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"M1" denotes model 1. denotes the homozygous major allele genotype of SNP A; denotes the heterozygous genotype of SNP A; denotes the homozygous minor allele genotype of SNP A; likewise for the notations in the other basic models.

Given a real matrix (Ainmathbb{R}^{mtimes n}), (operatorname{Col}_{i}(A)) denotes the ith column of A, and (operatorname{Row}_{i}(A)) denotes the ith row of A; '∗' denotes the Khatri-Rao product of matrices.

In other words, the elements of A denote the length of a ray that passes through the pixels of interest.

If B exists, it is unique and is called the inverse matrix of A, denoted A−1.

We define the potential of A, denoted as U(A|S, T), as follows.

The total amount of A, denoted by A T is determined by the initial conditions.

We use the superscripts of A denoting the quantities for autosomes.

denotes expectation, denotes the trace of a matrix, denotes the th entry of a vector.

For example, kilo- denotes a multiple of a thousand and milli- denotes a multiple of a thousandth; hence there are one thousand millimetres to the metre and one thousand metres to the kilometre.

For two structures S = and T =, the concatenated structure is denoted by S ∘ T. R· S denotes the structure S rotated by the rotation matrix R, i.e., R· S =. denotes the transpose of the vector and A T denotes the transpose of the matrix A. trace(A) denotes the trace of the matrix A. | | denotes the norm of the vector.

The Laplacian matrix of ((G, A)) is denoted by L.

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