This package implements a variety of nonparametric and parametric methods that are commonly used when the data set is a mixture of paired observations and independent samples. The package also calculates and returns values of different tests with their corresponding p-values. Bhoj, D. S. (1991) <doi:10.1002/bimj.4710330108> "Testing equality of means in the presence of correlation and missing data". Dubnicka, S. R., Blair, R. C., and Hettmansperger, T. P. (2002) <doi:10.22237/jmasm/1020254460> "Rank-based procedures for mixed paired and two-sample designs". Einsporn, R. L. and Habtzghi, D. (2013) <https://pdfs.semanticscholar.org/89a3/90bafeb2bc41ed4414533cfd5ab84a6b54b6.pdf> "Combining paired and two-sample data using a permutation test". Ekbohm, G. (1976) <doi:10.1093/biomet/63.2.299> "On comparing means in the paired case with incomplete data on both responses". Lin, P. E. and Stivers, L. E. (1974) <doi:10.1093/biomet/61.2.325> On difference of means with incomplete data". Maritz, J. S. (1995) <doi:10.1111/j.1467-842x.1995.tb00649.x> "A permutation paired test allowing for missing values".

Carries out a two-level sample selection where the possibility of an initially selected site not wanting to participate is anticipated, and the site is optimally replaced. The procedure aims to reduce bias (and/or loss of external validity) with respect to the target population. In selecting units and sub-units, sitepickR uses the cube method developed by Deville & Tillé', (2004) <http://www.math.helsinki.fi/msm/banocoss/Deville_Tille_2004.pdf> and described in Tillé (2011) <https://www150.statcan.gc.ca/n1/en/pub/12-001-x/2011002/article/11609-eng.pdf?st=5-sx8Q8n>. The cube method is a probability sampling method that is designed to satisfy criteria for balance between the sample and the population. Recent research has shown that this method performs well in simulations for studies of educational programs (see Fay & Olsen (2021, under review). To implement the cube method, sitepickR uses the sampling R package <https://cran.r-project.org/package=sampling>. To implement statistical matching, sitepickR uses the MatchIt R package <https://cran.r-project.org/package=MatchIt>.

It generates the roster of turn for an outlet which is flowing (water) 24X7 or 168 hours towards the area under command or agricutural area (to be irrigated). The area under command is differentially owned by different individual farmers. The Outlet runs for free of cost to irrigate the area under command 24X7. So, flow time of the outlet has to be divided based on an area owned by an individual farmer and the location of his land or farm. This roster is known as warabandi and its generation in agriculture practices is a very tedious task. Calculations of time in microseconds are more error-prone, especially whenever it is performed by hands. That division of flow time for an individual farmer can be calculated by warabandi'. However, it generates a full publishable report for an outlet and all the farmers who have farms subjected to be irrigated. It reduces error risk and makes a more reproducible roster. For more details about warabandi system you can found elsewhere in Bandaragoda DJ(1995) <https://publications.iwmi.org/pdf/H_17571i.pdf>.

Bayesian dynamic borrowing is an approach to incorporating external data to supplement a randomized, controlled trial analysis in which external data are incorporated in a dynamic way (e.g., based on similarity of outcomes); see Viele 2013 <doi:10.1002/pst.1589> for an overview. This package implements the hierarchical commensurate prior approach to dynamic borrowing as described in Hobbes 2011 <doi:10.1111/j.1541-0420.2011.01564.x>. There are three main functionalities. First, psborrow2 provides a user-friendly interface for applying dynamic borrowing on the study results handles the Markov Chain Monte Carlo sampling on behalf of the user. Second, psborrow2 provides a simulation framework to compare different borrowing parameters (e.g. full borrowing, no borrowing, dynamic borrowing) and other trial and borrowing characteristics (e.g. sample size, covariates) in a unified way. Third, psborrow2 provides a set of functions to generate data for simulation studies, and also allows the user to specify their own data generation process. This package is designed to use the sampling functions from cmdstanr which can be installed from <https://stan-dev.r-universe.dev>.

In some phase I trials, the design goal is to find the dose associated with a certain target toxicity rate or the dose with a certain weighted sum of rates of various toxicity grades. TITEgBOIN provides the set up and calculations needed to run a dose-finding trial using bayesian optimal interval (BOIN) (Yuan et al. (2016) <doi:10.1158/1078-0432.CCR-16-0592>), generalized bayesian optimal interval (gBOIN) (Mu et al. (2019) <doi:10.1111/rssc.12263>), time-to-event bayesian optimal interval (TITEBOIN) (Lin et al. (2020) <doi:10.1093/biostatistics/kxz007>) and time-to-event generalized bayesian optimal interval (TITEgBOIN) (Takeda et al. (2022) <doi:10.1002/pst.2182>) designs. TITEgBOIN can conduct tasks: run simulations and get operating characteristics; determine the dose for the next cohort; select maximum tolerated dose (MTD). These functions allow customization of design characteristics to vary sample size, cohort sizes, target dose limiting toxicity (DLT) rates or target normalized equivalent toxicity score (ETS) rates to account for discrete toxicity score, and incorporate safety and/or stopping rules.

Estimates and plots as a heat map the correlation coefficients obtained via the wavelet local multiple correlation WLMC (Fernández-Macho 2018) and the dominant variable/s, i.e., the variable/s that maximizes the multiple correlation through time and scale (Polanco-Martà nez et al. 2020, Polanco-Martà nez 2022). We improve the graphical outputs of WLMC proposing a didactic and useful way to visualize the dominant variable(s) for a set of time series. The WLMC was designed for financial time series, but other kinds of data (e.g., climatic, ecological, etc.) can be used. The functions contained in VisualDom are highly flexible since these contains several parameters to personalize the time series under analysis and the heat maps. In addition, we have also included two data sets (named rdata_climate and rdata_Lorenz') to exemplify the use of the functions contained in VisualDom'. Methods derived from Fernández-Macho (2018) <doi:10.1016/j.physa.2017.11.050>, Polanco-Martà nez et al. (2020) <doi:10.1038/s41598-020-77767-8> and Polanco-Martà nez (2023, in press).

Highest averages & largest remainders allocating seats methods and several party system scores. Implemented highest averages allocating seats methods are D'Hondt, Webster, Danish, Imperiali, Hill-Huntington, Dean, Modified Sainte-Lague, equal proportions and Adams. Implemented largest remainders allocating seats methods are Hare, Droop, Hangenbach-Bischoff, Imperial, modified Imperial and quotas & remainders. The main advantage of this package is that ties are always reported and not incorrectly allocated. Party system scores provided are competitiveness, concentration, effective number of parties, party nationalization score, party system nationalization score and volatility. References: Gallagher (1991) <doi:10.1016/0261-3794(91)90004-C>. Norris (2004, ISBN:0-521-82977-1). Consejo Nacional Electoral del Ecuador (2014)<http://cne.gob.ec/documents/Estadisticas/Atlas/ATLAS/CAPITULO%206%20web.pdf>. Laakso & Taagepera (1979) <https://journals.sagepub.com/doi/pdf/10.1177/001041407901200101>. Jones & Mainwaring (2003) <https://kellogg.nd.edu/sites/default/files/old_files/documents/304_0.pdf>. Pedersen (1979) <https://janda.org/c24/Readings/Pedersen/Pedersen.htm>. Golosov (2010) <https://ppq.sagepub.com/content/16/2/171.abstract>. Golosov (2014) <https://ppq.sagepub.com/content/early/2014/09/08/1354068814549342.abstract>.

NONMEM has been a tool for running nonlinear mixed effects models since the 80s and is still used today (Bauer 2019 <doi:10.1002/psp4.12404>). This tool allows you to convert NONMEM models to rxode2 (Wang, Hallow and James (2016) <doi:10.1002/psp4.12052>) and with simple models nlmixr2 syntax (Fidler et al (2019) <doi:10.1002/psp4.12445>). The nlmixr2 syntax requires the residual specification to be included and it is not always translated. If available, the rxode2 model will read in the NONMEM data and compare the simulation for the population model ('PRED') individual model ('IPRED') and residual model ('IWRES') to immediately show how well the translation is performing. This saves the model development time for people who are creating an rxode2 model manually. Additionally, this package reads in all the information to allow simulation with uncertainty (that is the number of observations, the number of subjects, and the covariance matrix) with a rxode2 model. This is complementary to the babelmixr2 package that translates nlmixr2 models to NONMEM and can convert the objects converted from nonmem2rx to a full nlmixr2 fit.

Allows clustering of incomplete observations by addressing missing values using multiple imputation. For achieving this goal, the methodology consists in three steps, following Audigier and Niang 2022 <doi:10.1007/s11634-022-00519-1>. I) Missing data imputation using dedicated models. Four multiple imputation methods are proposed, two are based on joint modelling and two are fully sequential methods, as discussed in Audigier et al. (2021) <doi:10.48550/arXiv.2106.04424>. II) cluster analysis of imputed data sets. Six clustering methods are available (distances-based or model-based), but custom methods can also be easily used. III) Partition pooling. The set of partitions is aggregated using Non-negative Matrix Factorization based method. An associated instability measure is computed by bootstrap (see Fang, Y. and Wang, J., 2012 <doi:10.1016/j.csda.2011.09.003>). Among applications, this instability measure can be used to choose a number of clusters with missing values. The package also proposes several diagnostic tools to tune the number of imputed data sets, to tune the number of iterations in fully sequential imputation, to check the fit of imputation models, etc.

An implementation of the multilevel (also known as mixed or random effects) hidden Markov model using Bayesian estimation in R. The multilevel hidden Markov model (HMM) is a generalization of the well-known hidden Markov model, for the latter see Rabiner (1989) <doi:10.1109/5.18626>. The multilevel HMM is tailored to accommodate (intense) longitudinal data of multiple individuals simultaneously, see e.g., de Haan-Rietdijk et al. <doi:10.1080/00273171.2017.1370364>. Using a multilevel framework, we allow for heterogeneity in the model parameters (transition probability matrix and conditional distribution), while estimating one overall HMM. The model can be fitted on multivariate data with either a categorical, normal, or Poisson distribution, and include individual level covariates (allowing for e.g., group comparisons on model parameters). Parameters are estimated using Bayesian estimation utilizing the forward-backward recursion within a hybrid Metropolis within Gibbs sampler. Missing data (NA) in the dependent variables is accommodated assuming MAR. The package also includes various visualization options, a function to simulate data, and a function to obtain the most likely hidden state sequence for each individual using the Viterbi algorithm.

clustComp is a package that implements several techniques for the comparison and visualisation of relationships between different clustering results, either flat versus flat or hierarchical versus flat. These relationships among clusters are displayed using a weighted bi-graph, in which the nodes represent the clusters and the edges connect pairs of nodes with non-empty intersection; the weight of each edge is the number of elements in that intersection and is displayed through the edge thickness. The best layout of the bi-graph is provided by the barycentre algorithm, which minimises the weighted number of crossings. In the case of comparing a hierarchical and a non-hierarchical clustering, the dendrogram is pruned at different heights, selected by exploring the tree by depth-first search, starting at the root. Branches are decided to be split according to the value of a scoring function, that can be based either on the aesthetics of the bi-graph or on the mutual information between the hierarchical and the flat clusterings. A mapping between groups of clusters from each side is constructed with a greedy algorithm, and can be additionally visualised.

Seed germinates through the physical process of water uptake by dry seed driven by the difference in water potential between the seed and the water. There exists seed-to-seed variability in the base seed water potential. Hence, there is a need for a distribution such that a viable seed with its base seed water potential germinates if and only if the soil water potential is more than the base seed water potential. This package estimates the stress tolerance and uniformity parameters of the seed lot for germination under various temperatures by using the hydro-time model of counts of germinated seeds under various water potentials. The distribution of base seed water potential has been considered to follow Normal, Logistic and Extreme value distribution. The estimated proportion of germinated seeds along with the estimates of stress and uniformity parameters are obtained using a generalised linear model. The significance test of the above parameters for within and between temperatures is also performed in the analysis. Details can be found in Kebreab and Murdoch (1999) <doi:10.1093/jxb/50.334.655> and Bradford (2002) <https://www.jstor.org/stable/4046371>.

Sample and cell filtering as well as visualisation of output metrics from Cell Ranger by Grace X.Y. Zheng et al. (2017) <doi:10.1038/ncomms14049>. CRMetrics allows for easy plotting of output metrics across multiple samples as well as comparative plots including statistical assessments of these. CRMetrics allows for easy removal of ambient RNA using SoupX by Matthew D Young and Sam Behjati (2020) <doi:10.1093/gigascience/giaa151> or CellBender by Stephen J Fleming et al. (2022) <doi:10.1101/791699>. Furthermore, it is possible to preprocess data using Pagoda2 by Nikolas Barkas et al. (2021) <https://github.com/kharchenkolab/pagoda2> or Seurat by Yuhan Hao et al. (2021) <doi:10.1016/j.cell.2021.04.048> followed by embedding of cells using Conos by Nikolas Barkas et al. (2019) <doi:10.1038/s41592-019-0466-z>. Finally, doublets can be detected using scrublet by Samuel L. Wolock et al. (2019) <doi:10.1016/j.cels.2018.11.005> or DoubletDetection by Gayoso et al. (2020) <doi:10.5281/zenodo.2678041>. In the end, cells are filtered based on user input for use in downstream applications.

This package provides a variety of original and flexible user-friendly statistical latent variable models for the simultaneous clustering and segmentation of heterogeneous functional data (i.e time series, or more generally longitudinal data, fitted by unsupervised algorithms, including EM algorithms. Functional Latent Data Models for Clustering heterogeneous curves ('FLaMingos') are originally introduced and written in Matlab by Faicel Chamroukhi <https://github.com/fchamroukhi?utf8=?&tab=repositories&q=mix&type=public&language=matlab>. The references are mainly the following ones. Chamroukhi F. (2010) <https://chamroukhi.com/FChamroukhi-PhD.pdf>. Chamroukhi F., Same A., Govaert, G. and Aknin P. (2010) <doi:10.1016/j.neucom.2009.12.023>. Chamroukhi F., Same A., Aknin P. and Govaert G. (2011). <doi:10.1109/IJCNN.2011.6033590>. Same A., Chamroukhi F., Govaert G. and Aknin, P. (2011) <doi:10.1007/s11634-011-0096-5>. Chamroukhi F., and Glotin H. (2012) <doi:10.1109/IJCNN.2012.6252818>. Chamroukhi F., Glotin H. and Same A. (2013) <doi:10.1016/j.neucom.2012.10.030>. Chamroukhi F. (2015) <https://chamroukhi.com/FChamroukhi-HDR.pdf>. Chamroukhi F. and Nguyen H-D. (2019) <doi:10.1002/widm.1298>.

Build spatially and temporally explicit process-based species distribution models, that can include an arbitrary number of environmental factors, species and processes including metabolic constraints and species interactions. The focus of the package is simulating populations of one or multiple species in a grid-based landscape and studying the meta-population dynamics and emergent patterns that arise from the interaction of species under complex environmental conditions. It provides functions for common ecological processes such as negative exponential, kernel-based dispersal (see Nathan et al. (2012) <doi:10.1093/acprof:oso/9780199608898.003.0015>), calculation of the environmental suitability based on cardinal values ( Yin et al. (1995) <doi:10.1016/0168-1923(95)02236-Q>, simplified by Yan and Hunt (1999) <doi:10.1006/anbo.1999.0955> see eq: 4), reproduction in form of an Ricker model (see Ricker (1954) <doi:10.1139/f54-039> and Cabral and Schurr (2010) <doi:10.1111/j.1466-8238.2009.00492.x>), as well as metabolic scaling based on the metabolic theory of ecology (see Brown et al. (2004) <doi:10.1890/03-9000> and Brown, Sibly and Kodric-Brown (2012) <doi:10.1002/9781119968535.ch>).

Identifying outcome relevant subgroups has now become as simple as possible! The formerly lengthy and tedious search for the needle in a haystack will be replaced by a single, comprehensive and coherent presentation. The central result of a subgroup screening is a diagram in which each single dot stands for a subgroup. The diagram may show thousands of them. The position of the dot in the diagram is determined by the sample size of the subgroup and the statistical measure of the treatment effect in that subgroup. The sample size is shown on the horizontal axis while the treatment effect is displayed on the vertical axis. Furthermore, the diagram shows the line of no effect and the overall study results. For small subgroups, which are found on the left side of the plot, larger random deviations from the mean study effect are expected, while for larger subgroups only small deviations from the study mean can be expected to be chance findings. So for a study with no conspicuous subgroup effects, the dots in the figure are expected to form a kind of funnel. Any deviations from this funnel shape hint to conspicuous subgroups.

To optimize clinical trial designs and data analysis methods consistently through trial simulation, we need to simulate multivariate mixed-type virtual patient data independent of designs and analysis methods under evaluation. To make the outcome of optimization more realistic, relevant empirical patient level data should be utilized when itâ s available. However, a few problems arise in simulating trials based on small empirical data, where the underlying marginal distributions and their dependence structure cannot be understood or verified thoroughly due to the limited sample size. To resolve this issue, we use the copula invariance property, which can generate the joint distribution without making a strong parametric assumption. The function copula.sim can generate virtual patient data with optional data validation methods that are based on energy distance and ball divergence measurement. The function compare.copula.sim can conduct comparison of marginal mean and covariance of simulated data. To simulate patient-level data from a hypothetical treatment arm that would perform differently from the observed data, the function new.arm.copula.sim can be used to generate new multivariate data with the same dependence structure of the original data but with a shifted mean vector.

This package provides users a quick exploratory dive into common visualizations without writing a single line of code given the users data follows the Analysis Data Model (ADaM) standards put forth by the Clinical Data Interchange Standards Consortium (CDISC) <https://www.cdisc.org>. Prominent modules/ features of the application are the Table Generator, Population Explorer, and the Individual Explorer. The Table Generator allows users to drag and drop variables and desired statistics (frequencies, means, ANOVA, t-test, and other summary statistics) into bins that automagically create stunning tables with validated information. The Population Explorer offers various plots to visualize general trends in the population from various vantage points. Plot modules currently include scatter plot, spaghetti plot, box plot, histogram, means plot, and bar plot. Each plot type allows the user to plot uploaded variables against one another, and dissect the population by filtering out certain subjects. Last, the Individual Explorer establishes a cohesive patient narrative, allowing the user to interact with patient metrics (params) by visit or plotting important patient events on a timeline. All modules allow for concise filtering & downloading bulk outputs into html or pdf formats to save for later.

This package provides tools for transforming, a posteriori time-scaling, and modifying phylogenies containing extinct (i.e. fossil) lineages. In particular, most users are interested in the functions timePaleoPhy, bin_timePaleoPhy, cal3TimePaleoPhy and bin_cal3TimePaleoPhy, which date cladograms of fossil taxa using stratigraphic data. This package also contains a large number of likelihood functions for estimating sampling and diversification rates from different types of data available from the fossil record (e.g. range data, occurrence data, etc). paleotree users can also simulate diversification and sampling in the fossil record using the function simFossilRecord, which is a detailed simulator for branching birth-death-sampling processes composed of discrete taxonomic units arranged in ancestor-descendant relationships. Users can use simFossilRecord to simulate diversification in incompletely sampled fossil records, under various models of morphological differentiation (i.e. the various patterns by which morphotaxa originate from one another), and with time-dependent, longevity-dependent and/or diversity-dependent rates of diversification, extinction and sampling. Additional functions allow users to translate simulated ancestor-descendant data from simFossilRecord into standard time-scaled phylogenies or unscaled cladograms that reflect the relationships among taxon units.

We quantitatively evaluated the assertion that says if one suit is found to be evenly distributed among the 4 players, the rest of the suits are more likely to be evenly distributed. Our mathematical analyses show that, if one suit is found to be evenly distributed, then a second suit has a slightly elevated probability (ranging between 10% to 15%) of being evenly distributed. If two suits are found to be evenly distributed, then a third suit has a substantially elevated probability (ranging between 30% to 50%) of being evenly distributed.This package refers to methods and authentic data from Ely Culbertson <https://www.bridgebum.com/law_of_symmetry.php>, Gregory Stoll <https://gregstoll.com/~gregstoll/bridge/math.html>, and details of performing the probability calculations from Jeremy L. Martin <https://jlmartin.ku.edu/~jlmartin/bridge/basics.pdf>, Emile Borel and Andre Cheron (1954) "The Mathematical Theory of Bridge",Antonio Vivaldi and Gianni Barracho (2001, ISBN:0 7134 8663 5) "Probabilities and Alternatives in Bridge", Ken Monzingo (2005) "Hand and Suit Patterns" <http://web2.acbl.org/documentlibrary/teachers/celebritylessons/handpatternsrevised.pdf>Ken Monzingo (2005) "Hand and Suit Patterns" <http://web2.acbl.org/documentlibrary/teachers/celebritylessons/handpatternsrevised.pdf>.

The git2rdata package is an R package for writing and reading dataframes as plain text files. A metadata file stores important information. 1) Storing metadata allows to maintain the classes of variables. By default, git2rdata optimizes the data for file storage. The optimization is most effective on data containing factors. The optimization makes the data less human readable. The user can turn this off when they prefer a human readable format over smaller files. Details on the implementation are available in vignette("plain_text", package = "git2rdata"). 2) Storing metadata also allows smaller row based diffs between two consecutive commits. This is a useful feature when storing data as plain text files under version control. Details on this part of the implementation are available in vignette("version_control", package = "git2rdata"). Although we envisioned git2rdata with a git workflow in mind, you can use it in combination with other version control systems like subversion or mercurial. 3) git2rdata is a useful tool in a reproducible and traceable workflow. vignette("workflow", package = "git2rdata") gives a toy example. 4) vignette("efficiency", package = "git2rdata") provides some insight into the efficiency of file storage, git repository size and speed for writing and reading.

This package provides functions for the estimation of intra- and inter-cohort correlations in the Vasicek credit portfolio model. For intra-cohort correlations, the package covers the two method of moments estimators of Gordy (2000) <doi:10.1016/S0378-4266(99)00054-0>, the method of moments estimator of Lucas (1995) <https://jfi.pm-research.com/content/4/4/76> and a Binomial approximation extension of this approach. Moreover, the maximum likelihood estimators of Gordy and Heitfield (2010) <http://elsa.berkeley.edu/~mcfadden/e242_f03/heitfield.pdf> and Duellmann and Gehde-Trapp (2004) <http://hdl.handle.net/10419/19729> are implemented. For inter-cohort correlations, the method of moments estimator of Bluhm and Overbeck (2003) <doi:10.1007/978-3-642-59365-9_2>/Bams et al. (2016) <https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2676595> is provided and the maximum likelihood estimators comprise the approaches of Gordy and Heitfield (2010)/Kalkbrener and Onwunta (2010) <ISBN: 978-1906348250> and Pfeuffer et al. (2020). Bootstrap and Jackknife procedures for bias correction are included as well as the method of moments estimator of Frei and Wunsch (2018) <doi:10.21314/JCR.2017.231> for auto-correlated time series.

GPUs are great resources for data analysis, especially in statistics and linear algebra. Unfortunately, very few packages connect R to the GPU, and none of them are transparent enough to run the computations on the GPU without substantial changes to the code. The maintenance of these packages is cumbersome: several of the earlier attempts have been removed from their respective repositories. It would be desirable to have a properly maintained R package that takes advantage of the GPU with minimal changes to the existing code. We have developed the GPUmatrix package (available on CRAN). GPUmatrix mimics the behavior of the Matrix package and extends R to use the GPU for computations. It includes single(FP32) and double(FP64) precision data types, and provides support for sparse matrices. It is easy to learn, and requires very few code changes to perform the operations on the GPU. GPUmatrix relies on either the Torch or Tensorflow R packages to perform the GPU operations. We have demonstrated its usefulness for several statistical applications and machine learning applications: non-negative matrix factorization, logistic regression and general linear models. We have also included a comparison of GPU and CPU performance on different matrix operations.

Density-based clustering methods are well adapted to the clustering of high-dimensional data and enable the discovery of core groups of various shapes despite large amounts of noise. This package provides a novel density-based cluster extraction method, OPTICS k-Xi, and a framework to compare k-Xi models using distance-based metrics to investigate datasets with unknown number of clusters. The vignette first introduces density-based algorithms with simulated datasets, then presents and evaluates the k-Xi cluster extraction method. Finally, the models comparison framework is described and experimented on 2 genetic datasets to identify groups and their discriminating features. The k-Xi algorithm is a novel OPTICS cluster extraction method that specifies directly the number of clusters and does not require fine-tuning of the steepness parameter as the OPTICS Xi method. Combined with a framework that compares models with varying parameters, the OPTICS k-Xi method can identify groups in noisy datasets with unknown number of clusters. Results on summarized genetic data of 1,200 patients are in Charlon T. (2019) <doi:10.13097/archive-ouverte/unige:161795>. A short video tutorial can be found at <https://www.youtube.com/watch?v=P2XAjqI5Lc4/>.