This contradiction exists in many subcultures, especially those dependent on defining themselves in terms of opposition to the mainstream.
Solving for the genotype probabilities is dependent on defining the transition probability matrix, T.
A growing, and often grass-roots, movement is seeking to develop the arts in Africa in a way that is not dependent on, or defined by, the West.
Generating pharmacophore models which encode accurate molecular recognition features are highly dependent on properly defined annotations.
How the HMM is best used is dependent on how defined the task is, availability of training data, and computational considerations.
for some non-negative sequences of integers { m n } with m n ≤ n ; ∀ n ∈ Z 0 +, where d ( T x n, T n x n ) < ε / 3 ; ∀ n ( ∈ Z 0 + ) > N 1, d ( T y n, T n y n ) < ε / 3 ; ∀ n ( ∈ Z 0 + ) > N 2, N = max ( N 1, N 2 ), D ¯ = D ¯ ( N ) = max N < j < ∞ ( D j 0 + D j ), and M ′ is a non-negative real constant, which is not dependent on n, defined by M ′ = M ′ ( N ) = max 1 ≤ j ≤ N d ( x j, y j ).
As Rebecca Traister wrote in an adapted excerpt of her 2016 book All the Single Ladies, "We are living through the invention of independent female adulthood as a norm, not an aberration, and the creation of an entirely new population: adult women who are no longer economically, socially, sexually, or reproductively dependent on or defined by the men they marry".
This increase in structured secondary structure suggests that binding of cholesterol was dependent on a defined secondary structure.
In the interim, anatomical validation of the derived white matter tracts is crucial, particularly as tractography is a subjective process, dependent on user defined parameters.
Phenotypes were simulated by adding residual effects that were drawn from a normal distribution with a mean of 0 and dispersion dependent on the defined heritability (Wimmer et al. 2013).
