We begin this section by introducing the intermediate variable q, p and rewrite (1.1) into the following saddle-point problem: begin{gathered} (mathrm{a}) quad q= D u, quad xin Omega, (mathrm{b}) quad p=-Kbigl {theta_{0}I_{x}^{beta}+(1- theta)_{x}I_{1}^{beta}}bigr) q, quad xinOmega, (mathrm{c}) quad u_{t}+ Dp=-Kbigl {theta_{a, (mathrm{d}) quad u(x,0}I_{x0}^{beta}
The hypothesis (event) that the target is moving on-road or off-road is modeled by a discrete variable q t ∈ {1,2} where the events {q t = 1} and {q t = 2} correspond to the hypotheses that the target is on-road and off-road, respectively.
The second term can be similarly calculated by using the change of variable q = x′ − x together with the trigonometric property: (21) cos (k · q + k · x + ϕ ) = cos (k · q ) cos (k · x + ϕ ) − sin (k · q ) sin (k · q + ϕ ).
This is done by introducing the auxiliary variables Q (5) and Q (6) to relax the equality constraints on the conditional covariance matrices R 2 | R ( 5 ) = R 2 ( 5 ) − R 2 R ( 5 ) R R ( 5 ), ‡ R 2 R ( 5 ), H and R 1 | R ( 6 ) = R 1 ( 6 ) − R 1 R ( 6 ) R R ( 6 ), ‡ R 1 R ( 6 ), H, respectively, before applying the (generalized) Schur complement condition.
Let the variable exponent q ( x ) be defined by 1 q ( x ) = 1 p ( x ) − ( 1 p 0 − 1 q 0 ).
An intervention is specified by specifying the values of the control variables, q.
This actualization of a variable q in the course of an interaction can be denoted as the quantum event q.
Our semi-supervised consensus clustering algorithm is described in Algorithm 2. Similar to [ 4], for a given n × d dataset of n samples and d genes, a n × q data subspace (q < d) is generated by (1) q = q min + ⌊ α (q max - q min ) ⌋ α ∈ [ 0,1] is a uniform random variable, q m i n and q m a x are the lower and upper bonds of the subspace.
According to Rosner and colleagues [ 56], if a primary regression model (Eq. 4.1) with a response variable Y contains only one error-prone explanatory variable Q j (bivariate scenario) correction for attenuation, consists simply of dividing the regression coefficient β naïve, j) of that variable Q j by the attenuation factor λj (Eq. 4.2).
