dataesr/scientific-paragraphs-categorization huggingface dataset:
This function can be used for any dimension of the problem. In comparison, regression of the scalogram or periodogram  [3]  is based on a linear fit of pairs of time series, and thus there does not exist an easy way to extend to more than two dimensions. multiwave package is based on  [4] , where we developed a wavelet-based approach using Whittle approximation for an efficient estimation of the long-memory parameters and the long-run covariance matrices. In addition, multiwave proposes an implementation of an alternative method using Fourier decomposition as described in  [18]   3. As it is described in this paper, multiwave is a very versatile package and opens the way to estimation of the long-memory parameters and the long-run covariance matrices using multivariate data sets. It is in particular not necessary to assume the stationarity of the time series as it is the case when using Fourier decomposition  [6].
The Whittle approximation is computed using either the coefficients of wavelet decomposition or the coefficients of Fourier decomposition when the time series are stationary. The package multiwave is divided in three parts. A first group of functions is dedicated to the simulation of multivariate long-memory time series; the main function is fivarma. A second group of functions is implementing the wavelet decomposition, through DWTexact and associated functions. Finally the computation of the estimators are coded using the Fourier decomposition in mfw and its derivatives and using the wavelet decomposition in mww and its derivatives. The mathematical background is detailed in a separate Section 2. The rest of the paper is dedicated to the description of the package multiwave. Simple examples of parametric models and real data are presented in Section 3 with corresponding functions of multiwave ready to apply.
Limits of the model Note that in definition (3) the operators are applied in a given order, where the lag operator is taken first. Changing the order of the lag operator and autoregression corresponds to model B of  [9]  and V ARF I models of  [17]  where X is obtained with equation diag(1 1 -L) d A(L) X(t) = B(L)u(t) , with similar notations than above. That is, X is obtained by fractional integration after autoregression, which is also called cointegration. The spectral density still satisfies the approximation (2) however the matrix Ω may no longer be Hermitian. Clearly multiwave package is not built to deal with such cases. We refer to alternative methods in literature, among others  [15, 17, 19]. Taking into account cointegration is a difficult problem that exceeds the scope of this paper.
Simulations of FIVARMA multiwave package proposes simulation functions for time series with a spectral density satisfying approximation  (2). The main function is fivarma which computes a parametric FIVARMA process defined in Section 2. 1. The input parameters of a F IV ARM A(q, d, r) process are the covariance matrix Σ of the innovation process u, the vector AR (AutoRegressive) (A k ) k=0,. ,q , A k ∈ R p×p , the vector MA (MovingAverage) (B k ) k=0,. ,r , B k ∈ R p×p , and the vector of long-range parameters d ∈ R p. FIVAR model of  [16]  is a subcase, corresponding to MA coefficients equal to zero. The parameters of fivarma are thus, in order, (N, d, cov_matrix, VAR, VMA) where cov_matrix= Σ and VAR and VMA denote respectively the sequences of matrices (A k ) k=0,. ,q and (B k ) k=0,. ,r.
Multivariate Fourier Whittle estimation As a first implementation, it is natural to use Fourier decomposition to approximate the spectral density of time series. Package multiwave proposes functions to compute MFW estimators: • mfw computes the multivariate Fourier Whittle estimators of both the long-range dependence parameters and the long-run covariance matrix. • mfw_cov_eval computes the multivariate Fourier-based Whittle estimator for the long-run covariance matrix for a given value of the long-range dependence d. • mfw_eval returns the value of the multivariate Fourier Whittle criterion with respect to d at a given value of d. The functions mfw_cov_eval and mfw_eval are internal functions of mfw. In mfw, we apply first a minimum search of mfw_eval with respect to d, and mfw_cov_eval is returning the estimation of Ω for the estimated value d.
Multivariate Wavelet Whittle estimation The functions applying MWW estimation in package multiwave are the following: • mww computes the multivariate wavelet Whittle estimators of the long-range dependence parameters and the long-run covariance matrix. • mww_cov_eval computes the multivariate wavelet-based Whittle estimator for the long-run covariance matrix for a given value of the long-range dependence d. • mww_eval returns the value of the multivariate wavelet Whittle criterion with respect to d at a given value of d. mww_cov_eval and mww_eval are internal functions of mww. In mww, we apply first a minimum search of mww_eval with respect to d, and mww_cov_eval is returning the estimation of Ω for the estimated value of d. MWW estimation is based on the wavelet transform of time series and mww needs the definition of a wavelet filter.
Wavelet transform and scalogram The wavelet decomposition in package multiwave is implemented using an exact discrete wavelet transform. • scalingfilter defines the wavelet filter (only Daubechies' wavelets are available). • computenj computes the number of wavelet coefficients for each individual scale. • DWTexact provides the wavelet transform of the data. • psi_hat_exact gives the Fourier transform of the wavelet function. • K_eval evaluates the value of the integral  (8). Example. To obtain the wavelet filter of a Daubechies' wavelet of order 4, that is with 2 vanishing moments, one should write: R> res_filter <-scaling_filter('Daubechies',4); R> filter <-res_filter$h R> filter [1] 0. 4829629 0. 8365163 0. 2241439 -0. 1294095 Next, given an N dimensional vector x, the wavelet coefficients of x are given by function DWTexact: R> # Simulation of the data R> N <-2^8 R> d0 <-0.
Conclusion The R package multiwave provides a versatile wavelet-based approach, as well as a Fourier-based approach, for estimating long-memory parameters and long-run covariance matrices of multivariate time series. The two estimation procedures are based on semi-parametric approaches of  [18]  and  [4]. The added value of the package is to provide estimations in long-range dependence multidimensional settings, which is not proposed presently by any R package to our knowledge. This paper describes the functions of the package multiwave and discusses some practical points for applications, including on a real data set. A simulation study shows first that multivariate estimation improves univariate estimation. The advantage of the wavelet-based procedure with respect to the Fourier-based estimation is its flexibility, allowing to take into account trends or nonstationarity.
Acknowledgements. The authors are grateful to  Shimotsu  (http://shimotsu. web. fc2. com/Site/Matlab_Codes. html)and to Faÿ, Moulines,  Roueff and Taqqu  for kindly providing the codes of their respective papers. This work was partly supported by the project  Graphsip  from  Agence Nationale de la Recherche  ( ANR-14-CE27-0001 ). S. A. was partly funded by a grant from la  RÃľgion RhÃťne-Alpes  and a grant from  AGIR-PEPS, UniversitÃľ Grenoble AlpesâĂŞCNRS.
We review its definition, and we describe how it is adopted in this paper, including the data and the algorithms to compute it. Based on the computation of these maps, we introduce several accessibility metrics to quantify the efficiency of the public transportation systems and the opportunities provided to the citizens in terms of mobility. The Results section describes several synthetic scores to allow a ranking of cities according to their accessibility patterns. Besides an overall evaluation, we focus in particular on the inequalities of accessibility in cities with respect to their space-time distribution. Finally, we draw some conclusions and highlight interesting future directions.
In order to compute the walking paths between stops of the public service and the hexagonal grid, we use the back-end version of the Open Source Routing Machine (OSRM)  [31]. The OSRM allows for the computation of shortest walking paths on the urban networks of each city, using the corresponding OpenStreetMap [32] network. As for the schedules of public transit, we relied on data released by public transports companies. Google adopted the GTFS standard file (https://developers. google. com/transit/gtfs/) to encourage public transport companies to release their data in a uniform way in order to be included in its map platform. It is nowadays possible to find hundreds of companies having released their data, and there are portals where this data is collected and exposed  [33]. The databases of public transportation systems are strongly heterogeneous across cities.
In some cases, some transportation means could be missing while other extra-urban ones could be included. For instance, for Berlin and London, the GTFS (General Transit Format System) data include all regional trains  [33]. To use a unique and general criterion about the inclusion of areas and transportation means, we adopted the OECD/EU definition of urban areas as functional economic units  [34]. The OECD/EU definition exploits the population density to identify an urban core (city core) and travel-to-work flows to identify the hinterland whose labor market is highly integrated with the core (commuting zones). With this definition in mind, we filtered out all the services lying outside both the cores and the hinterland regions from our tessellations. In addition to the database of public transportation systems, we used the population density data on coarse-grained to squares with a surface of 1 km 2.
The corresponding computational times range between less than two minutes for a medium-size city (like Rome) and about 30 minutes for a big city (for instance New York) on a single CPU of a standard personal computer. The algorithm is easily parallelizable, and it allows to use of the framework described here to implement planning tools where accessibility metrics can be computed in nearly real time (less than one minute of computation). A Python implementation of the computation framework used is released opensource on Github https://github. com/CityChrone/public-transport-analysis.
The availability of general scores for accessibility and inequalities could be the first step towards a more systematic evaluation of the present situation in urban contexts and careful planning of future scenarios. The citychrone. org platform is a relevant example in that direction, already allowing for both the visualization of all the accessibility metrics introduced here and the conception of new scenarios for improved mobility and accessibility. As a final remark, the inclusion of other data sources, such as points of interest in the accessibility metrics (e. g. workplaces, shops, schools, etc. ) or considering fluxes of people is quite straightforward in our framework and could lead to interesting results either in the global ranking of accessibility between cities and in the comparisons between city areas, by giving more importance to the purpose and popularity of certain trips.
Data, code and materials All the data used in this work can be freely accessed from public repositories  [34, 33, 35, 37]. Python source code used to compute the accessibility quantities and for the analysis performed are freely downloadable from the online public-transport-analysis GitHub repository [DOI:10. 5281/zenodo. 1309835] [48]. The hexagons tessellation and the related accessibility quantities computed can be download from the online openData GitHub repository [DOI: 10. 5281/zenodo. 1309927] [49]. In the same repository, there is also a CSV file (agency. csv) with the list of public transports agency used for each city. algorithms take a different approach by not looking at the graph structure of the problem. However, these algorithms have a significant limitation when considering footpaths between public transport stops in order to change means of transportation, reducing the performances in urban systems.
To test this idea, we have developed an algorithm that exploits our exact probabilities and compared it to a standard imputation algorithm. The comparison is based on applying these two algorithms to simulated RIL genotyping data, and doing so for many replicates. Specifically, for each replicate, we started with two homozygous parents having two homologous chromosomes of total length 150 cM on which we randomly positioned 100 markers. After producing from these a SIB RIL population of 100 individuals, we took the genotypes of each individual and transformed the calls by introducing missing data, selecting at random 10, 20, 30, 40, 50 or 70% of the markers for this change from a parental allele to "missing data. " For a standard imputation algorithm, we used the R package "missForest"  (Stekhoven and Buelhmann, 2012; Stekhoven, 2013)  that uses machine learning to estimate the most probable values underlying the missing data.
In effect, it applies a hidden Markov model that adjusts its parameters to the dataset. It outputs the imputed genotypes from which one can determine an associated error rate. This error rate depends on the realization of the RIL population, which is why we perform replicates. These values are displayed on the X axis of Figure  3  for each of the studied FIGURE 3 | Scatterplot comparison of imputation error rates. For each of the replicates simulated, the X axis gives the error rate for the missForest R package while the Y axis gives the error rate when using our code that exploits the exact multilocus genotype probabilities. For each fraction of missing data studied we display the points using a different color. values of the percentage of missing data. One clearly sees that the error rate increases with that percentage, a feature that is of course expected.
Then we select the L-locus genotype of maximum probability that is compatible with the calls at the two flanking markers, and this selected genotype specifies our imputation. The corresponding imputation errors are displayed on the Y axis of Figure  3. Clearly, our imputation method systematically out performs missForest, as expected since using the exact probabilities should be more reliable than using approximate ones. This is further quantified in the Supplementary Material. The imputation code is available online at https://github. com/olivier-c-martin/PMG_SIB_RILs. git and is internal documentation explains in greater detail the different algorithmic steps.
In 9/10 cases, an alternative U12 acceptor site was used, leading to exon skipping in a few instances, while in the remaining one, both alternative U12 donor and acceptor sites were used. The use of the least common donor and/or acceptor splice sites was supported by more than 10% of the reads in all three cell types for six of these events, indicating that they are not marginal. It should be noted that half of the splicing events produced alternative forms considered as noncoding in databases because they contain premature termination codons (PTCs).
Other types of U12-type intron alternative splicing Vast-tools and KisSplice identified respectively four and two U12/U2 splice site switchings in the fibroblast and amniocyte data sets, all of them in favor of the use of U2 splice sites in TALS patients. In particular, both cell types exhibited the same splice site switching event in the CCDC84 gene (shown for the fibroblast data sets in Fig. 3 , bottom). The balance of the transcripts derived from the use of either the U12-or the U2-type splice sites observed in controls (∼65%/35%, respectively) was strongly shifted toward the U2 sites-derived coding transcript in TALS patients (∼15%/85%) in both cell types, hence probably increasing the abundance of the functional full-length protein. Splicing efficiency of U12-type introns in LCL derived from a TALS patient The PCA analysis of PSI values obtained with our RNA-seq study showed that in TALS patients, the pattern of U12type IR in the LCL markedly differed from that seen in fibroblasts and amniocytes (Fig.
Gene pathways affected in cells derived from TALS patients Because 97% of the U12-type introns were retained in the TALS LCL data set, precluding classical enrichment analysis, we focused our attention on identifying genes and pathways impacted by U12-type intron missplicing on TALS fibroblasts and amniocytes. As a preliminary study, we first scrutinized the 26 genes with marked U12-type IR common to both data sets (Supplemental Table  S1 ), and found that a high proportion of them were involved in signal transduction (11/26), notably through Notch (C3orf17) or Sonic Hedgehog (IFT22, TMEM107) signaling pathways; genes involved in protein degradation were also represented in a substantial proportion (6/26). We next wanted to look into more details at U12 genes with misspliced transcripts, potentially leading to reduced level of functional proteins, taking into account all the statistically significant differential U12-type IR and U12/U2 splice sites switching found in the two cell types.
2015; Dinur Schejter et al. 2017; Heremans et al. 2018)  and early onset autosomal recessive cerebellar ataxia  (Elsaid et al. 2017) , or in protein components specific to the minor spliceosome, such as observed in isolated familial growth hormone deficiency  (Argente et al. 2014) , and myelodysplastic syndrome  (Madan et al. 2015). Actually, little is known about global U12 gene expression and U12-type intron splicing in physiological conditions in human cells. Therefore, we started our study by tackling these questions in our control data sets consisting of eight fibroblast, four amniocyte, and one lymphoblastoid cell line (LCL) samples derived from control fetuses and children. In these control cells, we found that (i) ∼60% of the 699 U12 genes are consistently expressed in the three different cell types, and (ii) the distribution of the levels of transcriptional expression of U12 genes is highly homogenous between these cell types and peaks at around 30 TPM, as observed for U2 genes.
After having determined the frame of U12 gene expression and U12-type intron splicing in the context of a functional minor spliceosome, we set out to identify the consequences of biallelic RNU4ATAC mutations within these cell types in five fibroblast, three amniocyte and one LCL samples derived from seven unrelated TALS patients. Rather surprisingly, we did not observe any impact of such mutations on U12 or U2 gene expression in fibroblasts or amniocytes derived from TALS patients, although we used the tool (DESeq2) and cutoffs [FDR ≤ 5%; |log 2 (FC)| ≥ 1] recommended for such a data set size (five patients vs. eight controls)  (Schurch et al. 2016). Our previous qRT-PCR study on fibroblasts derived from two homozygous g. 51G > A TALS patients and two age-and sex-matched controls (biosamples also included in the present study) had shown that 12 of the 22 tested U12 genes-chosen randomly among those reported as being expressed in the skin-presented a differential expression  (Edery et al.
The extreme rarity of the TALS syndrome and the premature death of the children affected with this disease did not permit us to collect additional blood samples up to now and hence analyze LCL biological replicates. Nevertheless, several lines of evidence support the assumption that peripheral blood cells may exhibit particularly pronounced U12-type IR: (i) This difference in U12type intron splicing efficiency was clearly visible when comparing cells derived from skin and blood taken the same day on the same TALS child, while no difference was seen for another TALS child between amniotic fluid taken in utero and skin at 10 mo of age (Supplemental Fig. S6 ); (ii) similar high levels of U12-type IR were observed in the RFMN MBC and TALS LCL data sets, despite the different pathologies, blood cell subtypes analyzed, gender and age of the patients, and RNA-seq settings (Fig.
4 ); (iii) a comprehensive analysis of IR performed on 52 human samples from different cell and tissue types showed that the highest percentage of retention was found in white blood cells (>30%, compared to <5% in fibroblasts)  (Braunschweig et al. 2014). We observed that the competition between the major and minor spliceosomes for splicing some introns, which we show here for the first time to occur physiologically in humans, is more favorable to the major spliceosome in TALS amniocytes, fibroblasts and LCL as compared to the situation seen in control cells. This was particularly pronounced for the CCDC84 gene, thereby increasing the amount of the full length protein of as yet uncharacterized function. Unexpectedly, exclusively in the TALS LCL data set (Supplemental Fig. S9 ), we found reads for all spliceosomal snRNAs at the exception of U6 and U6atac, an observation also made in a previous analysis of RFMN data sets  (Dinur Schejter et al.
The understanding of the molecular mechanisms involved in the pathogenesis of TALS will require additional transcriptomic analyses to be performed on different cell types at various developmental or differentiation stages, hence necessitating to generate induced pluripotent stem cells and/or develop animal models. Nevertheless, the present finding that TALS and RFMN blood cells share a similar pattern of U12-type IR and that the GO term analysis performed on the TALS fibroblast and amniocyte data sets showed an enrichment in immunity-linked terms suggest that thorough investigation of TALS immune phenotype should be carried out.
Identification of U12-type introns in the human genome U12DB, the U12 Intron Database (http://genome. crg. es/cgi-bin/ u12db/u12db. cgi) released in 2006 by T. Alioto with the aim to catalog U12-type introns of completely sequenced eukaryotic genomes  (Alioto 2007) , has not been updated since its launching. We updated the list of human U12-type introns using T. Alioto's scoring matrices on a more recent genome annotation [Gencode v19 (GRCh37)/Ensembl v75], the latest one at the time of the analysis of the pilot project data sets. Out of 289,023 introns annotated in Gencode v19, the pipeline classifies 846 of them as U12-type introns (Supplemental Table  S3 ). Those are located in 699 genes, of whom 105, 20, 3, and 1, respectively contained 2, 3, 4, and 5 U12-type introns. When more than one U12-type intron is present in a gene, in most cases (85/129), the coordinates of at least two of these U12-type introns overlap, indicating that the same U12-type intron can be spliced out using alternative U12 consensus splice sites.
However, it also does not compute exon-intron junction reads coverage. We argue that this latter quantification could still be of interest, as although it does not in-dicate the full intronic coverage, it still testifies that this peculiar intron's splice sites were not used for splicing. In other words, exon-intron junctions quantification does not indicate the type of the alternative splicing event (it could either be an IR or a alternative donor + acceptor), but still indicates the amount of unspliced intron. In order to force IRFinder to do the exon-intron quantification for all introns, we rewrote a specific test in its code (intronExclusion. pl, line 83: if ($newlen > 40 && ($newlen/$len) ≥ 0. 7) { replaced by if ($newlen > 0) }). For the special case of U12type introns with no informative base (167 cases), IRFinder 1.