Tools for visual inference. Generate null data sets
    and null plots using permutation and simulation. Calculate distance metrics
    for a lineup, and examine the distributions of metrics.

A computational method that infers copy number variations (CNVs) in cancer scRNA-seq data and reconstructs the tumor phylogeny. 'numbat' integrates signals from gene expression, allelic ratio, and population haplotype structures to accurately infer allele-specific CNVs in single cells and reconstruct their lineage relationship. 'numbat' can be used to: 1. detect allele-specific copy number variations from single-cells; 2. differentiate tumor versus normal cells in the tumor microenvironment; 3. infer the clonal architecture and evolutionary history of profiled tumors. 'numbat' does not require tumor/normal-paired DNA or genotype data, but operates solely on the donor scRNA-data data (for example, 10x Cell Ranger output). Additional examples and documentations are available at <https://kharchenkolab.github.io/numbat/>. For details on the method please see Gao et al. Nature Biotechnology (2022) <doi:10.1038/s41587-022-01468-y>.

The number of distinct alleles observed in a DNA mixture is informative of the number of contributors to the mixture. The package provides methods for computing the probability distribution of the number of distinct alleles in a mixture for a given set of allele frequencies. The mixture contributors may be related according to a provided pedigree.

Provides number-theoretic functions for factorization, prime 
    numbers, twin primes, primitive roots, modular logarithm and
    inverses, extended GCD, Farey series and continued fractions.
    Includes Legendre and Jacobi symbols, some divisor functions,
    Euler's Phi function, etc.

Validate, format and compare identification numbers used in Brazil.
  These numbers are used to identify individuals (CPF), vehicles (RENAVAN),
  companies (CNPJ) and etc.
  Functions to format, validate and compare these numbers have been 
  implemented in a vectorized way in order to speed up
  validations and comparisons in big datasets.