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This approximation involves fixation probabilities for each mtDNA type and a truncated Normal distribution for intermediate heteroplasmies (see 'Materials and methods').
This approximation involves the inversion of a k+1 dimensional matrix and is computationally efficient compared to the measures in Equations (3) and (1), which involve the inversion of m+1 and n Train dimensional matrices.
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It is valid only when the approximation involved in Equation (6) becomes exact, i.e., it can only separate quadratic or cubic phase signal components with single linear pass regions in the TCR plane corresponding to monotonic ICR laws.
Although the Kd is somewhat different, we consider that our data do reproduce the results of Kummel et al. (2011) within experimental error, considering the approximation involved in the single-site model.
A further approximation involves replacing Q x) by the Chernoff upper bound (1/2) exp(−x2/2) [8].
The proposed semi-exact closed-form approximation involves one parameter only, which is calibrated by means of a numerical optimization procedure taking into account a large database of cross-sections.
Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast.
The models were fitted with the assumption of the unstructured covariance matrix, but the Kenward-Roger method approximation involves inflating the estimated variance-covariance matrix of the fixed and random effects.
Unfortunately, because of the approximations involved, this argument does not prove the theorem about the area of a circle.
We will give a brief derivation of this equation in order to discuss the underlying assumptions to the derivation of this expression, the different ways in which this equation is solved, the approximations involved, and their advantages and disadvantages.
Due to the "Poisson approximation" involving this formulation, it may fall short for very narrow band processes and lower threshold levels of practical interest.
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