dataesr/scientific-paragraphs-categorization huggingface dataset:
Indeed, we point out that Vinnikov's code does not allow one to set either ξ = 1 or ξ = 0, and the smallest stable value of ξ we could find is ξ = 10 -4. Regarding the large ξ region, in the plots in Fig. 7  we have actually used ξ = 1-with = 10 -6 for both codes. Finally, we found severe numerical instabilities for 0. 6 ξ 0. 95. Therefore, we were not able to perform a comparison in this region. This also justifies the need for a new open and maintained evolution code. Moreover, the modular architecture of APFEL++ and PARTONS will facilitate the integration of higher-order corrections to the evolution, while this task would probably require an almost complete rewriting of Vinnikov's code.
In addition, we have worked out the consequences of the GPD sum rules on the evolution kernels, deriving equalities that need to be obeyed order by order in perturbation theory, finally showing that our one-loop calculation fulfils these equalities. Moreover, we have computed the conformal moments of our non-singlet evolution kernels showing that, as expected, they diagonalise upon Gegenbauer transform and that their eigenvalues coincide with the well-know DGLAP and ERBL one-loop anomalous dimensions. Finally, we have also explicitly shown that our computation reproduces previous results present in the literature. Our calculation has been implemented in the public code APFEL++ that in turn has been interfaced to PARTONS. This allowed us to perform detailed numerical studies. We have checked that DGLAP and ERBL evolutions are reproduced to very high accuracy in the ξ → 0 and ξ → 1 limits, respectively.
Moreover, we have checked that the evolution Fig. 7  Comparison between Vinnikov's code  [27]  and APFEL++. The evolution is performed at LO in the n f = 3 scheme (no threshold crossing) between the scales μ 0 = 2 GeV and μ = 10 GeV. As initial-scale distributions we have used the model of Refs. [61] [62] [63]  (GK model) setting t = -0. 1 GeV 2 as momentum transfer squared preserves GPD polynomiality. In addition, we have verified that our implementation of GPD evolution agrees with the evolution computed in conformal space. As a last check, we have compared our GPD evolution against another existing implementation, Vinnikov's code, finding general good agreement. In this paper, we limited ourselves to the one-loop (LO) evolution of unpolarised GPDs. The next natural shortterm step is the extension to longitudinally and transversely polarised evolutions.
In the longer run, we plan to implement the two-loop (NLO) corrections to the evolution. Facing a new era for GPD experiments at colliders, we believe that the public release of a documented and carefully checked implementation of GPD evolution equations meets the need of the hadron-physics community. The code is flexible and can run with any GPD model expressed in x space. It also provides for the first time an implementation of the variableflavour-number scheme in a public solver of GPD-evolution equations. We conclude by stressing once again that the implementation of GPD evolution presented here is publicly available in the APFEL++ code: https://github. com/vbertone/apfelxx that is in turn interfaced to the PARTONS framework: https://partons. cea. fr/partons/doc/html/index. html that gives access to a large variety of GPD models, some of which are used in this paper.
Acknowledgements We are grateful to  M. Diehl  and  A. Radyushkin  for stimulating discussions and for helping us interpret the results of previous calculations. We also thank  J. Rodriguez-Quintero  for useful discussions. V. B. is supported by the  European Union 's  Horizon 2020 research and innovation programme  under grant agreement STRONG 2020 -No. 824093. J. M. M. is supported by the  University of Huelva  under grant  EPIT2021.
lyrata  54  , but is considered highly mutagenic  47  , suggesting that TE superfamily characteristics rather than TE abundance determines nearby SNP abundance. On average, SNPs were closest to TEs from the CACTA superfamily (3123 bp, ranging from 73 to 13,896 bp) and most distal to TEs from the Harbinger superfamily (4595 bp, ranging from 65 to 21,559 bp). As expected under high levels of inbreeding (F IS > 0. 6), heterozygosity was low across most of the genome (Fig. 3a ). However, Copia, Harbinger and LINE elements manifested elevated levels of nearby heterozygosity under inbreeding (F = 4. 98** based on generalized mixed modeling, Supplementary Data 6), particularly downstream (Fig. 3a , F = 4. 36**, Supplementary Data 6). We refer to H TE as heterozygosity that remains high under inbreeding due to the presence of nearby TEs (here Copia and Harbinger elements).
While Copia and Harbinger elements were associated with elevated levels of heterozygosity particularly under inbreeding, LINE elements had high heterozygosity irrespective of inbreeding levels (Fig. 3b ). The TE Effect thus was limited to Copia and Harbinger elements. Heterozygosity also increased with increasing genomic distance from TEs, up to ca. 3. 5 kb, after which it generally decreased again (Fig. 2c ), but this effect was not significant (Supplementary Data 6). Across TE superfamilies, heterozygosity was significantly higher downstream than upstream of TEs (Fig. 3a, b  and Supplementary Data 6). Together, these findings suggest that TEs can impact downstream heterozygosity across the genome, in accordance with our hypothesis (Fig. 1-Q1 ). While Copia and Harbinger elements were associated with increased levels of nearby heterozygosity under inbreeding (F IS > 0.
Both types of selection are covered by our analysis of purifying selection (see Supplementary Fig. 2 ), with pseudo-overdominance and associative overdominance generating signatures of purifying selection (negative alpha values, low maf, predominant non-synonymous codon usage) and apparent purifying selection (negative alpha values, low maf, variable codon usage), respectively. Although fully disentangling the various types of overdominance remains challenging and some of our 'real' signatures of balancing selection may actually reflect pseudooverdominance  80  , our findings suggest that pseudo-overdominance and associative overdominance are strongly underrepresented in our dataset, particularly for the American lineage (Supplementary Fig. 2 ). The patterns observed in this study likely underrepresent the actual role of TEs in driving genome-wide variation and evolution.
The level of inbreeding and therefore genome-wide heterozygosity varies significantly across North American populations, which was in turn lower than heterozygosity estimates across Northern European samples  84. The program Stacks was used to call SNPs across 92 bp RAD loci aligned to the A. lyrata reference genome. Filtering was applied to remove incorrectly assembled loci and reduce the likelihood of incorporating genotyping errors (using only loci with a minimum read depth of 10). For analyses, we randomly selected only one SNP per RAD locus and only SNPs present in all individuals (so unlinked SNPs without missing data). We limited the dataset to highly qualitative SNPs through maintaining (i) minimum allele frequencies of 0. 05, (ii) no missing data, and (iii) an average read depth of 73.
18 (European samples) and 60. 09 (North American samples) per SNP (Supplementary Fig. 4 ). This resulted in a dataset of 5935 RAD loci (and thereby 5935 SNPS) across the two A. lyrata subspecies. Extracting those present in just North American or European populations, resulted in 1858 and 4398 SNPs respectively (Supplementary Data 1 and 2). TEs annotations were obtained from Legrand et al. 54. Briefly, libraries of consensus sequences representing repetitive elements were obtained from genome assemblies of A. thaliana, A. lyrata, and A. halleri using the TEdenovo pipeline of the package REPET  85. A bundle library was then obtained by pooling these libraries and was used to annotate TEs in the A. lyrata assembly also used for RAD sequencing (Phytozome v11), using the TEannot pipeline of REPET.
Inbreeding coefficients and signatures of selection The genome-wide inbreeding coefficient (F IS ) was calculated per sample using the R package "hierfstat" (see Supplementary Data 3 and 4 for input files). We further applied two approaches for detecting signatures of adaptive evolution associated with each TE superfamily. First, a multivariate approach implemented in PCadapt was used for the dual purpose of estimating relatedness among samples (multidimensional genetic background structure) and detecting signatures of natural selection identified as significant deviations from background genetic structure  86, 87. Based on the distribution of eigenvalues associated with the principal components (PCs) (Supplementary Data 7), we selected the first three PCs to represent background genetic structure and among-sample relatedness.
If alleles at these loci were rarer than expected under neutrality, we considered these SNPs candidates of purifying selection  77, 89, 90. Specifically, we considered SNPs with signatures of balancing selection (negative alpha values in Bayescan analysis) as candidates of purifying selection if their minimum allele frequency (MAF) was (i) smaller than the MAF of neutral SNPs, and (ii) smaller for non-synonymous as compared to synonymous codon usage. In any other cases, we considered SNPs with negative alpha values as candidates of balancing selection. Codon usage (4-fold and 0-fold positions in the A. lyrata reference genome) of individual SNPs was obtained using the New-AnnotateRef. py script  91.
Modeling the effects of TEs on heterozygosity and evolution We followed a stepwise modeling approach that allowed testing our hypotheses consecutively without running complex models with many parameters. We first ran an explorative mixed model (Model 0, Table  1 ) to: (i) identify TE superfamilies with elevated levels of heterozygosity under inbreeding, and (ii) reduce data complexity in subsequent models through replacing the TE superfamily variable (N = 13 levels) by a simple TE grouping variable ("TE Effect", N = 2 levels). TE effect thus refers to the potential of specific TE superfamilies (here Copia and Harbinger elements) to maintain nearby heterozygosity under inbreeding. This new grouping variable distinguishes between TE superfamilies that significantly impact heterozygosity under inbreeding (H TE ) and all other TEs (H 0 ).
To test whether this effect was exclusively associated with high inbreeding levels, the explorative model was run on a subset of the samples characterized by predominant self-fertilization and with inbreeding coefficients exceeding 0. 6 (Model 0a), and compared to a model with subset of the samples characterized by predominant outcrossing and with inbreeding coefficients below 0. 6 (Model 0b). The probability of a locus to be heterozygous was consistently modeled with the random effect "Relatedness", a categorical variable correcting for genetic relatedness among samples as revealed by the multivariate PCadapt analysis. Throughout our study, the probability of a locus to be heterozygous was modeled using a binomial distribution with cloglog link within the glmmTMB R package  92. Analysis of variance tables were produced using the lmer R package.
In addition, if TEs are involved in evolution irrespective of inbreeding levels, signatures of selection associated with TEs identified across the North-American samples should be predictive for evolutionary signatures in other populations (Q3 in Fig. 1 ). We correspondingly formulated two specific expectations on heterozygosity for an independent European dataset where inbreeding is strongly reduced, with inbreeding coefficients ranging from -0. 24 to -0. 64  82, 84. First, H O and H TE should be comparably high for the European dataset (as opposed to the inbred samples originating from North-America where H TE by definition is higher than H O, ). We thus modeled the "TE effect" on heterozygosity across European A. lyrata populations, while accounting for potential effects of SNP orientation relative to nearest TE.
We expect no TE effect on H Europe (i. e. H O = H TE ). To disentangle mating strategy effects from demographic effects on the inbreeding coefficient, we explored this expectation on two subsets that share the same outcrossing mating system but differ in inbreeding coefficients (F IS > -0. 3 vs. F IS < -0. 3), presumably due to strong demographic bottlenecks experienced by the most inbred European individuals  93. If mating system strategy is the driver of TE effects, than H 0 = H TE for both subsets. If demography drives TE effects, than H 0 = H TE only for the subset with F IS < -0. 3. Second, the proportion of SNPs under selection across TE superfamilies identified in the North-American dataset should be comparative for the European dataset. While very different outliers of selection are expected in Europe (distinct evolutionary histories and strong environmental differences), the general tendency of TE superfamilies to be involved in specific evolutionary processes may be similar between the North-American and the European samples.
To test this, we compared the proportion of outliers of each TE superfamily between the North-American and the European dataset (Pearson correlation). We applied the same outlier detection approaches used for the North-American dataset to the European accessions. All analyses were performed at the superfamily level because (i) the number of replicate TEs within families was too low to statistically analyze heterozygosity at the TE family level, and (ii) it allows to elucidate genome-and superfamily-wide relationships between TEs and nearby genetic diversity.
Gene ontology and essentiality analysis We used Blast2go to map and annotate the RAD loci containing the SNPs against all plant genomes to obtain gene ontology terms. With Fisher's exact tests (R package "TopGO"), we then assessed which biological processes and molecular functions were particularly overrepresented in (i) outliers of selection, (ii) SNPs near TE superfamilies that significantly increase heterozygosity under intense inbreeding (H TE ), and (iii) SNPs upstream vs. downstream of TEs. We hypothesized that outliers of divergent selection, and SNPs downstream TEs are enriched for stress-related processes (e. g. response to abiotic The probability of a locus to be heterozygous was consistently modeled with the random effect "Relatedness", a categorical variable correcting for genetic relatedness among samples as revealed by a multivariate PCadapt analysis.
Acknowledgements This work was supported by  Research Foundation Flanders  (grant numbers  FWO 12P6517N ,  FWO 12P6521N ), and by the  Natural Environment Research Council  ( NERC  project grant  NE/H021183/1  to  Barbara Mable , which generated the RAD data). We thank  Edinburgh genomics  for conducting the RAD sequencing. We also thank  Dr. Pierre Baduel  for his expert insights on the evolutionary importance of reference vs. nonreference TEs in A. thaliana.
Data availability Previously published transposon dataset under BioProject PRJNA495003 were used in this study. In addition, the previously published raw demultiplexed FASTQ files can be found in NCBI SRA database under accession SRP148549 and the IDs for the demultiplexed FASTQ files for individual BioSamples are SAMN09230090 -SAMN09230180. Source data are provided with this paper.
Furthermore, an indirect effect results from avoiding restrictions, through public health measures, on social, education, and economic activities. Here, we conduct a quantitative analysis of the overall economic effect of COVID certificates based on the weekly GDP estimates provided by the OECD Weekly Tracker  40. Resorting to a high-frequency indicator of economic activity is necessary to exploit the weekly variations in vaccination rates to identify the effect of vaccine uptake on economic activity. This paper innovates compared to previous analyses  41  , as the use of a high-frequency GDP proxy allows quantitative estimates of the economic impact of variations in vaccination rates. The impact of COVID certificates on the economy is modelled through its effect on vaccine uptake and the elasticity of the latter to weekly GDP, using data from all OECD and G20 member countries as used by the OECD Weekly Tracker (Methods D).
Methods Data. All data were retrieved in the first week of January 2022. Demographics, health infrastructure, and economic indicators. The indicators in Supplementary Table  1  (Appendix) support the claim that France, Germany, and Italy are similar in terms of demography, health infrastructure, and their economies. Health data. For all OECD and EU countries, the share of the population who received one dose of a COVID-19 vaccine, two doses of a COVID-19 vaccine, hospital admissions per 1 million, daily ICU patients per 1 million, daily deaths per 1 million, and population estimates have been retrieved from Our World In Data  46. For France age-stratified data on hospital admissions, ICU patients, and deaths was retrieved from official government sources (https://www. data. gouv. fr/fr/datasets/ synthese-des-indicateurs-de-suivi-de-lepidemie-covid-19/) and deaths outside hospitals from the French Institute for Demographic Studies (INED) (https://dccovid.
site. ined. fr/en/data/france/). For Italy age-stratified data on deaths was also retrieved from INED (https://dc-covid. site. ined. fr/en/data/italy/). Age-stratified vaccine uptake statistics for France and Italy were both retrieved from the European Centre of Disease Prevention and Control (note that such data is not available for Germany) (https://vaccinetracker. ecdc. europa. eu/public/ extensions/COVID-19/vaccine-tracker. html#age-group-tab). The share of different vaccines used until the end of 2021 in France, Germany, and Italy (made by BioNTech/Pfizer, Moderna, AstraZeneca, Janssen Pharmaceutica NV) have been retrieved from the official government sources (France: https://covidtracker. fr/vaccintracker/, Germany: https://impfdashboard. de/, Italy: https://www. governo. it/it/cscovid19/report-vaccini/).
OECD Weekly Tracker. The OECD Weekly Tracker (short 'Weekly Tracker') provides weekly estimates of economic activity based on Google Trends data and Fig. 4  Estimated ICU patients with and without COVID certificates. For France (a), Germany (b), and Italy (c), daily COVID-19 patients in intensive care units (ICUs) per million (7-day rolling average) in the actual intervention deployment (blue) and in the no-intervention counterfactual scenario (red). The red shaded area is the 95% confidence interval centred around the main estimate. The counterfactual for France is based on an age-stratified model. The other counterfactuals are not based on age-stratified models due to unavailable data. Green lines indicate levels at which previous lockdowns were instated. The black dotted vertical line is the date of the announcement of the COVID certificate.
The relationship between the search volume indices and GDP, f, is learnt at the quarterly frequency using official quarterly GDP series and quarterly aggregates of the search indices. It is then used to disaggregate GDP growth at the weekly frequency by applying f to the weekly search indices. The relationship between Google Trends variables and GDP growth is fitted using a neural network. It is trained using a dataset comprising the whole panel of observations from 46 countries. The Tracker measures the percentage difference in GDP relative to a pandemicfree counterfactual, where the counterfactual is taken to be the OECD Economic Outlook projection published in November 2019  47. Formally, the Tracker is defined as T w ¼ y w x w À 1; ð1Þ where y w is weekly GDP in week w, and x w is weekly GDP in a no-COVID counterfactual, proxied by a twelfth of quarterly GDP projected by the OECD Economic Outlook prior to the crisis.
The fit is robust with respect to slightly longer or shorter fitting windows. On the other hand, when using a much shorter window (e. g. , 60 days) estimates become very noisy with respect to the exact window length, likely because the fit does not appropriately pick up the curvature and inflection point of the logistic function. We use the function 'curve_fit' from Python's package 'scipy. optimize' over vaccine uptake and synthetic counterfactuals. We use block bootstrap to account for time dependence in the data with 1000 iterations and 30 non-overlapping blocks  50. The 95% confidence intervals are shown and reported throughout. Counterfactual vaccine uptakes. For each country, denote by V t ðvÞ for v 2 f0; 1; 2g the proportion of the population having received v doses at time t. We do not consider v ≥ 3 doses as individuals who were not vaccinated before the announcement of the COVID certificate were not eligible to receive a booster before early 2022; a counterfactual is thus not needed.
1, Appendix ). Finally, Vt ð0Þ ¼ 1 À Vt ð1Þ À Vt 2 ð Þ. For robustness, we estimated the impact of COVID certificates in Germany starting at the French announcement instead, and observed a slightly higher effect (i. e. , 1. 1 p. p. more by the end of the year). Assessing the impact of COVID certificates from the date it was announced in the country results in a more conservative estimate, as the potential impact of other countries' announcements is neglected. Age-stratified vaccine uptake. To estimate age-stratified vaccine uptake, we consider the population aged 60 and over (60+) and the rest, separately. This is particularly relevant as health outcomes are generally more severe for older people. As agestratified data are not available for Germany before mid-September 2021 it cannot be included in this analysis.
We use the innovation diffusion model to construct a counterfactual for the 60+ group for France and Italy. For all vaccination statuses v, the realised vaccination uptake for 60+ is denoted by V 60þ t ðvÞ, and the counterfactual is denoted by V60þ t ðvÞ. To ensure consistency with our overall estimates, we set counterfactual vaccine uptake for the 59 years old and below as the difference between the overall and the 60+ estimates. For the population aged 60 years and older, the fit is computed from the start of 2021 to the date of the announcement of the COVID certificate and then extended to the end of the year; the start date is chosen because by then the majority of the 60+ population was eligible for vaccination (Fig. 6 ). We use the function "curve_fit" from Python's package "scipy. optimize" over the vaccine uptake counterfactuals.
Age-stratified health outcomes. When the data are available, we analogously compute age-stratified (i. e. , 60 years old and above, and the rest of the population) health outcomes, as well as the corresponding counterfactuals. The total numbers are obtained by summing over all age groups. The lag parameters  53. We assume the lag between vaccination and full effectiveness is l vaccine ¼ 7 days, the lag between infection and hospital admission is l hosp ¼ 7 days, the lag between infection and ICU admission is l ICU ¼ 10 days, the total number of days in ICU is 8, so that an ICU patient has been admitted l stay ICU ¼ 4 earlier, and the average lag between infection and death is l death ¼ 14 days. Thus, for hospital admissions, the total lag is l vaccine þ l hosp ¼ 14; for ICU patients, the total lag is l vaccine þ l stay ICU þ l ICU ¼ 21; and for deaths, the total lag is l vaccine þ l death ¼ 21.
Acknowledgements We are grateful for comments and suggestions by  Laurence Boone ,  Anne Bucher ,  Maria Demertzis ,  Mathias Dewatripont ,  Luiz de Mello ,  Thierry Pech ,  Alain de Serres ,  David Turner , and seminar and expert consultation participants at  Bruegel (Brussels) ,  French Scientific Council (Paris) ,  European Centre for Disease Prevention and Control (Stockholm) ,  Institute for Interdisciplinary Innovation in healthcare (I3h, Brussels) ,  Institut Pasteur (Paris), OECD (Paris) , and  Terra Nova  (Paris). This work has been partially supported by  Bruegel ,  French National Research Agency (ANR)  through grant  ANR-19-CE48-0018-01 , and  University Paris Dauphine -PSL. All errors are ours.