We can model this by replacing the variables indicating the percentage of state and national voters who support same-sex marriage in the model with probabilistic variables indicating how likely it is that same-sex marriage has achieved majority status.
In the case of α + β + γ + δ ≥ 0, α + β + ζ > 0 and α + γ ≥ 0, we can obtain the desired result by replacing the variables x and y. □.
The upper bound in (57) follows from ([43] Lemma 2) by replacing the variables in play by their Gaussian counterparts, i.e., (bar {xi }_{t}) and (bar {n}_{t}) are Gaussian distributed with the same first- and second moments as ξ t and n t, respectively.
Briefly, the collapsation step merges all terms which correspond to configurations in which K i+1 is T-reachable from s, for each possible subset T of K i+1, into a single term by replacing the variables in these terms with a single variable denoted with z T. Thus, the coefficient of z T is the sum of the coefficients of the original terms that were collapsed.
The surrogate approach was then applied by replacing the variable indicating soil release with a time series of fine soil released during laboratory slaking.
The parameters of Equation 6 are determined as follows: Firstly, we can deduce the equations of the straight lines containing the different segments lRi of the ACF for τ ≥ 0 just by replacing the variable l in the top formula of Equation 3 by the variable i = [1,….., M - 1] used in Equation 4.
Similarly, by replacing the variable t with t p = a + p ( b − a ) / n for p = 0, …, n, we obtain the generalized linear system ∑ j = 1 m ∑ p = 0 n T q, p ( i, j ) ⋅ a j, p = f i ( t q ) + ∑ j = 1 m ∑ p = 0 n R q, p ( i, j ) ⋅ a j, p, i = 1, …, m ; q = 0, …, n, (9).
It can be applied to any other data by replacing fattyacid in the third line by the name of the object containing the data in the two-column way described above, and by replacing the variable names PE and FA by the names of the variables used in the dataset wherever PE and FA appear in the code.
For instance, a template "Which of the following animals is {?animal_name}?" can be instantiated by replacing the variable with rdfs:label of an animal.
In PCA the dimensionality of the dataset is reduced by replacing the original variables by a smaller number of newly formed variables that are linear combinations of the original variables and that explain the majority of the information (variability) from the experiment.
We now quantize the system, by replacing the classical variables with the operators written in terms of the annihilation and creation operators of the resonator excitation, (a_{j}) and (a_{j}^{dagger}).
