genetic mapping were then performed using JoinMap5 (https://www. kyazma. nl/index. php/JoinMap/; accessed 7 June 2022). Linkage mapping was performed in the «Hap» option for both 'Kiyomi' and 'Murcott' tangors. Markers were grouped using the independence LOD score. The phases (coupling and repulsion) of the linked marker loci were automatically detected by the software. Map distances were estimated in cM, using the regression mapping algorithm. After a first mapping round, singletons, i. e. , an individual genotype that suggested recombination with its two flanking markers, were identified and replaced by missing data, as recommended by van Os et al.
Drops were photographed (Figure  5a ) with a Leica DMLS microscope, and the number of pollen grains per drop was counted with the ImageJ 2. 0. 0rc-61/1. 52n software  [87]. The number of pollen grains per anther (NPGA) was calculated as follows: NPGA = (sum of NPG/(15 × 0. 3)) × (Vol/10) where the sum of NPGA is the total number of pollen grains counted in the 15 drops of 0. 3 µL; 10 is the number of anthers; and Vol is the volume (25, 50 o 100 µL) of staining solution added for pollen grain dispersion. Stain solution colored non-viable pollen grains as blue-green, and viable pollen grains as magenta-red. Since staining solution was used as a liquid medium to disperse the pollen grains, APF and NPGA values were evaluated simultaneously (Figure  5 ). To determine if there were significant differences between NPGA and APF variables of phenotyped hybrids, a one-way ANOVA test was performed using the Statgraphics Centurion XVI statistical software package, v16.
Seed Phenotyping for Polyembryony Fruits from the hybrids between 'Kiyomi' and 'Murcott' tangors were harvested when ripe, and seeds were then extracted. Each seed was peeled, eliminating the outer and inner seed coats with forceps. Seeds with only one embryo were classified as monoembryonic, whereas seeds with more than one embryo were recorded as polyembryonic. 3. 6. Genotype-Phenotype Association TASSEL v5. 2. 87  [88]  was used to perform the genotype-phenotype association study. Genotype and phenotype data sets were joined by the union of taxa using the Union Join command. Then, the genotype-phenotype association was evaluated using the GLM (general linear model) procedure under the default settings, and the results were displayed using the Manhattan plot graph.
Conclusions GBS was used to genotype 61 diploid hybrids from an F1 progeny recovered from crossing the male sterile and monoembryonic 'Kiyomi' tangor as the female parent with the male fertile and polyembryonic 'Murcott' tangor as the male parent. Raw sequences were aligned to the clementine genome and 6444 SNPs were obtained. After filtering for SNPs within genes and heterozygous for only one of the parents, we established the genetic map for each parent with the JoinMap. 5 software. The two maps, respectively, include 1374 and 697 markers, and encompass 1416. 287 and 1339. 735 cM for 'Kiyomi' and 'Murcott'. The two maps were globally highly syntenic and colinear with the C. clementina v1. 0 assembly; however, they confirmed previous constatations for probable small incongruences of the C.
Our contribution is fourfold. First, we developed a full methodology for the estimation of joint latent class models for multidimensional longitudinal data and survival time (possibly with competing causes). This model extends beyond the literature by handling multidimensional longitudinal data when Proust-Lima et al  14  considered multivariate longitudinal markers regrouped into a uni-dimensional latent process, and by considering multivariate Gaussian and non-Gaussian continuous markers possibly regrouped into distinct latent dimensions along with multi-cause (left-truncated) time-to-event when Sun et al  18  and Li et al  19  considered Gaussian markers possibly subject to detection limit, and classical survival data. Second, our methodology is made available to the community with a dedicated function in the user-friendly lcmm R software for latent process and latent class models estimation  20  along with documentation.
We focused on the repeated measures of six UMSARS-derived markers regrouped in three different dimensions: -Motor and function dimension assessed by a subscore of Activities of Daily Living (UMSARS I) and a subscore of Motor examination (UMSARS II); -Supine blood pressure (BP) assessed by the systolic BP and the diastolic BP; -The orthostatic change in BP assessed by the maximum change in systolic BP and in diastolic BP between supine position and standing position during 10 min (UMSARS III). We leveraged the data of the 598 patients enrolled between 2007 and 2019 who had at least one measure of each marker during the follow-up and no missing information on the main known MSA characteristics: gender, age at inclusion, duration since first symptoms, subtype of MSA (Cerebellar or Parkinson), level of diagnosis certainty (possible or probable).
Optimal number of latent classes Maximum likelihood is obtained for a fixed number of latent classes G, and the optimal number of latent classes thus needs to be a posteriori determined. Selecting the optimal number of clusters in mixture problems is a wide area of statistical research. 27  Among information criteria, the Bayesian Information Criterion (BIC) is usually favored. Defined as BIC(G) = -2( θG ) + p log(N) with the lower the better, it was repeatedly shown to correctly select the optimal number of latent classes in different mixture situations. 28, 29  However, as it is a likelihood-based criterion, the BIC mainly focuses on the fit of the model to the data and may lead in some contexts to a poorly discriminant latent class structure. 27, 30  The discriminatory power of the latent class structure can be assessed by an entropy measure defined as EN(G) = 1 + ∑ N i=1 ∑ G g=1 πig log( πig ) N log(G) with values closer to one indicating higher discrimination of the classes.
Software The maximum likelihood estimation of the joint latent class model is implemented in lcmm R package  20  with function mpjlcmm when considering K ≥ 1 repeated markers and Jointlcmm when considering K = 1 marker. Log-likelihood optimization is carried out by a robust Marquardt-Levenberg algorithm combined with stringent convergent criteria on the log-likelihood, the parameter and the first and second derivatives. This optimizer has been demonstrated to provide correct inference even in the case of complex log-likelihoods and/or relatively flat regions. 34  The package includes a gridsearch function for the parameter space exploration, and postfit functions for reporting the information criteria, posterior classification, goodness-of-fit, and predicted trajectories. 35.
DISCUSSION Given the complexity of some diseases and the richness of the data collected in cohort studies, methods to summarize multivariate longitudinal information, and capture heterogeneity become real assets in biostatistics. With this work and the associated implementation in the R package lcmm (function mpjlcmm), we provide a relevant and effective solution validated in simulations for summarizing information from multivariate markers measured repeatedly over time and clinical endpoints. In the MSA example, the approach summarized 6 marker trajectories and risk of death into five subgroups of patients with different profiles of progression that suggest distinct subphenotypes of the disease. In addition to unraveling a heterogeneous clinical progression, this method provides a simple parsimonious summary of complex disease progression that can then be used to explore new research directions, and markers of interest.
ACKNOWLEDGMENTS Computer time was provided by the computing facilities  MCIA (Mésocentre de Calcul Intensif Aquitain)  at the  University of Bordeaux  and the  University of Pau and Pays de l'Adour. We thank the  INSERM/UPS UMR1214 Technical  platform for the MRI acquisition and  Centre d'Investigation Clinique (CIC)  for the global coordination of the clinical study within  INSERM-DGOS 2013-2014  grant.
FUNDING INFORMATION This work was funded by the  French National Research Agency  (grant number  ANR-18-CE36-0004  for project DyMES), by  Appel d'Offre Interne of Bordeaux University Hospital  (grant  AOI 2011  for project  BIOMAS , grant  AOI 2014  for project  COGAMS ), by  PHRC  in 2012 ( DGOS 161 ), association  PSP France  for project  Biopark  and association  ARAMISE. MRI data acquisition was supported by a " Recherche clinique translationnelle " grant from  INSERM-DGOS 2013-2014.
34 On the chemical modeling side, the recent models of gas-35 grain chemistry in hot molecular cores presented by Garrod 36 et al. (2022)  predict that methylamine is predominantly formed rotational state of methylamine was successfully analyzed using the effective Hamiltonian approach (high-barrier "tunneling" approach) of Ohashi and Hougen  (Ohashi & Hougen 1987). In this approach, each t torsional state is fitted separately (with its own set of molecular parameters). The analysis yielded an accurate model of the rotational spectrum in the t = 0 state  (Ilyushin et al. 2005; Motiyenko et al. 2014) , but showed some limitations with respect to the t = 1 state. To overcome these limitations, we use a new hybrid model and the BELGI-hybrid code described in  Kleiner & Hougen (2015)  which takes into account all the torsional states arising from internal rotation of the methyl group of methylamine in a global way  (Kleiner & Hougen 2020).
The second large-amplitude motion of the NH 2 inversion is taken into account within the tunneling approach. In our first paper on CH 3 NH 2  (Kleiner & Hougen 2020) , we used a dataset for t = 0 and 1 that combines previously published data in the infrared  (Ohashi et al. 1987; Gulaczyk et al. 2017; Ohashi et al. 1988)  with data in the microwave spectral range  (Motiyenko et al. 2014; Ohashi et al. 1989; Kr ęglewski & Wlodarczak 1992; Ilyushin et al. 2005; Ilyushin & Lovas 2007) , which were fitted using the tunneling formalism from Hougen and Ohashi. We successfully fitted 11880 t = 1 ← 0 transitions in the far-infrared spectral range, as well as 2288 rotational transitions belonging to the ground torsional state t = 0 in the microwave spectral range, but we only fitted a limited number (137) of pure rotational transitions belonging to the first excited state t = 1-1.