In order to cope with such cases, the estimation is set to be the state vector associated to the maximum or the mean of all particle weights.
Following [15, 16], we let ζ k be the stoichiometry vector associated with edge i j ( k ) ∈ E. That is, the i th component of ζ k is −1, the j th component is 1, and all other components are zero.
Let the function (6) be differentiable with respect to time for (t in G subseteq D) and (c in C), and let r(t) be the tangential vector associated with the (regular) point ({mathbf{x}}_{c} (t) equiv (x_{1c} (t),x_{2c} (t),x_{3c} (t)) in T_{c} left( G right) subset S), where (dot{mathbf{x}}_{c} (t)ne0,,t in G subseteq D,) and (c in C) [cf. (7)].
If r i = (r i 1, r i 2,…, r ik ) is the vector associated with reaction i belonging to cluster c, R c is the average of r i for all n reactions in cluster c; that is, R c = (1/ n)∑ i =1 n r i = (R c 1,…, R ck ).
Let G(x;ξ) be a baseline cumulative distribution function (cdf) and ξ be the vector of associated parameters.
Let v 1 = (c 11, c 21)⊤ and v 2 = (c 12, c 22)⊤ be the characteristic vectors associated with the characteristic roots λ1 and λ2 of Φ, respectively, i.e. Φ v j = λ j v j, j = 1, 2. (2.6).
Let v i =(v i1,…,v ip ) T be the explanatory variable vector associated with the ith response variable y i for i=1,…,n.
The unit vector associated with the line-of-sight (LOS) of the m-th transmitter is ( {mathbf{r}}_m^{(t)} ), whereas ( {mathbf{r}}_n^{(t)} ) is the unit vector associated with the LOS of the n-th receiver.
where a is the steering vector associated with a hypothetical direction θ based on the known array structure.
where x is a d-dimensional feature vector, μ k)is the mean vector associated with class k, and ∑ is the covariance matrix.
