dataesr/scientific-paragraphs-categorization huggingface dataset:
The SM, in cooperation with the ROS (which is aware of the sub-network slice graph, resource allocation and consumption), may propose to change the resource allocation or to relocate a certain virtual function from one data centre to another one for the sake of data transport efficiency. All slice template modifications or virtual function placement requests are sent via the ROS to the DO. After the change of the virtual function placement, the SM makes necessary configuration changes, and the ROS updates its slice deployment-related database. The mentioned SM-ROS cooperation allows for the application-driven (sometimes QoE-based) resource allocation that is hard to achieve in the current MANO architecture, and it provides an efficient extension to the classical management that assumes a fixed allocation of resources.
Some simulations results In this section, we implement the procedure on the R software (developed by the CRAN project). We will restrict our attention to the estimation of the vector (K * , t * ) ; i. e the number of segments K * and the instants of breaks t *. For the performances of the estimator of the parameter θ * , we refer to the works of Ahmad and Francq (2016). For each process, we generate 100 replications following the scenarios considered. The estimated number of segments is computed by using QLIK criteria penalized with κ n = κ n , κ n = log n and κ n = log n 1/3. The value of the estimator κ n is calibrated by using the slope estimation procedure (see Baudry et al. (2010)) as described above. Once the regularization parameter κ n obtained, the dynamic programming algorithm is used to minimize the criteria.
Number of trades in the stock of Technofirst Secondly, we apply our change-point detection procedure to a financial time series data. We consider the daily number of trades in the stock of Technofirst listed in the NYSE Euronext group. It is a series of 1000 observations from 04 January 2010 to 20 April 2016 (see Figure  7 ). The data are available online at the website "https://www. euronext. com/en/products/equities/FR0011651819-ALXP". These data have been analyzed by Ahmad and Francq  [1]  with the PQMLE, and have concluded that the INGARCH(1,3) is more appropriate. We carry out an INGARCH(1,1) with the possibility of change in the observations. The slope estimation procedure obtained with u n = (log(n)) 2 returns κ n ≈ 23. 04 and the estimation of the number of segments is " K n = 3, i.
This unified definition simplified the derivation of the unbiased estimators for both allele-count and Pool-Seq read count data, that we implemented in a new version of our R package poolfstat  (Hivert et al, 2018)  together with methods that rely on the estimated fstatistics for historical and demographic inference. These methods include i) three-population test of admixture; ii) four-population test of treeness; iii) F 4 -ratio estimation of admixture proportion; and iv) fitting, visualization and (semi-automatic) construction of admixture graphs. For completion, we briefly present the underlying methods as implemented in the package. We then carried out a comprehensive evaluation of the whole package on both simulated allele count and Pool-Seq read count data, considering for the latter various sequencing coverages and the presence or not of sequencing errors.
Similarly, 1 -Q A 1 = 2p r (1 -p r )e -τ A (resp. , 1 -Q B 1 = 2p r (1 -p r )e -τ B ) where τ A (resp. τ B ) is the divergence time separating R and A (resp. B) on a diffusion timescale (i. e. , in drift units of 1 2N e where N e is the effective population along the branch). As a consequence, the resulting estimates of F 2 , F 3 and F 4 strongly depend on the underlying set of genetic markers and may not be compared across different datasets, even from the same populations. Various scaling procedure may actually helps in reducing this dependence. Scaling the F 2 with respect to the across population heterozygosity 1 -Q 2 leads to the standard definition of pairwise-population F S T in terms of IIS probabilities  (Rousset, 2007; Hivert et al, 2018)  which is also concordant with its original definition as the numerator of F S T  (Reich et al, 2009; Peter, 2016) : F S T (A; B) ≡ Q 1 -Q A,B 2 1 -Q A,B 2 = F 2 (A; B) 1 -Q A,B 2 6 where Q 1 = 1 2 Q A 1 + Q B 1 is the overall probability of sample two IIS genes within the same population (i.
1. 2 Unbiased parameter estimators from Pool-Seq read count and standard allele count data Let y i j be the allele count for an arbitrarily chosen reference allele and n i j the total number of sampled alleles (e. g. , twice the number of genotyped individuals for a diploid species) at SNP i in population j. For Pool-Seq read count data, the y i j 's are not observed and for a given pool j, it is assumed that n i j = n j (the haploid sample size) for each and every SNP. We thus similarly defined r i j as the read counts for the reference allele and c i j the overall coverage observed at SNP i in population j. If allele count data are directly observed, unbiased estimators of the IIS probability within population j (Q j 1,i ) and between a pair of populations j and k (Q j,k 2,i ) for a given SNP i are: Q j 1,i = y i j y i j -1 + n i j -y i j n i j -y i j -1 n i j n i j -1 = 1 -2 y i j n i j -y i j n i j n i j -1 and Q j,k 2,i = y i j y ik + n i j -y i j (n ik -y ik ) n i j n ik (4) For Pool-Seq read count, unbiased estimators of Q 1,i and Q 2,i are similarly defined as  (Hivert et al, 2018, eqns  A37 and A40): Q j 1,i = 1 - n j n j -1         1 - r i j r i j -1 + c i j -r i j c i j -r i j -1 c i j c i j -1         = 1 -2 n j n j -1 r i j c i j -r i j c i j c i j -1 and Q j,k 2,i = r i j r ik + c i j -r i j (c ik -r ik ) c i j c ik (5) Genome-wide estimates of all the parameters defined in eq.
In poolfstat, we implemented two functions that allow i) identifying candidate sets of unadmixed populations among all the genotyped ones (find. tree. popset); and ii) building rooted neighbor-joining tree (rooted. njtree. builder). Briefly, find. tree. popset implements a procedure consisting of i) discarding all the populations showing at least one significant three-population test (i. e. , displaying a negative F 3 Z-score lower than -1. 65 by default) among all the possible ones; and ii) identifying via a greedy algorithm the largest sets of populations for which all the possible quadruplets pass the four-population test of treeness (i. e. , with an absolute F 4 Z-score lower than 1. 96 by default). The rooted. njtree. builder function builds a scaffold tree from a candidate set of (presumably) unadmixed populations using the nj function from the ape package  (Paradis et al, 2004)  and then compare the consistency of population heterozygosities between the partitions of the tree to root it  (Lipson et al, 2013).
Overview of the new poolfstat package Tables  1  and 2  describe the main objects and functions implemented in our new version (v2. 0. 0) of the R package poolfstat publicly available from the CRAN repository (https://cran. r-project. org/web/packages/ poolfstat/index. html). In-depth analyses of two Pool-Seq and allele count simulated datasets (see below) are described for illustration purposes in the package vignette provided as Supplementary Vignette V1. Detailed documentation page of the different objects and functions can also be directly accessed from an R terminal with poolfstat loaded using the help function (or the ? operator). The package includes several functions to parse allele count (e. g. , genotreemix2countdata) or Pool-Seq (e. g. , vcf2pooldata) input data stored in various formats commonly used in population genomics studies (Table 2).
These functions allow to clearly distinguish these two different types of data by producing objects of either the so-called countdata (for allele count) or pooldata (for Pool-Seq data) classes (Table  1 ). This step is critical to further rely on the appropriate unbiased estimators for the F and D parameters. Some functions allow to perform subsequent manipulation of the input data, for instance to only consider some of the populations or to remove SNPs according to various criteria (Table  2 ). Pool-Seq read count data pairwisefst Store pairwise F S T estimates. This object is generated by the compute. pairwiseFST function. Estimates can be conveniently visualized with the heatmap or plot functions, the latter interfacing the plot fstats function of poolfstat. fstats Store F 2 , pairwise F S T , F 3 , F 3 , F 4 and D estimation results.
† Object already existing in the first poolfstat version. Seq read counts) according to the input object class (either countdata or pooldata). For the estimation of F S T , the computeFST and compute. pairwiseFST also implement (by default) estimators based on an Analysis of Variance framework that correspond to those developed by  Weir (1996)  for allele count data and by  Hivert et al (2018)  for Pool-Seq data. The fit. graph function implements the approach described above to estimate the parameters (i. e. , edge lengths and admixture rates) of an admixture graph that is stored in a graph. params object (Table  1 ). Such objects can be generated with the generate. graph. params function (Table  2 ) to include the target basis f -statistics and the error covariance matrix (denoted above f and Q, respectively) estimated with compute.
fstats (stored in an fstats object) and to specify the topology and the parameters of the admixture graph. Note that the graph. params2symbolic. fstats function allows exploring in details the properties of an admixture graph specified by a graph. params object by deriving a symbolic representation of all the F 2 , F 3 , F 4 and the model equations (see above) by internally relying on the Ryacas package for symbolic computation  (Andersen & Højsgaard, 2019). The fit. graph function then produced an object of class fitted. graph that includes the estimated edge lengths (in F 2 and also optionally in drift units) and admixture proportions together with (optionally) their 95% CI. For model fit assessment purposes, fitted. graph objects also include the BIC and Z-score of the residuals of the fitted basis f -statistics.
Such a comparison can (and should) be generalized to all the f 2 , f 3 and f 4 statistics (not just the ones forming the basis) using compare. fitted. fstats jointly applied to a fitted. graph and a fstats ob-  The poolfstat package includes several functions to assist construction of admixture graphs. As mentioned in the previous section, the find. tree. popset and rooted. njtree. builder functions allow to identify and build rooted tree(s) of scaffold of (presumably) unadmixed populations that may be used as starting graph(s). Besides, the add. leaf and graph. builder functions implement the above described heuristic to extent an existing graph (or tree) by adding one or several leaves (i. e. , genotyped populations). These functions generate a list of fitted. graph objects together with other information that may be helpful for graph comparison (e.
Data analyses • Two standard allele count datasets (namely AC m≥1% and AC m≥5% ) obtained by simple counting of the simulated individual (haploid) genotypes for each population (i. e. , assuming Hardy-Weinberg equilibrium within population) and removing SNPs with a Minor Allele Frequency (MAF) computed over all the individuals lower than 1% (for AC m>1% datasets) or 5% (for AC m>5% datasets) • Thirty Pool-Seq datasets (coded as PSλ = m>m t % ) for i) five different average sequencing coverages λ (equal to 30, 50, 75, 100 or 200 reads; a 30X Pool-Seq coverage representing a lower limit for population genomics studies); ii) two different MAF thresholds m t of 1% and 5% (MAF being estimated on the read counts over all the pools); and iii) three different sequencing error rates of 0 (no error), 1 and 2.
5 the two latter being representative of Illumina sequencers  (Glenn, 2011). Pool-Seq datasets were simulated from the AC m≥1% allele count datasets following a procedure similar to that described in  Hivert et al (2018). Briefly, the vector r i j = r i jk of read counts at SNP position i in population j for the nucleotide k (where by convention k = 1 and k = 2 for the derived and ancestral alleles respectively) was sampled from a Multinomial distribution parameterized as: r i j ∼ Multin y i j n j 1 - 3 + 1 - y i j n j 3 ; 1 - y i j n j 1 - 3 + y i j n j 3 ; 3 ; 3 ; c i j where y i j is the derived allele count for SNP i in population j (from the corresponding AC m>1% dataset); n j is the haploid sample size of population j (here n j = 50 for all j); and c i j = k=4 k=1 r i jk is the overall read coverage.
To introduce variation in read coverages across pools and SNPs, each c i j was sampled from a Poisson distribution with a parameter λ (the target Pool-Seq mean coverage). When = 0, only reads for the derived (k = 1) or ancestral (k = 2) alleles can be generated and the above Multinomial sampling actually reduces to a Binomial sampling following r i j1 ∼ Bin y i j n j ; c i j (and r i j2 = c i jr i j1 ). However, when > 0, sequencing errors might lead to non-null read counts for the two other alleles leading to tri-or tetra-allelic SNPs. Morevover, sequencing errors may also introduce spurious additional variation by generating false SNPs at monomorphic sites. To account for the latter, read count vectors r i j for all the 2 × 10 9 -I monomorphic positions i (where I is the number of SNPs observed in the considered AC m>1% dataset) were sampled as r i j ∼ Multin 1 -3 ; 3 ; 3 ; 3 ; c i j with coverages c i j sampled from a Poisson distribution (as c i j for polymorphic positions).
Yet, as usually done with empirical datasets, we applied a minimum read count filtering step consisting of disregarding all the alleles with less than 2 observed reads (over all the populations). Only bi-allelic SNPs passing the overall MAF threshold m f were finally retained in the final PSλ = m≥m t % datasets. Analyses of the simulated data were carried out with poolfstat (Supplementary Vignette V1). Briefly, each msms simulated dataset was converted into an AC m≥1% dataset in TreeMix format  (Pickrell & Pritchard, 2012)  further imported into a countdata object with genotreemix2countdata (Tables  1  and 2 ) and used to generate each corresponding AC m≥5% dataset using countdata. subset. To improve computational efficiency, the different PSλ = m>m t % Pool-Seq datasets were generated from the AC m≥1% countdata objects in the form of pooldata object using custom functions (not included in the package) coded in C++ and integrated within R using Rcpp (Eddelbuettel, 2013).
In addition, to evaluate the impact of the (bad) practice consisting of analyzing Pool-Seq data as if they were allele count data (i. e. , overlooking the sampling of reads from individual genes of the pool), we also created "fake" countdata objects from the different pooldata objects. We then used default options (unless otherwise stated) of i) computeFST to estimate genome-wide F S T over all the populations; ii) compute. fstats to estimate all the fand D-statistics; iii) compute. f4ratio to estimate admixture proportions; and iv) fit. graph to estimate the admixture graph parameters (Table  2 ). As the number of SNPs was variable across the different simulated datasets, we adjusted the number of successive SNPs defining a block for block-jackknife estimation of standard errors by dividing the total number of available SNPs by 500.
This thus resulted on average in 490 blocks of 4. 1 Mb over the genome for all the analyzed datasets (the simulated genomes consisting of 20 chromosomes). Note that the parameter estimates were always taken as the block-jackknife mean values rather than estimates over all SNPs (i. e. , including those in the chromosome ends). In practice, the differences between the two are insignificant (e. g. , Supplementary Vignette V1). For validation purposes, we also analyzed the 250 AC m≥1% datasets with programs from the AdmixTools suite  (Patterson et al, 2012)  after conversion to the appropriate input format using custom awk scripts. More specifically, we ran qpfstats (v. 200) to estimate the 15 basis f -statistics, i. e. , taking P1 as the reference population, the five f 2 of the form (P1,Px) and the ten f 3 of the form (P1;Px,Py) (where x = 2,.
Analysis of a real To allow for complete reproduction (and exploration) of our analyses, all the command lines used to analyze the D. suzukii Pool-Seq dataset are described in the Supplementary vignette V2. Briefly, we combined the 14 (bam) files, obtained by Olazcuaga et al (2020) after aligning the 14 Pool-Seq data onto the latest near-chromosome scale D. suzukii assembly  (Paris et al, 2020) , into an mpileup file using SAMtools 1. 9 with options -q 20 -Q20  (Li et al, 2009). Variant calling was then performed using VarScan mpileup2snp v2. 3. 4 Koboldt et al (2012)  run with options --min-coverage 10 --min-avg-qual 25 --min-var-freq 0. 005 --p-value 0. 5 (i. e. , with very loose criteria). After discarding positions mapping to non-autosomal contigs  (Paris et al, 2020) , the resulting vcf file was parsed with the vcf2pooldata function of poolfstat with default options except for i) the overall MAF threshold (computed from read counts) that was set to 5%; and ii) the minimal read coverage for each pool that was set to 50.
The resulting pooldata object was further filtered with pooldata. subset to discard i) all positions with a coverage higher than the 99th coverage percentile within at least one pool; and ii) discard all SNPs with MAF<5% over all the populations from the native area to favor ancestral SNPs. The final dataset then consisted of read counts for 1,588,569 bi-allelic SNPs with a median read coverage varying from 64 (US-Sok) to 95 (CN-Bei and US-Haw) among the 14 pools (Table  2  in the Supplementary Vignette V2). We defined blocks of 10,000 consecutive SNPs for block-jackknife estimation of standard errors leadint to a total of 145 blocks of 698 kb on average (varying from 414 kb to 2. 03 Mb). Hence, most analyses actually relied on 1,450,000 SNPs that mapped to the 15 largest contigs of the assembly (totaling 116 Mb).
Evaluation of poolfstat on simulated data Historical and demographic inference based on fand D-statistics has already been extensively evaluated in previous studies (e. g. ,  Patterson et al, 2012; Lipson et al, 2013; Peter, 2016). Therefore, the purpose of our simulation study was essentially threefold: i) to validate the estimators implemented in poolfstat by comparing, for allele count data, with those obtained with the reference AdmixTools suite  (Patterson et al, 2012) ; ii) to evaluate the performance of the estimators for Pool-Seq data as a function of read coverage and sequencing errors; and iii) to provide example datasets with known ground truth for illustration purposes.
Description of the simulated datasets We simulated 250 genetic datasets for six populations (named P1 to P6) each consisting of 25 diploid individuals and that were historically related by the admixture graph represented in Figure  1  (Material and Methods). Each of these datasets was further used as template to generate 2 allele count datasets (applying 1% or 5% threshold on the overall MAF for AC m>1% and AC m>5% datasets respectively) and to simulate 30 Pool-Seq datasets with five different mean read coverages (λ ∈ {30; 50; 75; 100; 200}); three sequencing error rates ( ∈ {0; 10 -3 ; 2. 5 × 10 -3 }) and two MAF (computed over all read counts) thresholds (referred to as PSλ = m>1% and PSλ = m>5% for 1% and 5% MAF thresholds, respectively). This thus lead to a total of 8,000 simulated datasets.
The average number of available SNPs and false SNPs (for PSλ =1 m≥m t % and PSλ =2. 5 m>m t % datasets) is given in Table  S1  for each of the 32 different types of datasets and represented as a function of the mean coverages λ and MAF thresholds in Figure  S1. Overall, 471,919 SNPs and 240,369 SNPs were available on average for allele count datasets at the 1% (AC m>1% ) and 5% (AC m>5% ) MAF thresholds respectively consistent with the L-shaped distribution of allele frequencies (Figure  S2A ). As expected from binomial sampling (Figure  S2B ), for Pool-Seq datasets generated with no sequencing error, the number of SNPs remained always lower than the AC m>1% datasets at the 1% MAF threshold although increasing with coverages from 13. 8% for PS30 =0 m>1% to 2. 01% for PS200m > 1% =0 datasets (see Table S1 legend for details).
Conversely, at the 5% MAF threshold, the number of SNPs was slightly higher than the AC m>5% datasets (from 2. 58% for PS30 =0 m>5% to 1. 51% for PS200 =0 m>5% ) which is related to i) the shape of the allele frequency spectrum (stochastic variation in read sampling leading to include more SNPs with 0. 01 < MAF < 0. 05 than exclude SNPs with MAF > 0. 05 from the simulated genotying data because they are more numerous); and ii) variation in the simulated read coverages that explains the decreasing trend with λ.
Comparison of poolfstat and Admixtools estimates for allele count data We first analyzed the 250 simulated AC m>1% datasets to estimate with both poolfstat and Admixtools programs i) the 15 basis f -statistics (taking P1 as the reference population) consisting of five f 2 and ten f 3 (Figure  3A ) and their corresponding error covariance matrix (Figure  3B ); ii) the 60 f 3 (Figure  3C ) and their associated Z-scores (Figure  3D ); and iii) the 45 D-statistics (Figure  3E ) and their associated Z-scores (Figure  3F ). The estimates were all found in almost perfect agreement between the two implementations with Mean Absolute Differences    C ) and E), poolfstat estimates correspond to block-jackknife means (i. e. , they only include SNPs eligible for block-jackknife). The given MAD' value is the MAD between AdmixTools and poolfstat estimates that include all SNPs (see documentation for the compute.
24 analyzing Pool-Seq data we also analyzed the simulated Pool-Seq datasets (focusing only on PSλ =0 m>m t % datasets, i. e. , simulated without sequencing error) as if they were allele count data. Overall, 42 different configurations were thus investigated each originating from the 250 allele count datasets simulated under the demographic scenario represented in Figure  1 , leading to a total of 42×250=10,500 analyses. Tables  3  and S2  provide the estimated power (True Positive Rate, TPR) and False Positive Rate (FPR) of the f 3 -and f 3 -based test of admixture for each configurations. As P6 was the only admixed population, each TPR was estimated as the proportion of f 3 (respectively f 3 ) with an associated Z-score < -1. 65 (95% significance threshold) for the (P6;P2,P3) population triplet (i.
Surprisingly, sequencing errors in Pool-Seq data also tended to increase the power from a negligible amount (less or close to 1%) at 5% MAF threshold to a quite substantial amount at 1% MAF threshold (decreasing with coverage and increasing with sequencing error rate). At the extreme, a power of 100% was even observed when λ ≤ 50 and ≥ 1. This trend was actually directly related to the proportion of false SNPs introduced by sequencing error (Figure  S1B ) that resulted in a downward bias of f 3 and f 3 estimates, although the underlying tests remained robust as all the estimated FPR were null except for PS50 =2. 5 m>1% data (FPR=6. 47%) which displayed the highest proportion of false SNPs (> 90%, Figure  S1B ). However, this observed apparent robustness of the three-population tests to false SNPs should be interpreted cautiously since it may rather result from the moderate to high expected f 3 and f 3 values in our simulated scenario for the population triplets that do not involve P6 as a target.