dataesr/scientific-paragraphs-categorization huggingface dataset:
There are no analytical formula for the Zernike moments of a cube. However, they can be computed symbolically using a symbolic algebra system (we have used Mathematica  [63] ). To achieve this, we generated the monomial expansion of the Zernike polynomials and then integrated them symbolically over the volume of the cube. This provided an exact symbolic result for each moment which was then evaluated to double precision. We compared the results of the double precision program PK (see above), of the exact algorithm (Algorithm 2), and of the finite precision algorithm (Algorithm 3, with TOL set to 10 -8 ) (both implemented in Shape2Zernike) with those exact values for Zernike moments up to order 100, using the following error function n = ∑ l l ∑ m=-l |c m nl (computed) -c m nl (exact)| 2. ( 41 ) Results are shown on Figure  7.
Original Order 20 Order 50 Order 300 The second row corresponds to a statue of the bust of Ippolita Sforza, sculpted by Francesco Laurana. It is available as part of the package MeshLab  [64]. The mesh includes 27,861 vertices and 49,954 triangles. We computed its Zernike moments using the finite precision algorithm with a tolerance of 10 -8 , up to order 300. We then reconstructed its shape using the same procedure described above for the gargoyle, with orders 20, 50, and 300. For N = 20, the reconstructed bust is incomplete, with no details on its surface. For N = 50, we start seeing faint features within the face, but the bottom of the bust is still incomplete. N = 300 gives us a much more accurate representation of the model, especially in the face. The third row corresponds to the smiling version of Jerry the Ogre, introduced by Carr et al.
Original Order 20 Order 50 Order 300 Figure  10  shows the quality of reconstruction of a protein shape from its Zernike moments at different orders. We consider two well studied proteins often used as models in computational structural biology, calmodulin (top row) and a triose phosphate isomerase (bottom row). Calmodulin is a calcium binding protein expressed in all eukaryotic cells. It is a small protein that consists of two small domains separated by a linker region. The flexibility of this linker is key to the ability of calmodulin to bind to a wide range of substrates  [67]. We considered the apo form (without ligand) of the human version of protein available in the Protein Data Bank  [32]  with the code 1CLL. This conformation is defined as the position of its 1133 atoms. We use the standard model in chemistry of representing a structure as a union of balls, with each ball corresponding to an atom.
The surface of this union of ball is represented as its skin surface  [68]. It is computed from the boundary of the union of these balls, where the center of a ball is given by the coordinates of the atom, and its radius is set to its van der Waals radius plus a probe radius of R = 1. 4 Å. We generated a quality mesh for the skin surface of calmodulin using the program smesh, described in details in  [65, 66]. The corresponding triangular mesh includes 203,400 vertices and 406,864 triangles. We computed its Zernike moments using the finite precision algorithm with a tolerance of 10 -8 , up to order 300. We then reconstructed a shape for calmodulin using the same procedure described above, with orders 20, 50, and 300. Those two domains of calmodulin are clearly separated in the absence of a ligand, as illustrated from its original surface.
For N = 20, the reconstruction shows the position of these two domains. However, it does not include any local features, while some of those features (i. e. , the presence of spherical patches) appear for N = 50, they are only clearly visible at much higher orders, as illustrated here for N = 300. Triose phosphate isomerase (TIM) is an enzyme that catalyzes the reversible interconversion of triose phosphate isomers  [69]. We considered the chicken version of the TIM protein available in the Protein Data Bank  [32]  with the code 1TIM. This conformation is defined from the positions of its 1870 atoms. We generated a quality mesh for its skin surface using the same procedure described above for calmodulin. The corresponding triangular mesh includes 398,658 vertices and 797,644 triangles. We then computed its Zernike moments using the finite precision algorithm with a tolerance of 10 -8 , up to order 300.
Original Order 20 Order 50 Order 300 The final example, illustrated in Figure  11 , corresponds to a brain surface. We use the brain surface data of one human subject from the Images and Data Archive of the USC Stevens Neuroimaging and Informatics Institute data set (accessed on 23 September 2022) (http://ida. loni. usc. edu). The brain surface obtained there is represented with a high quality oriented triangular mesh of genus zero, containing 65,538 vertices and 131,072 triangles. We computed its Zernike moments using the finite precision algorithm with a tolerance of 10 -8 , up to order 300. We then reconstructed the shape of the brain with orders 20, 50, and 300. Sulci, the grooves, and gyri, the folds, make up the folded surface of the brain. As the surface area of the brain increases from the formation of those sulci, more functions are made possible.
We did note however that as the number of moments that are computed increase, the memory requirement for each thread increases, leading to saturation effects in the parallelization speedup factor. This limitation related to memory would hinder a naive implementation of this algorithm on GPU. We are currently working on solutions to this problem. The free software implementing these algorithms is available at (accessed on 23 September 2022) (https://github. com/jerhoud). which we rewrite as S 1 n,l-1 (r 0 ) = -l + 1 l S.
Figure10. Reconstruction of Calmodulin (top row), and TIM (bottom row) from the Zernike moments computed from a triangle mesh representing their boundaries. Calmodulin (PDB code 1CLL) is a human small calcium binding protein while TIM (PDB code 1TIM) is the chicken triose phosphate isomerase. Both proteins are represented as a union of balls, with each ball corresponding to an atom. The surface of this union of balls, triangulated with the program smesh [65, 66] , serves as input to the computation of the Zernike moments of their shapes. We compare the reconstructions generated from three different maximum order N, N = 20, N = 50, and N = 300. The original shape is shown on the left. All figures were generated with MeshLab [64].
[60]tion (A15) provides a recurrence for computing S 1 nl (r 0 ) from S 0 nl (r 0 ). Integrals S k nl (r 0 ) with k odd, k > 1 can then be derived by repeated use of Equation (A12), starting with S 1 nl (r 0 ). Characteristics of the triangle quadrature rules used in our algorithms. All those rules were constructed with the program PolyQuad (accessed on 23 September 2022) (https://github. com/PyFR/Polyquad)byWitherdenand Vincent[62]. Stars near strengths identify the rules that are used in the finite precision algorithm. Te bound N min p (third column) is the empirically proposed bound on the number of points, N min p = (N + 1)(N + 2)/6 , as proposed by Xiao and Gimbutas[60]. E (fourth column) is the "efficiency", defined as: E = N min p /N p. Efficient quadrature rules have E close to 1.
Characteristics of the Triangle Quadrature Rules Used in This WorkTable A1. A1 [60]tion (A15) provides a recurrence for computing S 1 nl (r 0 ) from S 0 nl (r 0 ). Integrals S k nl (r 0 ) with k odd, k > 1 can then be derived by repeated use of Equation (A12), starting with S 1 nl (r 0 ). Characteristics of the triangle quadrature rules used in our algorithms. All those rules were constructed with the program PolyQuad (accessed on 23 September 2022) (https://github. com/PyFR/Polyquad)byWitherdenand Vincent[62]. Stars near strengths identify the rules that are used in the finite precision algorithm. Te bound N min p (third column) is the empirically proposed bound on the number of points, N min p = (N + 1)(N + 2)/6 , as proposed by Xiao and Gimbutas[60]. E (fourth column) is the "efficiency", defined as: E = N min p /N p.
MODIS snow products are distributed by the National Snow and Ice Data Center (NSIDC) to alleviate the processing of the MODIS data by end users. These products indicate the presence of snow along with a cloud mask  (Hall and Riggs 2015). Based on MODIS data only, the first author has developed a web-based tool to analyze in real-time the snow cover area in the Alps  (Alps Snow Monitor n. d. ). This tool has attracted some attention, especially in the context of the severe drought that affected the Alps during the winter of 2022 (European Commission. Joint Research Centre 2022). For example, this tool allowed us to reveal that on 2 March 2022, the snow cover area in the Alps had reached its lowest value since 2001. This finding was published on 5 March 2022  (Gascoin 2022). Later, we showed that the 2022 snow cover area in the Alps reached its minimum earlier than any other year since 2001 (figure  1 ).
Other similar tools use the MODIS record to provide information to the general public, e. g. 'Snow-CloudMetrics'  (Crumley et al 2020)  or 'Snow Today' (Snow Today Article | NSIDC Reports n. d. ). However, although the MODIS data record already spans 22 years, it does not reach the 30 year standards that are used by meteorological agencies to define climatological references. Hence, it could lead to non-robust assessments of the true extend of a given situation. Given the interest in having realtime information regarding snow cover in the Alps, we sought to provide a more robust contextualization of the MODIS observations. To this end, we used longer reanalysis data spanning the entire European Alps domain at a sufficiently fine spatial resolution for this mountain environment, namely, the Uncertainties in Ensembles of Regional ReAnalysis (UERRA) reanalysis at 5.
5 km resolution  (Soci et al 2016 , Morin et al 2021). A 30 year-long snow cover area climatology was generated from this dataset using machine learning to de facto generate MODIS-like data using the reanalysis for the time period before the onset of the MODIS observations. Here, we describe the tool and the method for generating this contextualization dataset. We discuss the implications of bringing together the best of the two worlds of space-borne observations (real-time, short time periods) with reanalysis data (longer-term).
ISBA-ES snow cover model is an intermediate complexity 12 layers snow scheme  (Boone and Etchevers 2001, Decharme et al 2016). This reanalysis provides estimates of daily snow depth values at 5. 5 km resolution  (Bazile et al 2017). The full documentation is available along the UERRA dataset in the Copernicus Climate Data Store (Lopez 2019). The UERRA snow depth data available from 1961 to 2015, were used as a predictor for the machine learning approach described below.
Model We trained a statistical model to predict the snow cover area of a given region of interest at the daily time step. For a given day, the input samples (predictors) are the snow depth values on that day extracted over the region of interest from the UERRA reanalysis. We tried linear regression and gradient boosting, two commonly used machine learning algorithms in geosciences and ecology. Gradient boosting is a flexible and efficient nonparametric statistical learning technique for classification and regression  (Friedman 2001). We used the implementation of the linear regression and gradient boosting regression functions in the Scikit-learn Python module (Pedregosa et al 2011). The model was optimized by minimizing the squared error between the training and predicted data. The data were randomly split into training (75%) and test (25%) subsets.
Discussion and conclusion Cloud computing platforms enable the development of services based on remote sensing data streams without having to develop infrastructure (data storage, updating, cataloging, processing, publishing). We developed our application in the Google Earth Engine, but it could be implemented in another server since it uses only public data and standard remote sensing image processing algorithms that are implemented in open-source software. We find that the error of our statistical model data slightly increased from the entire Alps domain to the river basin subdomains. These minimal performance losses were expected due to the reduction of the domain size, which tends to increase the uncertainty in MODIS data. It also reflects the effect of the uncertainties in the UERRA reanalysis at the local scale.
Sabater J et al 2021 ERA5-Land: a state-of-the-art global reanalysis dataset for land applications Earth Syst. Sci. Data 13 4349-83 Snow today article | NSIDC reports n. d. (available at: https:// nsidc. org/reports/snow-today) (Accessed 17 July 2022) Notarnicola C 2022 Overall negative trends for snow cover extent and duration in global mountain regions over 1982-2020 Sci. Rep. 12 13731 Overpeck J T, Meehl G A, Bony S and Easterling D R 2011 Climate data challenges in the 21st century Science 331 700-2 Parajka J and Blöschl G 2008 Spatio-temporal combination of MODIS images-potential for snow cover mapping Water Resour. Res. 44 W03406 Pearce W, Niederer S, Özkula S M and Sánchez Querubín N 2019 The social media life of climate change: platforms, publics, and future imaginaries Wiley Interdiscip.
Data and code availability A pre-release of the application and its previous version are available at https://labo. obs-mip. fr/ multitemp/apps/alps-snow-monitor/. The data and Python code to train the model and infer the snow cover fraction climatology is publicly available on Git-Hub (https://github. com/sgascoin/ModisExtension/ releases/tag/v1). Earth Engine JavaScript code to compute the snow cover fraction from MODIS products and the code of the web application are publicly available in this git repository (https:// earthengine. googlesource. com/users/sgascoin/apps). We acknowledge Dongdong Kong (China University of Geosciences) for sharing the temporal interpolation code (https://github. com/gee-hydro/gee_docs).
Solitude was assessed by asking whether the participant was alone in his home during the lockdown. Individuals who reported not being alone in their homes rated the quality of their relationships with the people with whom they were locked in using a 5-point Likert scale (1 = 'extremely bad, ' 5 = 'extremely good'). People alone in lockdown were not presented with this question and the missing value was replaced by the neutral response ('neither good nor bad'). This replacement was done in order to add this variable in the models while not removing all responses from people who are alone in their home. Note that the effect of this variable does not change in alternative models where all responses of lonely people are removed. Data analysis. R  77  was used for all analyses. The data and R scripts of the analyses are available online in an open directory (https:// osf.
io/ q2e6h/). To identify distinct groups in trajectories of depression and anxiety, we performed growth mixture modelling with the hlme function of the lcmm package  78. Growth mixture modelling (GMM) can be seen as a combination of latent class growth and linear mixed analyses  79, 80. Latent class growth analysis (LCGA) relies on the latent growth curve modelling approach in which repeated variables are used to estimate latent intercepts (i. e. , the level on the variable at the first time point) and slopes (i. e. , the rate of change in the outcome over time) for each individual. Then, individuals with similar intercept and slope parameters are classified into subgroups. LCGA is a particular case of GMM in which no within-group variance of the parameters is allowed. In other words, all individuals' growth trajectories are assumed to be that of the group, but it is unlikely that this assumption holds true with empirical data.
Although this variant was located at a non-coding region, functional annotation based on ENCODE data showed that it is placed in a proximal enhancer-like signature, downstream of NTF3 gene. Transcriptional enhancer elements are non-coding stretches of DNA that have a central role in regulating transcriptional activity  57, 58. Interestingly, non-coding SNPs, that have been associated with risk for numerous common diseases through GWAS, frequently lie in these genomic elements, probably affecting their function  59. Therefore, additional research is needed to delineate the impact of these variants on GD aetiology to enhance diagnosis, prevention strategies and treatment approaches. By using JASPAR CORE we found that rs7956189 also overlapped the binding site of WT1, a TF associated with depressive-like behaviour in mice  41.
cegen. org). Of the whole available sample, genotyped SNPs, which had a call rate lower than 80%, were outside Hardy Weinberg equilibrium (HWE), or were monomorphic and not considered for the analyses (n = 25). Statistical analyses. Haploview4. 2 for Windows  90  was used to analyse the LD and haplotype construction, as well as the risk association between the SNPs (single markers) and the haplotypes with GD diagnosis. In this study, the default parameters of the program were used: cut-off equal to 0. 001 for the Hardy-Weinberg equilibrium test (HWE), minimum genotype 75% and minimum minor allele frequency equal to 0. 001. The linkage case-control format was defined for the data file, and the haplotype block recognition was based on Gabriel's algorithm  91  , which uses the Hedrick's multiallelic D' to measure the degree of LD between the blocks (considering each haplotype within a block as an "allele" of that region) (the coefficient D' goes into the range -1 to + 1: D′ = 0 indicates that the two markers are independent [perfect equilibrium] and D′ = 1 indicates that no more than 3 of the 4 possible haplotypes are being observed in the sample [complete disequilibrium]).
Stata16 for Windows was used to perform other statistical analysis. T-test procedures compared means of data, and chi-square test (χ 2 ) and logistic regressions compared proportions of data and assessed the discriminative capacity of the SNPs to identify the presence of GD. Due to the multiple null-hypothesis tests, increase in Type-I error was controlled with Simes' correction method, based on the ordered p-values, less conservative than the classical Bonferroni procedure and particularly useful when several correlated test statistics are involved  92. Exploratory functional element analysis. The identification of regulatory elements overlapping the identified SNPs variants associated to GD was performed using SCREEN, a web interface for searching and visualizing the Registry of candidate cis-Regulatory Elements (cCREs) derived from ENCODE data  93.
The putative effect of variants analysed on TF binding motifs were computationally analysed via JASPAR. It is the largest open access database of matrix-based nucleotide profiles describing the binding preference of transcription factors from multiple species. JASPAR CORE database (http:// jaspar. gener eg. net/, version 5. 0) contains a curated and non-redundant set of profiles derived from published collections of experimentally defined transcription factor binding sites for eukaryotes  94. Here, we used the UCSC Genome Browser Track Hub that represents genome-wide predicted binding sites for TF binding profiles in the JASPAR database CORE collection. We then assessed whether the SNPs analysed were overlapping core consensus TF binding sequences and as such, they could potentially disrupt the binding of transcription factors or change their binding affinity.
Acknowledgements We thank  CERCA Programme/Generalitat de Catalunya  guaranteed institutional support. We also thank the  Ministerio de Ciencia, Innovación y Universidades  and the  Delegación del Gobierno para el Plan Nacional sobre Drogas ,  Instituto de Salud Carlos III (ISCIII) ,  CIBERobn  (an iniciative of ISCIII) and  FEDER funds/European Regional Development Fund (ERDF) , a way to build Europe.
Funding The present project has been founded by  CERCA Programme/Generalitat de Catalunya  guaranteed institutional support. In addition, the work was also supported by grants from the  Ministerio de Ciencia, Innovación y Universidades  (Grant  RTI2018-101837-B-100 ) and the  Delegación del Gobierno para el Plan Nacional sobre Drogas  ( 2021I031  and  2019I47 ),  Instituto de Salud Carlos III (ISCIII)  ( PI17/01167  and  PI20/00132 ) and co-funded by  FEDER funds/European Regional Development Fund (ERDF) , a way to build Europe. Additional support was received from  EU  Grant  Eat2beNice  ( H2020-SFS-2016-2; Ref728018 ),  PRIME  ( H2020-SC1-BHC-2018-2020 , ref. 847879) and  COST Action  ( CA19115 ). CIBERObn and CIBERsam are both initiatives of ISCIII. IB was partially supported by a  Post-Residency Grant  from the  Research Committee of the University Hospital of Bellvitge (HUB; Barcelona, Spain )  2020-2021.
Positive selection footprints in human populations. To investigate potential signatures of recent selection for alkaloids tolerance in human populations, we analyzed the extent of genetic differentiation and haplotype homozygosity in Native communities of the Central Andes exhibiting a long history of consumption of hallucinogenic cacti. For this, we used two genomic datasets including our target groups (within the area of influence of Andean shamanic practices) and reference populations (exhibiting native genetic background but outside the Central Andean region). Data-set 1 included the Aymara and Quechua as target populations and Yukpa and Bari as reference populations, while our Data-set 2 consisted of Aymara and Quechua as target groups, and Wichi and Yanesha as references (Fig. 1 ). Our principal component analysis showed that the retained individuals according to their genetic ancestry differentiated into five distinct genetic clusters corresponding to the Central Andean population (Aymara and Quechua), two North Andean/Caribbean populations (Baris and Yukpas-reference populations for Data Set 1), one Gran Chaco and one western Amazonia populations (Wichi and Yanesha-reference populations for Data Set 2; Table  S9 ; Figures  S4-S9 ).
Noticeably, all individuals from the Central Andes composed a condensed genetic group independently of the sampling scheme or dataset (Figure  S9 ). Our estimated genome-wide fixation index revealed that genetic differentiation with respect to central Andean groups (Aymara and Quechua) was larger for the reference communities Bari and Yukpa from the northern Andean region (Fst ~ 0. 08-0. 17), followed by the Wichi population from the Gran Chaco (Fst ~ 0. 08-0. 1) and to a lesser extent with the Amazonian Yanesha (Fst ~ 0. 04-0. 07), which is largely consistent with their geographic distributions (Fig. 1 ; Figure  S8 ). To assess whether our catalog of ortholog genes has been a target of recent positive selection in the Central Andean population, we calculated for each variant the integrated Homozigosity Score (|iHS|) for Extended Haplotype Homozigosity, and Likelihood Ratio Test (LRT) score for genetic differentiation (using Han Chinese as the general reference population and one reference population of South America: Yukpa or Bari for Data Set 1 and Yanesha or Wichi for Data Set 2).
Third, we acknowledge that many human orthologs of our candidate genes might not be shared across our studied datasets, resulting in the underestimation of the number of genes. Indeed, recent comparative studies of flies and humans recognize that the overall low number of reported genes associated to drug response, is likely due to the current low representation of human studies  33. This is especially critical in our case, as the reduced genotyping effort of South American Native communities implied a limited sampling for both our target and reference populations  83, 84. Thus, a larger collection of whole-genome sequences is necessary to supply larger sample sizes and SNP density to capture a larger number of genes and discriminate whether positive selection preferentially acted on protein-coding or regulatory regions.