An EM algorithm, Karl et al. (2013) <doi:10.1016/j.csda.2012.10.004>, is used to estimate the generalized, variable, and complete persistence models, Mariano et al. (2010) <doi:10.3102/1076998609346967>. These are multiple-membership linear mixed models with teachers modeled as "G-side" effects and students modeled with either "G-side" or "R-side" effects.

Fast scalable Gaussian process approximations, particularly well suited to spatial (aerial, remote-sensed) and environmental data, described in more detail in Katzfuss and Guinness (2017) <doi:10.48550/arXiv.1708.06302>. Package also contains a fast implementation of the incomplete Cholesky decomposition (IC0), based on Schaefer et al. (2019) <doi:10.48550/arXiv.1706.02205> and MaxMin ordering proposed in Guinness (2018) <doi:10.48550/arXiv.1609.05372>.

Calculates the cost of crossing in terms of the number of individuals and generations, which is theoretically 
    formulated by Servin et al. (2004) <DOI:10.1534/genetics.103.023358>. This package has been designed for selecting 
    appropriate parental genotypes and find the most efficient crossing scheme for gene pyramiding, especially for plant breeding.

Server implementation of 'GraphQL'
    <http://spec.graphql.org/>, a query language originally created by
    Facebook for describing data requirements on complex application data
    models.  Visit <https://graphql.org> to learn more about 'GraphQL'.

Genomic biology is not limited to the confines of the canonical B-forming DNA duplex, but includes over ten different types of other secondary structures that are collectively termed non-B DNA structures. Of these non-B DNA structures, the G-quadruplexes are highly stable four-stranded structures that are recognized by distinct subsets of nuclear factors. This package provide functions for predicting intramolecular G quadruplexes. In addition, functions for predicting other intramolecular nonB DNA structures are included.

Provides a comprehensive suite of genome-wide association study (GWAS) methods 
    specifically designed for biobank-scale data, including but not limited to, robust approaches 
    for time-to-event traits (Li et al., 2025 <doi:10.1038/s43588-025-00864-z>) and ordinal 
    categorical traits (Bi et al., 2021 <doi:10.1016/j.ajhg.2021.03.019>). The package also offers 
    general frameworks for GWAS of any trait type (Bi et al., 2020 <doi:10.1016/j.ajhg.2020.06.003>), 
    while accounting for sample relatedness (Xu et al., 2025 <doi:10.1038/s41467-025-56669-1>) or 
    population structure (Ma et al., 2025 <doi:10.1186/s13059-025-03827-9>). By accurately 
    approximating score statistic distributions using saddlepoint approximation (SPA), these 
    methods can effectively control type I error rates for rare variants and in the presence of 
    unbalanced phenotype distributions. Additionally, the package includes functions for simulating 
    genotype and phenotype data to support research and method development.